Nanostructured metals and alloys - Processing, microstructure, mechanical properties and applications

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Nanostructured metals and alloys

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Nanostructured metals and alloys Processing, microstructure, mechanical properties and applications Edited by Sung H. Whang

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Published by Woodhead Publishing Limited, 80 High Street, Sawston, Cambridge CB22 3HJ, UK www.woodheadpublishing.com Woodhead Publishing, 1518 Walnut Street, Suite 1100, Philadelphia, PA 19102-3406, USA Woodhead Publishing India Private Limited, G-2, Vardaan House, 7/28 Ansari Road, Daryaganj, New Delhi – 110002, India www.woodheadpublishingindia.com First published 2011, Woodhead Publishing Limited © Woodhead Publishing Limited, 2011 The authors have asserted their moral rights. This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. Reasonable efforts have been made to publish reliable data and information, but the authors and the publisher cannot assume responsibility for the validity of all materials. Neither the authors nor the publisher, nor anyone else associated with this publication, shall be liable for any loss, damage or liability directly or indirectly caused or alleged to be caused by this book. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming and recording, or by any information storage or retrieval system, without permission in writing from Woodhead Publishing Limited. The consent of Woodhead Publishing Limited does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from Woodhead Publishing Limited for such copying. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. ISBN 978-1-84569-670-2 (print) ISBN 978-0-85709-112-3 (online) The publisher’s policy is to use permanent paper from mills that operate a sustainable forestry policy, and which has been manufactured from pulp which is processed using acid-free and elemental chlorine-free practices. Furthermore, the publisher ensures that the text paper and cover board used have met acceptable environmental accreditation standards. Typeset by RefineCatch Limited, Bungay, Suffolk, UK Printed by TJI Digital, Padstow, Cornwall, UK

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Contents

Contributor contact details Introduction

xv xxi

S.H. Whang, New York University, USA

Part I Processing bulk nanostructured metals and alloys 1

Producing bulk nanostructured metals and alloys by severe plastic deformation (SPD)

1 3

R.Z. Valiev, Ufa State Aviation Technical University, Russia

1.1 1.2 1.3 1.4 1.5 1.6 1.7 2

Introduction The principles of severe plastic deformation (SPD) processing New trends in SPD processing for effective grain refinement Enhanced properties achieved using SPD processing Innovation potential of bulk nanostructured materials Conclusions References

3 4 8 22 33 34 35

Bulk nanostructured metals and alloys produced by accumulative roll-bonding

40

N. Tsuji, Kyoto University, Japan

2.1 2.2 2.3 2.4 2.5 2.6 2.7

Introduction The principle of accumulative roll-bonding (ARB) Processing details Change in microstructures during the process Mechanical properties of nanostructured metals fabricated by ARB Conclusions References

40 41 42 45 53 57 57

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3

Nanocrystalline metals and alloys prepared by mechanical attrition

59

S. Scudino and J. Eckert, IFW Dresden, Germany

3.1 3.2 3.3 3.4 3.5 3.6 3.7

Introduction Mechanical attrition Nanocrystalline phase formation by mechanical attrition Consolidation of nanocrystalline powders Conclusion and future trends Acknowledgements References

59 60 62 75 80 81 82

4

The processing of nanocrystalline steels by solid reaction

85

F.G. Caballero and C. García -Mateo , National Center for Metallurgical Research (CENIM-CSIC), Spain

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 5

Introduction The finest grain structures in steels Phase transformation theory: a powerful tool for the design of advanced steels, from micro to nano NANOBAIN steel: a material going to extremes Accelerating the bainite reaction at low temperatures Characterizing nanocrystalline bainitic steels at the atomic scale The mechanical properties of nanocrystalline bainitic steels Conclusion and future trends Sources of further information and advice Acknowledgements References

85 86

98 107 113 114 114 114

The processing of bulk nanocrystalline metals and alloys by electrodeposition

118

89 93 98

U. Erb , University of Toronto, Canada and G. Palumbo and J.L. Mc C rea , Integran Technologies Inc., Canada

5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9

Introduction Electrodeposition methods Examples of nanocrystalline metals and alloys prepared by electrodeposition Mechanical properties of nanocrystalline electrodeposits Corrosion properties of nanocrystalline electrodeposits Other properties of nanocrystalline electrodeposits Applications Acknowledgements References

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Bulk nanocrystalline and nanocomposite alloys produced from amorphous phase

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152

A. Inoue and D.V. Louzguine , Tohoku University, Japan

6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 7

Introduction The formation of bulk metallic glassy alloys The formation of a nanostructure by crystallization of the glassy phase, by deformation or directly from the melt on casting The formation of nano-quasicrystals The mechanical properties of nanocomposite alloys The magnetic properties of nanocomposite alloys Conclusions References

152 153 159 165 167 169 172 173

Severe plastic deformation and the production of nanostructured alloys by machining

178

J.B. Mann , M4 Sciences, USA, S. Chandrasekar , W.D. Compton , and K.P. Trumble , Purdue University, USA, C. Saldana , and S. Swaminathan , GE John F. Welch Technology Center, India, W. Moscoso and T.G. Murthy , Indian Institute of Science, India

7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9

Introduction The mechanics of severe plastic deformation (SPD) in machining A study of microstructure refinement Bulk forms with ultrafine-grained (UFG) microstructure Nanostructured particulate Surface nanostructuring Conclusions Acknowledgements References

Part II  Microstructure 8

Deformation structures including twins in nanograined pure metals

178 179 189 196 200 205 207 207 208 211 213

K. Hattar , Sandia National Laboratories, USA

8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8

Introduction Classical defect structures in nanograined metals Classical defect structures absent in nanograined metals Novel defect structures in nanograined metals The effect of initial microstructure on deformation structures Future trends Acknowledgements References

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9

Microstructure and mechanical properties of nanostructured low-carbon steel prepared by equal-channel angular pressing

243

Y.G. Ko , Yeungnam University, Republic of Korea, and D.H. Shin , Hanyang University, Republic of Korea

9.1 9.2 9.3 9.4 9.5 9.6 9.7 10

Introduction The microstructural evolution of low-carbon steel (LCS) The mechanical response of a nanostructured LCS alloy Enhanced tensile properties by grain refinement and microstructural modification Continuous shear drawing: a new processing method Conclusion References

243 244 261 268 270 272 272

Characteristic structures and properties of nanostructured metals prepared by plastic deformation

276

X. Huang , Technical University of Denmark, Denmark

10.1 10.2 10.3 10.4 10.5 10.6 10.7

Introduction Characteristic microstructures Hardening by annealing and softening by deformation Optimisation of microstructure and mechanical properties Conclusions Acknowledgements References

276 277 286 289 290 294 294

Part III  Mechanical properties

297

11

299

Strengthening mechanisms in nanocrystalline metals D.G. M orris , National Center for Metallurgical Research (CENIM-CSIC), Spain

11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 11.10

Introduction The deformation of polycrystals; the Hall–Petch model for strengthening; typical strength and hardness data Hall–Petch breakdown: a fine grain size limit to models Hall–Petch breakdown: the importance of defective materials Alternative deformation mechanisms at very fine grain sizes Strengthening caused by second-phase particles Strengthening caused by other factors: solute, order, twin boundaries Strengthening mechanisms in materials with ultrafine microstructure prepared by severe plastic deformation Conclusion and future trends References

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Contents

Elastic and plastic deformation in nanocrystalline metals

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329

M.Y. Gutkin , Russian Academy of Sciences, Russia

12.1 12.2 12.3 12.4 12.5 12.6 12.7

Introduction Elastic strains in nanocrystalline metals Plastic deformation in nanocrystalline metals Conclusions and future trends Sources of further information and advice Acknowledgements References

329 330 337 365 367 367 367

13

The mechanical properties of multi-scale metallic materials

375

Y.H. Zhao and E.J. Lavernia , University of California Davis, USA

13.1 13.2 13.3 13.4 13.5 13.6 13.7 14

Introduction Mechanical properties of multi-scale metallic materials Deformation and fracture mechanisms of multi-scale metallic materials Future trends Conclusions Acknowledgements References

375 383 405 425 425 426 426

Enhanced ductility and its mechanisms in nanocrystalline metallic materials

430

I.A. Ovid’ko, Russian Academy of Sciences, Russia

14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9

Introduction General aspects concerning the tensile ductility of materials Plastic flow mechanisms in coarse-grained metallic polycrystals, ultrafine-grained metals and nanocrystalline metals with intermediate grains Plastic flow mechanisms in nanocrystalline metals with the finest grains Specific features of crack nucleation and growth processes in nanocrystalline metallic materials Enhanced ductility of artifact-free nanocrystalline metals with narrow grain size distributions Enhanced ductility of nanocrystalline metals due to twin deformation and growth twins Enhanced ductility of nanocrystalline metals due to strain rate hardening Enhanced ductility of single-phase nanocrystalline metals with bimodal structures

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14.10

Enhanced ductility of nanocrystalline metallic composites with second-phase nanoparticles, dendrite-like inclusions and carbon nanotubes Conclusions and future trends Sources of further information and advice Acknowledgements References

451 452 454 455 455

The mechanical behavior of nanostructured metals based on molecular dynamics computer simulations

459

14.11 14.12 14.13 14.14 15

V.I. Yamakov , National Institute of Aerospace, USA

15.1 15.2 15.3 15.4 15.5 15.6 15.7 16

Introduction The structure and properties of grain boundaries in nanocrystalline (NC) metals by molecular dynamics (MD) simulation Deformation mechanisms in nanoscale grains Grain growth and microstructure evolution in NC metals Conclusions Acknowledgement References

459 461 465 472 476 477 477

The surface deformation and mechanical behavior in nanostructured alloys

481

L.L. Shaw , University of Connecticut, USA

16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 17

Introduction Mechanics aspects during surface severe plastic deformation Changes in the microstructure and stress states induced by surface severe plastic deformation Tensile properties of metals with a nanocrystalline surface and hardened layer Fatigue resistance of metals with a nanocrystalline surface and hardened layer Wear resistance of metals with a nanocrystalline surface and hardened layer Conclusions Acknowledgements References Fatigue behaviour in nanostructured metals

481 482 484 493 499 501 502 504 504 507

H.W. Höppel and M. Göken , Friedrich-Alexander University of Erlangen-Nuremberg, Germany

17.1 17.2

Introduction and motivation General findings on the fatigue behaviour and the fatigue lives of nanostructured model materials

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17.3 17.4 17.5 17.6 18

Contents

xi

Light metal alloys Fatigue behaviour and life of nanostructured steels Consequences and strategies for optimizing fatigue lives and cyclic deformation behaviour References

517 532 534 537

Superplastic deformation in nanocrystalline metals and alloys

542

A. Sergueeva , The Nanosteel Company, USA and A. Mukherjee , University of California Davis, USA

18.1 18.2 18.3 18.4 18.5 18.6 18.7 18.8 19

Introduction Theoretical predictions Superplasticity in nanocrystalline metals and alloys Specific features of superplasticity in nanocrystalline materials Deformation mechanisms Conclusions Acknowledgements References

542 543 546 568 578 587 590 590

Creep and high-temperature deformation in nanostructured metals and alloys

594

W. Yin , Williams Advanced Materials, USA

19.1 19.2 19.3 19.4 19.5 19.6

Introduction Temperature-dependent deformation in fine-grained pure metals Creep and high-temperature deformation in nanostructured alloys Deformation mechanisms and modeling Conclusions References

Part IV  Applications 20

Processing nanostructured metal and metal-matrix coatings by thermal and cold spraying

594 595 601 603 609 610 613 615

G.E. Kim , Perpetual Technologies Inc., Canada, V.K. Champagne , and M. Trexler , US Army Research Laboratory AMSRD-ARL-WM-MC, USA and Y. Sohn , University of Central Florida, USA

20.1 20.2 20.3

Introduction Nanostructured metal-base feedstock Thermal spray processing

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20.4

Thermal spray processing of nanostructured coatings: tungsten carbide-cobalt (WC-Co) coatings Thermal spray processing of nanostructured coatings: alumina-titania (n-AT) coatings Thermal spray processing of nanostructured coatings: titanium oxide coatings Thermal spray processing of nanostructured coatings: MCrAlY and NiCrAlY coatings The cold spray process Characteristics of cold spray material Cold-sprayed processing of WC-Co Cold-sprayed processing of non-cryogenically milled n-WERKZ AA5083 Future trends Sources of further information and advice Acknowledgements References

20.5 20.6 20.7 20.8 20.9 20.10 20.11 20.12 20.13 20.14 20.15 21

Nanocoatings for commercial and industrial applications

620 621 622 627 644 647 648 651 657 658 658 658 663

J.L. Mc C rea and G. Palumbo , Integran Technologies, Canada and U. Erb , University of Toronto, Canada

21.1 21.2 21.3 21.4 21.5 21.6

Introduction Overview of nanostructured metals and alloys Commercialization of nanostructured materials Current and emerging applications Conclusions References

663 664 666 669 683 684

22

Applying nanostructured steel sheets to automotive body structures

687

Y. Okitsu and N. Tsuji , Honda R&D Co., Ltd., Japan

22.1 22.2 22.3 22.4 22.5 22.6 22.7 22.8

Introduction The potential demand for nanostructured steels for automotive body structures Fabricating nanostructured low-C steel sheets Improving elongation in nanostructured steel sheets Crash-worthiness of nanostructured steel sheets Conclusions References Appendix

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23

Contents

Production processes for nanostructured wires, bars and strips

xiii

715

S. Torizuka , and E. Muramatsu , National Institute for Material Science, Japan, T. Komatsu , Komatsuseiki Kosakusho Co., Ltd., Japan and S. Nagayama , Tokushu Kinzoku Excel Co., Ltd., Japan

23.1 23.2 23.3 23.4 23.5 23.6 23.7 23.8 24

Introduction The production processes and properties of nanostructured steel bars The production processes and properties of nanostructured steel wire The production processes and properties of nanostructured steel strips Applications of nanostructured steels and their features Future trends Acknowledgements References Nanostructured plain carbon-manganese (C-Mn) steel sheets prepared by ultra-fast cooling and short interval multi-pass hot rolling

715 716 722 725 731 743 745 745

747

T. Tomida , K. Miyata , and H. Nishibata , Sumitomo Metal Industries Ltd., Japan

24.1 24.2 24.3 24.4 24.5 24.6 24.7 24.8

Introduction The concept of ultra-fast direct cooling and short interval multi-pass hot rolling (UDCSMR) and an experimental hot rolling mill Nanostructured carbon-manganese (C-Mn) steel sheets produced by UDCSMR Grain refinement mechanisms Deformation characteristics Welding and application to some prototype parts Conclusions References

Index

747 749 752 757 765 773 784 784 787

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Contributor contact details

(* = main contact)

Editor

Chapter 3

S. H. Whang Department of Mechanical Engineering Polytechnic Institute New York University NY 11201 USA

S. Scudino and J. Eckert* Institute for Complex Materials Leibniz Institute for Solid State and Materials Research Dresden (IFW Dresden) Helmholtzstr. 20 D-01069 Dresden Germany

E-mail: [email protected]

E-mail: [email protected] [email protected]

Chapter 1 R. Z. Valiev Institute of Physics of Advanced Materials Ufa State Aviation Technical University 12 K. Marx str. Ufa 450000 Russia E-mail: [email protected]

Chapter 4 F. G. Caballero* and C. García-Mateo National Center for Metallurgical Research (CENIM-CSIC) Avenida Gregorio del Amo, 8 Madrid 28040 Spain E-mail: [email protected]

Chapter 2 N. Tsuji Department of Materials Science and Engineering Graduate School of Engineering Kyoto University Yoshida-Honmachi, Sakyo-ku Kyoto 606-8501 Japan E-mail: [email protected]

Chapter 5 U. Erb* University of Toronto Dept. Materials Science & Engineering 184 College Street, Room 140 Toronto, ON M5S 3E4 Canada E-mail: [email protected]

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Contributor contact details

G. Palumbo and J. L. McCrea Integran Technologies Inc. 1 Meridian Road Toronto, ON M9W 4Z6 Canada E-mail: [email protected] [email protected]

Chapter 6 D. V. Louzguine* and A. Inoue WPI Advanced Institute for Materials Research Tohoku University 2-1-1 Katahira Aoba-Ku Sendai, 980-8577 Japan E-mail: dml@[email protected]

Chapter 7 J. B. Mann M4 Sciences West Lafayette IN 47906 USA

T. G. Murthy Department of Civil Engineering Indian Institute of Science Bangalore, India

Chapter 8 K. Hattar Sandia National Laboratories (505) 845-9859 PO Box 5800 Mail Stop 1056 Albuquerque NM 87185-1056 USA E-mail: [email protected]

Chapter 9 Y. G. Ko School of Materials Science and Engineering Yeungnam University Gyeongsan 712-749 Republic of Korea E-mail: [email protected]

S. Chandrasekar*, W. D. Compton, K. P. Trumble, C. Saldana, and W. Moscoso Center for Materials Processing and Tribology Purdue University West Lafayette IN 47907 USA E-mail: [email protected]

S. Swaminathan GE John F. Welch Technology Center Bangalore India

D. H. Shin* Department of Metallurgical and Materials Science Hanyang University Ansan 425-791 Republic of Korea E-mail: [email protected]

Chapter 10 X. Huang Danish-Chinese Center for Nanometals Materials Research Division Risø National Laboratory for Sustainable Energy Technical University of Denmark DK-4000 Roskilde Denmark E-mail: [email protected]

© Woodhead Publishing Limited, 2011



Contributor contact details

Chapter 11

Chapter 14

D. G. Morris National Center for Metallurgical Research (CENIM-CSIC) Avenida Gregorio del Amo, 8 Madrid 28040 Spain

I.A. Ovid’ko Institute of Problems of Mechanical Engineering Russian Academy of Sciences St. Petersburg Russia

E-mail: [email protected]

E-mail: [email protected]

Chapter 12

Chapter 15

M. Y. Gutkin Institute of Problems of Mechanical Engineering Russian Academy of Sciences Bolshoj 61 Vasilievskii Ostrov St. Petersburg 199178 Russia

V. I. Yamakov Durability and Damage Tolerance Branch NASA Langley Research Center Hampton VA 23681 USA

E-mail: [email protected] [email protected]

Chapter 13 Y. H. Zhao* Department of Chemical Engineering and Materials Science University of California, Davis 1231 Bainer Hall One Shields Avenue Davis CA 95616-5294 USA E-mail: [email protected]

E. J. Lavernia Department of Chemical Engineering and Materials Science University of California, Davis Davis CA 95616-5294 USA

xvii

E-mail: [email protected]

Chapter 16 L. L. Shaw Department of Chemical, Materials and Biomolecular Engineering University of Connecticut Storrs CT 06269 USA E-mail: [email protected]

Chapter 17 H. W. Höppel* and M. Göken Department of Materials Science and Engineering Institute I: General Materials Properties Friedrich-Alexander University of Erlangen-Nuremberg 91058 Erlangen Germany E-mail: heinz-werner.hoeppel@ww. uni-erlangen.de

E-mail: [email protected] © Woodhead Publishing Limited, 2011

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Contributor contact details

Chapter 18 A. Sergueeva* The Nanosteel Company Idaho Falls ID 83402 USA E-mail: [email protected]

A. Mukherjee University of California Davis California USA E-mail: [email protected]

Chapter 19 W. Yin Williams Advanced Materials Inc., Thin Film Products 42 Mount Ebo Road South Brewster NY 10509 USA E-mail: [email protected]

Chapter 20 G. E. Kim* Perpetual Technologies, Inc. 38 Place du Commerce Suite 11-163 Ile des Soeurs Quebec H3E 1T8 Canada E-mail: [email protected]

V. K. Champagne US Army Research Laboratory AMSRD-ARL-WM-MC Building 4600 Aberdeen Proving Ground MD 21005-5069 USA

M. Trexler US Army Research Laboratory AMSRD-ARL-WM-MC Building 4600 Aberdeen Proving Ground MD 21005-5069 USAY. Sohn Advanced Materials Processing and Analysis Center and Department of Mechanical, Materials and Aerospace Engineering University of Central Florida 4000 Central Florida Blvd. Orlando FL 32816-2455 USA

Chapter 21 J. McCrea* and G. Palumbo Integran Technologies 1 Meridian Road Toronto, ON M9W 4Z6 Canada E-mail: [email protected] [email protected]

U. Erb University of Toronto Dept. Materials Science & Engineering 184 College Street, Room 140 Toronto, ON M5S 3E4 Canada E-mail: [email protected]

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Contributor contact details

Chapter 22

T. Komatsu Komatsuseiki Kosakusho Co., Ltd. Production Department 942-2 Siga, Suwa Nagano 392-0012 Japan

Y. Okitsu* Automobile R&D Center Honda R&D Co., Ltd. 4930 Shimotakanezawa Haga-machi, Haga-gun Tochigi 321-3393 Japan E-mail: [email protected]. co.jp

N. Tsuji Department of Materials Science and Engineering Graduate School of Engineering Kyoto University Yoshida-Honmachi, Sakyo-ku Kyoto 606-8501 Japan E-mail: [email protected]

Chapter 23 S. Torizuka* and E. Muramatsu National Institute for Material Science Material Manufacturing and Engineering Station 1-2-1 Sengen, Tsukuba Ibaraki 305-0047 Japan

xix

E-mail: [email protected]

S. Nagayama Tokushu Kinzoku Excel Co., Ltd. New Functional Materials R&D H.Q. 56 Tamagawa, Tokigawa Saitama 355-0342 Japan E-mail: [email protected]

Chapter 24 T. Tomida*, K. Miyata and H. Nishibata Sumitomo Metal Industries, LTD. Corporate R&D Laboratories 1-8, Fuso-Cho Amagasaki Hyogo, 660-0891 Japan E-mail: tomida-tsr@sumitomometals. co.jp

E-mail: [email protected] [email protected]

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Introduction S. H. WHANG, New York University, USA Recent nanotechnology for material applications deals with a very wide range of material groups and various aspects of materials problems. Since the volume of the accumulated knowledge and database for the subjects stemming from worldwide research and development has been rapidly escalating, this book intends to limit its coverage to the recent progress on nanostructured metallic materials for structural applications. Since ‘nanostructured materials’ were first defined by Gleiter,1,2 research and development in the fields of nanostuctured materials have flourished over the last two decades. Currently nanostructured materials are conveniently defined as materials made of a microstructure less than 100 nm in length in at least one dimension whereas ultrafine-grained materials (UFG) possess a grain size range between 200 nm and less than 1 µm in diameter. But, for practical reasons, nanostructured metallic materials that have been prepared for research and development contain a wide range of grain size distribution from tens of nanometers to a submicrometer. For example, research on optimizing the mechanical properties of nanostructured materials requires manipulation of its bimodal and multimodal grain size distribution. In this case, the grain size ranges from nano size (NG) to submicron size (UFG). Therefore, for practical structural applications, it is envisioned that nanostructured bulk metallic materials may contain both nanoscale as well as submicron-scale microstructures in the future. This book deals with metallic materials that have various grain size distributions: nanoscale grains or nanomicrostructure other than nanograins or submicron scale grains or submicron microstructure other than submicron grains or a combination of all these. The history of metallic materials shows that an appetite for higher strength/ specific strength, and better ductility and toughness for structural applications has been the main driving force for research and development for better and even better materials in the last century, as well as this century. Recent nanostructurizing approaches to the metallic material systems continue this effort. To achieve this desire, scientists and engineers always look into smaller-scale worlds from micron- to submicron-, and submicron- to nano-dimensions for their solutions. Long before such recent endeavors became a fashion among materials scientists and engineers, it was recognized that nanoscale microstructure has great potential for changing the landscape in advanced engineering materials and manufacturing. For example, new high-strength aluminum alloys were produced for the first time utilizing the nanoscale Guinier-Preston zone3 and ultrafine-layered wire with extremely high strength4 long before the current nanotechnology debut. The xxi © Woodhead Publishing Limited, 2011

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Introduction

discovery of the Hall–Petch relationship also suggested that new high-strength materials might be fabricated with materials with nanoscale grain sizes. In the last two decades, research and development into nanostructured metallic materials have been largely focused on metallic materials with two different microstructures: nanograined structures and embedded nanomicrostructures other than nanograins; and also the effort has been largely devoted to four different subject areas: processing and fabrication, characterization of material properties, microstructural characterization, and engineering design and development for new products and applications. The first hurdle to overcome in this effort has been the large-scale processing of high quality of nanomaterial for use in research and development. Of course, many technically challenging problems emerge in the course of processing of such nanomaterials. In general, the bulk forms prepared by different processes contain different structural defects and impurities. As a result, the mechanical properties of the specimens of an alloy prepared by different processing routes exhibit substantial deviation, particularly in structure-sensitive properties such as deformation behavior, ductility, fatigue, superplasticity and creep. This deviation poses serious problems for scientists in the analysis and interpretation of the experimental results and in arriving at meaningful conclusions. In addition, many of the processes face other challenging engineering problems that require each process to demonstrate the feasibility of scaling-up for industrial applications. As the nanomaterials research fields continue to expand and the accumulation of knowledge from the research escalates, it becomes clear that it is increasingly difficult to cover the progress made in these fields adequately in a single publication. Thus, the focus of the current book is placed on the recent progress on nanostructured metallic materials in bulk forms, in their processing, microstructure, mechanical properties and structural applications. For those who are interested in these subjects and want to know the depth and breath of the issues, there are references available for additional reading, which have reviewed and summarized the progress made in these areas in the past.5–7 This brief introduction on the subject areas is given for readers who come from other fields.

Processing It is imperative to provide nanostructured metallic materials of sufficient quality and quantity for research and development in order to realize the envisioned progress in this field. There have been many processing approaches available for producing a small quantity of nanostructured metals based on ‘top-down’, and ‘bottom-up’ approaches1 in three different phase forms – vapor, liquid or solid – utilizing all available technological means. The bottom-up approach includes inert gas condensation, chemical vapor condensation, pulse electron deposition,

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etc. Nevertheless, the structural application requires a substantial quantity of nanostructured materials in three dimensions, which eliminates the majority of possible bottom-up processing approaches as candidates for the current effort, at least at this stage. Currently, that leaves only a handful of potentially viable processes for research and development in bulk nanostructured metallic materials. For these reasons, this book includes only those processing methods that could be serious candidates for producing nanostructured metallic materials in the near future. This book introduces several promising processing approaches for nanostructured metallic materials, which include 1) solid deformation processing: equal channel angular pressing (ECAP), high pressure torsion (HPT), accumulative roll-bonding (ARB), mechanical attrition (MA) and mechanical machining process (MM); 2) solid reaction processing: ultrafine bainite or pearlite structure in carbon steels using a combination of deformation and thermal reaction; and 3) liquid– solid transformation: involving a transformation from liquid to solid phases, e.g. from the molten phase to metallic glass and subsequently to crystallization; electrodeposition processing; and thermal spray processing, from molten droplets to solidified droplets containing nanograins.

Severe plastic deformation processes Historically, a large plastic deformation and the resulting microstructural refinement in metals and alloys have been investigated by a number of researchers.8–11 Nevertheless, the concept of relating severe plastic deformation (SPD) to ultrafine microstructure as well as unique properties has been put to test by Valiev and co-workers in the 1980s and thereafter,12–14 which has contributed to the popularization of current SPD technology for nanostructured metallic materials. Both high pressure torsion (HPT) pressing and equal channel angular pressing (ECAP)11 use the same principle: that hydrostatic pressure permits a very large shear deformation in ductile metals, at a strain as high as strain of 4–5, which translates into the dislocation density up to 1014–17 mm–1.15,16 Repeating the process cycle in SPD results in ultrafine grains (100–300 nm). On the other hand, although the ARB process as another form of SPD generates fine-grained microstructure by a large accumulative deformation similar to ECAP, the approach is substantially different in that in ARB processing,17,18 a very large accumulative deformation is applied to a thin sheet by a series of repetitive fold-and-roll processes without hydrostatic pressure where the surfaces of sheets in the folded sides convert to grain boundaries by cold welding. In the processing, the ultrafine grain refinement occurs by the introduction of new grains in the old grains during dynamic recovery and post annealing. Both ARB and ECAP deformation generate new grains of high angle grain boundaries, and the fraction of such boundaries increases with an increasing number of cycles. ARB is particularly advantageous for producing a sheet form of nanostructured metallic material.

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There are many roadblocks in the way of ECAP and HPT becoming industrially viable processes. They include the inability to produce the desired dimensions – length, width and thickness of continuous bulk forms – at this stage. Nevertheless, in one area, the wire processing by a large acumulative deformation is successful in producing the required dimensions. For example, a fine wire of Mn steel is made by drawing 10 mm diameter rods of a dual-phase microstructure of martensite and ferrite and of the composition of Fe-0.2C-0.8Si-1Mn (wt-%) into individual strands of 8 µm diameter wire. This wire drawing amounts to a huge deformation of a true strain in excess of 9. The dislocation cell size in the deformed wires is found to be 10–15 nm.19,20 Another form of SPD is mechanical attrition, which is basically high impact ball-milling, and produces very large plastic deformation. Although an initial development aimed to produce new alloys by mechanical alloying,21 the same technique can be employed to produce microstructural refinement. In the process, metallic powders undergo fracture and plastic deformation in which the powders can form mechanical alloying or generate nanoscale microstructures such as fine grains or fine precipitates. The deformed nanograins in this process exhibit deformation shear bands22 like any other highly deformed nanograins produced by other processing techniques. Nevertheless, these nanostructured powders are not a final product, but a precursor material. The nanopowders may be consolidated into nanostructured bulk materials or they can be sprayed for nanostructured coatings. Consolidating powders into a bulk material is a challenging process because of pores or oxides or other potential contamination introduced into the matrix, some of which are produced during milling and consolidation; and second, these precursor powders undergo microstructural coarsening or grain growth during thermal consolidation. A recent approach using a cryogenic atmosphere in mechanical attrition shows clear improvement in effective milling and a reduction in contamination.23 SPD metals with UFG can be produced by a conventional machining process, whose microstructual refinement mechanisms have been known for some time. The grain size produced in machining depends on processing parameters, but it can be as low as 200 nm. Besides, the machining can produce bulk forms of UFG products such as foils, sheets, or rods, directly from the coarse-grained bulk metals.24 The challenging aspect of this approach is to control the microstructure via machining parameters such as strain, strain rate and temperature throughout the entire operation. Alternatively, individual UFG chips produced can be consolidated into a bulk form by various consolidation techniques, which are still in the early stage of development.

Solid reaction processes Nanomicrostructures other than nanograin structures can be generated and produced in a controlled manner by thermal reaction and diffusion. One recent interesting approach is to examine the possibility of creating nanostructure in

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conventional high-strength steel material, which is difficult to process using conventional SPD approaches due to its high flow stresses. In the past, bainite steels have been in use for a long time, and the nucleation and kinetics of bainite formation have also long been understood. In another recent approach, the bainite reaction can be made to produce nanoscale bainitic ferrite plates (20–40 nm) by heat-treating bainite steel at relatively low temperatures for a longer duration. This is only possible in steels with a relatively high concentration of carbon. For example, in Fe-0.78-0.98 C-Si-Mn-Cr-Mo alloys, an enhanced nucleation of ferrite in austenite after supercooling is possible at the low temperatures (125–325oC) for one to six days’ holding time during which grain growth is suppressed.25,26 This type of steel containing nanostructures exhibits an extremely high strength comparable with that of maraging steels. The advantage of bainite steels over martensitic steels is that martensite steel has limited dimensionality due to the fact that it needs a high cooling rate to produce martensite, while nanoscale bainite steels can be produced in larger dimensions due to their flexible heat treatment requirements and no requirement of high cooling. Highsilicon bainite steels also exhibit a combination of high strength and toughness.26

Liquid–solid transformation processes Liquid–solid transformation processes have two different approaches. First, a molten alloy is solidified into an amorphous phase, from which nanocrystalline precipitates or nanograins can be produced by controlled heat treatment for crystallization.27 The amorphous matrix turns into partially or fully nanocrystalline matrix depending on heat treatment conditions. The maximum dimensions of a bulk amorphous metal, however, are limited due to the fact that 1) a critical cooling rate is required for amorphous formation and 2) each alloy has its own glass forming ability. The second process includes thermal spray coating, in which the feed material is melted and broken into fine droplets before solidifying on the substrate surface. In this process, the stability of the molten phase is important during melting and flight.28 The feedstock could be powders or solid wires. A general rule of thumb is that any material that has a stable molten phase and can be processed into the appropriate feed specifications, can be thermal sprayed. The heat source used to heat and accelerate the feedstock is generated either chemically via oxygen-fuel combustion or electrically via an arc.

Mechanical properties One of the most pronounced mechanical properties of nanostructured metals is their extraordinary high yield strength compared to those of conventional coarsegrained metallic materials. But, the downside of this material is its well-known poor ductility. Earlier efforts to test the strengthening behavior of nanometals with respect to grain size led to the discovery of a breakdown of the Hall–Petch (H–P)

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relationship.29,30 This unexpected behavior was identified as the ‘inverse H–P relationship’. Since then, this unexpected softening behavior of nanostructured metals has been a subject of intensive research and the center of discussion. Furthermore, not only is strain hardening (the result of characteristic dislocation pile-ups in coarse-grained metals) absent in nanostructured metals with grain size less than approximately 20 nm, but also any dislocation pile-up in nanograins has not been observed using high-resolution microscopy. Thus, in nanograined metals, grain boundary (GB) deformation has to be the main mechanism for plastic deformation, considering the fact that 1) nanograins become an inactive component in deformation, and 2) the volume fraction of grain boundary and triple junction under the single-digit grain size matrix could be anywhere from 10% to as much as 30%. For these reasons, the focus of research moved from grain deformation to grain boundary deformation for nanograined metals. For the last two decades, unique deformation mechanisms of nanostructured metals and alloys based on grain boundary deformation mechanisms have been investigated, in which each of different deformation modes such as tensile deformation, superplastic deformation, creep and fatigue failure has been studied separately to capture a complete picture of the deformation mechanisms. Research results on these subjects are presented and discussed throughout various chapters in Parts II and III of this book.

Strength and ductility The Hall–Petch relationship tells us that we could achieve strength in materials that is as high as their own theoretical strength by reducing grain size. Indeed, their strength continues to increase with decreasing grain size to approximately 20–30 nm where the strength peaks. Indeed, the peak yield strength of pure nanostructured copper with grain size approaching approximately 20 nm can reach as high as 800– 900 MPa 29,31–33 compared to 200 MPa for coarse-grained copper. But decreasing grain size beyond 20 nm reverses the H–P effect: in other words the material starts to soften instead of further strengthening. In general, nanostructured metals are characterized as having very high strength with poor ductility. In other words, the strength increase trades off with ductility in nanostructured metallic materials. As an exception, artifact-free nanocrystalline copper with a grain size of 30–60 nm was found to possess a very high yield strength, and good ductility such as a fracture strain of 0.06 to 0.12 (Eng).34,35 Such relatively ductile behavior of nanocopper may be explained by a number of models: dislocations stored in larger grains, grain boundary sliding, Coble creep (GB diffusion), localized shear microbands, twinning, etc. For nanostructured metals with a wide distribution of grain size, none of the above models can be excluded. But, when the grain size distribution is narrow and its median value is close to 20 nm or less, only grain boundary deformation modes, i.e. grain boundary sliding, grain boundary rotation or Coble creep must

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be considered since the grains are regarded as plastically non-deformable islands that are embedded in the network of grain boundaries. For nanostructured metals, it may be possible that all these GB deformation models are operating in an optimized manner.36 Another important factor is the effect of impurities on GB deformation. For example, nano-copper with contaminants does not exhibit such ductile behavior, probably due to the fact that the impurity has a negative influence on GB deformation, which is a subject of future investigation.

Deformation mechanisms In the past, tensile testing of nanostructured metallic materials has been performed with various grain sizes from the ultrafine scale to the nanoscale, as small as 10 nm in diameter. In addition, the samples prepared by different processing routes have contained different levels of atomic as well as macro defects. Thus, one must be careful in analysing and interpreting the experimental results from such diversified material sources. In fact, this has been a challenging aspect for investigating deformation mechanisms of nanostructured metals in the past. In general, the tensile deformation of nanostructured metals shows that the flow stress starts to decline right after yielding, indicating an absence of strain hardening behavior. This is an indicative of the fact that the dislocation pile-up doesn’t occur beyond the yield point in nanostructured metals. To explain this behavior, it is proposed that the number of dislocations in the pile-up continues to decline with decreasing grain size.37,38 Thus, there must be a critical grain size where a single Frank–Read source can operate in a grain. Near such a critical grain size, the dislocation pile-up would no longer occur due to the very high shear stress required for the generation of any additional dislocation, and consequently, the Hall–Petch relationship cannot be established. This would explain why the H–P relationship breaks down in nanostructured metals. For these reasons, dislocation pile-up mechanisms would no longer be useful for nanostructured metals with a grain size less than 20–30 nm. Thus, the focus has been shifted to grain boundary deformation in recent years. The fact that the volume percentage of grain boundary and triple junction significantly increases and reaches as much as 30% for a grain size less 10 nm makes GB deformation more significant. But the details of GB deformation in nanostructured metals are very complex. Furthermore, direct observation of deformation defect structures using high-resolution microscopy is scarce. Therefore, research into GB deformation mechanisms has largely taken two tracks: 1) developing theoretical approaches that are based on classical deformation models for superplasticity; 2) performing computer simulations based on molecular dynamics under various stress and temperature conditions. The theoretical approach is considered to test the predetermined framework against experimental measurements whereas MD simulations let atoms and groups of atoms play the game without knowing the outcome.

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From this prospect, MD simulations could provide insightful information about the process and mechanisms of plastic deformation. Since, in nanograined metals, tensile deformation, superplastic deformation and creep have a common thread, i.e. grain boundary deformation, it may be possible to develop a unified model that can describe these three deformation modes in the future. GB deformation models Although the three different deformation modes – time-independent deformation, superplasticity and creep–are connected through grain boundary deformation mechanisms, conceptually it can be said that each of the modes is made of different levels of contributions by stress-induced GB deformation and thermally-induced GB deformation. In general, it is understood that grain boundary sliding in nanostructured metals occurs by GB dislocations if dislocations are available under applied shear stress, and by thermally activated local shear events, which occur by uncorrelated individual atomic jumps and the movement of small groups of atoms. In particular, nanostructured metals are made of grains whose boundaries are not only nanoscale, but also in the non-equilibrium state (majority). Thus, thermally induced GB deformation becomes important in this type of materials. With such a conceptual background, Conrad et al.39 proposed that the macroscopic shear occurs due to thermally activated atomic shear in the nanograin boundary, i.e. GB sliding. Fu et al., following the idea of a neighbor-grainexchange mechanism in superplastic deformation by Raj et al.,40 introduced a plastic accommodation term to the thermal shear stress in Core–Mantle nanograins.41 The results show that the strain rate in nano-copper with grain size less than 10 nm at 300K could reach a significant level indicating that GB sliding would be real possibility under diffusional sliding with plastic accommodation. In recent years, Wang et al.42 suggested that grain rotation and grain coalescence in the direction of shear would be possible during plastic deformation. Ovid’ko demonstrated that such a rotation of grains could be indeed possible by creating disclinations during such a rotation.43 Furthermore, Murayama et al.44 reported that TEM images from a milled Fe sample showed a partial disclination dipole. Another deformation structure reported was shear band formation as a localized deformation mode in ultrafine-grained iron.45 Another important issue is non-equilibrium GB,46 which is a center of dislocation sink and generation. The fraction of non-equilibrium boundary increases with decreasing grain size. It is important to understand the role of the non-equilibrium GB in deformation. For example, 1) the emission of partial dislocations from triple junctions and non-equilibrium GB as part of the accommodation mechanisms to local shear events would trigger the formation of stacking faults and twins in nanograins, and 2) non-equilibrium GB acts as a dislocation sink and may assist dynamic recovery during deformation. Despite the

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limited success of analytical models, it is not possible to understand the complex dynamic process of GB sliding by analytical modeling as the process is characterized by the evolution, annihilation and mutual interaction of various defect structures in the process. MD simulations Scientists have often been unable to observe the evolution of deformation microstructure on an atomic scale by high-resolution microscopy. In the past, numerous interesting pieces of defect structures in nanostructured metals have been reported. On the other hand, regular mechanical testing continues to generate a large volume of experimental results that were usually not provided with the related microstructures. Therefore, to establish the property–structure relationship, computer simulations must play a crucial role in bridging the two different types of observation. In addition, other unexpected microstructural evidence that has been observed needs to be explained by theory or demonstrated by MD simulations. For example, some interesting microstructures observed by highresolution microscopy include stacking faults, twins in face-centred cubic (fcc) metals such as Al, Cu with high stacking faults energy, stacking fault tetrahedral, and disclinations. The challenging task is to understand why these defect structures are present only in nanostructured metals. To answer these questions, numerous theoretical models and computer atomic simulation techniques have been employed. In the early stage of investigations, for example, finite element (FE) simulations by Kim et al.47 were used to reproduce experimental tensile test results as well as the H–P plot for nano-Cu with grain size of 10–1000 nm. Kim used a ‘phase mixture mode’ in which nanomaterial consisted of two distinctive phases: initially dislocation-free crystalline matter at the center and the surrounding grain boundary (amorphous-like). Thus, during simulations, the dislocation pile-up was allowed in the crystalline matter while diffusional flow occurred in the grain boundary. The H–P plot generated by this scheme is in good agreement with experimental data. Nevertheless, FE simulations are not equipped to investigate the role of various defects in GB deformation or to predict the evolution of unexpected defect structures. In recent years, however, molecular dynamic (MD) computer simulations have demonstrated that they are powerful tools in investigating the deformation mechanisms in nanostructured metals. For example, twinning in deformed nanostructured Al was predicted by MD simulations,48 and was confirmed later by experiment.49 The deformation mechanisms in both time-dependent and time-independent deformation have been studied by MD simulations in the past. For time-dependent deformation, MD simulations have been focused on grain boundary diffusion, grain boundary sliding and emission of dislocations, particular partial dislocations and twins from grain boundaries.

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Despite their inherent deficiencies (see Chapter 15), MD simulations have already made a significant contribution in elucidating deformation mechanisms of nanostructured materials this decade. Such important events by MD simulations this decade include 1) confirmation of the inverse Hall–Petch relationship;50 MD models reasonably explained the transition from the hardening mode to the softening mode in nanostructured metals using two competing mechanisms: grain boundary mediated mechanisms (GB sliding, diffusion)51,52 and transgranular dominant mechanisms (dislocation slip, twinning, etc.) depending on grain size; 2) MD simulations showed the existence of Coble creep in nanostructured metals at relatively low temperatures;53 3) elucidating grain boundary-mediated deformation mechanisms in which the Shockley partial dislocations emitting from triple junction and GB are also a part of GB sliding.51,54 Yet, there are unresolved problems regarding the fundamental understanding of GB sliding mechanisms. There are two views: either stress-induced free-volume migration or stress-induced long-range atomic migration (diffusion) causes the deformation of nanograined metals. The fact that both GB sliding and GB diffusion are influenced by applied stress and temperature makes it difficult to separate one from the other. Second, such MD simulations that have been performed on fcc metals are not or almost not available for other crystal structures such as body-centred cubic (bcc), hexgonal close packed (hcp) and tetragonal structures. Thus, it is desired to have MD simulations for other nanostructured metals with different crystal structures other than fcc in the future.

Superplasticity and creep Both superplasticity (SP) and creep were observed in nanostructured metallic materials and in course grained metallic materials. The differences between the two deformation modes lie in the loading conditions: applied stress, strain rate, time duration and temperature. Nevertheless, the main deformation mechanism for both deformation modes remains in the grain boundary deformation regime. Since SP deformation occurs at higher strain rates and higher stresses while creep occurs under relatively low applied stress for a longer time frame, diffusion carries out the bulk of grain boundary deformation. One of the theories about GB sliding in SP deformation is that GB sliding is an operation of the sliding and rotation of entire grain groups along common sliding surfaces. The evidence of such a group sliding is the existence of steps along shear planes on a surface of post-deformed materials. Such ‘cooperative grain boundary sliding’ (CGBS) was observed indirectly in Ni3Al,55 Pd56 and directly in Nano-Ni3Al.57 For example, Ti-6Al-4V with a grain size 100–200 nm deformed at 725° at a strain rate range 10–1 to 10–3 s–1 yielded an elongation more than 500%, which is much higher than that in the microcrystalline state.58 It is logical to assume that higher diffusion flux as a component of CGBS in nanostructured metallic materials would assist GB sliding while lack of intragranular dislocation activity in nanostructured

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metallic materials (NMM) may negatively influence the grain boundary sliding. But, the fundamental classical mechanisms for SP and creep appear to remain in NMM. Understanding of SP and creep mechanisms must start with an understanding of the GB sliding mechanisms in NMM. Nanostructured Ni (20–40 nm grains) exhibits creep at RT. The test results well fit into the models of grain boundary sliding aided by grain boundary diffusion.59,60 Yin et al.61 studied the creep of nano-Ni from RT to 473 K. The activation energy calculated from the temperature dependence curve was 92 kJ/mol, which is activation energy for GB diffusion in Ni. Thus, at the moment, both grain boundary sliding and grain boundary diffusion can be considered as candidates for creep in nano-Ni in the temperature range RT to 473k. On the other hand, Yamakov et al.53 performed MD simulations for nano-Pd at elevated temperatures under high stresses assuming no grain growth. The results show that the creep was characterized as a Coble-type creep and GB sliding is an accommodating mechanism for the creep. The simulations showed a linear dependence of the creep rate with the applied stress. But, the linear relationship was unable to extrapolate to a low temperature regime, e.g. RT. The questions remain whether conditions of high stress and high strain rates at high temperatures used in the simulations can duplicate the real creep situation under low stress, low strain rate at low temperatures because different conditions would alter deformation mechanisms. It would take for a while for MD simulations to carry out creep deformation under reasonable conditions, because currently the limitations imposed on the computations are too severe. Another complication in analysing experimental data for creep is that in fact grain growth occurs in nanometals even at relatively low temperatures where the time duration for creep testing is significant for grain growth. Although both GB diffusion and GB sliding are an integral part of the creep, it is difficult to determine which is the dominant mechanism for a given stress and temperature at this time.

Fatigue Investigating the fatigue behavior of nanograined metals has rarely been done, mainly due to inadequate nanomaterial supply, and thus the majority of investigation has been focused on ultrafine-grained (UFG) metals and alloys with a grain size range of 100 nm–1 µm.62 Nevertheless, an interesting earlier piece of work on fatigue in nanostructured Ni was reported by Hanlon et al.63 In the report, nanocrystalline (NC) Ni was compared with UFC Ni and microcrystalline (MC) Ni with respect to its stresslife (S-N) fatigue behavior. NC Ni sheets with grain size 20 to 40 nm and UFC Ni sheets with grain size 300 nm were prepared by electrodeposition technique. The results show that the endurance limit significantly increased from MC Ni to both UFC Ni and NC Ni. There is no appreciable difference between NC Ni and MC Ni in terms of fatigue resistance. However, the fatigue growth rate of NC Ni is

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higher than that of UFC Ni, and much higher than that of MC Ni. Depending on the grain size, the refinement has a negative influence on fatigue crack growth resistance. Despite some preliminary evidence for the fatigue properties of nanometals, it is critical to conduct similar experiments with specimens of artifactfree and controlled impurity concentration at GB to confirm these results. It is too early to draw conclusions with only limited information. Fatigue life based on a S-N plot for pure UFG metals – copper, nickel and aluminum – has been investigated. The results show a significant increase in fatigue life in all these UFG metals compared to those of the counterpart coarsegrained metals, primary due to the increase in strength in UFG metals. Nevertheless, when fatigue life is regarded with respect to the plastic strain amplitude. UFG metals exhibit a deteriorated fatigue life compared to their coarse-grained counterparts. For UFG metals crack initiation is mostly a result of shear band formation and localized plastic deformation along these shear bands. Shear band formation appears to be the dominant mechanism to SPD-processed materials at this grain size range.64 But the key is the history of material processing, which would determine the microstructural characteristics and in turn has an influence on fatigue life. For example, SPD-processed UFG metals with a post-heat treatment result in a bimodal microstructure, which has a positive influence on fatigue life.65

Applications In the coming decades, structural applications will require energy efficient materials, e.g. with high specific strength, light weight and excellent durability. From this vantage point, nanostructured metals should have a bright future. Nevertheless, the development of products requires long-term commitment by the industry, and the odds that a product under development successfully makes it into the marketplace are still statistically quite low. Currently, a few products of nanostructured metallic material have found their way into the marketplace. For example, nanosurface coatings for corrosion protection and wear-resistant applications that are processed by electrodeposition, thermal spray and cold spray are already available for special applications. New nanostructured coating of cobalt-phosphorus alloy,66 as alternative to conventional hard chrome coating, shows excellent wear and corrosion properties. Due to growing environmental concern about the health risks of hexavalent chromium, this alternative looks attractive for practical applications. Thermal spraying of hard metals such as WC-Co67 and Ti-oxide, NiCrAlY62 by the high-velocity Oxyfuel (HVOF) processing yields high dense nanostructured coatings for wear and corrosion applications. Nowadays, the structural materials for aerospace and automobile applications and any other applications that are tied to power consumption are increasingly required to be energy efficient. Riding the trend, there is considerable effort to develop nanostructured steels that will meet such demands. But current effort has

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been focused on ultrafine-grain (UFG) ferrite single-phase steels,69,70 multi-phase steels,71 and nanostructured Bainite steels.25 UFG ferrite steel can be processed by hot rolling, followed by cold rolling in a conventional way, and the rolled sheets recrystallized at 525–700°C for two minutes in a salt bath. This UFG ferrite steel has been further developed into UFG-multi-phase steel to optimize the strength and ductility balance for highstrength automobile body applications. The multi-phases in this steel include austenite, bainite and martensite, in addition to ferrite grains. For very high strength structural applications, nanostructured bainite steels containing Si, Mn and Cr would be economically attractive compared to expensive maraging steels. These bainite steels have a yield strength of 1.4 GPa, a tensile strength of 2.2 GPa and fracture toughness (K1c) of 25 MPam1/2 at room temperature. Other ultrafine-grained steel materials come in bar, wire and strip form.72 Ultrafine-grained bars of low-carbon steel can be processed by multiple caliber rolling at 550°C and water quenching. Ultrafine-grained wires were made using a starting wire of 6 mm in diameter and by oval-square rolling repeatedly at 500°C until its diameter was reduced to 3 mm. The UF wires show a yield strength of more than 800 MPa, compared to that of the starting wire of 400 MPa. All these steels are some of the examples currently under development.

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Gleiter H. Prog Mater Sci 1989;33: 223. Gleiter H. Acta Mater 2000;48: 1–29. Guinier, A., Preston, D.A. Nature 1938;142: 569–570. Embury J.D., Fisher R.M. Acta Metall 1966;14: 147–159. Valiev R.Z., Langdon T.G. Prog Mater Sci 2006;51: 881. Koch C.C., editor, Nanostructured Materials – processing, properties and applications, Noyes publications, William Andrew Publishing, Norwich, New York (2007). Meyers M.A., Mishra D.J., Benson D.J. Prog Mater Sci 2006;51: 427–556. Erbel S. Metals Tech 1979;6: 482. Langford G., Cohen M. Trans. ASM 1969;82: 623. Saunders I., Nutting J. Metal Sci 1984;18: 571. Segal V.M., Mater Sci Eng 1995;A197: 157. Valiev R.Z., Kaibyshev O.A., Kuznetsov R.I., Musalimov R.Sh., Tsenev N.K. Dokl Akad Nauk SSSR (Reports of USSR Academy of Sciences) 1988;301(4): 864. Valiev R.Z., Krasilnikov N.A., Tsenev N.K. Mater Sci Eng  A 1991;137: 35. Valiev R.Z., Korznikov A.V., Mulyukov R.R. Mater Sci Eng A 1993;186: 141. Valiev R.Z., Islamgaliev R.K., Alexandrov I.V. Prog Mater Sci 2000;45: 103. Ungár T., Balogh L., Zhu Y.T., Horita Z., Xu C., Langdon T.G. Mater Sci Eng A 2007;444: 153. Saito Y., Utsunomiya H., Tsuji N. and Sakai T. 1999;47: 579. Tsuji T., Saito Y., Lee S.H., and Minamino Y. Adv. Eng. Mater, 2003;5: 338. Bhadeshia H.K.D.H. High strength steels. In Charles J.A., Greenwood G.W., Smith G.C., editors. Future Developments in Metals and Ceramics, London, Institute of Materials, 1992. p.25.

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Bhadeshia H.K.D.H., Harada H. Appl Sur Sci 1993; 67: 328. Benjamin J.S. Metall Trans 1970;1: 2943. Fecht H.J., Hellstern E., Fu Z., Johnson W.L. Metall Trans A 1990;21: 2333. Perez R.J., Huang B., Lavernia E.J. Nanostructure Mater 1996;7: 565. Brown T.L., Saldana C., Murthy T.G., Mann J.B., Compton W.D., Trumble K.P., King A.H., and Chandrasekar S. Acta Mater 2009;57: 5491. Caballero F.G., Bhadeshia H.K.D.H., Mawella J.A., Jones D.G., Brown P. Mater Sci Technol 2002;18: 279. García-Mateo C., Caballero F.G., Bhadeshia H.K.D.H. ISIJ Int 2003;43: 1238. Perepezko J.H. and Hebert R.J., J Metall 2002;5: 34. Kim G.E. Thermal Sprayed Nanostructured Coatings: Applications and Developments. In Koch C.C., editor, Chapter 3, Nanostructured Materials Processing, Properties, and Applications, 2nd Edition, William Andrew Publishing, 2007. Chokshi A.H., Rosen A., Karch J., Gleiter H. Scripta Mater 1989;23: 1679. Fougere G.E., Weertman J.R., Siegel R.W., Kim S. Scripta Metall Mater 1992;26: 1879. Embury J.D., Keh A.S., Fisher R.M. Trans Metall Soc AIME 1966;236: 1252. Hansen N., Ralph B. Acta Metall 1982;30: 411. Nieman G.W., Weertman J.R., Siegel R.W. Scripta Metall 1989;23: 2013. Youssef K.M., Scattergood R.O., Murty K.L., Horton J.A., Koch C.C. Appl Phys Lett 2005;87: 091904. Cheng S., Ma E., Wang Y.M., Kecskes L.J., Youssef K.M., Koch C.C., Trociewitz U.P., Han K. Acta Mater 2005;53: 1521. Ovid’ko I.A., Sheinerman A.G. Acta Mater 2009;57: 2217. Pande C.S., Masumura R.A., Armstrong W. Nanostruct Mater 1993;2: 323–331. Nieh T.G., Wadsworth J. Scripta Metall Mater 1991;25: 955–958. Conrad H., Narayan J. Scripta Mater 2000;42: 1025. Raj R., Ashby M. J Met Tans 1971;2A: 1113. Fu H.H., Benson D.J., Meyers M.A. Acta Mater 2001;49: 2567–2582. Wang Y.M., Ma E., Chen M.W. Appl Phys Lett 2002;80: 2395–2397. Ovid’ko I.A. Science 2002;295: 2386. Murayama M., Howe J.M., Hidaka H., Takaki S. Science 2002;295: 2433–2435. Wei Q., Kecskes L., Jiao T., Hartwig K.T., Ramesh K.T., Ma E. Acta Mater 2004;52: 1859–1869. Valiev R.Z., Islamgaliev R.K., Alexandrov I.V. Prog Mater Sci 2000;45: 103. Kim H.S., Estrin Y., Bush M.B. Acta Mater 2000;42: 493–504. Yamakov V., Wolf D., Phillpot S.R., Gleiter H. Acta Mater 2002;50: 5005. Chen M. et al. Science 2003;300: 1275. Kadau K. et al. Metall Mater Trans 2004; 35A: 2719. Shiiotz J., Di Tolla F.D., Jacobson K.W. Phys Rev B 1999;60: 11,971. Swygenhoven H.V., Spaczer M., Caro A., Farkas D. Phys Rev B 1999;60: 22. Yamakov V., Wolf D., Phillpot S.R., Gleiter H. Acta Mater 2002;50: 61. Swygenhoven H.V., Farkas D., Caro A. Phys Rev B 2000;62: 831. Zelin M.G., Mukherjee A.K., Acta Metall Mater 1995;45: 2359. Markmann J., Bunzel P., Rosner H. Scripta Mater 2003;49: 637. Sergueeva A.V., Mara N.A., Krasilnikov N.A., Valiev R.Z., Mukherjee A.K. Phil Mag 2006;86: 5797. Sergueeva A.V., Stolyarov V.V., Valiev R.Z., Mukherjee A.K. Mater Sci Eng A 2002;323: 318. Cai B., Kong Q.P., Cui P., Lu L., Lu K.. Scripta Mater 2001;45: 1407.

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60 Sanders P.G., Eastman J.A., Weertman J.R. Acta Mater 1997;10: 4019. 61 Yin W.M., Whang S.H. JOM 2005;1: 63. 62 Höppel H.W., Kautz M., Xu C., Murashkin M., Langdon T.G., Valiev R.Z., Mughrabi H.: Int J Fatigue 2006,28: 1001. 63 Hanlon T., Kwon Y.N., Suresh S. Scripta Mater 2003;49: 675–680. 64 Mughrabi H., Höppel H.W. In: Farkas D., Kung H., Mayo M., v. Swygenhoven H., Weertman J., editors. Structure and mechanical properties of nanophase materialstheory and computer simulation vs. experiment, Mat Res Soc Symp Proc Vol 634, Materials Research Society; 2001; p. B 2.1.1. 65 Höppel H.W., Valiev R.Z. Z Metallkunde 2002;93: 641. 66 Erb U., El-Sherik A.M. US Patent No. 5,352,266 (1994). 67 He J., Ice M., Dallek S., Lavernia E.J. Metall and Mater Trans A 2000;31A: 541. 68 Ajdelsztajn L., Picas J.A., Kim G.E., Bastian F.L., Schoenung J.M., Provenzano V. Mater Sci Eng 2002;A338: 33. 69 Tsuji N., Ito Y., Saito Y., Minamino Y. Scripta Mater 2002;47: 893. 70 Tsuji N., Okuno S., Koizum Y., Minamino Y. Mater Trans 2004:45: 2272. 71 Okitsu Y., Naito T., Takaki N., Sugiura T., Tsuji N. SAE Technical Paper 2010:201001-0438. 72 Ohmori A., Torizuka S., Nagai K., Koseki N., Kogo Y. Tetsu-to-Hagane, 8(2003): 781–788.

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1 Producing bulk nanostructured metals and alloys by severe plastic deformation (SPD) R.Z. VALIEV, Ufa State Aviation Technical University, Russia Abstract: Despite its promise, the use of nanostructured metals and alloys as a new generation of structural and functional materials has only recently been realized. Only in recent years has a breakthrough been made in this area, associated both with developing new methods for fabricating bulk nanostructured materials and with investigating the fundamental mechanisms that lead to novel properties in these materials. This chapter presents new concepts and principles in using severe plastic deformation (SPD) techniques to fabricate bulk nanostructured metals with advanced properties. Special emphasis is laid on analysing of the effect of the microstructural features of nanostructured materials fabricated by SPD on mechanical properties such as strength and ductility, fatigue strength and life, and superplasticity, as well as describing early examples of their innovative applications. Key words: bulk nanostructured materials, severe plastic deformation, advanced properties, strength and ductility, equal-channel angular pressing, high pressure torsion.

1.1

Introduction

The concept of ‘large plastic strains’, or deformations that are characterized by a high value of true accumulated strain (e ≥ 0.5) and are realized at relatively low temperature (≤ 0.4 melting point), is widely used in the branches of physics and mechanics that deal with the problems of strength and ductility of solid states.1–3 Large plastic deformations are actively engaged in practice, for example, in metal forming for shaping in the process of manufacturing semi-products and parts as well as for materials hardening. Traditionally, such methods of metal forming as drawing, extrusion, rolling and others are used for these purposes. Experimental methods for achieving very large strains are usually based on the rolling of strips or thin foils, e.g. with initial thickness of ~10 mm up to a final one of ~0.1 mm, which is equivalent to a 99% reduction in thickness (true strain e = 4.6). Therefore, true strains 4–4.5 are critical for shaping bulk billets by conventional metal forming methods, and as it was noticed in earlier works, the achievement of larger strains requires radically different processing techniques.4 It was suggested4,5 that such techniques may comprise the die-sets combining shear (torsion) and compression straining as they make it possible to deform the material without changing its form. Fracture in material is another problem encountered when achieving super-high strains. As is known, many metallic materials are exposed to quick fracture at room temperature even in the early stages of deformation. However, it is possible 3 © Woodhead Publishing Limited, 2011

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to increase the deformability of metals and alloys by imposing hydrostatic pressure. The phenomenon was first studied in detail by P.W. Bridgman (Harvard University), who was awarded the Nobel Prize for Physics in 1946 for his works in the sphere of high pressure.6 In the 1980s these ideas were realized by Polish4 and Russian scientists from Yekaterinburg, (formerly Sverdlovsk, USSR)7 in creating experimental die-sets for combined torsion and compression. The application of these devices achieved very large strains with true strains exceeding 8–10, which resulted in strong grain refinement in metals. The basic work was performed by scientists in Ufa in 1988,8 where this method was demonstrated for the first time, of producing ultrafinegrained (UFG) metals and alloys with high-angle grain boundaries that led to new properties. The latter was evidenced by revealing the so-called ‘low-temperature superplasticity’ in an UFG Al alloy. Later, in 1991 UFG materials were first obtained by means of another technique – equal-channel angular pressing (ECAP),9 during which the billet shape is also preserved and therefore very large strains are achieved by multi-pass processing. As demonstrated below, ECAP allows the production of UFG structures in bulk billets from different metals and alloys. Moreover, the technique is very promising for practical applications. This new approach to grain refinement, based on the achievement of very large true strains with e ≥ 6–8 under high pressure, was termed ‘severe plastic deformation’ (SPD)10 and attracted much attention with the further development of many SPD techniques.11–13 Besides, SPD processing routes and regimes for grain refinement were established for various metals and alloys.14 More complete definitions of SPD processing and ultrafinegrained (UFG) materials are presented in several recent overviews.11,12,15,16 It is important to emphasize that SPD-produced UFG materials are fully dense and their large geometric dimensions make it possible to study their properties thoroughly by means of mechanical and other tests. As a result, the subject of bulk ultrafine-grained materials produced by severe plastic deformation was introduced into scientific literature. The next important step along with the formation of UFG was finding nanostructural features in SPD-processed metals (non-equilibrium grain boundaries, dislocation substructures, segregations and nanoparticles and other elements) resulting in novel properties16 (see also section 1.3.3, this chapter). At this time, the fabrication of bulk nanostructured materials by SPD is becoming one of the most actively developing areas in the field of nanomaterials.12,17 The present chapter considers new trends in the development of SPD techniques, basic requirements for processing nanostructured materials with enhanced properties by means of SPD, and prospects for their practical applications.

1.2

The principles of severe plastic deformation (SPD) processing

Since the pioneering work on tailoring ultrafine-grained structures by SPD processing,9,10 two SPD techniques have attracted close attention and have

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recently been further developed. These techniques are high-pressure torsion (HPT)16,18 and equal-channel angular pressing (ECAP).16,19 In the last 10 to 15 years there have appeared a wide diversity of new SPD techniques: for example, accumulative roll bonding (ARB), multi-axial forging, twist extrusion and others (see other chapters for details). Nevertheless, processing by HPT and ECAP has remained the most popular approach and has recently acquired a new impulse for development through the modification of conventional die-sets and demonstrations that new opportunities are now available for involving these procedures in processing (see References 15, 18, 19). The fundamental principles of these two techniques are illustrated schematically in Fig. 1.1. Samples processed under HPT are disc-shaped (Fig. 1 (a) ). In this process, the sample, with a diameter ranging from 10–20 mm and thickness of 0.3–0.8 mm, is placed between anvils and compressed under an applied pressure (P) of several GPa. The lower anvil turns and friction forces lead to a shear straining of the sample. Under high pressure, the deforming sample does not break even at high strains.16 In HPT, an essential microstructural refinement is observed after deformation through one-half or one complete (360°) turn. But to produce a homogeneous nanostructure, with a typical grain size of about 100 nm or less, deformation by several turns is necessary (Fig. 1.2). The important role of applied pressure in the formation of a more homogeneous nanostructured state during HPT is also shown in recent work on nickel.20 Among different SPD techniques, HPT particularly

1.1  Principles of severe plastic deformation: (a) High-pressure torsion: a sample is held between anvils and strained in torsion under an applied pressure (P); (b) Equal-channel angular pressing: a work piece is repeatedly pressed through a special die.

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1.2  Transmission electron microscopy images of ultrafine-grained copper: (a) Copper processed by HPT at room temperature (P = 6 GPa, 5 turns); (b) Copper processed by ECAP (12 passes).

enables a refinement of the microstructure with maximum efficiency and often forms a UFG structure with a grain size less than 100 nm.16,18 For this reason, HPT is now widely used as an experimental technique for grain refinement in different laboratories all over the world. Moreover, in recent years it has been further developed by enlarging the size of specimens21,22 and by processing ringshaped samples23. Processing by ECAP (Fig. 1.1 (b) ) is now also the most established procedure for use with different metals and alloys and it is a very attractive technique for several reasons. First, it is relatively easy to set up and use an ECAP die. Second, exceptionally high strains may be imposed either through repetitive pressing of the same sample or by developing special multi-pass dies,24 rotary dies25 or sideextrusion facilities.26 Third, although ECAP is generally used with samples in the form of bars or rods, the process may be applied also to plate samples: for example, a recent report described the application of ECAP to an aluminum plate.27 Fourth, ECAP can be incorporated into conventional rolling mills for use in continuous processing28–31 or into the ECAP-conform process for the production of longsized rods and wires.32 In view of these many advantages, special attention has been paid recently to the principles of processing through the use of ECAP (see the reviews16,19,33). The ECAP technique was introduced by V. Segal et al. in 1981 as a technique for straining by a simple shear,34 however, as noted above, it was developed and first applied for producing UFG metals only in the early 1990s.9,10 Figure 1.3 shows a schematic illustration of the ECAP procedure.35 A die is constructed containing a channel that is bent through an abrupt angle – this angle is 90° in Fig. 1.3. A sample is machined to fit in the channel and the sample is then pressed through the die using a plunger. It is apparent from the illustration that the sample has the same cross-sectional dimensions before and after pressing, thereby

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1.3  The principle of ECAP processing, including a definition of the three orthogonal planes X, Y and Z.35

permitting repetitive pressings of the same sample. It is important to note also that retaining the same cross-sectional area differentiates processing by ECAP in a very significant way from more conventional industrial processes, such as rolling, extrusion or drawing, where the sample dimensions are reduced in each consecutive pass. Three orthogonal planes are illustrated in Fig. 1.3, where X is the transverse plane perpendicular to the flow direction, Y is the flow plane parallel to the side face at the point of exit from the die and Z is the longitudinal plane parallel to the top surface at the point of exit from the die. The strain imposed on the sample in each passage through the die depends primarily upon the angle, Φ, between the two parts of the channel (90° in Fig. 1.3) and also to a minor extent upon the angle of curvature, Ψ, representing the outer arc of curvature where the two channels intersect (0° in Fig. 1.3). To achieve optimum results, ECAP is generally conducted using a die having a channel angle of Φ = 90°19,36 and with this configuration it can be shown from first principles that for these angles the imposed strain on each pass is approximately equal to 1 with only a small, and almost insignificant, Ψ depending upon the arc of curvature.34,37

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1.4  The four processing routes in ECAP.24

When samples are pressed repetitively, different slip systems may be introduced by rotating the samples about the X-axis between consecutive passes through the die. In practice, four separate processing routes have been identified for use in ECAP: route A in which the sample is pressed repetitively without rotation between passes; route BA in which the sample is rotated through 90° around the extrusion axis in alternate directions between each pass; route BC in which the sample is rotated by 90° in the same sense between each pass; and route C where the sample is rotated by 180° between passes.38 These different processing routes are illustrated schematically in Fig. 1.4 and the distinction between these routes is important because the various routes introduce different shearing patterns into the samples39 leading to variations both in the macroscopic distortions of the individual grains in polycrystalline matrices40 and in the capability to develop a reasonably homogeneous and equiaxed ultrafine-grained microstructure.16,19,41–43

1.3

New trends in SPD processing for effective grain refinement

1.3.1 Development of SPD techniques and routes Since high-pressure torsion and equal-channel angular pressing were first used to produce UFG metals and alloys,9,10 processing regimes and routes have been established for many metallic materials, including some low-ductility and hardto-deform materials. High-pressure torsion and ECAP die sets have also been essentially modernized.19,44,45

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However, to date these techniques have been usually used for laboratory-scale research. The requirement of economically feasible production of ultrafine-grained metals and alloys essential to successful commercialization raises several new problems in the development of the SPD techniques. Highest priority tasks include reducing the material waste, obtaining uniform microstructure and properties in bulk billets and products, and increasing the efficiency of SPD processing. The solution for these tasks has been found by developing continuous ECA pressing32 and multi-step combined SPD processing46,47 for fabrication of longsized rods aimed at setting aimed at setting up production of nanostructured Ti materials for medical applications48 and, later, other metals. Some recent results of these works are presented below. Continuous equal-channel angular (ECA) pressing So far, of all SPD techniques, equal-channel angular pressing (ECAP), also known as equal-channel angular extrusion (ECAE),49 has attracted most attention, because it is very effective in producing UFG structures and can be used to produce UFG billets that are sufficiently large for various structural applications.16,19,44,45 However, the ECAP technique in its original design has some limitations, in particular, a relatively short length of work piece that makes ECAP a discontinuous process with low production efficiency and high cost. In addition, the ends of a work piece usually contain non-uniform microstructure or macro-cracks and have to be thrown away, thus a significant portion of the work piece is wasted and the cost of the UFG materials produced by ECAP is further increased. The key to wide commercialization of UFG materials is to lower their processing cost and waste through continuous processing. Several attempts have been made to this end. For example, repetitive corrugation and straightening50,51 have been developed recently to process metal sheets and rods in a continuous manner. The co-shearing process28 and the continuous constrained strip shearing process29 were recently also reported for continuous processing of thin strips and sheets with UFG structures. However, the question of further improving microstructure uniformity and properties remains topical in the development of these techniques. In our studies we have worked on combining the Conform process52 with ECAP to continuously process UFG materials for large-scale commercial production.32 In this invention, the principle used to generate frictional force to push a work piece through an ECAP die is similar to the Conform process, while a modified ECAP die design is used so that the work piece can be processed repetitively to produce UFG structures. We have designed and constructed an ECAP-Conform set-up that is schematically illustrated in Fig. 1.5. As shown in the figure, a rotating shaft in the center contains a groove, into which the work piece is fed. The work piece is driven forward by frictional forces on the three contact interfaces with the groove, which makes the work piece rotate with the shaft. The work piece is constrained to the groove by a

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1.5  A schematic illustration of an ECAP-Conform set-up.

stationary constraint die. The stationary constraint die also stops the work piece and forces it to turn an angle by shear as in a regular ECAP process. In the current set-up, the angle is about 90°, which is the most commonly used channel intersection angle in ECAP. This set-up effectively makes ECAP continuous. Other ECAP parameters (die angle, strain rate, etc.) can also be used. In our recent work32 we used commercially pure (99.95%) coarse-grained long Al wire with a diameter of 3.4 mm and more than 1 m in length for processing at room temperature with 1–4 passes using ECAP with route C, i.e. the sample was rotated 180° between ECAP passes. The starting Al wire had a grain size of 5–7 µm. Figure 1.6 shows an Al work piece at each stage of the ECAP-Conform process, from the initial round feeding stock to rectangular Al rod after the first ECAP pass. As shown, the rectangular cross-section was formed shortly after the wire entered the groove (see the arrow mark). The change is driven by the frictional force between the groove wall and the Al work piece. The frictional force pushes the wire forward, and deforms the wire to make it conform to the groove shape. After the wire cross-section changes to the square shape, the frictional force per unit of wire length increases because of the greater contact area between the groove and the wire. The total frictional force pushes the wire forward from the groove into the stationary die channel, which intersects the groove at a 90° angle. This part of the straining process is similar to that in the conventional ECAP process. Transmission electron microscopy observations have shown that the ECAPConform has led to microstructure evolution typical of the ECAP process.41,53 Figure 1.7 clearly indicates that the ECAP-Conform process can effectively

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1.6  An Al work piece in the process of ECAP-Conform.

1.7  A TEM micrograph from the longitudinal section of Al wire processed by ECAP-Conform with four passes.

refine grains and produce UFG structures in Al and now in CP (commercially pure) Ti.45 The tensile mechanical properties of the as-processed Al samples after 1 to 4 passes are listed in Table 1.1. It is obvious that the ECAP-Conform process has significantly increased the yield strength (σ0.2) and the ultimate tensile strength (σu),

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Table 1.1  Yield strength σ0.2, ultimate tensile strength σu, elongation to failure δ, and cross-section reduction (necking) ψ of Al samples processed with 1 to 4 passes Processing state

σ0.2, (MPa)

σu, (MPa)

Initial Al rod   47   71 After 1 pass 130 160 After 2 passes 140 170 After 3 passes 130 160 After 4 passes 140 180

δ, (%)

ψ, (%)

28 13 12 14 14

86 73 72 76 76

while preserving a high elongation to failure (ductility) of 12–14%. These results are consistent with those of Al processed by conventional ECAP.41 We also found that for Ti, the strength increased by more than twice after the ECAP processing as compared to the untreated Ti, and the same is true for Ti subjected to conventional ECAP. Thus, the newly developed continuous SPD technique, ECAP-Conform can successfully produce UFG materials. The continuous nature of the process makes it promising for producing UFG materials on a large scale, in an efficient and costeffective manner. However, further study is needed to investigate its ability with respect to grain refinement and properties improvement of various UFG materials. Combined SPD processing In solving the problem of fabrication of nanostructured Ti materials for medical applications, we showed the advantage of combining ECAP with other techniques of metal forming such as rolling, forging or extrusion.54,55 The advantages include effective shaping of long semi-products such as sheets, rods, etc as well as further enhancement of mechanical properties of UFG materials. For example, in Grade 2 CP Ti high-strength (YS = 980 MPa, UTS = 1100 MPa) with elongation to failure δ = 12% was attained using ECAP and extrusion. Also the results of investigations on processing of Ti rods of over 800 mm in length and 6.5 mm in diameter by a combination of ECAP and thermomechanical treatment including forging and rolling are very impressive.46,47 Figure 1.8 presents TEM micrographs of commercially pure (CP) Ti subjected to ECAP and thermomechanical treatment at 80%. It can be seen that combined processing results in significant additional grain refinement down to 100 nm in comparison with 300–400 nm after ECAP; however, a considerable elongation of grains takes place. Mechanical testing showed (Table 1.2) that in CP Ti, thermomechanical treatment after ECAP results not only in an increase in strength and recorded values of σ0.2 and σu, but also sufficient ductility is preserved. It is important that these strength values of nanostructured CP Ti are visibly higher

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1.8  Transmission electron microscopy micrographs displaying the microstructure of Grade 2 Ti after ECAP + TMT, 80%: (a) cross section; (b) longitudinal section. Table 1.2  Mechanical properties of the Ti billets at different stages of processing State

σu, (MPa)

σ0.2, (MPa)

Initial   440   370 ECAP 4 passes   630   545 ECAP 4 passes + 1150 1100 TMT ε = 80%

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δ, (%)

ψ, (%)

38 22 11

60 51 56

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than that of the Ti-6%Al-4%V alloy, which is widely used in structural and medical applications. It is also interesting that the microstructure and properties of the obtained rods are rather uniform, the dispersion of mechanical properties along the rod length does not exceed ±5%.47

1.3.2 Processing of bulk nanocrystalline materials Since the first works dating back to the early 1990s9,10 severe plastic deformation techniques have been used mostly for coarse-grained metals in order to produce ultrafine-grained materials through microstructure refinement. The final grain size produced depends strongly on both processing regimes and the type of material. For pure metals the mean grain size is typically about 100–200 nm after processing by HPT (high-pressure torsion) and about 200–300 nm after processing by ECAP. For alloys and intermetallics the grain size is usually even finer and in some cases as fine as 50–100 nm. However, it is very important for fundamental tasks and many advanced applications to have bulk nanocrystalline materials with a mean grain size less than 30–50 nm. Is it possible to produce such materials using SPD techniques? In recent years this problem has become the object of special investigations and two approaches have been proposed:16;56 SPD consolidation of nanopowders and SPD-induced nanocrystallization of amorphous alloys. SPD consolidation Already in the early work on SPD consolidation of powders57,58 it was revealed that HPT with high pressures of several GPa can provide a rather high density close to 100% in the processed disc-type nanostructured samples. For fabricating such samples via high-pressure torsion, the consolidation of both conventional powders and powders prepared by ball milling can be used. HPT consolidation of nanostructured Ni and Fe powders prepared by ball milling57,58 can be taken as an example. The conducted investigations showed that the density of the samples processed at room temperature was very high and close to 95% of the theoretical density of bulk coarse-grained metals. After HPT consolidation at 200° or 400°C the samples’ density was even higher and reached 98%. Transmission electron microscopy examinations showed the absence of porosity. The mean grain size is very small; it is equal to 17 nm and 20 nm for Ni and Fe, respectively. It is also very interesting to note that the value of microhardness of the Ni samples produced by HPT consolidation was 8.60 ± 0.17 GPa, the highest value of microhardness mentioned in literature for nanocrystalline Ni. SPD-induced nanocrystallization Recent investigations also show that SPD processing can control crystallization of amorphous alloys that may result in the formation of bulk nanocrystalline

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alloys with an ultrafine grain size and new properties.56,59 Recently this approach has also been used to produce and investigate nanocrystalline Ti-Ni alloys, widely known as alloys with shape memory effects. For this investigation, two alloys of the Ti-Ni system were used: melt-spun Ti50Ni25Cu25 alloy59,60 and cast Ti49.4Ni50.6 alloy.61,62 The amorphous structure of Ti50Ni25Cu25 alloy was confirmed by TEM and X-ray diffraction (Fig. 1.9 and 1.10).59,60 However, when the alloy was HPT-ed at room temperature, the x-ray diffraction still indicated the presence of an amorphous structure in the alloy, but TEM studies showed a structure full of nanocrystals with grain sizes of about 2–3 nm in it (Fig. 1.9 (c) ). The essential difference between this alloy in the amorphous state and in its HPT-ed state was revealed during subsequent annealing. As it can be seen in Fig. 1.10, the amorphous alloy was crystallized at 450°C, and formed a martensite phase B19 during cooling. The TEM micrograph of the alloy after annealing shows that the grain structure was rather non-uniform and contained a mixture of small grains and large grains with a size of about 1 micron (Fig. 1.9 (c) ). At the same time after HPT, crystallization occurs below 390°C and its micrograph shows a uniform nanocrystalline structure with a grain size of less than 50 nm (Fig. 1.9 (d) ).

1.9  Transmission electron microscopy image of rapidly-quenched alloy Ti50Ni25Cu25: (a) initial state (dark field); (b) after annealing at 450°C 10 min; (c) after HPT (dark field); (d) after HPT and annealing at 390°C 10 min.

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1.10  X-ray diffraction patterns of the Ti50(Ni, Cu)50 alloy: (a) initial rapidly quenched alloy (1); after annealing at 300°C 5 min (2); after annealing at 450°C 5 min (3) with the phase B19; (b) alloy after HPT(1); after HPT and annealing at 300°C 5 min (2); after HPT and annealing at 400°C 5 min, with the phase B2 (3).

It is interesting to note that the structure after cooling was an austenitic B2-phase; in other words, imposing severe plastic deformation on the amorphous alloy resulted in its crystallization during heating and changed its phase composition after further cooling to room temperature. In the coarse-grained alloy Ti50Ni25Cu25, the temperature of martensite transformation upon cooling equals ~80°C, which explains why there is a martensite phase in the alloy at room temperature. In this connection, the existence of only an austenitic phase after HPT and nanocrystallization can be related to the martensite transformation retard in the alloy with a nanocrystalline grain size. This finding was previously reported in the literature for ultrafine-grained Ti-Ni alloys.63 For the alloy Ti50Ni25Cu25, the critical grain size for martensite transformation is about 100 nm, below which the martensite transformation does not take place at room temperature. The amorphous state in Ti49.4Ni50.6 alloy can be obtained directly as a result of HPT processing (P = 6 GPa, n = 5 revolutions).61,62 Subsequently, the homogeneous nanocrystalline structure was produced by annealing of the HPT-ed material (Fig. 1.11). For instance, after annealing at 400°C for 0.5 h the mean grain size was about 20 nm (Fig. 1.11 (a), (b), and after annealing at 500°C, it was about 40 nm (Fig. 1.11 (c), (d). It is worth mention that according to HREM observations, such annealing removed the amorphous phase and produced welldefined grain boundaries, though there were still small distortions of the crystal lattice near some of the boundaries.

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1.11  Transmission electron microscopy micrographs of Ti49.4Ni50.6 alloy after HPT and annealing at 400°C (a, b) and at 500°C (c, d) for 0.5 h: (a, c) bright field images; (b, d) dark field images.

Tensile mechanical tests showed that the amorphous nitinol produced by HPT had much higher strength than at the initial microcrystalline state,61 but it was essentially brittle. Nanocrystallization results in the recorded value of yield strength for this material equal to 2650 MPa and an elongation to failure of about 5%. Thus, SPD consolidation of powders and SPD-induced nanocrystallization can be considered new SPD processing routes for fabricating bulk nanocrystalline materials. One of the advantages of these techniques is the possibility of producing fully dense samples with a uniform ultrafine-grained structure having a grain size less than 40–50 nm. Studies of the properties of these materials are of great interest for ongoing research because deformation mechanisms and, as mentioned above, phase transformations can essentially change the properties of materials with a small grain size.64,65

1.3.3 Basic rules for grain refinement For the formation of UFG structures with primarily high-angle grain boundaries through SPD processing, there have been defined five basic rules for grain refinement,66 four of which are related to the requirements for SPD processing regimes and routes while the fifth one is related to the intrinsic nature of the

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material under study. These rules are briefly considered below. A detailed description of SPD processing regimes and routes may be found in recent overviews on the subject.16,18,19 1. SPD processing at low temperatures (as a rule, less than 0.4 Tm) is referred to as a rather important requirement for its realization. Only under these conditions is it possible to achieve dislocation densities of 1014 m–2 or higher, up to the limiting values of 1016–1017 m–2,16,67 which are necessary for the formation of the UFG structure. Higher processing temperatures result in a lower accumulated dislocation density and an increase in grain size to more than 1 micron. 2. The degree of strain during processing (true strain) should exceed 6–8. Although the considerable refinement of the microstructure and the attainment of dislocation densities exceeding 1014 m–2 occur at a strain of 1–2,16 the formation of UFG structure with a majority of high-angle grain boundaries requires further straining. 3. High hydrostatic pressures, usually >1 GPa, are important for efficient SPD processing. High pressure contributes to the enhancement of deformability of the processed material and therefore, provides solidity of the billets even under high strain.11,19 Furthermore, the pressure affects the diffusion and thus suppresses the annihilation of deformation-induced lattice defects.68 4. The formation of equiaxed ultrafine grains depends on the vorticity of the metal flow. At the macrolevel, the vorticity is related to the non-monotonous character of deformation. For example, the ECAP route BC, in which the billet is rotated by 90° between each pass, is considerably more effective for grain refinement in comparison with route C, in which the billet position does not change.19 At the microlevel, the vorticity is associated with grain rotations and displacements.69 5. Grain refinement is also related to the atomic structure of the material processed. The ordering of alloys or low-stacking fault energy (SFE), all other conditions being equal, contributes to the enhancement of accumulated dislocation density and considerably reduces the grain size produced.16 For example, in Pd-20%Ag alloy with SFE = 125 mJ·m–2, in comparison with pure Pd with SFE = 190 mJ·m–2, during HPT (5 rotations and P = 6 GPa), the grain size produced equals 150 nm for Pd-20%Ag and 240 nm for Pd, respectively.70 These five rules are required and typically sufficient conditions for effective grain refinement by SPD processing.

1.3.4 Types of nanostructures Though it is possible to achieve a nanocrystalline structure with a grain size less than 100 nm in a number of metals and alloys by means of HPT, for SPD

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processing the formation of ultrafine-grained (UFG) structures with a mean grain size within the submicron range (i.e. with grains 200–500 nm in size) is typical. However, in the process of SPD, including ECAP, the formation of other structural elements takes place as well – that is, dislocation substructures, twins, grain boundary segregations and precipitations, which also produce a considerable influence on the properties of the materials after processing. Moreover, semiproducts in the form of rods, wires and sheets are produced by deformation and thermal treatment in sequence after ECAP, which additionally refines their microstructure and enhances their properties. In general, we can single out four types of nanostructural elements in the metals and alloys produced by SPD. It is possible to observe such nanostructures by the application of modern techniques for structural analysis – high-resolution transmission electron microscopy (HRTEM), 3D-atom probe, etc.16,19,71,72 These four types of structures are as follows: 1. Non-equilibrium grain boundaries. For example, as illustrated in Fig. 1.12,73 an excessively high density of dislocations, facets and steps are observed at grain boundaries of the UFG Al-3%Mg alloy after HPT, illustrating the nonequilibrium state of grain boundaries with crystal lattice distortions of 5–7 nm in width near boundaries.16,66 Such non-equilibrium grain boundaries are typical for different materials after SPD processing and their role in the mechanical behavior of UFG materials has been stressed in a number of works.16,66,74 2. Nanotwins, stacking faults, intragranular cells. These nanostructural elements are typical for the materials after HPT or ECAP at lower temperatures and/or those subjected to additional cold rolling, extrusion, and drawing. Figure 1.13 shows the TEM image of atom resolution of UFG Cu after ECAP and cold

1.12  Transmission electron microscopy images of non-equilibrium grain boundaries in the UFG Al-3%Mg alloy73 illustrating highresolution photographs of regions A and B.

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1.13  (a) TEM images of typical grain with high density of deformation twins in UFG Cu processed by ECAP with consequent cold rolling; (b) high-resolution TEM image taken from the <110> zone axis. Inset: twin relationship (white lines) and a Frank dislocation at a twin boundary, marked by arrow.75

rolling at liquid nitrogen temperature with clearly observed twins of 10–20 nm in size.75 Such nanostructured defects also have a considerable effect on material strength,75,76 for example increasing the yield stress in UFG Cu from 380 to 510 MPa.75 3. Segregation clusters, ‘clouds’. Recent investigations by a 3D atom probe directly testify the formation of impurity as well as alloying element segregations at grain boundaries in the UFG alloys processed by SPD,71,72,77 see e.g. Fig. 1.14.71

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1.14  Grain boundary segregations in the HPT-processed 6061 Al alloy (of system Al-Mg-Si): (a) TEM image of the 6061 Al alloy; (b) grain size distribution; (c) Mg, Cu and Si distribution in a 3D reconstructed volume analysed in the 6061 alloy by HPT (6 × 6 × 40 nm3).71

These segregations form ‘clouds’, and clusters 3–5 nm in size influence the formation and motion of dislocations, which provides additional strengthening of the alloys, in particular those based on aluminum, by more than 40%.71,78 4. Nano-sized particles – second-phase precipitations. The formation of particles has been observed in many alloys subjected to SPD after solution quenching.15,19 Figure 1.15 illustrates the example of such nanoparticles 10–20 nm in size pre­ cipitated in the UFG alloy Al 6061 after ECAP.79 The presence of nano-particles

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1.15  UFG structure of the alloy Al 6061 after ECAP with parallel channels (4 passes). The formation of nano-sized precipitations is clearly visible inside the grain after processing at selected areas A and B with larger magnification.79

originates from dynamic ageing and provides additional precipitation hardening of the alloys.19,79 Thus, the UFG metals and alloys processed by SPD techniques and, in particular, ECAP are characterized by a number of nanostructural elements that considerably influence their properties, as will be shown below. That is why these materials are referred to as the class of ‘bulk nanostructured materials’, and this definition is presently accepted by the international community (www. nanospd. org). It is important that the strength of such materials as shown in the next section may be considerably higher than that expected from the Hall–Petch relation.

1.4

Enhanced properties achieved using SPD processing

The ultrafine grain sizes and high-defect densities inherent in UFG materials processed by severe plastic deformation lead to much higher strengths than in their coarse-grained counterparts. Moreover, according to the constitutive relationship for superplasticity, it is reasonable to expect the appearance of low-temperature and/ or high-rate superplasticity in UFG metals.8,80–83 The realization of these capabilities is important for the future development of high-strength and wear-resistant materials, advanced superplastic alloys and metals of high fatigue life. The potential for achieving all of these qualities has raised a keen interest among scientists and engineers studying the mechanical and functional properties of these UFG materials. In this connection, the first works on the fabrication of bulk samples and billets using SPD were a crucial step in initiating investigations on the properties of

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UFG materials, because the use of SPD processing made it possible to conduct a series of systematic studies using various nanostructured metallic materials including commercial alloys.16,84–88

1.4.1 Strength and ductility at ambient temperature During the last decade it has been widely demonstrated that major grain refinement, down to the nanometer range, may lead to considerable hardness and strength in various metals and alloys but nevertheless these materials invariably exhibit low ductility under tensile testing.12,15,89,90 A similar tendency is well known for metals subjected to heavy straining by other processes such as rolling, extrusion or drawing. Strength and ductility are the key mechanical properties of any material, but these properties typically have opposing characteristics. Thus, materials may be strong or ductile but they rarely possess both characteristics. This dichotomy shown in properties is of a fundamental nature. As discussed in more detail in earlier reports,64 the plastic deformation mechanisms associated with the generation and movement of dislocations can be different in ultrafine grains or in strongly refined microstructures. This is generally equally true for SPD-processed materials. Thus, most of these materials have a relatively low ductility but they usually demonstrate significantly higher strength than their coarse-grained counterparts. High strength in SPD-processed materials is usually attributed to the formation of UFG structure via the classic Hall–Petch relationship, according to which the yield stress σy is calculated as:

σy = σ0 + ky * d –1/2,

[1.1]

where d is a grain size, σ0 and k are constant for the material. However, it has been found that in many cases the yield stress value in the UFG materials processed by SPD may be considerably higher than those calculated by the Hall–Petch relation.15,16,91 For example, this was shown in the studies of mechanical behavior of Ni subjected to ECAP and consequent rolling.91 Figure 1.1691,93–95 shows the difference in strength between the states of Ni, where grains contain dislocation substructures inside grains, and the states with grains without substructure. An attempt was made to describe the deviation quantitatively from the Hall– Petch rule by taking into account the presence of two types of boundaries: highangle boundaries (HAB) between grains, and low-angle cell boundaries (LAB) on the yield stress. Following,92 it was assumed that all type of boundaries including non-equilibrium grain boundaries with extrinsic dislocations contribute to the yield stress independently:

σy = σ0 + σLAB + σHAB + σNGBs and

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1.16  Yield stress as a function of a grain size for Ni. Note: Continuous line: material states with grains without substructure, dashed line: UFG Ni containing dislocation substructure.

σy = σ0 + Mα Gb((1.5Svθ/b)LAB )1/2 + ky * d –1/2 + Mα Gb(ρGBDs)1/2,

[1.3]

where σ0 is the threshold stress, M is the Taylor factor (M = 3), α is the constant (α = 0.24), G is the shear modulus (79 GPa), and b is the Burgers vector (0.249 nm). The Sv is associated with the cell size, θ is the misorientation angle of LAB, ky is the Hall–Petch constant. The d is the average grain size, ρGBDs is the density of extrinsic GB dislocations. Their numerical values are taken following references.91,92 The contributions of these different components for SPD Ni correspond well to the experimentally obtained data (Table 1.3). After HPT a homogeneous UFG structure was formed with mainly high-angle misorientations. So, after several passes, we neglect the contribution of low-angle boundaries. Thus, the analysis of mechanical test data shows that the presence of substructure and the nonequilibrium state of GB contributes stronger to the yield stress of SPD Ni than that predicted by the Hall–Petch rule. In addition to the dislocation substructure and non-equilibrium grain boundaries other nanostructural elements formed in the UFG materials processed by SPD, as it was shown above in section 1.2.3, may contribute to the change of yield stress and flow stress. This issue has recently been studied in detail for the case of super-strong UFG Al alloys,78 such as commercial Al alloys 1570 (Al-5.7Mg-0.32Sc-0.4Mn wt. %) and 7475 (Al-5.7Zn-2.2Mg-1.6Cu-0.25Cr, wt. %), with considerable magnesium content. Al-Mg system alloys are the basis for most popular commercial Al alloys. For grain refinement the solid-soluted alloys were subjected to high-pressure torsion (HPT), in which UFG structures were produced with applied pressure of 6 GPa and number of anvil rotations equaling to 10. The samples in the

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Table 1.3  The contribution in flow stress for SPD-processed Ni Processing of Ni

YS exp, (MPa)

YS calc, (MPa)

ECAP + rolling   990   980 HPT 1200 1190

σLAB , (MPa)

σHAB , (MPa)

σGBDs, (MPa)

510 –

280 460

170 710

Note: YS exp: experimental data, YS calc: calculated by means of equation [1.3].

form of disks 20 mm in diameter and 0.8 mm in width were cut out from the HPT-processed alloys for further tensile tests. Transmission electron microscopy analysis demonstrated that HPT leads to a complete transformation of the initial coarse-grained structure of the alloys into the UFG structure. In alloys 1570 and 7475, homogeneous UFG structures with a grain size of about 100 nm were formed after HPT (Fig. 1.17). It was also determined that HPT processing has a visible effect on the value of crystal lattice parameter a of Al alloys. For example, in the alloy 1570, its lattice parameter value after straining was reduced considerably in comparison with that at the initial state – from 4.0765 ± 0.0001 Å to 4.0692 ± 0.0003 Å, approaching the lattice parameter of pure Al, which resulted in the formation of Mg segregations at grain boundaries.78 Figure 1.18 shows the results of mechanical tests of the alloys 1570 and 7475. It can be seen that the UFG alloys after HPT at room temperature demonstrate recorded strength that exceeds more than two times the level of strength of the material subjected to standard hardening.

1.17  Typical UFG structure formed in the alloy 1570 after HPT processing at room temperature (dark field).

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1.18  Engineering stress–strain curves of the UFG alloys 1570 (a) and 7475 (b).

Figure 1.1978 shows the data for a number of Al alloys presented in the form of the Hall–Petch relation in which the yield stress (σ0.2) is plotted against the inverse square root of the grain size (d–1/2) for a UFG Al alloy 1100 produced by ARBrolling and consequent heat treatment96 as well as for an ECAP-processed alloy Al-3% Mg alloy.97 For the Hall–Petch relation in the 1100 alloy,96 the following

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1.19  The Hall–Petch relation for the alloys 1100,96 Al–3%Mg97 and data on the yield stresses of the UFG alloys 1570 and 7475.

parameters were set: σ0 = 6.0 MPa and ky = 105 (for the grain sizes in µm); for the ECAP-processed alloy Al-3% Mg,97 σ0 = 62 MPa and ky = 149. Figure 1.19 also shows the data obtained for the coarse-grained (CG) and UFG 1570 and 7475 alloys. From the available data it is seen that the YS values for the CG quenched alloys are close to the results for the Al-3% Mg alloy. However, for the UFG states with a grain size of 100–130 nm the value sy is considerably higher than calculated from the Hall–Petch relation for these grain sizes. The physical nature of this unusual effect of super-strength refers to the features of the GB states formed during SPD and, in particular, to the formation of GB segregation of alloying elements.71,77,78 The point is that in UFG materials with a grain size of about 100 nm the deformation mechanisms controlling the flow stress change.98,99 In the CG materials the generation of dislocations proceeds relatively easily and hardening is related to the hindering of their movement by various obstacles. In the UFG materials the process of dislocation generation occurs at the GBs and is the most difficult.74,99 In this connection, the change of GB states and the formation of GB segregants of alloying elements, in particular in Al alloys, may considerably harden the dislocation generation and result in the achievement of a high-strength state.78

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As is well known, the UFG materials are commonly defined as interfacecontrolled materials.100 At the same time in the UFG materials produced by the SPD techniques, grain boundaries may vary significantly depending on the regimes and routes of processing, and they can belong to high- and low-angle grain boundaries, special and random boundaries, equilibrium and non-equilibrium boundaries as well as containing GB segregations or precipitations.11,64,71,101–104 In this context there appears a possibility of controlling and enhancing the properties of UFG materials by varying the structure of GBs using SPD processing. This approach can be considered as an application of the principles of GB engineering to UFG metals and alloys.64,104,105 The concept of grain boundary engineering or grain boundary design was introduced by T. Watanabe,106 who had proposed that the properties of polycrystalline materials may be effectively changed by deliberate and careful tailoring of the distributions of boundary misorientation angles. This approach has been employed successfully in several studies including, for example, improving the susceptibility to intergranular stress corrosion cracking.107 However, there are generally difficulties in achieving different boundary distributions in conventional coarse-grained materials. In this connection, UFG materials in which GB structure features are associated with SPD processing regimes allow much more possibilities for GB engineering. The concept of GB engineering is also of special interest regarding recent findings of extraordinary high strength and good ductility in several bulk ultrafinegrained metals produced by severe plastic deformation.80,108–111 Let us consider in detail the three different approaches that were used in these investigations. In the first study, high-purity (99.996%) Cu was processed at room temperature using ECAP with a 90° clockwise rotation around the billet axis between consecutive passes in route BC.108 Cu samples, which were prepared in the initial coarse-grained condition as well as in three processed states (cold rolled, 2-pass ECAP and 16-pass ECAP 108), were uni-axial tensile-tested at room temperature. The resulting engineering stress–strain curves are shown in Fig. 1.20. It is apparent that the initial coarse-grained Cu, with a grain size of about 30 µm, typically has low-yield stress with significant strain hardening and a large elongation to failure. At the same time, cold rolling of copper to a thickness reduction of 60% significantly increases its strength, as shown by curve 2 in Fig. 1.20, but dramatically decreases its total elongation to failure. This result is consistent with the classical strain hardening behavior of metals. The same tendency is true also for Cu subjected to 2 passes of ECAP. However, further straining of Cu to 16 passes of ECAP, as shown by curve 4 in Fig. 1.20, simultaneously increases both the strength and the ductility. Furthermore, the increase in ductility is much more significant than the relatively minor increase in strength. Thus, the data for Cu processed by ECAP shown in Fig. 1.20 clearly demonstrate enhanced strength as well as ductility with accumulated deformation on increasing the number of passes from 2 to 16. At the time of the investigation in 2002, this was considered a very remarkable result, which had never been observed before in

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1.20  Tensile engineering stress–strain curves for Cu tested at 22°C with a strain rate of 10–3s–1: the processing conditions for each curve are indicated.108

metals processed by plastic deformation. Accordingly, the effect was termed the ‘paradox of strength and ductility in SPD-processed metals’, and the principles of this paradox are illustrated in Fig. 1.21, where it is apparent that conventional metals lie within the lower shaded quadrant.108 As seen in Fig. 1.21 for Cu and Al, cold rolling (the reduction in thickness is marked by each datum point) increases the yield strength but decreases the elongation to failure or ductility. The extraordinary combination of high strength and high ductility shown in Fig. 1.21 for the nanostructured Cu and Ti after processing by SPD clearly sets them apart from the other coarse-grained metals. In recent years, a similar tendency has been reported in a number of metals including Al,114,115 Cu,116 Ni117 and Ti,80 after processing through various types of severe plastic deformation such as ECAP, high-pressure torsion or accumulative roll bonding. Concerning the origin of this phenomenon, it has been suggested that it is associated with an increase in the fraction of high-angle grain boundaries with increased straining and with a consequent change in the dominant deformation mechanisms due to an increasing tendency for grain boundary sliding and grain rotation.64,108 An increase in the fraction of high-angle grain boundaries is also an example of GB engineering.105 Another approach to the problem of ductility enhancement that was suggested was the introduction of a bimodal distribution of grain sizes.109 In this study, nanostructured copper was produced through a combination of ECAP and subsequent rolling at the low temperature of liquid nitrogen prior to heating to a temperature close to ~450 K. This procedure gave a bimodal structure of micrometersized grains, with a volume fraction of around 25%, embedded in a matrix of nanocrystalline grains. The material produced in this way exhibited an extraordinarily high ductility but also retained a very high strength. The reason for this behavior is

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1.21  The paradox of strength and ductility in metals subjected to SPD (‘VAZL paradox’): the extraordinary combination of high strength and high ductility in nanostructured Cu and Ti processed by SPD (two upper points) clearly sets them apart from conventional coarse-grained metals (the lower points relating to metals of 99.5–99.9% purity).108

that, while the nanocrystalline grains provide strength, the embedded larger grains stabilize the tensile deformation of the material. Other evidence supporting the importance of grain size distribution comes from investigations on zinc,118 copper119 and an aluminum alloy.120 Furthermore, the investigation of copper119 showed that bimodal structures might increase ductility not only during tensile testing but also during cyclic deformation. This observation is important in improving the fatigue properties of materials. A third approach has been suggested for enhancing strength and ductility based on the formation of second-phase particles in the nanostructured metallic matrix,89 where it is anticipated that these particles will modify the shear band propagation during straining and thereby lead to an increase in ductility. The principle of achieving high strength and high ductility by introducing intermediate metastable phases was successfully realized recently in commercial Al-Zn-Mg-Cu-Zr121 and Al-10.8% Ag alloys after processing by ECAP and subsequent ageing.110 The principle of this approach is illustrated in Fig. 1.22 for the Al-Ag alloy where Vickers microhardness is plotted against the ageing time at 373 K for samples prepared by three different pretreatments: the solution-treated condition (ST), cold rolling (CR) and ECAP.110 For the solution-treated condition, the hardness is initially low but increases with ageing time and reaches a peak

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1.22  Variation of Vickers microhardness with ageing time for the Al-10.8%Ag alloy after solution treatment (ST), cold rolling (CR) and ECAP.110

value after 100 hours (3.6 × 105 s). For the cold-rolled condition, the hardness is higher but there is only a minor increase with ageing. The hardness is even higher after ECAP and further increases with ageing to a peak value after 100 hours. The relatively low values of hardness recorded after cold rolling in contrast with those higher values of ECAP samples is because the equivalent strain imposed on the sample is ~1.4 for CR and ~8 for ECAP so that the microstructure after CR consisted of subgrains or cell boundaries having low angles of misorientation. It was shown, using scanning TEM, that the peak hardness achieved after ECAP and ageing for 100 hours is due to precipitation within the grains of spherical particles with diameters of ~10 nm and elongated precipitates with lengths of ~20 nm. The spherical particles were identified as η-zones consisting of arrays of solute atoms lying parallel to the (001) planes and the elongated precipitates were identified as the plate-like γ' particles. It was shown also that additional ageing up to 300 hours led to a growth in the γ' particles and a very significant reduction in the density of the fine η-zones, thereby giving a consequent loss in hardening at the longest ageing time recorded in Fig. 1.22. The introduction of ageing after ECAP has an important influence on the stress– strain behavior at room temperature, as demonstrated in Fig. 1.23 where the tensile stress–strain curves of Al-10.8 wt% Ag alloy processed under four different conditions: 1) ECAP only; 2) ECAP and subsequent 100 h annealing at 373 K; 3) cold rolling and subsequent 100 h annealing at 373 K; and 4) solution treatment and subsequent 100 h annealing at 373 K.110 Thus, a combination of solution

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1.23  Tensile plots of stress versus strain at room temperature for the Al-10.8%Ag alloy after solution treatment (ST) or cold-rolling (CR) with ageing at 373 K for 100 h or ECAP without subsequent ageing and ECAP with ageing at 373 K for 100 h.110

treatment and ageing gives a reasonable tensile strength, an extensive region of uniform strain and good ductility, whereas CR and ageing gives an increased strength but very limited uniform strain and a marked reduction in the total ductility. For the ECAP-ed alloy, the strength is high in the absence of ageing but there is a negligible region of uniform strain and no significant strain hardening. By contrast, the sample processed by ECAP and aged for 100 h shows a similar high strength, a region of strain hardening and good ductility. In practice, the uniform strain of ~0.14 achieved in this specimen is similar to the uniform strain of ~0.17 in the sample after solution treatment and ageing. The elongation to failure of ~0.40 is comparable to, and even slightly exceeds, the elongation of ~0.37 recorded in the solution treatment and aged condition. These results demonstrate, therefore, the potential for producing high strength and good ductility in precipitation-hardened alloys. Thus, recent results show that grain refinement by ECAP can lead to a unique combination of strength and ductility in metallic materials. However, the achievement of these properties is associated with the tailoring of specific microstructures, which, in turn, are determined by the precise processing regimes and origin of any further treatments. In this case the concept of GB engineering plays also an important role in the enhancement of strength and ductility. That is why nowadays nanostructuring of metals for advanced properties comprises, as a rule, scientific as well as artistic aspects of tailoring of materials by means of SPD techniques. In return, strength and ductility are fundamental mechanical properties that are closely connected with many engineering properties of materials, in particular

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fatigue, fracture toughness, durability, wear resistance as well as creep and superplasticity. Such superior mechanical properties are highly desirable for the development of advanced next-generation structural materials and this has been an object of numerous investigations in the sphere of nanoSPD materials in the last several years.15,19,122 In fact, closer attention is now being paid to work on the enhancement of functional properties such as magnetic, electrical, super-elastic ones, etc., in the UFG metals produced by SPD.15,123,124 All this is very important in view of innovative applications of bulk nanomaterials.

1.5

Innovation potential of bulk nanostructured materials

Recent reports documented more than 100 specific market areas for nanostructured metals122,125 and it is evident that many of these new structural applications involve extreme environments where exceptional strength is needed. Potential near-future applications are presented schematically in Fig. 1.24 demonstrating some specific examples.122

1.24  Assumed innovation probability in various sectors vs. specific strength. The highest potential may be seen in applications and products under ‘extreme environments and/or with extreme specific strength’ requirements.

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Firstly, due to excellent biological compatibility combined with superior specific strength, it is probable that UFG titanium will enter the bio-medical market at an ever-increasing pace. Titanium and titanium alloys are currently used extensively as implant materials in traumatology, orthopaedics and dentistry.126 This is due to several characteristics including their excellent biocompatibility, good corrosion resistance and specific strength compared with other metals. The implant materials used in these areas are subjected to complex loads with additional biomedical and other technical requirements. Significant progress may be achieved here by increasing the specific strength of the implant materials, and thereby permitting the use of a smaller size with less invasive surgery. Recent investigations have shown that, due to nanostructuring, the fatigue strength of CP-Ti may be significantly increased to a level exceeding that of the coarse-grained Ti-6Al-4V alloy.48,127 Hence, there is also the potential to replace more expensive and less biocompatible alloys with commercial-purity titanium that is more biocompatible.48 Important requirements in all biomedical applications are corrosion resistance and excellent biocompatibility and both are fulfilled with titanium and most titanium alloys. Preliminary investigations of the corrosion behavior of nano-titanium suggest that corrosion resistance is improved by introducing a UFG microstructure.128 A second example with high innovative potential is the superplastic forming of light metals produced by SPD for the fabrication of products with both complex shapes and high specific strengths. It is anticipated that these products will have a wide range of applications in the aeronautic and automotive sectors as well as in the consumer product industry. The development of superplastic forming capabilities after SPD is now well established.129 Numerous experiments show that these superplastic properties are retained when large billets processed by SPD are subsequently rolled into thin sheets during superplastic forming operations.130–132 Furthermore, the ultrafine grain size is preserved after SPD forming and thus provides a very high strength at ambient temperatures, which is an important consideration for many structural applications. A third potential innovation lies in extreme low-temperature applications as in arctic environments and in the special processing applications associated with the oil and gas industries. This is especially important for low carbon and stainless ferritic steels where usually there is a sharp transition from ductile to brittle behavior with decreasing temperature. Extensive grain refinement due to SPD can significantly decrease the brittle–ductile transition temperature in these steels133,134 and this is especially important when undertaking construction work at high latitudes.

1.6

Conclusions

Processing by severe plastic deformation provides strong grain refinement and therefore an opportunity to enhance properties of metals and alloys making them

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attractive for new structural and functional applications. However, finding solutions to these problems is a complex challenge requiring an individual approach to the choice of processing routes and regimes and formation of certain nanostructures. The recent progress witnessed in this trend and many new works demonstrate unique opportunities to successfully do this. Limitations on the use of SPDprocessed materials to date, which have arisen primarily from their processing costs and the inherent wastage in conventional processing methods, are now being overcome through the development of new and continuous processing techniques. As these procedures become more developed, it is reasonable to anticipate that there will be significant advances in the use of nanomaterials in different areas of engineering and bio-medical applications. There is already every reason to believe that this breakthrough will take place in the coming years.

1.7

References

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58 Shen H., Li Z., Guenther B., Korznikov A.V., Valiev R.Z. Nanostr Mater 1995;6: 385. 59 Wilde G., Boucharat N., Dinda G.P., Rösner H., Valiev R.Z. Mater Sci Forum 2006;503–504: 425. 60 Gunderov D.V., Pushin V.G., Valiev R.Z., Valiev E.Z. Deformation and Fracture of Materials 2006;4: 22. 61 Sergueeva A.V., Song C., Valiev R.Z., Mukherjee A.K. Mater Sci Eng A 2003;339: 159. 62 Huang J.Y., Zhu Y.T., Liao X.Z., Valiev R.Z.. Phil Mag Lett 2004;84: 183. 63 Waitz T., Kazykhanov V., Karnthaler H.P. Acta Mater 2004;52: 385. 64 Valiev R.Z. Nature Mat 2004;3: 511. 65 Zhu Y.T., Langdon T.G. JOM 2004;56(10): 58. 66 Valiev R.Z. Int J Mat Res (formerly Metallkd) 2009;100: 757 67 Ungár T., Balogh L., Zhu Y.T., Horita Z., Xu C., Langdon T.G. Mater Sci Eng A 2007;444: 153. 68 Zehetbauer M.J. (ed.). Advanced Engineering Materials, Special Issue on Nanomaterials by Severe Plastic Deformation (SPD), Vol. 5, 2003. 69 Gutkin M.Y., Ovidko I.A. Appl Phys Lett 2005;87: 251916-1. 70 Kurmanaeva L., Ivanisenko Y., Markmann J., Kübel C., Chuvilin A., Doyle S., Valiev R.Z., Fecht H-J. Mater Sci Eng A 2010;527: 1776. 71 Nurislamova G., Sauvage X., Murashkin M., Islamgaliev R., Valiev R.Z. Phil Mag Lett 2008;88: 459. 72 Sha G., Wang Y.B., Liao X.Z., Duan Z.C., Ringer S.P., Langdon T.G. Acta Mater 2009;57: 3123. 73 Horita Z., Smith D.J., Furukawa M., Nemoto M., Valiev R.Z., Langdon T.G. J Mater Res 1996;11: 1880. 74 Valiev R.Z., Kozlov E.V., Ivanov Y.F., Lian J., Nazarov A.A., Baudelet B. Acta Metall Mater 1994;42: 2467. 75 Zhao Y., Bingert J.F., Liao X., Cui B., Han K., Sergueeva A.V., Mukherjee A.K., Valiev R.Z., Langdon T.G., Zhu Y.T. Adv Mater 2006;18: 2949. 76 Chukin M.V., Koptseva H.V., Valiev R.Z., Yakovleva I.L., Zrnik J., Covarik T. Vestnik MGTU 2008;1 (in Russian). 77 Liddicoat P.V., Liao X.Z., Zhao Y., Zhu Y., Murashkin M.Y., Lavernia E.J., Valiev R.Z., Ringer S.P., 2010, submitted to Nat. Commun. 78 Valiev R.Z., Enikeev N.A., Murashkin M.Y., Alexandrov S.E., Goldshtein R.V. Doklady Physics 2010;55(6): 267. 79 Valiev R.Z, Murashkin M.Yu, Bobruk E.V., Raab G.I. Mater Trans 2009;50: 87. 80 Valiev R.Z., Sergueeva A.V., Mukherjee A.K. Scripta Mater 2003;49: 669. 81 McFadden S.X., Mishra R.S., Valiev R.Z., Zhilyaev A.P., Mukherjee A.K. Nature 1999;398: 684 82 Valiev R.Z., Salimonenko D.A., Tsenev N.K., Berbon P.B., Langdon T.G. Scripta Mater 1997;37: 1945. 83 Kawasaki M., Langdon T.G. J Mater Sci 2007;42: 1782. 84 Lowe T.C., Valiev R.Z. Investigations and applications of severe plastic deformation. Kluwer, Dordrecht, The Netherlands, 2000. 85 Zhu Y.T., Langdon T.G., Valiev R.Z., Semiatin S.L., Shin D.H., Lowe T.C. (eds.) Ultrafine-Grained Materials III, Minerals, Metals and Materials Society, Warrendale, PA, USA, 2004. 86 Zehetbauer M.J., Valiev R.Z. (eds.) Nanomaterials by severe plastic deformation. Wiley-VCH Verlag, Weinheim, Germany, 2004.

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  87 Zhu Y.T., Varyukhin V. (eds.) Nanostructured materials by high-pressure severe plastic deformation. Springer, Dordrecht, The Netherlands, 2006.   88 Zhu Y.T., Langdon T.G., Horita Z., Zehetbauer M.J., Semiatin S.L., Lowe T.C. (eds.) Ultrafine-Grained Materials IV, Minerals, Metals and Materials Society, Warrendale, PA, USA, 2006.   89 Koch C.C. Scripta Mater 2003;49: 657.   90 Morris D.G. Mechanical behaviour of nanostructured materials. Trans Tech, UetikonZürich, 1998.   91 Krasilnikov N., Pakiela Z., Lojkowski V., Valiev R.Z. Sol St Phen 2005;101–102: 49.   92 Hugnes D.A., Hansen N. Acta Metall 2000;48: 2985.   93 Thompson A.W. Acta Metall 1975;23: 1337.   94 Xiao C., Mirshams R.A., Whang S.H., Yin W.M. Mater Sci Eng A 2001;301: 35.   95 Ebrahimi F., Bourne G.R., Kelly M.S., Matthews T.E. Nanostr Mater 1999;11: 343.   96 Tsuji N. Unique deformation behaviors of the ultrafine-grained aluminum alloys fabricated by accumulative roll bonding. In: Zhu Y.T., Varyukhin V. (eds.) Nanostructured materials by high-pressure severe plastic deformation. Springer Netherlands, 2006. p. 227.   97 Furukawa M., Horita Z., Nemoto M., Valiev R.Z., Langdon T.G. Phil Mag A 1998;78(1): 203.   98 Meyers M.A., Mishra A., Benson D.J. JOM 2006;58(4): 41.   99 Pande C.S., Cooper K.P. Prog Mater Sci 2009;54: 689. 100 Gleiter H. Prog Mater Sci 1989;33: 223. 101 Dobatkin S., Zrnik J., Nikulin S., Kovarik T., submitted to JPCS (Proc. of the 15th Int. Conf. on the Strength of Materials), 2009. 102 Zhao Y.H., Bingert J.F., Zhu Y.T., Liao X.Z., Valiev R.Z., Horita Z., Langdon T.G., Zhou Y.Z., Lavernia E.J. Appl Phys Lett 2008;92: 081903. 103 Furukawa M., Horita Z., Langdon T.G. J Mater Sci 2005;40: 909. 104 Valiev R. Mater Sci Forum 2008;584–586: 22. 105 Fujita T., Horita Z., Langdon T.G. Mater Sci Eng A 2004;371: 241. 106 Watanabe T. Res Mech 1984;11: 47. 107 Watanabe T., Fujii H., Oikawa H., Arai K.I. Acta Metall 1989;37: 941. 108 Valiev R.Z., Alexandrov I.V., Zhu Y.T., Lowe T.C. J Mater Res 2002;17: 5. 109 Wang Y., Chen M., Zhou F., Ma E. Nature 2002;419: 912. 110 Horita Z., Ohashi K., Fujita T., Kaneko K., Langdon T.G. Adv Mater 2005;17: 1599. 111 Zhao Y., Topping T., Bingert J.F., Thornton J.J., Dangelewicz A.M., Li Y., Zhu Y.T., Zhou Y., Lavernia E.J. Adv Mater 2008;20: 3028. 112 Parker E.R. Materials data book for engineers and scientists. McGraw-Hill, New York, NY, USA, 1967. 113 Brandes E.A., Brook G.B. Smithells metals reference book, 7th ed. ButterworthHeinemann, Oxford, UK, Ch. 22, 1992. 114 Höppel H.W., May J., Eisenlohr P., Göken M. Metallkd 2005;96: 566. 115 May J., Höppel H.W., Göken M. Scripta Mater 2005;53: 189. 116 Dalla Torre F., Lapovok R., Sandlin J., Thomson P.F., Davies C.H.J., Pereloma E.V. Acta Mater 2004;52: 4819. 117 Krasilnikov N., Lojkowski W., Pakiela Z., Valiev R. Mater Sci Eng A 2005;397: 330. 118 Zhang X., Wang H., Scattergood R.O., Narayan J, Koch C.C., Sergueeva A.V., Mukherjee A.K. Acta Mater 2002;50: 4823. 119 Mughrabi H., Höppel H.W., Kautz M., Valiev R.Z. Metallkd 2003;94: 1079. 120 Park Y.S., Chung K.H., Kim N.J., Lavernia E.J. Mater Sci Eng A 2004;374: 211.

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121 Islamgaliev R.K., Yunusova N.F., Sabirov I.N., Sergueeva A.V., Valiev R.Z. Mater Sci Eng A 2001;319–321: 877. 122 Valiev R.Z., Zehetbauer M.J., Estrin Y., Höppel H.W., Ivanisenko Y., Hahn H., Wilde G., Roven H.J., Sauvage X., Langdon T.G. Adv Eng Mater 2007;9: 527. 123 K. Suehiro, S. Nishimura, Z. Horita, Mater Trans, 2008;49: 102. 124 B. Straumal, S.G. Protasova, A.A. Mazilkin, B. Baretzky, D. Goll, D.V. Gunderov, R.Z. Valiev, Phil Mag Lett, 2009;89: 649. 125 Lowe T.C. JOM 2006;58(4): 28. 126 Brunette D.M., Tengvall P., Textor M., Thomsen P. Titanium in med. Springer, Heidelberg, 2001. 127 Stolyarov V.V., Zhu Y.T., Alexandrov I.V., Lowe T.C., Valiev R.Z. Mater Sci Eng A 2003;343: 43. 128 Balyanov A., Kutnyakova J., Amirkhanova N.A., Stolyarov V.V., Valiev R.Z., Liao X.Z., Zhao Y.H., Jiang Y.B., Xu H.F., Lowe T.C., Zhu Y.T. Scripta Mater 2004;51: 225. 129 Horita Z., Furukawa M., Nemoto M., Barnes A.J., Langdon T.G. Acta Mater 2000;48: 3633. 130 Akamatsu H., Fujinami T., Horita Z., Nemoto M., Langdon T.G. Scripta Mater 2001;44: 759. 131 Park K.T., Lee H.J., Lee C.S., Nam W.J., Shin D.H. Scripta Mater 2004;51: 479. 132 Nikulin I., Kaibyshev R., Sakai T. Mater Sci Eng A 2005;07: 62. 133 Korznikov A.V., Safarov I.M., Nazarov A.A., Valiev R.Z. Mater Sci Eng A 1996;206: 39. 134 Borisova M.Z., Yakovleva S.P., Ivanov A.M. Sol St Phen 2006;14: 97.

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2 Bulk nanostructured metals and alloys produced by accumulative roll-bonding N. TSUJI, Kyoto University, Japan Abstract: This chapter introduces the fabrication of bulk nanostructured metals and alloys by the accumulative roll-bonding (ARB) process. The principles and processing details of ARB are presented and discussed. The formation of ultrafine-grained structures in single-phased metals during ARB is illustrated using original experimental results. This process is understood in terms of grain subdivision: the ultrafine-grains essentially have the characteristics of deformation microstructures, which include large misorientation grain boundaries. Post-ARB annealing of aluminum and ferritic steel cause relatively continuous changes in the grain structure by a combination of recovery and grain growth. The ARB process can also fabricate non-equilibrium nanostructured materials, such as a composite of nanocrystals and metallic glass in the Cu + Zr multi-stack metal system. Ultrafine-grained metals fabricated by ARB exhibit two to four times more strength than the same metals with conventionally coarse-grained structures, but they also show limited tensile ductility, due to early plastic instability that occurs in the nanostructured materials. This observation also suggests the possibility of maintaining both high strength and adequate ductility by making the nanostructures multi-phased. Key words: severe plastic deformation, accumulative roll-bonding, ultrafine grains, non-equilibrium structures, grain subdivision, bulk mechanical alloying, mechanical properties.

2.1

Introduction

Accumulative roll-bonding (ARB) is a kind of severe plastic deformation (SPD) process for fabricating bulk nanostructured metallic materials.1 It has been clarified that bulk nanostructured metals and alloys, which are composed of ultrafine grains (UFGs) with a mean grain size of several hundreds of nanometers or nanocrystals with mean grain size of several tens of nanometers, can be fabricated by plastic deformation up to a very high strain (above logarithmic equivalent strain of 4~5), which is often called SPD.2 Various kinds of unique SPD processes, such as equal-channel angular extrusion (ECAE), high-pressure torsion (HPT), cyclic extrusion and compression (CEC), etc., have been developed for realizing bulk nanostructured metals.1,2 Among the SPD processes, ARB is advantageous for continuous production of sheet materials, since it uses rolling deformation in principle. In laboratory scale, ARB has been applied to various kinds of metals and alloys and has succeeded in producing bulky sheets having nanostructures. In this chapter, the principle of the ARB process, 40 © Woodhead Publishing Limited, 2011



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evolution of nanostructures during ARB, and mechanical properties of the nanostructured metals and alloys fabricated by ARB are introduced and summarized.

2.2

The principle of accumulative roll-bonding (ARB)

ARB was developed by Saito et al. in 1998.1,3 The principle of the ARB process is schematically illustrated in Fig. 2.1. ARB is a SPD process using rolling deformation. Rolling is the most advantageous metalworking process for continuous production of bulk materials with shapes of plates, sheets, bars, and so on. However, it is nearly impossible to achieve ultra-high plastic strain above a logarithmic equivalent strain of 4~5 by the conventional rolling, because the dimension of the materials (the thickness of sheets, for example) decreases with increasing total plastic strain applied. In the ARB process, for example, a sheet 2 mm thick is first rolled to a 50% reduction in thickness. The rolled sheet with a thickness of 1 mm and approximately twice the length of the original is cut into two, stacked together to make 2 mm thick material (initial thickness) (see Fig. 2.1), and the stack is rolled again. In order to obtain one-body solid material, the rolling in the ARB process is not only a deformation process but also a bonding process, which is known as roll-bonding, used for the production of clad sheets. To achieve good bonding between two stacked sheets, the contact surfaces of the sheets are degreased and wire-brushed typically before being subjected to rolling. Roll-bonding is sometimes carried out at elevated temperatures below the recrystallization temperature of the material, in order to make the bonding better and to reduce the rolling force. By repeating the procedure, one can apply a very large amount of plastic strain to the sheet material without changing the original dimensions. The von Mises equivalent strain (εeq) after n cycles of the ARB can be expressed as,

2.1  Schematic illustration showing the principle of the accumulative roll-bonding (ARB) process.

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,

[2.1]

where t0, t, and r are initial thickness of the stacked sheets, the thickness after rollbonding, and the reduction in thickness per cycle, respectively. Geometrical changes of the materials in the ARB process using 50% reduction per cycle (r = 0.5 in equation (2.1)) are summarized in Table 2.1. An equivalent strain of 4 can be achieved by 5 ARB cycles in this case, and after 10 ARB cycles the 1 mm-thick sheet contains 1024 original layers.

2.3

Processing details

The ARB process does not require any special equipment except for a rolling mill with enough capacity, which is another advantage of this method. Figure 2.2

Table 2.1  Geometrical changes of the material during the ARB where two pieces of the 1 mm thick sheets are stacked and roll-bonded by 50% reduction per cycle No. of cycles

1

2

3

4

5

6

7

8

No. of layers

2

4

8

16

32

64

128

256

512 1024

2n

No. of bonded boundaries

1

3

7

15

31

63

127

255

511 1023

2n –1

7.8

3.9

1.9

Layer 500 250 125 62.5 31.3 15.6 interval (µm)

9

10

1000/2n (1 – 1/2n) × 100

50

75

87.5 93.8 96.9 98.4 99.2 99.6 99.8 99.9

Equivalent strain

0.8

1.6

2.4

4

4.8

5.6

6.4

7.2

n

0.96

Total reduction (%)

3.2

. . . . . . . . .

8

2.2  (a) The two-high rolling mill used for the ARB process in the author’s group. (b) A channel guide for the stacked sheets on the entrance side of the mill.

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shows the rolling mill that has been used for the ARB process in the author’s group. The rolling machine is a conventional two-high mill with 310 mm roll diameter. Because the large reduction in 1 pass is necessary to achieve good bonding4 and roll-bonding is often carried out without lubrication to realize quick UFG formation,5,6 the rolling force during ARB becomes very large. For instance, the rolling force for a commercial purity aluminum sheet 40 mm in width reaches to 49 tons force in the seventh cycle of ARB at room temperature (RT) without lubrication.2 Thus, the rolling mill is required to have enough capacity. The rolling mill shown in Fig. 2.2 (a) has a capacity of 150 tons. The ARB process has been successfully applied to various kinds of metallic materials and actually produced bulky sheets with nanostructures. In most materials, the ultrafine lamellar boundary structures or the pancake-shaped ultrafine grains, whose average boundary spacing or grain thickness is much smaller than 1 µm, were formed uniformly in the materials after 5~6 cycles of ARB.1,2 The ARB-processed sheets with ultrafine-grained structures exhibited very high strength, which is two to four times higher than that of the starting materials with conventional grain sizes, as will be shown in a later section. It has been found, rather unexpectedly, that roll-bonding in the ARB process was not difficult for most of the ductile metallic materials, although degreasing and wire-brushing the contact surfaces before stacking were an indispensable step for a good bonding. The minimum required rolling reduction in 1 pass exists to achieve a good bonding,4 which depends on the kind of materials in use and the rolling conditions. The critical 1-pass reduction in ARB at RT is roughly 40~50%. In case of Al alloys, for example, oxide layers quickly cover the surfaces of the sheet even if wire-brushing is conducted. However, the oxide layers are very thin and brittle, and will not survive rolling. When a 50% reduction is used in rollbonding, the surface area increases by 100%, which means that so many fresh metallic atoms behind the oxide layer come to the surface during roll-bonding, i.e. create virgin surfaces that are not covered with oxide layers. The fresh metallic atoms on both sides of the sheet surfaces make close contact with each other to achieve bonding under great pressure from the roll-bite. This is a possible mechanism of roll-bonding in the ARB process. During repeated ARB cycles, bonding at the interfaces becomes increasingly stronger, since the bonding interfaces are repeatedly elongated to the rolling direction. As a result, even after fracture in a tensile test, exfoliation of the bonded interfaces could be seen only at the center of the sheet, which corresponds to the bonded interface in the most recent ARB cycle. A serious potential problem in the ARB process is cracking during rolling in some kinds of metals and alloys. The typical appearance of the ARB-processed aluminum alloys is shown in Fig. 2.3. In very ductile materials, such as pure Al, pure Cu and ultra-low-carbon steel, almost no cracking occurs even after many cycles of ARB. As a result, sound and large sheets filled with the UFG structures can be obtained. Figure 2.3a is such an example of the 1100-Al (99%Al) sheet

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2.3  Appearance of the ARB-processed Al alloy sheets. Thickness of the sheets is 1 mm. (a) 1100-Al ARB-processed by 5 cycles at RT. (b) 5083-Al ARB processed by 2 cycles at RT.

ARB-processed by 5 cycles at RT, whose dimensions are 1 mm thick, 55 mm wide and 320 mm long. On the other hand, some kinds of materials considerably lost workability with increasing ARB cycles. An example of severely cracked sheet of the 5083-Al (Al-4.7%Mg) ARB-processed by 2 cycles at RT is shown in Fig. 2.3 (b). The cracks generally start at the edges of the sheet due to tensile stress, and they sometimes propagate into the center of the sheet (Fig. 2.3 (b) ). Once such cracking occurs, it is difficult to proceed to the next cycle. However, there are some small techniques or know-how for avoiding cracking during rollbonding. As a result, the ARB process has been applicable to most of the metallic materials that can be deformed in rolling. The ARB process has been successfully applied to pure metals (Al, Fe, Cu, Ni, Ti and Zr), various kinds of Al alloys,

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Al-matrix composites, low-carbon steels, ferritic stainless steels, duplex stainless steels, high-Ni austenitic steels, dilute Cu alloys, brass, Cu-Ag alloys, and even Mg alloys, and UFG microstructures have been obtained in all cases after ARB over 5~6 cycles.2,7–10

2.4

Change in microstructures during the process

2.4.1 Formation of ultrafine grains in ARB In this section, the evolution of UFG structures during the ARB in single-phase metals is shown and discussed. Figure 2.4 shows the boundary misorientation maps obtained by electron backscattering diffraction (EBSD) measurement in a field-emission type scanning electron microscope (FE-SEM) for the ultra-lowcarbon interstitial free (IF) steel ARB-processed by various cycles at 500°C.11 In Fig. 2.4, high-angle boundaries with misorientations larger than 15° were drawn in bold black lines, while low-angle boundaries whose misorientations were between 2° and 15° were drawn in narrow grey lines. After 1-cycle ARB corresponding to just a 50% reduction, elongated initial grains involving many low-angle boundaries are observed. This is a typical microstructure conventionally seen in deformed metals. It should be noted, however, that newly formed highangle boundaries appeared in the vicinity of initial grain boundaries. The number and the density of the deformation-induced high-angle boundaries increased with more ARB cycles (i.e. strain), and finally the specimen was filled with the elongated grain structure, mostly subdivided by high-angle boundaries. The misorientation distribution in the samples shown in Fig. 2.4 is represented in Fig. 2.5. The ‘fHAGB’ in Fig. 2.5 indicates the fraction of high-angle grain boundaries. The 1-cycle ARB-processed specimen that had a typical deformation microstructure (Fig. 2.4 (a)) was mostly filled with low-angle boundaries (64%). It should be noted that in the EBSD analysis the misorientations under 2° were cut off in order to remove inaccuracy due to measurement and analysis in automatic orientation mapping. That is, the actual fraction of the low-angle boundaries must be much larger than 64%. The fraction of high-angle boundaries increased with increasing strain, and more than 80% of the observed boundaries were already high-angle in the specimen ARB-processed by 5 cycles (Fig. 2.5 (d) ). Other ARB-processed materials showed similar microstructural evolution to that in the IF steel described above.12,13 It has been clarified in various metals that the ultrafine microstructures are quite uniform throughout the thickness of the ARB-processed sheets.14,15 Figure 2.6 shows TEM micrographs of the IF steel (a) and the 1100-Al (b) ARB-processed by 6 cycles. The microstructures were observed from TD. These are the typical microstructures in the single-phased materials that have been ARB-processed by many cycles. Both materials showed quite similar microstructures elongated along RD, which corresponds to Fig. 2.4 (d). These are so-called lamellar boundary (LB) structures, which have been observed in heavily

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2.4  Boundary misorientation maps obtained by FE-SEM/EBSD measurements of the IF steel ARB-processed by (a) 1 cycle, (b) 2 cycles, (c) 3 cycles and (d) 5 cycles at 500°C without lubrication. The measurements were done on the longitudinal sections of the sheets.

rolled FCC metals.16 The mean spacing of the LBs was about 200 nm for both materials. As is shown statistically in Fig. 2.5, most of the boundaries in these microstructures are already high-angle ones, as has been also confirmed by FE-SEM/EBSD and Kikuchi-line analysis in TEM.

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2.5  Misorientation distributions of the boundaries observed in the EBSD measurements of the IF steel ARB-processed by (a) 1 cycle, (b) 2 cycles, (c) 3 cycles and (d) 5 cycles at 500°C without lubrication. The data taken throughout thickness of the ARB-processed sheets were summarized.

2.6  Transmission electron microscopy microstructures of singlephased materials ARB-processed by 6 cycles without lubrication. The microstructures were observed from TD of the sheets. (a) IF steel processed at 500°C. (b) 1100-Al processed at RT.

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2.7  Transmission electron microscopy micrograph (a) and corresponding boundary misorientation map (b) of the 1100-Al ARB-processed by 6 cycles at 200°C. Observed from TD. The misorientation angles (in degrees) superimposed in (b) were calculated from the precise orientation of each region measured by TEM/Kikuchi-line analysis.

Figure 2.7 is a TEM microstructure (a) of a commercial purity aluminum (1100-Al) ARB-processed by 6 cycles at 200°C together with the boundary map (b) of the identical area obtained through TEM/Kikuchi-line analysis.12,17 In the boundary map (Fig. 2.7 (b) ), the misorientations of the boundaries are also indicated in degrees. It is again shown that most of the observed boundaries (especially lamellar boundaries) are high-angle ones having quite large mis­ orientations. The boundaries between adjacent regions are not broad (or unclear) like dislocation-cell boundaries, but seem quite sharp. It can be concluded, therefore, that the elongated regions surrounded by high-angle boundaries are

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2.8  Schematic illustration showing grain subdivision mechanism during plastic deformation.

certainly ‘grains’ from a viewpoint of misorientation. At the same time, however, the morphology of the grains is elongated along the principal deformation direction, and the microstructure involves many low-angle boundaries and dislocations tangled within the grains. That is, the ultrafine grains fabricated by the ARB process (and by other SPD processes) are essentially deformation microstructures as well. The microstructural evolution during ARB (or during SPD in general) can be understood in terms of grain subdivision.18 The process of grain subdivision is illustrated in Fig. 2.8. Plastic deformation of metallic crystals is born basically by dislocation slips. In polycrystalline materials, the slip patterns (combination and number of slip systems operated) generally differ depending on locations even within an identical crystal. Different slip patterns result in different crystal rotation in producing misorientation between neighboring regions. The boundaries between such regions to bear the misorientation are called geometrically necessary boundaries (GNBs).16,18 In addition, the dislocations stored in the crystal tend to form low-energy configurations (LEC). The boundaries formed by such LEC dislocations are called incidental dislocation boundaries (IDBs).16,18 The original grain (crystal) is finely subdivided by the GNBs and IDBs with increasing plastic strain, which is the grain subdivision mechanism. The GNBs are especially important for UFG formation, as their misorientation increases with increasing plastic strain applied.16,18 So-called lamellar boundary structure has been reported in heavily cold-rolled aluminum,16 where lamellar boundaries are GNBs. The ultrafine lamellar structures observed in the present ARB specimens (Fig. 2.6) are quite similar to the lamellar boundary structure reported in heavily cold-rolled aluminum, though the proportion of high-angle boundaries in the ARB specimens is much higher than in the cold-rolled one.12 Because the mechanism of

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microstructure evolution is grain subdivision, the UFG structures produced by ultra-high straining are naturally deformation microstructures, though the subdivided regions (grains) have large misorientations to each other. This agrees well with the fact that the UFG microstructures obtained through the ARB involves many dislocations and low-angle grain boundaries (Figs. 2.4–2.7). It is also interesting that nano-sized deformation twins have been observed in UFG pure Cu19 and pure Al20 fabricated by the ARB process, as has been reported in the materials fabricated by other SPD processes.

2.4.2 Change in microstructures during subsequent heat treatments Subsequent annealing could change the microstructures of the ARB-processed materials.17,21,22 Figure 2.9 shows the TEM microstructures of the 1100-Al ARB processed and then annealed at various temperatures.21 During low temperature annealing, the recovery decreases the dislocation density inside the elongated ultrafine grains, and the ultrafine grains grow slightly. The specimen annealed at 225°C for 1.8 ks was found to contain equiaxed grains free from dislocations (Fig. 2.9 (d) ). It is quite difficult to distinguish these grains from conventionally recrystallized grains. It should be noted, however, that the mean grain size is still

2.9  Transmission electron microscopy microstructures of the 1100-Al ARB-processed by 6 cycles at 200°C without lubrication and then annealed at (a) 100°C, (b) 150°C, (c) 200°C, (d) 225°C, (e) 250°C and (f) 300°C for 1.8 ks. Observed from TD.

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around 1 µm, which cannot be achieved through a conventional deformation and recrystallization process. Further annealing causes grain growth, resulting in equiaxed grain structures having various mean grain sizes. Similar microstructural change has been observed in the ARB-processed IF steel as well.21,22 The changes in microstructures during annealing of ARB-processed pure Al and IF steel are fairly homogeneous and continuous. Such a continuous change of the grain structure is sometimes called continuous recrystallization,23 since it is greatly different from conventional recrystallization characterized by nucleation and growth of particular grains (discontinuous recrystallization). However, even in conventional recrystallization (discontinuous recrystallization), it is considered that no new recrystallized grains nucleate by thermal fluctuation of atoms, but potential nuclei existed in the deformed microstructure preferentially grow.24 In that sense, it might be confusing to use the term, continuous recrystallization. In the materials deformed to ultra-high strains, the finely subdivided structure is already full of high-angle grain boundaries, as is shown in Figs. 2.4, 2.5 and 2.7. Thus, it is reasonable to consider that the microstructural change during annealing of SPD processed materials (Fig. 2.9) can be a kind of normal grain growth accompanied by the recovery at grain interior. Here, it should be noted that both pure aluminum (face-centered cubic (fcc) metal with very high stacking fault energy) and IF steel (ferritic iron: body-centered cubic (bcc) metal) are the materials where recovery is enhanced to occur during annealing. In fact, recovery quickly occurs to decrease significantly the dislocation density at the grain interior in the ARB-processed and annealed Al (Fig. 2.9). In the case of the ARB-processed fcc metals having medium to low stacking fault energy, such as Cu and austenitic steels or the ARB-processed Ti, it has been found that as ARB-processed microstructures are similar to Al and IF steel, but recovery is difficult to achieve and discontinuous recrystallization happens during annealing.11,15,25 One example of discontinuous grow of ultrafine grains during annealing in the commercial purity Ti ARB-processed and annealed is shown in Fig. 2.10. Even in the ARB-processed pure Al, discontinuous growth of particular grains can be observed under certain annealing conditions.13 Figure 2.10 looks like conventional (discontinuous) recrystallization by nucleation and growth, or abnormal grain growth. On the other hand, the microstructural change shown in Fig. 2.9 are much more like normal grain growth. When the ARB process is carried out after solution treatment of materials, precipitation occurs during heat treatment (ageing) following the ARB. Since the ARB-processed specimens have UFG structures with a very high density of grain boundaries, the precipitation behaviors of the ARB-processed materials are significantly different from those of the conventional alloys with coarse-grained structures. For example, the precipitation kinetics from the UFG materials is much faster than that from coarse-grained ones, and sometimes stable phases directly appear during aging treatment, skipping the formation of the metastable phases that usually appear in conventional alloys.26,27

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2.10  Transmission electron microscopy microstructures of the commercial purity Ti ARB-processed by 6 cycles at RT with lubrication and then annealed at various temperatures for 1.8 ks. Observed from TD. (a) As ARB-processed. Annealed at (b) 200°C, (c) 300°C, (d) 400°C, (e) 450°C, and (f) 500°C.

2.4.3 Formation of non-equilibrium phases in ARB Processes similar to ARB had previously been carried out for bulk mechanical alloying of different metals or for fabricating multi-layered materials.28,29 However, roll-bonding was not used in such attempts, but diffusion bonding at elevated temperatures was carried out between each pressing or rolling procedure. Bulk mechanical alloying by the ARB process is of course possible, and nonequilibrium structures including an amorphous phase have been fabricated.30–32 An example of the formation of non-equilibrium nanostructures by the ARB process is introduced here. Sheets of pure Cu (99.96% purity) and pure Zr (99.2% purity), 200 mm in length, 50 mm in width, and 0.2 mm in thickness, were mutually stacked so that the total thickness becomes 1 mm. The overall composition of the multi-stacks was Cu-29at%Zr. The ARB process using 75% reduction per cycle was carried out at RT with lubrication. The ARB was repeated for up to 10 cycles, with an equivalent strain of 15.8, which corresponds to the conventional rolling of a huge plate with a thickness of 568 m down to 1 mm thickness. Figure 2.11 shows a high-resolution TEM microstructure of the Cu/Zr multi-stacks ARB-processed by 9 cycles at RT. A nano-lamellar structure

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2.11  High-resolution TEM microstructure of the Cu + Zr multi-stacks ARB-processed by 9 cycles (equivalent strain of 13.7) at RT. Observed from TD.

composed of mutual alignment of Cu layers and Zr layers is observed. The thickness of each Cu or Zr layer is below 10 nm. In some thinner Zr layers, no periodical contrast is recognized, indicating that an amorphous phase has been formed (indicated as ‘Amo’). Also at the interfaces between Cu layers and Zr layers, thin amorphous regions are observed. EDX analysis using nano-beam has clarified that atomistic scale mixing of Cu and Zr happens at interface regions during the ARB and eventually form an amorphous region.32 It has also been found that the subsequent heat treatment of ARB-processed stacks causes thermally induced amorphization to form sheets of nearly 100% metallic glass.33

2.5

Mechanical properties of nanostructured metals fabricated by ARB

Figure 2.12 shows the changes in the nominal stress–strain curves of the IF steel and 1100-Al during ARB. The ARB process for the IF and 1100-Al were carried out without lubrication at 500°C and RT, respectively. Both materials showed quite similar changes in the stress–strain curves. The strength and ductility were summarized in Fig. 2.13 as a function of the number of the ARB cycles. The strength of the materials increased roughly twice by one cycle of ARB, while the elongation greatly decreased. This is a typical mechanical property of strainhardened materials. The flow stress increased with increasing the ARB cycle, keeping similar shapes of the stress–strain curves. The elongation maintained nearly the same value after the second cycle. After seven cycles, the tensile strength reached 910 MPa in the IF steel and 340 MPa in the 1100-Al, respectively,

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2.12  Engineering stress–strain curves of the ARB-processed materials. (a) IF steel ARB processed at 500°C without lubrication. (b) 1100-Al ARB processed at RT without lubrication.

which were more than 3~4 times higher than those of the starting materials. In stress–strain curves, the ARB-processed specimens reached their maximum strength at early stage of the tensile test, followed by macroscopic necking. Consequently, the specimens had limited uniform elongation (about 1~3%), which is a common feature of the ultra-high strained materials independent of the SPD process.34 Actually, the same materials, deformed highly to the equivalent

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2.13  Strength (0.2% proof stress (s0.2) and tensile strength (sB)) and ductility (uniform elongation (eu) and total elongation (et)) obtained by tensile test at RT for the ARB-processed materials. (a) IF steel ARB processed at 500°C without lubrication. (b) 1100-Al ARB processed at RT without lubrication.

amount of strain, show nearly the same strength, regardless of the processes. Different elongation (ductility) has sometimes been reported in the nanostructured materials SPD-processed by different techniques, but we should note that tensile elongation is significantly affected by the shape and dimensions of the tensile specimens, and in many cases different types of specimens have been used in different groups. It should be emphasized, however, that the UFG materials fabricated by ARB (SPD) do not lose plasticity, because they can be rolled, compressed or bent to fairly high degrees of deformation. There have been many arguments on whether oxides formed at bonded interfaces affect the mechanical properties of the ARB-processed sheets or not. There must be a certain amount of oxides at bonded interfaces in the ARBprocessed materials. However, even after six ARB cycles that can produce a homogeneous UFG structure (Fig. 2.4), the number of bonded interfaces within the 1 mm sheet is only 63 and the interval of the bonded interfaces (the thickness of the original sheet) is 15.6 µm (Table 2.1), which is much larger than the mean grain size (~0.2 µm). The total volume of oxides would thus be relatively small. Therefore, it is believed that the effect of oxides on the mechanical properties of the ARB-processed sheets is not significant below about ten cycles, which is usually used for fabricating UFG structures. The stress–strain curves of commercial purity aluminum (ARB-processed and then annealed) are shown in Fig. 2.14. The change in microstructures during annealing has been already shown in Fig. 2.9. Flow stress of the material decreases with increasing annealing temperature, but tensile elongation, especially uniform elongation, recovers only after the mean grain size becomes larger than 1 µm. Quite similar changes in mechanical properties have been reported in the IF steel (ARB processed and annealed).21 The results show that even if the characteristics

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2.14  Engineering stress–strain curves of the 1100-Al ARB-processed by 6 cycles at 200°C without lubrication and then annealed at various temperatures indicated in the figure for 1.8 ks. Mean grain thickness (dt) in each specimen is also indicated.

of deformation microstructures in the ARB-processed specimens are diminished by annealing, the UFG specimens exhibit limited tensile ductility. The limited uniform elongation of the UFG materials is understood in terms of early plastic instability.21 Plastic instability condition, i.e. necking criteria in tensile test, can be simply expressed in the Considère equation shown below: [2.2]



Here, σ and ε are true stress and true strain, respectively. Grain refinement greatly increases flow stress, especially yield strength, of the material. On the other hand, strain-hardening is not enhanced by grain refinement. As a result, the plastic instability expressed in equation (2.2) is easily achieved in UFG materials. Therefore, it is necessary to enhance strain-hardening ability of the matrix in order to manage both high strength and ductility in nanostructured metals.35 Actually, a good balance of strength and ductility has been reported in multiphased nanostructured metals and alloys.35–39 It is noteworthy in Fig. 2.14 that the specimens having mean grain sizes smaller than 3 µm exhibit yield-point phenomena, nevertheless the material is pure aluminum. A number of such unique and unusual mechanical properties have been recently reported in nanostructured metals fabricated by ARB, such as an increase in tensile ductility with increasing ARB strain in particular Al alloys40

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and the hardening by annealing and softening by deformation phenomena, which are totally opposite to metallurgical common sense.41

2.6

Conclusions

In this chapter, the principles and processing details of the ARB process were explained, and further the nanostructure evolution and mechanical properties of the ARB-processed materials were presented and discussed. The ARB process is the only SPD process applicable to continuous production of large bulky materials, while another batch type SPD processes are disadvantageous for practical application. Although to adapt ARB into large-scale mass production of materials, such as those in the steel industry, is still difficult, very thin strips (~0.1 mm thick) of UFG stainless steel has already been already produced in a relatively smallscale industry using the principle of the ARB (see Chapter 23).42 The present manuscript clearly shows that the ARB is also a nice process at the laboratory scale for obtaining bulky samples having homogeneous nanostructures. By the use of the technique, we have been able to systematically acquire fundamental knowledge of bulk nanostructured metals and alloys.

2.7

References

  1 Tsuji N., Saito Y., Lee S.H., and Minamino Y. Adv. Eng. Mater. 2003: 5: 338.   2 Altan B.S., editor. Severe Plastic Deformation toward Bulk Production of Nanostructured Materials. New York: Nova Science Publishers, 2006.   3 Saito Y., Tsuji N., Utsunomiya H., Sakai T., and Hong R.G. Scripta Mater. 1998: 47: 893.   4 Tylecote R.F. The Solid Phase Welding of Metals. London: Edward Arnold, 1968.   5 Lee S.H., Saito Y.,Tsuji N., Utsunomiya H., and Sakai T. Scripta Mater. 2002: 46: 281.   6 Kamikawa N., Sakai T., and Tsuji N. Acta Mater. 2007: 55: 5873.   7 Tsuji N. in,2 p.545.   8 Terada D., Inoue M., Kitahara H., and Tsuji N. Acta Mater. 2008: 49: 41.   9 Dinda G.P., Rosner H., and Wilde G. Scripta Mater. 2005: 52: 577. 10 Perez-Prado M.T., del Valle J.A., and Ruano O.A. Scripta Mater. 2004: 51: 1093. 11 Tsuji N., Kamikawa N., and Minamino Y. Mater. Sci. Forum 2004: 467–470: 341. 12 Huang X., Tsuji N., Hansen N., and Minamino Y. Mater. Sci. Eng. A 2003: 340: 265. 13 Tsuji N., and Kamikawa N. Proc. of the 12th Int. Conf. on Aluminum Alloys (ICAA 12), 2010, The Japan Institute of Light Metals, pp. 1134–1140. 14 Kamikawa N., Tsuji N., and Minamino Y. Sci. Tech. Adv. Mater. 2004: 5: 163. 15 Li B.L., Tsuji N., and Kamikawa N. Mater. Sci. Eng. A 2006: 423: 331. 16 Hansen N., and Juul Jensen D. Phil. Trans. R. Soc. London A 1999: 357: 1447. 17 Ito Y., Tsuji N., Saito Y., Utsunomiya H., and Sakai T.J. Jpn. Inst. Metals 2000: 64: 429. 18 Hansen N. Metall. Mater. Trans. A 2001: 32: 2917. 19 Ikeda K., Yamada K., Takata N., Yoshida F., Nakashima H. and Tsuji N. Mater. Trans. 2008: 49: 24. 20 Ii S., Takata N., Ikeda K., Nakashima H. and Tsuji N. unpublished data.

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21 Tsuji N., Ito Y., Saito Y., and Minamino Y. Scripta Mater. 2002: 47: 893. 22 Tsuji N., Okuno S., Koizumi Y., and Minamino Y. Mater. Trans. 2004: 45: 2272. 23 Humphreys F.J., Prangnell P.B., and Priestner R. Curr. Opinion Solid State Mater. Sci. 2001: 5: 15. 24 Humphreys F.J., and Hatherly M. Recrystallization and Related Annealing Phenomena. Oxford: Pergamon, 1995. 25 Takata N., Yamada K., Ikeda K., Yoshida F., Nakashima H., and Tsuji N. Mater. Trans. 2007: 48: 2043. 26 Tsuji N., Iwata T., Sato M., Fujimoto S., and Minamino Y. Sci. Tech. Adv. Mater. 2004: 5: 173. 27 Terada D., Sato T., and Tsuji N. Proc. of the 30th Risø Int. Symp. on Mater. Sci. Roskilde: Risø National Laboratory, 2009: 351. 28 Atzmon M., Unruh K.M., and Johnson W.L. J. Appl. Phys. 1985: 58: 3865. 29 Yasuna K., Terauchi M., Otsuki A., Ishihara K.N., and Singu P.H. J. Appl. Phys. 1997: 82: 2435. 30 Sieber H., Wilde G., and Perepzko J.H. J. Non-Cryst. Solid 1999: 250–252: 611. 31 Sieber H., Wilde G., Sagel A., and Perpezko J.H. J. Non-Cryst. Solid 1999: 250–252: 616. 32 Ohsaki S., Kato S., Tsuji N., Ohkubo T., and Hono K. Acta Mater. 2007: 55: 2885. 33 Sun Y.F., Todaka Y., Umemoto M., and Tsuji N. J. Mater. Sci. 2008: 23–24: 7457. 34 Iwahashi Y., Wang J., Horita Z., Nemoto M., and Langdon T.G. Metall. Mater. Trans. A 1998: 29: 2503. 35 Tsuji N., Kamikawa N., Ueji R., Takata N., Koyama H., and Terada D. ISIJ Int. 2008: 48: 1114. 36 Tsuji N., Ueji R., Minamino Y., and Saito Y. Scripta Mater. 2002: 46: 305. 37 Ueji R., Tsuji N., Minamino Y., and Koizumi Y. Acta Mater. 2002: 50: 4177. 38 Okitsu Y., Takata N., and Tsuji N. J. Mater. Sci. 2008: 23–24: 7391. 39 Takata N., Ohtake Y., Kita K., Kitagawa K., and Tsuji N. Scripta Mater. 2009: 60: 590. 40 Kim H.W., Kang S.B., Tsuji N., and Minamino Y. Acta Mater. 2005: 53: 1737. 41 Huang X., Hansen N., and Tsuji N. Science 2006: 312: 249. 42 Tsuji N. Adv. Eng. Mater. 2010: 12: 701.

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3 Nanocrystalline metals and alloys prepared by mechanical attrition S. SCUDINO and J. ECKERT, IFW Dresden, Germany Abstract: This overview discusses the formation of nanocrystalline materials by mechanical attrition. The chapter starts with a description of the methods and the process variables typically employed for producing nanostructured phases by mechanical attrition. Experimental data for the resulting nanostructures obtained by mechanical milling of single phases as well as by mechanical alloying of phase mixtures are discussed for selected materials with an emphasis on the different mechanisms involved. Finally, problems and possible solutions for consolidating nanostructured powders are also addressed at the end of this chapter. Key words: mechanical attrition, mechanical alloying, powder metallurgy, nanocrystalline materials, consolidation.

3.1

Introduction

Nanocrystalline (also referred to as nanostructured or nanophase) materials are single- or multi-phase polycrystals with particle or grain sizes, layer thicknesses, or domain sizes in the nanometer range (typically less than 100 nm at least in one dimension). Due to their extremely small grain size, an appreciable fraction of the atoms in nanostructured materials are located in the grain boundaries.1 Such unique microstructural features lead to physical and chemical properties that may significantly differ from those of the corresponding coarse-grained materials with the same composition.2–5 In particular, a significant improvement of the mechanical properties, such as a substantial increase in strength and hardness with respect to conventional coarse-grained materials, has been observed in a number of alloys with nanoscale microstructures.2–5 However, one major drawback for the use of nanocrystalline materials in engineering applications is their often limited room temperature ductility.2–5 Nevertheless, recent findings have shown that grain refinement to the nanometer regime may also lead to enhanced plastic deformation,6 therefore, opening up new perspectives for the application of nanocrystalline phases as structural and functional materials. Two main strategies have been used for the preparation of nanocrystalline materials: (i) the bottom-up approach, which consists of building the nanostructure atom-by-atom or layer-by-layer and (ii) the top-down approach that consists of breaking down the microstructure into a nanostructure. Examples of the bottom-up approach are inert gas condensation, chemical vapor condensation and pulse electron deposition.1,7,8 The archetype technique of the top-down approach is 59 © Woodhead Publishing Limited, 2011

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mechanical attrition. This processing route has been widely used for the preparation of nanostructured materials and, different from the top-down approach, produces nanophase structures not by cluster assembly but by the structural decomposition of coarser-grained structures as the result of heavy cyclic plastic deformation.4,9 Mechanical attrition is one of the less sophisticated technologies and, in turn, also one of the most inexpensive to produce nanophase powders. In addition, it can be used for the processing of essentially all classes of materials.9 This, along with the additional advantage of the possible scaling up to tonnage quantities of processed material, has made mechanical attrition a very popular method for the synthesis of nanocrystalline materials, not only for the laboratory scale but also for potential industrial applications.9 In view of the importance of mechanical attrition as a method for nanocrystalline materials synthesis, this overview starts with a description of the methods and the process variables typically employed for producing nanostructured phases by mechanical attrition. Experimental data for the resulting nanostructures obtained by mechanical attrition of single- and multi-phase powders will be described for selected materials, and the mechanisms responsible for the formation of the different nanophase structures will be discussed. Consideration of the problems and challenges for the consolidation of nanostructured powders, as well as a discussion of the possible solutions, will also be addressed at the end of this chapter.

3.2

Mechanical attrition

Mechanical attrition of powders, first developed by Benjamin and coworkers10,11 in the 1970s, is a processing route that can successfully produce new alloys, phases and phase mixtures. This method for materials synthesis can circumvent many of the limitations of conventional alloying and allows the preparation of alloys and composites that cannot be synthesized via conventional casting or rapid solidification routes. Examples are uniform dispersions of ceramic particles in a metallic matrix or alloys of metals with rather different melting points with the aim of improving strength and corrosion resistance.10,11 Over the years, mechanical attrition has attracted enormous interest as a versatile non-equilibrium processing technique resulting in solid-state alloying beyond the equilibrium solubility limit and the formation of amorphous, quasicrystalline or nanostructured materials for a broad range of alloys, intermetallic compounds, ceramics and composites.4,9,12,13,14 Mechanical attrition is usually performed in ball mills capable of high-energy impact forces. For this purpose, a variety of different types of ball mills with different characteristics have been developed, including attrition mills, shaker mills, planetary mills, vibratory mills, etc.14 The milling process consists of loading the starting material and the grinding balls (typically steel or tungsten carbide) into a milling container (vial), which is violently shaken or rotated, depending on the

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mill used. The intensity of milling depends on the internal mechanics of the specific mill and, consequently, on the kinetic energy imparted to the grinding balls, as well as on mass, size and number of the balls. One serious problem in the processing of fine powders by mechanical attrition is potential contamination from the milling media or atmosphere.4,9,13 The small size of the powder particles and the consequent availability of large surface area, along with the continuous formation of new fresh surfaces during milling, contribute to the contamination of the powder.14 If, as in most cases, the milling vial and balls are made of steel, iron is the typical contaminant due to debris of the milling tools. The magnitude of contamination appears to depend on both the time and the intensity of milling.9,15 The other major source of contamination is from the milling atmosphere, i.e. oxygen or nitrogen. Atmospheric contamination is particularly severe for milling of reactive metals, such as titanium and zirconium,9,14 however, it can be drastically reduced by milling in an inert gas atmosphere (e.g. argon). Mostly, mechanical attrition is carried out under dry conditions but also milling with liquid or solid process control agents is possible,13,14 depending on the nature of the milled powders, in order to prevent sticking of the materials to the milling tools. The dynamics of mechanical attrition are extremely complex and strongly depend on the mill characteristics. However, for all types of ball mills the fundamental event of the milling process is the ball–powder collision, as schematically shown in Fig. 3.1. During milling the powder particles are trapped between the colliding balls and are subjected to repeated high-energy impacts, which induce heavy plastic deformations together with fracturing and cold-welding events. For a given composition, the deformation/fracture process, the potential phase transformations during milling and the final structure of the material depend on the powder material properties (e.g. hardness, fracture toughness, etc.), being different for single-phase materials or combinations of ductile/ductile, ductile/ brittle or brittle/brittle components,9 as well as on the milling parameters, i.e. the kinetic energy transferred to the powder and the local temperature during the impacts.9,12 The temperature that the powders experience during milling also depends on the type of mill used and on parameters such as vibration frequency or rotational velocity. Experimental observations and modeling of the mechanics, kinetics and the energy transfer during collision suggest that the temperature rise during milling is about ≤ 100–200 K.9,12 Adjusting or changing the milling conditions can affect the phase formation or can lead to phase transitions between different phases. Depending on the chosen experimental conditions (i.e. energy input, milling temperature), nanocrystalline and amorphous materials as well as quasicrystalline or crystalline phases can be synthesized by mechanical attrition. In addition, the different phases can be transformed into each other by additional milling at higher or lower milling intensity. In particular, this has been demonstrated for the crystal-to-quasicrystal transition, the crystal-to-amorphous transition, and the quasicrystal-to-amorphous transition.16–18

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3.1  Schematic illustration of the basic event occurring during mechanical attrition showing the trapping of powder particles between colliding balls.

3.3

Nanocrystalline phase formation by mechanical attrition

A fundamental feature of mechanical attrition is the development of nanoscale microstructures. As described above, during milling the powder particles are subjected to severe mechanical deformation from repeated high-energy impacts with the milling tools. Deformation occurs under shear conditions and high strain rates (~103–104 s–1), leading to the incorporation of lattice defects and to a continuous refinement of the initial structure of the powder particles to the nanometer regime.4,13 Extended milling may eventually lead to phase transformations, including nanocrystalline equilibrium and metastable phases.4,13 The final structure of a powder subjected to mechanical attrition may depend on the starting material used. Accordingly, mechanical attrition can be divided in two different routes depending on the starting material. The mechanical attrition of powders with different compositions (the mixture of elemental powders as well as

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of intermetallic compounds), in which material transfer occurs, is named mechanical alloying (MA), while the mechanical attrition of single composition powders, such as pure elements and single-phase intermetallic compounds, where material transfer is not required, has been termed mechanical milling (MM).19 In the following section, the evolution of nanocrystalline structures produced by mechanical milling of single phases as well as by mechanical alloying of phase mixtures is discussed with emphasis on the different mechanisms involved. Similarly, selected examples of phase transformation during milling of different starting materials are also presented.

3.3.1 Mechanical milling of single-phase materials Grain refinement to the nanometer regime is a universal phenomenon of the milling process and has been observed in almost all mechanically attrited materials, including pure metals, intermetallic compounds and multi-phase materials.4,9,13,14 The microstructural changes induced by mechanical attrition can be estimated by x-ray diffraction (XRD) methods. The XRD patterns exhibit increasing broadening of the diffraction peaks as a function of milling time, which is caused by size as well as internal strain effects.4,13 The individual contributions of these effects to the total broadening can be separated using standard techniques: the peak broadening due to the reduction of grain or crystallite size (the average coherently diffracting domain size) is inversely proportional to cos θ, whereas broadening due to lattice strain is proportional to tan θ.20,21 The characteristics of grain size refinement by mechanical attrition have been studied extensively in the past years with particular attention on mechanical milling of pure metallic elements. For example, Fecht et al.22–24 observed the continuous decrease of the grain size with increasing milling time down to about 9 nm for the body-centered cubic (bcc) metals and to about 13 nm for the hexagonal close packed (hcp) metals. Similar results in terms of grain refinement with milling time have been also reported for milling of a series of face-centered cubic (fcc) metals.25 Interestingly, the minimum grain size for the fcc elements was found to inversely scale with the melting temperature.25 A similar trend as observed for the fcc metals can be observed for milling of a series of hcp metals spanning over a wide range of melting temperatures (Fig. 3.2). On the other hand, MM bcc metals do not show any significant variation of minimum grain size with the melting temperature,22 probably because of the lack of milling experiments for bcc metals with low melting point. Along with the grain size refinement to the nanometer regime, milling of powders can introduce a considerable amount of lattice strain, which is most presumably linked to the dislocation density.25 In analogy with the minimum grain size, the maximum lattice strain introduced during milling is also meltingpoint dependent, and increases with the melting temperature of the specific metal (Fig. 3.3). The observed dependence of grain size and lattice strain on the melting temperature suggests that recovery rates during the milling process correlate with

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3.2  Minimum grain size obtained by mechanical milling for different fcc, hcp and bcc metals as a function of the melting temperature (data from Fecht et al.22, Eckert et al.25 and Nogales et al.31).

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3.3  Lattice strain for different mechanically milled fcc metals versus melting temperature (adapted from Eckert et al.25).

the melting point of the specific metal, thus preventing very small grain sizes for low-melting elements.25 Another important aspect of nanostructure formation by milling is the stored enthalpy, which is accumulated in the material as a result of the heavy mechanical deformation. This energy is released during heating to elevated temperatures due

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Stored enthalpy, kJ/mol

to recovery, relaxation processes within the boundaries and grain growth24 and can be determined using differential scanning calorimetry (DSC) measurements. As a typical example of mechanically attrited metals, Fig. 3.4 shows the stored enthalpy of MM Ni as a function of the reciprocal grain size.25 The stored enthalpy increases to a maximum value (which does not occur at the minimum grain size) and then decreases during further grain refinement. A plausible explanation for this behavior might be the increase of the impurity content during milling;25 however, a clear motivation for this phenomenon is still missing. The final energies stored during mechanical attrition largely exceed those resulting from conventional cold working of metals and alloys, such as cold rolling or wire drawing.23,25 During conventional deformation the stored enthalpy never exceeds more than a small fraction of the heat of fusion. However, in the case of mechanical attrition the energy stored can reach values corresponding to about 40% of the heat of fusion.25 Point defects and dislocations can account for only a fraction of this energy and, most likely, the major energy contribution is stored in the form of grain boundaries, and related strains within the nanocrystalline grains that are induced through grain boundary stresses.4 The minimum grain size obtainable by milling has been attributed to the competition between the heavy mechanical deformation and recovery by thermal processes and, in turn, by the minimum grain size that can sustain a dislocation pile-up within a grain and by the rate of recovery during milling.25 An estimate for the minimum dislocation separation in a pile-up Lc is given by Lc = 3Gb/π(1–ν)h, with shear modulus G, Burgers vector b, Poisson ratio ν, and hardness h of the

3.4  Stored enthalpy in mechanically milled Ni versus reciprocal grain size d (adapted from Eckert et al.25).

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material. Applying this relation to the milled fcc metals shows that the minimum grain size of fcc metals (d) follows a linear relation with Lc (Fig. 3.5, solid symbols). This gives a lower bound for the grain size of pure metals and reveals that a small grain size itself provides a limit for further grain refinement by milling.25 In addition, the reduction of the grain size is also limited by the rate of recovery during milling, which may be significant for metals with low melting points. It has been found22,24 that in the early stages of milling the deformation of milled powders is localized in shear bands containing a high dislocation density. By increasing the milling time, the lattice strain increases due to the increasing dislocation density and, at a certain strain level, the dislocations annihilate and recombine to small angle grain boundaries, separating the individual grains. The subgrains formed via this route are already in the nanometer size range (about 20–30 nm). With a longer milling time the grain size decreases gradually and the structure finally evolves into nano-grains separated by high-angle grain boundaries. At this stage, no further grain refinement is possible but only grain boundary sliding can occur, which does not refine the microstructure any further.4 These findings indicate that a high initial dislocation density and, thus, a large lattice strain, is necessary for significant grain size refinement by mechanical attrition. This is opposed by the recovery processes whose driving force is the energy stored in the grain boundaries of the milled material. Grain refinement and recovery are closely related to the minimum grain size d through the rate of each

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3.5  Minimum grain size obtained by milling of pure metals (solid symbols) and FexCu100–x solid solutions with different compositions (open symbols) versus the minimum distance between two dislocations Lc (adapted from Eckert32).

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process expressed as a function of the grain size, since d is the grain size at which the two rates are equal.32 In the case of metals with low melting temperatures, such as Al, the dislocation density is limited by recovery processes and, therefore, the minimum grain size achievable is most likely governed by the recovery rate. On the other hand, almost no recovery is expected to occur for refractory metals during milling, but a high level of internal strain is created due to the large number of dislocations and other deformation faults introduced. Therefore, the minimum grain size for these elements is limited by the stress required for plastic deformation via dislocation motion rather than by the recovery rate.25 Nanocrystalline phase formation can also be achieved by the mechanical milling of intermetallic compounds. For example, Hellstern et al.33,34 investigated the stability of several intermetallic compounds with CsCl (ordered bcc) structure under high-energy milling. Like the milling of pure metals, they observed a decrease of the grain size with increasing milling time to about 5–12 nm. This was accompanied by disordering of the lattice as shown by the decrease of the longrange order parameter, which became more pronounced with decreasing grain size and finally saturated at about 0.7.34 This indicates that the material does not disorder completely and that some residual chemical disorder (i.e. atoms on wrong sites. For example, in an A-B compound, A atoms on B sites and B atoms on A sites) is present within the nanocrystalline grains after milling. Still, an appreciable part of the strain will reside in the disorder, because atoms on the ‘wrong’ sublattice are to be accommodated on lattice sites, where they do not fit. This gives rise to strain.35 Indeed, MM of CsCl intermetallics introduces a lattice strain of about 2–3%, which is much larger than what is generally observed for pure metals (less than 1%). In addition, milling intermetallic compounds does not lead to a peak of the maximum stored enthalpy, as is typical for pure metals (Fig. 3.4), but the stored energy shows saturation to a maximum value.34 The degree of disordering during mechanical milling of intermetallic phases depends on the structure of the compound, as observed by Jang and Koch36 for the ordered fcc Ni3Al compound, which exhibits complete disordering during milling. Following grain refinement and lattice disordering, the mechanical attrition of intermetallics can lead to mechanically induced phase transformations, such as for the A-15 type Nb3Au compound,37 which exhibits the formation of a nanocrystalline bcc solid solution during milling. This behavior can be understood by considering the Au-Nb equilibrium phase diagram.35 The Nb3Au compound is stable at room temperature and transforms to the bcc solid solution of Au in Nb at elevated temperatures. The type of atomic disorder, obtained after milling, appears to be similar to that generated at high temperature. Similarly to high temperature treatments, milling introduces anti-site disorder in Nb3Au and brings the material into an increasingly higher disordered state, which corresponds to heat treatments at progressively higher temperatures.35 Therefore, in terms of disorder, milling is equivalent to an increase of temperature of the compound up to the point where the transition from Nb3Au to the bcc solid solution occurs.35 This was corroborated

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by the observation that the Au2Nb compound transforms to a nanostructured fcc solid solution of Nb in Au during milling, as predicted when considering the equilibrium phase diagram.38 Other possible phase transformations during milling involving intermetallic compounds include amorphization and the transformation into a different (complex) crystal structure (for a review see Bakker et al.35). Another interesting type of mechanically induced phase transition is the allotropic transformation of pure elements during milling. Examples are the elements of the Group IVB Ti, Zr, and Hf that undergo an hcp-to-fcc allotropic transformation during mechanical milling39–41 and Co,42 which shows a reversible hcp-to-fcc transformation that depends on the milling intensity used. Although recent results43 have shown that allotropic transformations in the Group IVB might be due to impurity contamination during milling, thus raising doubts about the real nature of these transformations, this type of transformation further demonstrates the versatility of mechanical attrition as a tool for the formation of new materials.

3.3.2 Mechanical alloying of phase mixtures Mechanical alloying of powders with different compositions (mixture of elemental powders as well as of intermetallic compounds) is perhaps the most used mechanical attrition technique for the preparation of a wide range of materials including supersaturated solid solutions, amorphous, quasicrystalline or nanostructured materials for a broad range of alloys, intermetallic compounds, ceramics and composites.4,9,12,13,14 The mechanism of nanocrystalline formation operating during MA is different with respect to MM of single phases since it involves material transfer during processing. Although the microstructural evolution during MA depends on the mechanical behavior of the powder components (i.e. ductile or brittle), the primary aspect of the process is the reduction of the diffusion distances between the different phases. For example, for MA of ductile/ductile components, in the early stages of mechanical alloying the particles are cold-welded and plastically deformed, leading to a characteristic layered structure consisting of various combinations of the starting constituents, as illustrated in Fig. 3.6.44 With increasing milling time the thickness of the individual layers decreases so much that it is no longer visible under an optical microscope.9,14 The structure undergoes severe deformation, work hardening and fracture. Fragments generated by this mechanism may continue to reduce in size, giving rise to a more and more refined microstructure.12 Alloying begins to occur at this stage due to the combination of decreased diffusion distances (interlayer spacing), increased lattice defect density, and any heating that may have occurred during the milling operation.14 This has been confirmed by Klassen et al.,45 who investigated the microstructure evolution during the early stages of MA of Ti-Al powder blends. For MA powder with composition Ti25Al75, transmission electron microscopy (TEM) investigations revealed that, after the

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3.6  Typical layered microstructure obtained during mechanical alloying.14

initial formation of an hcp solid solution by the diffusion of Al into Ti, a (partially) ordered Ll2 fcc phase with grain size of about 10–30 nm is formed between the alternating Ti and Al lamellae. The volume fraction of the Ll2 phase increases with increasing milling time until Al is entirely consumed. No additional phase transformation was observed upon further milling. The authors concluded that the Ll2 phase, observed in the final stage of milling, is already formed in the early stages of the phase reaction. In addition, the initial diffusion of Al into the Ti matrix and the resulting formation of the hcp solid solution permit to exclude that the formation of the Ll2 fcc phase at the interface occurs by the diffusion of Ti into the fcc Al. Therefore, the development of the nanocrystalline structure is not a result of a gradual grain refinement process, as observed during milling of pure metals, but it consists of numerous nucleation events at the Ti/Al interface followed by limited growth of the new phase.46 Another remarkable achievement of MA is the production of a homogeneous mixture of immiscible phases. For example, large non-equilibrium solid solubility has been attained by MA for a series of Fe-Cu powders,47 which are essentially

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immiscible and display a large positive enthalpy of mixing. The ultimate grain size of the binary Fe-Cu nanostructured solid solutions depends on the composition of the material (Fig. 3.7). The grain size can be reduced to only 20 nm for pure Cu, whereas it continuously decreases with increasing Fe content, reaching values below 10 nm for the Fe-rich fcc solid solutions. Similarly, the grain size decreases with increasing Cu content for single-phase bcc solid solutions. A second decrease of the bcc grain size occurs for samples with two-phase fcc/bcc microstructure, whereas the fcc grain size in this region is independent of composition. When the contributions of solution hardening and dispersion hardening are taken into account,32,48 the ultimate grain size of the Fe-Cu alloys scales with the minimum dislocation separation in a pile-up Lc (Fig. 3.5, open symbols) in the same manner as the data for pure fcc metals. This indicates that, similarly to MM of pure metals, the minimum grain size in MA Fe-Cu powders can also be attributed to the competition between the plastic deformation and the recovery behavior and demonstrates that both the alloy composition and the microstructure of the material determine the final grain size.32 Solid solubility extension far beyond the equilibrium values has also been reported for mechanically alloyed nanocrystalline Cu-M (M = Ti, Nb, Ni, Cr, Fe and Co),49 Ti-Ni,50 Ni-Nb51 and Al-Nb52 (for an exhaustive review on this topic see13). Among the different alloys characterized by extended solid solubility when prepared by MA, the Al-Mg system has been extensively investigated in recent years.53–60 The equilibrium solid solubility of Mg in Al is quite small at room temperature (about 1 at.%61). However, depending on the initial solute content in the elemental powder mixture, the milling parameters and the presence of control

3.7  Effect of composition on the minimum grain size achievable by mechanical alloying of FexCu100–x powders (adapted from Eckert32).

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processing agents, an extended solid solubility of Mg in Al can be achieved by MA of elemental powders. For example, Calka et al.53 showed that mechanical alloying allows to extend the solid solubility of Mg in Al up to 18 at.% in the case of Al70Mg30 and 45 at.% for Al50Mg50. Similarly, Zhang et al.54 and Schoenitz et al.56 observed for mechanically alloyed Al60Mg40 the formation of a solid solution containing 23 at.% and 20.8 at.% Mg, respectively. Recently, it was found that both MA of elemental powder mixtures and MM of the single-phase intermetallic compound with composition Al60Mg40 lead to the same product, i.e. a supersaturated Al(Mg) solid solution.60,62 Although MA and MM may lead to the formation of the same product (i.e. the Al(Mg) solid solution), the solid-state transformations induced by the two processing routes occur by different mechanisms due to the different starting materials used (phase mixtures and single-phase materials, respectively). MA is not a purely mechanical process but it involves interdiffusion, driven by the negative heat of mixing, of alternating thin layers as observed for the interdiffusion of thin films of pure metals.63,64 On the other hand, MM consists of energizing the equilibrium crystalline compound by the severe cyclic deformation provided by the milling process.19 Mechanical milling increases the energy of the compound by the generation of chemical disorder, point defects such as vacancies, and lattice defects (e.g. dislocations).14,21,35 In addition, an important contribution to the energy increase comes from the reduction of the grain size to the nanometer level and the consequent storage of energy in the grain boundaries, which constitute an appreciable fraction of the material volume.14,21,35 This energy is stored in the crystal up to a point at which it becomes unstable. The highly energized material then lowers its energy by transforming into a different atomic structural arrangement, e.g. the supersaturated solid solution. With this in mind, it is possible to draw a schematic illustration of the formation of the supersaturated Al(Mg) solid solution by MA and MM. Instead of lowering the Gibbs free energy of the system, such as for mechanical alloying, during mechanical milling the free energy of the equilibrium crystalline compound is raised to a level equal to or larger than that of the metastable phase. The process can be better understood by referring to Fig. 3.8, which schematically shows the Gibbs free energies for the different phases that may form during mechanical attrition of binary Al60Mg40. The straight line represents the free energy of the elemental powder mixture of the pure elements Al and Mg. The broad curve is the free energy of the metastable solid solution and the narrow curve is the free energy of the crystalline intermetallic compound β-Al3Mg2 with composition Al60Mg40. From thermodynamic point of view, the two processes are quite different. While for MA of the mixture of pure Al and Mg with a composition corresponding to that of the intermetallic compound β-Al3Mg2 (reaction [1] → [2]), the initial state has a Gibbs free energy larger than that of the final product (i.e. the solid solution), for MM of the intermetallic compound β-Al3Mg2 (reaction [3] → [2]), the initial state has a Gibbs free energy lower than that of the final product. In the first case the negative heat of mixing of the elemental powders provides the driving force for

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3.8  Schematic free energy diagram of the Al–Mg system for the different phases that may form during mechanical alloying of elemental powder mixtures and mechanical milling of the single-phase intermetallic compound (adapted from Scudino et al.60).

interdiffusion and eventually for metastable phase formation. On the other hand, no chemical driving force exists for the reaction [3] → [2] In this case, the free energy of the equilibrium intermetallic compound must be raised above that of the metastable solid solution by the mechanism previously mentioned. A microscopic model for MA, which explains intermixing in systems with positive mixing enthalpy, has been proposed by Schwarz.65 The model is based on dislocation-mediated intermixing through the diffusion of solutes along the dislocation cores (dislocation pipe diffusion). Mechanical alloying produces fresh metal/metal surfaces and a high density of dislocations. Due to the strong attractive interaction between solutes and dislocations, the solutes can diffuse along the dislocation cores with an activation energy which is about half of that needed for bulk diffusion. When a powder particle is trapped between colliding balls, for short time intervals on the order of milliseconds, it is subjected to a high stress pulse. As a result, some or all the dislocations in the particle are forced to glide and leave their previous positions. However, the solutes that have diffused along the dislocation cores are not able to follow the fast moving dislocations and, consequently, are left behind as strings of solutes in a highly supersaturated state, which have an excess chemical energy. Multiple repetition of this process leads to effective alloy intermixing and/or to stable and metastable phase formation.

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Besides thermodynamic considerations, kinetic aspects also play a central role on the phase selection during mechanical attrition. This is particularly important when different (stable and metastable) phases compete for the final product. Typical examples are the formation of amorphous or nanostructured quasicrystalline powders by mechanical alloying.12 The amorphous phase and most of the quasicrystalline materials are metastable with respect to the equilibrium crystalline phases, i.e. an energy barrier exists preventing these metastable phases from spontaneous crystallization.12,18 The thermodynamically stable state of a system is determined by a minimum in the Gibbs free energy G. In metallic systems, the Gibbs free energy of the equilibrium crystalline state Geq is always lower than that of the metastable phases Gmeta below the melting temperature. In order to form a metastable phase by mechanical attrition, the free energy of the equilibrium phase has to be firstly raised to a state G0 (Fig. 3.9). This high-energy state can be achieved by mechanical attrition through the mechanisms explained previously. The free energy of the system can be then lowered from G0 either by the formation of the metastable phase with free energy Gmeta or by the formation of the equilibrium phase. The equilibrium phase is thermodynamically favored, since the driving force ∆Geq = (G0 – Geq) is larger than that for metastable phase formation ∆Gmeta = (G0 – Gmeta). However, the formation of equilibrium or metastable phases depends on thermodynamic as well as on kinetic factors. The formation of the metastable phase is then possible if the system is kinetically restricted from reaching the equilibrium state of lower free energy, i.e. metastable phase formation proceeds considerably faster than the

3.9  Schematic representation of the basic principles of metastable phase formation by mechanical attrition.

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formation of the equilibrium phase from the initial state G0. At the same time, the metastable phase must not transform into the equilibrium phase as the reaction proceeds, i.e. the timescale for transformation of the metastable phase must be longer than that of metastable phase formation. These kinetic constraints can be summarized as12,18,66:

τ0→meta << τ0→eq

[3.1]

τ0→meta << τmeta→eq,

[3.2]

where τ0→meta and τ0→eq are the characteristic reaction times for the formation of the metastable and equilibrium phases, respectively, and τmeta→eq is the timescale for the transformation of the metastable phase. As already mentioned, phase transformations during milling and the final structure of the material depend on the milling parameters. Among these, the kinetic energy transferred to the powder during milling has the major influence. A good example of the effects of the milling intensity on phase formation during milling has been reported by Eckert et al.12,18 for mechanical alloying of Al-Cu-Mn powders. The authors observed that, depending on the milling conditions used, MA of elemental powders with composition Al65Cu20Mn15 leads to the formation of three distinct structural states: amorphous, quasicrystalline and crystalline phases. Phase selection depends on the milling intensity (Fig. 3.10). For example, milling of composite powders consisting of Al, Cu and Mn elemental powders at the highest milling intensity (int.9) leads to the formation of a crystalline structure,

3.10  Schematic illustration of the effect of the milling intensity on the possible phase transformations during mechanical alloying of Al65Cu20Mn15 powders (adapted from Eckert et al.18). Note that the intensity scale is arbitrary.

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whereas an amorphous phase is obtained by milling at the lowest intensity (int.5). For intermediate milling intensity (int.7), the quasicrystalline phase is formed. In addition, these structures can be transformed into each other by additional milling at higher or lower intensity. For example, by milling at relatively low intensity it is possible to achieve transformations from the more stable to the less stable states, as shown by the clockwise transformations in Fig. 3.10 (i.e. crystal-toquasicrystal (int.5) and quasicrystal-to-amorphous transitions (int.3)). As already mentioned in Section 3.2, the milling temperature is an important parameter in the milling process since it affects the properties of the powders and, as a result, influences the balance between cold welding and fracture during milling. A variation of milling that has recently attracted considerable interest as a method for nanocrystalline materials synthesis is cryomilling, in which milling is carried out at cryogenic temperatures.67 The main advantage of cryomilling over room temperature milling is that the milling time required to reach the final grain size is significantly shorter for cryomilling than that for conventional milling performed at ambient temperature. For example, Zhang et al.68 reported for mechanical attrition of Zn that the average grain size of cryomilled Zn is always smaller than that milled at room temperature after the same amount of milling time. In addition, the cryomilled material has a narrower grain size distribution than Zn milled at room temperature for the same time.68 This behavior has been attributed to the reduction of dynamic recovery and cold welding for milling at cryogenic temperatures. As a result, powder fracturing dominates the milling process and the grains are refined much faster than during room temperature milling and they can reach a smaller size for the cryomilled material.68

3.4

Consolidation of nanocrystalline powders

Although nanocrystalline materials in powder forms, such as mechanically attrited powders, can have considerable importance for certain applications (e.g. for hydrogen storage or catalytic applications29,69), for most of the applications the nanostructured powders need to be consolidated to achieve dense bulk specimens. Therefore, consolidation of nanocrystalline powders into fully dense bulk specimens is of primary interest for the development of near-net shape parts for technological applications. Powders can be consolidated by a variety of well-known and developed techniques, including cold-pressing followed by high-temperature sintering, cold and hot extrusion and hot isostatic pressing.4 The essence of these compaction techniques is to apply high pressure and high temperature to achieve full density. Less common consolidation techniques are spark plasma sintering70,71 or microwave72 and laser73 assisted sintering, which involve the use of pulsed electric current, microwave and laser irradiation to improve powder consolidation. These techniques are carried out at relatively lower temperatures for a shorter

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time than in conventional sintering processes. Therefore, they show a large potential for achieving fast and full densification of nanostructured materials suppressing grain growth. Regardless of the processing route used, the key to the successful consolidation of nanocrystalline materials is to achieve full densification with minimal grain growth and/or undesirable microstructural transformations. However, consolidation of nanostructured phases is not a trivial process and often results in either grain coarsening, or insufficient particle bonding.4 Consolidation of nanostructured phases into fully dense specimens with complete bonding between the initial particles is extremely difficult due to the fact that the nanocrystalline powders of interest are typically hard. Therefore, rather high temperatures have to be applied to soften the material so that plastic deformation allows better filling, and material flow by diffusion helps to remove the remaining porosity.4,74 However, diffusional processes do not only assist particle bonding and densification, but also cause grain coarsening to occur. This is linked to the considerable energy stored during milling (Fig. 3.4), which makes nanocrystalline phases highly unstable materials with a large driving force towards equilibrium. The stored energy is released during heating to elevated temperatures due to recovery-relaxation processes within the boundaries, and grain growth. Therefore, nanocrystalline materials cannot be heated at elevated temperatures for long periods without running the risk of inducing microstructural coarsening.75–77 Consequently, there is a strong interest in using as low temperatures as possible in order to avoid structural changes. High pressures can be used to compensate the low-temperature effect; however, using high pressure for consolidation bears the problem of cracking as the pressure is released.78–82 These characteristics severely limit the consolidation parameters that can be used and, as a result, temperature, pressure and the time span of the consolidation process have to be adjusted carefully in order to achieve a balance between good densification and limited grain growth. Almost any deviation from pure single-phase material will reduce the tendency for grain growth. This includes (i) grain boundary pinning to decrease grain boundary mobility through residual pores,83 impurities and solutes84 and secondphase particles,85 and (ii) reduction of the driving force for grain growth by lowering the grain boundary energy through the addition of solute atoms that segregate at the grain boundaries.86 The effectiveness of the latter approach has been recently verified by Darling et al.87 who studied the influence of solute Zr atoms on the stability of the grain size of nanocrystalline Fe produced by mechanical alloying. While the grain size in pure MA Fe was > 200 nm after annealing for 1 h at temperature T/Tm = 0.5 (where Tm is the liquidus temperature of the alloy), the addition of only 1 at.% Zr stabilized the grain size at 50 nm up to T/Tm = 0.92. These results demonstrate that solute segregation at the grain boundaries is very effective for stabilizing nanocrystalline phases against grain growth and offers the possibility of noticeably extending the temperature range for processing and applications of nanostructured materials.

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Very recently, there was a breakthrough in obtaining bulk nanostructured materials bypassing the difficulties inherent to the consolidation process of mechanically attrited powders, i.e. grain growth and possible phase transformation. The process is based on the in situ consolidation of bulk nanocrystalline materials during mechanical attrition.88 This is achieved by the selection of the proper milling conditions: temperature (liquid nitrogen and room temperature combinations), milling times at each temperature and ball-to-powder mass ratios.30,88 By this method, fully dense nanocrystalline spheres up to 10–15 mm in diameter can be formed for a variety of pure metals (e.g. Zn, Cu, Al30,88,89) and alloys (e.g. Zn-Al, Al-Mg, Cu-Al2O330,90) (Fig. 3.11). These can then be pressed into disks for a variety of mechanical tests. A remarkable example of this approach is the in situ consolidation of pure Cu.89 Fully dense Cu spheres with diameters up to about 8 mm can be obtained through the combination of liquid nitrogen temperature and room temperature milling. Milling at liquid nitrogen temperature allows for a higher dislocation density than can be obtained during milling at room temperature and also suppresses dynamic recovery and recrystallization, leading to the formation of a powder with nanocrystalline structure. Further milling at room temperature allows in situ consolidation of the Cu sample into fully dense spheres through repetitive cold welding processes. TEM results reveal a final average grain size of only 23 nm (Fig. 3.12 (a) ) and a narrow grain size distribution (Fig. 3.12 (b) ) can be achieved by in situ consolidation. The in situ consolidated nanocrystalline Cu is remarkably strong (stronger than all previous nanostructured Cu6,89), reaching an ultimate tensile strength of about 1100 MPa, which is about five times higher than that of the coarse-grained Cu sample (Fig. 3.13). At the same time, the in situ consolidated Cu displays good tensile ductility (14% uniform elongation and 15.5% elongation to failure). This ductility is much larger than that observed for other nanocrystalline materials of similar grain size.89 Another important feature of the stress–strain curve (Fig. 3.13) is the large strain hardening observed in the plastic region. Strain hardening is often limited in nanocrystalline materials. The absence of strain hardening is generally attributed to the absence of dislocation activity during deformation due to the impossibility for dislocations to pile-up in grains with size ≤ 20 nm.91 However, TEM reveals dislocation activity and dislocation pile-up at

3.11  Examples of in situ consolidated bulk nanocrystalline materials.30

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3.12  (a) TEM micrograph and corresponding selected area diffraction pattern of the typical microstructure in the in situ consolidated nanocrystalline Cu; (b) statistical distribution of grain size obtained from multiple TEM images of the same sample.89

the grain boundaries in the deformed in situ consolidated Cu, which might be responsible for producing the strain hardening effect observed.89 This indicates that even very small nano-grains can deform by dislocation motion. As well, this processing route can be successfully used to produce nanostructured Al-based alloys with remarkable room temperature mechanical properties. For example, a bulk nanocrystalline Al-5% Mg (at.%) alloy has been prepared using in situ consolidation during mechanical alloying at liquid nitrogen and room

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3.13  Typical tensile stress–strain curve for the in situ consolidated bulk nanocrystalline Cu sample (average grain size 23 nm) in comparison with that of a coarse-grained polycrystalline Cu sample (average grain size larger than 80 µm) (adapted from Youssef et al.89).

3.14  Tensile stress–strain curves for the samples: annealed, coarsegrained (55 µm) Al-5083 alloy; nanocrystalline Al-5083 alloy produced through cryomilling and consolidation by hot isostatic pressing (HIP) and extrusion at 523 K; bulk in situ consolidated nanocrystalline Al-5%Mg alloy (26 nm) (adapted from Youssef et al.92).

temperature.92 The nanocrystalline structure produced during in situ consolidation was a supersaturated solid solution of Mg in Al with average grain size of 26 nm and a relatively narrow grain-size distribution. Tension tests reveal that the in situ consolidated Al-5% Mg is characterized by excellent mechanical properties (Fig. 3.14): the yield strength reached 620 MPa (four times that of the

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coarse-grained Al-5083 alloy), and the ultimate strength was 740 MPa. A significant tensile ductility was obtained with an elongation to failure value of 8.5%. Strain hardening was also observed, which is believed to derive from accumulation of dislocations during plastic deformation.

3.5

Conclusion and future trends

Over the years, mechanical attrition has attracted enormous interest as a versatile non-equilibrium processing technique for the production of nanocrystalline materials for a broad range of single- and multi-phase systems. Mechanical attrition is one of the less sophisticated technologies and, in turn, also one of the most inexpensive ones to produce nanophase powders. In addition, it can be used for the processing of essentially all classes of materials. This, along with the additional advantage of the possible scaling up to tonnage quantities of processed material, has made mechanical attrition a very popular method for the synthesis of nanocrystalline materials not only for the laboratory scale but also for potential industrial applications. The central event of the milling process is the ball–powder collision. Powder particles are trapped between the colliding balls during milling. They undergo repeated severe plastic deformation and fracture processes leading to the incorporation of lattice defects and to a continuous refinement of the initial structure of the powder particles to the nanometer regime. Extended milling may eventually lead to phase transformations, including nanocrystalline equilibrium and metastable phases. The nature of these processes depends on the starting material, thus being different for MA of phase mixtures and MM of single-phase materials. The mechanism of nanocrystal formation operating during MA is different with respect to MM of single phases since it involves atomic mixing during processing. The development of the nanocrystalline structure during MA is not a result of a gradual grain refinement process, as observed during MM of pure metals, but it consists in numerous nucleation events at the interface between the phases followed by limited growth of the new phase. The final grain size achievable by mechanical attrition depends on the intrinsic properties of the material. For pure metals, a general relation based on the competition between the plastic deformation and the recovery behavior of metals and alloys can be inferred. This relation can be extended to alloys when the contributions of solution hardening and dispersion hardening are considered. Hence, the structural state of the material must be taken into account for an adequate description of the grain size effects in nanocrystalline materials. For most potential applications, mechanically attrited powders have to be consolidated to achieve dense bulk nanocrystalline specimens. However, consolidation of nanostructured phases is not a trivial process and special care has to be taken with respect to accurate control of the consolidation parameters in order

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to achieve dense bulk specimens without inducing microstructural coarsening or possible phase transitions. With this respect, recent results demonstrate that solute segregation at the grain boundaries is very effective for stabilizing nanocrystalline phases against grain growth and offer the possibility of noticeably extending the temperature range for processing and applications of nanostructured materials. The difficulties inherent to the consolidation process of nanostructured powders can be overcome by the in situ consolidation of bulk nanocrystalline materials during mechanical attrition. The in situ consolidated nanocrystalline samples display very encouraging mechanical properties regarding the combination of high tensile strength and good ductility at room temperature. Nanocrystalline materials provide many interesting topics for the study of microstructure property relations, offering both the potential to discover and to develop new materials and properties, and a way to test models and understanding of mechanical deformation. Also, the development of materials with nanoscale microstructure as technological materials not only requires a basic understanding of the role of chemistry and structure on determining properties, but also an understanding of how to create such structures during large-scale fabrication. Such basic understanding is now developing for mechanically attrited powders, and interest in these nanostructured materials is growing. Fabrication processes for large-volume production are already being developed, and with the careful optimization of procedures for preparing specific materials for specific applications, the importance of this new class of materials is bound to grow.

3.6

Acknowledgements

The authors gratefully acknowledge the support of Deutsche Forschungs­ gemeinschaft (DFG) (Grants No. EC 111/7, EC 111/8, EC 111/9, EC 111/10, EC 111/12, EC 111/16 and Lu 217/17), the EU within the frameworks of the European Network of Excellence on Complex Metallic Alloys NoE CMA (contract No. NMP3-CT-2005-500140) as well as Deutscher Akademischer Austauschdienst (DAAD). Special thanks are given to many coworkers, in particular, F. Ali, F. Baier, B. Bartusch, M. Calin, J. Das, S. Deledda, M. Frey, A. Gebert, R. Günther, G. He, G. Liu, W. Löser, N. Mattern, C. Mickel, H. Kempe, J.S. Kim, K.B. Kim, A. Kübler, U. Kühn, G. Kumar, A. Reger-Leonhard, M. Sakaliyska, M. Samadi Khoshkhoo, H. Schulze, F. Schurack, M. Seidel, M. Stoica, K.B. Surreddi, and S. Venkataraman, who have all contributed in one way or another to the results presented in this overview. Finally, the authors would like to thank M. Baricco, M.D. Baró., L. Battezzati, R. Birringer, J.M. Dubois, H.-J. Fecht, A.L. Greer, M. Heilmaier, W.L. Johnson, D.H. Kim, R. Kirchheim, C.C. Koch, U. Köster, C.E. Krill, D.V. Louzguine, D.G. Morris, B.S. Murty, N.K. Mukhopadhyay, J.H. Perepezko, K. Samwer, L. Schultz, D.J. Sordelet, K. Xia, W. Xu, A.R. Yavari, and M. Zehetbauer for many valuable discussions.

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3.7

References

  1 Gleiter H. Prog Mater Sci 1989;33: 223.   2 Siegel R.W. In: Nastasi M., Parkin D.M., Gleiter H., editors. Mechanical properties and deformation behavior of materials having ultra-fine microstructures. NATO ASI Series, 233. Dordrecht: Kluwer; 1993.   3 Edelstein A.S., Cammarata R.C. Nanomaterials: synthesis, properties and applications, Bristol: IOP Publishing; 1996.   4 Koch C.C. Nanostructured materials: processing, properties and potential applications. Norwich, NY: Noyes Publications, William Andrew Publishing; 2002.   5 Meyers M.A., Mishra A., Benson D.J. Prog Mater Sci 2006;51:427.   6 Ma E. JOM 2006;58: 49.   7 Suryanarayana C. Inter Mater Rev 1995;40: 41.   8 El-Sherik AM, Erb U. J Mater Sci 1995;30: 5743.   9 Koch C.C. Mechanical milling and alloying. In: Cahn R.W., Haasen P., Kramer E.J., editors. Materials Science and Technology, Vol. 15. Weinheim: VCH Verlagsgesellschaft; 1991. 10 Benjamin J.S. Metall Trans 1970;1: 2943. 11 Benjamin J.S. Sci Am 1976;234: 40. 12 Schultz L., Eckert J. Mechanically alloyed glassy metals. In: Güntherodt H.J., Beck H., editors. Glassy metals III, topics in applied physics, Vol. 72. Berlin: Springer; 1994. 13 Suryanarayana C. Mechanical alloying and milling. New York: Marcel Dekker; 2004. 14 Suryanarayana C. Prog Mater Sci 2001;46: 1. 15 Scudino S., Eckert J., Yang X.Y., Sordelet D.J., Schultz L. Intermetallics 2007;15: 571. 16 Eckert J., Schultz L., Urban K. Appl Phys Lett 1989;55: 117. 17 Eckert J., Schultz L., Urban K. Acta Metall Mater 1991;39: 1497. 18 Eckert J., Schultz L., Urban K. Europhys Lett 1990;13: 349. 19 Koch C.C. Scripta Mater 1996;34: 21. 20 Williamson G.K., Hall W.H. Acta Metall 1953;1: 22. 21 Suryanarayana C., Norton M.G. X-ray diffraction: a practical approach. New York: Plenum; 1998. 22 Fecht H.J., Hellstern E., Fu Z., Johnson W.L. Metall Trans A 1990;21: 2333. 23 Fecht H.J. Nanostructured Mater 1995;6: 33. 24 Hellstern E., Fecht H.J., Garland C., Johnson W.L. MRS Symp Proc 1989;132: 137. 25 Eckert J., Holzer J.C., Krill III C.E., Johnson W.L. J Mater Res 1992;7: 1751. 26 Oleszak D., Shingu P.H. J Appl Phys 1996;79: 2975. 27 Wang K.Y., Shen T.D., Quan M.X., Wei W.D. J Mater Sci Lett 1993;12: 1818. 28 Shen T.D., Koch C.C., McCormick T.L., Nemanich R.J., Huang J.Y., Huang J.G. J Mater Res 1995;10: 139. 29 Zaluska A., Zaluski L., Ström-Olsen J.O. J Alloys Comp 1999;288: 217. 30 Zhang X., Wang H., Kassem M., Narayan, J. Koch C.C. Scripta Mater 2002;46: 661. 31 Nogales E., Montone A., Cardellini F., Méndez B., Piqueras J., Semicond Sci Technol 2002;17: 1267. 32 Eckert J. Nanostructured Mater 1995;6: 413. 33 Hellstern E., Fecht H.J., Fu Z., Johnson W.L. J Mater Res 1989;4: 1292. 34 Hellstern E., Fecht H.J., Fu Z., Johnson W.L. J Appl Phys 1989;65: 305. 35 Bakker H., Zhou G.F., Yang H. Prog Mater Sci 1995;39: 159. 36 Jang J.S.C., Koch C.C. J Mater Res 1990;5: 498. 37 Di L.M., Bakker H. J Appl Phys 1992;71: 5650.

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38 Di L.M., Bakker H., Bárczy P., Gácsi Z. Acta Metall Mater 1993;41: 2923. 39 Manna I., Chattopadhyay P.P., Nandi P., Banhart F., Fecht H.J. J Appl Phys 2003;93: 1520. 40 Manna I., Chattopadhyay P.P., Banhart F., Fecht H.J. Appl Phys Lett 2002;81: 4136. 41 Seelam U.M.R, Suryanarayana C. J Appl Phys 2009;105: 063524(1–8). 42 Huang J.Y., Wu Y.K., Ye H.Q. Appl Phys Lett 1995;66: 308. 43 Seelam U.M.R., Barkhordarian G., Suryanarayana C. J Mater Res 2009;24: 3454. 44 Zhang D.L. Prog Mater Sci 2004;49: 537. 45 Klassen T., Oehring M., Bormann R. J Mater Res 1994;9: 47. 46 Koch C.C. Nanostructured Mater 1997;9: 13. 47 Eckert J., Holzer J.C., Johnson W.L. J Appl Phys 1993;73: 131. 48 Eckert J., Holzer J.C., Krill III C.E., Johnson W.L. J Mater Res 1992;7: 1980. 49 Chen T.D., Koch C.C. Acta Mater 1996;44: 753. 50 Schwarz R.B., Petrich R.R., Saw C.K. J Non-Cryst Solids 1985;76: 281. 51 Lee P.Y., Koch C.C. J Non-Cryst Solids 1987;94: 88. 52 Hellstern E., Schultz L., Bormann R., Lee D. Appl Phys Lett 1988;53: 1399. 53 Calka A., Kaczmarek W., Williams J.S. J Mater Sci 1993;28: 15. 54 Zhang D.L., Massalski T.B., Paruchuri M.R. Metall Mater Trans A 1994;25: 73. 55 Lu L., Zhang Y.Z. J Alloys Comp 1999;290: 279. 56 Schoenitz M., Dreizin E.L. J Mater Res 2003;18: 1827. 57 Al-Aqeeli N., Mendoza-Suarez G., Labrie A., Drew R.A.L. J Alloys Comp 2005;400: 96. 58 Shoshin Y.L., Mudryy R.S., Dreizin E.L. Combustion & Flame 2002;128: 259. 59 Singh D., Suryanarayana C., Mertus L., Chen R-H. Intermetallics 2003;11: 373. 60 Scudino S., Sakaliyska M., Surreddi K.B., Eckert J. J Alloys Comp 2009;483: 2. 61 Massalski T.B. Binary alloy phase diagrams. ASM International; 1992. 62 Scudino S., Sperling S., Sakaliyska M., Thomas C., Feuerbacher M., Kim K.B., Ehrenberg H., Eckert J. Acta Mater 2008;56: 1136. 63 Schwarz R.B., Johnson W.L. Phys Rev Lett 1983;51: 415. 64 Schröder H, Samwer K, Köster U. Phys Rev Lett 1985;54: 197. 65 Schwarz R.B. Mater Sci Forum 1998;269–272:665. 66 Schultz L. Phys Bl 1988;44: 247. 67 Witkin D.B., Lavernia E.J. Prog Mater Sci 2006;51: 1. 68 Zhang X., Wang H., Koch C.C. Rev Adv Mater Sci 2004;6: 53. 69 Mulas G., Monagheddu M., Cocco G., Cutrufello M.G., Ferino I., Rombi E. J Mater Synth Proc 2000;8: 385. 70 Mamedov V. Powder Metall 2002;45: 322. 71 Olevsky E.A., Kandukuri S., Froyen L. J Appl Phys 2007;102: 114913–1(12). 72 Yadoji P., Peelamedu R., Agrawal D., Roy R. Mater Sci Eng B 2003;98: 269. 73 Singh S.S., Roy D., Mitra R., Subba Rao R.V., Dayal R.K., Baldev Raj, Manna I. Mater Sci Eng A 2009;501: 242. 74 Swinkels F.B., Wilkinson D.S., Arzt E., Ashby M.F. Acta Metall 1983;31: 1829. 75 Sanders P.G., Fougere G., Thompson L.J., Eastman J.E., Weertman J. Nanostructured Mater 1997;8: 243. 76 Gertsman V.Y., Birringer R. Scripta Metall Mater 1994;30: 577. 77 Birringer R. Mater Sci Eng A 1989;117: 33. 78 Gutmanas E.Y., Trusov L.I., Gotman I. Nanostructured Mater 1994;4: 893. 79 Sadangi R.K., Kear B.H., McCandlish LE. Nanostructured Mater 1993;2: 563. 80 Cline C.F., Hopper R.W. Scripta Metall 1977;11: 1137.

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Nanostructured metals and alloys Schwarz R.B., Kasiraj P., Vreeland T., Ahrens T.J. Acta Metall 1984;32: 1243. Jain M., Christman T. Acta Metall Mater 1994;42: 1901. Hahn H., Logas J., Averback R.S. J Mater Res 1990;5: 609. Averback R.S., Höfler H.J., Tao R. Mater Sci Eng A 1993;166: 169. Hillert M. Acta Metall 1988;36: 3177. Koch C.C. J Phys: Conf Series 2009;144: 012081(1–8). Darling K.A., Chan R.N., Wong P.Z., Semones J.E., Scattergood R.O., Koch C.C. Scripta Mater 2008;59: 530. Zhu X.K., Zhang X., Wang H., Sergueeva A.V., Mukherjee A.K., Scattergood R.O., Narayan J., Koch C.C. Scripta Mater 2003;49: 429. Youssef K.M., Scattergood R.O., Murty K.L., Horton J.A., Koch C.C. Appl Phys Lett 2005;87: 091904(1–3). Zhang D.L., Raynova S., Koch C.C., Scattergood R.O., Youssef K.M. Mater Sci Eng A 2005;410–411: 375. Wang N., Wang Z., Aust K.T., Erb U. Mater Sci Eng A 1997;237: 150. Youssef K.M., Scattergood R.O., Murty K.L., Koch C.C. Scripta Mater 2006;54: 251.

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4 The processing of nanocrystalline steels by solid reaction F.G. CABALLERO and C. GARCÍA-MATEO, National Center for Metallurgical Research (CENIM-CSIC), Spain Abstract: A new generation of steels has been designed, which on transformation at low temperature (200–350°C), lead to a nanoscale microstructure, known as NANOBAIN. The microstructure consists of slender crystals of ferrite, whose controlling scale compares well with that of carbon nanotubes (20–40 nm). NANOBAIN presents the highest strength/toughness combinations ever recorded in bainitic steels (~2.5 GPa/40 MPa m1/2). These alloys show better mechanical properties of quenched and tempered low-alloy martensitic steels and match the critical properties of maraging steels, which are at least thirty times more expensive. These excellent properties are mainly a consequence of the formation of bainitic ferrite plates just a few nanometers thick without using severe deformation, mechanical processing or rapid cooling. This new nanostructured steel has significant potential in the transport, construction and offshore industries, as well as defence applications. Key words: steels, phase transformations, bainite, mechanical properties, atom probe tomography.

4.1

Introduction

Strength is a term that needs to be used with care. A material can be made stronger by reducing its size in order to avoid defects; carbon nanotubes fall into this category since their strength collapses as they are made into ropes with dimensions in the micrometer scale. Alternatively, strength can be achieved by packing the material with defects that interfere with the motion of dislocations. However, the deformation process by which the defects are introduced places limits on the dimensions in which the material can be produced. Another method of making strong materials is to reduce the scale of the microstructure using heat treatment. The gigapascal steels rely for their strength on fine martensitic microstructures, which are generated during rapid cooling. This also limits the size of the components that can be produced with uniform properties. This chapter reviews a novel method for making extremely strong and cheap nanocrystalline steel without using deformation, rapid heat-treatment or mechanical processing. Furthermore, the material can be produced in a form that is large in all its three dimensions, and has a plethora of other properties useful in engineering design. This new generation of ultrahigh-strength steels with desirable levels of toughness has awakened great interest in the technical and scientific community. The excellent properties achieved are mainly a consequence of the formation of nanoscale bainitic ferrite plates at very low temperatures. 85 © Woodhead Publishing Limited, 2011

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Temperatures at which iron diffusion occurs during bainite transformation are inconceivable. In that sense, the microstructure and its characterization at an atomic level represent a scientific milestone.

4.2

The finest grain structures in steels

The strength of materials is known to increase in inverse proportion to the crystal grain size following the Hall–Petch relationship. Thus, continuous efforts have been made to improve the strength of structural materials by refining crystal grain sizes by controlling recrystallization via thermomechanical treatments. In steels, fine grain size means 1–10 µm, and until recently effective processing techniques to reduce the grain size of these materials to less than 100 nm did not exist. Although mechanical milling and alloying can process the powders containing nanosized grains, grain growth cannot be suppressed during consolidation processes such as sintering and hot pressing. Therefore, processing bulk nanoscrystalline materials for structural applications still poses a big challenge, particularly in using an industrially viable process. Recent developments of various severe plastic deformation (SPD) processes,1,2 such as equal-channel angular pressing (ECAP), accumulative roll-bonding (ARB) and high-pressure torsion (HPT), have opened up new ways to produce steels with nanosized grain structure, and it is in principle possible to scale up ECAP and ARB to an industrial scale. The main advantage of these SPD techniques is that, unlike powder consolidation processes, the materials are free of porosity. The final grain size is typically less than 300 nm in most metals and alloys which gives rise to a significant strengthening; however, the main drawbacks of bulk nanoscrystalline materials are the lack of both ductility and thermal stability.3 Therefore, various attempts are being made to achieve both high strength and ductility by modifying the nanostructures. Many studies on SPD have been applied to single-phase materials to refine grain size. Applications of SPD to multiphase microstructures have also been attempted to explore the possibility of obtaining ultrafine composite nanostructures.4–10 One classical example of SPD of two-phase alloys can be seen in well-known pearlite wire, which is widely used as suspension cables, tire cords and fishing wires. By cold-drawing pearlite to a high strain of more than 4, the pearlite lamellar spacing is reduced to a few tens of nanometers, and a strength exceeding 3 GPa can be commonly obtained.11–13 A similar concept was used to develop the commercial steel wire known as Scifer, which has an ultimate tensile strength of 5.5 GPa and yet is very ductile in fracture.14–16 Scifer is made by drawing a dual-phase microstructure of martensite and ferrite in a steel with the composition of Fe-0.2C0.8Si-1Mn (wt.%) in the form of 10 mm diameter rods, into strands which individually have a diameter of 8 µm. This amounts to a huge deformation with a true strain in excess of 9. The dislocation cell size in the material becomes 10–15 nm. This is where much of the strength of Scifer comes from.15,16

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The main difficulty in using deformation to increase strength is that the deformation necessary to accumulate a large number density of defects limits the size and form of the product, in the case of Scifer to that of a strand. Deformation processes, such as ECAP and ARB, maintain the overall dimensions, but the range of shapes that can be achieved is limited.1,17–19 In general, there is still a large gap between SPD processes on the laboratory scale for fundamental research and their application in large-scale production. Combining plastic deformation and phase transformation has been widely used in conventional thermomechanical processes in steels.20,21 The most successful example is controlled rolling, with accelerated cooling for plates of low-C steels.21 In this process, the target of refinement is ferrite. The mechanisms of the microstructural refinement are recrystallization of austenite, enhanced nucleation of ferrite from deformed (unrecrystallised) austenite under large supercooling, and inhibition of grain growth of the obtained ferrite. Microalloying of Ti and/or Nb and precise control of rolling conditions (temperature, reduction and pass schedule) have realized a minimum average grain size of 5 µm.21 The fine-grained plates exhibit excellent toughness, as well as high strength. However, the minimum grain size of ferrite in bulk steels is still limited to around 5 µm. In a number of research projects carried out in late 1990s, the principle of controlled rolling was investigated thoroughly under more severe conditions. That is, the finishing rolling was carried out at a much lower temperature (approximately 500–700°C) in greater one-pass reduction of over 50%. As a result, a 1 µm grain size was achieved on the laboratory scale.22 What then is the theoretical minimum grain size that can be achieved using this technology? This question can be answered by noting that the excess energy stored in the form of grain boundaries cannot exceed the free energy 23 For an equiaxed change ∆Gγα V owing to the transformation of the austenite. polycrystalline grain structure, the grain boundary surface per unit volume SV – is related to the grain size L (mean lineal intercept) by the equation – SV = 2/L. Then the stored energy per unit volume due to the grain boundaries is:

[4.1]

where σ is the energy per unit area of boundary. The limiting grain size is obtained by equating this stored energy to the driving force:

[4.2]

For equiaxed austenite grains, it becomes:

[4.3]

It follows that the smallest ferrite grain size can be achieved when all of ∆GVγα is used up in creating α/α grain boundaries, so that:

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[4.4]

This relationship would have to be modified when the austenite is pancaked before transformation and there are other details such as crystallographic texture that need to be taken into account.23 – The variation in the limiting ferrite grain size (Lαmin) is shown in Fig. 4.1 as a function of ∆GVγα, calculated using equation (4.3) with σα = 0.6 J m–2; given the – absence of data, the 2σγ /Lγ term in equation (4.4) was set to zero. These calculations are presented as the ‘ideal’ curve in Fig. 4.1. The curve indicates that at large grain – sizes, Lαmin is sensitive to ∆GVγα and therefore to the undercooling below the equilibrium transformation temperature. However, reductions in grain size in the sub-micro range require huge values of ∆GVγα, meaning that the transformations would have to be suppressed to large undercoolings to achieve fine grain size. As shown in Fig. 4.1, the points are experimental data; in some cases it is assumed that the grain size quoted in the literature corresponds to the mean lineal intercept. The curves, marked low and high Mn, represent calculated values of – Lαmin after allowing for recalescence.23 Also plotted on Fig. 4.1 are points corresponding to measured ferrite grain sizes from the low and high Mn steels as – described by Yokota et al.;23 it is evident that Lα = Lγmin except at the lowest undercooling. Despite the large scattering, the data indicate that in spite of tremendous efforts, the smallest ferrite grain size obtained commercially using thermomechanical processing is stuck at ~1 µm. The reason for this is recalescence, which is the heating of the sample caused by release of the latent heat of transformation at a rate which is so high that it cannot easily be dissipated by diffusion. This rise in temperature owing to recalescence reduces the effective undercooling and therefore the driving force for transformation.23 It can been seen from Fig. 4.1 that the recalescence corrected curves show better agreement with the experimental data, indicating that at large

4.1  Plot of logarithm of ferrite grain size versus free energy change at Ar3 temperature. © Woodhead Publishing Limited, 2011



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undercooling, the achievement of fine grain size is limited by the need to dissipate enthalpy during rapid transformation. Displacive transformations lead to fine microstructures as a natural consequence of their atomic mechanisms. The martensite phase exhibits a lath morphology, which has been recognized to be heavily dislocated and hierarchically substructured into packets, blocks and laths.24,25 The transformation-induced dislocation density of lath martensite has been found in the order of the heavily deformed metals, with a lath thickness less than a few hundred nanometers.26 Very strong martensitic steels with strength >3 GPa already exist.27 This kind of martensite is produced in fairly large steel samples by rapid cooling from the austenitic condition. However, the dimensions can be limited by the need to achieve a uniform microstructure, a fact implicit in the original concept of hardenability. To increase hardenability requires the addition of expensive alloying elements. The rapid cooling can lead to undesirable residual stresses28,29 that can ruin critical components and have to be accounted for in component life assessments. Recently, an innovative design procedure based on phase transformation theory30 has been successfully applied to design strong, tough and affordable nanocrystalline steel without using deformation, rapid heat-treatment or mechanical processing. Furthermore, the material can be produced in a form that is large in all its three dimensions. The new material relies on a microstructure called bainite, which has been known since 1930; the novelty is in the alloy design which leads to the fine scale and controlled response to heat treatment.

4.3

Phase transformation theory: a powerful tool for the design of advanced steels, from micro to nano

It has long been known that alloying the steel with about 2 wt.% of silicon can in appropriate circumstances yield a carbide-free microstructure, which is a mixture of bainitic ferrite and carbon-enriched residual austenite. The silicon does not dissolve in cementite and hence suppresses its precipitation from austenite. Cementite is a cleavage and void-initiating phase that is best eliminated from strong steels. However, the full benefits of this carbide-free bainitic microstructure have frequently not been realized. This is because the transformation to bainitic ferrite stops well before the equilibrium carbon concentration in austenite is reached.31–34 There remain large regions of untransformed austenite that decompose under stress to hard, brittle martensite. The problem, which is essentially thermodynamic in origin, can be solved by altering the relative stabilities of the austenite and ferrite phases. The essential principles governing the optimization of such microstructures are now well established. Everything must be done that encourages an increase in the amount of bainitic ferrite so as to consume the blocks of austenite.35,36 With careful design, impressive combinations of strength and toughness have been reported for highsilicon bainitic steels.35–39 More recently, it has been demonstrated experimentally

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that models based on the atomic mechanism of displacive transformation can be applied successfully to the design of carbide-free bainitic steels, the only experiments needed are those to validate the theoretical predictions.40,41 Toughness values of nearly 130 MPa m1/2 were obtained for strength in the range of 1.6–1.7 GPa. This compares well with maraging steels, which are at least ninety times more expensive. The details of the design method, which is based on the discipline with which the atoms move during transformation, are as follows. Bainite grows without diffusion in the form of tiny plates known as ‘sub-units’; each plate grows to a limited size, which is determined by the plastic accommodation of the shape deformation accompanying transformation. One consequence of diffusionless growth is that the plates can be supersaturated with carbon, in which case the carbon partitions into the residual austenite soon after the completion of bainite growth. Diffusionless growth of this kind can only occur if the carbon concentration of the parent austenite is less than that given by the T o′ curve. The To curve is the locus of all points, on a temperature versus carbon concentration plot, where austenite and ferrite of the same chemical composition have the same free energy. The T ′o curve is defined similarly, but taking into account the strain energy associated with the fact that the shape deformation accompanying the displacive transformation is accommodated, at least partially, by plastic relaxation. The carbon content of the austenite at the termination of phase transformation for different temperatures in different steels is shown in Fig. 4.2. The calculated values for T o′ and paraequilibrium Ae 3′ phase boundaries are also plotted. Likewise, the same types of calculation, but not considering the stored energies of the related phases, are presented as To and Ae3. The measured concentrations in austenite at temperatures below the BS temperature (see Fig. 4.2) lie closer to the T o′ or To value boundaries and far from the paraequilibrium phase boundaries (Ae3 and Ae 3′ lines) for all the steels. The results are consistent with a mechanism in which the bainite grows without diffusion, but with excess carbon partitioning into the austenite soon after transformation. The reaction is said to be incomplete since transformation stops before the phases achieve their equilibrium compositions. In contrast, the measured carbon content of retained austenite at temperatures above the BS temperature in steels with a carbon content of 0.3 wt.% corresponds to that given by the Ae3 and Ae 3′ lines. The presence of Widmanstätten ferrite formed at the highest temperatures in these steels suggests that this trend is consistent with the difference between the growth mechanisms for Widmanstätten and bainitic ferrite formation, the former involving carbon diffusion control with equilibrium partitioning of carbon, and the latter involving that bainite initially forms having a full supersaturation of carbon and grows by a mechanism essentially displacive in nature.42 It follows that the maximum amount of bainitic ferrite that can form in the absence of carbide precipitation is limited by the T o′ curve; this is a severe limitation if large quantities of blocky austenite remain in the microstructure at the point where transformation stops. The design procedure avoids this difficulty

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4.2  Calculated phase boundaries for different steel grades together with X-ray experimental data representing the carbon concentration of the austenite that is left untransformed after cessation of the bainite/ Widmanstätten reaction.

in three ways: by adjusting the T o′ curve to greater carbon concentrations using substitutional solutes, by controlling the mean carbon concentration, and by minimizing the transformation temperature. It is worth pointing out that attempts have been made to interpret the T o′ criterion differently. One theory argues that the reason why the bainite reaction stops © Woodhead Publishing Limited, 2011

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prematurely is because of the plastic work done as the plate grows by a displacive mechanism overwhelms the driving force for transformation.43,44 However, the theory is derived incorrectly in that the calculated work is divided by the fraction of remaining austenite, whereas it is in fact per unit quantity of bainite. Furthermore, there is an upper limit to the amount of work done in plastic accommodation; this is the strain energy associated with an elastically accommodated plate, amounting to 400 J mol–1.45 An alternative interpretation46 requires local equilibrium at the interface, contradicting atomic resolution experiments that show the absence of substitutional solute partitioning.47,48 Returning now to the design, it is known that blocky austenite should be avoided to ensure good toughness. The size of these blocks (which may transform to brittle martensite under stress) must be less than or comparable to that of other fracture initiating phases such as non-metallic inclusions. A reduction in the scale of the microstructure enhances both strength and toughness; this leads naturally to the conclusion that the microstructure is best generated at low temperatures. The question then arises, what is the lowest temperature at which bainite can be obtained? In order to answer this question, one must be able to reliably calculate the highest temperature at which bainite can form. This requires a consideration of both nucleation and growth. Bainite can only form below the T o′ temperature when:

[4.5]

∆Gγα

where GSB  400 J is the stored energy of is the free energy change accompanying the transformation of austenite into ferrite without any change in chemical composition. The first condition therefore describes the limit to growth. The second condition refers to nucleation; thus, ∆Gm is the maximum molar Gibbs free energy change accompanying the nucleation of bainite. GN is a universal nucleation function based on a dislocation mechanism of the kind associated with martensite.42,49–50 The variation of GN with temperature is well behaved even for the high carbon steels of interest here.51 Together with the growth condition, the function allows the calculation of the bainite start temperature, Bs , from knowledge of thermodynamics alone. An example calculation is presented in Fig. 4.3, which reveals the important result that extraordinarily low transformation temperatures can be achieved because the bainite and martensite start temperatures remain separated. The rate of reaction is also important since transformation must be achieved in a realistic time. For this purpose, a method34 developed to allow the estimation of isothermal transformation diagrams can be used, with the chemical composition as an input. Calculated time–temperature–transformation (TTT) diagrams indicate the time required to initiate transformation. Such calculations also help design the hardenability of the alloy so as to avoid interfering reactions such as allotriomorphic ferrite and pearlite. mol–1

bainite42;

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4.3  Computed martensite-start, Ms, and bainite-start, Bs, temperatures in Fe-2Si-3Mn-C alloy system.

4.4

NANOBAIN steel: a material going to extremes

Low transformation temperatures are associated with fine microstructures, which in turn possess strength and toughness. The theory described above has been used to develop steels that transform to bainite at temperatures as low as 125°C, in timescales that are practical (Table 4.1). The low Bs temperature is a consequence of the high carbon concentration and, to a lesser extent, solutes such as manganese or chromium, which in the present context increase the stability of austenite relative to ferrite. The molybdenum is added to ameliorate any temper-embrittlement phenomena due to inevitable impurities such as phosphorus. The alloys all contain sufficient silicon to suppress the precipitation of cementite from any austenite. In the steels designated NANOBAIN 1 and 2 (Table 4.1), bainite can take between 2 to some 60 days to complete transformation within the temperature range 125– 325°C.52,53 In a commercial scenario it may be useful to accelerate transformation without losing the ability to utilize low temperatures. Certain elements increase the free energy change when austenite transforms and hence should accelerate its decomposition; hence, the cobalt and aluminium containing alloys in Table 4.1. Table 4.1  Compositions of NANOBAIN alloys, wt.% Steel NANOBAIN NANOBAIN (at.%) NANOBAIN NANOBAIN

C 1 2 3 4

Si

Mn

Cr

Mo

V

0.79 1.59 1.94 1.33 0.30 0.11 0.98 1.46 1.89 1.26 0.26 0.09 (4.34) (2.76) (1.82) (1.28) (0.14) (0.09) 0.83 1.57 1.98 1.02 0.24 – 0.78 1.49 1.95 0.97 0.24 –

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Co

Al

– –

– –

1.54 1.60

– 0.99

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4.4  Microstructure formed by isothermal transformation in NANOBAIN 2 at: (a) 200°C for a day; (b) 200°C for two days; and (c) 200°C for six days.

Micrographs after isothermal transformation of austenite to bainitic ferrite at 200°C at different time intervals in NANOBAIN 2 are illustrated in Fig. 4.4. After a day of holding time at 200°C, bainite transformation has not started and a mixture of martensite and retained austenite is obtained by quenching (Fig. 4.4 (a) ). © Woodhead Publishing Limited, 2011



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A longer annealing time (two days) at this temperature was required to obtain a significant amount of bainitic transformation, as shown in Fig. 4.4 (b). Transformation is completed after six days of holding time, when a fully bainitic microstructure (~90% bainite) is obtained (Fig. 4.4 (c) ). The calculated34,54,55 TTT diagrams for the initiation of transformation in NANOBAIN 1 and 2 are shown in Fig. 4.5, which also contain experimental data for the reaction times. The upper C-curve represents the onset of reconstructive transformations such as allotriomorphic ferrite and pearlite, whereas the lower curve is for bainite. The measured values for a detectable degree of transformation are in reasonable agreement with those calculated, except at the highest temperature (300–400°C) where the time period required is underestimated. X-ray analysis was used to estimate the quantities of retained austenite present at the point where transformation ceases (Fig. 4.6 (a) ). The retained austenite fraction is expected to increase for the higher transformation temperature because less bainite forms; this is in contrast to the situation with low-carbon alloys, where a larger fraction of bainite favours the retention of austenite because of the portioning of carbon into the austenite.

4.5  Calculated TTT diagrams for the initiation of transformation, and measured times for the commencement (filled points) and termination of reaction (open circles): (a) NANOBAIN 1; (b) NANOBAIN 2.

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The maximum amount of bainite that can be obtained at any temperature is limited because the carbon content of the residual austenite must not exceed that given by the T ′o curve. At that point, the enriched austenite can no longer transform into bainite. The carbon concentrations of the austenite and bainitic ferrite as determined from X-ray analysis for NANOBAIN 2 are also presented in Fig. 4.6. The evolution of carbon in austenite and bainitic ferrite during transformation at 200°C is shown in Fig. 4.6 (b). Similarly, the carbon content of the austenite and bainitic ferrite at the termination of bainite reaction for different transformation temperatures is shown in Fig. 4.6 (c). The measured carbon concentrations in austenite lie closer to the T o′ value boundary and far from the paraequilibrium phase boundary. This trend is

4.6  X-ray experimental data on: (a) volume fractions of retained austenite; (b) carbon content in bainitic ferrite and retained austenite of the microstructure obtained by isothermal transformation at 200°C for 2 to 10 days in NANOBAIN 2; and (c) X-ray results corresponding at the termination of bainite reaction for different transformation temperatures in NANOBAIN 2. Xo represents the overall carbon content of the steel. T o′ and the paraequilibrium A’3 curves were calculated according to Bhadeshia.55

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4.6  Continued.

consistent with a mechanism in which the bainite grows without any diffusion, but with excess carbon partitioning into the austenite soon after transformation. The reaction is said to be incomplete since transformation stops before the phases achieve their equilibrium compositions. The transmission electron micrograph in Fig. 4.7 illustrates a typical microstructure of low-temperature bainite, with slender plates that are incredibly thin and long, giving a most elegant fine scale structure, which is an intimate mixture of austenite and ferrite. Dislocation debris is evident in both the bainitic ferrite and the surrounding austenite. Extensive transmission microscopy failed to reveal carbides in the microstructure, only a few minute (20 nm wide and 175 nm long) cementite particles in the ferrite within NANOBAIN 1 transformed at

4.7  Transmission electron micrographs of microstructure obtained at 200°C for 15 days in NANOBAIN 2.

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190°C for two weeks.52 Quite remarkably, the plates formed at 200°C in Steel B (Fig. 4.7) have a width that is less than 50 nm, with each plate separated by an even finer film of retained austenite. It is this fine scale that is responsible for much of the tenacity of the microstructure, with hardness values in excess of 600 HV and strength in excess of 2.5 GPa.52 The dispersion of films of austenite undoubtedly helps render the steel tough. Analysis indicates that the largest effects on plate thickness are the strength of the austenite, the free energy change accompanying transformation and a small independent effect due to transformation temperature.56 In the present case, the observed refinement is a consequence mainly of high carbon content and the low transformation temperature on enhancing the strength of the austenite.

4.5

Accelerating the bainite reaction at low temperatures

Slow transformation gives the ability to transform large components to a uniform microstructure free from residual stresses or complex processing. Suppose, however, that there is a need for more rapid heat treatment. The transformation can easily be accelerated to complete the processing within hours (as opposed to days), by making controlled additions of substitutional solutes to the steel, such that the free energy change as austenite changes into ferrite is enhanced. There are essentially two choices: aluminium and cobalt, in concentrations less than 2 wt.%, have been shown to accelerate the transformation in the manner described.57 Both are effective, either on their own or in combination. They work by increasing the driving force for the transformation of austenite; they have therefore been added to make NANOBAIN 3 and 4, which should then transform more rapidly. Fig. 4.8 (a) shows the increase in the reaction rate due to the cobalt; the effect is particularly large when both elements are added. A further rate increment is possible by refining the austenite grain size (Fig. 4.8 (b)). An increase in the free energy change also means that a greater fraction of bainite is obtained, which may have the additional advantage of increasing the stability of the austenite.57

4.6

Characterizing nanocrystalline bainitic steels at the atomic scale

The complexity of bainite formation mechanism and kinetics, and the apparent diversity of its microstructural appearance, gives rise to disagreement in identifying its correct definition. However, the well-known difference in carbide distribution between bainite formed at high and low temperatures, viz. intralath and interlath respectively, appears to exist in a majority of steels and makes the classical nomenclature of upper and lower bainite useful, both in describing the microstructural appearance and in classifying the overall reaction mechanism.

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4.8  (a) Kinetics of bainite formation at 200°C in NANOBAIN 2–4 steels; (b) effect of prior austenite grain on bainite formation at 200°C in NANOBAIN 3 steel.

Both upper and lower bainite consist of plates of ferrite, known as sub-units, separated by cementite. The plates of ferrite grow in aggregates called sheaves of bainite. Within each sheaf, the plates of ferrite are parallel and share a common crystallographic orientation. The essential difference between upper and lower bainite is with respect to the carbide precipitation. In upper bainite, the bainitic ferrite is free of precipitation; carbides grow from the regions of carbon-enriched austenite, which are trapped between the sub-units of ferrite. In contrast, lower bainitic ferrite contains a fine dispersion of plate-like carbides within the bainitic ferrite plates. The carbide particles usually precipitate in a single crystallographic orientation such that their habit plane is inclined at ~60° to the plate axis. There are many observations that reveal that lower bainitic cementite forms within supersaturated ferrite by a displacive mechanism without the partitioning of substitutional solute.58 The cementite lattice is generated by the deformation of the ferrite crystal structure, at a rate controlled by the diffusion of carbon. The iron/substitutional solute content ratio thus remains constant everywhere and subject to that constraint, the carbon achieves equality of chemical potential; the cementite is then said to grow by paraequilibrium transformation. In contrast, the precipitation of carbides in upper bainite is a secondary process that does not interfere with the mechanism of formation of bainitic ferrite except

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in the sense that any precipitation from austenite will deplete its carbon content, thereby promoting further transformation. In fact, the precipitation of cementite from austenite during bainite formation can be suppressed using silicon as an alloying element because the driving force for precipitation is dramatically reduced when the cementite is forced to inherit the silicon present in the parent phase.59 The bainitic microstructure in high silicon steels, commonly known as carbide-free bainite, consists of fine plates of bainitic ferrite separated by carbonenriched regions of retained austenite. As mentioned above, extensive transmission electron microscopy (TEM) of this novel microstructure has failed to reveal carbide particles inside the bainitic ferrite. This is indeed an interesting observation, since at these temperatures, the steel with such high carbon levels would transform to a lower-bainitic microstructure. After extensive aging at 200°C for two weeks, just a few 20 nm wide and 175 nm long cementite particles have been observed inside a thicker bainitic ferrite plate in NANOBAIN 2.60 The difference between upper and lower bainite comes from a competition between the rate at which carbides can precipitate from ferrite and the rate with which carbon is partitioned from supersaturated ferrite into austenite.61 The precipitation of cementite from lower bainite can occur at temperatures below 125°C, in time periods too short to allow any substitutional diffusion of iron atoms. The long-range diffusion of carbon atoms is of course necessary, but because carbon resides in interstitial solution, it can be very mobile at temperatures as low as –60°C.62 The formation of cementite or other transition carbides of iron such as ε-carbide, in these circumstances of incredibly low atomic mobility, must differ from diffusional decomposition reactions. It has been suggested that63 the cementite lattice is generated by a displacive mechanism with paraequilibrium, i.e. a homogeneous deformation of supersaturated ferrite combined with the necessary diffusion of carbon. The X-ray diffraction analysis results in Fig. 4.6 (b) indicated that the carbon concentration in the bainitic ferrite was much higher than that expected from paraequilibrium thermodynamics between austenite and ferrite.60 This supersaturation was attributed to the trapping of carbon at the dislocations in the bainitic ferrite. Using transmission electron microscopy, Smith64 estimated a mean dislocation density of 4 × 1014 m–2 in a Fe-0.07C-0.23Ti wt.% alloy when isothermally transformed to bainite at 650°C. This relatively high dislocation density is attributed to the fact that shape deformation accompanying displacive transformations is accommodated partially by plastic relaxation.65 However, no direct observation has been yet reported of the interstitial carbon Cottrell atmosphere in bainitic ferrite. In this sense, atom probe tomography (APT) was used to characterize at the atomic scale bainitic microstructures formed at 200 and 300°C in NANOBAIN 2 bainitic steel. The large field of view and rapid analysis capability of this technique facilitated the analysis of dislocations in these materials.

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4.6.1 Solute distribution during transformation Five at.% carbon isoconcentration surface and concentration profiles from NANOBAIN 2 annealed at 200°C for four days are shown in Fig. 4.9. The distribution of carbon atoms in the analysis volume is not uniform and carbon-rich and carbon-depleted regions are clearly distinguishable. As no crystallographic information was available, the carbon-enriched regions of the atom maps are assumed to represent a region of austenite, as its carbon content is higher than the average value of 4.3 at.%, and the low carbon (< 1 at.%) regions indicate the ferrite phase. This figure shows an example of an austenite-ferrite interface for a transformation temperature of 200°C. For instance, comparison of APT results and the corresponding X-ray analysis for NANOBAIN 2 is presented in Table 4.2. In most cases, the APT results on carbon content of both bainitic ferrite and austenite are lower than those measured by X-ray. This is because APT estimate is a simple counting of atoms within the selected volume of matrix of ferrite or austenite that does not contain any carbon-enriched regions such as dislocations and boundaries, and not an average of a larger volume that may be enriched in carbon as in the X-ray estimate. However, both techniques confirm the small extent of carbon enrichment in the residual austenite compared to nominal carbon concentration of the steel and the high level of carbon in bainitic ferrite, well beyond that expected from paraequilibrium with austenite (~0.12 at.% C). APT results also indicate that the amount of carbon in bainitic ferrite increases as the transformation temperature decreases. It is also clear from the APT data in Fig. 4.9 that there is no significant segregation of either substitutional elements or carbon to the austenite–ferrite interface. Consistent with previous work,31 quantitative data confirms the absence of any partitioning of the substitutional elements between the phases involved. The results are fully consistent with the diffusionless transformation of austenite to bainite.66 The absence of any significant carbon build-up at the interface indicates that the interface must be semi-coherent, with a high degree of coherency, consistent with the shape change effect mentioned earlier. Thus, the interface may not provide a very large sink for carbon atoms.

Table 4.2  Carbon content in austenite and bainitic ferrite in NANOBAIN 2 steel Isothermal heat X-ray analysis Atom probe tomography treatment Austenite Bainitic Austenite Bainitic ferrite ferrite 200°C – 144 h 300°C – 8 h

(6.60 ± 0.44) at.% (2.92 ± 0.30) at.% (5.39 ± 0.18) at.% (0.62 ± 0.10) at.% (5.67 ± 0.44) at.% (1.37 ± 0.30) at.% (6.85 ± 0.22) at.% (0.52 ± 0.04) at.%

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4.9  Five at.% carbon isoconcentration surface and concentration profiles of selected volume showing austenite and ferrite regions obtained from NANOBAIN 2 transformed at 200°C during four days.

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4.6.2 Carbon trapped in defects A carbon atom map obtained from NANOBAIN 2 annealed at 200°C for two days is shown in Fig. 4.10. The carbon-enriched region at the top-left of the atom map represents austenite and the low carbon regions indicate the ferrite phase. Finally, the linear features with significant levels of carbon are speculated to be dislocations in the vicinity of a ferrite–austenite interface. The carbon, manganese, molybdenum and silicon atom maps of a selected volume orientated normal to a linear segment of the dislocation are also shown in Fig. 4.10. It is evident from these atom maps that dislocations only trap the carbon atoms, as originally suggested by Kalish and Cohen.67 The size of the Cottrell atmosphere in the vicinity of the dislocation was

4.10  Carbon atom map of dislocations in the vicinity of a ferrite– austenite interface (54 nm × 52 nm × 99 nm), and projected atom maps showing carbon segregation about dislocation in NANOBAIN 2 transformed at 200°C for two days.

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estimated from the envelope method68 to be approximately 5–6 nm. The average carbon level of the Cottrell atmosphere was estimated to be 7.4 ± 0.1 at.% C. This value is in good agreement with the prediction of Cochardt et al.69 of a saturation carbon concentration of 6–7 at.% in the region around the core. Wilde et al.70 also observed a maximum carbon concentration within a dislocation atmosphere of 8 at.% C from an energy-compensated optical position-sensitive atom probe analysis of a quenched and room temperature aged Fe-C alloy. The relatively high dislocation density associated with bainitic ferrite is often attributed to the fact that the shape deformation accompanying the displacive transformation is accommodated at least partially by plastic relaxation. Then the resulting dislocation debris introduced into the austenite can be inherited by any bainite that forms subsequently.65 Plastic relaxation may also follow in the bainite itself, since the yield stresses of both ferrite and austenite decrease with increasing transformation temperature. Plastic relaxation of the shape change has been observed experimentally, when pre-polished samples of austenite are transformed to bainite, the adjacent austenite surface does not remain planar but, instead, exhibits curvature that is characteristic of slip deformation.71 Observations of the transformation using hot-stage TEM revealed that the growth of bainite is accompanied by the formation of dislocations in and around the bainite,72 and direct observations of the austenite–ferrite interface also provide evidence of plastic accommodation in both phases.73 Sandvik and Nevalainen74 demonstrated that the austenite adjacent to the bainitic ferrite undergoes twinning deformation and that the density of twins increases as the transformation temperature decreases. It is known that impurities such as phosphorus, calcium and silicon boundaries can segregate on incoherent twin boundaries with high free volume.75–77 Carbon atom map in Fig. 4.11 shows a very fine scale modulation in NANOBAIN 2 transformed at 300°C for four hours. Results suggest that carbon is also segregated at microtwins in retained austenite (average carbon content of 5.3 at.%). It is believed that solute segregation on defects, as those presented in Figs. 4.10 and 4.11, plays an important role on carbon redistribution during bainite transformation. Dislocations associated with plastic relaxation in austenite are inherited by any bainite that forms subsequently, and segregation at dislocations is expected to bind and hence prevent or hinder the carbon atoms from diffusing out of the ferrite lattice. This explains the high level of carbon that exists in the bainitic ferrite after transformation and the small extent of carbon enrichment detected in the residual austenite. Moreover, the increase in the amount of carbon in bainitic ferrite as the transformation temperature decreases is consistent with the fact that the dislocation density of bainitic ferrite is higher the lower the reaction temperature.78

4.6.3 Cementite formation in lower bainite Matas and Hehemann79 first suggested that the initial carbide in lower bainite is ε-carbide, which is subsequently replaced by cementite. The rate at which the © Woodhead Publishing Limited, 2011



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4.11  Carbon atom map showing carbon segregation about microtwins in retained austenite for NANOBAIN 2 transformed at 300°C for four hours.

ε-carbide converts to cementite increases with temperature, but also depends on the steel composition. In fact, a high silicon concentration retards the reaction, as is commonly observed in the tempering of martensite.80 The detection of ε-carbide instead of cementite in lower bainite implies the existence of a carbon supersaturation in bainitic ferrite.81 However, ε-carbide is not always found as a precursor to the precipitation of cementite in lower bainite. Bhadeshia and Edmonds73 failed to detect ε-carbide in a high silicon medium carbon steel even during the early stages of the lower bainite transformation. This has been the case in the present investigation. Initially, TEM was unable to reveal carbide particles inside bainitic ferrite; however, after a large and equivalent set of accumulated APT results, cementite has been identified as the lower bainite carbide despite the high carbon and high silicon content of the steel. An example of carbide particle precipitated inside bainitic ferrite for NANOBAIN 2 transformed at 200°C for ten days is shown in carbon and silicon atoms maps presented in Fig. 4.12. The carbon level allows identifying the type of carbide precipitated inside bainitic ferrite (~25 at.% for cementite and ~30 at.% for ε-carbide). Beside the apparent low carbon concentration of cementite, it is clear from these results that paracementite is observed. In earlier APT works on steels, apparent low carbon

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4.12  Carbon and silicon atom maps showing cementite particle precipitated inside bainitic ferrite in NANOBAIN 2 transformed at 200°C for ten days.

concentrations of cementite were also reported.82–84 These results are consistent with those reported for cementite precipitation in martensite during the early stages of tempering.82,85 Although the carbon concentration changes at the cementite–ferrite interface, silicon does not change at all through the interface, indicating that the concentration of silicon is uniform throughout both phases. Since silicon does not partition and is expected to favour the precipitation of ε-carbide, the absence of ε-carbide precipitation in this high-carbon bainitic steel can be only rationalized in terms of carbon trapping at dislocations, as suggested by Kalish and Cohen.67 Thus, APT results confirm that the ε-carbide stage is missed in the precipitation sequence due to the high carbon tied up at the dislocations.

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The mechanical properties of nanocrystalline bainitic steels

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The hardness of the nanostructured bainite can be as high as 690 HV, with tensile strengths in excess of 2.2 GPa, compressive strength in excess of 3 GPa, ductility in the range of 5–30% and fracture toughness (KIC ) values up to 45 MPa m1/2. A summary of the mechanical properties obtained for NANOBAIN 3 and 4 steels is illustrated in Fig. 4.13. The obtained microstructures exhibit an extraordinary combination of properties, with yield strengths (YS) greater than 1.2 GPa, and ultimate tensile strengths (UTS) ranging from 1.77 to 2.2 GPa (Fig. 4.13 (a)), the latter in the case of the 200°C microstructure. Such a combination of properties

4.13  Transformation temperature dependences of (a) UTS and YS; (b) total elongation; (c) fracture toughness K IC in NANOBAIN 3 and 4 steels; and (d) engineering stress–strain curves at room temperature, of NANOBAIN 4 microstructure obtained following transformation at the temperatures indicated. © Woodhead Publishing Limited, 2011

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has never before been achieved in bainitic steels. KIC values and ductility both decrease as the strength increases (Fig. 4.13 (b) and 4.13 (c) ). The microstructures obtained by transformation at 300°C exhibit total elongation ~30% and fracture toughness of 44 MPa m1/2 and 51 MPa m1/2 for NANOBAIN 3 and 4 respectively, very high values if compared with those obtained by transformation at 200°C, where elongation is reduced by ~20% and toughness by almost half. The transformation temperature dependence of engineering stress versus strain curves for NANOBAIN 4 is shown in Fig. 4.13 (d). Deformation of bainitic microstructures at room temperature is characterized by continuous yielding, as might be expected from microstructures with unlocked dislocations introduced by the plastic accommodation of the shape change. Although there is evidence that ferrite retains an excess concentration of carbon, even after annealing, the majority of dislocations are believed to be mobile. The gradual yielding behavior sometimes persists after stress-relief heat-treatments. There are a variety of obstacles to dislocation motion (solute atoms, boundaries, thin films of retained austenite), each with a different ability to obstruct plastic deformation. Many of the obstacles are not uniformly distributed, so dislocations can penetrate at low stresses into obstacle-free areas giving rise to a gradual deviation from elastic deformation. Another scale of heterogeneity can arise when a representative fraction of softer phase is included in the microstructure, such as blocks of retained austenite. Plastic deformation at first focuses in the softer phase; the hard phase only begins to deform when the softer phase has strain hardened sufficiently to transfer load, therefore leading to a continuous yielding. As is evident in Fig. 4.13 (d), plastic deformation is uniformly distributed along the gauge length of the samples, showing little or no necking; in other words, most or all of the total elongation achieved is uniform elongation. There are several operative strengthening mechanisms that are expected to contribute to the microstructure strength: the excess carbon concentration in ferrite, the thickness of the bainitic ferrite plates and the ferrite dislocation density (Fig. 4.14). It has been found that there is a strong correlation between the carbon content and the calculated dislocation density, Fig. 4.15, which corroborates that carbon must be trapped at dislocations in the bainitic ferrite, as ATP revealed. Therefore, there may be no independent contribution of carbon in solid solution, but rather, through its effect on the mobility of dislocations. Theory indicates that the contribution to strength due to the size of the plates is given by ∆σ 115(L)–1,86–88 where L2t is the mean linear intercept in micrometers, and that due to the dislocation density89 is given by ∆σ 7.3410–6(ρ)0.5, where ρ is in m–2, being ∆σ in MPa. Figure 4.16 represents the contributions of the two strengthening mechanisms in both alloys after correcting by the corresponding bainitic ferrite fractions. It is easily shown that much of the strength of lowtemperature bainite is due to the extremely fine plates of ferrite. Thus, at the lowest transformation temperatures (200°C) with >80% of the finest bainitic ferrite present in the microstructures, the contribution is about 1.6 and 1.1 GPa for NANOBAIN 3 and 4 respectively; on the other hand, the increment due to

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4.14  Quantitative microstructure results on NANOBAIN 3 and 4 steels: carbon content in bainitic ferrite, its plate thickness and dislocation density obtained after isothermal transformation at different temperatures and times, ensuring that bainitic transformation was finished.

4.15  Plot showing the relation between ferrite dislocation density and its carbon content following transformation.

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4.16  Strengthening contributions versus transformation temperature after correcting by their corresponding bainitic ferrite fractions.

dislocations is about 0.5 GPa for both alloys. As the transformation temperature increases and the microstructures become coarser and less dislocated, these contributions become weaker, as Fig. 4.16 illustrates for the microstructure obtained after transformation at 300°C in both steels. It is difficult to separate the effect of retained austenite on strength in these steel from other factors. Qualitatively, austenite can affect the strength by transforming to martensite during testing, the transformation-induced plasticity (TRIP) effect. The low yield/ultimate tensile strength ratios (YS/UTS) in Fig. 4.13 (a) are due to the presence of austenite and the large dislocation density in the microstructure.90 Consequently, retained austenite increases the strain-hardening rate of the steel. Similarly, toughness and ductility are controlled by the volume fraction of retained austenite,74 ductile phase compared to the bainitic ferrite, and its ability to transform to martensite under strain. This effect strongly depends on the chemical composition and morphology of the retained austenite.73,91 Thus the microstructures obtained after isothermal heat treatment at 300°C, with austenite fractions of 0.25 and 0.37 for NANOBAIN 3 and 4 respectively, exhibit the best results in terms of total elongation and fracture toughness (Fig. 4.13 (b) and (c)) © Woodhead Publishing Limited, 2011



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when compared with the microstructures obtained after transformation at 200°C, with austenite fractions of 0.13 and 0.17 for NANOBAIN 3 and 4 respectively. Strain hardening is characterized by the incremental strain-hardening exponent defined as n = d(ln σ)/d(ln εp), where σ = kε pn represents the flow curve in the region of uniform true plastic deformation (εp) and k is the strength coefficient. The variation of the incremental work hardening exponent n as a function of true strain in NANOBAIN 3 transformed at different temperatures is shown in Fig. 4.17. The straight line corresponds to the instability criterion εp = n. It appears that the different strength-ductility combinations in these advanced bainitic microstructures are associated with completely different work-hardening behaviors. The large true uniform strains of specimen treated at 300°C are due to a high retained austenite fraction that continuously increases the incremental work-hardening n after a sharp decrease at low plastic strains. In the microstructure obtained by transformation at 250°C, after reaching a maximum n smoothly decreases until the onset of necking. For the microstructures obtained at 200°C the situation completely differs from that previously described at higher transformation temperatures: a high increase of n during the first stages of plastic deformation is followed by a drastic drop that ends at low levels of plastic deformation. The mechanisms occurring during tensile deformation can be explained by the correlation between the shape of n versus true strain curves and the rate at which retained austenite transforms to martensite under strain.92–95 The 200°C microstructure, with low fractions and lowest stability of the austenite, rapidly transform at very small strains. As a result, there is little benefit of the straininduced transformation. The situation changes as the fraction of more stable

4.17  Curves of the incremental work hardening exponent, n, of bainitic microstructures obtained in NANOBAIN 3 steel by transformation at different temperatures (200, 250 and 300°C) and tested at room temperature. The straight line represents the instability criterion.

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austenite increases in the microstructure. For 250°C microstructure, retained austenite starts to transform immediately after the initial maximum n, and transformation proceeds until the instability criterion is reached. On the other hand, high fractions of very stable austenite are present at 300°C microstructures, as a result, transformation starts well after the maximum n and continues progressively up to necking. Finally, the properties of the present alloys are compared against published data in Fig. 4.18,39,96 highlighting the fact that novel bainitic steels exhibit an

4.18  Comparison of ultimate strength versus fracture toughness of: (a) conventional quenched and tempered steels (QT), maraging steels, other bainitic steels39 and NANOBAIN steels; and (b) strength versus total elongation of conventional steels96 and NANOBAIN steels. Note: IF: interstitial free, CMn: carbon manganese, BH: bake hardenable, IS: isotropic, DP: dual phase, CP: complex phase.

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exceptional combination of mechanical properties that places this new type of microstructures in an advantageous position for different applications such as transport, construction and offshore industries, as well as defence applications.

4.8

Conclusion and future trends

It is clear that bainite can be obtained by transforming at very low temperatures. There is then very a low possibility that iron or substitutional solutes will diffuse. A consequence of the low transformation temperature is that the plates of bainite are extremely fine, 20–40 nm thick, making the material very strong. This is a bulk nanocrystalline material that is cheap and can be obtained without severe deformation processing. When this feature is combined with the fact that the plates of ferrite are interspersed with austenite, it becomes possible to create novel strong and tough steels. In this regard, the potential for industrial application is large because the alloys are routinely manufactured. As is always the case, there remain many parameters that have yet to be characterized, for example the fatigue and stress corrosion properties. Moreover, the alloys designed so far either transform slowly over a period of many days, or have to be alloyed with cobalt and aluminium in order to accelerate transformation. In the future, it is possible that rapid transformation could be engineered by controlling the manganese concentration. The key will be to do this without compromising properties. Finally, high-carbon steels are difficult to weld because of the formation of untempered, brittle martensite in the coarse-grained heat-affected zones of the joints. The martensite fractures easily, leading to a gross deterioration in the structural integrity of the joint. For this reason, the vast majority of weldable steels have low-carbon concentrations. Therefore, it would be desirable to make the low-temperature bainite with a much reduced carbon concentration. Preliminary calculations indicate that carbon is much more effective in maintaining a difference between the MS and BS temperatures than are substitutional solutes which reduce ∆Gγα simultaneously for martensite and bainite. Substitutional solutes do not partition at any stage in the formation of martensite or bainite; therefore, both transformations are identically affected by the way in which the substitutional solute alters the thermodynamic driving force. It is the partitioning of carbon at the nucleation stage that is one of the distinguishing features of bainite when compared with martensite. This carbon partitioning allows bainite to form at a higher temperature than martensite. This advantage is diminished as the overall carbon concentration is reduced. These results are discouraging from the perspective of designing a low-carbon bainite with a fine microstructure obtained by transforming at low temperatures. However, the issue is worth investigating further since the original theory has a number of approximations. In the future, the Fe-Mn-Ni-C system should be explored in the context of these calculations, bearing in mind the desire to design low carbon alloys in which the BS temperature is suppressed.

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Sources of further information and advice

Research groups working on NANOBAIN MATERALIA Research Group, CENIM-CSIC, Madrid, Spain http://www. cenim.csic.es/materalia/PaginaWebEnglish/WebMateralia.html Phase Transformations & Complex Properties Research Group, University of Cambridge, Cambridge, UK http://www.msm.cam.ac.uk/phase-trans/

Key books to consult: R.W.K. Honeycombe and H.K.D.H. Bhadeshia: Steels, Microstructure and Properties. Edward Arnold, London (1995). H.K.D.H. Bhadeshia: Bainite in steels, 2nd ed. Institute of Materials, London (2001). M.K. Miller: Atom Probe Tomography. Kluwer Academic/Plenum Press, New York (2000).

4.10 Acknowledgements It is a special pleasure to acknowledge Professor H.K.D.H. Bhadeshia for his support guidelines on NANOBAIN research and development. Research at the Oak Ridge National Laboratory SHaRE User Facility was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, US Department of Energy.

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Ballinger N.K., Gladman T. Met Sci 1981; 15: 95. Jacques P.J., Girault E., Harlet P., Delannay F. ISIJ Int 2001; 41: 1061. Itami A., Takahashi M., Ushioda K. ISIJ Int 1995; 35: 1121. Sakuma Y., Matlock D.K., Krauss G. Metall Trans 1992; 23A: 1233. Sugimoto K., Kobayashi M., Hashimoto S. Metall Trans 1992; 23A: 3085. World Auto Steel. World Steel Association. Middletown (OH): Available from: http:// www.worldautosteel.org [accessed 1 July 2009].

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5 The processing of bulk nanocrystalline metals and alloys by electrodeposition U. ERB, University of Toronto, Canada, G. PALUMBO and J.L. McCREA, Integran Technologies Inc., Canada Abstract: This chapter deals with the synthesis of nanocrystalline metals, alloys and metal matrix composites using the electrodeposition method. The first part of the chapter covers the fundamentals of electrodeposition from aqueous solutions and reviews experimental details for several specific nanomaterials. This will be followed by a summary of mechanical, corrosion and other properties reported for these materials over the past two decades. The chapter includes several examples of industrial applications for these advanced materials. Key words: electrodeposition of nanomaterials, metals, alloys and composites, mechanical, corrosion, electrical, thermal and magnetic properties, industrial applications.

5.1

Introduction

There are five general approaches to making nanocrystalline materials: solid state processing, liquid phase processing, vapor phase processing, chemical synthesis and electrochemical synthesis. For each general approach, many different specific methods have been developed to produce nanomaterials in different shapes including thin films, powders, nanodots and nanowires or compact three-dimensional bulk nanomaterials. This chapter deals with electrodeposited bulk nanomaterials. Electrodeposition belongs to the general group of electrochemical synthesis methods. Other methods in this group of techniques include electroless deposition, galvanic displacement deposition or immersion plating, and electrodeposition under oxidizing conditions. The chapter will focus on recent advances in electrodeposition from aqueous solutions. Electrodeposition from organic solutions, molten salts or ionic liquids will not be covered here. Furthermore, the main focus of this review will be on metals, alloys and metal-matrix composites. Electrodeposition of organic films, conductive polymers, semiconductors and oxides will not be included in this chapter. Electrodeposition has been used for more than a century in several application areas including primary metal production (e.g. electrowinning and electrorefining), direct manufacturing (e.g. electroforming of large structural objects or small components for microelectromechanical systems) and surface finishing (e.g. decorative coatings, corrosion and wear-resistant coatings, functional coatings).1–3 118 © Woodhead Publishing Limited, 2011



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There are numerous reports in the literature that have dealt with electrodeposits with extremely small crystal size and the property enhancements that can be achieved in such materials by grain size reduction. However, it was only throughout the 1980s that the full potential of electrodeposition as a production route for nanocrystalline materials was recognized.4,5 The earliest patents on nanomaterials made by electrodeposition were issued in the mid 1990s.6,7 The superior properties first observed on nanocrystalline nickel electrodeposits resulted in one of the world’s earliest large-scale industrial applications of nanomaterials in 1994: the so-called electrosleeve process for in situ repair of nuclear steam generator tubing.8–10 This process has been implemented in both Canadian CANDU and US pressurized water reactors. Essentially, this application is a nanocrystalline Ni-P microalloy electroform (~ 1 mm in thickness, 50–100 nm grain size) deposited on the inside of steam generator tubes to effect a complete structural repair at sites where corrosion, stress corrosion cracking and other degradation phenomena compromised the structural integrity of the tubes. The early success of nanocrystalline metal electrodeposits accelerated 1) research efforts in this area by numerous groups around the world, and 2) the development of applications in several sectors, including energy, automotive, aerospace, consumer product and defense industries.11–18 Several review articles on the electrodeposition method have been published over the past decade.19–25

5.2

Electrodeposition methods

The four most important components of a typical electroplating system are 1) an appropriate electrolyte, often referred to as the plating bath, 2) a power supply, usually either a direct current (DC) or pulsed current (PC) power supply, 3) the cathode onto which the material is electrodeposited and 4) the anode. Figure 5.1 shows that, in addition, a heater and electrolyte stirring are often used, mainly to enhance the diffusion of metal ions and other species in the plating bath.

5.2.1 Electrolyte The electrolyte is an aqueous solution containing several ingredients. The most important is the salt of the metal to be deposited on the cathode. Metal salts include sulfamates, sulfates, chlorides, cyanides, fluoroborates, pyrophosphates and others. These salts provide the initial metal ion concentration in the plating bath. Many baths contain several salts of the same metal. For example, in the so-called Watts nickel plating bath both nickel sulfate and nickel chloride are used, the latter in a much smaller concentration. In addition to providing some Ni2+ ions, the main role of the nickel chloride is to increase the bath conductivity and to aid in the nickel anode dissolution. For alloy deposits that contain two or more metals, salts of each component are added to the bath. For example, to electrodeposit Zn-Ni binary alloys a bath

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5.1  Schematic diagrams showing experimental set-up (top) and current versus time curve (bottom) for conventional direct current plating.

containing both zinc chloride and nickel chloride can be used. Other alloying elements include non-metals such as phosphorus or boron, which must also be added to the bath in the right concentration. An example is Ni-P deposited from a plating bath containing nickel sulfate and phosphorous acid, the latter as the source of phosphorus. Composite deposits can be made by adding a second phase in the form of fine particles, whiskers or fibres to the electroplating bath. The second phase is then codeposited with the metal matrix to form the composite material. Examples are Ni-SiC, Ni-carbon nanotubes, Cu-Al2O3, etc. Many plating baths contain buffers. Buffers have the property that they maintain the plating bath pH by neutralizing both acid and base changes in the solution. Examples of buffers used in metal plating are boric acid (H3BO 3) for nickel or zinc–nickel plating at low pH or potassium orthophosphate/phosphate (KH 2PO 4/ K3PO 4) mixtures for plating of palladium from high pH solutions.1

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Metal ions in an aqueous solution are usually hydrated, i.e. surrounded by several water molecules (solvation sheath), usually expressed as shown in equation 5.1.

[5.1]

For example, for Ni2+ the number x is either 4 or 6.1 When water molecules are replaced by other ions or molecules (i.e. complexing agents) the metal is referred to as a metal ion complex. Complex formation can considerably change the properties of the metal ions in the solution and in particular the metal ion deposition, which involves complex dissociation to form free metal ions. Complexing agents, also referred to as ligands, are particularly important in the co-deposition of alloys where they help to bring the deposition potentials/activities of the individual metals closer together. Complexed ions are usually written as follows:

[5.2]

Examples are:

[5.3]

[5.4]

Many complexing agents have been used in alloy plating. For example, for Ni-Fe-Cr ternary alloys alone, the list is very large, including di-methyl formamide (DMF, HCON(CH 3)2), ethylene-diamine-tetra-acetate (EDTA, (HO 2CCH 2)2 NCH 2CH 2N(CH 2CO 2H)2), sodium citrate (Na3C6H5O7 × 2 H2O), urea (NH 2 CONH 2) and glycolic acid (HOCH 2CO 2H). Other bath ingredients include addition agents to achieve specific deposit properties in terms of brightening, stress relief, hardening, leveling, grain refining or surface smoothing. One particular example is the use of saccharin (benzoic sulfimide (C7H5NO 3S)) in nickel electroplating. Saccharin in this plating bath has a dual purpose. It is a grain refiner and stress reliever at the same time, typically added to the plating bath in low concentrations of about a few grams per liter.1

5.2.2 Power supplies in conventional electroplating Most electroplating operations use direct current plating as shown in Fig. 5.1. Direct current is usually supplied from rectifiers, although older rotating DC generators may still be in operation in some industries. In direct current plating, an important plating variable is the current density, I, usually expressed in units of mA/cm.2 Electrodeposition often involves more than one single electrochemical reaction at each the anode and cathode. For example, during the electrodeposition from a low pH bath containing Mez+ and H+ ions, the following reactions occur at the cathode:

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[5.5]



[5.6]

The metal deposition process involves various steps including diffusion of ions from the bulk of the electrolyte to the cathode and through the Nernst diffusion layer, formation of the first adions on the cathode surface, surface diffusion of the adions, nucleation of the crystals and growth of the crystals. When charge transfer associated with the metal ion deposition is the slow, rate-determining step, equation 5.7 gives the limit in terms of current density, IL , which is controlled by the transport of Mez+ ions from the bulk of the electrolyte to the cathode:1

[5.7]

where D is the diffusion coefficient of the deposited Mez+ species, F is the Faraday constant, z the number of electrons involved in the metal ion reduction, Cb the concentration of Mez+ ions in the bulk electrolyte and δ the diffusion layer thickness. Direct current electrodeposition at current densities higher than the limiting current density usually produces poor deposits as the process then involves cathodic reactions other than metal ion deposition. The limiting current density is strongly dependent on solution agitation. For example, for the case of a rotating electrode it has been shown1 that the limiting current density changes with the angular speed of rotation (ω) as follows:

[5.8]

where ν is the kinematic viscosity of the electrolyte, Cb the concentration of the solution and a is the rotating disk surface area. The weight of the deposit is given by the following equation:

[5.9]

where I is the applied current density, t is the plating time, A is the atomic weight of the deposited metal, z the number of electrons, and F is the Faraday constant. The current efficiency (CE) of a plating process is a measure of the actual metal deposition (Wmetal) relative to the theoretically possible metal deposition (Wtotal), when no other reactions occur at the cathode.

[5.10]

In most cases the current efficiency is less than 100%, indicating that other reactions do indeed occur at the cathode such as the hydrogen evolution reaction given in equation 5.6. For example, nickel plating from a Watts-type bath has a high current © Woodhead Publishing Limited, 2011



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efficiency of more than 90%, which means that less than 10% of all electrons in the process are used to produce hydrogen gas. On the other hand, the current efficiency for chromium plating is much lower, typically of the order of 10–30%.26

5.2.3 Cathodes and cathodic reactions When the purpose of electrodeposition is to create a permanently modified surface, the cathode is usually the finished workpiece. Electroplating is then carried out until the required coating thickness is reached. Subsequently the workpiece is removed from the plating bath, rinsed and dried. Typical plating operations include rack plating, barrel plating, reel-to-reel plating and brush plating. On the other hand, in processes such as electroforming27–29 the cathode is used only as a temporary mandrel or mold to deposit the material in the shape of a specific final object. Following the electrodeposition process the electroformed object is separated from the mold by mechanical means. The mold can then be reused to deposit the next piece either in batch processing (Fig. 5.2) or as a continuous process such as in foil plating (Fig. 5.3). Titanium or steel cathodes are frequently used in such processes. The cathodic reactions in terms of overall metal deposition are often given as in equation 5.5. However, it should be noted that the reactions can be much more complex involving several intermediate steps. For example, for the electrodeposition of Ni from a Watts-type bath, the cathodic reaction given in equation 5.11 is usually presented:

[5.11]

However, it is more likely that deposition involves the following reactions:30,31

5.2  Schematic diagram showing net-shape manufacturing of an electroformed product. Source: Courtesy of Nickel Development Institute, Toronto, Canada.

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[5.12] [5.13]

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5.3  Schematic diagram showing continuous electrodeposition of nanocrystalline sheet/foil. Source: Courtesy of Integran Technologies, Inc., Toronto, Canada.



[5.14]

5.2.4 Anodes The anode completes the electric circuit in the plating cell (Fig. 5.1). Two types of anodes are typically used. The first type is a dissolvable anode of the same material as the electroplate, which replenishes the bath with metal ions as they are deposited on the cathode. Often the anode material is contained in a mesh basket made of titanium (Fig. 5.1), the latter being inert in many electroplating baths because of the protective titanium oxide layer on the surface. Anode material is periodically replenished in the anode basket. The second type of anode is referred to as the dimensionally stable anode (DSA). Supplied as sheet or mesh, these anodes are made of platinum coated/clad titanium or niobium with platinum thicknesses typically of the order of 0.1–0.25 mm. These anodes are chemically inert and do not replenish the plating bath with metal ions. Therefore, periodic additions of metal salts to the plating bath are required to maintain the ion concentration within a certain operating range.

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5.2.5 Structure evolution in conventional electrodeposits Under conventional electroplating conditions, the microstructural evolution with increasing deposit thickness is as shown in Fig. 5.4. Initially, numerous crystals are nucleated on the cathode, which usually have different crystallographic orientations with respect to the substrate material. With increasing deposit thickness there is a competition between nucleation of new crystals and growth of existing crystals. Many operating conditions (e.g. low current density) promote crystal growth where certain crystal orientations grow faster than others. As a result, the initial fine-grained structure changes with increasing deposit thickness to a large-grained, often columnar grain structure as seen in Fig. 5.4 (b) for an iron deposit. The grain size in the initial layer is very small and cannot be easily resolved in the etched cross-section. However, the columnar large grained structure that developed with increasing deposit thickness is clearly visible in Fig. 5.4 (b). It should be noted that the thickness of the initial fine-grained structure is often found to be strongly dependent on the pH of the electrolyte. For example, for nickel deposited from a Watts-type bath, the thickness decreased from about 150 µm at a pH of 0.5 to about 20 µm at a pH of 3.0 and completely disappeared at a pH of 3.5.32

5.2.6 Structure evolution in nanocrystalline electrodeposits It has been shown that nanocrystalline metals can be produced by electrodeposition under electrochemical conditions that promote crystal nucleation and suppress crystal growth.6,7,33,34 The conditions leading to massive nucleation of crystals can be achieved by selecting plating parameters that 1) allow for very high

5.4  Schematic diagram (a) and cross-sectional scanning electron micrograph (b) of an iron electrodeposit showing grain size and shape evolution with increasing deposit thickness. Arrows indicate growth direction.

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deposition rates and 2) reduce the diffusion of adatoms over the surface of the growing deposit. The current density applied during plating has two important effects on electrocrystallization. It increases the rate of metal ion reduction on the surface and reduces the critical crystal nucleation size, rc, which is inversely proportional to overpotential, η/current density, I, as shown in the classical Gibbs–Kelvin equation:35

[5.15]

where σ is the interfacial tension of the metal/solution interface, M the molecular weight, ρ the density and z · F the molar charge. The effect of over-potential/ current density on the critical crystal size is shown schematically in Fig. 5.5 in the form of free energy versus crystal size graphs. Figure 5.5 clearly shows that higher current density results in smaller crystal sizes. However, conventional DC plating is limited by the limiting current density (equation 5.7) above which electrochemical reactions other than metal deposition

5.5  Effect of over-potential/current density on critical crystal nucleation size.

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occur on the cathode. For this reason, pulsed current electrodeposition was introduced,6,7,33 as shown schematically in Fig. 5.6. In this case the current, Ipeak, during the current on time (Ton) can be significantly higher than the limiting DC current density. However, in order to replenish the double layer with metal ions by diffusion from the bulk of the electrolyte before other cathode reactions begin to dominate, the current is turned off for a certain period of time, Toff. Usually Toff is longer than Ton. The important electrical parameters during pulse plating include the pulse frequency, f, the duty cycle, θ, and the average current density, Iave:

[5.16]

5.6  Schematic diagrams showing experimental set-up (top) and current versus time curve (bottom) for pulsed current plating.

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[5.18]

More recent research efforts have concentrated on producing electrodeposited nanomaterials with different structure types. These include structurally graded materials in which the grain size changes in cross-section, materials with broader or bimodal grain size distribution and nanocomposites consisting of two or several distinct phases36 or nanotwinned electrodeposits.37 Such structures allow for interesting property optimizations, such as high strength combined with high ductility or high electrical conductivity.

5.3

Examples of nanocrystalline metals and alloys prepared by electrodeposition

As pointed out in section 5.1, there have been numerous early studies on electrodeposited metals with extremely fine grain size, however, without particular emphasis on identifying in a systematic way those plating parameters that would lead to nanocrystalline materials. The first alloys that were studied with emphasis on nanocrystalline material formation were Ni-P electrodeposits.4,5 Earlier studies had shown that these alloys could be produced with both conventional polycrystalline and amorphous structures.38 An electrolyte and plating conditions as shown in Table 5.1 were used to study nanocrystal formation.4,5 As can be seen from this table, electrodeposition was carried out using DC plating and the main variable was the concentration of phosphorous acid (H3PO 3) in the plating bath. It was shown that the phosphorus content in the electrodeposit increased with increasing phosphorous acid concentration in the plating bath, likely by the following reactions39 in addition to the reactions for Ni reduction given in equations 5.11 through 5.14:

[5.19]

Table 5.1  Electrolyte composition and plating conditions used for the synthesis of nanocrystalline Ni-P alloy deposits4,5 Compound

Concentration (g/l)

Plating conditions

Ni2SO 4 × 7H2O NiCl2 × 6H2O

150 45

pH T (°C)

1.5 80

IDC (mA/cm2) Ipeak(mA/cm2) Ton(msec) Toff (msec)

100 – – –

H3PO 4 50 H3PO 3 0–40

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[5.20]



[5.21]

The resulting deposits were supersaturated solid solutions of P in Ni, with P concentrations up to 24 at.% for the highest concentration of phosphorous acid in the plating bath. It was further shown that the structures of the deposits were crystalline for low P-concentrations in the deposit, less than 4 at.%. On the other hand, deposits containing more than ~ 15 at.% P were amorphous. For the intermediate concentration range, rapid grain size reduction was observed and nanocrystalline deposits with grain sizes down to less than 3 nm and towards the amorphous limit were observed with increasing phosphorus content. Figure 5.7 shows brightfield and darkfield transmission electron micrographs of a Ni-5.2 at.% P deposit with an average grain size of 6.1 nm. Since the early 1990s numerous other nanomaterials have been produced by electrodeposition, many of which are summarized in Table 5.2. These include pure metals such as Ni, Co, Pd, Cu and Zn, binary and ternary alloys including Ni-Zn, Co-W, Co-Fe, Ni-F-Cr and Ni-Zn-P, and composite materials, for example Ni-Al2O3, Ni-SiC, Ni-P-BN or Ni-carbon nanotubes. It should be noted that many bath formulations and electroplating parameters have been developed for different materials by various research groups. In the following examples details will be given for several specific materials produced in our laboratories over the past 20 years. Table 5.3 summarizes the important electrochemical conditions used in the synthesis of nanocrystalline nickel produced from a Watts-type electrolyte.33 Note that these materials were produced by pulsed current deposition using a peak current density of 1900 mA/cm2, which is about 4–5 times higher than the limiting DC current density for nickel plating. In addition, the plating baths contained

5.7  Brightfield (a) and darkfield (b) transmission electron micrographs of a Ni – 5.2 at.% P electrodeposit with an average grain size of 6.1 nm in planar section.

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Nanostructured metals and alloys Table 5.2  Examples of nanocrystalline metals, alloys and metal matrix composites that have been produced by electrodeposition Material

References

Material

References

Ni Co Pd Cu Zn Ni-P Ni-Fe Ni-Zn Co-W Co-Fe Pd-Fe

[6, 33] [6, 40] [41] [40, 42] [43] [4, 5] [44, 45] [46, 47] [48] [49] [50]

Ni-Fe-Cr Ni-Zn-P Co-Fe-P Ni-SiC Ni-Al2O3 Cu-Al2O3 Ni-P-BN Ni-MoS2 Ni-Al (particles) Ni-Nanocarbon tubes

[51–53] [54] [55] [56, 57] [58, 59] [60] [18] [18] [61] [62]

Table 5.3  Electrolyte composition and plating conditions used for the synthesis of nanocrystalline Ni deposits33 Compound

Concentration (g/l)

Ni2SO 4 × 7H2O 300 NiCl2 × 6H2O 45 H3BO 3 45 C7H5NO 3S 0–10

Plating conditions pH T (°C) IDC (mA/cm2) Ipeak(mA/cm2) Ton(msec) Toff (msec)

2.5 65 – 1900 2.5 45.0

saccharin (C7H5NO 3S) in various concentrations (0–10 g/l) as a grain refiner. Figure 5.8 presents scanning electron microscope (SEM) micrographs showing the surface morphology of deposits without and with saccharin additions. These micrographs clearly show that in the absence of saccharin (Fig. 5.8 (a) ) large crystals with sizes in the micrometer range are obtained. These deposits exhibited a relatively large surface roughness and dull appearance. With increasing saccharin concentration the surface morphology changed to a more colony-type structure in which individual grains cannot be resolved in the SEM (Fig. 5.8 (b) ). Transmission electron microscopy was used to determine the grain size of the deposit as a function of saccharin concentration in the bath; the results are given in Table 5.4. A small addition (0.5 g/l) of saccharin is sufficient to reduce the crystal size from >1µm to about 40 nm. Further increases in saccharin additions to 5 g/l reduced the grain size further to about 10 nm. Even higher saccharin concentrations (10 g/l) had no major additional effect on grain size. Figure 5.9 shows a schematic diagram and a brightfield transmission electron micrograph of a nanocrystalline nickel electrodeposit in cross-section through the

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5.8  Scanning electron micrographs showing surface structure of electrodeposited polycrystalline nickel without saccharin (a) and nanocrystalline nickel with a saccharin addition of 5.0 g/l in the plating bath (b). Table 5.4  Effect of saccharin concentration on grain size and sulfur content of nanocrystalline nickel electrodeposits produced from a Wattstype plating bath33 Saccharin concentration (g/l) Grain size (nm)

Sulfur concentration (ppm)

  0 >1000   0.5 40   2.5 20   5.0 10 10.0   9

<100 750 1200 1550 1650

5.9  Schematic diagram (a) and cross-sectional brightfield transmission electron micrograph (b) of a nickel deposit showing relatively uniform and equiaxed nano grain structure. Arrows indicate growth direction.

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deposit and the substrate. In this case the saccharin concentration in the bath was 5.0 g/l. In comparison with the iron deposit presented in Fig. 5.4, this nickel electrodeposit shows a relatively uniform grain size of about 10 nm throughout the entire deposit thickness. No transition from initially small grain size to large, columnar grain size was observed here. In other words, the combination of pulseplating at high current density and the addition of saccharin as a grain refiner maintained the plating conditions that result in massive nucleation, regardless of deposit thickness. Increasing saccharin concentration in the plating bath also resulted in higher sulfur concentrations in the electrodeposits, increasing from less than 100 ppm for saccharin-free electrolyte to about 1650 ppm at 10 g/l of saccharin additions (Table 5.4). The uptake of S in the electrodeposit is related to the formation of breakdown products for the saccharin molecule during plating. This phenomenon has been studied in great detail for electrodeposits produced from saccharincontaining plating baths.3 One of these breakdown products is benzamide (C7H7NO) shown in Fig. 5.10. It should be noted that sulfur impurities from the use of saccharin additions in the electrolyte can have detrimental effects for some properties of nanocrystalline nickel. In such cases, sulfur-free additives can be used, e.g. EDTA: ethylene-diamine-tetra-acetate.23

5.10  Benzamide (top) is one of the breakdown products from benzoic acid sulfimide (bottom).

Table 5.5  Electrolyte composition and plating conditions used for the synthesis of nanocrystalline Co-W alloy deposits48 Compound

Concentration (g/l)

CoSO 4 × 7H2O 60 Na2WO 4 × 2H2O 130 KNaC4H4O6 380 NH 4Cl 50 NH 4OH pH adj.

Plating conditions pH T (°C) IDC (mA/cm2) Ipeak(mA/cm2) T on(msec) Toff (msec)

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Table 5.6  Electrolyte composition and plating conditions used for the synthesis of nanocrystalline Zn-Ni deposits47 Compound

Concentration (g/l)

ZnCl2 50–300 NiCl2 × 6H2O 50–300 H3BO 3 40 CH 3(CH 2)11OSO 3Na 0.1

Plating conditions pH T (°C) IDC (mA/cm2) Ipeak(mA/cm2) Ton(msec) Toff (msec)

3.5 25–80 – 1000–3600 0.2–1.0 2.0–5.25

Examples for electrolyte composition and plating conditions for two binary alloys, Co-W48 and Zn-Ni46,47 are shown in Table 5.5 and Table 5.6, respectively. For the case of Co-W alloys a 24 factorial design approach was used to identify plating conditions that would yield polycrystalline, nanocrystalline and amorphous microstructures. The low and high values for temperature, Ipeak, Ton and Toff are given in table 5.5. The electrolyte contained cobalt sulfate (CoSO 4) and sodium tungstate (Na2WO 4) as the sources for cobalt and tungsten ions, respectively. Rochelle salt (KNaC4H4O6) and ammonium chloride (NH 4Cl) were added as complexing agents. Ammonium hydroxide was used to adjust the pH of the solution to 8.5. The results of this study have shown that for this particular system the change in bath temperature has little effect on the microstructure of the deposits. On the other hand, the low current density generally produced polycrystalline deposits as expected. At the low Toff value the amorphous structure was favoured, while at high Toff the nanostructure was predominant. Examples of microstructures together with X-ray diffraction patterns for polycrystalline, nanocrystalline and amorphous Co-W alloys are shown in Fig. 5.11. Zinc–nickel alloys were electrodeposited from a bath containing zinc chloride (ZnCl2) and nickel chloride (NiCl2) as sources of metal ions (Table 5.6). Boric acid (H3BO 3) was used as a buffer, and the bath also contained sodium lauryl sulfate (CH 3(CH 2)11OSO 3 Na) as a wetting agent.46,47 Pulse-plating conditions are also given in Table 5.6. In this system, temperature is very important as it controls the composition of the alloys. Considerable grain refinement was achieved in these deposits with increasing nickel content. Nanocrystalline deposits were obtained for nickel concentrations between 10 and 50 wt%. At even higher concentrations a transition to an amorphous-like structure was observed. The examples of binary Co-W and Zn-Ni nanodeposits have clearly shown that the interplay of the various plating parameters including bath composition, current density, Ton and Toff, temperature and bath additives can be rather complex. This complexity increases even further when the alloys contain three or more alloying elements, such as the ternary alloy examples shown in table 5.2. In this context it is important to note that electrodeposited nanomaterials are usually far from

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5.11  Scanning electron micrographs (left) and X-ray intensity versus 2θ diffraction patterns (right) for (a) polycrystalline, (b) nanocrystalline and (c) amorphous Co-W alloys.48

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equilibrium structures, not only in terms of the very high grain boundary and triple junction defect density but also regarding the phase formation. In many cases, extensive solid solutions are formed with solubility levels far beyond the solubilities observed in conventionally processed alloys with the same overall composition. This has been observed in all three alloy systems discussed here: Ni-P, Co-W and Zn-Ni. Considerable shifts in phase field stability regions have been observed in these and other nanocrystalline alloys as shown, for example, in Fig. 5.12 for the case of Co-Fe alloy deposits. The final example to be discussed in this section on synthesis is the Ni-SiC composite material presented in Table 5.7.56,57 The plating bath contained two nickel salts, boric acid as a buffer and saccharin as a grain refiner. Beta silicon carbide particles (average particle size: 0.4 µm) were added in two concentrations: 20 and 100 g/l. Depending on the parameters for Ton, Toff and Ipeak, composite materials containing up to 10 vol% SiC were obtained. The Si-C particles were finely distributed with some particle agglomeration in the nanocrystalline nickel matrix, which had grain sizes in the 10–15 nm range.

5.12  Phase fields in equilibrium structures and electrodeposited non-equilibrium structures for cobalt-iron alloys.49

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Nanostructured metals and alloys Table 5.7  Electrolyte composition and plating conditions used for the synthesis of nanocrystalline Ni-SiC composites56,57 Compound

Concentration (g/l)

NiSO 4 × 7H2O 300 NiCl2 × 6H2O 45 H3BO 3 45 C7H5NO 3S β-SiC 20 or 100

5.4

Plating conditions pH T (°C) IDC (mA/cm2) Ipeak(mA/cm2) Ton(msec) Toff (msec)

4.5 60 – 50–900 5–10 5–10

Mechanical properties of nanocrystalline electrodeposits

The mechanical properties of electrodeposited nanomaterials have been studied in numerous investigations over the past 20 years using a wide range of methods including microhardness tests, nanoindentation, tensile and compression testing at various strain rates, adhesive, abrasive and scratch wear testing, as well as fatigue testing. Most studies focused on nanocrystalline nickel,6,10,19–21,63–95 Ni-Fe45,52,53,96–106 and Ni-P.4,107–112 Copper electrodeposits37,113–119 and nanocrystalline cobalt120–125 have also been studied in detail. Other binary alloys include Ni-Co,126 Ni-Cu,127 Ni-W128,129 and Co-Cu.130 Only a few studies have looked at composite materials such as Ni-Al2O3,59 Ni-SiC56,57,131 or Ni-Si3N4.132 As for many other types of nanomaterials produced by different synthesis methods, early mechanical property measurements were limited to hardness testing because materials were not available in sufficient quantities for other tests. As more material was produced, most tensile testing was done on miniaturized specimens, not in accordance with standard test requirements. However, upon scaling up the electrodeposition process in commercial operations, materials with sizes and shapes suitable for meaningful testing according to ASTM standards became available.89 Another important factor to consider when comparing mechanical property data presented in the various studies is the quality of the nanomaterial itself. Many electrodeposits contained impurities (e.g. sulfur, carbon, hydrogen), which were either intentionally or unintentionally introduced during the electrodeposition process. These impurities can have a considerable influence of the mechanical properties, in particular ductility. Furthermore, comparisons of mechanical properties presented in different studies must take details of the microstructures into consideration. Most studies used materials with relatively equiaxed grain shapes. However, grain size distribution and crystallographic textures can vary from material to material depending on the processing parameters. For this group of equiaxed materials the most important structural defects are the grain boundaries and triple junctions, and the volume fractions of atoms associated with these defects increase rapidly

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with decreasing grain size. On the other hand, one particular type of nanostructured electrodeposits has a microstructure consisting of relatively large grains on the order of micrometers in diameter which are subdivided by many twin boundaries, often referred to as nanotwinned or nanoscale lamellar structure. These structures are then mainly characterized by their very high twin boundary density. Many of the copper electrodeposits listed above show this particular structure. Most of the early mechanical property studies used nanocrystalline nickel, nickel–phosphorus and nickel–iron. For example, the mechanical and other physical properties of nickel with equiaxed nanostructures as a function of grain size obtained from early studies performed in our own laboratories have been presented as property-grain size graphs in several publications.16,22 Table 5.8 summarizes hardness, yield strength, Young’s modulus and abrasive wear resistance data for one particular series of the early nanocrystalline nickel deposits extracted from these graphs as a function of grain size, covering the range from 10 µm to 3 nm. The abrasive wear resistance is expressed here as the Taber wear index (TWI), which is the material loss per 1000 revolutions of abrasive wear action. In other words, the lower the TWI value, the higher the abrasive wear resistance of the material. Table 5.8 also shows the intercrystalline volume fraction Vic, as a function of grain size d, for a grain boundary thickness of ∆ = 1 nm and assuming a grain shape of a regular 14-sided tetrakaidecahedron:133 Vic = 1– [(d – D)/d]3.

[5.22]

This total intercrystalline volume fraction can be further separated into two contributions: Vgb from grain boundaries and Vtj coming from triple junctions, as per equations [5.23] and [5.24], respectively: Vgb = [3 D (d – D)2] /d 3,

[5.23]

Vtj = Vic – Vgb.

[5.24]

Table 5.8  Young’s modulus (E), hardness (H), and Yield strength (σy), Taber wear index (TWI) for nickel as a function of grain size and intercrystalline volume fraction Grain size (nm)

Vic (%)

E (GPa)

H (GPa)

σy (MPa)

TWI

10 000 1 000 100 50 20 10 5 3

0.03 0.29 2.97 5.88 14.26 27.10 48.80 70.40

207 207 207 207 200 190 185 170

1.3 2.6 3.7 4.5 5.8 6.4 5.5 5.3

200 400 680 720 780 920 780 N/A

37 30 26 23 22 20 N/A N/A

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For the following sections it should be noted that the absolute values for the different properties presented in Table 5.8 are not the most important factors to consider; absolute values varying considerably from study to study. What should be considered here are the general trends observed for the properties with respect to grain size reduction; these trends being directionally similar in many studies, not only for nickel but also for other electroplated nanomaterials.

5.4.1 Young’s modulus Table 5.8 shows that the Young’s modulus is not strongly affected by grain sizes between 10 µm and 20 nm. A small reduction is observed only at very small grain sizes, which was explained by the reduced Young’s modulus of the interface component, which reaches values up to 70% at the smallest grain size of 3 nm (Table 5.8). Extensive nanoindentation measurements have shown that the Young’s modulus of interfaces (grain boundaries and triple junctions) is reduced by about 20% compared with the value for isotropic polycrystalline nickel.109 Therefore, a reduction in the Young’s modulus of nanocrystalline materials is observed only at very small grain sizes. This is consistent with earlier observations on nanocrystalline materials produced by ball milling.134

5.4.2 Hardness, yield strength and wear resistance Hardness, H and yield strength, σy, show a strong grain size dependence (Table 5.8) and initially follow the Hall–Petch relationship:

[5.25]

[5.26]

where Ho, σyo are the hardness and yield strength values at large grain sizes and d is the grain size of the material. For example, the hardness increases from 1.3 GPa at 10 µm grain size to 6.4 GPa at 10 nm grain size, Table 5.8. For these two different grain sizes the yield strength increases from 200 MPa to 920 MPa. It should be noted that directionally similar hardness and strength increases were observed in many of the studies referenced at the beginning of this section, not only for nickel but also for Ni-Fe and Ni-P and other systems. Overall, these studies have shown that the Hall–Petch relationship is observed to be applicable down to grain sizes in the 20–10 nm grain size range for many electrodeposited nanomaterials. However, for grain sizes less than ~10 nm, the hardness of nanocrystalline nickel (Table 5.8) as well as Ni-Fe, Ni-Fe-Cr and Ni-P19 was found to decrease. An example for this inverse Hall–Petch behavior is shown for the hardness of nickel in Fig. 5.13.65 A similar curve for the yield strength of

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5.13  Vickers hardness of nanocrystalline nickel as a function of grain size in a Hall–Petch plot.65

nanocrystalline Ni was presented elsewhere.66 This behavior clearly demonstrates that at very small grain sizes, dislocation slip – the basis of regular Hall–Petch strengthening – is no longer the dominant deformation mechanism. At these small crystal sizes other mechanisms (e.g. diffusional creep, grain boundary sliding, grain rotation) become more important as will be discussed in much more detail in other chapters of this book. Several studies have used hardness values to estimate yield strength values for nanocrystalline metals when tensile data were not available. The following relationship between hardness, H, and yield strength, σy, was frequently used:

[5.27]

However, Table 5.8 shows that such a relationship does not apply for nanocrystalline nickel. In fact, a recent study89 has shown that this relationship is not applicable in general for a very large number of different nanocrystalline electrodeposits and significantly over-estimates the intrinsic yield strength of this group of materials. Instead, it was shown that the relationship given in equation [5.28] is a more reliable expression:

[5.28]

where σuts is the ultimate tensile strength. As long as the nanocrystalline electrodeposits showed sufficient (>5%) ductility to sustain tensile deformation to

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a discernable peak load, equation [5.28] can be used to estimate tensile strength from hardness measurements. For more brittle materials with tensile elongations less than 5%, the relationship given in equation [5.28] was also found to be invalid. Both abrasive and adhesive wear studies have shown that the wear resistance of nanocrystalline nickel increases with decreasing grain size.65,71 Table 5.8 shows the effect of grain size on the abrasive wear resistance (Taber wear index). This behavior is in agreement with Archard’s law, which states that the wear resistance is inversely proportional to the hardness of the material, which in turn initially increases with decreasing grain sizes. It is interesting to note that according to Archard’s law the wear resistance should decrease in nanomaterials that show the negative Hall–Petch behavior. This was indeed observed for both Ni-P111 and Ni-W73 electrodeposits.

5.4.3 Ultimate tensile strength and tensile ductility Because of the initial material size and shape limitations and the impurity problems mentioned earlier in this section, it is currently impossible to predict the intrinsic ultimate tensile strengths and ductilities that could potentially be achieved by grain size control in nanocrystalline electrodeposits. Early results were very disappointing in terms of ductility. For example, the ductility of Ni was observed to decrease from over 50% at a grain size of 100 µm to about 1% at a grain size of ~10 nm.16 Many other studies also found very low ductilities and many electrodeposits failed in a completely brittle fashion without onset of necking instability. Over the past several years considerable progress has been made in producing nanocrystalline electrodeposits which much improved ductility and very high ultimate tensile strength in cobalt,120,121 nickel-based alloys89 and copper.37,118 For example, for cobalt and some nickel–iron nanodeposits ultimate tensile strength values in excess of 2000 MPa and ductilities in the 5–15% range can now be achieved. There are several contributing factors for the higher ductility/ultimate tensile strength values observed in more recent studies. First, improved synthesis methods have been developed with much better control of impurities and other deposition defects such as hydrogen pits or co-deposited hydroxides.89 Second, thicker and larger samples are now available for testing following standard testing procedures. Early testing was often done on very thin specimens very close to plane stress conditions, which usually yield lower ductility values. Third, the development of nanotwinned electrodeposits has shown that the high density of twin boundaries can produce a unique combination of high strength and high ductility.37,118 Fourth, there is now considerable evidence that wide/bimodal grain size distributions,87 and co-deposited second phase particles can enhance ultimate tensile strength and ductility of nanomaterials57 and even produce superplastic

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behavior in some cases131,132 when the nickel matrix grain size was in the range of 50–200 nm. Superplasticity was also observed in electrodeposited nickel containing sulfur impurities, deformed at temperatures between 350 and 400°C.68,84 However, the interpretation of these results is difficult because of 1) the substantial grain growth before and during high-temperature deformation that produced grain sizes in the micrometer range, and 2) the formation of sulfurenriched grain boundaries that may have resulted in a liquid grain boundary phase.

5.5

Corrosion properties of nanocrystalline electrodeposits

The corrosion properties of electrodeposited nanomaterials have been reported in many studies dealing with Ni and Ni-based alloys,135–153 nanocrystalline Co,154–157 Zn and Zn-Ni alloys158,159 and nanocrystalline Cu.160–162 A detailed analysis of the findings reported in the various investigations is beyond the scope of this review. However, the main results of these studies have shown the following. First, contrary to earlier concerns, the high grain boundary and triple junction densities found on the surfaces of electrodeposited nanomaterials do not compromise their corrosion performance. The general shapes of the potentiodynamic polarization curves for various materials in acidic, basic or neutral chloride solutions were not significantly affected by grain size in most cases. Materials that show passivity in the polycrystalline form also showed passivity in the nanocrystalline form. Some materials showed slightly higher or lower current densities in some regions of the active, passive and trans-passive portions in the polarization curves, but overall the nanomaterials and their polycrystalline counterparts showed very similar behavior. Some materials also displayed a shift in open circuit potential indicating that the nanostructure catalyzes the hydrogen evolution reaction on some materials. Second, for materials that do show passivity, the structure and chemical composition of the passive layers were found to depend on grain size. This is due to the high density of defects (grain boundaries and triple junctions) that intersect the free surface of the nanomaterials. The defect structure that forms in the passive layer is strongly influenced by the substrate defects. It was also found that impurity atoms in the nanomaterials could have a substantial effect on the nature of the passive film. However, even with a defective structure, the passive films on nanomaterials still provide considerable protection for the material exposed to various electrochemical conditions. Third, materials that are susceptible to preferential attack along grain boundaries can benefit enormously by grain size reduction. This is clearly seen in Fig. 5.14 which shows cross-sectional micrographs of polycrystalline and nanocrystalline (grain size 20–30 nm) nickel both containing about 1000 ppm by weight of sulfur after potentiodynamic polarization in a 0.25M Na2SO 4 solution at a pH of 6.5.145 The polycrystalline material shows excessive attack along the grain boundaries with considerable weakening of the structure deep inside the material. On the other hand,

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5.14  Scanning electron micrographs of cross-sectional corrosion morphologies in polycrystalline (top) and nanocrystalline (bottom) nickel containing 1000 ppm sulfur. Note that σ represents either internal or externally applied stresses.

corrosion attack on the nanocrystalline nickel shows numerous, but only superficial, surface pits with no deep penetration into the bulk of the material. In other words, for nanocrystalline nickel, the corrosion attack is more or less spread out over the entire surface rather than being concentrated along the grain boundaries as seen for polycrystalline nickel. This has a tremendous effect on the performance of the materials in service. Many components in application have either internal stresses or are subjected to external stresses, both schematically indicated by the σ arrows in Fig. 5.14. For the polycrystalline material, extensive grain boundary corrosion has not only reduced the effective cross-sectional load-bearing capacity, the deep corrosion grooves at the grain boundaries also can act as stress concentrations; both factors contributing to conditions that can lead to unpredictable and catastrophic failures. On the other hand, the more or less uniform corrosion of the nanocrystalline material results in predictable overall thickness reduction. Therefore a component’s lifetime can be easily estimated as long as the average corrosion rate of the nanomaterial is known, for example, from polarization or immersion tests.

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The effect of sulfur impurities on the corrosion behavior of nanocrystalline and polycrystalline nickel was discussed by Kim et al.145 One of the critical points to consider is the distribution of sulfur throughout the material. For constant overall sulfur content, the sulfur concentration per unit grain boundary area is much smaller in nanocrystalline nickel compared to polycrystalline nickel. For example, if it is assumed that all impurities segregate to grain boundaries, it can be shown that the maximum grain boundary sulfur concentration decreases by three orders of magnitude when the grain size is reduced from 10 µm to 10 nm. In other words, at constant bulk sulfur concentration, nanocrystalline nickel is expected to have cleaner boundaries than polycrystalline nickel.

5.6

Other properties of nanocrystalline electrodeposits

The physical properties of conventional metals and alloys are either structuresensitive or structure-insensitive.163 Structure-sensitive properties include tensile strength, hardness, electrical resistivity and thermal conductivity at low temperatures, coercivity, magnetostrictiction and magnetic permeability. On the other hand, density, elastic moduli, thermal expansion, specific heat, heat of fusion and saturation magnetization belong to the group of properties that are relatively structureinsensitive. Sensitivity and insensitivity are with respect to structural changes, for example by grain size reduction, increases in dislocation density or low concentrations of solute additions. In section 5.4 on the mechanical properties of nanocrystalline electrodeposits, it has already been shown that tensile strength and hardness are strongly dependent on grain size, while the Young’s modulus is relatively grain size independent. Table 5.9 shows how grain size and intercrystalline volume fraction affect room temperature electrical resistivity, ρ, saturation magnetization, MS, and thermal expansion, α, of nickel over a grain size range from 10 µm to 10 nm. The values given in Table 5.9 were again taken from grain size–property graphs presented earlier.16 Table 5.9  Electrical resistivity (ρ), saturation magnetization (MS), and thermal expansion coefficient (α) for nickel as a function of grain size and intercrystalline volume fraction Grain size (nm)

Vic (%)

ρ (µΩ cm)

MS (kA/m)

α (x 10–6/K)

10 000 1 000 100 50 20 10

0.03 0.29 2.97 5.88 14.26 27.10

8.5 8.5 8.8 9.0 13.0 20.0

502 500 500 495 489 488

11.2 11.1 11.0 10.8 10.7 10.6

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Table 5.9 shows that the room temperature electrical resistivity is strongly dependend on grain size, in particular for grain sizes less than 100 nm for which the intercrystalline volume fractions rapidly increase. This is as expected because grain boundaries and triple junctions are very effective electron scattering centers. The grain size dependence for the room temperature electrical resistivity of nickel was given by the following equation:164

[5.29]

where d is the grain size. In this equation the factor 2.37 comes from the grain shape of the 14-sided tetrakaidecahedron, 2.82 × 10–6 µΩ cm2 is the specific grain boundary resistivity term and 8.33 µΩ cm is the resistivity due to electron scattering on phonons and other defects in the material including vacancies, dislocations and impurities. On the other hand, Table 5.9 shows that saturation magnetization, MS, changes very little with grain size in nickel.165 This is consistent with results obtained in linear muffin-tin orbital atomic sphere approximation calculations that evaluated the effect of structural disorder introduced by grain boundaries on the local magnetic moments in nickel.166,167 These studies have shown that the magnetic moments in different types of grain boundaries (e.g. several coincidence site lattice boundaries and a completely amorphous boundary) are not strongly affected by the structure of boundary defects. Similarly, grain size had very little effect on the saturation magnetization in nanocrystalline Co, Co-Fe, Co-W, Ni-Fe and Ni-P electrodeposits.168–170 In alloy deposits it is only the composition that controls the saturation magnetization. Table 5.9 further shows that grain size and intercrystalline volume fraction have no significant effect on the thermal expansion of electrodeposited nickel.171 Again this is consistent with results from a molecular-dynamics simulation study,172 which showed that grain boundaries have only a small effect on the thermal expansion of a material. Other structure-insensitive properties in nanocrystalline nickel include density173 and specific heat,171 two properties that show structure-insensitivity also for conventional materials. From the property examples shown in Tables 5.8 and 5.9 it is interesting to note that structure-sensitivity and structure-insensitivity observed in conventional materials are largely maintained when the grain size is reduced to the nanometer range in electrodeposited materials in which the main structural defects are the high volume fractions of grain boundaries and triple junctions. This is in contrast to nanomaterials produced by other synthesis methods such as inert gas condensation, ball milling or crystallization of amorphous precursors that often contain other defects such as porosity or residual amorphous phase. In these materials considerable changes have been observed for several structureinsensitive properties such as thermal expansion, specific heat, Young’s modulus

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and saturation magnetization. These differences have been discussed elsewhere in more detail.22,174,175

5.7

Applications

Electrodeposition is a relatively low-cost production route to make nanocrystalline metals, alloys and composite materials. It is a low-temperature, single-step process and produces fully dense nanostructures, free of porosity often found in materials made from nanocrystalline powder precursors. The electrodeposition method for nanomaterials is a drop-in technology that can make use of existing electroplating and electroforming infrastructure and electrolyte ingredients such as metal salts and bath additions. Switching from conventional electroplating to nanoplating requires only modest capital investment, for example for a change over from DC plating to pulse plating. From an engineering point of view, electrodeposition is an extremely versatile and flexible technology. First, there are many different metals, alloys and composites that can be readily deposited in nanocrystalline form to meet specific application needs. Second, these materials can be deposited in a variety of different product shapes and forms including thin and thick coatings, free-standing sheet, foil, tubes, wires, plates, molds and even powders for some applications. Table 5.10 Table 5.10  Various shapes and applications of nanocrystalline products made by electrodeposition and electroforming Shapes

Applications

Thin coatings Surface modification for wear and corrosion resistance; catalytic   surfaces Thick coatings ElectrosleeveTM ; repair of worn components Sheet, foil Gaskets; pressure control membranes; hydrogen purification  membranes; thermal barriers; solar energy absorbers; microfoils; soft magnets Tubes, wire Surgical tools; missile guidance systems; miniature gamma   radiation sources Mesh Filters; precision sieve screens; razor foils; printing screens;   centrifuge screens Plate Structural applications Foam Filters; electromagnetic shielding; battery electrodes; catalyst   carriers Molds Embossing tools for holograms; compression, injection and   pattern molds Free forms Precision bellows; erosion shields for helicopters; trust   chambers for rocket engines; components for micromagnetic   motors, micro-optics, microactuators and microfiltration; shaped   charge liners; precision reflectors and mirrors; nozzles Powder Catalysts; reinforcements

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summarizes typical applications for the various product shapes of nanocrystalline electrodeposits. Many of these applications have been previously discussed in more detail.11–13,15,18,20,22,55 Chapter 22 will discuss several of these applications with emphasis on some of the more recently developed nanometal-enabled hybrid materials.

5.8

Acknowledgements

Financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Ontario Research Fund (ORF) is gratefully acknowledged.

5.9

References

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55 Palumbo G., Erb U., McCrea J.L., Hibbard D.G., Brooks I., Gonzalez F., Panagiotopoulos K. In: AESF SUR/FIN Technical Proc. Orlando (FL); American Electroplaters and Surface Finishers; 2002; p. 204. 56 Zimmerman A.F., Clark D.G., Aust K.T., Erb U. Mater Lett 2002;52: 85–90. 57 Zimmerman A.F., Palumbo G., Aust K.T., Erb U. Mater Sci Eng 2002;A328: 137–146. 58 Erb U., El-Sherik A.M., Palumbo G., Aust K.T. Nanostr Mater 1993;2: 383–390. 59 Qu N.S., Chan K.C., Zhu D. Scripta Mater 2004.50: 1131–1134. 60 Talbot J.B. In: AESF SUR/FIN Technical Proc. Orlando (FL): American Electroplaters and Surface Finishers; 2003; p. 701. 61 Zhou Y., Peng X., Wang F. Scripta Mater 2004;50: 1429–1433. 62 Chen X.H., Cheng F.Q., Li S.L., Zhou L.P., Li D.Y. Surf Coat Tech 2002;155: 274–278. 63 Hughes G.D., Smith S.D., Pande C.S., Johnson H.R., Armstrong R.W. Scripta Metall 1986;20: 93–98. 64 El-Sherik A.M., Erb U., Palumbo G., Aust K.T. Scripta Metall Mater 1992;27: 1185–1188. 65 El-Sherik A.M., Erb U. In: Smith F.N. et al., editors. Nickel–Cobalt 97, Applications and Materials Performance, Vol. V. Montreal (PQ): Metallurgical Society of CIM; 1997; p. 257. 66 Wang N., Wang Z., Aust K.T., Erb U. Mater Sci Eng 1997;A237: 150–158. 67 Ebrahimi F., Bourne D.G., Kelly M.S., Matthews T.E. Nanostr Mater 1999;11: 343–350. 68 McFadden S.X., Zhilyaev A.P., Mishra R.S., Mukherjee A.K. Mater Lett 2000;45: 345–349. 69 Yin W.M., Whang S.H. Scripta Mater 2001;44: 569–574. 70 Xiao C., Mishrams R.A., Wang S.H., Yin W.M. Mater Sci Eng 2001;A301: 35–43. 71 Jeong D.H., Gonzalez F., Palumbo G., Aust K.T., Erb U. Scripta Mater 2001;44: 493–499. 72 Dalla Torre F., van Swygenhoven H., Victoria M. Acta Mater 2002;50: 3957–3970. 73 Schuh C.A., Nieh T.G., Yamasaki T. Scripta Mater 2002;46: 735–740. 74 Ebrahimi F., Ahmed Z. Mater Charact 2002;49: 373–379. 75 Schwaiger R., Moser B., Dao M., Chollacoop N., Suresh S. Acta Mater 2003;51: 5159–5172. 76 Kumar K.S., Suresh S., Chisholm M.F., Horton J.A., Wang P. Acta Mater 2003;51: 387–406. 77 Ebrahimi F., Ahmed Z. J Appl Electrochem 2003;33: 733–739. 78 Hanlon T., Kwon Y.N., Suresh S. Scripta Mater 2003;49: 675–680. 79 Wang Y.M., Cheng S., Wei Q.M., Ma E., Nieh T.G., Hamza A. Scripta Mater 2004;51: 1023–1028. 80 Mishra R., Basu B., Balasubramaniam R. Mater Sci Eng 2004;A373: 370–373. 81 Dalla Torre F., Spätig P., Schaüblin R. Acta Mater 2005;53: 2337–2350. 82 Dalla Torre F., van Swygenhoven H., Schaüblin H., Spätig P., Victoria M. Scripta Mater 2005;53: 23–27. 83 Wang Y.M., Hamza A.V., Ma E. Appl Phys Lett 2005;86:241917: 1–7. 84 McFadden S.X., Mukherjee A.K. Mater Sci Eng 2005;A395: 265–268. 85 Ebrahimi F., Ahmed Z., Li Q. Mater Manuf Proc 2006;21: 687–693. 86 Wang Y.M., Hamza A.V., Ma E. Acta Mater 2006;54: 2715–2726. 87 Gu C.D., Lian J.S., Jiang Z.H., Jiang Q. Scripta Mater 2006;54: 579–584. 88 Cavaliere P. Comp Mater Sci 2008;41: 440–449. 89 Brooks I., Lin P., Palumbo G., Hibbard G.D., Erb U. Mater Sci Eng 2008;A491: 412–419.

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  90 Shen Y.F., Xue W.Y., Wang Y.D., Liu Z.Y., Zuo L. Surf Coat Tech 2008;202: 5140–5145.   91 Kulovits A., Mao S.X., Wiezorek J.M.K. Acta Mater 2008;56: 4836–4845.   92 Kang J.X., Zhao W.Z., Zhang G.F. Surf Coat Tech 2009;203: 1815–1818.   93 Wang C.L., Zhang M., Nieh T.G. J Phys D: Appl Phys 2009;42: 115405: 1–7.   94 Prasad M.J.N.V., Suwas S., Chokshi A.H. Mater Sci Eng 2009;A503: 86–91.   95 Wu X.L., Zhu Y.T., Wei Y.G., Wei Q. Phys Rev Lett 2009;103: 205504: 1–4.   96 McCrea J.L., Palumbo G., Hibbard G.D., Erb U. Rev Adv Mater Sci 2003;5: 252–258.   97 Li H., Ebrahimi F. Mater Sci Eng 2003;A347: 93–101.   98 Li H., Ebrahimi F. Appl Phys Lett 2004;84: 4307–4309.   99 Li H., Ebrahimi F. Adv Mater 2005;17: 1969–1972. 100 Li H., Ebrahimi F. Acta Mater 2006;54: 2877–2886. 101 Li H., Ebrahimi F., Choo H., Liaw P.K. J Mater Sci 2006;41: 7636–7642. 102 Wei H., Hibbard G.D., Palumbo G., Erb U. Scripta Mater 2007;57: 996–999. 103 Ebrahimi F., Li H. J Mater Sci 2007;42: 1444–1454. 104 Yang Y., Imasogie B., Fan G.J., Liaw P.K., Soboyejo W.O. Metall Mater Trans 2008;39A: 1145–1156. 105 Li L., Ungar T., Wang Y.D., Fan G.J., Yang Y.L., Jia N., Ren Y., Tichy G., Lendvai J., Choo H., Liaw P.K. Scripta Mater 2009;60: 317–320. 106 Fan G.J., Li L., Yang B., Choo H., Liaw P.K., Saleh T.A., Clausen B., Brown D.W. Mater Sci Eng 2009;A506: 187–190. 107 Palumbo G., Erb U., Aust K.T. Scripta Metall Mater 1990;24: 2347–2350. 108 Jeong D.H., Erb U., Aust K.T., Palumbo G. Mater Sci Forum 2002;925: 408–412. 109 Zhou Y., Erb U., Aust K.T., Palumbo G. Z Metallk 2003;94: 1157–1161. 110 Jeong D.H., Erb U., Aust K.T., Palumbo G. J Metast Nanostr Mater 2003;15–16: 635–642. 111 Jeong D.H., Erb U., Aust K.T., Palumbo G. Scripta Mater 2003;48: 1067–1072. 112 Zhou Y., van Petegem S., Segers D., Erb U., Aust K.T., Palumbo G. Mater Sci Eng 2009;A512: 39–44. 113 Lu L., Sui M.L., Lu K. Science 2000;208: 1463–1466. 114 Lu L., Li S.X., Lu K. Scripta Mater 2001;45: 1163–1169. 115 Jia D., Ramesh K.T., Ma E., Lu L., Lu K. Scripta Mater 2001;45: 613–620. 116 Lu L., Schwaiger R., Shan Z.W., Dao M., Lu K., Suresh S. Acta Mater 2005;53: 2169–2179. 117 Hakamada M., Nakamoto Y., Matsumoto H., Iwasaki H., Chen Y.Q., Kusuda H., Mabuchi M. Mater Sci Eng 2007;A457: 120–126. 118 Lu L., Chen X., Huang X., Lu K. Science 2009;323: 607–610. 119 Zhang H., Jiang Z., Qiang Y. Mater Sci Eng 2009;A517: 316–320. 120 Karimpoor A.A., Erb U., Aust K.T., Wang Z., Palumbo G. Mater Sci Forum 2002; 386–388: 415–421. 121 Karimpoor A.A., Erb U., Aust K.T., Palumbo G. Scripta Mater 2003;49: 651–656. 122 Wang L., Gao Y., Xu T., Xue Q. Mater Chem Phys 2006;99: 96–113. 123 Fan G.J., Fu L.F., Qiao D.C., Choo H., Liaw P.K., Browning N.D. Scripta Mater 2006;54: 2137–2141. 124 Karimpoor A.A., Aust K.T., Erb U. Scripta Mater 2007;56: 201–204. 125 Cavaliere P. Mater Sci Forum 2007;561–565:1299–1302. 126 Gu C.D., Lian J.S., Jiang Z.H. Adv Eng Mater 2006;8(4): 252–256. 127 Ebrahimi F., Ahmed Z., Li H. Appl Phys Lett 2004;85: 3749–3751. 128 Schuh C.A., Nieh T.G., Iwasaki H. Acta Mater 2003;51: 431–443.

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129 Giga A., Kimoto Y., Takigawa Y., Higashi K. Scripta Mater 2006;55: 143–146. 130 Nakamoto Y., Yuasa M., Chen Y., Kusuda H., Mabuchi M. Scripta Mater 2008;58: 731–734. 131 Chan K.C., Wang C.L., Zhang K.F., Pang C. Scripta Mater 2004;51: 605–609. 132 Chan K.C., Wang G.F., Wang C.L., Zhang K.F. Scripta Mater 2005;53: 1285–1290. 133 Palumbo G., Thorpe S.J., Aust K.T. Scripta Metall Mater 1990;24: 1347–1350. 134 Shen T.D., Koch C.C., Tsui T.Y., Pharr G.M. J Mater Res 1995;10: 2892–2896. 135 Rofagha R., Langer R., El-Sherik A.M., Erb U., Palumbo G., Aust K.T. Scripta Metall Mater 1991;25:2867–2872. 136 Rofagha R., Langer R., El-Sherik A.M., Erb U., Palumbo G., Aust K.T. Mater Res Soc Symp Proc 1992;238: 751–755. 137 Rofagha R., Erb U., Ostrander D., Palumbo G., Aust, K.T. Nanostr Mater 1993;2: 1–10. 138 Rofagha R., Splinter S.J., Erb U., McIntyre N.S. Nanostr Mater 1994;4: 69–78. 139 Wang S., Rofagha R., Roberge P.R., Erb U. Electrochem Soc Proc 1995;95–8: 244–255. 140 Tang P.T., Watanabe T., Anderson J.E.T., Bech-Nielsen G. J Appl Electrochem 1995;25: 347–352. 141 El-Sherik A.M., Erb U. Plat & Surf Fin 1995;82(9): 85–89. 142 Splinter S.J., Rofagha R., McIntyre N.S., Erb U. Surf Anal 1996;24: 181–186. 143 Gonzalez F., Brennenstuhl A.M., Palumbo G., Erb U., Lichtenberger P.C. Mater Sci Forum 1996; 225–227: 831–836. 144 Saito M., Jamada K., Ohashi K., Yasue Y., Sowaga Y., Osaka T. J Electrochem Soc 1999;146: 2845–2848. 145 Kim S.H., Aust K.T., Erb U., Ogundale G., Gonzalez F. In: AESF SUR/FIN Technical Proc. Orlando (FL): American Electroplaters and Surface Finishers; 2002; p. 225. 146 Benea L., Bonora P.L., Borello A., Martelli S. Wear 2002;249: 995–1003. 147 Mishra R., Balasubramaniam R. Corr Sci 2004;46: 3019–3029. 148 Gu C.D., Lian J.S., He J.G., Jiang Z.H., Jiang Q. Surf & Coat Techn 2006;200: 5413–5418. 149 Peng X., Zhang Y., Zhao J., Wang F. Electrochim Acta 2006;51: 4922–4927. 150 Sriraman K.R., Ganesh Sundara Raman S., Seshadri S.K. Mater Sci Eng 2007;A460– 461: 39–45. 151 Steward R.V., Fan G.J., Fu L.F., Green B.A., Liaw P.K., Wang G., Buchanan R. Corr Sci 2008;50: 946–953. 152 Zamanzad-Ghavidel M.R., Raeissi K., Saachti A. Mater Lett 2009;63: 1807–1809. 153 Lee H.B., Wuu D.S., Lee C.Y. Lin C.S. Metall Mater Trans 2010;41A: 450–459. 154 Kim S.H., Aust K.T., Erb U., Gonzalez F., Palumbo G. Scripta Mater 2003;48: 1379–1384. 155 Kim S.H., Franken T., Hibbard G.D., Erb U., Aust K.T., Palumbo G. J Metast Nanostr Mater 2003;15–16: 643–648. 156 Aledresse A., Alfantazi A.M. J Mater Sci 2004;39: 1523–1526. 157 Jung H., Alfantazi A.M. Electrochim Acta 2006;51: 1806–1814. 158 Youssef K.M.S., Koch C.C., Fedkiw P.S. Corr Sci 2004;46: 51–64. 159 Alfantazi A.M., Erb U. Corrosion 1996;52: 880–888. 160 Yu J.K., Han E.H., Lu L., Wei X.J., Leung M. J Mater Sci 2005;40: 1019–1022. 161 Tao S., Li D.Y. Nanotechnology 2006;17: 65–78. 162 Yu B., Woo P., Erb U. Scripta Mater 2007;56: 353–6. 163 Ruoff A.L. Introduction to Materials Science. Englewood Cliffs NJ: Prentice Hall; 1972.

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164 McCrea J.L., Aust K.T., Palumbo G., Erb U. Mater Res Soc Symp Proc 2000;581; 461–466. 165 Aus M.J., Szpunar B. El-Sherik A.M., Erb U., Palumbo G., Aust K.T. Scripta Metall et Mater 1992;27: 1639–1643. 166 Szpunar B., Erb U., Aust K.T., Palumbo G., Lewis L.J. Mater Res Soc Symp Proc 1994;318: 447–482. 167 Szpunar B., Erb U., Palumbo G., Aust K.T., Lewis L.J. Phys Rev B 1996;53: 5547–5556. 168 Aus M.J., Cheung C., Szpunar B., Erb U. J Mater Sci Lett 1998;17: 1949–1952. 169 Szpunar B., Aus M.J., Cheung C., Erb U., Palumbo G., Szpunar J.A. J Magn Magn Mater 1998;187: 325–336. 170 Cheung C., Aus M.J., Erb U., McCrea J.L., Palumbo G. In: Proc, 6th International Conference on Nanostructured Materials. NANO 2002, Rutgers Univ, (NJ): Nanotechnology Enterprises Inc; 2002. CD-ROM. 171 Turi T., Erb U. Mater Sci Eng A 1995;203: 34–38. 172 Szpunar B., Lewis L.J., Swainson I., Erb U. Phys Rev B 1999;60: 10,107–10,113. 173 Haasz T.R., Palumbo G., Aust K.T., El-Sherik A.M., Erb U. Scripta Metall et Mater 1995;32: 423–426. 174 Erb U., Palumbo G., Szpunar B., Aust K.T. Nanostr Mater 1997;9: 261–270. 175 Aust K.T., Erb U., Palumbo G. In: Suryanarayana C et al., editors. Processing and Properties of Nanocrystalline Materials. Warrendale (PA): TMS; 1996; p. 11.

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6 Bulk nanocrystalline and nanocomposite alloys produced from amorphous phase A. INOUE and D.V. LOUZGUINE, Tohoku University, Japan Abstract In this chapter we review a large set of the research results related to formation and characterization of bulk nanocrystalline and nanocomposite alloys produced by crystallization of an amorphous/glassy phase or directly from the melt on cooling. The formation of bulk glassy alloys and their processing routes are also outlined. Nanocrystallizing glassy samples leads to the formation of composites containing nanoscale crystalline or quasicrystalline particles. The structure, general physical, thermal, mechanical and magnetic properties of these nanostructured materials are discussed. Some of these composites possess a better combination of mechanical properties than those of fully glassy or crystalline alloys. For example, nanoscale crystalline and quasicrystalline phases play a very important role in ductilization of bulk glassy alloys. Nanostructured ferromagnetic alloys and glassy-nanocrystal composites possess good soft magnetic properties and create an important application area for such materials. Key words: bulk, nano, crystalline, composite, alloy, amorphous, glassy, magnetic, material.

6.1

Introduction

As a rule bulk metallic alloy samples have a polycrystalline structure after solidification. Even casting of commercial alloys into a thin mould (with a cavity thickness of about 1 mm) produces a crystalline structure that is typical for metallic materials. Although oxide glasses have been known long ago, active research activities on metallic glassy alloys started after the formation of the first Au-Si sample with an amorphous structure in 1960.1 This became possible by using a rapid solidification technique for casting of metallic liquids at a very high cooling rate of 106 K/s when molten Au-Si and Pd-Si alloys undergo glass transition (vitrification) on cooling. Such alloys required extremely high cooling rate (from metallurgical viewpoint) for vitrification. For a long time Pd-Cu-Si and Pd-Ni-P system glassy alloys produced in a bulk form after flux treatment, which helps to suppress heterogeneous nucleation, were known to be the best metallic glass formers2,3 but remained a laboratory curiosity. However, a large number of bulk glassy alloys (also called bulk metallic glasses) defined as 3-dimensional massive glassy (amorphous) objects with a size not less than 1 mm in any dimension (by other definition 10 mm) have been produced since the end of the 1980s. The high glass forming ability of some alloy compositions has enabled the 152 © Woodhead Publishing Limited, 2011



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production of bulk metallic glasses in the thickness range of 100–102 mm by using various casting processes.4,5,6 Metallic glasses obtained in thin film, ribbon or bulk forms are metastable at room temperature and devitrify/crystallize on heating. Such a devitrification process leads to the formation of a nanostructure in many alloys. Nanostructured material can be defined as a substance that contains very small grains or particles of typically 1 to 100 nm in size (more strictly speaking in one or more dimensions). These nanostructured materials exhibit unique and superior properties, and for this reason they are subjects of high interest to scientists in various fields of physics, chemistry and materials science.7,8 Although the same nanomaterial can be produced using different techniques, the production technique often significantly influences the properties of metallic glass-originated nanomaterials. If the process involves nucleation and growth then a high nucleation rate and a low growth rate of the precipitating phase are required in order to obtain a nanostructure. Such conditions are usually obtained under primary crystallization/devitrification with a long-range diffusioncontrolled growth.

6.2

The formation of bulk metallic glassy alloys

Depending upon their glass-forming ability (GFA), glassy (amorphous) alloys can be produced using various processing methods. Alloys having a low GFA can be prepared in an amorphous state by condensation from a vapor phase.9 This method is, however, high on power consumption and not efficient for the preparation of bulk glassy metals. Some glassy alloys can be produced by a solid-state reaction using mechanical attrition10 such as ball milling11 or by severe plastic deformation.12,13 Another method for producing glassy metals is electrodeposition from a solution.14,15 The two methods mentioned above are efficient but also heavy on power consumption. Much more productive is rapid solidification from a liquid phase16 by melt-spinning or Cu-mold casting, for example, or from quartz crucible through a nozzle (Fig. 6.1), liquid forging and so on. Bulk glassy alloys with an extraordinarily high GFA 4–6,17 among metallic alloys have been widely produced since the breakthrough achieved in the end of 1980s and the beginning of the 1990s.18,19 They are greater in size compared to melt-spun ribbons or thin films, and thus represent higher commercial interest as structural materials. Since these discoveries, many other bulk glassy alloys have been produced.20–24 They can be produced at cooling rates of the order of 100, 10, 1 K/s and even less, which is much lower than those of 104–106 K/s required for vitrification of marginal glassformers using a rapid solidification technique. The bulk glassy alloys possess three common features summarized in,4 i.e. 1) the alloys belong to multicomponent systems, 2) the constituent elements have significant atomic size ratios above 12%, and 3) most of the alloying elements in such alloys have a large and negative mixing enthalpy with each other (although

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6.1  Bulk glassy sample casting technique, scheme.

some of the alloying elements like Ni and Cu, often presenting in the bulk glassy alloys, for example, have a moderately positive mixing enthalpy with each other). At present bulk metallic glasses already have some important applications4,6,25 and it is believed that these will increase in the near future.26,27 On the other hand, if the GFA of the alloy is insufficiently glassy or amorphous, powder samples can be produced by mechanical alloying or gas atomization techniques,28 for example, and then consolidated into bulk form by hot pressing in a WC die,29 spark plasma sintering (SPS)30 technique by applying pulsed direct current (Fig. 6.2) or some other techniques. For example, Ni-based bulk metallic glassy samples31,32 with a size of 20 mm were fabricated by spark plasma sintering of gas-atomized Ni52.5Nb10Zr15Ti15Pt7.5 glassy powders (Fig. 6.3 and Fig. 6.4). The structure, thermal stability and interface characteristics of the powder particles in the sintered specimens were investigated. Sintered glassy specimens with nearly 100% relative density were obtained by the SPS process at

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6.2  Schematic representation of spark plasma sintering technique.

6.3  Scanning electron microscope micrograph of the cross section of the sintered Ni52.5Nb10Zr15Ti15Pt7.5 specimen obtained at a sintering temperature of 773 K.

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6.4  Dimensions of the SPS compact.

the sintering temperature of 773 K under a loading pressure of 600 MPa. The consolidation was achieved with a relatively low sintering temperature, a short holding time and rapid cooling during the SPS process. Spark plasma sintering, as a newly developed rapid sintering technique, has great potential for producing dense glassy specimens or nanocrystalline materials in a short sintering time. In the SPS process, pulsed electrical current flows directly through the powder material being sintered, and high heating efficiency is achieved (Fig. 6.2). The application of pulsed DC voltage induces various phenomena caused by electrical and thermal effects, providing advantages that could not be obtained using conventional sintering processes. Aluminum-based bulk glassy samples of high relative density were obtained by warm extrusion of atomized amorphous powders33 though they have rather low GFA owing to a high density of so-called quenched-in nuclei in some glasses. This fact, as well as a low reduced glass-transition and devitrification temperature,34 limits the glassy sample’s critical thickness below 1 mm. Owing to the absence of crystalline lattice and dislocations, a unique deformation mechanism35,36 is realized in bulk glassy alloys, which thus exhibit high strength37 (~2 GPa for Cu-, Ti-, Zr-based, ~3 GPa for Ni-based, ~4 GPa for Fe-based, ~5 GPa for Co-based alloys), high hardness, good wear resistance38 and large elastic deformation. For example, (Fe, Co)-Cr-Mo-C-B-Tm glassy alloys prepared in a cylindrical form with a diameter of 18 mm demonstrate an excellent GFA and high strength exceeding 4 GPa.39 Some bulk metallic glasses exhibit significantly higher compressive ductility40,41 compared to the others. Their ductility can be related to Poisson’s ratio ν,42 in situ nanocrystallization43 or glassy phase separation.44 Nevertheless localized shear deformation is a dominant plastic-deformation mode at room temperature.45 The fatigue-endurance limits of some Zr-based alloys are comparable with those of high-strength structural alloys.46 Many of the metallic glassy alloys have a high corrosion resistance.47,48 Iron- and cobalt-based alloys exhibit good soft magnetic properties,49,50 while Nd-based alloys show hard magnetic properties.

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One should also mention that some bulk glassy alloys contain clear mediumrange order (MRO) zones51 or nanoscale particles52 in an as-solidified state, even though these precipitates do not produce diffraction peaks in the XRD and selected-area electron diffraction pattern (SAED) due to their small volume fraction. An example of MRO zones is shown in Fig. 6.5. Although binary bulk glassy alloys exist,53,54,55 their GFA is low (a critical thickness of the sample that achieves the glassy state without crystallization does not exceed 2 mm), some of them were reported to contain nanoparticles and they are formed in narrow composition ranges. On the other hand, an addition of a third element56 enhances their GFA. Bulk glassy alloys can be thermo-mechanically shaped or welded in the supercooled liquid regions by electromechanical shaping technology at low applied stresses due to the high electrical resistivity of glassy alloys.57 Some of the glassy alloys exhibit ‘superplasticity’ (actually good fluidity) on being heated to a supercooled liquid region.58 Bonding of glassy alloys can be achieved by laser,59 electron-beam60 and friction welding.61 Several attempts have also been made to explain the GFA of these alloys based on different criteria. These include the reduced glass transition temperature, Trg = Tg/Tl62 where Tg is the glass-transition temperature and Tl is the liquidus temperature (though overall validity of this criterion has been questioned recently);63,64 the width of the supercooled liquid region (∆Tx) defined as Tx – Tg where Tx is the crystallization onset temperature;65 and the γ = Tx/(Tg + Tl)

6.5  Medium range order zones in Ni50Pd30P20 alloy, encircled in the HRTEM image. The insert in the top left corner is a Fast Fourier Transform of the area encircled in the center. One can admit the existence of sharp spots.

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parameter,66 which somehow combines both ∆Tx and Tg/Tl criteria into a single parameter and many other criteria.67 It has also been clearly shown that purely extrinsic factors also have a significant influence on the GFA.68 The role of minor additions in the formation of metallic glasses was also discussed.69 Another important point relates to the nonequilibrium eutectic, as the best glass-forming compositions are found not exactly at the equilibrium eutectic point but somewhat shifted usually towards a more refractory eutectic component,70 while Tg is not significantly different in the observed range. This most likely takes place owing to the shift of the eutectic point with supercooling/undercooling at a high enough cooling rate because casting conditions of bulk glassy samples are far from equilibrium.71 However, binary (Si or Ge)-Ni and ternary (Si or Ge)-Ni-Nd alloys showed that the principles for achieving a good GFA known so far are necessary conditions, but not always sufficient conditions.72 It was found that the higher GFA of the Ge-Ni-Nd alloy compared to the Si-Ni-Nd alloy cannot be explained on the basis of the widely used parameters such as geometrical and chemical factors, viscosity and diffusion data. It was suggested that the electronic structure characteristics,72,73 for example electronegativity difference, should be taken into consideration. The electronegativity of the constituent elements is an important factor influencing the GFA and the temperature interval of the supercooled liquid region of the glass-forming alloys.74 The atomic packing density for non-crystalline structures is a geometrical factor influencing GFA.75 A mixture of atoms with different sizes enables their dense packing. The importance of efficient atomic packing for the formation of metallic glasses was shown recently,76,77 as the specific radius ratios are preferred in the compositions of metallic glasses. These features are also closely connected with so-called λ criterion for good GFA.78 It has been also postulated that electron concentration: number of valence electrons per atom (e/a value) affects the GFA79 by analogy with Hume–Rothery phases related to certain valence electron concentration. However, as many glassy alloys contain transition metals which have multiple valences, it is difficult to decide which valency value should be taken into consideration in a particular case. The glass-transition phenomenon in metallic glasses has been studied extensively. Three kinds of approaches have been formulated:80,81,82 the glassy phase is just a frozen liquid, and thus, glass-transition is a kinetic phenomenon and no thermodynamic phase transformation takes place; glass transition may be a secondorder transformation as follows from the shape of the curves for the thermodynamic parameters, for example, specific volume or enthalpy, which exhibit a continuity at the glass-transition temperature while their derivatives like thermal expansion coefficient or heat capacity exhibit a discontinuity (in a certain approximation) at the glass-transition temperature; glass transition may be a first-order transformation. A thermodynamic aspect of glass transition is known as the Kauzmann paradox.83

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The formation of a nanostructure by crystallization of the glassy phase, by deformation or directly from the melt on casting

Nanoscale particles of a crystalline or a quasicrystalline phase can be readily formed by crystallization/devitrification of the glassy alloys. This indirect method of production of the nanostructure requires formation of the glassy phase in the initial stage and its subsequent full or partial devitrification on heating. Such a method leads to the formation of a highly homogeneous dispersion of nanoparticles in various alloys. The difference in the devitrification pathways of glassy alloys is often connected with the state of the matrix phase prior to devitrification. It can be amorphous, glassy or supercooled liquid. Amorphous alloys like Al-Nd-Ni-Co do not transform to a supercooled liquid before crystallization (Fig. 6.6) upon conventional heating rate. Glassy alloys like Al-YNi-Co form the supercooled liquid region on heating prior to crystallization (Fig. 6.6) and in general have a better GFA compared to amorphous alloys which do not exhibit Tg on heating. Marginal glass-formers like Al-Y-Ni-Co-Cu (Fig. 6.6) have pre-existing nuclei84 or even nanoparticles in the amorphous matrix, and thus the initial heat flow signal in the DSC, marked as A, is related to the beginning of growth of these nuclei or particles. Although it might be difficult to establish an intrinsic physical difference between amorphous and glassy alloys such a slightly arbitrary differentiation in relation with the devitrification behavior is useful. The formation of a supercooled liquid has a significant influence on the devitrification process in metallic glasses.85 Alloys devitrifying from the supercooled liquid exhibit a tendency to form metastable phases and phases with high crystallographic symmetry on devitrification compared to similar alloys that crystallize.86 This may be connected with the change of the local atomic structure in the supercooled liquid region due to higher atomic mobility compared to that in the glassy phase. Below Tg the crystalline products of devitrification in some alloys inherit the as-solidified structure of the metallic glass. Four types of phase transformations were found to occur during devitrification of the glassy alloys: 1) polymorphous (a product phase has the same composition as the glassy phase), 2) primary (a product phase has a composition different from that of the glassy phase), 3) eutectic (eutectoid) transformation (two or more phases nucleate and grow conjointly) and 4) spinodal/binodal decomposition involving a phase separation of the glassy phase prior to crystallization/devitrification.87 When the devitrification occurs by nucleation and growth mechanism (amorphous alloy does not have pre-existing nuclei), a high nucleation rate leading to a high number density of the precipitates in the order of more than 1021 m–3 and low growth rate of the precipitating phase are required in order to obtain a nanostructure88 in many alloys. The kinetics of the devitrification process has been also analyzed. It is also

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6.6  Differential scanning calorimetry traces of three representative Al-based alloys exhibiting glass-transition on heating (alloyed with Y), crystallization without glass-transition (alloyed with Nd) and marginal glass-forming alloy which has pre-existing nuclei and nanoparticles (Cu-bearing alloy).

found that about 1 MHz frequency ultrasonic vibrations promote the crystallization of Pd40Ni40P20 bulk glass.89 Devitrification of glassy alloys can be analyzed by the Kolmogorov–Johnson– Mehl–Avrami general exponential equation for the fraction transformed x(t):90 X(t) = 1 − exp(−Kt n),

[6.1]

where t is time and n is the Avrami exponent in the case of a single-stage reaction and steady-state nucleation. Crystallization kinetics of many glassy alloys obeys this mechanism. For example, Fig. 6.7 shows the Avrami plot for a Cu45Zr45Ag10 glassy alloy, which exhibited eutectic-type crystallization causing simultaneous formation of oC68 (Cu,Ag)10Zr7 and tP4 (Ag,Cu)Zr solid-solution phases by nucleation and

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6.7  The Avrami plot for Cu45Zr45Ag10 glassy alloy heat-treated isothermally at 717 K in a DSC device. Coefficient of determination (R2) for linear function fitting is 0.99998. Only every 5th data point is shown as a filled circle for better visibility of the linearity of the plot.

3-dimensional interface-controlled growth. As expected, the Avrami exponent for this process is close to 4. Nanostructured alloys are readily obtained from the primary devitrification of glasses with a long-range diffusion-controlled growth. The primary devitrification process of a highly supercooled liquid or amorphous phase often has high nucleation frequency, low crystal growth rate, high concentration gradient of solute element at liquid/solid interface resulting from low atomic diffusivity, formation of metastable phases, formation of a residual amorphous phase with high solute concentration, and so on. Another type of phase transformation in an amorphous solid leading to the formation of a nanostructure is spinodal decomposition.91 There are some data suggesting that in particular cases nanocrystalline structure can be obtained after eutectic92 and polymorphous93 devitrification of glassy alloys. Nevertheless, the most common mechanism leading to formation of a nanostructure is primary crystallization. Different Al-RE-TM glasses (where RE: rare earth; TM: transition metals) show primary precipitation of the Al solid solution (α-Al) nanoparticles on heating94 with a high nucleation rate exceeding 1020–1021 m–3s–1.95 The formation of α-Al at the primary crystallization stage is quite typical for Al-based amorphous alloys and glass-formers, for example: Al-Y-Ni-Co,96 Al-Fe-Y, Al-Fe-Nd97 and others. The investigations showed very low concentration of the alloying elements in nanocrystalline98 Al in accordance with the phase diagrams of Al-RE and Al-TM.99 Segregation of the RE metal having low trace diffusivity in Al to the α-Al/amorphous phase interface is considered to be one of the most important reasons for their low growth rate. Extended X-ray absorption fine structure analysis of grain boundaries in the nanocrystalline Fe85Zr7B6Cu2 alloys also showed a low Fe content in the grain boundaries between the bcc (body-centered cubic) Fe solid solution nanograins. Although in most of the alloys the

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nanocrystalline precipitates were found not to contain dislocations the addition of Pd to Al-Y-Ni-Co alloys caused formation of the highly dispersed primary α-Al nanoparticles about 3–7 nm in size upon solidification homogeneously embedded in the glassy matrix, and the direct observation of micro-strain and dislocations quenched in nanoparticles with a size below 7 nm is provided.100 Clearly heterogeneous nucleation was observed during formation of the Fe nanocrystals.101 The structure of Fe-based soft magnetic alloys like: Fe73.5Cu1Nb3Si13.5B9102 and Fe84Zr3.5Nb3.5B8Cu1103 after annealing consist of bcc Fe nanocrystals below 20 nm in size well dispersed in the amorphous matrix. The devitrification of the Fe73.5Cu1Nb3Si13.5B9 alloy starts from the formation of Cu-enriched zones.104 Precipitation of a nanoscale α-(Fe,Co) phase105 was observed in the Fe40Co40Cu0.5Zr9Al2Si4B4.5 alloy (Fig. 6.8). As has been shown by means of atom probe field ion microscopy as well as by high-resolution transmission electron microscopy106 Cu atoms form nanoclusters in the Fe73.5Si13.5B9Nb3Cu1 amorphous matrix, which act as the nucleating sites for heterogeneous nucleation of the bcc Fe particles on devitrification.107 The density of the clusters estimated by 3-dimensional atom probe is in the order of 1024 m–3 at the average cluster size of about 2–3 nm. Yavari and Negri108 discussed nanocrystallization process of soft magnetic Fe-based amorphous alloys using the concentration gradients of the elements that are insoluble in the primary crystalline phase. The transformation of the glassy phase to a supercooled liquid region altered the crystallization behavior of Al85Y4Nd4Ni5Co2,109 Al85Y8Ni5Co2 as well as some other Al-based glassy alloys110,111 which exhibited different devitrification

6.8  Bright-field TEM image of Fe40Co40Cu0.5Zr9Al2Si4B4.5 alloy annealed for 15 min at 873 K showing the formation of nanoparticles. Inset shows the selected-area electron diffraction pattern.

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behavior above and below the onset glass-transition temperature (Tg), while no such a feature was found in the Al-RE-Ni-Co amorphous alloys (glassy alloys exhibit glass-transition on heating while amorphous do not) showing no Tg. Thus, the devitrification behavior of Al-RE-Ni-Co metallic glasses can be classified as follows: (1) If an alloy does not show Tg on heating prior to devitrification (crystallization) and exhibits nucleation and growth transformation mechanism, it forms intermetallic compound(s) (IM) or IM + nanoscale Al particles. (2) If an alloy does not show glass transition on heating prior to devitrification and has pre-existing nuclei, it forms nanoscale primary Al grains. (3) If an alloy shows glass transition on heating and exhibits nucleation and growth transformation mechanism, it forms nanoscale Al particles above Tg and IM + Al or IM below Tg. The exception found in Ref.112 with large ribbon thickness of about 40 µm is more likely related to the pre-existing α-Al nuclei. The devitrification behavior of Al-based glassy and amorphous alloys was also recently associated with a topological empirical criterion (λ) defined as:78,113

[6.2]

where Ci is concentration of the i-th alloying element while ri is a solute atom radius and rAl is Al atom radius. The λ parameter predicts whether the compositions exhibit supercooled liquid region (λ > 0.1) or not (λ < 0.1). Such a transition at different Ni/RE ratio has been also observed in Al-Y-Ni114 and Al-La-Ni alloys.115 Intermetallic compounds can also be formed into a nanoscale size of precipitates. For example, the devitrification of the Ti50Ni20Cu23Sn7 alloy begins from the primary precipitation of nanoscale equiaxed particles of cF96 (Pearson Symbol) Ti2Ni solid solution.116,117 Formation of such a nanoscale cF96 phase has also been observed in the Zr- and Hf-based alloys.118 The growth rate of cF96 phase at a constant temperature is non-linear which indicates the diffusion-controlled growth mechanism. An extremely low growth rate of cF96 crystals was observed on the primary crystallization of the Hf55Co25Al20 glassy alloy.119 Very small cF96 Hf2Co clusters of 2–5 nm in size are formed in the sample annealed at 907 K for 0.9 ks, which causes appearance of the broad diffraction peaks (Fig. 6.9). These clusters are not visible in the bright-field TEM images,119 while XRD pattern of the sample annealed for 0.9 ks at 907 K is already different from that of the as-solidified state: the broad diffraction peak from about 30 to 45 degrees 2θ splits into five narrower peaks. The factors leading to nano-devitrification can be connected with the occurrence of heterogeneities such as oxygen impurity-enriched clusters, spinodal

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6.9  X-ray diffraction pattern of the Hf55Co25Al20 glassy alloy annealed at 907 K for 0.9 ks. The location of the five strong peaks (Gaussian fitting) corresponds to that of cF96 Hf2Co phase. Source: Louzguine et al.119 reprinted with permission from Elsevier Science.

decomposition in the liquid or glass120 and homogeneous nucleation in partitioning systems.121 In many cases diffusive redistribution of the alloying elements on a short scale precedes crystallization. Mg-Ni-Mm and Mg-Ni-Y-Mm (where Mm denotes Mischmetal – a natural mixture of several rare-earth metals) glassy alloys show a multistage crystallization behavior.122 The local structure of the as-solidified Mg86Ni10Y2Mm2 and Mg82Ni14Y2Mm2 metallic glasses containing MRO zones changes prior to the formation of the crystalline phases. Changes in the amorphous halo peak occur after heating to the first DSC exothermic peak, which indicates redistribution of the alloying elements in the amorphous matrix forming Mg-enriched zones. This process occurs without an incubation period. Comparison of the long-term thermal stabilities of different metallic glasses has been carried out using continuous heating transformation (CHT) diagrams123 constructed by applying a corollary from the Kissinger analysis method. Continuous heating transformation diagrams also can be recalculated from the isothermal ones using a method close to that used for steels. Nanoparticles in the glassy matrix can be produced directly from the melt. A nanomaterial consisting of icosahedral particles with a diameter below 10 nm was obtained in Zr-Pt alloy124 by casting. The formation of the nanoscale icosahedral phase during casting may indicate that the icosahedral short-range order exists in the melt of Zr-Pt binary alloy. Plastic deformation can cause nanoscale devitrification of a glassy phase. For example, deformation of some Al-RE-TM amorphous alloys at room

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temperature causes precipitation of deformation-induced α-Al particles of 7–10 nm in diameter within the shear bands on bending125 or nano-indentation.126 This effect was also observed in a Ni-based glassy alloy.127 It has been suggested that a local temperature rise can play a role in mechanically induced devitrification.128 One should also mention electron-beam irradiation induced crystallization.129,130 A general observation is that it causes primary nanocrystallization even in alloys that exhibit eutectic transformation mechanism on heating. However, it tends to indicate a non-thermal crystallization.

6.4

The formation of nano-quasicrystals

Nanoscale quasicrystals are formed on devitrification in various metallic glassy alloys.131 An icosahedral quasicrystalline phase (a 3-dimensional quasicrystal while 2- and 1-dimensional quasiperiodic structures also exist) having a longrange quasiperiodic translational and an icosahedral orientational order, but with no 3-dimensional translational periodicity, was initially discovered in Al-Mn alloys132 and later in some other binary Al-TM alloys and different ternary Al-based alloys.133 After that the icosahedral phase was observed in Ga-, Ti-, Mg- and Pd-based alloys as well as Cd-, rare earth- and Zn-based alloys.134,135 It has been found that reduced supercooling before crystallization from the melt was found to be the lowest for quasicrystals, larger for crystal approximants (crystals which structure is somewhat similar to those of certain quasicrystals) and largest for the crystalline phases. The nucleation barrier scales with the supercooling, and thus, local icosahedral order is considered to exist in some supercooled liquids and glasses. A low energy barrier for nucleation of the icosahedral phase may explain the fact that only growth of the pre-existed icosahedral nuclei was observed in the Zr65Ni10Al7.5Cu7.5Ti10Ta10 alloy.136 Formation of the nanoscale icosahedral phase was observed in the devitrified Zr-Cu-Al, Zr-Al-Ni-Cu137 and Zr-Ti-Ni-Cu-Al138 glassy alloys containing an impurity of oxygen above about 1800 mass ppm, although no icosahedral phase is formed if oxygen content is lower than 1700 mass ppm. The nanoscale icosahedral phase was obtained in devitrified Zr-Al-Ni-Cu-Pd,139 Zr-Pd, Zr-Pt140 and other system alloys at much lower (about 800 mass ppm) oxygen content. The nanoscale icosahedral phase has been produced in the NM (noble metals)-free Zr-Cu-Ti-Ni141 and Zr-Al-Ni-Cu142 glassy alloys with low oxygen content, below 500 mass ppm. The icosahedral phase in Zr-based alloys is often formed in cooperation with cF96 phase and cI2 βZr solid solution phase.143 In the rapidly solidified TixZryHfzNi20 system alloys the nanoscale icosahedral phase forms in the composition ranges close to that of the cI2 β solid solution phase and complex cF96 phase formation ranges.144 Moreover, cI2 β solid solution and icosahedral phases were found to have close chemical compositions. A transformation from glassy + β-Zr to glassy + icosahedral structure was observed in Zr65Ni10Al7.5Cu7.5Ti5Nb5 alloy on heating by a single-stage transformation with

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diffusion control. β-Zr solid solution particles were found to dissolve in the glassy phase, while the nanoscale particles of the icosahedral phase precipitate after the completion of the first exothermic reaction,145 which is considered to be a singletype reaction somewhat similar to peritectic one. The nanoscale icosahedral quasicrystalline phase has been also produced upon heating glassy Hf-based alloys containing Pd146,147 or Au. Hafnium-based alloys have a higher tendency to form a cubic cF96 phase compared to Zr-based ones. The alloys in the systems in which an equilibrium Hf-based cF96 phase exists do not show the formation of the icosahedral phase from the amorphous matrix. The metastable cF96 phase and the icosahedral phase are formed by primary devitrification from the amorphous phase inheriting the structure of the icosahedral clusters. As these two phases are obtained in the alloys with similar compositions and due to local structural similarities between these two phases, one can say that these phases are produced from the same clusters and the free energy difference is a leading factor for the formation of one phase or another. The formation of the nanoscale icosahedral phase was observed in the Cu-based alloys containing Pd148 and Au while Ag- and Pt-bearing alloys did not form the icosahedral phase. Palladium in the Cu60Zr30Ti10 glass-former changes its devitrification pathway,149 inducing nucleation and diffusion-controlled growth of a nanoicosahedral phase (Fig. 6.10) from the supercooled liquid region in the initial stage of the devitrification process.

6.10  Transmission electron microscopy image of the Cu55Zr30Ti10Pd5 alloy annealed at 750 K for 1.2 ks. (a) Bright-field image, (b) dark-field image, and (c) selected-area electron diffraction pattern. The dark-field image was taken with the sharp rings in (c). Nanobeam diffraction patterns of 5-, 3- and 2-fold symmetries are inserted in (a), (b) and (c), respectively. Source: Data taken from Louzguine et al.148 with permission from Elsevier Science.

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A bulk glassy alloy sample of Cu-Zr-Ti was reported to contain nanoscale crystalline particles (about 5 nm size)150 in as-solidified state whereas the samples of the Cu-Zr-Ti-Pd alloy containing 5 at.% Pd were glassy. The nanoscale particles of the cP2 (Pearson Symbol) CuZr phase were observed in the as-solidified Cu50Zr30Ti10Pd10 bulk glassy sample. The dissolution of the CuZr nanoparticles took place on heating up to supercooled liquid region owing to the instability of the CuZr phase below 988 K.149,151 According to the Cu-Zr phase diagram, the CuZr phase undergoes eutectoid transformation at 988 K, which is above the supercooled liquid region of the Cu50Zr30Ti10Pd10 alloy (about 750–800 K). The nanoscale CuZr phase becomes thermodynamically unstable and dissolves on heating in the supercooled liquid above Tg when atomic diffusion is enhanced by temperature.

6.5

The mechanical properties of nanocomposite alloys

Bulk glassy alloys demonstrate high yield strength (σy), nearly 2% elastic strain and relatively low Young’s modulus (E). Thus, they have a high performance index σy2/E.152 However, highly inhomogeneous deformation localized in shear bands153 limits their ductility. Thus, the ductilization of bulk metallic glasses is an important technological challenge. Devitrification of the glassy alloys leads to the formation of the composite nanomaterials containing crystalline phase precipitates in the residual glassy phase matrix. Mechanical strength and ductility of glassy alloys can be improved by the precipitates of nanocrystalline or nanoquasicrystalline phase. For example, a Zr65Al7.5Cu7.5Ni10Pd10 alloy having nanoscale icosahedral phase particles embedded in the glassy matrix showed a better combination of the mechanical properties compared to the as-cast glassy sample154 without precipitates. Its Young’s modulus, 0.2% proof stress, ultimate tensile strength, total percentage deformation including elastic deformation are 85 GPa, 1640 MPa, 1750 MPa, and 2.2%, respectively, in the bulk glassy form and 88 GPa, 1780 MPa, 1830 MPa, and 3.1%, respectively, in the 2-phase (nanoquasicrystalline + glassy phase) form. The inclusion of a precipitating phase in this alloy causes deviation and blockage of the operating shear bands, which thus improves the plasticity of the alloy. However, because the single-phase icosahedral phase alloys are extremely brittle155 it is difficult to consider that the icosahedral phase itself has plastic deformability. Thus, its good mechanical properties are attributed to the existence of the residual intergranular glassy phase, while the icosahedral particles can act as a resisting medium against the shear deformation. Also, nanocrystalline precipitates increase the room-temperature mechanical strength of the Zr-AlCu-Pd,156 Zr-Al-Cu-Pd-Fe and (Zr/Ti)-Cu-Al-Ni157 bulk glassy alloys. Some bulk glassy-crystal composites with enhanced ductility have been produced by proper alloying in other Zr-158,159 and Cu-based alloys.160,161 The nanoscale icosahedral

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(Fig. 6.10) or crystalline particles can act as a resistant agent against the shear deformation. Amorphous alloys of Al-RE-TM possess a high tensile strength exceeding 1200 MPa162 and good bend ductility, that is, showing ability of being bent through 180° without fracture.163,164 The homogeneous dispersion of the nanoscale fcc (face-centered cubic) α-Al particles in the amorphous matrix causes a drastic increase in the tensile fracture strength to 1560 MPa165 which is a record number for the high strength Al-based glassy or crystalline alloys. The Al88Y2Ni9Fe1 amorphous alloy containing 7% volume fraction of the fcc-Al particles with a size of about 3–7 nm has a high tensile fracture strength of 1320 MPa and 1260 MPa with the particle volume fraction of 24%, respectively.166 These particles can be formed by controlling the cooling rate upon solidification or by annealing glassy alloys. The largest strength value was obtained when the volume fraction of α-Al phase reached 25%.167 The significant decrease in tensile fracture strength by the further increase in Vf is due to the embrittlement of the remaining amorphous phase by the progress of structural relaxation and enrichment in the solute elements.168 The (Al0.84Y0.09Ni0.05Co0.02)95Sc5 amorphous alloy has an ultra-high tensile fracture strength slightly exceeding 1500 MPa, which surpasses those for all other Al-based fully crystalline and fully amorphous alloys reported to date.169 It opens the possibility of further strengthening such an alloy by nanoscale crystallization. In metallic glasses the deformation is concentrated in the shear bands of maximum shear stress, which maintain about 45° with the load (tensile or compressive) direction. The width of the shear bands is about 10–20 nm. It is considered that the nanoscale α-Al particles can act as an effective barrier against the shear deformation of an amorphous matrix.170 At the same time, it was also suggested171 that the hardening could be attributed mainly to solute enrichment of the residual glassy matrix due to lowering of the Al content. This theory well describes the hardening of the material. As the hardness of fully amorphous or partially crystalline alloys correlates well with the solute content in the amorphous phase, it is suggested that not only α-Al particles but also the amorphous matrix has some role in the hardening and embrittlement of the alloy. However, in some cases, formation of the primary α-Al particles was found to deteriorate mechanical properties and decrease the tensile strength and hardness. Partial substitution of Ni by Cu in the Al85Y8Ni5Co2 metallic glass causes formation of the nanoscale α-Al particles and drastically decreases the tensile strength and hardness values of the alloy.172 Copper, which has a much lower absolute value of heat of mixing with Al, Y and Co than Ni has with these metals, may be responsible for such a decrease in the properties. Thus, Cu may weaken the interaction needed for the stability of the glass, thus resulting in the disappearance of Tg and precipitation of α-Al nanocrystals. In addition, the volume fraction of the α-Al nanocrystals in Al85Y8Ni3Co2Cu2, for example, is

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much lower than that in the primarily devitrified Al85Y8Ni5Co2 metallic glass. It was found that the α-Al inter-particular distances in the Al85Y8Ni3Co2Cu2 metallic glass significantly exceed the particle size itself. Thus, α-Al particles cannot act as an effective barrier against the shear deformation in the amorphous matrix.

6.6

The magnetic properties of nanocomposite alloys

Magnetic materials compose another very important and developing application field of nanostructured alloys. The connection between nanostructure and magnetic properties is a topic of intensive investigations. Ferromagnetic alloys can exhibit hard or soft magnetism depending on their coercivity. Magnetic materials having coercivity above about 104 A/m are considered to be hard while soft magnetic materials have a coercivity below 103 A/m.

6.6.1 Soft magnetic alloys A typical magnetization curve of a soft magnetic alloy (also called a magnetically soft alloy) is given in Fig. 6.11. Classical examples of Fe-based soft magnetic materials with mixed nanocrystalline and amorphous structure, as shown in Fig. 6.7, for example, are Finemet Fe73.5Cu1Nb3Si13.5B9102 and Nanoperm Fe84Zr3.5Nb3.5B8Cu1103 alloys. The structure consists of bcc Fe nanocrystals below 20 nm in size finely dispersed in the amorphous matrix. The addition of Cu, Nb or Zr is responsible for bcc Fe grain refinement and formation of a nanostructure in these alloys.

6.11  Magnetization curve of a Co-Fe-Ta-B glassy sample. Source: Courtesy of P. Sharma.

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Atom probe field ion microscopy and high-resolution TEM studies showed173 that Cu formed nanoclusters in the Fe73.5Si13.5B9Nb3Cu1 amorphous matrix, which work as heterogeneous nucleation sites for bcc Fe particles on devitrification. The studies by X-ray absorption fine structure (XAFS) also showed that Cu clusters with near-fcc structure were present from the very early stages of the devitrification process.174 The density of the clusters is of the order of 10–24 m–3 while the average cluster size is about 2 nm.175 The above-mentioned alloys show high permeability, for example, 100 000 in the case of Fe84Zr3.5Nb3.5B8Cu1 alloy, high magnetization saturation up to 1.5 T and low hysteresis losses.176 Soft magnetic materials of Fe-Zr-B also exhibit high magnetization saturation (Ms) of 1.60–1.70 T under an applied field of 800 kA/m as well as high effective permeability of 13 000–15 000 at 1 kHz. Typical nanocrystalline bcc Fe89Hf7B4 and Fe84Nb7B9 alloys subjected to the optimum annealing exhibit high magnetization saturation above 1.5 T, as well as high effective permeability at 1 kHz above 20,000. For a long time soft magnetic alloys were limited to marginal glass-formers. Soft magnetic properties of thick (Fe, Co)-RE-B glassy alloys were studied.177 Bulk glassy alloys exhibiting a wide supercooled liquid region before crystallization were found in Fe-(Co,Ni)-(Zr,Nb,Ta)-(Mo,W)-B system.178 These alloys have a high Tg of about 870 K and the supercooled liquid region close to 90 K. The high thermal stability of the supercooled liquid enabled the production of bulk glassy alloys with diameters up to 6 mm, which exhibit a high compressive strength of 3800 MPa, high Vickers hardness of 1360, and high corrosion resistance. These glassy alloys exhibit a large magnetization saturation of 0.74–0.96 T, low coercivity of 1.1–3.2 A/m, high permeability exceeding 1.2 × 104 at 1 kHz, and low magnetostriction of about 12 × 10–6. Boron addition is reported to suppress growth of bcc-Fe grains and to stabilize the amorphous matrix. Alloys of Fe82(Zr,Hf,Nb)7B10Cu1 exhibit good soft magnetic properties especially in the high-frequency range.179 Nanocrystalline Fe42.5Co42.5Nb7B8 alloys with a structure consisting of nearly spherical bcc grains with size from 5–10 nm dispersed in the residual amorphous matrix exhibit a high saturation magnetization of 1.90 T and a low coercivity (Hc) of 60 A/m.180 It also exhibits a high Curie temperature (Tc) exceeding 1173 K. The segregation of Nb element in the intergranular amorphous phase increases the thermal stability of the amorphous phase and suppresses the grain growth of the bcc phase. The high thermal stability of the structure and the high Curie temperature are necessary properties of a soft magnetic material for high-temperature application. The Fe-M-B (M = Zr, Hf, or Nb) alloys also show low core losses.181 The Fe66Nb4B30 ferromagnetic bulk glassy alloy with high B content was produced by fluxing and casting.182 It also forms a nanostructure upon initial crystallization on heating. Soft magnetic properties are determined by the nature of the nanocrystal-glassy phase coupling. The origin of the good soft magnetic properties is connected with the formation of the nanoscale bcc-Fe structure and the achievement of rather

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strong magnetic coupling between the bcc grains through the intergranular ferromagnetic amorphous phase.

6.6.2 Hard magnetic alloys Hard magnetic alloys (also called magnetically hard alloys) have sufficiently high coercive force as a resistance to demagnetizing fields with coercivities exceeding 10 kA m–1. These alloys can be used as permanent magnet materials with high magnetic induction that is retained because of a strong resistance to demagnetization, for example, as a result of high anisotropy. Hard magnetic alloys can be produced by crystallization of the glassy phase. For example, permanent magnetic materials consisting mainly of Fe3B with Nd2Fe14B phase were obtained by annealing Nd4.5Fe77B18.5 rapidly solidified alloys.183 The microstructure is composed of magnetically soft Fe3B nanoscale grains and magnetically hard Nd2Fe14B phases. High remanence (Br) of 0.8 T is obtained due to the remanence enhancement effect of exchange-coupled magnetic grains. The remanent polarization (Jr) of this material is 1.2 T and the maximum energy product (BH)max = 97 kJ/m3 while its coercivity Hc = 240 kJ/m. The influence of the heating rate on the microstructure of Fe3B/Nd2Fe14B nanocomposite magnets has also recently been studied.184,185 High coercivity values exceeding 300 kA/m were obtained in amorphous Nd5Fe72Cr5B18 crystallized into Fe3B/Nd2Fe14B state.186 Amorphous alloys of Fe-Nd-B containing 88–90 at.% Fe at 923–1023 K form a nanostructure consisting of bcc-Fe, Fe14Nd2B and the residual amorphous phase. They exhibit good hard magnetic properties, i.e. Br of 1.28 T, coercive field (iHc) of 252 kA/m and (BH)max of 146 kJ/m3 for Fe89Nd7B4.187 Ferromagnetic Nd90-xFexAl10 bulk amorphous alloys with high coercive force at room temperature were obtained by a copper mold casting method. The maximum diameter of the cylindrical amorphous samples with a length of 50 mm is about 7 mm. Neither glass transition nor supercooled liquid region was observed in these alloys in the temperature range before crystallization, which makes them different from previous bulk glassy alloys exhibiting a wide supercooled liquid region before crystallization. The bulk amorphous Nd70Fe20Al10 alloy has ferromagnetism with the Curie temperature (Tc) of about 600 K, which is much higher than the highest Tc (about 480 K) for the Nd-Fe binary amorphous alloy ribbons. The remanence (Br) and intrinsic coercive force (iHc) for the bulk Nd60Fe30Al10 alloy are 0.122 T and 277 kA/m, respectively, in the as-cast state and 0.128 T and 277 kA/m, respectively, in the annealed state for 600 s at 600 K. The Br and iHc decrease to 0.045 T and 265 kA/m, respectively, for the crystallized sample. The hard magnetic properties for the bulk amorphous alloys are presumably due to the homogeneous development of ferromagnetic clusters with large random magnetic anisotropy.188 The low coercivity of Fe3B/Nd2Fe14B magnets imposes a limit on their application. The bcc-Fe/Nd2Fe14B nanomaterials have higher coercivity than

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those for Fe3B/Nd2Fe14B magnets. Coercivity Hc of 480 kA/m and (BH)max of 160 kJ/m3 are reported for bcc-Fe/Nd2Fe14B nanomaterials. The structure consists of two phases: magnetically hard Nd2Fe14B with nanoparticles of α-iron on grain boundaries. Grain size of the Nd2Fe14B is below 30 nm and particle size of the α-iron is below 10 nm.189 The α-Fe/Nd2Fe14B nanostructured magnet of Fe89Nd7B4 composition contains residual amorphous phase and shows Br = 1.22 T, Hc = 240 kA/m and (BH)max = 130 kJ/m3. This alloy has high iron and low boron concentration.190 It has been also found that the rapidly solidified (Fe0.65Pt0.35)83B17 alloy possesses higher coercivity in the annealed state compared to binary Fe-Pt alloys.191 Remanence (Br), Mr /Ms, Hc, and (BH)max of the rapidly solidified Fe80-xPtxB20 (x = 20,22,24) ribbons in the annealed state are in the range of 0.93– 1.05 T, 0.79–0.82, 375–487 kA/m, and 118–127 kJ/m3, respectively (Br is remanence, Hc is coercivity, Ms is magnetization saturation, (BH)max is maximum energy product). Good hard magnetic properties result from the exchange magnetic coupling between the nanoscale magnetically hard γ1 tP4 FePt and magnetically soft γ cF4 Fe(Pt) solid solution as well as Fe2B phases.192 Rapidly solidified alloys of Fe-Pt-P were also found to possess good magnetic properties.193 Although these are rapidly solidified samples, they can be compacted by SPS or hot pressing. Alloys of (Fe0.75Pt0.25)75–70B25–30 were also found to possess good hard magnetic properties including high intrinsic coercivity values up to 400 kA/m in the nanocrystallized state.194 They are promising candidates for nanocomposite permanent magnets. The structure of the rapidly solidified (Fe0.75Pt0.25)75B25 alloy contains a limited volume fraction of the nanoscale cubic cF4 Fe(Pt) solid solution particles of about 4 nm in size embedded in the amorphous matrix. The nanoparticles of cF4 Fe(Pt) phase start growing at the elevated temperatures and then undergo forming of the tP4 FePt compound of about 15 nm in size which is followed by the formation of the tI12 Fe2B phase from the residual amorphous matrix.

6.7

Conclusions

Nanocrystallization on heating that is observed in various bulk metallic glassy alloys leads to the formation of the composites containing nanoscale crystalline or quasicrystalline particles. The formation of the nanocomposites leads to a better combination of mechanical properties than those of fully glassy and fully crystalline alloys. Nanoscale crystalline and quasicrystalline phases play a very important role in ductilization of bulk glassy alloys as they act as the effective barriers for shear bands propagation. This can open an area for future applications of these alloys as structural materials. Magnetic materials are another very important field of applications of nanostructured and composite metallic materials that are produced by partial crystallization of bulk glassy alloys.

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7 Severe plastic deformation and the production of nanostructured alloys by machining J.B. MANN M4 Sciences, USA, S. CHANDRASEKAR, W.D. COMPTON, K.P. TRUMBLE, Purdue University, USA, C. SALDANA and S. SWAMINATHAN, GE John F. Welch Technology Center, India and W. MOSCOSO and T.G. MURTHY, Indian Institute of Science, India Abstract: This chapter describes the production of nanostructured materials using severe plastic deformation (SPD) inherent to machining. The SPD can be controlled, in situ, to access a range of strains, strain rates and temperatures, enabling deformation-microstructure maps to be created. By tuning the SPD parameters, various nanoscale microstructures (e.g. nanocrystalline, nanotwinned, bimodal) can be engineered; and by constraining the chip formation, bulk forms (e.g. foil, sheet and rod) with nanocrystalline and ultrafinegrained microstructures are produced. Chip formation in the presence of a superimposed modulation enables the production of nanostructured particulate with controlled shapes including fiber, equiaxed and platelet types. SPD conditions also determine the deformation history of the machined surface, enabling microstructural engineering of surfaces. These diverse nanostructuring characteristics of machining are united by their common origins in the SPD phenomena prevailing in the deformation zone. Implications for large-scale manufacturing of nanostructured alloys, optimization of SPD microstructures, and consolidation–recycling of industrial machining chips are also briefly discussed. Key words: machining, severe plastic deformation, nanostructured alloys.

7.1

Introduction

The common applications of machining are in producing components with desired geometry and surface topography by the removal of unwanted material in the form of chips. Inherent to this chip formation is a condition of severe plastic deformation (SPD) that is characterized by the development of large plastic strains under controllable strain rates and temperatures. An important consequence of this SPD is the extensive change to the micro- and nanoscale structure of both the chip and machined surface.1 The SPD in machining can be controlled to access a far wider range of deformation parameters than is feasible with conventional SPD methods such as Equal-Channel Angular Pressing (ECAP) and High-Pressure Torsion (HPT), or even by more specialized techniques such as Dynamic Plastic Deformation (DPD). This enhanced control enables broader studies of the individual and interactive effects of strain, strain rate and temperature 178 © Woodhead Publishing Limited, 2011

Severe plastic deformation and production of nanostructured alloys 179 on large-strain deformation phenomena. After a brief review of the underlying mechanics, this chapter will give examples of the employ of machining-based SPD for a host of applications, including fundamental studies of microstructure refinement and bulk-form manufacture of nanostructured materials. First considered are the unique capabilities that chip formation affords to investigations of microstructure refinement, as deformation parameter control vis-à-vis tunable machining process parameters can be used to engineer novel nanoscale microstructures (e.g. nanostructured, bimodal, nano-twinned) that may otherwise be inaccessible with the usual SPD routes. Important aspects of the associated microstructures developed in these studies are highlighted, while correlating low deformation rate microstructures produced by machining with those of conventional SPD methods. As will be seen in the ensuing, this has particular relevance for the construction of deformation-microstructure maps that are likely of interest to materials researchers and structural designers alike. This is followed by consideration of the design of various machining-based SPD platforms for the creation of nanostructured materials in bulk and particulate forms and the application of such configurations to a host of alloy systems. Finally, controlled surface nanostructuring is presented as an emerging area for which the application of machining-based SPD techniques offers promise.

7.2

The mechanics of severe plastic deformation (SPD) in machining

The role of deformation in microstructure refinement is best illustrated in the seminal work of Embury and Fisher2 on deformation of pearlite and Langford and Cohen3 on iron. For example, Langford and Cohen achieved large plastic strains by repeated wire drawing and found the microstructure of deformed iron wire to be composed of grains in the sub-micrometer size range; these microstructure changes yielded a significant increase in the flow stress of the wire. The use of deformation to study microstructure refinement has received a major impetus in the last two decades as a result of the development of various Severe Plastic Deformation (SPD) methods. The most well studied among these are Equal-Channel Angular Pressing (ECAP), Accumulative Roll-Bonding (ARB) and High-Pressure Torsion (HPT), all of which are designed to impose large plastic strains by the cumulative application of deformation in multiple passes. These methods have been quite effective at producing bulk ultrafine-grained (UFG) materials, and have provided significant insights into the mechanisms of microstructure refinement. Perhaps more importantly, their emergence has established SPD as the primary route for developing UFG microstructures in bulk metals and alloys.2–5 However, they are not without limitations. Firstly, the physical configurations used to realize these methods typically limit deformation to small strain rates (<10 2 s–1) and ‘low’ deformation zone temperatures, effectively narrowing the envelope of deformation parameters that can be accessed. This can be particularly troublesome, for example, in the processing of

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moderate-to-high strength alloys that are difficult to deform at low strain rates due to the mechanical limitations of forming equipment. Furthermore, multiple passes of deformation are needed to reach large plastic strains using these methods, this resulting in a degree of uncertainty in the actual deformation parameters (e.g. strain, strain rate) and, as such, the deformation history. As will be seen in the following, machining-based SPD offers an attractive alternative in this regard, as it is a singlepass configuration with access to a wider range of deformation parameters through enhanced control of deformation rate and the associated intrinsic plastic dissipation;6–7 these interactively determine strain rate and temperature in the deformation zone. Figure 7.1 shows a schematic of plane-strain machining wherein a sharp, wedge-shaped tool removes a preset depth of material, the undeformed chip thickness (t0), by moving in a direction perpendicular to its cutting edge. The deformation rate is V0 and the chip forms by shear concentrated in a narrow deformation zone that is idealized as a shear plane. The geometry of the deformation and the average shear strain (γ ) in the chip are determined by the shear angle (φ) and the rake angle (α), parameters that are analogous to the thickness reduction ratio and die angle in conventional deformation processes (e.g. drawing and extrusion). Measurements of the undeformed (t0) and deformed chip thickness (tc) provide an estimate of φ and γ  through the following relations:8



γ = cot(φ) + tan(φ – α)

7.1  Plane-strain machining showing machining variables and deformation zone (shaded).

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[7.1]

[7.2]

Severe plastic deformation and production of nanostructured alloys 181 where λ, the chip thickness ratio (tc /t0), is typically greater than 1 in conventional plane-strain machining. Equations (7.1) and (7.2) can be combined into a single expression to estimate the shear strain as:

[7.3]

As suggested by Eq. (7.3), a range of strains can be imposed in the chip by appropriate selection of α. Indeed, plastic strains up to 15 can be achieved in a single pass in the machining of ductile metals such as copper.6–7 It should be noted that λ in Eq. (7.3) is only partially controllable, as tc is determined by the underlying characteristics of the chip formation process. While this provides a straightforward determination of strain, this characterization is based on an upper-bound model that assumes that the strain is imposed entirely in a plane. A more thorough characterization of the actual deformation field is possible by in situ measurement of strain rate and strain from high-speed imagery of the deformation using particle image velocimetry (PIV).9,10 In PIV, velocities and displacements are obtained by analyzing the motion of ensembles of particles imaged during deformation. Strain rate and strain fields, including the tensor components, are then derived from these velocities and displacements. Figure 7.2 (a) and 7.2 (b) show examples of velocity and effective strain rate (dε/dt = 1/√3 dγ /dt) distributions obtained using PIV on images of the machining of pure copper with α = +20° and V0 = 5 mm/s. The strain rate field is particularly useful for characterizing both the extent and uniformity of the deformation field as it provides a measure of how strain is incrementally imposed during deformation. The deformation zone is readily identifiable from this field as the region of highest strain rate, this also corresponding to the region of maximum velocity change in Fig. 7.2 (a). The spatial extent of this region, or deformation zone thickness – ∆ – is measured as ~100 µm for this particular SPD condition. Furthermore, the uniformity of strain rate across this zone, with the exception of a small region of higher strain rate in the immediate vicinity of the cutting edge, suggests that the deformation in the bulk of the chip is relatively homogeneous. The strain is obtained in PIV by path integration along particle trajectories in the strain rate field.10–11 For this SPD condition, consideration of trajectory AB in Fig. 7.2 (b) gives a shear strain of 2.05 in the chip. This can be compared with a value of 2.3 obtained using the upper-bound model of Eq. (7.3) with λ = 2.5 (measured). Indeed, close agreement between the strains obtained from direct PIV measurements and those from upper-bound estimates has also been observed for a range of SPD conditions. Furthermore, determination of the strain tensor is possible by studying the deformation of arbitrary control volumes as they traverse the deformation zone, as is shown in Fig. 7.2 (b) with the deformation of an initially square element into a parallelogram. Such an analysis is valuable for understanding texture development during SPD.

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7.2  (a) Velocity and (b) strain rate field in SPD of copper by machining (α = 20° and V0 = 5 mm/s) as measured using Particle Image Velocimetry (PIV). The strain is obtained by integration of the strain rate field along particle trajectories, such as AB. An initially square element deforms into a parallelogram as it traverses the deformation zone. ∆ is the average thickness of the deformation zone which for this SPD condition is ~100 µm.

Rigorous characterization of deformation parameters, by PIV for example, can be quite important for a host of investigations. However, estimates of deformations parameters based on an upper-bound formulation, as in Eq. (7.3), might be more practical in various situations given the straightforward nature of their application. An underlying assumption of the upper-bound model is that the deformation zone can be approximated as a single shear plane. However, as apparent in Fig. 7.2, this zone has finite extent. Generally, the deformation zone thickness (∆) typically decreases with the increasing deformation rate, and may increase with increasing undeformed chip thickness. In a variety of metals and alloys, ∆ is typically small (~ 50 µm or less) and relatively constant for V0 > 100 mm/s, a fact established by PIV, metallography and microstructure/hardness characterization,7,12–15 and by slip line field (SLF) and finite element analyses.13–14,16 Even when the deformation zone is somewhat thicker, the largest strain increments remain highly localized in a narrow region reminiscent of the shear plane.10,13–14,16–18 Thus, in general, the approximation of the deformation zone as a shear plane is not unreasonable and is used in the present study to estimate thermo-mechanical SPD parameters of strain rate, temperature and strain. The effect of SPD by machining in imposing microstructure changes in the chip is revealed in the optical micrographs of partially formed pure copper and titanium chips, shown in Fig. 7.3 (a) and 7.3 (b) respectively. These chips were created in specially devised ‘quick-stop’ experiments wherein the machining was suddenly interrupted. While large grains are visible in the bulk, the chips reveal only flow lines indicative of large-strain deformation. Furthermore, the lack of a

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Severe plastic deformation and production of nanostructured alloys 183

7.3  Quick-stop images of machining process with copper (right) and titanium (left).

visible grain structure in the polished and etched chip portions suggests that the grain size is in the sub-micrometer range. The change in the microstructure from that of the bulk to that of the chip is seen to be quite abrupt, occurring over a narrow zone – the shear plane. Figure 7.3 (a) also lists the Vickers hardness values in different regions of the partially formed copper chip sample. The hardness shows more than a two-fold increase across the shear plane, consistent with refinement of the microstructure.

7.2.1 Strain rate In contrast to the conventional SPD methods, machining provides a framework in which the effective strain rate in the deformation zone can be varied over a broad range by varying the deformation rate, V0.1,19 From PIV measurements, such as those shown in Fig. 7.2, dε/dt in the deformation zone can be directly measured and a representative value assigned to this deformation parameter for a given set of machining conditions.10 For example, dε/dt is ~20 s–1 in the machining of pure copper at V0 = 5 mm/s (Fig. 7.2 (b)). When SPD is carried out with a tool of fixed α, typically a condition of constant strain, then the PIV measurements show that dε/dt increases approximately linearly with V0 as dε/dt = KV0, for V0 < 100 mm/s. Similar inferences have been made from grid-based deformation analysis at low speeds.13–14 This range of deformation rates may be termed as low-strain rate deformation with dε/dt values typically in the range of 1 s–1 to 10 3 s–1. While the PIV measurements can be carried out at larger deformation rates of up to a few meters per second, such data are only now becoming available. Nevertheless, the linear dependence of dε/dt on V0 may be used to estimate strain rate at these higher speeds, as this relationship has been shown to be equally valid at larger deformation rates based on metallographic characterization of the deformation zone thickness and SLF analysis.8,13–15 This is based on the fact that:

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[7.4]

where ∆ is the thickness of the deformation zone, usually determined by one of the aforementioned characterization methods, and γ is estimated using Eq. (7.3). Observations have shown that, to first order, ∆ is essentially constant (~ 50 µm) over a wide range of deformation rates, particularly at the higher V0, supporting the linear dependence of dε/dt on V0. These conclusions have been further confirmed by finite element characterization of the deformation zone in machining.16 Thus, dε/dt can be estimated by taking Eq. (7.4) together with Eq. (7.3) and measurements of ∆, or by extrapolating the PIV measurements to higher V0. Based on PIV results and hardness/microstructure characterization of the deformation, ∆ is taken to be 50 µm for V0 > 100 mm/s and 100 µm otherwise. The strain rate in ECAP corresponds to that observed at the lower deformation rates in machining. This is due to the similarity in the deformation rates in ECAP (1 mm/s to 10 mm/s) and low-speed machining, and the close correspondence between their respective deformation fields, as confirmed by PIV measurements of the deformation.20 Contours of constant (iso) strain rate in γ – V0 space can be derived from Eq. (7.4). When ∆ is taken as 50 µm for V0 > 100 mm/s and 100 µm otherwise, as in the illustrative example with copper below, the constant dε/dt contours are hyperbolae in these two velocity regions.

7.2.2 Temperature Estimates of the deformation zone temperature can be made using established thermal analyses that are based on the upper-bound model, and which use measured deformation forces and deformation rates as inputs.8,21–22 Typically, these analyses assume heat generation to arise from plastic dissipation at the shear plane and generally all yield similar values for T. Indeed, these analytical temperature estimates agree well with temperatures measured directly using infra-red (IR) thermographic and thermocouple methods.21,23–25 The analysis of Boothroyd21 may be used to estimate the deformation zone temperature as a function of the machining (SPD) variables. This analysis gives:

[7.5a]

where Γ is the fraction of shear plane heat flowing into the work material, us is the specific cutting energy (energy/volume) due to shear, c is the heat capacity and ρ is the density of the work material, tw is the chip width and Fs is the shear component of the resultant force, FR, as defined in Fig. 7.1. Γ is obtained as:22

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Severe plastic deformation and production of nanostructured alloys 185



[7.5b]

where k is the thermal conductivity of the work material. Eq. (7.5) in the form above assumes that all of the plastic work at the shear plane is converted into heat. In practice, this is a good approximation since typically the fraction converted is measured to be in excess of 0.9 (90%) for a variety of metals. Direct measurements of the stored energy of cold work carried out using differential scanning calorimetry in copper chips also are in good agreement with this fraction, so Eq. (7.5) can be used in practice to estimate T. The duration that an elemental volume is exposed to this temperature is 0.1 ms to 10 ms for the conditions discussed herein.1 Since T is directly determined by the intrinsic plastic deformation-induced heating, the principal variables controlling it are V0 and α in Eq. (7.5a). While these parameters also affect the strain rate in Eq. (7.4), the specific values of dε/dt and T prevailing during the SPD can be determined as a function of V0 and α using Eqs. (7.3)–(7.5) and, hence, can be varied in a systematic way. Additional independent control of this temperature is possible through local heating or cooling of the workpiece prior to the deformation, an example of which will be seen in the cryo-SPD experiment presented.

7.2.3 Zener–Hollomon parameter The temperature and strain rate dependence of plastic deformation can be analyzed using the Zener–Hollomon parameter (Z ), which incorporates both of these variables as:

[7.6]

where T is the deformation temperature, Q is the activation energy for the operative thermally activated process and R is the gas constant. The Zener–Hollomon parameter was originally proposed to describe the combined effect of strain rate and temperature on flow stress of metals for deformation at or below room temperature.26–27 Z increases with increasing dε/dt and with decreasing T, containing within it the observed equivalence between higher strain rates and lower temperatures. Certain deformation-induced microstructure changes which are influenced by strain rate and temperature could also be interpreted in terms of this parameter. For example, the equivalence of high strain rates and low temperatures has been postulated to hold as well for dynamic recovery involving dislocation annihilation.27–28 Recently, deformation

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twinning in SPD of copper and titanium has been interpreted using the Z parameter.29,30 The selection of an appropriate activation energy in Eq. (7.6), however, requires careful consideration. When deformation conditions and microstructure vary significantly across a narrow deformation zone, as in SPD, it is difficult to justify a specific value for Q that is unambiguously characteristic of the deformation. In such conditions, the use of smaller Q values characteristic of the deformation has been suggested.27 In the ensuing analysis, Q for grain boundary diffusion has been used.

7.2.4 Texture When chip formation occurs by shear in a deformation zone of small width, the direction of maximum elongation in a sheared element of the chip is oriented at an angle ψ with respect to the shear plane, as shown in Fig. 7.1. This causes a circle or square element in the initial bulk material to be deformed into an ellipse or parallelogram, respectively, in the chip (Fig. 1.2 (b) ). The ‘texture’ angle (ψ) may be used to describe the ‘macroscopic texture’ in the chip created by the SPD and can be estimated as:31,32

[7.7]

The texture angle can be varied within limits by appropriate selection of the machining variables α and λ, highlighting another aspect of SPD by machining. Direct measurement of ψ is possible from PIV characterization of the strain tensor, as the direction of the largest principal strain is the direction of maximum elongation. For the SPD condition corresponding to Fig. 7.2, the PIV analysis gives an angle of 50.7° for ϕ + ψ; this is the angle between one of the principal directions and the direction of V0. The corresponding value for ϕ + ψ estimated using Eqs. (7.1–7.3) and (7.7) is 44.3° (ϕ = 23.9° and ψ = 20.4°), which is reasonably close. By combining such estimates with microstructure analysis, correlations can be established between the deformation path and evolution of texture.

7.2.5 Constrained chip formation – Large Strain Extrusion Machining Precise control of the deformation parameters (dε/dt, T and γ ) in conventional machining is limited in that the input variable λ in Eq. (7.3) is only partially controllable. In this regard, a constrained variant of the chip formation process – Large Strain Extrusion Machining (LSEM) – offers capability beyond conventional machining as a controlled method of SPD.33,34 Figure 7.4 (a) shows a configuration of LSEM in which the thickness of the chip after deformation is controlled a priori by a constraining tool edge. An analogous rotary configuration

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Severe plastic deformation and production of nanostructured alloys 187

7.4  Mechanics of large strain extrusion machining (LSEM): (a) schematic showing geometry of constrained chip formation in a linear press configuration; (b) constrained chip formation in a turning configuration; and (c) variation of shear strain and normalized hydrostatic pressure (p/2k) in the deformation zone with chip thickness ratio (λ). k is the shear yield strength of the material.

is shown in Fig. 7.4 (b). The position of the constraining edge can be set such that the chip thickness at the die exit (tc) can be greater or less than that the thickness of the material entering the deformation zone (t0). This affords LSEM full control of strain through the chip thickness ratio, λ, unlike in conventional machining where λ cannot be fixed a priori. Furthermore, Eqs. (7.3)–(7.5), which relate the deformation parameters to the controllable variables in machining, apply equally as well to SPD by LSEM. These relationships can also be used to estimate the deformation parameters in a single pass of ECAP, with V0 as the pressing speed, tc = t0, and α set equal to the die inclination angle minus 90°. Figure 7.4 (c) shows that the strain in LSEM is independently controlled by λ and α. Indeed, a 2-parameter dependence of strain enables a final deformation state to be realized by multiple deformation paths, each of which should results in a unique flow field and texture. This provides for flexibility in control of strain, microstructure and texture. Furthermore, the microstructure of samples created using LSEM has shown a one-to-one correlation with the microstructures

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produced by conventional machining under equivalent SPD conditions. Fig. 7.4 (c) also shows that extraordinarily high levels of strain can be imposed in a single pass by LSEM at small λ. The hydrostatic pressure (p/2k) in the deformation zone is also quite large under such conditions, decreasing with increasing λ, based on a slip line field analysis. The combination of large strain and hydrostatic pressure at small λ makes this process condition somewhat akin to that in HPT, and especially valuable for deformation of alloys of limited workability (e.g. Ti, Mg, cast materials).

7.2.6 Comparison of the deformation field in SPD by machining versus other methods The deformation field in machining is a steady-state field that involves the flow of material and heat through the deformation zone. In comparison, the deformation conditions in ECAP represent a relatively narrow band about V0 ~ 1 mm/s in γ – V0 space (see also Fig. 7.5 and the associated discussion). Particle Image Velocimetry (PIV) measurements of the ECAP deformation zone show that it is quite similar to that observed in machining at small deformation rates (Fig. 7.2). The use of larger deformation rates in ECAP is non-trivial given the layout of typical ECAP configurations and inertial effects, which limit the exploration of

7.5  Deformation conditions accessed in the SPD of pure copper. Contours of constant strain rate (d/dt) are shown overlaid on the graph. The ‘coordinates’ (a, b) of the points represent the strain rate, d/dt, and the deformation zone temperature, T, respectively.

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Severe plastic deformation and production of nanostructured alloys 189 the combined effects of strain rate and temperature. However, ECAP can be used to explore strains in excess of machining, albeit using multiple passes of deformation at small deformation rates.35 The deformation rate in HPT can be varied within some range, though much less widely than in machining, by varying the platen rotation speed.35 Furthermore, the strains that can be realized by HPT are much larger than even those of ECAP. However, the deformation field is not steady state, depending on the twist of the sample. The deformation field also is inhomogeneous and is characterized by gradations in strain rate and strain across the sample. Regarding DPD, moderate strain rates of ~103 s–1 can be imposed at smaller strains (~3) by using multiple deformation passes.29 The DPD deformation field also is not steady state, and inertial effects likely hinder imposition of large strains and strain rates.

7.2.7 Machining as an experimental platform As outlined in Sections 7.2.1–7.2.4, the thermo-mechanical deformation parameters of strain, strain rate and temperature in the deformation zone can be systematically varied by appropriate selection of α, λ and V0. This controllability can be leveraged to study material property changes arising in SPD. While this notion has been recognized for some time in the context of using machining as a property test for estimating constitutive mechanical properties,8,36 it also is the subject of recent interest.37,38 What has not been considered thus far are the applications of machining to study microstructure development. Their use to manufacture bulk material forms has only been considered recently.6,7 These applications are reviewed below.

7.3

A study of microstructure refinement

The versatility of machining to study microstructure development over a wide range of deformation parameter space is illustrated by the results of SPD experiments carried out with copper of high purity (99.999%, Alfa Aesar) as a model material system (Fig. 7.5 and Fig. 7.6). The physical properties of the copper were an initial grain size of 0.9 mm, Vickers hardness of 73 ± 3 kg/mm,2 specific heat c = 385 J/kg·K, density ρ = 8900 kg/m3 and thermal conductivity k = 400 W/m·K. A range of deformation conditions – shear strains of 1 to 15, strain rates of 10 s–1 to 105 s–1 and deformation temperatures up to 250°C (0.4 TM) – were imposed in the copper by appropriate selection of the machining input variables, a from –30° to 50° and V0 from 10 mm/s to 5 m/s; Eqs. (7.3)–(7.5) were used to correlate these variables with the SPD conditions.1,19 Microstructure refinement at temperatures well below room temperature (cryo-SPD) was explored by immersing the deformation setup in liquid nitrogen at –196°C.1,19 Chip samples were typically 50 mm in length, 4 mm in width and 0.5 to 2.5 mm in thickness. The microstructure of the samples was characterized by transmission

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7.6  Transmission electron microscopy images of the microstructure of copper at select experimental conditions of strain and deformation rate. The points A, C, etc. correspond to the identically labeled points in Fig. 7.5, so as to facilitate mapping of the experimental deformation conditions on to the microstructures.

electron microscopy (TEM), orientation imaging microscopy (OIM) and optical microscopy, and hardness by Vickers indentation.1,19,39 Figure 7.5 shows the range of SPD conditions, including temperature and strain rate, mapped in γ – V0 space for copper. The shear strain ranges from about 1 to 15 over the different sets of SPD conditions that are represented in the experimental data. The strain rate (dε/dt) and deformation zone temperature are listed as coordinates (dε/dt, T ) beside each of the experimental points in Fig. 7.5, with higher values of V0 corresponding to larger values of dε/dt and T. Contours of constant strain rate are also shown in the figure (see discussion in Section 7.2.1 regarding estimation of dε/dt). The dε/dt values range from about 10 to 3 × 105 s–1 and T values range between 30°C and 250°C for V0 between 10 mm/s to 5 m/s. The corresponding ln Z values are in the range of 20 to 100.1 The extreme left hand side of Fig. 7.5 represents the deformation conditions typically accessible in ECAP.1,5,19,40 The microstructure and hardness were analyzed as a function of the deformation rate and strain, and also in terms of strain rate and temperature. Figure 7.6 shows TEM micrographs of the microstructure of the copper after the SPD at select

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Severe plastic deformation and production of nanostructured alloys 191 conditions of V0 and γ. These conditions were selected to highlight key aspects of the microstructure at different combinations of SPD parameters; the points corresponding to these micrographs are labeled with the same corresponding letters as in Fig. 7.5 to facilitate direct comparison with the associated deformation parameters. The general range of hardness values in the different SPD regions are shown in the γ – V0 plane in Fig. 7.7; specific values at select deformation conditions are reported and discussed in detail elsewhere.1 The coefficient of variation (CV) on the hardness, which is the ratio of the standard deviation to the mean, is also provided in Fig. 7.7.

7.3.1 Microstructure evolution at small deformation rates A broad range of UFG microstructures can be seen in the images in Fig. 7.6. At γ ~ 2.1 and V0 = 13 mm/s, the lowest strain and smallest deformation rate used, the microstructure consists of cellular structures and elongated subgrains having broad, diffuse boundaries consisting of forest dislocations (point A in Fig. 7.6). Geometrically necessary boundaries (GNBs)41 are also seen to be forming, these indicated by arrows in the micrographs. At this SPD condition, the SAD pattern resembles more of a single-crystal type pattern that is indicative of substructures with very small misorientations. The hardness of this microstructure

7.7  Deformation-microstructure map for copper showing schematically, microstructures characteristic of the different SPD conditions. The dotted curves demarcate, roughly, regions with different microstructures. Average and variance of hardness for these microstructures are also provided.

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(~142 kg/mm2) is substantially greater than that of the bulk material. This suggests rapid initial hardening at low strains (Fig. 7.7). Indeed, this steep initial increase in strength for copper has been noted in ECAP,42 uniaxial compression43 and machining.44 At a higher γ of ~5, the microstructure is composed of elongated subgrains with sharper boundaries (point C, Fig. 7.6) and the distance between the GNBs decreases from ~190 nm to ~170 nm. The SAD pattern also indicates an increase in misorientation between the dislocation substructures. Higher strains at V0 = 13 mm/s give grain and subgrain structures with equiaxed morphology and larger misorientations (points D and E, Fig. 7.6), the development of which likely involves continuous dynamic recrystallization45 at the relatively small deformation temperatures (T ~ 40°C) characteristic of this set of SPD conditions. Furthermore, the equiaxed structures at γ ~ 12 (point E) are somewhat larger (345 nm) than those at γ ~ 8 (270 nm, point D), This likely due to growth associated with increases in strain energy and somewhat higher deformation temperatures.1 This microstructure evolution with increasing strain at small deformation rates, including a switchover from elongated substructures to the highly misoriented equiaxed grain structures, is consistent with what has been demonstrated in SPD of OFHC copper (99.95%) by machining.44 It is also consistent with multi-pass SPD of copper by ECAP.40,42 For these conditions, the hardness saturates at 150– 160 kg/mm2 with small variations (CV ~5%), see also Fig. 7.7.1

7.3.2 Deformation twinning Next we consider the microstructures developed at low strains when the strain rate is varied from about 102 s–1 to 105 s–1 by examining a portion of the γ – V0 space along a horizontal line through γ ~ 1.5 in Fig. 7.6. At the higher strain rates, deformation twinning is prevalent, characterized by a dense array of nanoscale twins of width ~20 nm. The twinning was observed at both V0 = 1.67 m/s and 4.4 m/s (points L and S in Fig. 7.6), corresponding to dε/dt of about 2 × 104 s–1 and 7 × 104 s–1, respectively. The overall microstructure at V0 = 1.67 m/s is heterogeneous, with some regions consisting of a high density of nanoscale twins and other regions exhibiting low-misorientation dislocation substructures interspersed with twins (point L in Fig. 7.5 and 7.6). A similar dense array of nanoscale twins was observed at V0 = 4.4 m/s. The twin density in this microstructure is somewhat lower, possibly due to a higher deformation zone temperature that promoted dislocation slip at the expense of twin formation (T ~ 160°C, Fig. 7.5). The hardness of the twinned microstructures corresponding to points L and S is in the range of 120–140 kg/mm2 (Fig. 7.7). While this is lower than the peak hardness levels recorded in copper, it is not significantly different from that of the subgrain microstructures produced at the same strain levels under the small deformation rate condition. Similar nanoscale twinning was observed in cryogenic SPD of copper, with the degree of twinning increasing with increasing strain rate. Figure 7.8 shows a cryoSPD microstructure at dε/dt ~ 103 s–1 and γ ~ 1.6 that is more homogeneous than

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Severe plastic deformation and production of nanostructured alloys 193

7.8  Transmission electron microscopy images of the copper microstructure after cryo-SPD at γ  ~ 1.6 and strain rate of ~103 s–1 showing dense nano-twinning.

that corresponding to points L and S in Fig. 7.6, with most of the grains showing significant nanoscale twinning and average twin widths of ~20 nm. The hardness of this highly twinned microstructure is 175–200 kg/mm,2 substantially greater than that of the twinned structures of Fig. 7.6. Nano-twinned microstructures are of considerable interest since they exhibit Hall–Petch strengthening analogous to conventional nanostructured materials while also maintaining appreciable ductility.46 Furthermore, they have been found to exhibit unusual thermal stability characteristics.47

7.3.3 Discontinuous dynamic recrystallization and bimodal microstructures The unique combination of deformation parameters realized in SPD by machining enabled characterization of the onset and evolution of discontinuous dynamic recrystallization in copper. This can be seen in the microstructure evolution as a function of γ at V0 = 1.67 m/s (points L, M, N and O in Fig. 7.6). In this strain rate range of 104 s–1 to 105 s–1, the twinned microstructure gives way to an elongated subgrain structure with small misorientations (point M) at γ  ~ 5, followed by the onset of a discontinuous type of recrystallization at γ  ~ 7 (T ~ 200°C) at point N. The deformation-induced heating is important, in conjunction with the strain, for facilitating this type of recrystallization.45 Indeed, further increase in strain and

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deformation temperature results in large micron-sized grains, as at point O (Fig. 7.6). Figure 7.7 shows that the onset and progression of dynamic recrystallization is also accompanied by a dramatic loss in strength, with hardness values decreasing from about 140 kg/mm2 to 75 kg/mm2 at strains of 7 and higher. The deformation zone temperature corresponding to the onset of recrystallization is in the range of 200–250°C (Fig. 7.5), with the lower temperatures associated with larger strains. Dynamic recrystallization accompanying a similar evolution of microstructure with strain was also observed at larger deformation rates, as in point Q in Fig. 7.6, at V0 = 2.5 m/s. An intriguing feature of this evolution is the occurrence of a bimodal (composite) type of microstructure, composed of ultrafine subgrains and micron-sized grains at γ ~ 4. This microstructure has a hardness of 127 kg/mm2 with a large variation (CV ~ 25%) compared to that of the other microstructures (Fig. 7.7). This large CV is consistent with a partially recrystallized microstructure consisting of ‘hard’ and ‘soft’ regions. This was also evident in two distinct distributions of hardness with 70% of the points centered at 145 kg/mm2 and the remainder distributed about 85 kg/mm.2 Similar large hardness variations were observed at other similar deformation conditions. Bimodal microstructures, composed of a mixture of ultrafine and micron-sized grains, are of interest as they have been observed to possess potentially attractive combinations of ductility and strength.48 The most interesting aspect of the current processing, however, is that this microstructure was engineered, in situ, during the SPD by using the intrinsic deformation-induced heating. The creation of bimodal UFG microstructures, to date, has generally involved complex, multi-stage thermo-mechanical deformation processing routes.48,49

7.3.4 Fully recrystallized microstructures When the deformation conditions of temperature and strain exceed threshold levels, recrystallization of the copper is expected to occur in situ. These thresholds for complete dynamic recrystallization can be identified from Fig. 7.6 and 7.7. The microstructure in this region is seen to be composed of a mixture of large and small grains, several micrometers in size (Fig. 7.9). As in the partially recrystallized microstructure of point Q, annealing twins are seen in fully recrystallized microstructures corresponding to points N and O (Fig. 7.6). The hardness values of these microstructures are ~75 kg/mm,2 similar to those of the copper in an annealed condition. For a given strain rate, the threshold strain for recrystallization decreases with increasing deformation temperature (Fig. 7.6 and 7.7), typical of classical deformation-induced recrystallization.27

7.3.5 Homogeneity of microstructure Figure 7.10 shows OIM data for copper chips created at near-ambient deformation conditions39 for three different strains (γ ~ 3, 7 and 11). The inverse pole

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Severe plastic deformation and production of nanostructured alloys 195

7.9  Optical micrograph corresponding to point R(V0 = 2.5 m/s, = 6.7) showing some large recrystallized grains (>50 µm) interspersed with smaller micrometer-sized grains.

7.10  Orientation imaging microscopy (OIM) analysis, including inverse pole figure (IPF) map, pole figure and misorientation distribution, for copper subjected to shear strain of (a) 3, (b) 7 and (c) 11 (based on Swaninathan et al.39).

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figure (IPF) map for a strain of 3 shows elongated grains containing dislocation structures within as evident from the color changes within the grain (Fig. 7.10 (a)). The high-angle boundaries (>15°) are marked by black lines in the IPF map. The pole figure shows the presence of rotated (from the initial material) cube texture components, as well as two variants of the B-fiber shear texture component. At still larger strains, γ ~ 7, the IPF map shows presence of ultrafine elongated structures (Fig. 7.10 (b)). The pole figures at this strain show continuous distributions along A and B shear texture fibers and absence of any cube texture components.39 The IPF map at a strain level of 11, however, shows only equiaxed ultrafine grains along with a well-developed shear texture containing B-fiber and the C component. The misorientation distributions show an increase in the population of high-angle boundaries as the strain level increases. An OIM study of the deformation along three mutually orthogonal flow directions in the chip showed uniformity of microstructure throughout the chip volume.39 The development of such a homogeneous microstructure is consistent with a relatively uniform deformation field at the micro-scale, as confirmed by PIV 1,19,50 and evident in Fig. 7.2. Inverse pole figure maps determined for each of the chip faces using OIM (Fig. 7.10) show characteristic shear deformation components with nearly homogeneous texture in the volume of the chip. These observations of uniformity, both in microstructure and texture, throughout the chip volume are particularly encouraging for production of bulk nanostructured alloys.

7.3.6 Deformation-microstructure map The interactive effects of strain, strain rate and temperature on microstructure development could be extensively explored by using machining to probe the envelope of deformation conditions in Fig. 7.5, a range of conditions substantially more diverse than is achievable in ECAP, HPT or DPD. This has been done to develop a deformation-microstructure map for copper.19 Figure 7.7 shows such a map that identifies the microstructures observed in different portions of deformation parameter space. Among other uses, this type of map can guide selection and/or optimization of SPD conditions to realize specific nanoscale microstructures (e.g. nano-twinned, equiaxed, bimodal and combinations thereof). Machining also can be used to develop similar maps for other metals and alloys, even alloys of higher strength that are difficult to deform to large plastic strains over a range of deformation rates by conventional multi-pass SPD methods.

7.4

Bulk forms with ultrafine-grained (UFG) microstructure

Chip formation by machining, as demonstrated in the above results for Cu, offers a means for producing nanostructured materials with controllable microstructures. While chips of macroscopic dimensions can be created by the unconstrained chip

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Severe plastic deformation and production of nanostructured alloys 197 formation in machining, shape and size control of the chips would be advantageous and could complement the microstructure control earlier demonstrated. It is in this regard that the constrained chip formation process – LSEM (see Section 7.2.5) – offers capability for applying controlled SPD in the production of geometrically defined bulk forms, including sheet, foil and wire.34 LSEM has been implemented in a rotary configuration for production of continuous foil34 and in a linear configuration for production of sheet.1 The linear configuration enables manufacture of larger-sized samples due to the increased load capacity of the press equipment used in this configuration. Additionally, a non-plane–strain rotary configuration has been used to produce nanostructured samples in wire and rod forms. Figure 7.11 shows examples of sheet, rod and foil created by LSEM in a diverse set of material systems, including pure metals (Ta, Ti and Cu) and alloys (e.g. Al 6061-T6) with a range of properties in terms of workability and strength. The microstructure of several of these metal and alloy samples are shown in Fig. 7.12 and 7.13, with the Inconel 718, Ti and Al 6061-T6 composed of sub-100 nm grains at higher strains. All of these samples have substantially higher hardness than the corresponding microcrystalline bulk material,51,52 a consequence of the nanoscale microstructure. Figure 7.14 shows the hardness values for the initial microcrystalline bulk alloy and the nanostructured chips. The microstructure in each case is determined by the interactive effects of strain, strain rate and temperature, as illustrated in the SPD results for copper earlier. In the steels, the refinement is reflected in the reduction of interlamellar spacing of

7.11  Bulk forms produced by LSEM using a linear press configuration (left) and a rotary lathe configuration (right).

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7.12  Bright-field TEM micrographs of chips cut from (a) commercially pure Ti, γ ~ 3, grain size: 80 nm, (b) 52100 steel with equi-axed nanoscale ferrite grains [330 nm] and dispersed carbide particles, (c) Al 6061-T6, γ ~ 3, grain size: 200 nm and (d) Inconel 718, γ ~ 8, grain size: 120 nm.

7.13  (a) An optical micrograph of bulk 1080 steel showing a coarse pearlite microstructure; (b) microstructure of 1080 steel chip with occurrence of two distinct pearlitic ensembles – refined pearlite and broken pearlite, as a result of the SPD by machining (based on Shankar et al.53).

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Severe plastic deformation and production of nanostructured alloys 199

7.14  Bar chart showing increases in hardness for a variety of material systems after deformation by machining.

pearlite, including break-up of the cementite at large strains (Fig. 7.13).53 Through single-pass machining-SPD of eutectoid (1080) steel, it has been possible to reproduce the microstructure evolution as a function of strain (up to shear strain of ~6.5) achieved through incremental SPD, as in the pioneering drawing experiments of Embury and Fisher to shear strains of ~7.2 The machining route has also demonstrated the creation of precipitation-treatable alloys (Ni-based alloys, Al 6061) with enhanced strength, thermal stability and ageing kinetics. This was achieved by combining SPD of these alloys in the solution-treated and homogenized condition, followed by suitable thermal treatments.17,54 These early results demonstrate the capability to produce bulk forms with nanoscale microstructure in material systems of commercial interest using LSEM. Furthermore, the transformation of an ‘undeformed chip’ of rectangular crosssection into a rod of circular cross-section, as is the case in the rod and wire, indeed shows that large shape transformations can be achieved by LSEM, a likely consequence of the unique (controllable) thermo-mechanical conditions prevailing in the deformation zone. Optimization of microstructure for specific performance characteristics (e.g. strength, ductility, thermal stability) once completed, will provide the basis for setting the LSEM parameters needed to attain specific nanoscale microstructures in these bulk forms. These nanocrystalline bulk forms can be used as precursor materials for structural components with enhanced strength and wear resistance. Micro- or macro-manufacturing processes such as EDM, laser machining, punching and stamping, micro-turning and micro-milling55 can be used to ‘cut out’ components from the bulk forms for these components. Figure 7.15 shows a set of small gears for a micro-power system produced from one of the nanostructured Inconel 718 foils using micro-EDM.51 This approach to making micro-scale components from

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7.15  A pair of micro-scale gears created from nanostructured Inconel 718 foil using micro-EDM (Agie AC Vertex 2F). The foil was produced by LSEM with λ = 3.5, γ ~ 4, V0 = 0.5 m/s (based on Saldana et al.51).

nanostructured alloys is quite versatile as it can be applied to manufacture microelectromechanical system (MEMS) components from functional materials, including those suited to withstand severe operating environments.

7.5

Nanostructured particulate

The chip formation process may be scaled down to produce particulate of controlled geometry with ultrafine-grained (UFG) microstructures. Potential applications for such materials include reinforcements in structural composites and precursors for powder metallurgy components. These metal particulates are currently produced by a range of processes that imparts characteristic morphology and microstructure to the particles.56 These processes generally yield broad size distributions that require classification. Furthermore, particle morphology and microstructure are highly process-dependent. For example, the evolution of particle size, shape and microstructure in high-energy milling is a consequence of several factors including, milling media, initial charge characteristics, environmental conditions and milling time.57 The milling process is also limited by the contamination associated with the high surface area exposed during repetitive comminution steps and limited control of the particle/agglomerate size. Particulate metals also can be produced through a variant of the machining process – modulation-assisted machining (MAM) – that superimposes a lowfrequency modulation (<1000 Hz) during machining to effect discrete chip formation.1,58,59 In MAM, the chip formation process can be discretized and scaled

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Severe plastic deformation and production of nanostructured alloys 201 down to powder particle size levels (≥20 µm) by controlling the modulation parameters together with the machining conditions (Fig. 7.16). Control of particle size and shape is possible as they are determined by the tool motion and, hence, the modulation and machining conditions.58 Additionally, the microstructure of each particle is controlled by the same SPD parameters as in conventional chip formation. Figure 7.16 shows a schematic of MAM with sinusoidal modulation, Asin(2π fmt), superimposed in the direction of undeformed chip thickness. The instantaneous undeformed chip thickness varies as t0(t) = t0 + 2Acos(2π fmt – π fm / fw)sin(π fm /fw), where t0 is the usual undeformed chip thickness or feed per revolution in the absence of modulation (i.e. conventional machining). If A is sufficiently large, then a discrete chip or particle results.58–60 The minimum value of the amplitude required for particle formation is 2A = t0, this occurring when fm /fw = (integer + ½).58 Further details regarding the relationship between the particle geometry and the modulation/machining conditions are discussed elsewhere.1,61 Regarding production concerns, particle formation by MAM is best achieved with a sequence of machining passes on a lathe, although other kinematic configurations (e.g. face turning, plunge radial turning) have been also employed. Figure 7.17 shows examples of equiaxed-, fiber- and platelet-type particles of Al 6061-T6 produced with a controlled sinusoidal modulation applied using a

Asinwt

7.16  Schematic of machining with modulation superimposed in the direction of undeformed chip thickness. The surfaces created in two successive machining passes of the tool are shown. In turning, each machining pass would be along the circumference of the workpiece with V0 = πdfw , where d is the diameter of the workpiece and fw is its frequency of rotation. A particle forms whenever the tool disengages from the workpiece. The size and shape of each particle are determined by the intersection of two successive machining passes as shown.

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7.17  Scanning electron micrographs of Al 6061-T6 particulate produced by MAM: (a) equiaxed, (b) fiber, and (c) platelet shapes. Note uniformity in size and shape of the particles. The corresponding MAM conditions (d, fw, t0, fm) were as follows: (a) 6 mm, 3 rps, 0.150 mm, 0.050 mm/rev, 181.5 Hz; (b) 6 mm, 3 rps, 0.600 mm, 0.01875 mm/rev, 325.5 Hz; (c) 2 mm, 2 rps, 0.050 mm, 0.0025 mm/rev, 25 Hz.

commercially available modulation device (TriboMAM ®, M4 Sciences).58 The extraordinary uniformity of particle shape is apparent from the SEM micrographs (Fig. 7.17). Uniformity of size was verified by optical microscopy; the standard deviation of the particle size less than 3% of the mean particle size. Regarding microstructure, the particles created by MAM were found to consist of sub-200 nm grains.1 This is consistent with microstructures reported for conventional SPD of Al 6061-T6.52 As is the case with chips produced by conventional by SPD, the refinement of the microstructure alters the mechanical properties of the particulate, and the particles were found to have a Vickers hardness of 154 ± 3 kg/mm2 as compared to a bulk material hardness of 110 ± 2 kg/mm.2 Other experiments have demonstrated production of particles with sizes ranging from 20 to 2000 µm and aspect ratios up to 200, and application to materials systems such as Ti, copper and stainless steels. The machining approach has some interesting advantages with respect to current particulate production methods. For example, in the case of high-aspect ratio fiber production, the current methods suffer from high capital investment costs as well as the typical complications that accompany multi-stage deformation processing. Figure 7.18 depicts a process that is widely used to make high-aspect ratio fibers, bundle wire drawing, wherein rods are collectively drawn down to wires of small diameters, followed by unbundling and cutting of the individual wires into fibers. In-process and intermediate annealing procedures are also needed to effect this multi-stage drawing. This method may be contrasted with the relative simplicity of fiber-making using MAM, which essentially is a singlestage shape transformation process. With regard to the economics, each cutting edge produces fm particles per second, which can be converted into a mass production rate. Production rates typical of industrial powder manufacturing are indeed possible by, for example, using multiple cutting edges and parallelizing the process. Furthermore, nanostructuring of the particles occurs rapidly, on the order of a millisecond, in

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Severe plastic deformation and production of nanostructured alloys 203

7.18  Method for making high-aspect ratio metallic fibers through multi-stage bundle wire drawing. Source: Adapted from S. Amamoto, US Patent 6,316,122B1, November 13, 2001.

contrast to high-energy milling where tens of hours of processing are usually needed. Perhaps, the most intriguing benefit of MAM is that its deterministic nature ensures a high process yield in terms of particle size. In summary, the capability of MAM for effecting concurrent control of particle microstructure and morphology is unmatched by conventional methods.

7.5.1 Particulate consolidation The UFG particulate produced by machining, whether by conventional comminution (e.g. hammer milling) of industrial chips or MAM, can, potentially, be consolidated to produce a wide variety of monolithic and composite bulk forms. Compared to conventional powder metallurgy62 particles in the size range of 5 to 200 µm, where the grain size is typically in the order of the particle size, the UFG particles contain millions of grains. At the same time, the problems of agglomeration and surface contamination encountered in consolidation of sub-micrometer sized powders (nanoparticles),63 due to their high surface area, are eliminated. However, given the high driving force for coarsening (e.g. recrystallization, grain growth, Ostwald ripening), maintaining a fine grain structure during thermo-mechanical consolidation represents a key challenge. The sintering temperatures necessary to effect inter-particle bonding and densification by diffusion, for example, are typically above 0.5Tm, which typically exceeds the recrystallization temperature. While much remains to be learned about the thermal coarsening of nanostructured alloys, including solute segregation, precipitate pinning, and crystallographic texture effects, several low-temperature consolidation strategies have been demonstrated for the UFG particulate. One low-temperature consolidation strategy that has been demonstrated is powder extrusion.64 High hydrostatic pressures combined plastic shear in the deformation zone disrupts particle surface oxides, enabling densification and metallurgical bonding at ambient temperatures. Extruding 100- to 200-µm Al 6061-T6 chip particulate at room temperature gave poor bonding due to the high strength of the particles limiting plasticity. By combining the machining chip particulate with a pure aluminum powder and extruding at room temperature to a

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reduction ratio of 10:1, complete bonding was achieved, with densities over 98%. Figure 7.19(a) shows that the UFG alloy particles deformed little, if any, during extrusion while the soft aluminum flowed completely around them under the intense shear. Nano-indentation measurements suggested little loss of the hardening from machining in the UFG particles. Similar results have been obtained for other aluminum alloy systems. Another promising direction for densifying the UFG particulates in composite configurations, is through infiltration processing. Figure 7.19(b) shows the result of infiltrating Al 356 casting alloy into an M2 tool steel chip preform. Nano-indentation yielded mean hardness and Young’s modulus values not significantly different from those of a commercially available Al-SiC composite.65 Furthermore, the hardness of the reinforcements appeared to be only marginally decreased by the heating (~700°C) during infiltration. Compared to conventional ceramic particle reinforcements for aluminum and magnesium matrix composites (e.g. SiC, Al2O3), the high-strength UFG steel reinforcements should offer significantly improved wetting for liquid state processing. The degree to which these factors enable conventional die casting equipment to effect rapid and complete infiltration, with minimal time at temperature, is currently under investigation. These observations pertaining to occurrence of UFG microstructures in industrial machining chips, and methods of using the same via consolidation and composites processing routes, have implications also for recycling of industrial machining chips into high-value products.

7.19  (a) Optical (DIC) micrograph of Al 6061-T6 UFG particulate (100–200 µm) extruded at room temperature with an equal proportion of pure Al powder (~60 µm). Note complete bonding of UFG alloy particles (in relief) in pure Al matrix. (b)  Optical micrograph (BF) showing composite produced by infiltration of M2 tool steel chips (lighter) with Al 356 matrix. No interface reaction product can be resolved. A few nano-indentations can be seen.

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7.6

Surface nanostructuring

In chip formation, the machined surface and its immediate vicinity (sub-surface) are also subjected to high levels of deformation.66 The strains in this region are large (γ > 5) and decay with depth into the sub-surface.1 Similar inferences pertaining to the strain field have come from metallography, grid deformation13 and electron microscopy.67 As such, a fine-scale microstructure may be expected on the machined surface. Indeed, UFG microstructures have been observed on surfaces created by a number of different material removal processes.15 For example, copper surfaces created by abrasive machining have been shown to be comprised of equiaxed grains, ~30 nm, with an orientation texture similar to that of rolling.68 A microstructure consisting of ~100 nm grains has also been observed on hard steel surfaces generated under select machining conditions.69–72 These UFG microstructures are analogous to those found in sliding,73 rolling,74 mechanical attrition,75 and HPT. While the occurrence of such features on machined surfaces has long been recognized, what has not been explored is the possibility of systematically engineering specific microstructures in the surface. For machining, this concept is based on the close correspondence between the deformation histories of the material evolving into the machined surface and that of the chip.66,76 To demonstrate nanostructuring of surfaces by controlled machining SPD, oxygen-free high conductivity (OFHC) copper (99.95%, Goodfellow) and brass (70% Cu–30% Zn) samples were machined at near-ambient temperature and at –196°C under plane-strain conditions using a sharp, high-speed steel tool.1,66 The samples were sheets, 3 mm in width, with initial grain sizes of 35 µm (Cu) and 200 µm (brass), and Vickers hardness of 77 ± 3 kg/mm2 (Cu) and 80 ± 5 kg/mm2 (brass). An undeformed chip thickness of 100 µm to 200 µm and machining speeds of up to 500 mm/s were used. The strain imposed in the deformation zone was varied by using tool rake angles of –30° to +50°. Figure 7.20 shows PIV measurements of strain with depth from the machined surface for brass and copper. The strain values at the surface were estimated as ~5 (+20° rake) in the Cu and ~3 (+10° rake) and ~10 (–30° rake) in the brass. The strains in the corresponding chips were determined by PIV and are shown by points A, B and C.1,47,66 The close correspondence between the chip and surface strains is not surprising, given that the material constituting the bulk of the chip and the machined surface experience similar deformation history. Similar arguments may be made using analysis of particle trajectories in grid deformation experiments.13,67 Further evidence for the similarity between the deformation levels on the machined surface and chip comes from the hardness data for copper presented.66 The hardness of the machined surface is substantially greater than that of the bulk material prior to machining (dotted line in the figure). Furthermore, the hardness values at the surface and of the corresponding chip are essentially the same for different machining conditions. This equivalence is especially striking at

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7.20  Variation of strain with depth from the machined surface in copper and brass. The dotted curves are extrapolations used to estimate the strains at the surface. The strain values in the chip are marked as A (brass, +10° rake), B (copper, +20° rake) and C (brass, –30° rake). Inset shows TEM pictures of a microstructure on the machined surface and of a chip created under a similar deformation condition (γ ~ 8). Both of these microstructures are seen to be very similar, highlighting the equivalence between chip and surface microstructures for the same process conditions.

some of the more special deformation conditions, such as in the cryo-SPD and machining with a +50° rake angle tool. The cryo-SPD condition shows very high hardness values (~180 kg/mm2) for both the chip and machined surface, undoubtedly a consequence of the enhanced refinement occurring in both of these regions at this condition. When machining with the +50° rake angle tool at nearambient temperature, the deformation strain is much smaller (γ ~ 1) than with the –10° rake tool (γ ~ 8), resulting in smaller levels of microstructure refinement on the machined surface and in the chip.1 The inset TEM images in Fig. 7.20 also show a high degree of similarity between the chip and near-surface microstructures, in this case equiaxed UFG microstructures with grain size of ~200 nm, reflective of essentially identical deformation histories. Electron Backscatter Diffraction (EBSD) of the material on the work surface and deformation zone also supports this microstructure equivalence.18,66

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Severe plastic deformation and production of nanostructured alloys 207 The basis for controlling microstructure and mechanical properties of surfaces created by machining is provided by the close correspondence between the strains on the machined surface and chip. The SPD parameters can be reasonably estimated using the shear plane model described in Section 7.2, enabling correlation with the controllable machining variables of cutting speed, rake angle and chip thickness ratio. Taken together with a deformation-microstructure map, such as that outlined for copper in Fig. 7.7, the controllable machining variables may be tuned to set appropriate SPD conditions for generating specific surface microstructures.

7.7

Conclusions

The deformation that occurs during chip formation can be controlled, in situ, to access a wide range of strains, strain rates and temperatures. This is used in the present study to demonstrate the creation of a variety of nanoscale microstructures in the chip including equiaxed, bimodal and nano-twinned structures. A map is outlined for SPD of copper that describes the interactive effects of strain, strain rate and temperature on microstructure. This type of map is may be used to optimize process parameters to engineer materials with interesting combinations of microstructure, texture and mechanical properties. By adding dimensional control to the chip formation process through LSEM, bulk forms such as foil, sheet and rod are produced with controllable nanocrystalline and UFG microstructures. A newly developed chip formation process, modulation-assisted machining (MAM), enables the production of nanostructured particulate with controlled particle shapes (e.g. fiber, equiaxed and platelet). Large-scale manufacturing of nanomaterials by LSEM and MAM in structural alloy systems of interest is currently being explored. Lastly, the SPD conditions prevailing in the deformation zone are shown to determine the deformation history of the machined surface and, consequently, also the microstructure. This suggests that machining can also be used to engineer surfaces with specific micro- and nanoscale structures. The uses of machining for materials manufacturing represent deformation processing applications of this class of processes. While these applications are diverse, they are united by their foundation in the SPD phenomena that prevails in the deformation zone during chip formation. Furthermore, these newer applications likely are subject to processing constraints similar to those of component manufacture, including those related to tool wear, workability of materials and equipment capability.

7.8

Acknowledgements

This work was supported in part by NSF grants CMMI-0626047 and CMMI0800481; the Oak Ridge National Laboratory; the U.S. Department of Energy’s

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FreedomCAR Program via Pacific Northwest National Laboratories contract DE-AC06–76RL01830; and a Ford University Research Program award all to Purdue University; NSF grants STTR-0944980 and SBIR-0822879 to M4 Sciences LLC; and an NSF Graduate Research Fellowship to CS. Microscopy work at the Oak Ridge National Laboratory’s High Temperature Materials Laboratory was sponsored by the US Department of Energy, Office of Energy Efficiency and Renewable Energy, Vehicle Technologies Program. We are grateful to Dr Larry Allard of Oak Ridge for assistance with some of the transmission electron microscopy. Drs S. Lee, B.C. Rao (IIT Madras, India), and M. Ravi Shankar (University of Pittsburgh, Pittsburgh, USA); and T.L. Brown and Y. Guo (Purdue University) are acknowledged for their contributions to some of the results reported herein. We also appreciate the support of Professor Terry R. McNelley, Naval Postgraduate School, Monterrey, CA, with the OIM analysis.

7.9

References

  1 Brown T.L., Saldana C., Murthy T.G., Mann J.B., Compton W.D., Trumble K.P., King A.H., and Chandrasekar S. Acta Mater, 2009; 57:5491.   2 Embury J.D., Fisher R.M. Acta Metall 1966; 14:147.   3 Langford G., Cohen M. Trans ASME 1969; 62:623.   4 Segal V.M., Reznikov V.I., Drobyshevskiy A.E., Kopylov V. Rus Metall 1981; 1:99.   5 Valiev R.Z., Islamgaliev R.K., Alexandrov I.V. Prog Mater Sci 2000; 45:103.   6 Brown T.L., Swaminathan S., Chandrasekar S., Compton W.D., Trumble K.P., King A.H. J Mater Res 2002; 17:2484.   7 Swaminathan S., Shankar M.R., Lee S., Hwang J., King A.H., Kezar R., Rao B.C., Brown T.L., Chandrasekar S., Compton W.D., Trumble K.P. Mat Sci Eng A 2005; 410:358.   8 Shaw M.C. Metal cutting principles. Oxford University Press, New York, 1984.   9 Gnanamanickam E.P., Lee S., Sullivan J.P., Chandrasekar S. Proceedings of the Society for Experimental Mechanics Annual Conference and Exposition on Experimental and Applied Mechanics 2007; 1080. 10 Lee S., Hwang J., Shankar M.R., Chandrasekar S., Compton W.D. Metall Mater Trans A 2006; 37:1633. 11 Thomsen E.G. Yang C.T., Kobayashi S. Mechanics of plastic deformation in metal processing. Macmillan, 1965. 12 Keciouglu D. Trans ASME 1958; 80:158. 13 Oxley P.L.B. Mechanics of machining. Ellis Horwood, New York, 1989. 14 Oxley P.L.B., Hastings W.F. Proc R Soc Lond A 1977; 356:395. 15 Samuels L.E. Metallographic polishing by mechanical methods (4th ed). American Society for Materials International, 2003. 16 Sevier M., Yang H.T.Y., Lee S., Chandrasekar S. Metall Mater Trans B 2007; 38:927. 17 Shankar M.R., Chandrasekar S., King A.H., Compton W.D. Acta Mater 2005; 53:4781. 18 M’Saoubi R. and Ryde L. Mat Sci Eng A 2005; 405:339. 19 Saldana C., Swaminathan S., Brown T.L., Mann J.B., Compton W.D. and Chandrasekar S. ASME J Mfg Sci Eng 2010; 132:030908. 20 Lee S. Ph.D thesis, Purdue University, 2006. See also Chandrasekar S. and Trumble K.P., In situ characterization of large strain deformation field in severe plastic

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Severe plastic deformation and production of nanostructured alloys 209 deformation, presentation at Ultrafine Grained Materials (UFG) 2006, Kloster Irsee, Germany, September 24–26, 2006. 21 Boothroyd G. Proc I Mech E 1963; 177:789. 22 Weiner J.H. Trans ASME 1955; 77:1331. 23 Hwang J., Kompella S., Chandrasekar S., Farris T.N. ASME J Trib 2003; 125:377. 24 Narayanan V., Krishnamurthy K., Hwang J., Chandrasekar S., T.N. Farris, Madhavan V. Measurement of Temperature Field at the Tool–Chip Interface in Machining, NSF Workshop on Research Needs in Thermal Aspects of Material Removal Advanced Technology Research Center, Oklahoma State University, June 10–12, 2003. 25 Davies M.A., Ueda T., M’Saoubi R., Mullany B., Cooke A.L. CIRP Ann 2007; 56:581. 26 Zener C., Hollomon J.H. J Appl Phys 1944; 15:22. 27 Backofen W.A. Deformation processing. Addison-Wesley, 1972. 28 Christian J.W., Mahajan S. Prog Mater Sci 1995; 39:1. 29 Li Y.S., Zhang Y., Tao N.R., Lu K. Acta Mater 2009; 57:761. 30 Saldana C., Shankar M.R., Murthy T.G., Huang C., Gnanamanickam E., Chandrasekar S. Proceedings of the 11th CIRP conference on Modeling of Machining Operations, NIST, 2008. 31 Dautzenberg J.H., Zaat J.H. Wear 1973; 23:9. 32 Townend G.H. J Appl Phys 1947; 18:784. 33 De Chiffre L. Int J Mac Tool Des Res 1976; 16:137. 34 Moscoso W., Shankar M.R., Mann J.B., Compton W.D., Chandrasekar S. J Mater Res 2007; 22:201. 35 Valiev R.Z. and Langdon T.G. Prog Mater Sci 2006; 51:881. 36 Drucker D.C. J Appl Phys 1949; 20:1013. 37 Maekawa, K., Obikawa, T., Yamane, Y., Childs, T.H.C., 2000, Metal Machining: Theory and Applications. Butterworth-Heinemann, UK. 38 Adibi-Sedeh A.H., Madhavan V. and Bahr B.J. ASME J Mfg Sci Eng 2003; 125:656. 39 Swaminathan S., Brown T.L., Chandrasekar S., McNelley T.R. and Compton W.D. Scrip Mater 2007; 56:1047. 40 Mishra A., Kad B.K., Gregoric F., Meyer M.A. Acta Mater 2007; 55:13. 41 Hughes D.A., Hansen N., Bamman D.J. Scrip Mater 2003; 48:147. 42 Torre F.D., Lapovok R., Sandlin J., Thomson P.F., Davies C.H.J., Pereloma E.V. Acta Mater 2004; 52:4819. 43 Steeds J.W. Proc R Soc Lond A 1966; 292:343. 44 Swaminathan S., Shankar M.R., Rao B.C., Compton W.D., Chandrasekar S., King A.H., Trumble K.P. J Mater Sci 2007; 42:1529. 45 Humphreys F.J., Hatherly M. Recrystallization and related annealing phenomena (2nd ed). Elsevier, Oxford, 2004. 46 Lu L., Shen Y.F., Chen X.H., Qian L.H. and Lu K. Science 2004; 304:422. 47 Saldana C., Murthy T.G., Shankar M.R., Stach E.A., Chandrasekar S. Appl Phys Lett 2009; 94:021910. 48 Wang Y.M., Ma E. Acta Mater 2004; 52:1699. 49 Wang Y.M., Chen M., Zhou F., Ma E. Nature 2002; 419:912. 50 Gnanamanickam E.P., Lee S., Sullivan J.P. and Chandrasekar S., Meas Sci Tech 2009; 20:095710. 51 Saldana C., Yang P., Mann J.B., Moscoso W., Gill D.D., Chandrasekar S. and Trumble K.P. Mat Sci Eng A 2009; 503:172. 52 Swaminathan S., Shankar M.R., Rao B.C., Compton W.D., Chandrasekar S., King A.H. and Trumble K.P. J Mater Sci 2007; 42:1529.

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53 Shankar M.R., Verma R., Rao B.C., Chandrasekar S., Compton W.D., King A.H. and Trumble K.P. Metall Mater Trans A 2007; 38:1899. 54 Shankar M.R., Rao B.C., Chandrasekar S., Compton W.D. and King A.H. Scrip Mater 2008; 58:675. 55 Rajurkar K.P., Levy G., Malshe A., Sundaram M.M., McGeough J., Hu X., Resnick R. and DeSilva A., CIRP Ann 2006; 55:643. 56 Lenel F.V. Powder Metallurgy: Principles and Applications, Metal Powder Industries Federation, Princeton, NJ, 1980. 57 Witkin D.B. and Lavernia E.J., Prog Mater Sci 2006; 51:1. 58 Mann J.B., Shankar M.R., Chandrasekar S., Compton W.D. and Moscoso W, Machining Method to Controllably Produce Chips with Determinable Shapes and Sizes, US Patent 7,628,099, December 8, 2009. See also Mann J.B., Chandrasekar S. and Compton W.D., Tool-Holder Assembly and Method for Modulation-Assisted Machining, US Patent 7,587,965, September 15, 2009. 59 Toews H.G., Compton W.D. and Chandrasekar S., Prec Engg 1998; 22:1–9. 60 Chhabra P.N, Ackroyd B., Compton W.D., Chandrasekar S. Proc Inst Mech Engrs B 2002; 216:321. 61 Mann J.B., Saldana C., Chandrasekar S., Compton W.D. and Trumble K.P. Scrip Mater 2007; 57:909. 62 Lenel, F.V. Powder Metallurgy Principles and Applications, Metal Powder Industries Federation, Princeton, NJ, 1980. 63 Sanders, P.G., Fougere, G.E., Thompson, L.J., Eastman, J.A. and Weertman, J.R. Improvements in the synthesis and compaction of nanocrystalline materials. Nanostruct Mater 1997; 8:3, 243–252. 64 Roberts, P.R. and Ferguson, B.I. Extrusion of Metal Powders, Inter Mater Rev 1991 36:2, 62–79. 65 Clyne, T.W. and Withers, P.J. An Introduction to Metal–Matrix Composites, Cambridge, 1995. 66 Calistes R., Swaminathan S., Murthy T.G., Huang C., Saldana C., Shankar M.R., Chandrasekar. S. Scripta Mater 2009; 60:17. 67 Ramalingam S., 1967, Plastic Deformation in Metal Cutting, Ph.D. Thesis, University of Illinois. 68 Turley D.M., Samuels L.E. Metallog 1981; 14:275. 69 Rogers H.C. Ann Rev Mater Sci 1979; 9:283. 70 Matsumoto Y., Barash M.M. and Liu C.R. J Eng Indus 1986; 108:169. 71 Akcan S., Shah S., Moylan S.P., Chhabra P.N., Chandrasekar S. and Yang H.T.Y. Metall Mater Trans A 2002; 33:1245. 72 Ramesh A., Melkote S.N., Allard L.F., Riester L. and Watkins T.R. Mat Sci Eng A 2005; 390:88. 73 Rigney D.A. Wear 2000; 245:1. 74 Hughes D.A., Chrzan D.C., Liu Q., Hansen N. Phys Rev Lett 1998; 81:4664. 75 Zhu K.Y., Vassel A., Brisset F., Lu K., Lu J. Acta Mater 2004; 52:4101. 76 Mann J.B., Saldana C., Moscoso W., Murthy T.G., Huang C., Swaminathan S., Rao B.C., Shankar M.R., Compton W.D., Trumble K.P., Chandrasekar S. 2008, Unusual Applications of Machining, Proc 23rd All India Int Ind Manf Tech Des Res Conf, pp. 47–55.

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8 Deformation structures including twins in nanograined pure metals K. HATTAR, Sandia National Laboratories, USA Abstract: This chapter discusses deformation structures observed in nanograined metals and the proposed formation mechanisms associated with each defect structure. This review is limited to experimental observations in pure metals and predominately to transmission electron microscopy studies due to the length scale of interest. The defect structures that have been observed and will be discussed include: perfect and partial dislocation structures, twins, dislocation loops, disclinations, and other unexpected defect structures. Several of these defects are not observed or are not present at equivalent densities in coarse-grained metals, suggesting the activation of alternative deformation mechanisms. These effects will be highlighted by a few key experiments. Theory and modeling will be used to aid the interpretation of the experimental results, particularly in cases in which time-resolved results at the appropriate spatial resolution are not available. Key words: deformation structures, transmission electron microscopy (TEM), deformation mechanisms.

8.1

Introduction

8.1.1 Nanograined defects in historical perspective Despite the fact that mechanical deformation and metallurgy date back to antiquity, the study of deformation defect structures in metals began in the 1930s when Orowan, Taylor, and Polanyi proposed the concept of edge dislocations. Since that discovery, extensive research along with new experimental and modeling tools has resulted in the discovery of a multitude of deformation defects in metals. Great advances in the discovery and characterization of defect structures in metals resulted from the introduction of the transmission electron microscope (TEM), which permitted direct observation of these defects and their interactions with each other. The type, size, and density of the defect structures found in structural metals, which vary from nearly perfect single crystals to severely plastically deformed structures, are a result of the materials processing history and composition. In this chapter, we will discuss the defect structures observed in high purity nanograined metals that are 1–100 nm in grain size and produced by a variety of methods. Most of the observations will be limited to a variety of TEM characterization techniques due to the resolution needed for the characterization of nanoscale defects in nanograined metals. Real-time TEM observations of the 213 © Woodhead Publishing Limited, 2011

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deformation dynamics will be referenced heavily, as they often provide the greatest insight into the formation and destruction of the deformation structures. This chapter will begin with a characterization of the classical defect structures observed in nanograined metals including: grain boundaries, twins, and dislocations. Classical deformation structures, which are absent from nanograined metals such as dislocation networks, cell structures, and pile-ups, will be discussed next. The third main topic to be discussed is the unique defect structures that have been reported in nanograined metals, but are uncommon in coarse-grained metals. These uncommon defects include five-fold twin formations, disclinations, and agglomerated grains. The effect of initial microstructure on the active deformation mechanisms and the resulting deformation defect structure will be emphasized. Finally, the chapter will end with a brief description of the potential future trends in the field and suggested literature for the reader with further interest in this area.

8.1.2 Short review of well established structures Before discussing the defect structures in nanograined metals, a basic understanding of the common defect structures present in coarse-grained metallic structures is necessary. The defect structures present in metals can be defined by either their dimensionality or the process by which they were introduced into the crystal structure. Using a bubble raft model, Table 8.1 illustrates the classical defects commonly found in metal systems based on their dimensionality. The top row has 0-D defects that include the omission of an atom, vacancy, the inclusion of either an atom larger, smaller, or different in some capacity from the matrix, interstitial or substitutional atom. The second row shows an individual edge dislocation, a 1-D defect, which is identified by the Burgers vector arrowed. The third row shows a grain boundary, a misorientation of the same lattice structure, and an interface between different lattice structures. Two-dimensional defects are the most common defect in nanograined metals. Three-dimensional defects include voids, as illustrated in the last row of Table 8.1, and precipitates. The distinction of defect structures produced by process route is not as definitive, although a general trend suggests that the greater the energy put into deformation, the more complex the defect structure. The combination of the defect dimensionality, density, and character has a direct effect on the properties and performance of any material and is thus worthy of investigation. Readers new to this field are referred to the classical and introductory literature.1–9 The details of the formation and destruction active in many of these structures are still under investigation, although much progress has been made through a combination of in situ TEM investigations and computational models.

8.2

Classical defect structures in nanograined metals

Several defect structures that have been experimentally observed in nanograined metals are also commonly observed in coarse-grained metals, but at densities and

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Deformation structures including twins in nanograined pure metals 215 Table 8.1  Potential defect structures in crystalline lattices arranged by dimensionality

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under circumstances not regularly seen in coarse-grained metals. These defects include dislocations, stacking faults, twins, grain boundaries, and point defect agglomerations. A comparison will be made of the character and density of these defects as a function of grain size.

8.2.1 Perfect dislocations Dislocation motion and interactions are at the core of all deformation and failure mechanisms in ductile metallic systems. As has been discussed throughout the chapters of this book, much of the study of nanograined metals has emphasized the effects of limited grain volume on the hindrance or absence of classical dislocation mechanisms and processes. Dislocation density and dislocation structures are commonly identified by TEM using a variety of imaging conditions. Identification of dislocations becomes more difficult as the grain size decreases and multiple grains are present through the thickness of the TEM foil. Despite these difficulties, dislocations have been observed in nanograined metals with grains as small as 10 nm.10 Figure 8.1 (a) illustrates a common dislocation structure seen in a coarse grained Al-Mg-Sc alloy. As is often the case in coarse-grained alloys, the dislocations interact with themselves as well as with grain boundaries, particles, and any other structural defects in the material. As the grain size decreases, the time for which a mobile dislocation is present within a grain decreases; this decreases the probability that the dislocation will have time to interact with other dislocations and limits the interactions with the surrounding grain boundaries. The interaction of a limited number of dislocations on at least two slip systems can be seen in Fig. 8.1 (b). When the grain size decreases to 10 nm, the number of dislocations present in the film decreases substantially due to dislocation repulsion forces. These dislocations are often reported as dislocation dipoles indicated in Fig. 8.1 (c) from Shan et al.’s work on nanograined Ni. The decreased presence of dislocations and, more importantly, of dislocation interactions has a significant effect on the mechanical properties of nanograined metals. This decreased presence will be discussed in more detail in Section 8.3.

8.1  (a) Common dislocation structure seen in Al-Mg-Sc alloy. (b) Dislocation present within a 1 µm grain of high-purity Al. (c) Dislocation present in a 10 nm diameter grain in Ni.10

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8.2.2 Partial dislocations (stacking faults) Partial dislocations are commonly observed in coarse-grained metals and alloys with low stacking-fault energy. The interactions of these partial dislocations have been found to play a significant role in the deformation and failure processes. It has been suggested from the theory and computational models that as grain size decreases, perfect dislocations become less dominant and partial dislocations occur more frequently. In order to understand the potential difference in defect structure, Yamakov et al.11 developed a deformation map for nanograined metals in which the deformation mechanism is determined to be simply a function of stress, grain size, and stacking-fault energy, as seen in Fig. 8.2.11 The three dominant mechanisms were determined to be grain boundary mediated deformation, partial dislocation slip, and full dislocation slip. These mechanisms were identified by simulating strain in nanograined Al with an average grain size of 32 nm and varying the stacking-fault energy. The change in deformation mechanism to grain boundary mediated processes results in a change in the Hall– Petch relationship as the grain size decreases. At the smallest grain size, this results in an inverse relationship between grain size (d ) and yield stress (σ ):

.

[8.1]

8.2  Deformation map delineating the active deformation mechanism as a function of grain size based on MD computer simulations,11 where r and d are defined in equation 8.2.

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This proposed mechanism and the associated deformation map, Fig. 8.2,11 have resulted in intense discussions within the field and have been accepted as incomplete due to recent experimental studies. This model does not take into account any deformation mechanisms associated with grain growth that have recently been reported to be active in nanograined metals during deformation.10,12,13 Normalized values of stress (σ∞ /σ∞ ) and grain size (r/d ) make Yamakov et al.’s deformation map applicable to a wide variety of metals.



[8.2]

The applied stress (σ ) is normalized by the resolved shear stress at which the dislocation splitting distance is infinity (σ∞). This resolved shear stress is the stacking-fault energy (γ ) and a set of constants based on the elastic modulus and the Shockley partial dislocation type. The grain diameter is normalized by the placement of the equilibrium dislocation splitting distance (r0) in the numerator of the abscissa. The term r0, as shown in Equation 8.2, is based on the elastic modulus and the Shockley partial dislocation type, as well as the Burgers vector (b), and the stacking-fault energy (γ ). The mechanism demarcation lines indicated in Fig. 8.2 are dependent on a variable (r) that is a function of the equilibrium dislocation splitting distance (r0 ), the applied stress (σ ), and the resolved shear stress at which the dislocation splitting distance is infinity (σ∞). Although the motion of partial dislocations has been proposed to dominate in many nanograined metals, limited experimental research exists showing the presence of either partial dislocations or partial dislocation structures.14 Complex partial dislocation structures are known to exist in coarse-grained low stackingfault energy metals; these structures include dislocation node structures that result in interacting partial dislocations. This is in contrast to the structures seen in deformed nanograined Au, a low stacking-fault metal that does not show significant signs of partial dislocation structures.15 Partial dislocations and the subsequent stacking faults have been reported in nanograined metals. For example, Liao et al. observed both deformation twins and stacking faults as wide as 6.8 nm in cryogenically ball-milled Al, despite a bulk stacking-fault energy of 166 mJ m–2.16,17 In general, partial dislocations and stacking faults do not appear to play a major role in the deformation structure formed in nanograined metals.

8.2.3 Twins Deformation twins are a significant defect structure in many face-centered cubic (FCC) metals with low stacking-fault energy. Several suggested mechanisms

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8.3  Image of a deformation twin in Al near crack tip.18

exist for the formation of twins from deformation. Figure 8.3 shows frames captured from an in situ TEM video of the deformation and failure of sputterdeposited Al thin films.18 An interesting aspect of this experiment is the presence of a twin in the grain adjacent to the one responsible for blocking the crack. Although the twin is ahead of the blunting crack tip and may have formed because of the stress field associated with the crack, its formation was not observed dynamically. The density of twins around the fracture surface was greater than in the rest of the gauge section, suggesting that deformation twinning occurred in association with crack blunting.18 These twins have been observed in nanograined and ultra-fine grained FCC metals with low and high stacking-fault energy.17,19–22 Several models suggested that a change in activation volume, strain rate sensitivity, or confining pressure as grain size decreases would result in an increased propensity for twinning.23–26 The addition of twins during the deformation process may act to both relieve stress in a given grain and provide an additional defect structure to limit continued slip activity by providing an additional boundary.27 Deformation twinning is therefore an active mechanism in many nanograined metals and may play a significant role in the mechanical properties.

8.2.4 Grain boundaries The essential defects of nanograined metals are two-dimensional defect structures known as grain boundaries. The dynamics of grain boundaries and resulting defect structures dictate the mechanical properties of nanograined metals. The types and structures of these grain boundaries are highly dependent on the alloy composition and processing steps in the manufacturing of nanograined metals. In general, nanograined structures produced using bottom-up approaches are more

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prone to possessing voids and greater free volume at the grain boundaries.28,29 In contrast, nanograined and ultra-fine grained metals formed by severe plastic deformation and other top-down approaches often contain dislocations in or near the grain boundary.30 In either case, the multitude and often the types of grain boundaries found in nanograined metals are far-from-equilibrium and thus not always stable under standard temperature and pressure. Recent studies have begun to investigate the effects of controlling both the grain size and grain boundary type in an effort to completely engineer a material from the grain boundary up.31,32 Understanding and controlling the response of grain boundaries during plastic deformation is essential for predicting the mechanical properties of nanograined metals and determining potential applications of these materials. One investigation into the understanding of these instabilities and how they may be controlled, deformation-induced grain growth, will be discussed extensively in Section 8.4.1.

8.2.5 Point defects and resulting structures: dislocation loops and stacking-fault tetrahedra Dislocation loops and stacking-fault tetrahedra are defects associated with the collapse of a large number of point defects into lower energy defect structures. Dislocation loops can either be the absence or addition of an extra plane of atoms within a crystalline structure. Stacking-fault tetrahedra are pyramidal structures formed in FCC metals in which the faces of the pyramid are stacking faults that lie on intersecting {111} planes. Dislocation loops have been proposed to be formed from a variety of techniques including dislocation– dislocation interactions during extensive deformation.1,33 The high concentration of vacancies that are needed to form stacking-fault tetrahedra have been reportedly produced by a variety of means including rapid quenching from temperatures near Tm,34,35 irradiation with energetic particles,36 dislocation– dislocation interactions,37 diffusion-induced grain boundary migration under specific temperatures and migration rates,38 annealing and recrystallization following severe plastic deformation,39 and high strain rate (as high as 108 s–1) deformation.40 In severe plastic deformation used to form ultra-fine grained and nanograined metals, it appears that both dislocation loops and stacking-fault tetrahedra can form from mechanical deformation at room temperature. This suggests that the extensive plasticity of either nanograined or ultra-fine grained metals provides a source for a supersaturation of vacancies that results in the formation of dislocation loops and stacking-fault tetrahedra. Dislocation loops and stacking-fault tetrahedra were identified by Dalla Torre et al. in equalchannel angular pressed Cu that was neither irradiated nor quenched. The stacking-fault tetrahedra are black triangles and the dislocation loops are black dots or black and white lobes under the bright-field imaging conditions used in Fig. 8.4.39

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8.4  Stacking-fault tetrahedra (arrowed) and dislocation loops in ECAP Cu.39

8.3

Classical defect structures absent in nanograined metals

Greater insight into the properties of nanograined metals may be gained from the classical defect structures absent, rather than those present. This section will detail the defect structures that are commonly seen in bulk deformed metals, but are seldom, if ever, reported in nanograined metals. This discussion will include the description of dislocation locks, cell structures, and intergrain sources. A comparison between the microstructure commonly seen in deformed coarsegrained and nanograined metals will be made on the possible mechanistic differences and resulting alteration to the mechanical properties.

8.3.1 Classical structures absent The variety of classical structures commonly seen in deformed coarse-grained FCC metals is not present in nanograined metals and thus warrants discussion. These structures include dislocation locks, dislocation pile-ups, dislocation tangles, dislocation cell structures, and intergrain dislocation sources. Although all of these structures are different and play significantly different roles in the deformation and failure mechanisms as well as the mechanical properties of metals, they all have in common multiple dislocation interactions, which are needed to form them. Much of what has been discussed thus far relates to the possible breakdown of the Hall–Petch relationship between yield strength and grain size. The Hall–Petch relationship is an empirical observation that has been associated with many of the mobile defect structures that are often absent in nanograined metals.7,41–45 There are a variety of potential dislocation lock

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8.5  A series of micrographs showing (a) dislocation pile-up at a grain boundary; (b) dislocation emission from a grain boundary in stainless steel.46

structures possible in FCC metals; all of which combine two or more dislocations of different slip character within a grain or grain boundary to form sessile dislocation structures from glissile dislocation combinations. Once locks are formed, they provide an impediment to dislocation motion within a grain. This significantly decreases the free path along which the dislocation can proceed. Dislocation pile-ups are arrays of dislocations on the same slip plane and of similar character that apply a local stress on an immobile feature in the microstructure. The pile-up can contain a multitude of dislocations, which can result in a significant stress concentration as is illustrated in Fig. 8.5 (a). The dislocations produced during deformation can either originate from a grain boundary as shown in Fig. 8.5 (b) or internally within a grain by Frank–Read sources.46 Dislocation sources provide the slip and thereby deformation necessary in the crystal without inducing failure. The hindrance of these sources was the first mechanistic explanation for the empirical Hall–Petch effect. Dislocation tangles and cell structures are more complex structures, which evolve to contain a large number of dislocations. These structures will often include dislocation locks and pile-ups. The range of dislocation structures that include locks, pile-ups, and cell structures is complex and important to many of the properties of ductile metals, but appears to be absent from most nanograined systems.

8.3.2 Reasons for the absence of classical structures in nanograined metals The absence of these features can be directly correlated with the lack of space available for their development within a nanograined structure. This lack of defect-free volume often found in nanograined metals in combination with the short mean free path between boundaries means that the probability of dislocation– dislocation interactions occurring during the time it takes for these defects to proceed from one grain boundary to the other is significantly less than in coarsegrained metals. This decreased probability of dislocation–dislocation interaction

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Deformation structures including twins in nanograined pure metals 223 results in fewer dislocation locks and other complex multiple dislocation structures forming within the matrix of nanograined metals. Dislocation pile-ups containing a few dislocations have been observed in nanograined metals,13,30 but pile-ups of the size seen in Fig. 8.5 (a) are physically impossible in nanograined metals due to dislocation–dislocation repulsion.47 The limitation of pile-up size results in a limit on the stress applied to the grain boundary and a limit on the slip transferred from one side of the grain to the other.48 This lack of pile-up stress hinders the cross-slip of dislocations in the pile-up that results in both slip on other slip systems and the formation of more complex dislocation structures resulting from dislocation–dislocation interactions.46 The large amount of stress that is applied from large dislocation pile-ups can result in some of the strain being transferred across the grain boundary in the form of new dislocations being generated from the grain boundary. An example of dislocation cross-slip and slip transfer across the grain boundary can be seen in Fig. 8.6.46 The lack of defects, mainly dislocations, within the grains, including dislocation locks to pin the grain boundaries on, means that if dislocations were to move across a grain it would occur very rapidly. This type of dislocation motion would

8.6  A series of micrographs showing (a) cross-slip and (b) slip transfer due to the large dislocation pile-up seen in Fig. 8.5 (a) in stainless steel.46

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not result in the development of complex microstructure within the grains, but may have a significant effect on the grain boundary character. As a result, the grain boundaries are expected to be the location for all the complex interactions that occur during the plastic deformation of nanograined metals.

8.3.3 The effect of missing structures on mechanical properties The lack of these complex defect structures that result from dislocation–dislocation interaction in deformed nanograined metals has a substantial impact on the deformation and failure mechanisms. In coarse-grained metals, these defect structures increase in density as the number of dislocations and thus the probability of their interaction increases. The resulting increase in new structures to pin dislocation motion leads to work hardening, which can significantly prolong the time between initial deformation and final failure. However, in nanograined metals, the lower probability of interaction results in little to no work hardening. Most nanograined metals show minimal ductility prior to catastrophic failure, significantly limiting their application.49–51

8.4

Novel defect structures in nanograined metals

The final class of defect structures in nanograined high purity metals is the completely unexpected defect structures seen in nanograined metals that are not common or have never been reported in traditional coarse-grained metals. The three structures related to deformation are: larger agglomerated grains, five-fold twin structures, and disclinations.

8.4.1 Agglomerated grains A coarsened microstructure commonly results from deformation processes in high-purity nanograined metals. Deformed metals with an initially nanograined microstructure will often have regions containing larger grains that can be correlated to the regions of the highest stress during deformation.52 These grains come in a variety of shapes and sizes with occasional indications for oblong grains in the direction of the greatest stress.52,53 These structures have been identified by both in situ TEM deformation studies and post-mortem TEM analysis.12,53,54 This coarsening of grains during deformation is in direct contrast to the refinement of grain structure during the room temperature deformation of coarse-grained metals. Three possible mechanisms have been proposed for grain growth in nanograined metals. The traditional mechanism is that grain boundaries migrate by the transfer of atoms across the grain boundary, resulting in a change in the dominant grain orientation. The driving force for this change is often associated with grain

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Deformation structures including twins in nanograined pure metals 225 boundary curvature.55 This mechanism is highlighted in Fig. 8.7 (a) and 8.7 (b). In Fig. 8.7 (a), a small concave grain with four sides is present in a microstructure dominated by stable six-sided grains. The shape of the grains produces an instability that results in the shrinkage and elimination of the grain. This likely occurs through atomic shuffling across the grain boundaries resulting in the progression of the grain boundary in the direction highlighted by the arrows. The collapse of this grain boundary results in the formation of two triple junctions with angles of 120°56 that are indistinguishable from the surrounding stable grain boundary structure, Fig. 8.7 (b). It should be noted that all polycrystalline systems are theoretically unstable in comparison to single crystals with certain grain boundary types and structures having an energetic local minimum.57–59 Recently, it has been suggested by Molecular Dynamics computer simulations and reported experimentally that grain growth in nanograined materials can occur via grain rotation at room temperature under an applied load.10,60,61 In order for this mechanism to occur, a large amount of free volume must be present in the

8.7  Proposed grain boundary migration mechanisms: (a) grain boundary migration and (b) the resulting microstructure; (c) grain rotation and (d) the resulting microstructure; (e) grain boundary elimination and (f) the resulting microstructure.

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grain boundaries of a far-from-equilibrium structure as illustrated by the thicker grain boundaries and the atypical grain shape shown in Fig. 8.7 (c). A small grain with extensive free-volume at the grain boundaries is highlighted. Local stresses applied to the grain can result in atomistic shuffling in the grain boundaries that has been predicted to result in grain boundary rotation along the direction of the arrow in Fig. 8.7 (c). If the grains to the left and the right of the grain are of the same orientation, then the rotation of the grain can result in the formation of an oblong grain as seen in Fig. 8.7 (d). Cahn and Taylor developed a mathematical model to explain the combination of grain boundary sliding and grain rotation.62 In this model, the tangential motion of grain boundaries was a result of biased grain boundary diffusion.62 Another explanation of grain growth via grain rotation was proposed by Rath et al.63 In their model, introducing a simple stable dislocation structure produces a small-angle grain boundary encircling a region that is rotated relative to the surrounding matrix. This dislocation-based model shows that grain boundary motion may produce grain rotation if the necessary grain misorientation and grain boundary structure are present.63 In another proposed model, grain growth is caused by grain boundary annihilation or alteration due to the bombardment and accommodation of a large number of mobile dislocations.64–66 Figures 8.7 (e) and 8.7 (f ) illustrate the proposed mechanism for dislocation mediated grain growth. This mechanism is associated with a large active dislocation density and thus is thought to occur in samples under extreme stress states. Figure 8.7 (e) shows an unstable grain structure in which a high density of dislocations is piled up on a weak or lowangle grain boundary as indicated. After continued build-up of local stresses, the grain boundary absorbs and emits dislocations into the matrix and potentially along the grain boundary to the extent that the grain boundary structure can no longer be clearly identified. Instead, the orientation between the grains becomes a general transition associated with high dislocation density and without the clear demarcation of grain orientation found with grain boundaries,1 as is illustrated in Fig. 8.7 (f ). The grain coarsening observed here is in stark contrast to the deformation structures observed in coarse-grained metals after deformation at room temperature. It is typical for intense deformation in coarse-grained microstructures to result in the refinement of the grains. This can be seen in the formation of complex dislocation cell structures that form barriers to further dislocation motion. The 3D structures formed from fatigue deformation of Cu-16%Al single crystals at 28 MPa, 34 MPa, and 41 MPa are seen in Fig. 8.8.67 The initial structure seen in the Cu alloy after 28 MPa shows dislocation activity on two slip systems. As the extent of fatigue increases, the densities of dislocations and structures resulting from dislocation–dislocation interaction increase. These defects include dislocation loops, dense dislocation arrays. This type of refinement is assumed to be the mechanism that is used for the formation of ultra-fine and nanograined structures by severe plastic deformation processes. Grain boundaries are known to be

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Deformation structures including twins in nanograined pure metals 227

8.8  Three-dimensional view of dislocation structures in Cu-16%Al after fatigue deformation at (a) 28 MPa, (b) 34 MPa and (c) 41 MPa. The planes are indexed and in (d) the {111} planes are indicated.67

destroyed in coarse-grained metals during dynamic recrystallization. This process can be seen in Fig. 8.9, in which a triple boundary in an aluminum alloy is destroyed. This process is associated with superplastic forming and is a result of applied load, while at elevated temperature. The grain structure in metals can be refined to an ultra-fine or nanograined structure using severe plasticity,68 but it has also been shown to undergo grain growth at room temperature from an applied load.53 It is hypothesized that this grain growth due to applied load is seen in nanograined structures deformed at room temperature because of the lack of complex dislocation interactions necessary for grain boundary formation and the high amounts of stress applied to far-from-equilibrium boundaries. An example of grain growth both directly ahead of the crack tip and in the plastic zone due to room temperature straining will be discussed in Section 8.5. The formation of a coarse-grained structure, as a result of deformation in nanograined metals, has a significant effect on the properties and performance of

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8.9  Series of micrographs showing the destruction of a triple junction in Al-4Mg-0.3Sc alloy at nominally the superplastic deformation temperature.69

nanograined metals. Large grains found in localized regions of high stress reduce the strength significantly in the local region and increase local dislocation slip promoting failure to occur within this region.70 The localized deformation in these large grain regions results in localized plasticity and failure with limited global deformation resulting in premature failure of traditionally ductile metals. The lack of knowledge on the factors controlling the formation of the agglomerated grain deformation structure represents a significant hindrance to the application of nanograined materials and is thus an area of intense investigation.12,71

8.4.2 Star twins Another defect structure not observed in coarse-grained metals, but occasionally observed in nanograined metals, is the five-fold twin structure, also known as star twins. This structure entails the union at a single junction of five twins and was first observed in Au and other FCC nanoparticles.69–72 An example of such structure in a gold nanoparticle which is undergoing sintering at elevated temperatures is shown in Fig. 8.10.72 These structures in the nanoparticles have been well studied and have been accredited to the decreased surface energy gained by the formation of the far-from-equilibrium five-fold twin structure. These structures have been observed in nanograined metals produced by various methods.73,74 Similar to nanoparticles with five-fold symmetry, the formation of these non-equilibrium structures in bulk metals has also been associated with the decreased energy gained by the formation relative to the grain boundary energy.73 In grains of 20 nm or less produced by severe plastic deformation, five-fold deformation twins were observed. These defects are present only in nanograined metals, due to the increasing geometrically necessary lattice strain imposed by the

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Deformation structures including twins in nanograined pure metals 229

8.10  High resolution TEM of a five-fold twinned Au nanoparticle as it undergoes sintering with a neighboring particle.72

increased lattice mismatch as the structure increases in size. From these results, Zhu et al. were able to develop a proposed mechanism that would permit the formation of five-fold twins from severe plastic deformation.74,75 Five-fold twin structures are not commonly observed in nanograined metals and as a result are not believed to have a significant effect on their mechanical properties.

8.4.3 Disclinations Disclinations are line defects similar to dislocations and will be the final defect structure discussed in this chapter. In contrast to dislocations that displace a local region, disclinations are violations in rotation symmetry of the crystal. Disclinations are defects that are not commonly associated with deformation in coarse-grained metals. High-resolution TEM has been used to identify disclination dipoles in mechanically milled nanocrystalline Fe.76,77 The formation of these rotational defects, seen in Fig. 8.11, is theorized to permit turbulent behavior in the solid metal during severe plastic deformation. It has been stipulated that these defects are present in nanograined metals not only as a result of severe plastic deformation, but also as a result of the increased reliance on intergrain sliding during the deformation process. The observation of disclinations in nanograined metals supports the hypothesis that nanograined metals deform predominantly via grain boundary mechanisms rather than dislocation slip.76,77

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8.11  (a) Transmission electron microscopy micrograph of nanocrystalline Fe powder. (b) Same micrograph with overlaying lines indicating planes of atoms. (c) Schematic of the plane structure with the location of the two disclinations identified.76

8.5

The effect of initial microstructure on deformation structures

The deformation structure formed in a given nanograined metal is highly dependent on the processing history of the metal and the resulting microstructure. This effect is true for all materials, but is of greater significance in nanograined structures due to their very high percentage of atoms not in stable lattice correlation. The variety of possible processing histories that can form nanograined structures can result in various percentages of free volume and types of grain boundaries within the microstructure. Characterization and testing of nanograined metals with the same purity and average grain size but created by different processing routes have shown that neither the microstructure nor the resulting mechanical properties of the two metals are equivalent.28 This suggests that the grain size distribution, types of defects present in the grains, and grain boundaries have a significant effect on the active deformation mechanisms and resulting mechanical properties. The microstructures formed during the production of nanograined materials can be controlled to contain many non-equilibrium structures, as demonstrated below. This effect can be clearly observed in a detailed study of the active deformation and failure mechanisms and properties of nanograined pulsed-laser deposited (PLD) Ni as a function of grain size. The three microstructures, seen in Fig. 8.12, chosen for investigation were nearly monodispersed nanograined Ni film present in the as-released freestanding condition, Fig. 8.12 (a) and 8.12 (b), the micro­ structure with maximized bimodal distribution, Fig. 8.12 (c) and 8.12 (d), and the ultra-fine grained Ni films, Fig. 8.12 (e) and 8.12 (f ). The bright-field image, Fig. 8.12 (a), of the as-released microstructure contains only nanograined Ni grains as confirmed by the select area diffraction (SAD) pattern insert that contains uniform rings of constant brightness, which is typical of fine-grained metals with no preferred texture. The histogram associated with Fig. 8.12 (a), which quantifies the grain size distribution, is presented in Fig. 8.12 (b). The average grain size ranged from 4 nm to 39 nm with a mean of 13 nm. This resulted

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Deformation structures including twins in nanograined pure metals 231

8.12  The microfabricated structure: (a) The initial nanograined microstructure of Ni film after release from Si; (b) Associated histogram of grain size distribution of the nanograined structure; (c) The bimodal microstructure of Ni film after annealing for 1 hour at 548 K; (d) Associated histogram of the mixed structure; (e) The ultra-fine grained microstructure of Ni film after annealing for 1 hour at 598 K; (f) Associated histogram of the ultra-fine grained structure.

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in a standard deviation of 5.3 nm as can be seen in Table 8.2. The vast majority of the 960 grains measured, 90%, are within the range of 5 nm and 20 nm. This results in a maximum grain size to average grain size ratio of 2.9. For comparison, the average grain size in these microfabricated samples is larger, and the distribution broader, than that in the as-deposited Ni films.78 For example, a 90 nm-thick film deposited on rock salt and not subject to microfabrication was found to have an average grain size of 9 nm with a standard deviation of 3 nm, suggesting that despite both being monodispersed high-purity nanograined metals, the process history associated with microfabrication altered the grain size distribution. A bimodal grain size distribution, seen in Fig. 8.12 (b), was achieved through a one-hour anneal at 548 K. The microstructure contains several large grains with scalloped grain boundaries and a myriad of unexpected internal defects. The SAD pattern inserted in Fig. 8.12 (c) shows that continuous rings are maintained due to the nanograined matrix, but the rings are no longer of uniform intensity due to the presence of these large grains. The histogram of grain size distribution presented in Fig. 8.12 (d) shows that the average grain size has nearly doubled to 25 nm from the initial grain size. The range of grain sizes has increased significantly, varying from 4 nm to 435 nm, resulting in a standard deviation of 40 nm as seen in Table 8.2. The ratio of maximum grain size measured to average grain size is 17.2, yet 70% of the grains remain in the range of 5 nm and 20 nm. The line-intercept method identified 25 ultra-fine grains, larger than 100 nm, in the region analyzed. This accounts for only 3.7% of the 681 grains measured as seen in Table 8.3. The initial microstructure was completely eliminated after annealing for one hour at 598 K and developed into large nanograins and small ultra-fine grains, as can be seen in Fig. 8.12 (e). The SAD pattern, Fig. 8.12 (e) insert, is now neither uniform in brightness nor continuous, and is typical of ultra-fine grained crystalline structures. The grain size distribution shown in Fig. 8.12 (f ) is significantly different from the as-deposited distribution, Fig. 8.12 (b). The average grain size has increased by nearly an order of magnitude of 150 nm with a broad distribution Table 8.2  The mean, median, largest, and smallest grain size, as well as the total number of grains for annealing treatments applied to 90 nm-thick PLD Ni films for in situ TEM straining Condition

Total number of grains

Mean (nm)

Median Standard Maximum Minimum Max (nm) deviation (nm) (nm) mean (nm)

As-deposited

960

13

12

5

39

4

3

548 K 1 hr

681

25

15

40

435

4

17

598 K 1 hr

116

150

145

81

436

23

3

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Deformation structures including twins in nanograined pure metals 233 Table 8.3  Ratios derived from the grain size distribution annealing treatments applied to 90 nm-thick PLD Ni films for in situ TEM straining. The 10 × initial average, ultra-fine grain, 5 × average, and Tukey outliers are normalized by the total number of grains per histogram. The deviation from as-deposited and log normality are based on the Kolmogorov–Smirnov analysis Condition 10x average (%)

10x Ultra-fine 5x Tukey Log initial grains average outliers normality average (%) (%) (%) (%) (%)

Deviation from asdeposited (%)

As-deposited 0.0 548 K 0.6 598 K 0.0

0.0 3.1 54.3

0.0 20.6 42.2

0.0 3.7 69.8

0.0 3.2 0.0

3.3 9.5 0.9

0.0 0.0 1.0

ranging from 23 nm to 436 nm (Fig. 8.12 (f ) ). This resulted in a standard deviation of 81 nm, seen in Table 8.2. The maximum grain size to average grain size ratio is 2.9, comparable to that of the as-released films. No grains remain in the 5 nm to 20 nm range and ultra-fine grains account for 70% of the 116 grains measured in an area of identical size to the previous histograms. This distribution is only one of the three to show any similarity to a log normal distribution based on the Kolmogorov–Simirnov test as seen in Table 8.3 and described by Kirkman.79 This control of microstructure permits the study into the relationship of grain size distributions, not just average grain size, with deformation and failure mechanisms active during straining. The deformation and failure of a PLD Ni freestanding film annealed at 548 K for 1 hour was observed during in situ TEM pulsed straining experiments using a custom-built straining device. The bimodal grain size distribution produced by annealing of these films, evident in Fig. 8.12 (c) and 8.12 (d), provides the opportunity for a multitude of deformation mechanisms. Evidence for a variety of mechanisms including dislocation pile-ups, twinning, stress-driven grain growth, localized thinning, crack blunting, ligament necking, and even what is interpreted to be grain agglomeration were present during the deformation and failure of the films with a bimodal structure. Plasticity was observed up to 2 µm in front of the crack tip with extensive plasticity observed in a region up to 500 nm directly vicinal to the tip, as will be discussed in Fig. 8.13 and Fig. 8.14. Dislocation activity was observed in the large grains within the plastic zone without any observable change in the small surrounding grains. The solidified Ni droplets, or splats, present in the film were found to have no observable interaction with crack propagation despite it propagating within 100 nm of the splat. Closer to the crack tip, severe microstructural rearrangement occurred in both the large grains and the nanograins. In the region of the Ni film directly ahead of the crack tip undergoing thinning, the large grains contained active full dislocations whereas the nanograins underwent the process termed grain agglomeration by Shan et al.10 The combination of these processes resulted in a thinning and

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8.13  Still frames taken from an in situ TEM deformation experiment of a custom-built PLD Ni device annealed at 548 K for 1 hour showing grain growth 240 nm ahead of the crack tip: (a) A still frame with migrating boundary outlined; (b) The same region 0.10 seconds later with the new boundary demarked.

eventual local failure of the film. No observation of deformation or failure was observed to occur in any grains identified as being metastable hexagonal closepacked (HCP) phased despite a portion of the large grains being of this character. Deformation was seen in a grain containing a rich debris field. Despite these observations, no interactions of dislocations with stacking-fault tetrahedra were discernable. This work also provided direct evidence for stress-driven grain growth. An example of this effect is shown in the images presented in Fig. 8.13. To illustrate the grain growth, a portion of the grain boundary of a grain 240 nm from the nearest crack is highlighted. The new position of the boundary after stress-driven grain growth is highlighted in Fig. 8.13 (b). The grain boundary sweeps out an area of 250 nm2 in less than 0.1 s. Grain growth of this nature was observed in several grains within the plastic zone. The progression of the crack through the film was often halted due to the large grains present in the bimodal microstructure, as is shown in Fig. 8.14 (a). In this image, a crack that was progressing from left to right was halted on the two large grains indicated. The left-most large grain indicated in Fig. 8.14 (a) separates the primary crack from the microcrack, formed on the other side of the grain. The second large grain present in front of the secondary crack also hindered crack progression. In situ TEM observations of this region showed dislocation activity in both grains during pulse straining followed by extensive necking in the thinned region between the crack and microcrack. Figure 8.14 (b) and 8.14 (c) are postmortem micrographs of the fracture surface. A set of large grains along the fracture surface indicates severe plasticity including necking down to nearly a point. One of the large grains contains two dislocation pile-ups present on opposite planes

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Deformation structures including twins in nanograined pure metals 235

8.14  Fracture surface of PLD Ni device annealed at 548 K for 1 hour: (a) A crack temporarily halted with one large grain spanning crack spacing and the other in front of the crack tip; (b) Necked region containing two dislocation pile-ups; (c) Large grain containing both dislocations and a twin.

and originating near the same region containing slightly more than 15 dislocations each in a grain with a length of 130 nm. Figure 8.14 (c) shows another region of large grains along the fracture surface. In this micrograph, both a dislocation pile-up and a twin are labeled. The dislocation pile-up contains 12 identifiable dislocations. The thin twin, near an area previously exposed to high stresses, was confirmed by SAD. Significant necking was evident along the fracture surface of the PLD Ni film annealed at 548 K for one hour, but not on the fracture surface of the as-deposited Ni film. Analysis of the fracture surface of the annealed PLD Ni films by both the scanning electron microscope (SEM) and TEM revealed

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extensive dislocation activity in the large grains that resulted in significant plasticity along the fracture. Further insight into the mechanisms active in the film as a function of grain size and distribution can be gained from the comparison of the fracture surfaces in the three freestanding PLD Ni films produced by microfabrication and annealed to varying conditions (Fig. 8.15). In Fig. 8.15 (a), the film, after release from the substrate, failed during straining in the TEM. The location of crack initiation and propagation was not observed at the time of failure. Cross-sectional SEM images of the film show no sign of necking in the film. The fracture surface of this film shows limited signs of plasticity. On the fracture surface of a PLD Ni film annealed at 548 K and shown in Fig. 8.15 (b), three different microstructures are encountered. In the center of the image, the fracture surface intersects a nanograined region in which the surface appears similar to that seen in Fig. 8.15 (a). To the left of this region, a cusp is observed along the fracture surface as it cuts through a large grain. Detailed observation of this grain and other large grains along the fracture surface reveals limited necking within the large grains. In the far right of Fig. 8.15 (b), a region is seen in which the fracture surface passes through a nanograined region vicinal to a large grain present in the film. The crack propagated through these three regions with no tendency to avoid any of them. The fracture surface of the PLD Ni sample annealed at 598 K for one hour, Fig. 8.15, is dominated by dislocation motion within a plastic region. Necking of the film can be seen in multiple grains in Fig. 8.15 (c). The plasticity observed in this film is similar to the classical expectation for coarse-grained foils.1,80,81 The combination of dynamic observation of deformation and failure in bimodal PLD Ni and detailed observation of the fracture surface have shown that a variety of mechanisms can be operative in the same region of the film simultaneously dependent on the processing history of the metal.

8.6

Future trends

Current trends in the field would suggest the maturation of studies into nanograined FCC metals. Since Gleiter’s first suggestion that nanograined metals may have unique properties over 20 years ago,82 intensive research has been undertaken to develop processing, characterization, and testing tools, and evaluate the structure of nanograined metals. As such, the field is beginning to lose its novelty and the research is becoming less ground-breaking and more detailed in nature. This is exemplified in the decreased interest in the inverse Hall–Petch relationship by leading research groups. Likewise, a trend is observed in the expansion of the field to pure BCC, HCP, and alloy systems being tested by increasing the number of methods for a greater variety of electrical, thermal, mechanical, and other properties.

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Deformation structures including twins in nanograined pure metals 237

8.15  Fracture surfaces of the PLD Ni films produced by microfabrication with: (a) the initial nanograined microstructure; (b) the bimodal grain size distribution from annealing for 1 hour at 548 K, and (c) ultra-fine grained microstructure from annealing for 1 hour at 598 K.

A promising trend in the field is the publishing of more thorough studies into the governing mechanisms and controlling factors that determine the deformation structures formed in nanograined metals. One of the greatest advances in recent history is the development and refinement of processes for producing nanograined

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metals with lower contamination levels and well-controlled grain boundary structures. The advancement in the processing-microstructure correlation has resulted in a split in the nanograined field between the metals produced by topdown approaches and those produced by the bottom-up approaches. It is generally accepted that these sets of materials have very different initial microstructure, and as a result, will likely have differing active deformation mechanisms and resulting deformation defects. Along with studies of greater depth, the research into deformation defects in nanograined metals should expand in all dimensions to include investigations employing a greater range of techniques and materials systems. These material systems should include alloy systems with both solutes and precipitates, as strengthening and grain size stabilizing elements; more applied systems such as nanograined titanium alloys and oxide-dispersed steels; and various crystal systems. The investigation into different crystal systems, alloy compositions, and processing history will assist in the settlement of debate on the effect length-scale transitions have on the active mechanisms and resulting structures, as well as result in a better understanding of the defect structure and the active mechanisms, and development of nanograined metal applications in industry. Beyond the development in processing and analysis, the greatest potential in the identification of defect structures may come from the recent advances in highresolution microscopy. Three recent techniques that have undergone significant development are aberration-corrected TEM, tomography, and atom probe microscopy. Recent developments in spherical and chromatic aberration-corrected TEM provides increased resolution and chemical mapping, which are essential for detailed analysis of nanograined structures. The further potential for increased resolution and a widened pole piece gap offered by spherical and chromatic aberration corrected TEM provides the opportunity to include a wide range of in situ techniques not previously possible. This should result in techniques for better understanding of the unique deformation structures in nanograined metals and the related formation mechanisms. Three-dimensional electron tomography is another technique that has progressed significantly and also has a potential for continued development. The automation of this technique provides three-dimensional structural information with relative ease to a wide variety of sample geometries, microstructures, and chemistries. The final technique that could potentially have a large impact on defect structures in nanograined metals research is atom probe microscopy. This technique identifies the location and type of element present in a material. With sufficient increases in resolution, it would be able to determine the exact relationship between local chemistry and microstructure within complex nanograined alloys. One piece of equipment that would be of great benefit to the field, but is not currently available is a non-destructive tool capable of rapid evaluation of the internal and grain boundary defects in bulk nanograined metals. It is also foreseen that current trends in computation capabilities will continue to increase greatly. This will result in the development of more robust computer

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Deformation structures including twins in nanograined pure metals 239 models that should then be able to predict the evolution of more complex structures over greater time periods. Overall, it appears that understanding of nanograined deformation and deformation structures through advances in new tools is progressing out of its infancy and expanding into a broad range of fields. For greater depth in mechanical properties,1,47,83 grain boundary structure,84 or electron microscopy85,86 the reader should consult the classical text on the subject referenced.

8.7

Acknowledgements

This work is supported by the Division of Materials Science and Engineering, Office of Basic Energy Sciences, US Department of Energy both at Sandia and under grant DE-FG02–07ER46443. Sandia National Laboratories is a multiprogram laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy’s National Nuclear Security Administration under contract DE-AC04–94AL85000.

8.8

References

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Deformation structures including twins in nanograined pure metals 241 48 I.M. Robertson, A. Beaudoin, K. Al-Fadhalah, L. Chun-Ming, J. Robach, B.D. Wirth, A. Arsenlis, D. Ahn and P. Sofronis, Materials Science and Engineering A 400–401 (2005) 245. 49 Y. Wang, M. Chen, F. Zhou and E. Ma, Nature 419 (2002) 912. 50 D. Farkas, H. Van Swygenhoven and P.M. Derlet, Physical Review B (Condensed Matter and Materials Physics) 66 (2002) 060101. 51 H. Huang and F. Spaepen, Acta Materialia 48 (2000) 3261. 52 F.R.N. Nabarro, Scripta Materialia v 39 (1998) p 1681. 53 D.S. Gianola, S. Van Petegem, M. Legros, S. Brandstetter, H. Van Swygenhoven and K. J. Hemker, Acta Materialia 54 (2006) 2253. 54 K. Hattar, D.M. Follstaedt, J.A. Knapp and I.M. Robertson, In situ TEM observation of Stress-Induced Grain Growth, (2010). 55 T. Gladman, Grain Size Control (Maney Publishing, London, 2004). 56 A.C. Ferro and M.A. Fortes, Interface Science 5 (1997) 263. 57 E.M. Bringa, A. Caro, Y. Wang, M. Victoria, J.M. McNaney, B.A. Remington, R.F. Smith, B.R. Torralva and H. Van Swygenhoven, Science 309 (2005) 1838. 58 H. Van Swygenhoven, A. Caro and D. Farkas, Scripta Materialia, 5th International Conference on Nanostructured Materials (NANO 2000), Aug. 20–25, 2000 44 (2001) 1513. 59 H. Van Swygenhoven, M. Spaczer and A. Caro, Nanostructured Materials, Proceedings of the 1998 TMS Annual Meeting & Exposition, Feb. 15–19, 1998 10 (1998) 819. 60 A.J. Haslam, S.R. Phillpot, D. Wolf, D. Moldovan and H. Gleiter, Materials Science & Engineering A (Structural Materials: Properties, Microstructure and Processing) A318 (2001) 293. 61 H. Li, Advanced Engineering Materials 7 (2005) 1109. 62 J.W. Cahn and J.E. Taylor, 52 4887. 63 B.B. Rath, M. Winning and J.C.M. Li, Applied Physics Letters 90 (2007) 161915. 64 V. Bata and E.V. Pereloma, Acta Materialia 52 (2004) 657. 65 V. Bata and E.V. Pereloma, Scripta Materialia 51 (2004) 927. 66 J.A. Wert, Scripta Materialia 50 (2004) 1487. 67 H. Inui, S.I. Hong and C. Laird, Acta Metallurgica 38 (1990) 2261. 68 R.Z. Valiev and I.V. Alexandrov, 58 1003. 69 L.M. Dougherty, I.M. Robertson and J.S. Vetrano, Acta Materialia 51 (2003) 4367. 70 B.L. Boyce, Proceedings of the SPIE – The International Society for Optical Engineering Reliability, Testing, and Characterization of MEMS/MOEMS II, Jan. 27–29, 2003 4980 (2003) 175. 71 S.M. Allameh, Journal of Materials Science 38 (2003) 4115. 72 M. Briceno, K. Hattar, J. Damiano, D. Nackashi and I.M. Robertson, In-situ TEM study of the sintering process of gold nanoparticles using ultra-fast heating stage (2010). 73 J. Urban, 33 1009. 74 Y.T. Zhu, X.Z. Liao and R.Z. Valiev, Applied Physics Letters 86 (2005). 75 Y.T. Zhu, X.Z. Liao and R.Z. Valiev, Applied Physics Letters 86 (2005) 103112. 76 M. Murayama, J.M. Howe, H. Hidaka and S. Takaki, Science 295 (2002) 2433. 77 I.A. Ovid’ko, Science 295 (2002) 2386. 78 K. Hattar, D.M. Follstaedt, J.A. Knapp and I.M. Robertson, 56 794. 79 T.W. Kirkman, Statistists to Use, at http://www.physics.csbsju.edu/stats/ (1996). 80 M.P. Dewald and W.A. Curtin, Modelling and Simulation in Materials Science and Engineering 15 (2007) 193.

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9 Microstructure and mechanical properties of nanostructured low-carbon steel prepared by equal-channel angular pressing Y.G. KO, Yeungnam University, Republic of Korea and D. H. SHIN, Hanyang University, Republic of Korea Abstract: This chapter reviews the microstructural evolution of nanostructured low-carbon steels during equal-channel angular pressing (ECAP) and subsequent heat treatments. Regarding microstructural evolution, most ferrite phase grains are significantly refined by grain subdivision related to various slip systems of <111>{110}, <111>{112} and <111>{123}, which are mainly operated by ECAP shear strain, while pearlite colonies are deformed by mechanical fragmentation. When appropriate subsequent heat treatments are selected, a significant portion of carbon atoms are redistributed uniformly during ECAP deformation, leading to a uniform distribution of nanoscale cementite particles. The mechanical properties of the nanostructured steel samples are also examined, focusing on microstructural modifications to overcome their inherent mechanical drawbacks arising from dynamic recovery and nanoscale grains. Key words: nanostructured low-carbon steel, equal-channel angular pressing (ECAP), microstructural evolution, mechanical properties.

9.1

Introduction

Over the past decade, the materials science and engineering community has paid considerable attention to nanostructured metallic materials due to their unique properties, particularly their superior mechanical properties, which offer opportunities for a variety of structural applications.1–14 Previous studies have shown that the mechanical properties of nanostructured metallic materials differ greatly from those of traditional coarse- and fine-grained metallic materials.15–20 Since the milestone work by Segal et al.,21 equal-channel angular pressing (ECAP) has been regarded as one of the most promising processes for fabricating advanced metallic materials with nanoscale grains. Its advantages have spurred a great deal of research on ECAPed metallic materials, which have found successful applications in metallic systems such as aluminum,22 iron,23–25 and titanium10,14 alloys. Among these materials, a special focus is placed here on the microstructure and mechanical properties of nanostructured low-carbon steel (LCS) in light of two main considerations. In conventional LCS steels, structural refinement of the grain size from ~10 to ~1 µm led to an increase in yield strength by as much as ~500 MPa, and a decrease in the ductile–brittle transition temperature below roughly –350 K. Thus, extensive efforts have been devoted to the development of 243 © Woodhead Publishing Limited, 2011

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ferrous alloys with submicron-level grain sizes by the aforementioned processing technologies. Considering the enhanced mechanical properties and concomitant commercial potential of nanostructured low-carbon steel (LCS), an overall review would provide a fundamental understanding along with assessing the current development of new types of ferrous alloys. Second, since an LCS alloy consists of two phases, i.e. ferrite and pearlite, its deformation behavior differs markedly from that of single-phase materials. Although pearlite has a much smaller volume fraction than ferrite in LCS, its effect on the mechanical properties of steel is disproportionately large. In addition, the microstructural evolution of pearlite during ECAP is expected to be complex due to the existence of hard cementite lamellar plates. In this chapter, we reviewed recent progress on microstructural evolution and the resulting mechanical properties of nanostructured LCS samples, which were analyzed through transmission electron microscopy (TEM) based and theoretical approaches. We also reviewed several metallurgical strategies that had intended to overcome the shortcomings of mechanical properties of nanostructured LCS, such as a lack of strain hardenability.

9.2

The microstructural evolution of low-carbon steel (LCS)

9.2.1 The microstructural evolution of LCS by equal-channel angular pressing (ECAP) Figure 9.1 displays the optical microstructure of an ECAPed LCS as a function of the number of ECAP passes with route C where the sample is rotated 180° along its longitudinal axis. The X-plane is the plane perpendicular to the longitudinal axis of the sample, and the Y- and Z-planes denote the side-viewed and top-viewed planes along the longitudinal axis of the sample, respectively. The initial sample reviewed here is a LCS sample consisting of pearlite of approximately 15% (dark phase) with the remainder being ferrite (bright phase) shown in Fig. 9.1 (a). Both phases are nearly globular and their size is ~30 µm. Several common microstructural changes with ECAP deformation were noted regardless of the planes: 1) the constituent phases became smaller and more irregular with repetition of pressing as can be seen from Fig. 9.1 (b)–(e); 2) the ferrite grain boundaries of the sample after a single pass were visible as shown in Fig. 9.1 (b), but there existed many dim contours inside them, likely indicative of the fragmentation of ferrite grains due to extensive strain;26 and 3) it is difficult to identify the initial ferrite grain boundaries, and the dim contours became extensive beyond two or more passes of the pressing as shown in Fig. 9.1 (c)–(f ). Referring to the pearlite colony size as a qualitative measure of the mechanical fragmentation, the fragmentation on the X-plane was even more severe than that on the Y-planes. With an odd number of passes, the micrographs of the Y-plane showed that the grains were severely elongated along the direction of ~30° inclined to its

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9.1  Optical micrographs of (a) the initial sample, (b) one-pass, (c) two-pass, (d) three-pass, and (e) four-pass ECAP-deformed samples with respect to the viewing planes (X, Y, and Z planes).24

longitudinal axis, which was fairly similar to the macro-shear direction imposed by ECAP as shown in Fig. 9.1 (b) and (d). With a subsequent even number of passes, both phases restored the near-equiaxed shape as shown in Figs. 9.1 (c) and (e). These microstructural changes were anticipated when route C was used.27–29 Despite the significant inherent difference in yield strength and plastic deformation between pearlite and ferrite phases, the presence of severely elongated phases after an odd number of passes and the restoration of their equiaxed shape after a subsequent even number of passes were observable. Under severe plastic deformation conditions, the macroscopic deformation behavior of pearlite was quite similar to that of ferrite. In terms of deformability, no cracking was observed in the LCS samples that were subjected to severe plastic straining while the strength and plastic deformation behaviors of pearlite and ferrite all vary. Two factors could account for this observation: 1) a soft ferrite phase with a large

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volume fraction could accommodate plastic incompatibility between two phases, and 2) a hard pearlite phase is capable of sustaining plastic deformation to some extent. Figure 9.2 (a) presents a TEM image of ferrite in the deformed samples viewed from the Y-plane. The initial microstructure exhibited a relatively low dislocation density. After a single pass, the microstructure mainly consisted of parallel shear bands of elongated grains with a length of ~2 µm and width of ~0.5 µm, showing considerable grain refinement (Fig. 9.2 (b) ). The corresponding selected-area electron diffraction (SAED) pattern was characterized by individual spots, implying that most of the boundaries of fine grains formed by a single pass would be of low angle. The microstructure after two passes (Fig. 9.2 (c) ) contained fairly equiaxed grains with widths comparable to those of grains obtained by the first pass. However, the SAED pattern showed the appearance of additional rings and extra spots, indicating the formation of high-angle grain boundaries. Near-equiaxed ultra-fine grains of 0.2–0.3 µm diameter, which were finer than those obtained at two passes, resulted from four-pass treatment (Fig. 9.2 (d) ). In addition, the number of rings in the SAED

9.2  Transmission electron microscopy images of ferrite phase grains in (a) the initial sample, (b) one-pass, (c) two-pass, and (d) four-pass ECAPed LCS samples taken from the Y-plane presenting main shear deformation.24

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pattern increased and the spots became more diffused as compared to the previous observations. The increase in the number of the rings and the spots with repeated passes indicates that the grain size reduction rose with increasing number of pressings by evolution from low-angle boundaries, which appeared after the first pass, to highangle boundaries. From TEM observations, however, ferrite grain boundaries after ECAP were not well defined and the existence of extensive extinction contours along grain boundaries was evident. These observations indicated that ferrite grain boundaries formed by ECAP were in a non-equilibrium state having a high internal stress due to long-range order lattice distortion. These general features associated with the microstructural changes observed in ferrite phases are consistent with those in ECAP-deformed aluminum alloys reported in the literature.7,26,30–32 On the other hand, the deformation behavior of pearlite differed from that of the ferrite phase during ECAP. The initial morphology of pearlite in the LCS sample consisted of a well-developed continuous lamellar structure, as shown in Fig. 9.3 (a).

9.3  Transmission electron microscopy images of pearlite colonies in the initial and ECAP-deformed LCS samples showing the morphological changes in cementite: (a) the initial sample, (b) severely necked cementite after four-pass, (c) mechanically curled and wavy cementite plates after four-pass, and (d) globular cementite and sharp slip lines (marked by two black arrows) after four-pass.24

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After four-pass ECAP, the microstructure of the pearlite phase is represented by two typical features according to cementite morphology. The first feature is that cementite plates remained parallel to each other but were in a discrete form, indicating the occurrence of a breakage of cementite lamellae during ECAP (Fig. 9.3 (b) ). The second feature is that the discrete cementite lamellae were severely curled and wavy (Fig. 9.3 (c) ). The occurrence of severe necking was also evident along the cementite plate length. In some cases, as shown in Fig. 9.3 (d), a globular cementite33,34 and a sharp slip line35 were observed. The observation of both severe necking and a sharp slip line indicated that a breakage of the cementite lamellae occurred. It is of interest that the cementite lamellae exhibited a considerable capability for plastic deformation as shown in Fig. 9.3 (b)–(d), given that the cementite is prone to fracture with ease in a brittle manner under uni-axial tensile mode on account of the few slip systems available.36 Such plastic deformation behavior of cementite could be attributed to the presence of severely elongated pearlite after an odd number of passes and the restoration of its equiaxed shape after a subsequent even number of passes. To shed light on this unusual behavior, a comparison with the earlier work on a pearlitic steel wire deformed via conventional drawing would be helpful.33 Under the nearly same effective strain, severely ECAP-deformed cementite in the pearlite phase was quite similar to that observed in a heavily cold drawn pearlitic steel wire.33,34 For the heavily cold drawn pearlitic steel wire, it is generally accepted that severely deformed cementite plates are found on the planes of the lamellae aligned along the drawing axis while curled wavy cementite plates are observed on the planes of the lamellae, which are not aligned along the drawing axis. When cementite was subjected to uni-axial tensile deformation, (001)[010], (010)[001] and (100)[010] slip systems were operative, but they were insufficient for cementite to deform plastically without inducing significant cracks.37 Accordingly, the TEM observations showing considerable plastic deformation of cementite suggested that the additional slip systems might operate under the deformation mode accompanied by ECAP, the deformation mode of which was documented to be shear. In the cold drawing process, pearlite was subjected to a hydrostatic stress state. Under the hydrostatic stress state, – – additional slip systems of (110)[111] and (011)[111] became active. Cementite thereupon possessed a number of slip systems sufficient for homogeneous plastic deformation.21,38 Still, it is doubtful whether the stress state induced by ECAP is comparable to that induced by the cold drawing process. Based on the observation that cementite deformed plastically in Fig. 9.3 (b)–(d), however, it is likely that ECAP deformation could develop a complex stress state where a sufficient number of slip systems for the plastic deformation of cementite are in operation.

9.2.2 Grain refinement mechanism Slip system at the first pass of ECAP Figure 9.4 (a) presents a TEM micrograph of a LCS sample viewed from the <111> zone axis after the first pass of ECAP. The ferrite microstructure mainly consists of

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parallel bands of elongated grains having a width of 0.3 µm. The extended parallel band boundaries are called lamellar-type boundaries (LBs). The corresponding SAED pattern shows that LBs are mainly low-angled and the direction of the bands is primarily parallel to the <111> direction. Inside the band interior, dislocation cell boundaries (DCBs) were also detected. The dislocation density inside a cell enclosed by DCBs is relatively low. DBs were typically found to be either normal to LBs or 30° and 60° inclined to LBs. This kind of boundary structure was reported to be typical for heavily deformed metallic materials. In order to identify the slip system operating during ECAP, first it is important to recognize that the direction of the deformation band should be parallel to the intersecting line between the viewing plane normal to the selected zone axis and the slip plane on which deformation occurred. The direction of the deformation band is thus equivalent to that of the projection of the slip plane, which contains both the slip direction and the direction of the deformation band, on the viewing plane. Figure 9.4 (b) suggests a probable grain refinement mechanism of a LCS alloy from the standpoint of dislocation slip activities based on analysis of TEM data. A pictorial illustration satisfying this condition is presented in order to –– identify the slip systems operating at the first pass of ECAP. When the [111] – direction was selected as the viewing direction, two of the slip planes (110) and –– (112) in the body-centered cubic (bcc) crystal system could contain the [110] deformation band direction, which was the major deformation band direction formed at the first pass. In order to identify the slip plane more definitively, it was necessary to rotate the viewing direction in TEM. Using this tilting method, the –– – (112) plane with the [111] slip direction was characterized as the slip plane. It was noted that, in a different region, planes belonging to the {110} family were also identified as the slip plane. Accordingly, it was evident that the slip systems of

9.4  (a) Transmission electron microscopy micrograph of the first pass ECAPed LCS sample and (b) pictorial illustration for formation of the deformation band and identification of the corresponding slip systems operating at the first pass.39

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{110}<111> and {112}<111>, which are typical in a bcc crystal system, were the major slip systems operating in the LCS alloy during the first pass of ECAP. Slip system at the second pass of ECAP Figure 9.5 (a) shows a TEM micrograph of a LCS sample viewed from the <111> zone axis after the second pass of ECAP. Equiaxed grains were formed by the second pass, but their average size of ~0.5 µm was slightly larger than the width of the subgrain bands formed by the first pass. From the SAED pattern, it was obvious that, at least in this area, the misorientation between sub-grains increased compared with that of the sample deformed by a single pass. Even though the portion of ultra-fine equiaxed grains was large, some sub-grain bands remained. This implies that twopass ECAP was insufficient to produce a homogeneous structure despite the considerable grain refinement. Many boundaries were aligned along either the <110> or <112> directions, similar to those in the sample after a single pass. However, detailed inspection of Fig. 9.5 (a) reveals the presence of additional boundaries having several different angles with respect to the <110> direction. The <110> direction is the alignment direction of LBs as well as sub-grain bands. The observation of sub-grain boundaries with other directions reveals that new slip systems operated in the course of the following deformation. Accordingly, the boundaries appeared to be serrated as shown in regions 1 and 2 in Fig. 9.5 (a). A TEM analysis was conducted on the two-pass ECAPed sample. In addition to the <110> and <112> directions, the boundaries having several different angles with respect to the <110> direction were observed. This reflects that dislocations belonging to several different slip systems moved and, thereby, formed cell boundaries inside the initial sub-grain bands to accommodate the strain energy. To understand the deformation characteristics induced by the second pass, a pictorial illustration is

9.5  (a) Transmission electron microscopy micrograph of the second pass ECAPed LCS sample and (b) pictorial illustration for formation of the deformation band and identification of the corresponding slip systems operating at the second pass.39

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– provided in Fig. 9.5 (b). In the second pass, the [111] direction became the slip – direction if the [111] direction could be the slip direction operating at the first pass. – The intersection between the viewing plane of (111) and the slip plane of (110) – – – containing the [111] slip direction was aligned along the [112] direction, displaying the direction of the new deformation band. It was noted that, on the viewing plane of – – – (111), the [112] direction was normal to the [110] direction, which coincides with the direction of deformation bands formed by the first pass. Accordingly, based on the –– – – TEM image observed in the direction of [111], the boundaries aligned along the [112] direction appeared to be normal to the LBs formed by the first pass. By the same – logic, boundaries representing the [213] and [101] deformation bands appeared to be – inclined 79° and 60°, respectively, to the LBs formed by the first pass. The [213] and – – – – [101] deformation bands were associated with the (211)<111> and (101)<111> slip systems, respectively. Figure 9.6 (a) provides a TEM micrograph of the serrated

9.6  Transmission electron microscopy micrograph showing an example of the serrated boundaries found in (a) the two-pass ECAPed LCS sample, viewed by a <111> zone axis, and (b) its schematic description including the slip system corresponding to the individual bands and the angular relationship between them.39

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boundary observed in the two-pass ECAPed sample, viewed by the <111> zone axis, as well as its schematic description, including the slip system corresponding to the individual bands and the angular relationship between bands. The angular relationship between deformation bands formed by the first and second passes described above was in excellent accordance with that measured experimentally in Fig. 9.6 (b). Thus, similar to the first pass, the {112}<111> and {110}<111> systems could be considered as slip systems operating at the second pass. However, the initial shear bands formed at the first pass inhibited dislocations on other slip systems from crossing the bands. As a result, all of the possible slip systems belonging to the {112}<111> and {110}<111> slip system families should operate to accommodate deformation during the second pass. Hence, nanoscale dislocation cells enclosed by the {112} and {110} planes were formed.39–41 Formation of high-angle grain boundary The microstructures after four-pass ECAP are shown in Fig. 9.7, in which equiaxed grains with an average grain size of 0.2–0.3 µm were formed. Similar to previous findings,42–45 this confirms that grain refinement was most pronounced at the initial stage of ECAP but was not significant at large strains. This is because, with an increment in the amount of applied strain, the dislocation movement on the new slip systems would be restricted by the presence of the initial shear bands and, thus, they should rotate so as not only to accommodate strain but also to maintain an even shear strain distribution at grain boundaries once sub-grains appear. In order to examine the grain orientation relationship between two adjacent nanostructured grains, a Kikuchi pattern analysis was carried out. Some examples

9.7  Transmission electron microscopy micrograph of the four-pass ECAPed LCS sample.39 (Hereafter, all samples were subjected to four-pass ECAP).

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9.8  Transmission electron microscopy Kikuchi patterns showing the misorientation relationship between adjacent nanostructured ferrite grains of the ECAPed LCS sample.39

of the Kikuchi patterns of the four-pass ECAPed sample viewed from the <111> zone axis are shown in Fig. 9.8. As illustrated above, the directions of the grain boundaries in grain 1 were aligned along the <110> and <112> directions. The average misorientation angles across the boundaries aligned along the <110> and <112> directions were ~15° and ~10°, respectively. The Kikuchi patterns and the SAED patterns at large strains confirmed that the portion of high-angle boundaries increased with increasing the number of the pressing passes and that, thereby, they became the dominant structure at the large deformation strain.39

9.2.3 Microstructural evolution of LCS alloy by post-ECAP annealing Annealing behavior of ferrite phase The microstructural changes of ferrite phase in LCS alloy processed by ECAP and post-ECAP annealing treatments are shown in Fig. 9.9. Little grain growth

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9.9  Transmission electron microscopy and optical images showing the annealing behavior of nanostructured ferrite grains in the ECAPed LCS sample annealed for 1 h at various temperatures of (a) 723, (b) 753, (c) 783, (d) 813 K, and (e) 873 K.25

occurred at relatively low annealing temperatures of 693–783 K. As shown in Fig. 9.9 (a), however, the portion of well-defined grain boundaries increased and a considerable annihilation of lattice dislocations was noticed. Several interesting features were noticed in the sample annealed at 753 K (Fig. 9.9 (b) ): 1) slight but notable grain growth took place; 2) most grain boundaries were well defined; 3) in some grains (marked by grain  A), dislocation cells were observed; and 4) dislocation density inside individual grains became low. By annealing at 783 K (Fig. 9.9 (c) ), most boundaries became well defined, but their appearance was

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somewhat different from that observed in the sample annealed at 753 K (Fig. 9.9 (b) ). In addition, the existence of a dislocation wall (marked by arrows) was found, but extinction contours remained. These facts indicate that recovery was still in process. At 813 K (Fig. 9.9 (d) ), large, dislocation-free grains were observed and recrystallization was virtually completed at the annealing temperature of 873 K (Fig. 9.9 (e) ). The variation of ferrite grain size in 4 ECAPed LCS sample with annealing temperature is presented in Fig. 9.10. From Fig. 9.10, it is noticed that annealing behavior is different with respect to annealing temperature, resulting in two different regions whose boundary is determined at 783 K. This fact is mainly due to two different mechanisms such as recovery and recrystallization operated during heat treatments. Below 783 K, the microstructural change during annealing showed that a recovery process was dominant and indicated that recovery could be attributed to a process associated with the dissociation of lattice dislocations into extrinsic boundary dislocations during annealing. This finding is consistent with the experimental observation of an earlier high-resolution electron microscopy (HREM) study on an ECAPed aluminum alloy37 showing the existence of a large number of extrinsic dislocations at the non-equilibrium grain boundary region. At this temperature range, the grain size did not increase significantly with increasing annealing temperature. As a first approximation, the grain growth behavior in this regime was examined by applying the general equation for grain growth:

9.10  A grain size variation of ferrite phase with annealing temperatures.25

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[9.1]

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where d is the grain size at a given annealing time, d0 is the initial grain size, K0 is a constant, t is the annealing time, n is a constant with a value close to a unity, Q is the activation energy for grain growth and RT has its usual meaning. Using Eq. [9.1], Q can be obtained by plotting (d2–d02) against (1/T) in a semi-logarithmic scale at the same annealing time. Such a plot is depicted in Fig. 9.11 where d0 was taken as ~0.3 µm. The value of the activation energy was calculated to be ~106 kJ/mol. This value was lower than the activation energies for several kinetic processes associated with ferrite grain growth such as volume diffusion (~280 kJ/mol), grain boundary diffusion (~164 kJ/mol) of Fe in alpha-iron,46 grain boundary mobility of pure iron (~147 kJ/mol),47 and carbon diffusion in alpha-iron above 673 K (~141 kJ/ mol)46 Wang et al.48 reported that the activation energy for grain growth of an ECAPed Al-Mg alloy in the unrecrystallized regime was only 20% of that for self-diffusion of pure aluminum. Indeed, activation energy for grain growth in the unrecrystallized regime was ~0.35. This agrees well with the suggestion that nonequilibrium grain boundaries induced by severe plastic straining show higher mobility compared with those subjected to little or less plastic strain.49,50 Above 783 K, the ferrite phase of the LCS sample consisted of an unrecrystallized area and a recrystallized area, resulting in a bimodal grain size distribution. The

9.11  A plot of log (d 2–d02) vs. 1/T for the estimation of the apparent activation energy for grain growth of ferrite phase in the ECAPed LCS samples.25

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activation energy for grain growth in this regime was estimated as ~230 kJ/mol by taking, as a first approximation, the average value of the recrystallized ferrite grain size at each temperature and d0 = 0.3 µm. This value was lower than that for volume diffusion (~280 kJ/mol) of Fe in alpha-iron. However, it is worth mentioning that the estimation of activation energy for grain growth in this regime is less meaningful than that for the regime below 783 K due to the non-uniform distribution of the recrystallized ferrite grain size and the difficulty of determining the initial value of the recrystallized ferrite grain. In conclusion, up to 783 K, the grains were relatively stable and grain growth took place slowly with increasing annealing temperature. Above 783 K, the grains seemed to be unstable, showing a bimodal grain size distribution, i.e. coexistence of coarse grains and nanoscale grains.25,51 Annealing behavior of pearlite structure For the pearlite structure, no significant morphological change was observed below 753 K compared to the as-ECAPed sample (Fig. 9.3). However, the spheroidization of a large portion of cementite started to appear at 783 K (Fig. 9.12 (a) ). The spheroidized cementite particles remained at the initial cementite lamellar domain. In addition, some images of spheroidized cementite particles were not definite but relatively dim and diffused. This indicates that carbon in cementite dissolved locally into the pearlitic ferrite. At the same annealing temperature of 783 K, the dislocation density in pearlitic ferrite remained high compared to that in the ferrite phase (Fig. 9.9 (c) ). At 813 K (Fig. 9.12 (b) ), the microstructure of pearlite consisted of nearly spheroidal cementite particles with an average aspect ratio of ~2 and fine ferrite grains. It is worth noting that, under the same annealing conditions, the size of recrystallized ferrite grains within the pearlite structure was smaller than that in the group of ferrite grains (Fig. 9.9 (d) ); this is mainly due to a grain boundary pinning effect by fine cementite particles.

9.12  Transmission electron microscopy images showing the microstructure change of pearlite in the ECAPed LCS samples annealed for 1 h at various temperatures of (a) 783 and (b) 813 K.25

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As explained above, the spheroidization of cementite was clearly observed above 753 K and nearly completed at 813 K. This result was consistent with the morphological changes of cementite in heavily cold drawn pearlitic steel wire.33 To examine the influence of intense plastic strain on the enhancement of the spheroidization behavior of cementite, the initial sample prior to ECAP was annealed at 783 K and its pearlite structure is shown in Fig. 9.13. Comparison of Fig. 9.12 (a) (ECAPed alloy) and Fig. 9.13 (initial pre-ECAPed alloy), where both alloy samples were annealed under the same conditions, led to the conclusion that the kinetics of spheroidization occurred only in the ECAPed sample. It has been established that, in the case of heavily cold drawn pearlitic steel wire, severe plastic strain leads to enhanced spheroidization of cementite due to relatively easy carbon dissolution from deformed cementite into pearlitic ferrite during bluing treatment.52–55 Gridnev and Garririlyuk56 proposed that easy carbon dissolution during the bluing treatment of heavily cold drawn pearlitic steel wire could be attributed to higher binding energy between dislocations in pearlitic ferrite and carbon atoms than that between the Fe atoms in cementite and the carbon atoms. However, researchers find fault with this suggestion since both binding energies are roughly the same: the former and the latter are 0.55 and 0.50 eV, respectively.57,58 Languillaume et al.59 explained the easy carbon dissolution behavior by suggesting that the driving force for carbon dissolution was increased by an increase in the cementite/pearlitic ferrite interfacial energy due to the formation of slip steps at the cementite/pearlitic ferrite interface during the heavy cold drawing process. In addition, Hong et al.60 suggested that, in the same LCS materials, excessive imperfections would be introduced into cementite

9.13  Transmission electron microscopy image of pearlite in the initial LCS sample without ECAP annealed at 783 K for 1 h.25

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by severe plastic deformation and their existence resulted in a comprised nonstoichiometric cementite composition, facilitating easy carbon dissolution. Accordingly, given that the microstructural change of pearlite in the ECAPed LCS alloy during annealing was very similar to that observed during the bluing treatment of the heavily cold drawn pearlitic steel wire, the enhanced spheroidization of cementite here could be attributed to easy carbon dissolution from cementite into pearlitic ferrite caused by severe plastic deformation of cementite.

9.2.4 Formation of fine cementite precipitates The TEM micrograph of the LCS sample after annealing at 813 K for 1 h presented in Fig. 9.14 reveals a number of spherical cementite precipitations within a pearlite colony. In some of the colonies, depending on their inclinations to the main shear direction, rod-like cementite particles were restored, whereas they successfully transformed into spherical precipitates during the annealing. From the TEM images taken of the annealed sample, the dislocation density was observed to be of the order of 1014 to 1016 m–2, although it was expected that the dislocation density within ferrite grains of the annealed sample would reduced due to the static recovery. As discussed earlier by several researchers,1,61 the decomposition reaction occurred not only during the deformation stage but also during the annealing stage. As such, static annealing of the ECAPed ferrous alloy at 813 K for 1 h would be beneficial for the decomposition of the entire pearlite colonies and the uniform precipitation of cementite particles. This extraordinary phenomenon demonstrates a potential new processing route of forming fine precipitates by

9.14  Transmission electron microscopy image of a spheroidized pearlite colony in the ECAPed LCS sample annealed at 813 K for 1 h.61

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the static annealing of severely deformed steel, instead of the conventional heat treatment route including normalizing, quenching and aging treatment. As the formation energy of cementite is relatively low and the dislocationcementite interaction energy was estimated to be approximately ~0.5 eV,62 the cementite might be decomposed by the interaction with the stress field of dislocations, as indicated in a previous report.60 In the presence of the internal stress field of dislocation, the net number of extra carbon atoms segregated per unit length of a dislocation (N/L) was estimated by the following Eq. [9.2]:63 ,

[9.2]

where C0 is the equilibrium concentration in the matrix, b the Burgers vector of the edge component, ν Poisson’s ratio, G equals E/2(1 + ν), E Young’s modulus, Vs the atomic volume of carbon and Va the interstitial site volume of ferrite steel. As the cementite became nano-sized, the experimentally determined C0 value64 was adjusted using the Gibbs–Thompson relationship.65 For the adjustment, the cementite was assumed to be a sphere of ~20 nm in diameter and has a surface energy of 1 J/m2.66 Using the above equation, the excess carbon concentration (ECC) was calculated as a function of temperature at different dislocation densities (1014–1016m–2). As shown in Fig. 9.15, the ECC value was a strong

9.15  Excess carbon concentration calculated as a function of annealing temperature. The dislocation density changed from 1014 to 1016 m–2.65

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function of the dislocation density and became negligible as the density decreased to less than 1014 m–2. Although the rate constant for the decomposition reaction was not determined, the calculated ECC value, which was 10–20% of the equilibrium concentration, was considered to be large enough for the decomposition reaction to proceed at a reasonable rate. Therefore, a group of high dislocation density might promote the decomposition of the cementite via interaction with the dislocations. For a uniform distribution of cementite particles, the carbon atoms released from the decomposition reaction should diffuse away from the colonies toward ferrite grains and precipitate during the static annealing treatment. On the basis of a microstructural analysis utilizing TEM, the dislocation density in the pearlite colony was much higher than that inside the ferrite grains. As the ECC value was sensitive to the dislocation density as shown in Fig. 9.15, the ECC value in the colony was relatively higher, as compared to that inside the ferrite grain, which would induce a diffusion flux towards the ferrite grains. With the carbon diffused away from the colony towards the ferrite grains of low dislocation density, the grain would became supersaturated with carbon atoms, providing a favorable condition for precipitation.

9.3

The mechanical response of a nanostructured LCS alloy

9.3.1 Mechanical properties Figure 9.16 shows the deformation behavior of the ECAPed LSC alloy with respect to the number of ECAP operations, corresponding to effective strain. The increase in hardness was most pronounced at the first pass and thereafter, the strengthening became less significant for further deformation. This finding is in line with the observation of microstructural evolution that grain refinement was most significant at the first pass. It is also consistent with previous observations reported for various ECAPed materials.14–16 After the initial pressing, the hardening behavior of the ferrite phase was more considerable than that of pearlite. With an increasing number of passes, however, the hardening tendency in both grains was toward saturation. Tensile properties of the ECAPed LCS alloy are shown in Fig. 9.17. The trend of the variation of yield strength and ultimate tensile strength with the pass number agreed with that of the hardness data (Fig. 9.16). It was found that, without the aid of compositional changes, the nanostructured grains could give rise to tensile strength higher than 900 MPa together with reasonable elongation of ~10%. This suggested that, among strengthening mechanisms, inducing a nano-grained structure is advantageous for improving strength without significant loss of ductility.17 Stress–strain curves of the initial, ECAPed and ECAPed-annealed LCS samples are shown in Fig. 9.18, and the values of their tensile properties are listed

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9.16  A plot of micro-hardness vs. the pass number for each of the constituent phases of the ECAPed LCS sample.17

9.17  Tensile properties of the ECAPed LCS samples with increasing number of operation.17

in Table 9.1. Particular attention should be paid to strain hardening behavior. The initial samples exhibited moderate strain hardenability with large uniform ductility after Lüders strain, whereas the as-pressed and annealed samples exhibited no strain hardening behavior, a general feature of nanostructured metals reported

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9.18  Engineering stress–strain curves of the initial, ECAPed, and ECAPed-annealed LCS samples.18

Table 9.1  Ferrite grain sizes and tensile properties of the LCS samples Treatments

d (µm)

YS (MPa)

UTS (MPa)

ef (%)

As-received As-ECAPed ECAP + Annealed at 753 K for 72 hrs

30 0.2 ~ 0.3 0.45

310 937 683

480 943 720

29.9 10.9 20.2

previously.25,27,39,61 Depending upon the annealing condition, however, this strain hardenability was successfully restored with a sacrifice of strength.

9.3.2 Deformation mechanism Ultra-high strength Similar to the case of other nanostructured metals, the tensile deformation behavior of the nanostructured LCS alloy was characterized by the absence of strain hardening as well as ultra-high strength. Since the nanostructured LCS samples exhibited negligible strain hardening, their ultra-high strength could not be explained solely by the dislocation pile-up mechanism. However, as noted by Valiev et al.,50 the

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dislocation bow-out model, which was used to explain the mechanical behavior of nanostructured materials, is applicable. In the context of the dislocation bow-out model,67,68 yielding occurred when the dislocation configuration reached a semicircle and the critical stress for this condition was approximated by the following expression: ,

[9.3]

where G is the shear modulus, b is the Burgers vector, ν is Poisson’s ratio and L is the average dislocation length. For grain size larger than 100 nm, L was equivalent to ρ–½ where ρ is the dislocation density.69 With the aid of Eq. [9.3], the yield stress of nanostructured materials could be expressed as: ,

[9.4]

where σ0 is the friction stress and M is the Taylor factor. Using equations [9.3] and [9.4], the yield strength of ferrite phase in the ECAPed LCS sample was estimated as 728 MPa with the following values: G = 78 GPa, b = 2.48 × 10–10 m, ρ = 1015 m–2, ν = 0.33, M = 2.78 for bcc structure, and σ0 = 76 MPa.8 Although there existed some variation in dislocation density when TEM was used, the use of the value of 1015 m–2 does not appear to be erroneous since ρ for several nanostructured materials by the ECAP process was reported to be on the order of 1015 m–2.7,49 It is also important to consider that the LCS sample consisted of ~85% of ferrite phase with the remainder being pearlite phase. Hence, the yield stress of the ECAPed LCS sample could be approximated by the rule of mixture: ,

[9.5]

where V is the volume fraction and the superscripts f and p denote ferrite and pearlite, respectively. Due to a lack of reliable data on the application of ECAP to high-carbon steel consisting of a fully pearlite structure, σ ysp should be deduced from that of a cold drawn pearlitic steel. Under the same amount of effective strain, σ ysp of the heavily drawn pearlitic steel was in a range of 1800–2000 MPa.34 Our estimation showed a yield stress of 850–880 MPa, which was still lower than obtained above (937 MPa). Valiev et al.49 also used the dislocation bow-out model to predict the strength of nanostructured pure copper at ambient temperature. They argued that some deviation of the estimated value based on dislocation bowout from the experimental value could be attributed to 1) the actual dislocation density and 2) the supplementary effect of internal stress. A lack of strain hardenability: dynamic recovery As shown in Fig. 9.18, the nanostructured LCS sample exhibited no strain hardening under tension deformation. The absence of strain hardening in ultrafine grained (UFG) steels was examined in terms of dynamic recovery. During

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tensile deformation, dislocations causing intragranular strain are trapped at the grain boundaries if no strong obstacles for lattice dislocation motion existed inside the grains. The kinetics of dynamic recovery is closely related to the spreading of trapped lattice dislocations (TLDs) into the grain boundaries.49,70,71 The change of dislocation density owing to dynamic recovery by TLD spreading into the grain boundaries could be described by the following generalized equation

[9.6]

. where ρ is the dislocation density, t is the time, α is a constant, ε is the strain rate, b is the Burgers vector, d is the grain size and ξ is the characteristic time for TLD spreading into the grain boundaries. At steady state deformation, i.e. (∂ρ/∂t) = 0:

[9.7]

For the ECAPed sample, ξ was ~21 s with ρ = 1015 m–2, b = 2.48 × 10–10 m, . d = 0.25 × 10–6 m, α = 2.4 and ε = 1.33 × 10–3 s–1. The deformation time to reach the maximum point in stress was ~22 s. Therefore, lattice dislocations contributing to intragranular strain were trapped at interfaces, and they subsequently spread into the grain boundary concurrently during deformation. As a result, there is no accumulation of lattice dislocations and, consequently, no strain hardening is expected. For a sample annealed at 753 K for 72 hrs, the dislocation density decreased by several orders of magnitude, but the ferrite grain size increased only by a factor of 2. In this case, the value of ξ decreased drastically but the deformation time became more prolonged due to the larger elongation. Accordingly, it was natural that strain hardening was observed to some extent in the sample annealed at 753 K for 72 hrs.18,19 A lack of strain hardenability: mean free length of dislocation Figure 9.19 shows the dislocation distribution observed in tensile-deformed steel without ECAP (d = 30 µm) at different strain levels. Prior to the tension test, the dislocation density was relatively low (Fig. 9.19 (a) ); but after 5% deformation (Fig.9.19 (b) ) the dislocations were distributed randomly inside grains with high density. A dislocation cell structure with an average diameter of 0.35 µm was formed at the engineering strain of 15% (Fig. 9.19 (c) ). The tensile deformed microstructure of the steel annealed at 753 K for 72 hrs after ECAP is shown in Fig. 9.20. Most ferrite grains in the ECAP-deformed sample were elongated (Fig. 9.20 (a) ), indicating that considerable intragranular strain was induced during deformation. In addition, an inspection with higher magnification (Fig. 9.20 (b) ) revealed that the dislocations were not distributed uniformly inside the grains but were localized in the vicinity of the grain boundaries.

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9.19  Transmission electron microscopy images showing the distribution and density of lattice dislocation in tensile-deformed LCS sample without ECAP at different strain levels: (a) before testing, (b) e = 5% and (c) e = 15%.18

9.20  (a) Transmission electron microscopy image showing tensiledeformed LCS sample annealed at 753 K for 72 hrs after ECAP and (b) magnified image of the same sample showing dislocation distribution near to grain boundaries.18

At the initial stage of plastic deformation, the dislocation density increased and its distribution was relatively uniform at the grain interior, causing strain hardening. As plastic deformation proceeds, a dislocation cell structure was formed due to dislocation entanglement. Under these conditions, the cell size was equivalent to

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the mean free dislocation length (L).72 The mean free dislocation length was inversely proportional to the shear stress (τ).

[9.8]

The cell size at different stress levels could then be approximated by the following simple relationship for the same material:

[9.9]

With the cell size (δ1 = 0.35 µm) measured from the deformed sample without ECAP and the stresses inferred from Fig. 9.18, the cell size (δ2) of the other sample is estimated from Eq. [9.9] and listed in Table 9.2. In the estimation, the engineering stress in Fig. 9.18 was converted to the corresponding shear stress by the generalized relationships. Two findings are noted from Table 9.2. First, for the ECAP-deformed sample annealed at 753 K for 72 hrs, the measured cell size, 0.35 µm, is almost identical with that estimated from Eq. [9.9], 0.24 µm, thus demonstrating the validity of Eq. [9.9]. Second, the ferrite grain sizes of nanostructured LCS samples were comparable to the estimated cell sizes within a factor of 2 at the corresponding stress levels. The negligible strain hardening during tensile deformation of the nanostructured LCS sample could be attributed to the mean free dislocation length at the corresponding stress level being comparable to the ferrite grain size. Consequently, dislocation entanglement largely took place at the grain interior of nanoscale grains, thus affecting strain hardenability. In coarse-grained LCS materials, the equiaxed dislocation cells were not subjected to shape changes even at relatively high strains. This indicates that the cell formation occurred continuously during deformation, implying that the cell formation is a kind of relaxation process that causes a reduction in the strainhardening rate.73 The uniform distribution of lattice dislocation with high density

Table 9.2  Dislocation cell sizes calculated by Eq. 1.9 and ferrite grain sizes of the LCS samples

τ1

τ2

As-received

276

δ1

δ2

0.35

δ

Remarks

30

Strain hardening

As-ECAPed 486 0.20 0.2 ~ 0.3

Weak strain hardening

ECAP + Annealed 396 0.24 0.45 at 753 K for 72 hrs

Slight strain hardening

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at the initial stage of deformation, but with further deformation, it changed into a cell structure consisting of hard and soft regions. For the cell structure the hard region is the cell wall region with tangled dislocations while the soft region is the dislocation-free cell interior. In nanostructured materials, the TLDs at the grain boundaries, one of the relaxation processes, occurred at the onset of plastic deformation without a uniform distribution of lattice dislocation, since the grain size is comparable or even smaller than the mean free dislocation length. This analysis indicates that the strain-hardening rate would be negligible during plastic flow of nanostructured metallic materials, but the hardening rate would be restored with post-ECAP annealing.

9.4

Enhanced tensile properties by grain refinement and microstructural modification

9.4.1 LCS alloy containing vanadium carbides Since strain-hardening characteristics rapidly diminish with a decreasing of grain size down to a nanometer level, we introduced fine vanadium carbides to the nanostructured LCS sample in order to alleviate the inherent mechanical drawback discussed above. A LCS sample with an addition of 0.34 wt% vanadium was prepared and deformed by ECAP with the same working conditions. Details of the procedures have been described elsewhere.20 As indicated by the arrows in Fig. 9.21 (a), nanoscale precipitates of 5–10 nm were observed at the area of high dislocation density in the ECAPed LCS sample, which did not contain precipitates prior to ECAP operation. These precipitates formed during ECAP at 623 K were identified as V3C4 by an energy dispersive spectra analysis (Fig. 9.21 (b) ). The precipitates are believed to have originated from strain-induced precipitation,

9.21  (a) Transmission electron microscopy image showing the existence of nanoscale vanadium carbides at the area of high dislocation density in the ECAPed LCS sample and (b) qualitative chemical analysis of them.20

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where nucleation sites are the heterogeneous regions such as dislocations of high density formed by ECAP.

9.4.2 Dual-phase LCS alloy Within the framework of strain gradient plasticity, two different kinds of dislocations played different roles on plastic deformation; that is, statistically stored dislocations influence deformation itself, whereas geometrically necessary dislocations (GNDs) operate for strain hardening.74 Among a variety of ferrous alloys, a dual phase structure consisting of ferrite and martensite is a representative structure having a large number of GNDs. It is well established that the excellent strain hardenability of dual phase steel is mainly due to the existence of glissile dislocations newly formed during intercritical annealing followed by water quenching after ECAP.75–79 These dislocations, which have been observed at ferrite grains close to martensite, act as GNDs, making it possible to achieve high strain hardenability.80 Details of processing conditions can be found in Ref.81 As shown in Fig. 9.22 (a), the microstructure of the nanostructured dual-phase steel consisted of equiaxed ferrite grains (0.8 µm in size) and martensite grains (0.9 µm in size). Both ferrite grain size and martensite island size were found to have a submicrometer scale and the volume fraction of martensite was about ~30%. A SEM micrograph with higher magnification (Fig. 9.22 (b) ) revealed that the martensite ('M' in Fig. 9.22 (b) ) was in an isolated blocky type82 and existed in minute quantities at ferrite/ferrite boundaries. Again, a nanostructured dual phase microstructure with a uniform distribution of each constituent phase could be attained by three distinctive steps associated with thermo-mechanical treatment. First, during ECAP, carbon atoms from pearlitic cementite were dissolved and, thereby, diffused toward ferrite phase grains. This uniform distribution of equilibrium/excessive carbon atoms allowed an austenite phase to form uniformly during intercritical annealing. During water quenching, austenite grains were

9.22  Scanning electron microscopy images of (a) the nanostructured dual-phase steel and (b) nanostructured dual-phase steel with higher magnification.81

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transformed into martensite islands, generating a number of mobile dislocations in ferrite grains adjacent to martensite by volume expansion. Tensile testing of the nanostructured dual phase steel showed that, unlike most nanostructured materials that show a poor strain-hardening rate, the dual phase exhibited a good combination of high strength and ductility (extensive strain hardenability). This demonstrates that strain gradient plasticity has a high potential to enhance the strain hardenability of nanostructured materials.

9.5

Continuous shear drawing: a new processing method

Although severe plastic deformation of metals and alloys utilizing ECAP has recently been regarded as a promising method for tailoring nanostructure as well as decomposing lamellar or dendrite structure, the batch process of ECAP generated a technical problem, which limits its actual applications. Thus, one of the approaches currently being considered to develop a method that is suitable for the continuous processing is the use of equal-channel angular drawing (ECAD), where samples are deformed in a drawing fashion instead of pressing, as the length of sample would likely no longer be limited by the buckling instability during deformation.83–86 However, Luis et al.,86 based on finite element method (FEM) calculations, validated what was found by actual experiments, that the deformation of ECAD is inevitably accompanied by both appreciable corner gap and severely localized necking. This is presumably due to the fact that the deformation is more dominated by drawing than by shearing when the sample passes through the shear plane. We suggested a new type of ECAD termed continuous shear drawing (CSD) in conjunction with an effort to modify the design of the die in order to avoid dimensional inhomogeniety of the sample during deformation. According to an upper bound analysis84 and FEM results,85 the use of ECAD clearly caused unstable deformation of a number of fine meshes when the inner angles became less than 120°. As shown in Fig. 9.23, a die with an inner angle of 135° was designed to avoid the formation of pronounced necking, which is noxious to further deformation. A CSD die was also prepared by reducing the diameter of the exit channel so as to impose higher strain compared to ECAD. Considering the reduced geometry of the exit channel, an additional strain was imparted to samples when the samples experienced one passage. The total effective stain (εT) accumulated from the CSD process was the sum of the shear strain87 and the drawing strain: ,

[9.10]

where φ, li and lf are the half of inner angle in die and the initial and the final diameters of sample, respectively. The annealing behavior of three different samples with no deformation, drawing and CSD is shown in Fig. 9.24 (a). The annealed sample without deformation

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9.23  Schematic description of the proposed die used for CSD technique.

9.24  Scanning electron microscopy images showing spheroidization behavior at a subcritical temperature of 973 K (a) for 10 hrs in sample with no prior deformation, (b) for 5 hrs in sample deformed via conventional drawing and (c) for 1 h in sample deformed via CSD method.

shows remnant thin-striped cementite phases. The other samples deformed via drawing and CSD methods required 5 hrs and 1 h, respectively in order to achieve a uniform microstructure with fine cementite (Fig. 9.24 (b) and 9.24 (c) ). From these results, the CSD method is thought to possess a commercial potential for

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use as an intermediate step of wire manufacture, as it could reduce annealing time by promoting the rate of spheroidization of the pearlitic-cementite phase. Moreover, as compared to the result yielded by conventional drawing, the use of the CSD technique combined with an annealing treatment led to a microstructure having fine cementite dispersed uniformly in the ferrite matrix due to straininduced spheroidization.

9.6

Conclusion

The change in microstructure and the variations in tensile properties of nanostructured LSD alloy fabricated by ECAP together without/with various post-ECAP annealing treatments have been reviewed. The grain refinement of LSD alloy was achieved by grain subdivision due to the operation of multiple slip systems of <111>{110}, <111>{112} and <111>{123}. A comparison between the ferrite grain size of a nanostructured LCS sample and the dislocation cell size of its coarse-grained counterpart formed during tensile deformation revealed that the cell formation was unlikely to occur in the former, thus implying that the low strain hardening rate could be attributed to two factors: dynamic recovery and nanoscale grains comparable to the mean free length of dislocations. First, the feasibility of enhancing the strain hardenability of the nanostructured LCS sample was explored by comparing the microstructure and stress–strain behavior of two LCS samples without/with vanadium carbides. Second, the strain hardening behavior of a dual-phase steel via both ECAP and intercritical annealing followed by water quenching was investigated. In addition, we developed a continuous approach based upon CSD in which shear and drawing deformation are conjugated. It appears that the use of CSD would be advantageous for achieving a microstructure incorporating fine cementite particles, which are dispersed uniformly throughout the matrix due to strain-induced spheroidization.

9.7

References

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11 Wang Y., Chen M., Zhou F., Ma E. Nature 2002;419: 912. 12 Mishra R.S., Stolyarov V.V., Echer C., Valiev R.Z., Mukherjee A.K. Mater Sci Eng 2001;A298: 44. 13 Sergueeva A.V., Stolyarov V.V., Valiev R.Z., Mukherjee A.K. Mater Sci Eng 2002; A323: 318. 14 Ko Y.G., Jung W.S., Shin D.H., Lee C.S. Scripta Mater 2003;48: 197. 15 Furukawa M., Horita Z., Nemoto M.,Valiev R.Z., Langdon T.G. Acta Mater 1996;44: 4619. 16 Nakashima K., Horita Z., Nemoto M., Langdon T.G. Acta Mater 1998;46: 1589. 17 Shin D.H., Seo C.W., Kim J., Park K.T., Choo W.Y. Scripta Mater 2000;42: 695. 18 Shin D.H. Met Mat Inter 2001;7: 573. 19 Park K.T., Kim Y.S., Lee J.G., Shin D.H. Mater Sci Eng 2000;A293: 165. 20 Park K.T., Han S.Y., Shin D.H., Lee Y.K., Lee K.S. ISIJ Inter 2004;44: 1057. 21 Segal V.M. Mater Sci Eng 1995;A197: 157. 22 Chang S.Y., Lee J.K., Park K.T., Shin D.H. Mater Trans 2001;42: 1074. 23 Shin D.H., Kim W.J., Choo W.Y. Scripta Mater 1999;41: 259. 24 Shin D.H., Kim B.C., Kim Y.S., Park K.T. Acta Mater 2000;48: 2247. 25 Shin D.H., Kim B.C., Park K.T., Choo W.Y. Acta Mater 2000;48: 3245. 26 Markushev M.V., Bampton C.C., Murashkin M.Y., Hardwick D.A. Mater Sci Eng 1997;A234: 927. 27 Nemoto M., Horita Z., Furukawa M., Langdon T.G. Met Mater 1998;4: 1181. 28 Furukawa M., Iwahashi Y., Horita Z., Nemoto M., Langdon T.G. Mater Sci Eng 1998;A257: 328. 29 Berbon P.B., Furukawa M., Horita Z., Nemoto M., Tsenev N.K., Valiev R.Z., Langdon T.G. Mater Sci Forum 1996;217: 1013. 30 Valiev R.Z., Sailmomenko D.A., Tsenev N.K., Berbon P.B., Langdon T.G. Scripta Mater 1997;37: 1945. 31 Iwahashi Y., Furukawa M., Horita Z., Nemoto M., Langdon T.G. Metall Mater Trans1998;A29: 2245. 32 Nam W.J., Bae C.M. Mater Sci Eng 1995;A203: 278. 33 Bae C.M., Dissertation PhD. POSTECH, Korea 1999. 34 Porter D.A., Eastering K.E. Acta Metall 1978;26: 1405. 35 Langford G. Metall Trans 1977;8A: 861. 36 Inoue A., Ogura T., Masumoto T. Trans JIM 1977;17: 143. 37 Servillano J.G. Mater Sci Eng 1975;A21: 221. 38 Maurer K., Warrington D.H. Phil Mag 1967;15: 321. 39 Shin D.H., Kim I., Kim J., Park KT. Acta Mater 2001;49: 1285. 40 Kim J.R., Kim I.Y., Shin D.H. Scripta Mater 2001;45: 421. 41 Shin D.H., Kim J., Park K.T. Met Mater Inter 2001;7: 431. 42 Mishra R.S., Semiatin S.L., Suryanarayana C., Thadhani N.N., Lowe T.C. Ultrafine Grained Materials, TMS, Warrendale, PA 2000. 43 Nakashima K., Horita Z., Nemoto M., Langdon T.G. Mater Sci Eng 2000;A281: 92. 44 Gholinia A., Prangnell P.B., Markushev M.V. Acta Mater 2000;48: 1115. 45 Iwahashi Y., Horita Z., Nemoto M., Langdon T.G. Acta Mater 1998;46: 3317. 46 Askill J. Tracer Diffusion Data for Metals, Alloys and Simple Oxides; Plenum Press, New York (NY); 1970. 47 Hillert M. Metall Trans 1975;6A: 5. 48 Wang J., Iwahashi Y., Horita Z., Furukawa M., Nemoto M., Valiev R.Z., Langdon T.G. Acta Mater 1996;44: 2973.

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49 Valiev R.Z., Kozlov E.V., Ivanov Y.F., Lian J., Nazarov A.A., Baudelet B. Acta Metall. Mater 1994;42: 2467. 50 Lian J., Valiev R.Z., Baudelet B. Acta Metall Mater 1995;43: 4165. 51 Park K.T., Shin D.H. Mater Sci Eng 2002;A334: 79. 52 Read H.G., Reynolds W.T., Hono JrK, Tarui T. Scripta Mater 1997;37: 1221. 53 Makii K., Yaguchi H., Kaiso M., Ibaraki N., Miyamoto Y., Oki Y. Scripta Mater 1997;37: 1753. 54 Makii K., Yaguchi H., Minamida T., Kaiso M., Ibaraki N., Oki Y. Tetsu-to-Hagane 1997;83: 42. 55 Shin D.H., Han S.Y., Park K.T., Kim Y.S., Paik Y.N. Mater Trans 2003;44: 1630. 56 Gridnev V.N., Garririlyuk V.G. Phys Metals 1981;4: 531. 57 Kamber K., Keeter D., Wert C. Acta Metall Mater 1961;9: 403. 58 Kalish D., Kohen M. Mater Sci Eng 1970;A6: 156. 59 Languillaume J., Kapelski G., Baudelet B. Acta Mater 1997;45: 1201. 60 Hong M.H., Reynolds W.J., Tarui Jr. T., Hono K. Metall Mater Trans 1999;A30: 717. 61 Shin D.H., Kim Y.S., Lavernia E.J. Acta Mater 2001;49: 2387. 62 Kubaschewski O., Alcock C.B. Metallurgical Thermo-Chemistry; Pergamon Press, Oxford 1979: 284. 63 Hirth J.P., Lothe J. Theory of Dislocations; McGraw-Hill, New York (NY) 1968: 464. 64 McGannon H.E. The Making, Shaping and Treating of Steel (9th ed.); USS, Pittsburgh (PA) 1971:328. 65 Murr L.E. Interfacial Phenomena in Metals and Alloys; Addison-Wesley Publishing Co, New York (NY) 1975: 5. 66 Schaffer J.P., Saxena A., Antolovich S.D., Snaders Jr T.H. The Science and Design of Engineering Materials; RD Irwi, Inc: Chicago 1995: 92. 67 Hirth J.P., Lothe J. Theory of Dislocations, 2nd edn; Wiley: New York (NY) 1982: 971. 68 Lian J., Baudelet B., Nazarov A.A. Mater Sci Eng 1993;A172: 23. 69 Kuhlmann-Wilsdorf D. Mater Sci Eng 1989;A113: 1. 70 Lojkowski W. Acta Metall Mater 1991;39:1892. 71 Nazarov A.A., Romanov A.E., Valiev R.Z. Scripta Metall Mater 1990;24: 1929. 72 Khulmann-Wilsdorf D. Work Hardening (eds., Hirth J.P. and Weertman J.); Gordon and Breach, New York (NY) 1968: 97. 73 Humphreys F.J., Hatherly M. Recrystallization and Related Annealing Phenomena; Pergamon, Oxford (UK) 1995: 25. 74 Needleman A., Gil Sevillano J. Scripta Mater 2003;48: 109. 75 Matlock D.K., Zia-Ebrahimi F., Krauss G. Deformation Processing and Structure, ASM; Metals Park, USA 1982: 47. 76 Son Y.I., Lee Y.K., Park K.T., Lee C.S., Shin D.H. Acta Mater 2005;53: 3125. 77 Shin D.H., Park K.T. Mater Sci Eng 2005;A410–411: 299. 78 Shin D.H., Kim W.G., Ahn J.Y., Park K.T., Kim Y.S. Mater Sci Forum 2006;503–504: 447. 79 Hwang B.C., Kim Y.G., Lee S.H., Hwang D.Y., Shin D.H. Metall Mater Trans 2007;A38: 3007. 80 Aldazabal J., Gil Sevillano J. Mater Sci Eng 2004;A365: 186. 81 Park K.T., Han S.Y., Ahn B.D., Shin D.H., Lee Y.K., Um K.K. Scripta Mater 2004;51: 909. 82 Cai X.L., Garratt-Reed A.J., Owen W.S. Metall Trans 1985;A16: 543. 83 Chakkingal U., Suriadi A.B., Thomson P.F. Mater Sci Eng 1999;A266: 241.

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84 Alkorta J., Rombouts M., Messenmaeker J.D., Froyen L., Sevillano J.G. Scripta Mater 2002;47: 13. 85 Luis C.J., Garcés Y., González P., Berlanga C. Mater Manuf Proc 2002;17: 223. 86 Zisman A.A., Rybin V.V., Van Boxel S., Seefeldt M., Verlinden B. Mater Sci Eng 2006;A427: 123. 87 Iwahashi Y., Wang J., Horita Z., Nemoto M., Langdon T.G. Scripta Mater 1996;35: 143.

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10 Characteristic structures and properties of nanostructured metals prepared by plastic deformation X. HUANG, Technical University of Denmark, Denmark Abstract: This chapter focuses on describing the characteristic microstructures of nanostructured metals produced by plastic deformation to ultrahigh strains and their correlation with hardening by annealing and softening by deformation. The results suggest that optimising microstructure and the mechanical properties of nanostructured metals can be achieved by a combination of post-process heat treatment and deformation. Key words: nanostructured metals, transmission electron microscopy (TEM), boundary spacing and misorientation, dislocation density, unusual mechanical behaviours.

10.1 Introduction Nanostructured metals produced by plastic deformation to ultrahigh strains constitute a special class of nanomaterials with characteristic microstructures and properties. Over the last decades progress has been made in many areas: • New processes have been introduced, such as high-pressure torsion (HPT), equal-channel angular pressing (ECAP), and accumulative roll bonding (ARB), which enable the researcher to impose extremely high strains to a metal without change in the sample geometry. • Characteristic microstructural parameters and their distribution have been quantified including grain size, boundary misorientation and dislocation density. • Characteristic mechanical properties have been analysed such as strength, tensile ductility, strain rate sensitivity and flow instabilities, and the effect of post-process annealing and deformation on these properties. • Strengthening mechanisms and the relationship between microstructural parameters and mechanical properties have been explored. • New approaches for optimising mechanical properties by manipulating the microstructure have been investigated. Some of these areas are reviewed and discussed in other chapters of this book. This chapter will focus on characteristic microstructural parameters in nanostructured face-centred cubic (fcc) Al and body-centred cubic (bcc) interstitialfree (IF) steel produced by ARB at room temperature and 500°C, respectively, and fcc Ni produced by HPT at room temperature. The compositions of these metals 276 © Woodhead Publishing Limited, 2011

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Table 10.1  Chemical composition of a commercial purity Al (JIS1100) (mass%) Si 0.11

Fe 0.55

Cu 0.11

Mn 0.01

Mg 0.02

Ti 0.02

B 0.0007

V Ni Al 0.011 0.003 Bal.

Table 10.2  Chemical composition of an IF steel (mass%) C 0.002

N 0.003

Si 0.01

Mn 0.17

P 0.012

Cu 0.01

Ni 0.02

Ti 0.072

Fe Bal.

Table 10.3  Chemical composition of a commercial purity Ni (mass%) C Si Mn P S Cr Fe Al Co Cu Ti Mg Ni 0.006 0.003 0.015 0.025 0.001 0.001 0.44 0.004 0.035 0.012 0.002 0.003 Bal.

are shown in Tables 10.1–10.3. Then the correlation between microstructural characteristics and mechanical properties is discussed with an emphasis on recent observations of unusual mechanical behaviours. The observations and analyses lead to suggestions for new approaches for optimisation of microstructure and properties of nanostructured metals.

10.2 Characteristic microstructures 10.2.1  Microstructural parameters The key microstructural parameters characterising nanostructured metals are microstructural morphology, spacing between boundaries, misorientation across boundaries, fraction of high-angle boundaries, and density of dislocations present in dislocation boundaries (<15°) and interior dislocations present in the volume between the boundaries.1,2 Elongated or lamellar microstructures are typically present in nanostructured metals produced by monotonic deformation, such as cold rolling,3 ARB,4 HPT,5,6 and ECAP route in which the sample rod doesn’t rotate between the passes.7 For such a directional 2D morphology, a selection of the observation plane is essential and it has been shown that most quantitative information can be obtained by inspection of the longitudinal plane as this is the best section to reveal the microstructural details,5,8 and that TEM is the most precise technique for obtaining the required microstructural parameters from a single sample section.2,9 In addition to TEM, electron backscatter diffraction (EBSD) in a scanning electron microscope has been extensively used to characterise the microstructural

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morphology, texture and misorientation of nanostructured metals and alloys.10,11 However, EBSD is incapable of revealing boundaries with misorientation angles of less than 2° for highly deformed metals and it cannot resolve individual dislocations in the volume between the boundaries. As a determination of these parameters is critical for an analysis of the mechanical behaviour of nanostructured metals, all microstructural results to be reported in the following have been obtained by a TEM characterisation of the longitudinal section. A semiautomatic Kikuchi pattern analysis technique has been used to obtain statistical data for grain orientation and boundary misorientation angles.12 The ARB Al and IF steel samples have been deformed to von Mises strains of about 5 and the HPT Ni samples have been deformed to von Mises strains over an extremely large range from 5 to 300. The specific microstructural parameters are the following: • Spacing between boundaries: 1) perpendicular to the rolling plane in ARB and to the torsion plane in HPT (dt), 2) parallel to the rolling direction in ARB and to the shear direction in HPT (dl) • Misorientation angle across the boundaries: 1) average angle (θav), 2) distribution of angles and 3) frequency of high-angle boundaries (θ ≥ 15°) and very low-angle boundaries (θ ≤ 3°). • Density of loose dislocations present in the volume between the different types of boundaries (ρ0).

10.2.2 Nanostructured Al produced by accumulative roll bonding (ARB) Figure. 10.1(a) illustrates a TEM microstructure in the longitudinal section of a commercial purity Al (99.2% pure, see Table 10.1) sheet processed at room temperature by non-lubricated ARB for six cycles (corresponding to a von Mises strain of about 5),13 showing a well-developed very fine lamellar microstructure similar to that seen in Al-1200 samples cold rolled to high strains.3 The boundary spacings for both the lamellar boundaries, dt, and interconnecting boundaries, dl, were measured and are given in Table 10.4.13 The lamellar boundary spacing is refined to 180 nm which is finer than the lamellar boundary spacing of about 300 nm obtained in the AA1200 Al cold rolled to comparable strain levels.3 Figure 10.1b shows the distribution of misorientation angles measured for all boundaries.13 A bimodal distribution is seen, with one peak located below 2° and the other located between 40° and 55°. The fraction of boundaries below 3° and that of high-angle boundaries (>15°) are listed in Table 10.4. Similar bimodal distributions have also been reported for the nanostructured pure Al produced by cold rolling3 and ECAP 14–16 and the relationship between the boundary angle distribution and the evolution of microstructure and texture during deformation to large strain has been analysed.17 Within the volume between the boundaries, the presence of individual dislocations

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10.1  (a) Transmission electron microscopy image showing a lamellar structural morphology and dislocation configurations in the nanostructured Al (JIS1100, 99.2% pure) processed by six-cycle ARB to εvM = 4.8. (b) Histogram showing the distribution of boundary misorientation angles.13 Table 10.4  Structural parameters of nanostructured commercial purity Al 1100 (99.2%) and IF steel processed by non-lubricated ARB to 6 cycles19 Material

dt(nm) dl(nm) dl /dt

Al (JIS1100) 180 IF Steel 210

600 620

3.3 3.0

θav (°) f(θ ≥ 15°) (%) t(θ < 3°) (%) ρ0(m–2) 27.3 24.2

66.3 59.8

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1.3 × 1014 6.3 × 1013

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and dislocation tangles is observed. Sample tilting in the TEM confirmed that almost all lamellae contain dislocations although the dislocation density varies from lamella to lamella. The average dislocation density was measured to be about 1.3 × 1014 m–2.18

10.2.3  Nanostructured interstitial-free (IF) steel by ARB Figure 10.2 shows the TEM microstructure and the misorientation angle distribution for an IF steel (see Table 10.2) processed by ARB at 500°C for six cycles.19 The microstructure exhibits a lamellar morphology, Fig. 10.2 (a), similar to that observed in the nanostructured Al sample (Fig. 10.1 (a) ). The presence of loose dislocations and dislocation tangles in the volume between the lamellar boundaries is also clearly seen in the micrograph. Figure 10.2 (b) illustrates a bimodal distribution of misorientation angles, resembling that obtained in

10.2  (a) Transmission electron microscopy image showing a lamellar structural morphology and dislocation configurations in the nanostructured IF steel processed by six-cycle ARB at 500°C to εvM = 4.8. (b) Histogram showing the distribution of boundary misorientation angles.19

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10.2  Continued.

the nanostructured Al (Fig. 10.1 (b) ). The average spacing between the lamellar boundaries and interconnecting boundaries and the density of loose dislocations are given in Table 10.4.

10.2.4  Nanostructured Ni by high-pressure torsion (HPT) The microstructure in a commercial purity Ni (99.5% pure, see Table 10.3) processed by HPT up to a strain of 300 has been analysed in detail by TEM.6 The TEM results were obtained from the longitudinal section parallel to the torsion axis (see Fig. 10.3) rather than from the torsion plane as investigated in previous studies.20,21 Figure 10.3 shows the microstructure at a strain of 8.7. A typical lamellar microstructure is seen, where the lamellar boundaries are nearly parallel to the torsion plane (±10°). In the volumes between the lamellar and interconnecting boundaries, dislocation clusters and individual dislocations can be observed. These types of microstructural features are maintained at higher strains up to 300, as shown in Fig. 10.4. However, with increasing strain, the lamellar boundaries sharpen and decrease their width. There is a clear tendency for the microstructural morphology to be more equiaxed at extremely high strains (see Fig. 10.4(b) ) while maintaining some directional appearance characteristic of microstructures at lower strains. In addition to the lamellar boundaries, interconnecting boundaries and loose dislocations, two new microstructural features, namely small equiaxed crystallites (Fig. 10.5(a) ) and deformation twins (Fig. 10.5(b) ), were also observed in samples deformed to strains ≥12. The equiaxed crystallites are isolated in the microstructure: they form at triple junctions and are in general surrounded by high-angle boundaries. The sizes of these equiaxed crystallites range from

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10.3  (a) A schematic drawing showing the sampling for TEM observation. (b) Transmission electron microscopy micrograph showing a typical lamellar structure formed in pure Ni deformed by HPT to εvM = 8.7. The shear direction is marked by the double arrows.6

30–130 nm. The deformation twins are in general only 10–50 nm wide and they are inclined with respect to the lamellar boundaries (Fig. 10.5 (b) ). The total volume fraction of equiaxed crystallites and deformation twins is quite low (<5%). The distributions of misorientation angles across all boundaries at von Mises strains of 100 and 300 in HPT Ni are shown in Fig. 10.6. A bimodal distribution of misorientation angles is observed even at such high strains. The fraction of high-angle boundaries is about 65–75% and the fraction of boundaries with misorientation angles less than 3° is about 10–20%. © Woodhead Publishing Limited, 2011

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10.4  A typical lamellar structure is observed at (a) εvM = 100, which evolves into a more equiaxed structure as the strain is increased to (b) εvM = 300.6

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10.5  Transmission electron microscopy observation of (a) equiaxed crystallites and (b) deformation twins (indicated by the dashed lines) in HPT Ni in the longitudinal plane at a von Mises strain of 12.6

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10.6  Histograms showing the distribution of misorientation angles across all boundaries in pure Ni samples deformed by HPT to von Mises strains of (a) 100 and (b) 300. At both strain levels, the misorientation angles show a typical bimodal distribution with one peak appearing at the lowest angles and the other at high-angles.6

10.2.5  Summary The results described above demonstrate three characteristic microstructural features for the three nanostructured metals Al, Ni and IF steel produced by monotonic straining either by ARB or HPT. (1) After processing to strains of 5 or above, a lamellar microstructure has formed and the lamellar boundary spacing has decreased to about 200 nm for ARB Al and IF steel at a strain of about 5, and to about 50 nm for HPT Ni at a strain of 300.

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(2) A bimodal distribution of misorientation angles has developed in all three metals, which is maintained even at extremely high strains in HPT Ni. The proportion of high-angle boundaries (≥15°) in the microstructure is typically 60–70%. A significant fraction (10–20%) of dislocation boundaries with misorientation angles below 3° is present in the microstructure, indicating a continuous formation of low-angle boundaries during the deformation process. (3) The presence of loose dislocations is observed in the volume between the boundaries in all three materials and the dislocation density is of the order of 1014 m–2. The microstructural characteristics and the evolution in microstructural parameters and their distribution link the present observation to a universal pattern of microstructural subdivision on a finer and finer scale with increasing strain observed for medium to high stacking-fault energy materials deforming by dislocation glide.22,23 These characteristic microstructural features in the highly strained state are distinctly different from those of recrystallised materials which in general are characterised by a rather small proportion of low-angle boundaries and a very low density of dislocations within the grains. These characteristic microstructural features of deformed nanostructured metals can be further modified by postprocess treatments such as annealing and deformation. Interestingly, unusual mechanical responses to post-process annealing and deformation have been observed in nanostructured metals, which will be demonstrated for nanostructured Al18 in the following section.

10.3 Hardening by annealing and softening by deformation The mechanical properties have been determined for a very large number of nanostructured metals and alloys,24–26 and several common and characteristic features have been observed: 1) a very high strength with a value several times higher than that observed in coarse-grained samples, 2) a small uniform elongation of typically a few percent, followed by a relatively large post-uniform elongation, and 3) an increased strain rate sensitivity of the flow stress.27,28 As an example, the stress–strain curves of a nanostructured Al produced by non-lubricated ARB for six cycles (see Fig. 10.1 for microstructure) and the coarse-grained initial material are compared in Fig. 10.7. In an attempt to improve the ductility while maintaining the high strength of the as-ARB-processed Al (Fig. 10.7), a low temperature annealing at 150°C for 30 minutes was introduced.18 The stress–strain curve of the annealed sample is curve 2 shown in Fig. 10.8. Compared with curve 1 of the as-ARB-processed sample, the yield stress in curve 2 slightly increased, and the elongation decreased markedly. This is in contrast to the expected behaviour after annealing – a decrease in strength and an increase in elongation or ductility. Similar observations of a decrease in the

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10.7  Tensile stress–strain curves of a nanostructured Al (JIS1100, 99.2% pure) processed by six-cycle ARB compared with a coarsegrained sample (undeformed).19

10.8  Engineering stress–strain curves for nanostructured Al (JIS1100, 99.2% pure) samples.19 Curve 1, processed by six-cycle ARB (as in Fig. 10.7); Curve 2, same material as 1, plus annealing at 150°C for 30 minutes; Curve 3, same material as 2, plus 15% cold rolling.

elongation and an increase in strength after low temperature annealing have also been reported in nanostructured Al produced by ECAP.29,30 Also unexpectedly, when the annealed sample is subsequently deformed 15% by cold rolling, a decrease in strength and increase in elongation from that of curve 2 was seen (curve 3 in Fig. 10.8). This unusual annealing-induced hardening and deformationinduced softening phenomenon was repeatedly produced by applying further annealing and deformation cycles to the samples.18 Recently similar effects of annealing and cold rolling were observed31 in a nanostructured Al processed by ARB to 10 cycles under well-lubricated conditions, and the phenomenon was also found32 in nanostructured bcc IF steel, as shown in Fig. 10.9. Taken all these

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10.9  Engineering stress–strain curves for nanostructured IF steel samples.19 Curve 1, processed by six-cycle ARB at 500°C; curve 2, same material as 1, plus annealing at 400°C for 30 min; curve 3, same material as 2, plus 15% cold rolling.

observations together, it can be concluded that the occurrence of annealing-induced hardening and deformation-induced softening phenomenon does not depend on the material and the technique used to produce the nanostructured metal, but on the microstructural characteristics of the nanostructured metal and the microstructural changes induced during post-process annealing and deformation. A microstructural characterisation of nanostructured Al after annealing followed by cold rolling has shown that the most significant changes in microstructural parameters are a decrease in the loose dislocation density during annealing and a reintroduction of dislocations by cold rolling.18 This indicates that the presence of a certain amount of interior dislocations in the nanostructure causes softening rather than hardening as typically observed in conventional coarse-grained materials. Based on the assumption that the closely spaced highangle boundaries act as dislocation sinks, it has been suggested that the density of mobile dislocations present in the as-processed nanostructured metals is reduced by a low temperature (recovery) annealing. As a result, a higher stress level is required to activate new dislocation sources when the annealed samples are subjected to tensile straining, a phenomenon which has been called dislocation source-limited hardening.33 When dislocations are reintroduced during the cold rolling step, the yield stress will decrease as mobile dislocation and easy dislocation sources are now available. Such a correlation between the density of dislocation sources and the strength has similarities to the behaviours of samples with nanoscale dimension,34,35 and samples which contain nanotwins.36 It is concluded that the availability of dislocation sources or the lack of such sources can significantly affect the yield stress. The operation of a source-limited hardening mechanism in the nanostructured Al may underpin the observation that the experimental yield stress is higher than the calculated one when only

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considering forest hardening from dislocations and Hall–Petch strengthening from grain boundaries.13,18 The dislocation source-limited hardening has recently been analysed in detail for high purity aluminium (99.99%) which was ARB processed and annealed,33 and it appears that this mechanism operates over the grain size range where enhanced localised shear deformation (Lüders banding) occurs. This grain size range for Al varies from the nanometre scale to a few micrometers, probably depending on the impurity levels. Due to this additional hardening, the Hall–Petch slope in this grain size range positively deviates from that typical for recrystallised microstructures with large grain sizes.

10.4 Optimisation of microstructure and mechanical properties The observation of deformation-induced softening suggests that instead of annealing, post-process deformation can be used as an approach to optimise the balance between strength and ductility of nanostructured metals.37,38 In recent studies, the effect of post-process cold rolling has been investigated for nanostructured Al39 and IF steel32 produced by ARB followed by low temperature annealing. In the following the results obtained in nanostructured IF steel are demonstrated and discussed based on detailed microstructural analysis at different rolling reductions. The ARB processed nanostructured IF steel samples (see Table 10.4) were annealed at 400°C for 30 minutes, and then the annealed samples were cold rolled to 5–50% thickness reductions. Figure 10.10 shows the stress–strain curves of samples of as-annealed (curve 1) and as-annealed followed by cold rolling

10.10  Engineering stress–strain curves for nanostructured IF steel samples. Curve 1, processed by six-cycle ARB and annealed at 400°C for 30 minutes; curves 2–6, same material as 1, plus 5, 10, 15, 30 and 50% cold rolling, respectively.

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(curves 2–6). It is seen that deformation by 5–15% cold rolling induces a clear decrease in the strength and a significant enhancement in the elongation (curves 2, 3 and 4) as compared with the annealed sample (curve 1). Remarkably, after 30% cold rolling (curve 5), the yield strength and UTS are comparable with those of the annealed sample (curve 1), but the uniform elongation and the total elongation are significantly larger than those of the annealed sample (curve 1). Further strengthening is observed after 50% cold rolling (curve 6); the sample shows a stress level higher than all the other samples over the entire plastic strain range until fracture occurs. Figure 10.11 shows the strength (a) and elongation (b) determined from the stress–strain curves as a function of the rolling reduction, which reveals that both the strength and elongation are better in the samples cold rolled by 30–50% than in the samples as-ARB processed and annealed, indicating a simultaneous improvement of strength and ductility. Figure 10.12 shows TEM observations of samples annealed at 400°C for 30 minutes (a), and afterward cold rolled to 15% (b) and to 50% (c) thickness reductions. The microstructural parameters were quantified and are shown in Table 10.5. Compared with the as-ARB sample, a slight increase in the lamellar boundary spacing (220 nm) and a decrease in the dislocation density (4.0 × 1013 m–2) were observed after annealing. In samples deformed to 15%, the lamellar boundary spacing is reduced to 180 nm and a large number of dislocations are introduced, increasing the average dislocation density to 8.0 × 1013 m–2. These dislocations are mostly present as single dislocations, whereas the extent of dislocation tangling is not pronounced. With an increase in the rolling reduction to 50%, a significant decrease in the lamellar boundary spacing and an increase in dislocation density are found. Furthermore, dislocation tangles and networks were often observed within the lamellae, indicating strong interaction between dislocations. As a result, both the density of the dislocations that is free to move when a stress is applied and the free length of dislocation segments that can act as dislocation sources decrease. Therefore, the softening effect by mobile dislocations and easy dislocation sources is reduced and a large portion of the dislocations present in such a microstructure will contribute to a dislocation forest hardening, leading to a net increase in strength and a decrease in elongation. To summarise, the results shown above for nanostructured IF steel and those reported previously for nanostructured Al39 suggest that tailoring the dislocation structure by post-process heat treatment and deformation is a promising approach for optimisation of mechanical properties of nanostructured metals.

10.5 Conclusions A precise characterisation of microstructural parameters by TEM has led to an identification of common and characteristic microstructural features, namely, narrowly spaced high-angle boundaries, a relatively high fraction of very lowangle boundaries (<3°) and a high density of loose dislocations (~1014 m2) in the

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10.11  Effect of rolling reduction on the strength (a) and ductility (b) of the ARB samples in Figure 10.10 supplemented with data on the ordinate from samples in the as-processed condition.32

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10.12  Transmission electron microscopy structures of the IF steel specimens processed under different conditions: (a) ARB + 30 minutes; (b) same material as (a), + 15% cold rolling; and (c) same material as (a), + 50% cold rolling.32

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10.12  Continued.

Table 10.5  Mechanical properties, boundary spacing and dislocation density of the ARB, annealed and cold-rolled IF steel32 Treatment

σ0.2 MPa

As-ARB 633 ARB + 400°C for 676   30 minutes ARB + 400°C for 657   30 minutes + CR15% ARB + 400°C for 869   30 minutes + CR50%

σUTS euniform% etot% MPa

dt nm

dl nm

ρ0 (m–2)

895 909

1.7 1.4

4.4 1.6

210 220

620 650

6.3 × 1013 4.0 × 1013

833

2.4

6.5

180

650

8.0 × 1013

1008

2.3

4.7

120

460

3.4 × 1014

volume between the boundaries. These microstructural characteristics and their interaction lead to a mechanical behaviour of both as-processed and annealed samples different from that observed for a conventionally refined recrystallised microstructure, where the strength is controlled by the grain size. In addition to dislocation and boundary strengthening, the dislocation source limited strengthening owing to the removal of mobile dislocations especially through a post-process annealing has to be taken into account in order to understand the high strength and mechanical behaviour of nanostructured metals. It follows that

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tailoring the dislocation microstructure by annealing or post-process deformation is important when optimising the strength and ductility combination. In addition to or in combination with ways of such microstructural manipulation other routes may be explored for example changing the impurity level or introducing fine precipitates or dispersed particles.

10.6 Acknowledgements The author gratefully acknowledges the Danish National Research Foundation for supporting the Danish–Chinese Center for Nanometals, within which part of this work was performed. The authors would like to thank Niels Hansen, Dorte Juul Jensen, Nobuhiro Tsuji, Andy Godfrey, Naoya Kamikawa, Hongwang Zhang, Grethe Winther, Wolfgang Pantleon and Brian Ralph for stimulating discussions.

10.7 References   1 Hansen N. Metall Mater Trans A 2001;32A:2917. DOI: 10.1007/s11661–001–0167-x   2 Huang X. J Mater Sci 2007;42:1577. DOI 10.1007/s10853–006–0988–5.   3 Liu Q., Huang X., Lloyd D.J., Hansen N. Acta Mater 2002;50:3789. DOI: 10.1016/ S1359–6454(02)00174-X.   4 Tsuji N., Saito Y., Lee S.H., Minamino Y. Adv Eng Mater 2003;5:338. DOI: 10.1002/ adem.200310077.   5 Huang X., Vorhauer A., Winther G., Hansen N., Pippan R., Zehetbauer M. In: Zhu Y.T., Langdon T.G., Valiev R.Z., Semiatin S.L., Shin D.H., Lowe T.C, editors. Ultrafine Grained Materials III, Warrendale PA: TMS (The Minerals, Metals & Materials Society); 2004; p.235.   6 Zhang H.W., Huang X., Hansen N. Acta Mater 2008;56:5451. DOI:10.1016/j. actamat.2008.07.040.   7 Iwahashi Y., Horita Z., Nemoto M., Langdon T.G. Acta Mater 1998;46:3317. DOI: 10.1016/S1359–6454(97)00494–1.   8 Winther G., Huang X., Godfrey A., Hansen N. Acta Mater 2004;52:4437. DOI: 10.1016/j.actamat.2004.05.050.   9 Mishin O.V., Godfrey A., Ostensson L. Metall Mater Trans A 2006;37A:489. DOI: 10.1007/s11661–006–0020–3. 10 Prangnell P.B., Bowen J.R., Apps P.J. Mater Sci Eng A 2004;375–377:178. DOI: 10.1016/j.msea.2003.10.170. 11 Li B.L., Tsuji N., Kamikawa N. Mater Sci Eng A 2006;423:331. DOI: 10.1016/j. mesa.2006.02.028. 12 Liu Q. Ultramicroscopy 1995;60:81. DOI: 10.1016/0304–3991(95)00049–7. 13 Huang X., Kamikawa N., Hansen N. Mater Sci Eng A 2008;483–484:102. DOI: 10.1016/j.msea.2006.10.173. 14 Cabibbo M., Blum W., Evangelista E., Kassner M.E., Meyers M.A. Metall Mater Trans 2008;39A:181. DOI: 10.1007/s11661–007–9350-z. 15 Dvorak J., Sklenicka V., Horita Z. Mater Trans 2008;49:15. DOI: 10.2320/matertrans. ME200719. 16 El-Danaf E.A., Soliman M.S., Almajida A.A., El-Rayes M.M. Mater Sci Eng A 2007;458:226. DOI: 10.1016/j.msea.2006.12.077.

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17 Hughes D.A., Hansen N. Acta Mater, 2000;48:2985. DOI: 10.1016/S1359– 6454(00)00027–6. 18 Huang X., Hansen N., Tsuji N. Science 2006;312:249. DOI: 10.1126/science.1124268. 19 Huang X., Kamikawa N., Tsuji N., Hansen N. ISIJ International 2008;48:1080. 20 Valiev R.Z., Ivanisenko Y.V., Rauch E.F., Baudelet B. Acta Mater 1996;44:4705. DOI: 10.1016/S1359–6454(96)00156–5. 21 Zhilyaev A.P., Nurislamova G.V., Kim K., Baró M.D., Szpunar J.A., Langdon T.G. Acta Mater 2003;51:753. DOI: 10.1016/S1359–6454(02)00466–4. 22 Hughes D.A., Hansen N. Phil Mag 2003;83:3871. DOI: 10.1080/ 14786430310001605560. 23 Lu K, Hansen N. Scripta Mater 2009;60:1033. DOI: 10.1016/j.scriptamat.2009.02.027. 24 Tsuji N., Ito Y., Saito Y., Minamino Y. Scripta Mater 2002;47:893. DOI: 10.1016/ S1359–6462(02)00282–8. 25 Koch C., Ovid’ko I., Seal S., Veprek S. Microstructural Nanocrystalline Materials – Fundamentals and Applications, Cambridge: Cambridge University Press; 2007. 26 Meyers M.A., Mishra A., Benson D.J. Prog Mater Sci 2006;51:427. DOI: 10.1016/j. pmatsci.2005.08.003. 27 May J., Hoppel H.W., Goken M. Scripta Mater 2003;53:189. DOI: 10.1016/j. scriptamat.2005.03.043. 28 Kim H.W., Kang S.B., Tsuji N., Minamino Y. Acta Mater 2005;53:1737. DOI: 10.1016/j.actamat.2004.12.022. 29 Bowen J.R., Prangnell P.B., Juul Jensen D., Hansen N. Mater Sci Eng A 2004; 387–389:235. DOI: 10.1016/j.msea.2004.01.127. 30 Yu C.Y., Kao P.W., Chang C.P. Acta Mater 2005;53:4019. DOI: 10.1016/j. actamat.2005.05.005. 31 Terada D., Houda H., TsujiN. J Mater Sci 2008;43:7331. DOI: 10.1007/s10853–008– 2809–5. 32 Kamikawa N., Huang X., Hansen N. In: Grivel J.C., Hansen N., Huang X., Juul Jensen D., Mishin O., Nielsen S.F., Pantleon W., Toftegaard H.L., Winther G., Yu T., editors. Nanostructured metals: Fundamentals to Applications, Roskilde: Risø National Laboratory for Sustainable Energy; 2009; p.205. 33 Kamikawa N., Huang X., Tsuji N., Hansen N. Acta Mater 2009;57:4198. DOI: 10.1016/j.actamat.2009.05.017. 34 Greer J.R., Oliver W.C., Nix W.D. Acta Mater 2005;53:1821. DOI: 10.1016/j. actamat.2004.12.031. 35 Shan Z.W., Mishrashra R.K., Asif S.A.S., Warren O.L., Minor A.M. Nature Mater 2008;7:115. DOI: 10.1038/nmat2085. 36 Lu L., Chen X., Huang X., Lu K. Science 2009;323:607. DOI: 10.1126/science.1167641. 37 Huang X., Kamikawa N., Hansen N. Mater Sci Eng A 2008;493:184. DOI: 10.1016/j. msea.2007.04.131. 38 Huang X. Scripta Mater 2009;60:1078. DOI: 10.1016/j.scriptamat.2009.02.018. 39 Huang X., Kamikawa N., Hansen N. J Mater Sci 2008;43:7397. DOI: 10.1007/ s10853–008–2873-x.

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11 Strengthening mechanisms in nanocrystalline metals D.G. MORRIS, National Center for Metallurgical Research (CENIM-CSIC), Spain Abstract: This chapter examines the strengthening achieved as crystalline metals have their grain sizes reduced from large values down to the nanoscale. The well-known Hall–Petch strengthening observed as grain size reduces from large values continues well into the nano-regime, with a saturation or loss of strengthening sometimes observed for grains smaller than several tens of nanometres. This so-called inverse Hall–Petch dependence is often a consequence of material imperfections. New deformation mechanisms can, however, operate for grains smaller than tens of nanometres. The importance of second-phase particles, solute additions and ordering in strengthening nanoscaled materials is discussed, as well as the strengthening achieved by twin boundaries. The strengthening mechanisms in the nanostructured materials fabricated by severe plastic deformation are also considered. Key words: strengthening in nanomaterials, Hall–Petch strengthening, grain boundaries, particle strengthening, solute hardening.

11.1 Introduction One of the most interesting features of nanocrystalline materials is the possibility of increasing their strength to very high levels, approaching even what can be regarded as the theoretical strength for crystalline materials. This chapter will examine the strengthening achieved as the grain size of crystalline metals is reduced from the macroscopic to the microscopic level (from millimetres to microns) and then further, towards the nanolevel. For materials with large grains, the build-up of stress concentrations at grain boundaries as deformation takes place in one grain, followed by the initiation of deformation in the second grain, leads to steady strengthening as grain size refines. This process, described by the well-known Hall–Petch relationship, continues to grain sizes well towards the nano-regime. In some experimental studies, such Hall– Petch strengthening continues to grains of only a few nanometres in size, while in other studies a saturation or even loss of strengthening is observed for grains smaller than some tens of nanometres. This loss of hardening has been termed the inverse Hall–Petch dependence. The origin of this loss of strengthening is examined, and seen to be often a consequence of material imperfections. As grain size falls below several tens of nanometres, however, a variety of other deformation mechanisms can operate, leading to changes in strengthening. These different deformation mechanisms are considered here, and their effect on strength discussed. 299 © Woodhead Publishing Limited, 2011

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Most of the basic studies of nanocrystalline strengthening consider single-phase, often single-element material. The role of second-phase particles in strengthening nanoscaled materials is considered, and shown to be of considerable interest, as indeed is the strengthening achieved by solute additions or by ordering of the matrix. A high density of twin boundaries, or many nanothickness twinned regions, can also lead to considerable improvements in strength, with the attractive possibility of retaining better ductility or toughness. Such more complex nanocrystalline materials have been little examined and deserve further research attention. Finally, the strengthening mechanisms operating in nanostructured materials fabricated by severe plastic deformation will be considered. Such materials contain a mixture of dislocations and tangles, low-angle boundaries, as well as the usual high-angle grain boundaries, with each contributing to the overall strength.

11.2 The deformation of polycrystals; the Hall–Petch model for strengthening; typical strength and hardness data Reducing grain size has long been seen as one of the most important ways to increase strength, with increased yield strength (σy) related to grain size (d) by the Hall–Petch equation:

σy = σ0 + k d –1/2

[11.1]

where σ0 is a friction stress and k a constant. This model for strengthening is based on the concept of strain within one grain being blocked by a grain boundary, leading to a grain-size dependent dislocation pile-up and stress concentration that induces new slip systems to operate in the second grain.1 A smaller grain size implies a proportionally smaller pile-up, with reduced stress concentrating factor, to activate the new source, considered to lie within the neighbouring grain. This dependence of strength on a reciprocal square root of grain size is well established for conventional metals and alloys, although a dependency ranging from reciprocal cube root to reciprocal two-thirds root has been reported. The extension of Hall– Petch strengthening to the nanoscale has been reviewed on several occasions.2–5 Figure 11.1 shows an example of the hardness–reciprocal square root of grain size representation for Fe, with this grain refinement generally achieved by milling powders.6–13 The data are reasonably well grouped, showing two linear regions, for coarse grain sizes (above 100 nm) and for very fine grain sizes. Clearly the Hall–Petch representation of hardening may be extended from very coarse grains to these finest grains, about 5–6 nm in size. Within the nano-regime, however, the Hall–Petch slope k is reduced from that typical of coarse-grained materials. Figure 11.2 shows the corresponding Hall–Petch representation for a wide range of Cu samples prepared by plastic straining,14,15 milling or inert gas condensation techniques,16–19 with most of the powder samples compacted to bulk material. An extremely wide range of strengthening behaviour is observed,

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11.1  Variation of hardness of milled Fe related to the reciprocal square root of the grain size, i.e. a Hall–Petch representation. Source: Graph taken from Guduru et al.,13 with source data indicated in the text.

11.2  Variation of yield stress of Cu related to the reciprocal square root of the grain size. Sources of data14–19 are indicated in the figure, which is adapted from Meyers et al.4 Note that the lines shown are simply guides for the eye, illustrating the different families of strength variation observed during various studies by different researchers.

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from a high value of Hall–Petch slope, similar to very coarse grains,14,15 a very low value of Hall–Petch slope from coarse to fine grains,16,18,20 a moderate Hall– Petch slope to some intermediate grain size followed by an absence of hardening,19,21–24 or a moderate Hall–Petch slope to an intermediate grain size but followed by notable softening for finer grains.17 Similar results have been obtained on a range of other nanocrystalline materials.25–28 As will be discussed later in this chapter (Section 11.4) the unusual saturation of strength or softening found by some researchers at very fine grain sizes can generally be related to imperfections of material processing, for example retained porosity after powder compaction, leading to somewhat lower hardness and compressive strength and especially to reduced strength or premature failure when tested in tension.18,19 The Hall–Petch model has been many times criticised for relying on pile-up dislocation configurations, which are rarely observed in deformed materials, for producing stress concentrations near grain boundaries and for considering that the fresh Frank–Read type source lies within the new grain. Li29 proposed instead that grain boundary ledges, on boundaries following deformation, acted as the sources for dislocations for propagation into the undeformed grain. This concept was subsequently modified by Ashby30,31 who proposed that geometrically necessary dislocations were created near grain boundaries where the deforming grain interior evolved to the undeforming grain boundary region. Meyers and Ashworth32 subsequently proposed a model, called the core-and-mantle model, which considered the polycrystalline material as a composite of hard grain boundary region with softer grain interior region. This model was based on the Ashby model of storage of geometrically necessary dislocations near grain boundaries, and also on the experimental observation of higher densities of stored dislocations near such boundaries and at triple points. This model was further extended by Benson et al.33 to consider the nanoscale region where grain boundaries and triple points occupy a large fraction of the total volume. The low density of dislocations in grain interiors (core) allowed relatively easy dislocation glide and low work hardening, while the grain boundary regions (mantle) required extensive dislocation cutting and cross-slip such that both strength and work hardening rate were increased. The composite material strength (σC) could be described in terms of area fractions occupied by grain interior (AG) and boundary regions (AGB ) and the strengths of these respective regions (σG and σGB ) as:

σC = AG σG + AGB σGB

[11.2]

The area fraction occupied by the hardened grain boundary region, including the triple point region, depends on the value of grain size relative to the thickness of the hardened region. Making various assumptions about the relation between thickness of the hardened region and grain size, a variation of composite strength with grain size (d) is deduced:

σC = σG + k1 (σGB – σG) d –1/2 – k2 (σGB – σG) d–1

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[11.3]



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From such ideas, we can understand that for large grain sizes (near the micron) the reciprocal square root term in equation 11.3 dominates, and the classical Hall– Petch dependence is observed. For very fine grain sizes, however, the reciprocal grain size term becomes dominant, and material strength will decrease. In an intermediate regime the apparent Hall–Petch slope will fall steadily, as strengthening evolves from classical Hall–Petch behaviour to strength saturation. Such saturation and eventual strength loss will occur at grain sizes similar in magnitude to the thickness of the grain boundary hardened region, which is presumably for grain sizes of several tens of nanometres. In summary, strengthening as grain size is reduced can reasonably well be understood on the basis of classical dislocation theories, modified to take account of the large area of grain boundaries and their associated hardened regions as grain size falls to the nanolevel. A Hall–Petch dependency of yield strength (with reciprocal square root of grain size) is understood for coarse grain sizes in terms of the importance of hardened grain boundary regions where high dislocation densities accumulate during deformation. At grain sizes somewhere below 100 nm, the area fraction occupied by hardened grain boundary regions becomes large, with the thickness of this region a high fraction of grain size, and yield stress increases at a slower rate, eventually saturating at a strength maximum before falling.

11.3 Hall–Petch breakdown; a fine grain size limit to models The Hall–Petch or Meyers–Ashworth models show that strength can be expected to increase proportionally with the reciprocal square root of grain size, and can be expected to be valid as long as the grains have sufficient space to retain the pile-up or hard-mantle/soft-core dislocation morphology. At very small grain sizes, however, there may be insufficient space to allow an array of more than 1–2 dislocations, which is hardly a pile-up, and equally there may not be space for the core and hardened morphology to be retained. Hence some fine grain size limit to the Hall–Petch type strengthening–grain size relationship may be expected. At the same time, there are many observations of very low dislocation densities found in nanocrystalline materials after plastic deformation, and deformation is observed to localise into intense shear bands.4,28,34,35 Deformation is typically associated with very low levels of work hardening, corresponding to the lack of an intense substructure forming during deformation. These observations appear inconsistent with the formation of pile-ups or intensely deformed grain-boundary regions. Such strain localisation into intense shear bands, and associated loss of work hardening capability, is already observed for grain sizes just below the micron (the transition from homogeneous to inhomogeneous deformation occurs in the 1000–100 nm grain size range), which is considerably above the grain size where the Hall–Petch relationship begins to fail, see Fig. 11.1 and 11.2. This would imply that the homogeneous–heterogeneous strain distribution has no

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direct influence on the strengthening-grain size behaviour. Trelewicz and Schuh28 disagree with this conclusion, however, since they observed homogeneous flow down to grain sizes of the order of 20 nm, just as the Hall–Petch relationship fails. The grain size where strain concentration by dislocation arrays is no longer possible has been examined on several occasions. Nieh and Wadworth36 considered the case where the elastic repulsion between the first and second dislocations of a nascent pile-up is greater than the material strength, since this implies that only single dislocations would be found in the given grain. This suggested a critical grain size (dc), below which no pile-ups could form and hence Hall–Petch strengthening no longer be possible, given by: dc = G b/{(1–ν) Hv},

[11.4]

where G is the shear modulus, b the Burgers vector, ν the Poisson’s ratio and Hv the material hardness. Scattergood and Koch37 and Koch38 developed an analogous relationship by arguing that the Hall–Petch dependence would break down when the applied flow stress is sufficiently high to bow single dislocations, by a Frank–Read or Orowan type process, and the subsequent hardening-grain size relationship would be: Hv = Hv0 + k (1/2παc).{ln(d/r0)}.d–1/2,

[11.5]

where Hv is the hardness of the material with grain size d, Hv0 the hardness of single crystal material, k the Hall–Petch slope, αc is 1/2π {ln(dcrit/r0)}, with dcrit the critical grain size where Hall–Petch dependence no longer applies, and r0 the dislocation core size. An alternative approach by Pande et al.39 analyses the stress concentration at the pile-up tip in terms of the number of dislocation and the pile-up length, and shows that the Hall–Petch relationship can be respected down to pile-ups containing only about 2–3 dislocations, at which point the stress concentration becomes insufficient. Examining these various expressions for limiting grain size36–38 leads to the conclusion that the Hall–Petch relationship can be expected to be valid down to grain sizes of about 5–10 nm for Fe, 10–20 nm for Al and Cu, 10–15 nm for the ceramic TiO2, with possibly larger values for materials such as some intermetallics with complex dislocation core structures. This conclusion is in general agreement with the data compiled in Fig. 11.1, showing that the Hall–Petch relationship is respected for Fe down to a grain size of at least 6–7 nm, but only in partial agreement with the Cu data of Fig. 11.2. In this figure, grains larger than about 20 nm generally show good grain-size hardening, while finer grains show great scatter and incompatibility of observed strength changes.

11.4 Hall–Petch breakdown: the importance of defective materials The results presented in Fig. 11.1 and 11.2 and discussed above show that the strength–grain size dependence may be described by the Hall–Petch relationship

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down to grain sizes of about 6 nm (for Fe; Fig. 11.1) or show highly variable behaviour for grains smaller than 50–100 nm (for Cu; Fig. 11.2). Classical dislocation theories suggest that such a relationship could well be valid down to grains sizes of approximately 5–20 nm. The next section will deal with other deformation mechanisms that may operate in materials with such very fine grain sizes, while the present section analyses the role of imperfections in the nanocrystalline state that appear to be responsible for the unusual and highly variable strength behaviour sometimes observed for grain sizes below about 100 nm. The term defective materials is used here to describe materials for which behaviour is dominated by processing inhomogeneities that are not, as such, intrinsic features of the nanocrystalline state. This distinction between unusual and intrinsic nanocrystalline mechanical behaviour is particularly important in view of early ideas that grain boundaries in nanocrystalline materials were somehow special40 and hence different behaviour might be possible from that expected of fine but normal material. Such early ideas suggested that grain boundaries in nanocrystalline materials had a lower atomic density than normal grain boundaries, with a more open atomic structure. Detailed studies of grain boundaries by High Resolution Electron Microscopy, however,41 confirm that the atomic structure is very similar to that of equivalent boundaries in normal polycrystalline materials, with no evidence of any special structure. Figure 11.3 shows three examples of results for Ni-base alloys where the Hall– Petch relationship is clearly not respected for grain sizes below 15 nm, 20–40 nm, and 120 nm, respectively.5,28,42–43 In many such cases where behaviour different from the Hall–Petch relationship is found for relatively large grain sizes, simultaneous changes to microstructure or chemistry can be noted with changes to grain size. Thus, in the case of the electrodeposited Ni-Fe samples, Fig. 11.3 (a), the change of grain size is associated with a considerable change in Fe content.42 Nanocrystalline materials prepared by electrodeposition, Fig. 11.3 (b),28 often show major changes of chemical composition as grain size changes, with often poorly soluble metal or metalloid elements such as C, S or W present.28,44–46 Such changes of composition, which may concentrate at grain boundary regions or be associated with changes of microstructure or texture47 can, themselves, lead to significant changes of mechanical behaviour, thus making very uncertain the analysis of grain size dependence. The final example shown in Fig. 11.3 (c)43 relates to an initially glassy Ni-P alloy, annealed to crystallise to different grain sizes. In this case there remains doubt about the possible retention of an amorphous layer between grains at grain boundaries for the finest grain sizes, and thus the true grain size dependence may be masked by other, dominating factors. Many of the variable results found with regards to strength of nanocrystalline materials, especially those showing a low Hall–Petch slope, an apparent saturation of strength as the grain size refines, or an inverse Hall–Petch slope – all illustrated in Fig. 11.2 – were obtained by the study of inert-gas condensed powders which were subsequently compacted under vacuum by warm pressing.16,22 These

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11.3  Variation of hardness with grain size for several nanocrystalline Ni-base samples, where anomalous, non-Hall–Petch dependence is observed for fine grain sizes. Sources: Data taken from (a) Cheung et al.;42 (b) Trelewicz and Schuh;28 and (c) Lu et al.43

materials are known to be highly flaw-sensitive20,22,24,48 with considerable improvement in mechanical properties as the surface state of the mechanical testing samples is improved by better surface polishing,18 or significantly higher strength when tested in compression (or by hardness) than when tested in tension.19,24,26 The role of defects remaining after processing, especially the presence of retained porosity and gaseous impurities, is highly important in reducing strength and ductility, but also elastic modulus and other properties.19,26 The retained gaseous content can be considerable, and will presumably lie at grain boundaries and cause significant changes in mechanical behaviour. As such, there is considerable doubt as to whether the observation of strengthening behaviour different from that expected from the Hall–Petch relationship (Fig. 11.2) is really due to the grain size variation, or is more likely associated with significant

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amounts of retained porosity and gases, as well as changes in the perfection of grain–grain bonding. Experiments comparing changes of strength as the nanocrystalline grain size is varied by different condensation–compaction conditions, or by annealing compacted materials, are worthy of especial attention.21,49 Annealing a given sample to coarsen grain size can lead to strengthening – that is to an inverse Hall–Petch strength–grain size relationship. On the other hand, changing the evaporation–condensation– compaction conditions to obtain material with finer grain size also leads to increased hardness. The implication of these studies is that finer grain size, for equivalent grain boundary quality, and possibly different porosity and gas content, will lead to increased hardening; annealing alone will both coarsen grains and lead to improved bonding at boundaries and hence also strengthen these materials. The important role of porosity, possibly imperfect grain boundary bonding, and retained gas content for this family of nanocrystalline materials is emphasised by noting the numerical values of such imperfections, and the progress in improving processing.7,50 Despite optimisations of processing conditions, retained gas contents of ½–1 at.% each of hydrogen and oxygen are still found, with porosity levels as high as several percent. Such optimised materials are still likely to have mechanical properties significantly affected by imperfections. At the same time, it should be remembered that early samples (e.g. in 1990) prepared by such methods, contained significantly higher levels of imperfections, and such early strength–grain size behaviours should be treated with great caution. As a final point, it should be remembered that this family of nanocrystalline materials will be expected to contain high densities of additional defects, for example stacking faults and high internal strain,51 which may contribute to additional strengthening. Also, making this field subject to further uncertainty, it should be recalled that the clean nanocrystalline materials are highly unstable,52 and may suffer changes of microstructure and grain size both during mechanical testing and during waiting periods (days, weeks) between material fabrication and testing.

11.5 Alternative deformation mechanisms at very fine grain sizes It has been shown that it is possible to extend classical dislocation theories for hardening by grain boundaries down to grain sizes of the order of 5–30 nm, and thereafter it is uncertain whether such models are valid. There are nevertheless two other possible scenarios for changes of mechanism: 1) that well-known deformation mechanisms for coarse-grained materials may be activated by especially fine grain sizes and high boundary areas, or 2) that new mechanisms may appear at these very fine grain sizes and where very high stresses are required for conventional dislocation mechanisms. These will be the two aspects covered in the present section. First, we recall classical deformation mechanisms found in

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normal polycrystalline materials that may be activated by very fine grain size, and then analyse the applicability of such mechanisms in various experimental studies. Secondly, we present several new mechanisms and again analyse their applicability to nanocrystalline materials.

11.5.1 Classical deformation mechanisms activated by fine grain sizes Deformation mechanisms often found in conventional polycrystalline metals at somewhat elevated temperatures include diffusional creep and grain boundary sliding.4,5,44 These may be activated at lower temperatures (i.e. room temperature) in materials with nanocrystalline grains since the deformation rate increases rapidly with decrease of grain size. Two diffusional creep mechanisms may be considered, namely Nabarro– Herring creep,53,54 equation 11.6, and Coble creep,55 equation 11.7. The stronger grain size dependence exhibited by Coble creep means that this mechanism is more likely at nanograin sizes.

[11.6]

[11.7]

. where ε is the creep rate under the applied stress σ in material of grain size d, Ω is the atomic volume, k the Boltzmann constant, T the absolute temperature, Dl is the lattice diffusivity, Dgb the grain boundary diffusivity and δ the grain boundary thickness. These deformation mechanisms are characterised by a creep rate that increases linearly with applied stress and with reciprocal square (Nabarro–Herring) or reciprocal cube (Coble) of grain size. Alternatively, sliding at grain boundaries may be the controlling deformation mechanism56,57 with, again, lattice diffusion (equation 11.8) or grain boundary diffusion (equation 11.9) controlling stress relaxation at triple points, leading to creep rates of:

[11.8]



[11.9]

In these equations, G is the shear modulus and b the Burgers vector, with other parameters having the same meaning as in equations 11.6 and 11.7. The creep rate now depends on the square of applied stress and again reciprocal square or

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reciprocal cube of the grain size. An examination of the dependence of creep rate on applied stress and grain size, as well as an examination of the temperature dependence of creep rate, which will vary with the activation energies for lattice diffusion (Ql) or grain boundary diffusion (Qgb), thus allows the determination of the operating deformation mechanism.

11.5.2 Analysis of deformation of inert-gas condensed compacted-powder materials Section 11.4 examined the saturation of or loss of strength observed in the inert gas condensed and compacted nanocrystalline materials at very fine grain sizes in terms of the possible importance of flaws remaining from imperfect fabrication. It is interesting to examine to what extent this strength saturation or loss may be caused by the onset of diffusional or sliding mechanisms requiring less applied stress than that expected by extrapolation of the Hall–Petch dependency. The strength saturation or fall at the finest grain sizes has been observed on several occasions, and the possible onset of diffusional creep mechanisms suggested as a cause.16,22 Chokshi et al.,17 for example, analysed the softening found in Cu and Pd at grain sizes below about 15–20 nm in terms of the Coble creep mechanism, finding qualitative agreement. A later study of the temperature dependence of hardness of nanocrystalline copper by Huang et al.,23 however, found a strong increase in hardness at low test temperatures that could not be explained by creep mechanisms. More detailed creep studies by Nieman et al.,18,20 and by Sanders et al.58 sometimes found linear creep,20 that is, a steady increase in strain with time, but the creep rate measured was several orders of magnitude lower than expected for Coble creep, even without considering possible enhanced grain boundary diffusivity due to open grain boundary structures. Other studies18,58 found that creep rates were not constant with time, as expected in diffusional creep and grain boundary sliding models, but instead decreased steadily. Creep rates dropping to much lower levels (several orders of magnitude) than expected in relation to the fastest Coble creep mechanisms have also been observed, possibly explained by grain boundaries having special orientations, or being low-angle boundaries where vacancy emission and absorption is much slower than for general boundaries. In summary, the experimental data supporting the theory that diffusional or sliding creep mechanisms operate in these nanocrystalline materials at room temperature are inconclusive and unconvincing. Creep-like timedependent deformation may indeed be observed on loading, but deformation rate may slowly decrease with time, as some exhaustion of the mechanism takes place, possibly related to the special nature of the grain boundaries and to some evolution with strain/time leading to more difficult vacancy emission or absorption.

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11.5.3 Analysing deformation of other nanocrystalline materials The results of some studies of creep-like deformation of nanocrystalline materials prepared by crystallization of metallic glasses and by electrodeposition are considered here to provide an overview picture of deformation mechanisms. Studies of crystallised Ni-P and Fe-B-Si alloys59–61 show much faster creep deformation for nanocrystalline grain sizes (27–28 nm) than for micron grain sizes. Analyses of the stress dependence and temperature dependence of creep rate appear generally consistent with the operation of Coble creep. Significant creep strain during a primary stage has been noted,61 however, suggesting that other deformation mechanisms are also taking place. Absolute values of stress and temperature dependencies are nevertheless sometimes unusual, and it is clear that the deformation mechanisms occurring are more complicated and not completely understood. Room temperature creep of electrodeposited nanocrystalline metals has been examined on several occasions,44,62–64 considering the influence of grain size, applied stress and test temperature, typically slightly above room temperature. These are usually single-phase metals (e.g. Cu, Ni) containing small amounts of impurities necessary for obtaining the nanostructure. Grain sizes are typically about 6–50 nm. Wang et al.44 examined the stress dependence of creep in nanocrystalline nickel with grain sizes of 6–40 nm, finding that the Hall–Petch relationship described strength down to grain sizes near 25–40 nm, but thereafter softening occurred. Grain boundary sliding was found for grain sizes of 20–40 nm, with dislocation creep becoming important when high stresses were applied. Much higher creep rates were found for material with 6 nm grain size, explained by diffusional creep, presumably Coble creep. The creep rate was not constant with time, however, and it again seems that the deformation processes taking place are more complicated than simply sliding or diffusional creep. Another study64 of the creep behaviour of electrodeposited Ni with grain size of 30 nm again found significant primary creep before the onset of a steady-state regime that appeared to be controlled by Coble creep. Again in this study, a transition in deformation mechanism, to dislocation creep, was found at slightly higher temperatures. Creep deformation in nanocrystalline electrodeposited Cu with grain size of 30 nm has been examined on several occasions.62,63 As observed for Ni, a significant primary creep stage was observed before a steady-state regime was established, where the creep rate varied linearly with applied stress, and the temperature sensitivity suggested a low activation energy, consistent with deformation controlled by Coble creep. More detailed investigation indicated, however, the existence of a strong internal stress (friction or back stress), only slightly lower than the applied stress. It was again suggested that the grain boundaries were imperfect sources or sinks for vacancies and many of these were low-angle or special/twin boundaries, a consequence of the electrodeposition process.

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In summary, several studies have shown that Coble creep-like behaviour, or sometimes grain boundary sliding, may occur in nanocrystalline materials – based on the weak stress dependence of creep rate and low values of activation energy. It is, however, difficult to explain all aspects of this creep-like behaviour: notably a significant primary creep stage with the subsequent creep rate falling logarithmically and perhaps never becoming truly steady-state, and the detection of very significant internal or friction stresses opposing strain accumulation. It is still not completely certain whether the deformation observed is produced by diffusional/sliding creep mechanisms, whether such deformation is modified by the special nature of the grain boundaries present in nanocrystalline materials, or whether other, new deformation mechanisms are operating.

11.5.4  New experimental analysis of mechanical behaviour Significant information for understanding deformation mechanisms in nanocrystalline materials has been obtained by analysis of deformation as a thermally activated process and the examination of parameters such as activation energy (∆G or ∆F) and activation volume (∆V). The present section examines these experimental analyses and the following section discusses the relevance for suggesting new deformation processes. . Treating deformation as a thermally activated process,3,4,65 the strain rate γ can be written as:

[11.10]

. where γ 0 is a constant, ∆G(τ*eff) the Gibbs free energy of activation of the stressdependent controlling process, k the Boltzmann constant, T the absolute temperature, ∆F the Helmholtz free energy (activation energy) and ∆V* the effective activation volume. τ*eff is the effective shear stress, with τ*eff = τappl – τµ, and τappl the applied shear stress and τµ the athermal contribution to flow stress, i.e. long-range internal stresses opposing flow. Shear stress and strain may be . . related to applied stress and strain by τ = σ/√ 3 and γ = √ 3 ε, or γ = √ 3 ε. Activation energy can be determined by studying changes in strain rate as the temperature changes for the same effective stress. Activation volume can be determined from changes in strain rate as the effective stress changes, at constant temperature. There are two ways to achieve this, by jumping the strain rate, giving:

[11.11]

where ∆V is the apparent activation volume and ∆σ the change in applied stress as . . the strain rate jumps from ε1 to ε2, or alternatively by examining stress changes during stress relaxation at constant total strain, giving:

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[11.12]

where ∆τ is the stress fall as a function of relaxation time t, and C a time constant. These two tests give an apparent activation volume which differs from the true activation volume (∆V*) as ∆V = Ω.∆V*, where Ω is a factor depending on sample hardening during the tests and the test machine elasticity. The true activation volume can be determined by repeating stress relaxation tests, but such sophisticated tests are in fact rarely carried out. Such tests have suggested that the true activation volume is smaller than the apparent activation volume by a factor of about 2 to 3.65 The important point about analysing activation energy and volume is that these parameters are good indicators of the controlling deformation mechanism. It is rare that activation energies are measured65 since achieving temperature changes without possible structural changes is difficult, but several measurements of activation volume have been reported.2,3,65–67 Diffusional mechanisms, for example Nabarro–Herring and Coble creep, are characterised by activation volumes of about the atomic volume (or b,3 where b is the Burgers vector). Similar values are presumably expected for grain boundary sliding. Dislocation movement (through a dislocation forest) in normal polycrystalline materials is characterised by activation volumes of the order of 1000 b3 (where a long dislocation segment moves forward by a few Burgers vectors to cut through a forest dislocation). Studies of activation volume in nanocrystalline materials show intermediate values for ∆V, of the order of 10–100 b,3 as illustrated in Figure 11.4, taken from

11.4  Values of activation volume measured in Cu and Ni for materials with a wide range of grain sizes, from the micron level down to the nanoscale. Source: Data taken from Dao et al.3

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Dao et al.3 This figure shows values of apparent activation volume measured in Cu and Ni as the grain size decreases from the micron level to about 20 nm. The activation volume decreases from about 1000 b,3 typical of dislocation movement through a forest, to about 10 b3 for the smallest grains. Similar values are reported for other nanocrystalline face-centred cubic (fcc) materials. Nanocrystalline body-centred cubic (bcc) metals show different behaviour since Peierls stresses play a significant role.3,4 The small values of activation volume in the nanocrystalline fcc materials, derived from the large strain rate sensitivity, and seen also in a large temperature dependence of flow stress, indicate that neither conventional dislocation segments passing through dislocation forests nor diffusional creep processes control plastic deformation in these nanocrystalline metals. Measurements of activation energy are few: Wang et al.,65 for example, determined a value of about 110 kJ/mol, corresponding to about 0.2Gb3 for nanocrystalline nickel, but it is difficult to find a clear explanation for this value.

11.5.5 Suggestions for new deformation mechanisms in nanocrystalline metals Based on the analysis of strain rate sensitivity of flow stress, but also following insight gained from molecular dynamics modelling of such deformation, as well as detailed examinations of deformation by transmission electron microscopy, a new consensus of deformation mechanisms in nanocrystalline metals, with grain size significantly below 50 nm, is emerging.3,4,65 It has been known for a long time that work hardening is low in nanocrystalline metals,5 which may be related to the very limited build-up of dislocation density and the absence of dislocation substructure during deformation. A more common observation is the nucleation of individual dislocations at grain boundaries, which then cross the grain, disappearing into the opposite grain boundary.68–71 Examination of deformed materials by transmission electron microscopy is often frustrating since few dislocations remain. The dislocations emitted may be perfect dislocations for the given lattice, or imperfect dislocations that trail stacking faults or lead to twin development. This appearance of dislocations, and their subsequent disappearance, is also consistent with studies showing broadening of diffraction peaks during, but not after, deformation.72 Other studies73 show grain rotation occurring during deformation, presumably as dislocations move also within the grain boundaries. Deformation controlled by the emission of such single dislocations is consistent with the small activation volumes determined, noting that this activation volume will be described as ∆ = β.d.b.b, where d is the grain size, b the Burgers vector, and β a factor of value 1/4–1/10 considering that the source emitting the dislocation segment is a small fraction of the grain size. Activation volume will fall as grain size reduces, to values of tens of b3 for grain sizes of 20 nm, as in Fig. 11.4. There is thus good agreement between activation volumes and the model of single

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dislocation emission.2,3,65–67,74 This same model also implies that there is a tension–compression asymmetry of flow stress in nanocrystalline materials.75 Noting that the applied flow stress must supply an energy 1/2Gb2.l, where G is the shear modulus, b the Burgers vector and l the segment length (proportional to grain size) during creation of the new dislocation segment, it is clear that energy and stress requirements can be significantly reduced when partial, Shockley dislocations are instead emitted: energy is reduced to 1/6Gb2.l. This explains the activation of imperfect dislocation sources at very fine grain sizes, leading to stacking fault or twin appearance.2,69–71,74 Such nucleation of partial dislocations will be easier in materials with low stacking fault energy (Ag, Cu) than in materials with high stacking fault energy (Al, Ni, Pd), but such deformation faults have indeed also been observed in deformed nanocrystalline Al and Ni. The appearance of such partial dislocations from the corresponding sources can be seen as a mechanism of softening, since such sources operate at stresses below that required for the equivalent perfect dislocation source. Finally, we note that molecular dynamics simulation of deformation in nanocrystalline materials76–78 is consistent with the experimental analyses in showing a transition from emission of perfect dislocations at grain boundary sources to partial dislocations at very fine grain sizes.79,80 At the same time, atomic shuffling is seen inside the grain boundaries, somewhat similar to a grain boundary sliding or accommodation process. These simulations are consistent in showing easier deformation, at lower flow stresses, for grain sizes below about 10–15 nm.81–83 Thus, mechanical property analysis, transmission electron microscope investigation, and molecular dynamics simulation are essentially consistent in seeing an evolution of deformation mechanism as grain size reduces to very fine levels. For grain sizes above 50 nm, conventional dislocation behaviour can be expected, with stress concentrations and deformation propagation from one grain to another. For grain sizes of 20–50 nm, there is a transition to single dislocation emission from grain boundaries as the controlling process. In the grain size range 10–20 nm, the dislocations emitted change from being perfect dislocations to partial ones, with stacking faults and twin faults created by deformation. Below 10 nm, the role of grain boundary dislocations, atomic shuffles, and grain rotations becomes important, with stress falling to lower levels.

11.6 Strengthening caused by second-phase particles Second-phase particles contribute to strengthening, as for conventional polycrystalline materials, where the particles are much finer than the grain size and distributed both within grains and at grain boundaries. For significant strengthening the particles must be relatively large, say 3–10 nm, and the simple discussion below considers that they are big enough not to be cut by dislocations, such that the Orowan mechanism operates. Such particles have sizes similar to the

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grain size when this is fine, and in this case it is better to consider that the material is a composite mixture of matrix grains and particles. Orowan hardening by fine particles, size φ, present in volume fraction f in a material of grain size d >> φ, can be described as:

[11.13]

where m is the Taylor factor, G the shear modulus, b the Burgers vector and λ the separation of particles on the shear plane.84 The parameter λ is related to particle size as λ = φ / √ f. Since particles tend to pin grain boundaries, for materials in quasiequilibrium after preparation by annealing (for powder consolidation, precipitation, coarsening, etc.) grain size and particle size are related, for example by the Zener relation, d = 0.66 φ/f, and hence grain size and particle separation are related:

[11.14]

As such, it is clear that Orowan strengthening models can only be used for materials containing a small volume fraction of second-phase particles, say less than 10%, and then the model applies independently of the grain size, nanoscale to microscale. Figure 11.5 shows an analysis of strengthening in copper alloys containing secondphase particles,84 where strength is related, via equation 11.13, through the Orowan mechanism. A good description of the particle strengthening, i.e. σOR proportional to {1/(λ–φ).ln(φ /2b)}, is seen down to particle sizes of about 7 nm. Figure 11.6 shows some microstructures of these deformed particle-strengthened copper materials, where particle-dislocation interaction is clear. Since particle size can be related to grain size, equation 11.14, the strengthening may be re-expressed in terms of grain

11.5  Analysis of strengthening in Cu-bcc particle materials in terms of the Orowan strengthening model, see text for details. Source: Morris and Morris.84

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11.6  Transmission electron micrographs illustrating dislocation– particle interactions in Cu-bcc particle materials of fine grain size. Source: Morris and Morris.84

size, by the Hall–Petch equation (equation 11.1, σ y = σ0 + k d –1/2) with relatively good agreement found. The numerical value of the Hall–Petch slope, k, is 0.28 MPa√ m, however, much greater than the accepted values for a Cu matrix.85,86 This analysis confirms that the major strengthening is due, in this case, to the particles present, and grain boundary strengthening is less important. A quantitative evaluation of Hall–Petch strengthening (equation 11.1) and Orowan hardening (equation 11.13), making use of the particle–grain size relation (equation 11.14) confirms that Orowan particle strengthening will dominate strengthening in Cu for particle sizes below about 20 nm and grain sizes below about 200 nm (for material with 5–10% second phase). The slower strengthening observed in Fig. 11.5 as the second-phase particles refine to very fine sizes (the near saturation in Fig. 11.5) may be due to particles shearing or to the loss of a homogeneous particle distribution with many particles trapped at the grain boundaries. Another study examined hardening in nanocrystalline FeAl alloys and related strength to grain size87,88 (Fig. 11.7), with data characterised by exactly the same

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Hall–Petch slope as Fe (Fig. 11.1). These materials also contained fine Al2O3 particles, from oxidation during powder milling and during hot consolidation to solid material. The oxide particles are very fine here, less than 3 nm (see Fig. 11.8) and dislocations propagate with little effort since, presumably, they can shear the weak particles. Oxide particle coarsening on heat treating this material leads to initial strengthening, before softening through particle and grain coarsening – this evolution is indicated by the sequence of arrows in Fig. 11.7. More significant hardening has been produced in FeAl intermetallic by the addition of 30%TiC to the material, as indicated by the high-pressure data in Fig. 11.7.89–91 These materials retained fine grain size, 20–30 nm, after high-temperature, high-pressure

11.7  Hardness of several FeAl materials related to grain size by the Hall–Petch relationship. Data points connected by arrows indicate the hardness evolution on ageing, as oxide precipitates form.88 Highest hardness is achieved after high pressure, high temperature consolidation of FeAl-TiC composites.89–91

11.8  Transmission electron micrograph illustrating dislocation–particle interactions (arrowed) in FeAl.88

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consolidation, but hardness can no longer be analysed by the Orowan model since both FeAl and TiC are of similar size and the material should be considered as a composite with mixed grains of the two phases. When second-phase particles are present in large volume proportion (>10%) or the particles have a similar or larger size than the matrix grains, it is better to analyse material and hardness as a composite, where the rule of mixtures provides a good description (hardness is an area or volume-adjusted average of the hardness of the components). He and Ma92 examined hardness in Cu-Fe composites, with an Fe content between 15 and 90%, and grain sizes of 25–45 nm for both phases, to find material hardnesses significantly greater than expected from the rule of mixtures, considering nanocrystalline Cu and nanocrystalline Fe. They concluded that the bcc–fcc interphase boundaries were much stronger than usual grain boundaries in either single phase Cu or single phase Fe. On the other hand, in studies on materials of Cu matrix and bcc second-phase additions,93,94 the hardness observed for mixtures with Cu grain sizes between 10 and 60 nm fit well to the Hall–Petch relationship with a good value for the slope, k (0.16 MPa√ m). In these cases, however, the volume fraction of bcc phase was small (5–10%) and bcc particles were somewhat larger than the Cu grain size, such that most boundaries present were standard fcc–fcc grain boundaries, and only few were bcc–fcc interphase boundaries. Guduru et al.13 also studied Fe mixed with Al2O3 and analysed hardness in terms of the rule of mixtures. This was justified since the Fe matrix grain size was about 10 nm but the Al2O3 particles about 50 nm. The experimental hardness was much greater than predicted by the rule of mixtures, see Fig. 11.9, and it was

11.9  Hardness of Fe milled with Al2O3 and with Pb, indicating that the data do not fit to the composite rule of mixtures.13 © Woodhead Publishing Limited, 2011



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argued that the much harder Al2O3 particles created a local heavily work-hardened zone in the neighbouring Fe grains due to the large number of geometrically necessary dislocations that formed there during deformation. While most attention is given to strengthening by second-phase additions, and large second-phase particles seem generally associated with poorer ductility, there is some evidence that correctly sized and distributed second-phase particles might improve ductility. Dutta et al.95 found that spherical second-phase particles of size slightly smaller than the matrix grain size, arranged on grain boundaries, might improve ductility by homogenising strain distribution during deformation. Finally, reiterating Koch,96 relatively little has been studied about the role of second-phase particles in affecting strength, toughness and ductility of nanocrystalline materials. There appears to be ample scope for improvement, and this area is one worthy of further investigation.

11.7 Strengthening caused by other factors: solute, order, twin boundaries There are few studies that explicitly examine the role of solute or order of the nanocrystalline matrix in affecting mechanical behaviour. Guduru et al.13 examined nanocrystalline Fe-Pb mixtures prepared by milling, using X-ray diffraction to confirm that the Pb had been dissolved. The disappearance, following milling, of diffraction peaks corresponding to Pb is insufficient, as such, to confirm Pb dissolution since X-ray diffraction is insensitive to the presence of small amounts of second phase present as fine particles. At the same time, however, the researchers observed a significant displacement of the matrix reflections, confirming the likely solution of up to about 5% Pb. Similar results on Pb dissolution during milling have also been observed by other researchers, see13 for details. Fig. 11.9 shows the evolution of hardness with Pb addition, with a large increase with the 5% Pb addition. Hardness would be expected to fall if the Pb were present as secondphase particles, according to the composite rule of mixtures, indicated in Fig. 11.9. Examination of expected hardening by the large Pb atoms in the Fe matrix according to the Fleischer solution-hardening model showed, however, that even greater hardening should be expected. The authors speculated that the Pb atoms were not all uniformly distributed in solution and that some Pb could be present as segregation at grain boundaries or as sub-nanometric clusters, too small to be detected by standard diffraction methods. Preparation of nanomaterials by milling techniques often leads to disordering of many intermetallics,97,98 which can modify mechanical behaviour. For nanocrystalline FeAl, subsequent annealing at 150–250°C leads to reordering87,88,98 but, as indicated in Fig. 11.7 by the arrows showing hardness evolution on annealing, there is no noticeable hardness change during this re-ordering.88 One possible explanation is that the super-partial dislocation separation is so large for many such intermetallics that it is similar to the

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nanocrystalline grain size and deformation is then accomplished by the partial dislocations that characterise the disordered matrix, somewhat analogous to the operation of partial dislocation sources (Shockley dislocations or twinning dislocations) suggested by molecular dynamics modelling. Finally, while the theoretical models (Hall–Petch/Core-and-Mantle/Molecular Dynamics) do not clearly explain the role of solution additions on hardening, the evolution from a single perfect dislocation source to a single partial dislocation or twinning dislocation source, however, is clearly eased by alloying to lower stacking fault energy. Improved strength is found also with finely spaced twins introduced by electrodeposition99 or by rapid straining, especially at low temperatures100–102 in materials with low stacking fault energy. Such twin strengthening can be found in grains of any size with the strengthening now determined by twin spacing instead of grain boundary spacing.99 A significant advantage of nanospaced twin boundaries appears to be that ductility or toughness can remain high at the same time as strengthening is achieved.101,103 Twins appear to act as barriers to dislocation slip operating in the parent grain, in much the same way as grain boundaries, requiring new slip activation in the twinned region or the parentoriented region found behind the subsequent twin boundary.104 Strengthening should then be described by the same formulation as for grain boundaries, such as the Hall–Petch approach. An alternative approach is to consider the twinned regions, which have nanoscale thickness determined by the close spacing of the pairs of bounding parent–twin interfaces, as hard regions of a composite, and then the overall material strength is given by a composite model of mixed hard and soft regions.101 The low-energy, coherent twin boundaries appear, however, to be able to spread stress concentrations much more than occurs at grain boundaries, and hence are not the sites for crack or cavity nucleation as are grain boundaries or their triple points. This ability to suffer plastic deformation and store dislocations means also that the twin-strengthened materials possess some work hardening,101,103 more than for nanoscale grainboundary-strengthened materials, which is a second reason for the improved ductility of these materials.

11.8 Strengthening mechanisms in materials with ultrafine microstructure prepared by severe plastic deformation Techniques of severe plastic deformation have been developed over the past about 20 years and shown to lead to microstructural refinement, towards the nanoscale, and to significant strengthening.105,106 Techniques such as Equal-Channel Angular Pressing (ECAP) and High-Pressure Torsion (HPT) have been used to impose strains to of the order of (true strain) and above 100 for ECAP and HPT, respectively. Submicron or nanostructures can eventually be achieved at very high

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strains in materials where recovery is slow or where multiple phase components impose strong microstructural refinement. At the relatively low strains (2–8) generally achieved by the popular ECAP technique, however, the microstructure is composed of random dislocations within dislocation cell walls or low-angle grain boundaries (LAGB), contained within a smaller density of grain boundaries, or high-angle grain boundaries (HAGB). For example, deforming Al or Cu by ECAP to strains of 1–2 produces elongated dislocation cells; deforming to strains of 4 produces more equiaxed dislocation cell/subgrains; while deforming to strains of 10 produces microstructures of scale about 100–500 nm, where 50–70% of the boundaries have misorientations above 15°, i.e. are defined as HAGB.105–107 Gubizca et al.108 obtained similar dislocation cell structures in Al and Al-Mg alloy of size about 250–75 nm, respectively, after deforming to a strain of 2–8, where a dislocation density of 2 × 1014 – 2 × 1015/m2, respectively, was measured. Similar structures are obtained in Fe and FeAl intermetallics,109,110 where dislocation cellular structures are obtained after strains below 10, and nanocrystalline structures after strains above 100 imposed by HPT. After strains of about 3, the microstructure shows many randomly arranged dislocations inside a dislocation cell structure of size 200 nm with an average misorientation of 10° and 15% of boundaries being HAGB. A histogram of the distribution of boundary misorientations in this material, FeAl rolled to a strain near 3, is illustrated in Fig. 11.10. Various explanations of strengthening during such severe plastic deformation have been proposed. Valiev et al.109 argued that strengthening was caused by the many grain boundaries, i.e. by Hall–Petch strengthening, after heavy deformation

11.10  Histogram showing distribution of boundary misorientations in Fe3Al rolled to a true strain of 3.3. Analysis by Electron Back-Scatter Diffraction in a Scanning Electron Microscope. Source: Adapted from Morris et al.110

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to a nanocrystalline state. Gubizca et al.,108 however, related strengthening (∆σρ), through the Taylor equation, to the measured dislocation density (ρloose) as:

[11.15]

where α is a factor of value about 0.3, M the Taylor factor, G the shear modulus, and b the Burgers vector. Leseur et al.111 examined milled Fe and argued that a Hall–Petch dependence of hardening, i.e. ∆H α 1/√ d, could be expected for grain size d above 1 µm, but a subgrain size dependence, i.e. ∆H α 1/d, for cells or subgrains smaller than 1 µm, i.e. about 50–1000 nm. In addition, they noted that hardening could be increased by nanosized oxide particles introduced during milling. Hansen85,86 has discussed how dislocation cell boundaries can be regarded essentially as additional dislocations, producing Taylor hardening, by converting cell boundary area and misorientation into equivalent dislocation density, ρeff. This approach seems reasonable but does not take complete account of the interaction of dislocation stress fields of closely spaced dislocations of different types, which will partially annihilate and reduce overall effectiveness as a barrier. With this approach, the strengthening from dislocation cell boundaries (LAGB) can be written:

[11.16]

with ρeff = Svθ/b = 3θ/dcb, and hence:

[11.17]

where ρeff is the effective dislocation density inside cell walls, Sv the surface area of boundaries per volume, θ the boundary misorientation, and dc the cell size. Note that equation 11.17 has the same dependency of strengthening on reciprocal square root of size as the Hall–Petch equation, with the effective Hall–Petch slope given by kcell = MαG√ (3θb). For small-cell boundary misorientations, the boundaries are much weaker than usual grain boundaries, but for misorientations reaching about 15° the value of kcell is approximately that of kH-P, justifying the common consideration that this misorientation marks the distinction between LAGB and HAGB. Based on these arguments, the strength of a moderately deformed material should be seen as the sum of matrix friction stress σ0, including any particle or solution terms, a loose dislocation term ∆σρ taking account of dislocations inside cells, a dislocation cell term ∆σcell, and a Hall–Petch term ∆σHP taking account of HAGB strengthening, thus:

[11.18]

An analysis of strengthening in heavily rolled Fe3Al as strain level increases is shown in Fig. 11.11, where the dislocation hardening term ∆σρ and the

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11.11  Analysis of hardening taking place during heavy rolling of Fe3Al. Flow stress is interpreted as the sum of the initial, undeformed strength, an increase due to dislocation hardening, and hardening by cell boundaries (LAGB) created by deformation. Source: Taken from Morris et al.110,112

cell-LAGB hardening term ∆σcell are seen to add to the initial material strength (σ0 + ∆σHP ) to provide a good description of the experimental strength.110,112 It can thus be understood that initial structural changes during deformation will cause rapid hardening as loose dislocations and dislocation cells are introduced, and only later will grain size hardening be significant as grain size is reduced significantly when LAGB (cell walls) slowly transition to HAGB (grain boundaries). Eventually, at nanoscale grain sizes, dislocation and cell hardening will be lost. A simple description of hardness as related to grain size (i.e. ∆H ∝ 1/√ d) or as related to dislocation cell size (i.e. ∆H ∝ 1/dc) will have some validity, each in its own given microstructural regime. Figure 11.12109,110,112–115 compares hardening in Fe/Fe3Al/FeAl during severe working, and shows how the 1/d dependence provides a better description of behaviour, with less data scatter, during the first stage of microstructure refinement, whilst the 1/√ d dependence is better for grain sizes smaller than approximately 100 nm. As a final comment, however, for grain sizes greater than about 50 nm, where a certain density of randomly arranged dislocation can be found (after deformation), and especially for grain sizes greater than about 100 nm, where dislocation cellular substructures are expected, the complete analysis of hardening must rely on equation 11.18, taking account of the density and misorientation of boundaries, as well as the presence of any loose dislocations.

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11.12  Analysis of hardening during cold working or milling of Fe/Fe3Al/ FeAl in terms of (a) reciprocal grain/cell size, or (b) reciprocal square root grain/cell size. Sources: Data taken from Valiev et al.;109 Fecht et al.;113 Todaka et al.;114 Zadra et al.;115 Morris et al.110,112

11.9 Conclusion and future trends There now appears to be good understanding of the reasons for strengthening by grain size refinement, and especially the evolution from Hall–Petch behaviour, dependent on local stress concentrations in one grain inducing strain in neighbouring regions, to individual dislocation nucleation and glide, and eventually partial dislocation operation. Grain boundaries can be seen as both obstacles for dislocations and as sources, but the role of grain boundary sliding or diffusion, as well as the ideas of some special structure or behaviour of the boundaries, seems to be discredited.

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Studies today concentrate on materials produced by new fabrication methods, including those prepared by severe plastic deformation and the nano-pillar class of samples, and on improving ductility or toughness at the same time as strength. The role of alloying to complex crystal structures and mixed-phase microstructures, which will surely improve both nanostructure stability as well as overall mechanical behaviour, remains poorly understood and worthy of further attention. Specific references have been made throughout this chapter to important scientific publications. This is invaluable reading for a more profound understanding of this area. For the more general reader interested in a slightly deeper overview understanding of nanostructural strengthening than that presented here, the following reviews or general reports are recommended reading. Morris5 gives a simple, now somewhat outdated overview of fabrication and mechanical behaviour of nanocrystalline metals. Meyers et al.4 present a very complete analysis of strengthening in these materials. The importance of strain rate in analysing deformation is examined in some excellent publications by Asaro and Suresh,2 Wang et al.65 and Dao et al.3 Finally, information on severe plastic deformation and its materials is reviewed by Valiev et al.105 and Valiev and Langdon.106

11.10 References   1   2   3   4   5   6   7   8   9 10 11 12 13 14 15 16 17 18 19 20 21 22

Cottrell A.H. The mechanical properties of matter. McGraw-Hill, New York. 1964. Asaro R.J., Suresh S. Acta mater 2005;53: 3369. Dao M., Lu L., Asaro R.J., De Hosson J.T.M., Ma E. Acta mater 2007;55: 4041. Meyers M.A., Mishra A., Benson D.J. Progress in mater sci 2006;51: 427. Morris D.G. Mechanical behaviour of nanostructured materials. Trans Tech Publications. Uetikon-Zurich, Switzerland, 1998. Jang J.S.C., Koch C.C. Scripta metall et mater 1990;24: 1599. Fougere G.E., Weertman J.R., Siegel R.W. Nanostructured mater 1995;5: 127. Zhu M., Fecht H-J. Nanostructured mater 1995;6: 921. Rawers J.C., Korth G. Nanostructured mater 1996;7: 25. Malow T.R., Koch C.C. Acta mater 1998;46: 6459. Munitz A., Livne Z., Rawers J.C., Adams J.S., Fields R.J. Nanostructured mater 1999;11: 159. Jia D, Ramesh KT, Ma E. Acta mater 2003;51: 3495. Guduru R.K., Scattergood R.O., Koch C.C., Murty K.L., Guruswamy S., McCarter M.K. Scripta mater 2006;54: 1879. Embury J.D., Keh A.S., Fisher R.M. Trans metall soc AIME 1966;236: 1252. Hansen N., Ralph B. Acta metall 1982;30: 411. Nieman G.W., Weertman J.R., Siegel R.W. Scripta metall 1989;23: 2013. Chokshi A.H., Rosen A., Karch J., Gleiter H. Scripta metall 1989;23: 1679. Nieman G.W., Weertman J.R., Siegel R.W. J mater res 1991;6: 1012. Sanders P.G., Eastman J.A., Weertman J.R. Acta mater 1997;45: 4019. Nieman G.W., Weertman J.R., Siegel R.W. Scripta metall et mater 1990;24: 145. Fougere G.E., Weertman J.R., Siegel R.W. Nanostructured mater 1993;3: 379. Gertsman V.Y., Hoffman M., Gleiter H., Birringer R. Acta metall et mater 1994;42: 3539.

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  63 Jia D., Ramesh K.T., Ma E., Lu L., Lu K. Scripta mater 2001;45: 613.   64 Yin W.M., Whang S.H., Mirshams R., Xiao C.H. Mater sci eng 2001;A301: 18.   65 Wang Y.M., Hamza A.V., Ma E. Acta mater 2006;54: 2715.   66 Wang Y.M., Ma E. Appl phys letts 2004;85: 2750.   67 Vehoff H., Lemaire D., Schuler K., Waschkies T., Yang B. Int J mater res 2007;98: 259.   68 Kumar K.S., Suresh S., Chisholm M.F., Horton J.A., Wang P. Acta mater 2003;51: 387.   69 Chen M., Ma E., Hemker K.J., Sheng H., Wang Y., Cheng X. Science 2003;300: 1275.   70 Liao X.Z., Zhao Y.H., Srinivasan S.G., Zhu Y.T., Valiev R.Z., Gunderov D.V. Appl phys letts 2004;84: 592.   71 Zhu Y.T., Liao X.Z., Srinivasan S.G., Zhao Y.H., Baskes M.I., Zhou F., Lavernia E.J. Appl phys letts 2004;85: 5049.   72 Budrovic Z., Van Swygenhoven H., Derlet P.M., Van Petegem S., Schmitt B. Science 2004;304: 273.   73 Shan Z., Stach E.A., Wiezorek J.M.K., Knapp J.A., Follstaedt, Mao S.X. Science 2004;305: 654.   74 Asaro R.J., Krysl P., Kad B. Phil mag letts 2003;83: 733.   75 Cheng S., Spencer J.A., Milligan W.W. Acta mater 2003;51: 4505.   76 Schiotz J., Vegge T., Di Tolla F.D., Jacobsen K.W. Phys rev 1999;B60: 11,971.   77 Van Swygenhoven H., Caro A., Farkas D. Scripta mater 2001;44: 1513.   78 Derlet P.M., Hasnaoui A., Van Swygenhoven H. Scripta mater 2003;49: 629.   79 Van Swygenhoven H., Caro A. Phys rev 1998;B58: 11,246.   80 Van Swygenhoven H., Derlet P.M., Froseth A.G. Nature materials 2004;3: 399.   81 Schiotz J., Di Tolla F.D., Jacobsen K.W. Nature 1998;391: 561.   82 Schiotz J., Jacobsen K.W. Science 2003;301: 1357.   83 Van Vliet K.J., Tsikata S., Suresh S. Appl phys letts 2003;83: 1441.   84 Morris D.G., Morris M.A. Acta metall mater 1991;39: 1763.   85 Hansen N. Scripta mater 2004;51: 801.   86 Hansen N. Adv eng mater 2005;7: 815.   87 Morris-Muñoz M.A., Dodge A., Morris D.G. Nanostructured mater 1999;11: 873.   88 Morris D.G., Gutierrez-Urrutia I., Muñoz-Morris M.A. Scripta mater 2007;57: 369.   89 Krasnowski M., Witek A., Kulik T. Intermetallics 2002;10: 371.   90 Krasnowski M., Kulik T. Intermetallics 2007;15: 201.   91 Krasnowski M., Kulik T. Intermetallics 2007;15: 1377.   92 He L., Ma E. Nanostructured mater 1996;7: 327.   93 Botcharova E., Freudenberger J., Schultz L. Acta mater 2006;54: 3333.   94 Venugopal T., Prasad Rao K., Murty B.S. Acta mater 2007;55: 4439.   95 Dutta A., De P.S., Mishra R.S., Watson T.J. Mater sci eng 2009;A513–514: 239.   96 Koch C.C. Scripta mater 2003;49: 657.   97 Benameur T., Yavari A.R. J mater res 1992;7: 2971.   98 Morris D.G., Amils X., Nogues J., Surinach S., Baro M.D., Muñoz-Morris M.A. Int J of non-equilib proc 2002;11: 379.   99 Lu L., Shen Y.F., Chen X.H., Qian L.H., Lu K. Science 2004;304: 422. 100 Li Y.S., Tao N.R., Lu K. Acta mater 2008;56: 230. 101 Zhang Y., Tao N.R., Lu K. Acta mater 2008;56: 2429. 102 Tao N.R., Lu K. J mater sci technol 2007;23: 771. 103 Qin E.W., Lu L., Tao N.R., Tan J., Lu K. Acta mater 2009;57: 6215. 104 Christian J.W., Mahajan S. Prog mater sci 1995;39: 1. 105 Valiev R.Z., Islamgaliev R.K., Alexandrov I.V. Progress in mater sci 2000;45: 103.

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106 Valiev R.Z., Langdon T.G. Progress in mater sci 2006;51: 881. 107 Cabibbo M., Evangelista E., Kassner M.E., Meyers M.A. Microstructure and strength of metals processed by severe plastic deformation. In: Zhu Y.T., Langdon T.G., Horita Z., Zehetbauer M.J., Semiatin S.L., Lowe T.C., editors. Ultrafine Grained Materials IV, TMS, Warrendale, 2006; p.237. 108 Gubicza J., Chinh N.Q., Langdon T.G., Ungar T. Microstructure and strength of metals processed by severe plastic deformation. In: Zhu Y.T., Langdon T.G., Horita Z., Zehetbauer M.J., Semiatin S.L., Lowe T.C., editors. Ultrafine Grained Materials IV, TMS, Warrendale, 2006; p.231. 109 Valiev R.Z., Ivanisenko Y.V., Rauch E.F., Baudelet B. Acta mater 1996;44: 4705. 110 Morris D.G., Gutierrez-Urrutia I., Muñoz-Morris M.A. J mater sci 2008;43: 7438. 111 Leseur D.R., Syn C.K., Sherby O.D. Mater sci eng 2007;A463: 54. 112 Morris D.G., Gutierrez-Urrutia I., Muñoz-Morris M.A., to be published. 113 Fecht H.J. Formation of Nanostructures in Metals and Composites by Mechanical Means. In: Zehetbauer M.J., Valiev R.Z., editors. Nanomaterials by Severe Plastic Deformation, Wiley-VCH, Weinheim, 2004; p.30. 114 Todaka Y., Umemoto M., Yin J., Liu Z., Tsuchiya K. Mater sci eng. 2007;A462: 264. 115 Zadra M., Casari F., Lonardelli I., Ischia G., Molinari A. Intermetallics 2007;15: 1650.

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12 Elastic and plastic deformation in nanocrystalline metals M.Y. GUTKIN, Russian Academy of Sciences, Russia Abstract: This chapter discusses theoretical models that describe structure, elastic strains and different mechanisms of strain relaxation and plastic deformation of nanocrystalline metals. Special attention is paid to structure, strained state and the pentagonal symmetry of nanoparticles, in which context the disclination models and channels of strain relaxation are reviewed. For nanocrystalline metals, various grain boundary stress sources and concentrators are examined with regard to their capacity to initiate the mechanisms of plastic deformation. Theoretical modeling of dislocation generation, deformation twinning, rotational and superplastic deformation, and athermal stress-induced grain growth is considered in detail. Key words: strained state in nanoparticles, mechanisms of plasticity in nanocrystalline metals, generation of dislocations and twins, rotational and superplastic deformation, athermal stress-induced grain growth.

12.1 Introduction Outstanding mechanical properties of nanocrystalline metals (NCMs) have attracted much attention since the end of the 1980s when first NCMs had been fabricated and studied. In particular, it became at once clear that the behavior of defects and mechanisms of plastic deformation in NCMs and conventional polycrystalline metals are rather different.1,2 However, the experimental study of defects in NCMs has met many difficulties, which determines the importance of theoretical modeling and computer simulations. This chapter reviews some analytical theoretical models that describe deformation phenomena in NCMs. Section 12.2 is devoted to elastic strains in as-fabricated NCMs. Our view is that understanding the initial strained state should be considered as the first and necessary step in modeling the deformation processes in NCMs. Moreover, the assumptions on the elastic-state characteristics of a representative NCM volume form the basis of the majority of theoretical models describing various mechanisms of plastic deformation and fracture in NCMs. That is why we pay much attention to elastic strains here. Starting from peculiarities of elastic-strain distribution and relaxation in isolated nanoparticles and their conglomerates, we then briefly consider grain boundary (GB) stress sources and concentrators in NCMs. In the stress fields of these GB sources and concentrators, various mechanisms of plastic deformation can start working, including dislocation emission from GBs, generation of deformation twins, GB migration, transformation and decay, etc. 329 © Woodhead Publishing Limited, 2011

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Theoretical models of these mechanisms are considered in Section 12.3. Then in the same section the interplay between translational and rotational modes of plastic deformation is discussed together with mechanisms that provide local changes in misorientation angles of GBs and can result in grain rotation. The theoretical models, which describe the effects of strengthening and softening of NCMs under superplastic deformation, are also reviewed there. It is demonstrated that most of the models under discussion can be analysed within a unified energy approach, where some critical values of parameters (for example, a critical value of the applied shear stress) are calculated to state the conditions necessary for the barrierless activation of the deformation mechanisms. When possible, theoretical estimates are compared with available experimental data that allows one to conclude that the model is either realistic or is not.

12.2 Elastic strains in nanocrystalline metals As-fabricated NCMs are always the subject of residual elastic strains. For example, Wunderlich et al.3 evaluated one of the first transmission electron microscopy (TEM) studies of a NCM (nc-Pd with the grain size of 4–9 nm, which was fabricated by high-pressure compaction of nanocrystallites condensed from the gas phase) and showed that many GBs have severely distorted nearboundary regions with smaller atomic density and higher level of elastic strains. In general, their sample contained about 25% of highly strained material. Similar conclusions followed from comparison of earlier experimental data from Mössbauer spectroscopy,4 positron lifetime spectroscopy,5,6 X-ray diffraction,7 EXAFS 8 and neutron diffraction.9 Later, in the middle of the 1990s, residual elastic strains were investigated in detail in NCMs obtained by severe plastic deformation.10 The general result was that the elastic strains were distributed inhomogeneously over the grains: they reached their maximum values in the vicinity of GBs and demonstrated an exponential slope at a distance of several nanometers from the GBs. To understand the origin of the residual elastic strains in NCMs, it is reasonable to start from the main features of NCM structure. Usually NCMs consist of crystalline grains (ranging from several to approximately one hundred nanometers in diameter), which are separated by GBs. The GBs meet each other at linear junctions that are called double if two GBs meet, triple if three GBs meet, etc. In their turn, the GB junctions meet each other at point nodes, which can be fourfold, fivefold, etc. Most GB junctions and their nodes are triple and fourfold, respectively. Their total volume fraction drastically increases with grain refinement and can reach up to 50% in fine-grained NCMs.1 As follows from these structural peculiarities of NCMs, there are two main reasons for their unique mechanical and physical properties: the first one is the nanoscopic grain size, and the second one is the unusually high density of GBs, GB junctions and junction nodes. Let us first consider the origin of residual elastic strains in isolated nanoparticles (or nanoclusters) and then in their conglomerates.

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12.2.1  Nanoparticles Residual elastic strains appear in isolated nanoparticles due to various reasons such as surface stress, pentagonal symmetry, presence of defects, phase transformations, etc. The physical origin of the surface stress is that the chemical bonding of atoms at the crystal surface is different from the bonding of atoms in the crystal bulk.11 Therefore, the equilibrium distance between the surface atoms differs from that between the bulk atoms, and the subsurface atomic layers occur in elastically strained state. For an isotropic spherical nanoparticle of radius R, there is a rough estimate of the average distortion of the interatomic distance a caused by surface tension that reads2,12:

[12.1]

where K is the volume compressibility coefficient and γ is the specific surface energy. For typical values of parameters K ~ 10–11 m3/J, γ ~ 1 J/m2 and R ~ 10 nm, this estimate gives approximately, 0.67·10–3, that is about one-tenth of a percent.2 It has also been noted that parameters entering equation [12.1] are size dependent.2 In particular, the surface energy of a nanoparticle depends on its radius R as13

[12.2]

where γ0 is the specific surface energy of a bulk crystal, α ≈ 1 and β ≈ α2 ≈ 1 are numerical coefficients. Thus, the surface energy γ decreases with decreasing nanoparticle radius R. It is worth noting that the surface energy of nanoparticles also decreases with increasing temperature (see, for example, Jia et al.14 and references therein). Nevertheless, equation [12.1] demonstrates the main contribution of radius R to the elastic strains caused by the surface stress in nanoparticles. The majority of isolated nanoparticles are synthesized in the single crystalline state;15 however, they also demonstrate a large variety of structures and shapes. ‘The next most common structure is probably simple twins, although there is rarely any publication of statistical data of particle populations. Of rather lower probability except for gold and silver is multiply twinned particles’ (Marks,15). Among the multiply twinned particles, fivefold-twinned nano- and microparticles have attracted much attention due to their pentagonal symmetry, which is impossible in bulk single crystalline solids (see, for example, the reviews2,15–22 and recent papers).23–26 Fivefold-twinned nanoparticles can have shapes close to regular decahedra, icosahedra or pentagonal prisms. De Wit27 and Galligan28 independently pointed out a direct relation between the structure of fivefold-twinned nanoparticles and disclinations (see also2,19,29). For illustration, de Wit27 suggested considering the undeformed body, which consists

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of five face-centered cubic (FCC) crystals oriented with the (1 ¯1 0) plane in the plane of the paper (Fig. 12.1 (a) ). Each crystal is in twin orientation with respect to the adjacent one, so that AC, AD, AE, and AF are twin boundaries. The angle between each pair of (1 1 1) and (¯1 ¯1 1) planes is 70°32' . Therefore the resulting polycrystal has a wedge BAB' with an apex angle of 7°20'. If the two sides of this wedge are brought together they will form a twin boundary, while at the same time a positive wedge disclination is created at A, where five twin boundaries terminate (Fig. 12.1 (b) ). Thus, the final configuration has no wedge-like cusp BAB' but contains a partial disclination of strength ω = 7°20', which creates inhomogeneous elastic strains and stresses in the polycrystal. In the case of decahedral nanoparticles (Fig. 12.2 (a) ) or pentagonal rods (Fig. 12.2 (b) ), there is only one such ‘star disclination’ whose line coincides with the pentagonal symmetry axis.27 In icosahedral nanoparticles, there are six such disclinations whose lines pass through twelve icosahedron vertices (Fig. 12.2 (c), see Ref. 19 for details). The idea to use the disclination concept has been very productive because it gives a straightforward way of modeling the elastic strains and stresses in fivefoldtwinned nanoparticles. For example, de Wit27 approximated the decahedral nanoparticle by a section of a cylinder containing a wedge disclination of strength ω along its axis. In this case the non-vanishing stress components (in cylindrical coordinates r, ϕ and z) read: [12.3]

12.1  De Wit’s schematics27 of partial disclination formation in the core of a fivefold twin in FCC crystals. (a) Initial undeformed state of a polycrystal consisting of five FCC crystals, each in twin orientation ¯ with respect to its neighbour; the plane of the paper is (1 1 0) and AC, AD, AE, and AF are twin boundaries. (b) A positive partial wedge disclination at A on which terminate the five twin boundaries AB, AC, AD, AE, and AF.

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12.2  Partial positive wedge disclinations of strength ω in (a) decahedral nanoparticle, (b) pentagonal rod, and (c) icosahedral nanoparticle.

where D = G/[2π(1–ν)], G is the shear modulus, ν is the Poisson ratio, and R is the cylinder radius. It is seen from equation [12.3] that the central region of the nanoparticle is compressed while its periphery is stretched. Indeed, the hydrostatic stress component σ = 1/3Trσij = 1/3 Dω (1+ν)[2ln(r/R)+1], is negative at r < 0.6R, zero at r ≈ 0.6R and positive at r > 0.6R. The stresses are singular at r = 0, which is a generic feature of solutions for defects (like cracks, dislocations, disclinations, etc.) within the classical theory of elasticity. Using an extended version of the elasticity theory (say, the strain-gradient,30,31 non-local32 or nonlinear33 theory of elasticity), one can dispense with such singularities. For example, in the framework of the strain-gradient elasticity, the hydrostatic stress component at the line of a positive wedge disclination, which is placed at the distance ~ 1 µm from a negative wedge disclination of the same strength, is estimated as30,31 σ ≈ –6Dω(1+ν), which gives σ ~ –D ~ –G/4 for ω = 7°20' ≈ 0.128 and ν = 0.3. Lazar34 has used the field theory of elastoplasticity to consider a wedge disclination in the center of a cylinder of radius R and obtained σ ≈ –1.14Dω(1+ν) at the dislocation line for R = 10/κ, where κ is the gradient coefficient, which can be estimated as ~ 10 nm–1. Then we get σ ~ –D/5 ~ –G/20 for R ~ 1 nm at the same values of ω and ν. Thus, the level of G/20 can be considered as the lower magnitude of σ in the finest nanoparticles, while G/4 as its upper magnitude in the coarse nanoparticles. Anyway, the compression in the nanoparticle center is very high. Moreover, it follows from equation [12.3] that the strain energy (per unit disclination length) is27 WDh = 1/8Dω2R2. Therefore, one can expect the activation of various mechanisms of stress relaxation when the nanoparticle radius will increase. The same results are valid for pentagonal rods, which can be modeled by long elastic cylinders containing positive wedge disclinations along their axes.2,19,29 Howie and Marks35 extended the disclination description to icosahedral nanoparticles (Fig. 12.2 (c) ). They considered:

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an elastic sphere having the same missing volume (about 12%), but spread uniformly throughout the sphere. This is equivalent to an angular average of the strains, and may be visualized as a multitude of thin radial cones, each subtending a very small solid angle dω at the centre, with small angular gaps between them in the unstrained state. The cones are now constrained by external forces to remain of the same length R while they are distorted sideways until they touch, are then ‘glued’ together. (Howie and Marks35)

This process, which replaces the discrete set of six wedge disclinations each of strength ω ≈ 7°21' by continuously distributed cone defects each of infinitely small strength dω, produces the distributed disclination which is now called Marks–Ioffe disclination.36 The Marks–Ioffe disclination is characterized by the eigenstrain εθθ * = εφφ * = 6ω/4π ≈ 0.0613 and creates the elastic stresses:35

[12.4]

where (r, θ, φ) is the spherical coordinate system with the origin in the center of the sphere. Again the central region of the nanoparticle is compressed while its periphery is stretched. The hydrostatic stress σ = 4/3Dω(1+ν)[3ln(r/R)+1] is negative at r < 0.7R, zero at r ≈ 0.7R and positive at r > 0.7R. The stress components [12.4] are singular at r = 0. The strain energy is35 WIc = 4/3Dω2(1+ν)R3. Since the strain energy of the fivefold-twinned nanoparticles drastically increases with their radii, the nanoparticle structure is unstable with respect to various transformations. This may concern the surface faceting37 and reconstruction,38 structural modification and transition to ‘normal’ single crystalline state,15,18–23 and formation of specific defect structures, which accommodate in part the initial strained state.2,15,18–25,36 In particular, Gryaznov et al.39 have theoretically considered the following relaxation channels of elastic stresses inside the pentagonal whiskers: 1) creating an edge dislocation inside the whisker, 2) opening a gap in the whisker, 3) creating a compensating negative partial wedge disclination near the whisker surface, 4) splitting the pentagonal axis (in terms of splitting the positive wedge disclination (Fig. 12.2 (a) ) into a pair of similar disclinations of the same total strength), 5) growing a single crystalline (non-pentagonal) region in the whisker center, and 6) displacing the pentagonal axis from the whisker center. The authors calculated and compared the energy changes, which are characteristic for the relaxation channels, and concluded that the principal channels are dislocation creation, displacement and splitting of the pentagonal axis. Recently Kolesnikova and Romanov have analysed the formation of a circular prismatic dislocation loop in the cross section of a pentagonal whisker40 and growth of a misfitting layer on the whisker surface41 as potential channels of stress relaxation. The latter stress relaxation channel has also been applied to icosahedral nanoparticles.36 For the case of an atomically heterogeneous pentagonal whisker, Panpurin and Gutkin42 have studied the nucleation of a

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precipitate in the shape of a finite-length cylinder coaxial to the whisker. In the approximation that the precipitate is subject of an axial positive eigenstrain ε*, they have demonstrated that nucleation and growth of the precipitate are energetically preferable if ε* is smaller than a critical value εc. If the eigenstrain is large (ε*<εc, ε*~εc) then the optimal shape of the precipitate is a thin disk, if small (ε*<<εc) then it is an elongated thin cylinder. Concluding this section, it is worth noting that fivefold twinning has been observed not only in separate nanoparticles but also in their dense conglomerates obtained by inert gas condensation and compaction43 and by severe plastic deformation.44–47 Recent theoretical scheme48 and computer simulations49–51 have demonstrated that fivefold twins can be formed by a subsequent glide of Shockley partial dislocations in a nanocrystalline FCC material under extremely high local shear stresses.

12.2.2  Grain boundary sources of elastic strains When nanoparticles compose dense conglomerates, i. e. nanocrystalline solids, the principal sources of elastic strains are defects associated with grain boundaries (GBs). It is also the case with GBs in coarse-grained polycrystalline materials, where the approach of periodic dislocation networks can be applied.52 As was shown by many authors, in NCMs, the GBs are naturally short, often wavy, stepped and curved, and contain various extrinsic defects,3,10,53–62 especially when the NCMs are produced by one of the methods of severe plastic deformation. These GBs are commonly called non-equilibrium GBs.10 The most powerful GB defects are extrinsic GB dislocations,63 GB and triple-junction disclinations.64–67 All these defects are capable of creating long-range fields of elastic strains and stresses even in the absence of external loading. Such long-range elastic fields were registered in many experiments and attributed to various GB defects (see, for example,10,59,61,68–73). Since the ensemble of GB defects in NCMs is rather irregular, their theoretical description within the periodic approach52 would be incorrect. In the framework of analytical continuum modeling, which is the subject of the present review, two main alternative approaches can be considered. The first one was suggested by Nazarov et al.74–77 who introduced some elements of disorder in modeling two-dimensional square networks of non-equilibrium GBs. The non-equilibrium GBs were modeled as GBs containing some typical self-screened configurations (edge dislocation dipoles and wedge disclination quadrupoles) of extrinsic GB dislocations75,76 and GB junction disclinations.76,77 The extrinsic GB dislocations were disordered due to the random distribution of slip lines in grains. The disorder was approximated by the uniform–random distribution, ‘which means that the probability function of dislocation positions is uniform along GBs’.76 The disorder of the GB junction disclination ensemble, which appears due to incompatibilities of the plastic deformation of neighbouring grains, concerned their strengths:

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Due to the random orientation of grains, the strengths of disclinations are also random variables. However, they are not completely independent. Indeed, a slip in each grain tends to form a disclination quadrupole with a strength ωij depending on the strain of the grain. Quadrupole strengths ωij are random variables, which can be considered as independent. The mean value of ωij is equal to zero. Then, the strength Ωij of a junction disclination is the sum of strengths of four disclinations76 . . .

appearing at the junction of four neighbouring grains. Within such a model, Nazarov et al.76 estimated the root mean square elastic strain εi, excess GB energy γex and volume expansion ∆V/V of a NCM. For nc-Ni3Al with the grain size d = 50 nm, the contribution of extrinsic GB dislocations was calculated as εi ≈ 5.8·10–3, which is in the range of experimental data εi ≈ (5. . .10)·10–3.68 The disclination contribution was estimated by εi ≈ 3·10–3. For γex and ∆V/V in Al with d = 100 nm, the dislocation and disclination contributions were estimated as γex ≈ 0.3 and 0.06 J m–2, and ∆V/V ≈ 4·10–4 and ∆V/V ≈ 0.08·10–4, respectively.76 Thus, it was shown that the dislocation contributions prevail over the disclination contributions in the NCMs under discussion. Later examples for some other NCMs showed the same proportions.77 It is worth noting, that application of this approach is limited by the case of relatively coarse-grained NCMs with rather large grain size d (≥ 50 nm) obtained by severe plastic deformation, because in relatively fine-grained NCMs with d < 50 nm, some of the assumptions used (for example, about intragranular slip, high density of extrinsic GB dislocations and GB junction disclinations, etc.) stop working. Within the second approach, they consider a representative element of the GB defect structure and neglect the effect of similar neighbouring elements, thus suggested a weak elastic interaction between them. This approach allows one to describe in detail the elastically strained state in vicinity of the chosen element and is especially effective for modeling the initial stages of plastic deformation and fracture in ‘weak sites’ of NCMs. Earlier theoretical works of this direction have been discussed in monograph,78 while some recent models and results are the subject of Section 12.3 of the present chapter.

12.2.3  Grain boundary stress concentrators Apart from various defects, which create their proper elastic fields even in the absence of external loading (see Section 12.2.2), GBs in NCMs often contain defects which serve as stress concentrators under external load, such as pile-ups of GB dislocations, second-phase particles, nanocracks and nanopores. Pile-ups of GB dislocations can be formed in the process of GB sliding, which occurs via the motion of mobile GB dislocations with the Burgers vectors parallel to the GB planes. Triple junctions of GBs are effective obstacles for the gliding GB dislocations and, therefore, act as the places where pile-ups form under an applied

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shear stress. At certain conditions, GB sliding can dominate over other mechanisms of plastic deformation in NCMs,72,78–82 in which case one can expect massive formation and subsequent transformation78 of GB dislocation pile-ups. As follows from the classical dislocation theory,83 the stress concentration in the head of a dislocation pile-up is in direct proportion with the number of the pile-up dislocations. Therefore, the GB triple junctions, where the GB dislocation pileups form, must be subject to very high shear stresses and serve as places of further plastic relaxation72,78,80,82 or crack nucleation.84–86 In pure NCMs produced by severe plastic deformation, second-phase particles often form from a small amount of substitutional solutes, which are always present in the material and surrounding atmosphere.59,87 These ultrafine particles are located along GBs and their junctions, create their proper misfit strains and also serve as concentrators of external stresses. For example, the extended TEM studies of Kozlov et al.87 and Koneva59 have revealed the presence of Cu3Sn(Sb), Cu3N, Cu3O and CuO nanoparticles in ultrafine-grained Cu, and of Ni4N, NiO and Ni2O3 nanoparticles in ultrafine-grained Ni. Elastic fields of these nanoparticles have also been demonstrated. The role of pores and cracks as external stress concentrators is well known. Their presence in as-prepared and plastically deformed NCMs is also well documented.3,43,84,88–91 This especially concerns the inert gas condensed NCMs, where the porosity is always rather high. The capacity of pores and cracks to concentrate external stresses has been used in a number of theoretical models describing the activation of various mechanisms of plastic deformation in NCMs.92–96

12.3 Plastic deformation in nanocrystalline metals In recent years, the principal features and mechanisms of plastic deformation in NCMs have been comprehensively described in a number of reviews10,97–130 and books.78,131–133 Here we give some general remarks and briefly consider some recent theoretical models illustrating a large variety of deformation processes in NCMs. Depending on the grain size d and test conditions, the following basic mechanisms of plastic deformation can be realized in NCMs (Fig. 12.3): (a) slip of lattice dislocations, (b) slip of GB dislocations, (c) mass transfer along GBs (Coble creep), (d) mass transfer along GB triple junctions, (e) migration of GBs, (f) deformation twinning, and (g) rotation of grains. Some of these mechanisms can compete with each other. Due to the grain distribution in size, different mechanisms of plasticity can dominate in different grains. In relatively large grains (d > 20–30 nm), the lattice dislocation slip usually dominates over the other mechanisms, while in relatively small grains (d < 20 nm), GB mediated mechanisms of plasticity dominate. In the next subsection we consider some theoretical models of dislocation nucleation in nanograins.

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12.3  Schematics of mechanisms of plastic deformation acting in nanocrystalline metals: (a) slip of lattice dislocations, (b) slip of grain boundary dislocations, (c) mass transfer along grain boundaries (Coble creep), (d) mass transfer along triple junctions, (e) migration of grain boundaries, (c) deformation twinning, and (g) rotation of grains.

12.3.1  Mechanisms of dislocation generation It is well known that the action of standard dislocation sources (like Frank–Read ones) is suppressed in NCMs, and GBs serve as the principal sources of lattice dislocations. However, some additional mechanisms of dislocation nucleation can also be activated under very high elastic stresses typical for NCMs under deformation. One of such possible mechanisms is the non-local homogeneous nucleation of nanoscale loops of ‘non-crystallographic’ partial dislocation, whose Burgers vector magnitude continuously grows during the nucleation process.134,135 In contrast with the standard mechanism of local homogeneous nucleation of a perfect or partial lattice dislocation with fixed Burgers vector B (Figs. 12.4 (a)–(d) ), which is characterized by a high-energy barrier,83,136 this ‘special’ mechanism represents the nucleation of a finite glide dislocation loop of size L with variable strength s (Figs. 12.4 (a), 12.4 (e)–(g) ). The latter model was motivated by experimental HREM observations of similar nonstandard atomic configurations called ‘nanodisturbances’ in Gum Metal,137 which are capable of reversibly transforming to dipoles of lattice dislocations under an applied stress.138 Homogeneous nucleation of a glide loop of ‘non-crystallographic’ partial dislocation (Figs. 12.4 (a), 12.4 (e)–(g) ) in an infinite elastically isotropic solid under the action of an external shear stress τ is accompanied by a change ∆W in the total energy of the system. For the loop having a shape of a planar square of size L and characterized by the Burgers vector s, whose magnitude lies within the interval 0 < s ≤ B, the energy change can be approximated by equation:135 , [12.5]

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12.4  Two-dimensional representation of crystal lattice transformations corresponding to (a)–(d) standard homogeneous generation and extension of a gliding square loop of perfect lattice dislocation with Burgers vector B, and (e)–(g) non-local homogeneous generation of a gliding square loop of ‘non-crystallographic’ partial dislocation with a finite size L and small Burgers vector s (0 < s ≤ B) under an external shear stress τ. When s increases and achieves the magnitude b, the latter loop is transformed into a ‘normal’ loop of partial lattice dislocation with Burgers vector b; with further increase of s, it transforms into a ‘normal’ loop of perfect lattice dislocation with Burgers vector B ≈ 2b.135

where D = G/[2π (1–ν)], G is the shear modulus, ν is the Poisson ratio, b ≈ B/2 is the magnitude of a partial lattice dislocation, x = s/b and y = L/b are the dimensionless parameters, and γ  (x) is the specific (per unit area) energy of a generalized stacking fault approximated as follows:135



[12.6]

The system of equation [12.6] describes a ‘two-humped’ dependence, which has its minimum corresponding to the specific energy γ0 of a conventional stable stacking fault, and two maximums corresponding to the energy γm of two unstable stacking faults. Similar ‘two-humped’ dependences of the energy γ on the shear s,

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which characterize generalized stacking faults in various solids, were obtained in many computer simulations.139–143 The function ∆W(x, y) was analysed for two typical NCMs, Al and Ni, with the following values of the model parameters: for Al,83,141 G = 27 GPa, ν = 0.31, b ≈ 0.143 nm, γ0 = 99 mJ/m2 and γm = 164 mJ/m2; for Ni,83,142 G = 73 GPa, ν = 0.34, b ≈ 0.125 nm, γ0 ≈ 120 mJ/m2 and γm ≈ 170 mJ/m2. With equations [12.5] and [12.6], the maps for the energy change function ∆W(x, y) were calculated.135 Three of these maps for Al at various magnitudes of the applied shear stress τ are shown in Fig. 12.5. For Ni, the energy maps are similar in their general features. In both the cases, Al and Ni, when τ is relatively small, there are two characteristic energy barriers along the axes x = s/b and y = L/b (Fig. 12.5 (a)). These barriers must be overcome in order to nucleate a dislocation loop. For Al, the saddle point ∆Ws(τ = 2GPa) ≈ 4.55 eV has approximate coordinates (s/b ≈ 0.83, L/b ≈ 22). For Ni, the saddle point ∆Ws(τ = 3GPa) ≈ 19.05 eV is located approximately at (s/b ≈ 0.72, L/b ≈ 48). These values of ∆Ws are high, and the loop can hardly nucleate. If τ is large enough (τ ≥ 3.7 GPa for Al and τ ≥ 4.4 GPa for Ni), the situation drastically changes (Fig. 12.5 (b), 12.5 (c) ). The ‘left’ energy barriers disappear and a dislocation loop can nucleate through increase of its strength s and size L without any barrier. The thick arrowed curves approximately show the barrier-less evolution of a dislocation loop in the (s/b, L/b) space or, in other terms, the (x, y) space. Let us consider in detail stages of barrier-less evolution shown in Fig. 12.5 (b), (c). When τ is comparatively small (Fig. 12.5 (b) ), the dislocation loop first grows mainly in size. The dislocation strength s is rather low (s ≤ b/20) at this stage. When the dislocation loop parameters, s and L, achieve the first critical region (x ≈ xc1, y ≈ yc1) in the map of ∆W(x, y), the loop stops extending and starts to grow in strength. The point (xc1, yc1) corresponds to disappearance of ‘left’ minima at the contours y(x). As a result, the loop of fixed size increases in strength and finally transforms into a loop of perfect lattice dislocation. When τ is comparatively large (Fig. 12.5 (c) ), the loop first grows in both size and strength (here s ≤ b/10) and also attains the first critical region. After this event, the dislocation loop increases in strength until x ≈ 1, corresponding to the Burgers vector of a partial lattice dislocation. This area of the map may be considered as the second critical region (x ≈ xc2, y ≈ yc2), where the ‘right’ minima at the contours y(x) appear. Between the above second critical region and the third critical region (x ≈ xc3, y ≈ yc3), where the ‘right’ minima at the contours y(x) disappear, evolution of the dislocation loop parameters occurs through growth of both the size and strength of the loop. When the loop parameters, s and L, cross the third critical region, the dislocation loop again practically stops extending and only increases in strength until it reaches the Burgers vector of perfect lattice dislocation. Thus, the special mechanism of homogeneous nucleation135 can effectively operate in a barrier-less way and produce loops of partial and perfect lattice dislocations in NCMs (Al, Ni) deformed at high mechanical stresses. This level of external stress can be achieved in shock-wave and indentation load regimes.

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12.5  Maps of the energy change ∆W(x, y), where x = s/b and y = L/b, for pure Al under the external shear stress (a) τ = 2 GPa, (b) 3.7 GPa, and (c) 4 GPa. The values of ∆W are given in eV. The bold dot in map (a) shows the saddle point. The thick arrowed curves in maps (b, c) approximately image the barrier-less evolution of a dislocation loop in strength and size. The insets in plots (b, c) show the enlarged maps for small s and L.

Besides, with the existence of numerous stress sources and concentrators in NCMs (see Section 12.2), local stresses can reach very high values and thereby cause the homogeneous nucleation of dislocation loops in these materials at even quasistatic load regimes. Recently, ultrahigh strain rate (>107 s–1) and pressures

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(20–70 GPa) have been achieved in experiments144 on laser-driven compression of nc-Ni with grain sizes of 30–100 nm. Postmortem TEM characterization revealed that the nanocrystalline structures survived the shock load and that the dislocation slip mechanism is essential or even dominant. In particular, the dislocation density was estimated to be around 1016 m–2 in a nc-Ni sample after compression at 40 GPa pressure on nanosecond timescales. The origin of this remarkably high dislocation density has been not identified. In the context of the theoretical results,135 the non-local homogeneous nucleation of dislocation loops appears likely to be responsible for a generation of high-density dislocation ensembles in nanocrystalline Ni (and, probably, other NCMs) under shock-wave deformation. Among the most important issues for the mechanical behavior of NCMs is their ability to suppress plastic flow localization in shear bands.145–147 This has generated interest in identifying the role of GBs and their transformations in the formation and evolution of shear bands in NCMs. In ductile NCMs with comparatively large grains with size d ≥ 30 nm, where the lattice dislocation slip is still dominant, GBs can serve as effective sources of perfect and partial lattice dislocations. In earlier theoretical models148–150 of emission of perfect lattice dislocations by high-angle GBs in fine-grained materials, the emission intensity was assumed to be controlled by movement and transformations of GB dislocations148 and disclinations.149,150 These processes are too slow to cause the formation of high-density ensembles of mobile lattice dislocations that would carry large plastic strains in shear bands. At the same time, NCMs contain lowangle GBs consisting of lattice dislocations.151 Such low-angle GBs undergo structural transformations under internal stresses in coarse-grained polycrystalline materials.63 It seems natural to expect the same in mechanically loaded NCMs, too. Below we briefly discuss some theoretical models of GB transformations under external loading. Following Bobylev et al.,152–154 consider a model low-angle tilt boundary terminated at triple junctions of GBs in a nanocrystalline sample (Fig. 12.6 (a) ). The low-angle boundary in its initial state (in the absence of mechanical load) is represented as a straight wall of periodically arranged edge dislocations with Burgers vector b and characterized by the misorientation angle θ being in the Frank relationship, sin(θ/2) = b/(2h),63 with the period h and the Burgers vector magnitude b. Also, for definiteness, the angle θ is assumed to be in compensating relations, θ +θ1+θ2 = 0 and –θ +θ'1+θ'2 = 0, with the tilt misorientation parameters, (θ1, θ2) and (θ'1, θ'2), of the GBs adjacent to the upper and bottom triple junctions, respectively. In other words, the upper and bottom edges of the finite dislocation wall in its initial state (Fig. 12.6 (a) ) completely compensate for the disclination defects A and B (shown as triangles) at the upper and bottom junctions of the adjacent GBs, respectively. The action of a shear stress τ on the edge dislocations, composing the low-angle GB, causes their displacements from the initial positions (Fig. 12.6 (b)). At a critical value τ = τc, one of the dislocations releases and starts

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12.6  Decay of a low-angle tilt boundary represented as a dislocation wall AB: (a) initial state of the wall, (b) bowing of the wall, and (c) decay of the wall.

moving far from the initial GB plane. This is immediately followed by decay of the dislocation wall as a whole (Fig. 12.6 (c) ). As a result, a group of lattice dislocations released from the decayed low-angle GB move, causing local plastic deformation and the formation of an elongated grain. Following experimental data,145,155 such elongated grains are characteristic structural elements of shear bands in nanocrystalline Fe. A similar process of decay of a low-angle boundary has been observed in molecular dynamics simulations of plastic deformation in nc-Ni,156 Al157 and Pd.158 The wall decay transforms the GB triple junctions into uncompensated double junctions A and B (Fig. 12.6 (c) ). They become stress sources of disclination type, characterized by strength ±ω = ±θ. The stress field of the disclination dipole AB causes a hampering force on the moving lattice dislocations after the decay of the GB. The critical shear stress τc was calculated within 2D dislocation dynamics.152–154 As an example, the decay of a GB composed of N = 15 dislocations and characterized by angle θ = 0.1 (≈5.7°) in nanocrystalline Fe was studied in detail.153 It was found that at τ ≤ 1.53 GPa, the dislocations made some oscillations and were finally stabilized at some equilibrium positions, which were shifted further with increasing τ (see curves 1 to 5 in Fig. 12.7 (a) ). When τ  > τc (here τc = 1.53 GPa), the central dislocation moved far away from its initial position (see curve 6 in Fig. 12.7 (a)), and the GB decayed as a whole. The analysis of stability of low-angle GBs with different parameters showed that τc grows in a roughly linear way with rising θ (see curve 1 in Fig. 12.7 (b) ). On the other hand, the dependence of τc on the number N of dislocations, and thereby the GB length d (= Nh) at a constant value of θ, is very weak. This means that very short GBs in very small grains and comparatively long GBs in large grains decay at close values of the critical stress τc, if they have the same misorientation θ. The decay of a low-angle GB results in the formation of moving lattice dislocations that elastically interact with other lattice dislocations composing

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12.7  (a) Temporal dependence of the position x of the 8th dislocation in a low-angle GB with θ = 0.1 and N = 15, for τ = 0.5, 1.0, 1.4, 1.52, 1.53 and 1.54 GPa (curves 1, 2, 3, 4, 5 and 6, respectively). (b) Dependences τc(θ) for ωl = 0°, 1°, 3°, and 5° (curves 1, 2, 3, and 4, respectively).

neighbouring low-angle GBs. This interaction is able to stimulate decays of the neighbouring low-angle GBs and avalanche-like release of new mobile lattice dislocations.153,154 The main results are demonstrated in Fig. 12.7 (b), where the curves τc(θ) are plotted for different values of the strength ωl characterizing a disclination dipole that has been formed after the decay of a neighbouring lowangle GB. As was expected, the critical shear stress τc decreases with rising ωl. The phenomenon in question is able of causing plastic flow localization (carried by lattice dislocations released by low-angle GBs) in deformed NCMs containing high-density ensembles of low-angle GBs. As shown experimentally, high-angle GBs bow (become curved)84,159 and emit partial lattice dislocations47,159–164 that can provide deformation twinning in NCMs. To account for these experiments, Bobylev et al.153 extended the above model to the case of high-angle GBs containing GB dislocations. In general, high-angle GBs contain intrinsic dislocations with small Burgers vectors associated with misorientation of such GBs. They cannot glide easily in the grain interior, in contrast to the lattice dislocations. However, high-angle GBs bow and emit partial dislocations into adjacent grains in mechanically loaded NCMs (Fig. 12.8). Bobylev et al.153 first considered the GB bowing under a shear stress τ by means of 2D dislocation dynamics that account for the additional hampering force due to an increase of the GB length. Solution of the system of dynamics equations, adapted to this case, gives new equilibrium positions of the GB dislocations and, as a corollary, an equilibrium configuration of the high-angle GB in its curved state (Fig. 12.8 (b)). Now let one of the GB dislocations located at the curved GB split into an immobile GB dislocation and a mobile Shockley dislocation that moves in the adjacent grain interior under a stress τ (Fig. 12.8 (c) ). The authors

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calculated the energetics of the dislocation emission, which was considered as a transformation of the system from its initial state with the energy W1 (Fig. 12.8 (b) ) to the final state with the energy W2 (Fig. 12.8 (c)). The dislocation emission is energetically favourable, if the energy difference ∆W = W2 – W1 – A is negative. Here A is the work spent to transfer the Shockley dislocation under the stress τ. The energy difference ∆W was analysed for the exemplary case of pure nanocrystalline Cu, when the GB is characterized by the deviation ω of the GB tilt misorientation θ from that, θ0, of a low-energy (favourable) GB in the same material.63 The favourable GB Σ = 5/(210) with165 misorientation angle θ0 = 36.87° and specific energy γ = 0.9 J·m–2 was used. It was shown that an increase in τ enhances the splitting and emission processes (Fig. 12.9 (a) ). At the same time, the dislocation emission is energetically unfavourable at low τ and is hampered with rising ω (Fig. 12.9 (b) ).

12.8  Evolution of a high-angle GB with intrisic GB dislocations: (a) initial state, (b) bowing of GB, and (c) splitting of a GB dislocation and emission of a partial Shockley dislocation. The partial dislocation has Burgers vector with the edge (be) and screw (bs) components. Its glide causes a stacking fault. The immobile GB dislocation has the Burgers vector with the edge (bgb – be) and screw (–bs) components.

12.9  The energy change ∆W via the path lp of the 5th partial dislocation in the case of high-angle GB containing N = 20 GB dislocations, for (a) ω = 3° and τ = 0.4, 0.6, 0.8, and 1.0 GPa (curves 1, 2, 3 and 4, respectively); and (b) τ = 1 GPa and ω = 3°, 5°, 7°, and 9° (curves 1, 2, 3 and 4, respectively).

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Let us discuss now the emission of partial dislocation by a GB disclination. Following Gutkin et al.,166 consider a 2D model of a NCM with positive and negative wedge GB disclinations of a mean strength ω. Let such a disclination ensemble consist of disclination dipoles with a mean arm (grain size) d, which are distant by 2R from each other, and d < R (Fig. 12.10 (a) ). In this case, one can analyse a separate GB disclination dipole as a source for generation of lattice dislocations (Fig. 12.10  (b) ). Within an energy-based approach, we calculated some critical values of the external shear stress τ which correspond to the generation of a lattice dislocation, its localization in the bulk of the grain and its absorption by the opposite GB, depending on the principal parameters of the model: d, θ, and α (see Fig. 12.10 (b) ). For example, in Fig. 12.11,166 the curves τc(θ) are shown which were calculated for the case of pure nanocrystalline Al at ω = 0.1 (≈6°), α = 10° and d = 10, 20 and 30 nm. The curves τc(θ) determine (if exist) those regions at the (θ,τ) diagram, where three typical arrangements of partial dislocations must appear in a grain: I, when partial dislocations are localized near their GB sources; II, when they are spread inside the grain; and III, when they cross the grain and are absorbed by the opposite GBs. An increase in the grain size d is accompanied with an extension of the

12.10  (a) 2D model of a NCM with positive and negative wedge GB disclinations. (b) Emission of a partial Shockley dislocation from a moving GB disclination. The positive GB disclination moves by a distance l (l = b/[2sin(ω/2)] is the spacing between the intrisic GB dislocations with the Burgers vectors (b), thus emitting a lattice dislocation. This dislocation may be either partial, with the Burgers vector having the edge (b2) and screw (b3) components, or perfect, with the Burgers vector 2b2. At the place of generation, a difference GB dislocation forms, whose Burgers vector has either the edge (b1 = b – b2) and screw (–b3) components, or only the edge component (b – 2b2), respectively. The position of the negative GB disclination sets by the initial dipole arm L ≈ d and the azimuthal angle θ. The angle α determines the orientation of the dislocation gliding plane with respect to the GB.

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12.11  Critical stress τc via the azimuthal angle θ for different values of the grain size: (a) d = 10 nm, (b) d = 20 nm, and (c) d = 30 nm.

θ ranges, where the emission of partial dislocations must occur, and drastic changes in distribution of regions I, II and III (see Gutkin et al.166 for details). It is worth noting that these characteristic types of defect arrangements were observed in molecular dynamics simulations (for example, see156,157). As follows from calculations,166 there exist two characteristic grain sizes in nanocrystalline Al: dc1 (≈ 5 nm) and dc2 (≈ 30 nm). When d ≤ dc1, the generation of partial dislocations by GBs needs smaller values of τ than that of perfect dislocations, in the full range of possible values for θ and α. When d ≥ dc2, the generation of perfect dislocations becomes more energetically preferable for any of possible θ and α. In the grains of intermediate size, dc1 < d < dc2, the generation of either partial or perfect dislocations may dominate, depending on the values of the angles θ and α. Above we have considered some 2D models. However, the lattice dislocation slip, deformation twinning and GB sliding in real NCMs are 3D processes conducted by dislocation loops (DLs). In this context, a 3D description of the deformation mechanisms in terms of DLs seems to be important. As noted in Ref.167 the effective way of interaction between different modes of plastic deformation in NCMs is the generation of new DLs at the pre–existent DLs of other types. For example, pre-existent grain boundary DLs (GBDLs) can serve as sources for perfect or partial lattice DLs (Fig. 12.12 (a), 12.12 (b) ) or GBDLs (Fig. 12.12 (c) ). The pre-existent perfect or partial lattice DL can generate either a perfect or partial lattice DL into the neighbouring grain (Fig. 12.12 (d) ) or a GBDL (Fig. 12.12 (e) ). To summarize, there are 9 variants of the DL generation at the pre-existent DLs, depending on the types (GB, perfect lattice, partial lattice) of these DLs. These variants are called the modes for the DL generation at preexistent DLs. All these modes were analysed within a 3D energy-based approach for the exemplary case of nanocrystalline Al with the grain size d ranging from 10 to 100 nm.167 The basic results are briefly as follows: 1) loops of perfect lattice dislocations operate as effective sources for GB, partial and perfect lattice DLs (in order of preference); 2) loops of partial lattice dislocations serve as

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12.12  Different modes of generation of a new gliding DL at a segment of the initial gliding DL: (a,b) a lattice DL is emitted by a GBDL, (c) a GBDL is emitted by a GBDL, (d) a lattice DL is emitted by a lattice DL, (e) a GBDL is emitted by a lattice DL. In all the cases, a new DL is generated at a GB or at a triple junction of GBs.

effective sources for GB and partial lattice DLs (in order of preference), but are not effective to generate perfect lattice DLs; 3) loops of GB dislocations can be effective sources for GBDLs, while they are not so effective for generation of partial lattice DLs; GBDLs hardly can generate perfect lattice DLs. With these results, grains in NCMs can be divided into the three basic categories: relatively large (d ≈ 30 to 100 nm), intermediate (d ≈ 10 to 30 nm) and finest (d ≈ 3 to 10 nm) grains. The lattice dislocation slip effectively operates in large grains. The most effective sources of new DLs here are loops of perfect lattice dislocations, in which case the lattice slip enhances intense GB sliding. In intermediate grains, the conventional lattice dislocation slip is severely suppressed. The most effective sources of new DLs here are loops of partial (twinning) lattice dislocations, which enhance GB sliding. In the finest grains, GB sliding dominates over the lattice dislocation slip and deformation twinning. Here GBDLs serve as effective sources of new GBDLs that cause intense GB sliding. A further development of these 3D models was conducted by Bobylev et al.168,169 with the aim to explain anomalously wide stacking faults (SFs) between partial dislocations in nanocrystalline Al. The theory of DLs was used to calculate the system energy more accurately compared to some earlier models.105,170–173 By means of an original algorithm, the authors investigated both the generation of partial dislocation semi-loops and the dependence of the SF

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width on the grain size and applied stress level. They showed that anomalously wide SFs in nanocrystalline Al are caused by high stresses but not by small grain size as was derived in the earlier models. On the other hand, it was noted168 that ‘such high stresses are possible in nanocrystalline Al because the normal dislocation activity is suppressed by the small grain size. Therefore, although the small grain size is not directly connected with anomalously wide SFs in nanocrystalline Al, it represents the primary cause of this phenomenon.’

12.3.2  Generation of deformation twins As is well known, deformation twins (DTs) do not appear in coarse-grained metals with relatively high values of SF energy γ. A typical example is Al. The situation dramatically changes in the case of nanograins. DTs in nanocrystalline Al were observed in electron microscopy experiments.159–161 To explain this phenomenon, a number of theoretical models94,105,168–179 have recently been suggested that describe anomalously wide SFs whose overlapping would create DTs in nc-Al. However, some of these models105,168–174,179 deal with only one or two SF strips and cannot directly be used in a description of the generation of thick DT lamellae observed experimentally in nc-Al,160,161 Cu,47,180,181 Ni,84,182– 187 Pd188 and Ta.189 Following the experiment, the DT lamellae have typical thickness of several nanometers and occupy regions between opposite GBs in nanograins. Sometimes DT lamellae form V-, T- and X-shaped configurations studied in detail by Zhu et al.190 Let us briefly consider some models that describe the generation of thick DT lamella at GBs in NCMs. It seems rather evident that probability of DT nucleation increases in vicinity of stress sources and concentrators. Extrinsic GB dislocations can stimulate the emission of Shockley partials (see Section 12.3.1); however, their density is not so high and their stresses are not strong enough for initiation of thick DT lamella nucleation.176 Possible alternatives are GB disclinations176,177 and cracks,94 which create strong and long-range stress fields. In the model,176 a DT lamella is nucleated under the action of an applied stress and the stress field of a dipole of GB or junction wedge disclinations (Fig. 12.13 (a)). The model176 was used to consider pure nanocrystalline Al and Cu with d ≈ 30 nm. It was shown that, if the disclination strength ω and external shear stress τ are high enough (but still realistic for these NCMs), the DT generation is characterized by the absence of any energy barrier. The critical stress τc causing the emission of the first twinning dislocation is rather low (≈0.1 GPa and ≈0.3 GPa, for Cu and Al, respectively, at ω = 0.5). As the DT thickness (equal to δ (n –1), where δ is the distance between neighbouring {111} atomic planes and n is the number of emitted Shockley partials) increases, the critical stress τc (n) of the emission of new twinning dislocations first grows, then levels off, and again grows (Fig. 12.13 (b) ). Thus, there are two stages of local hardening and an

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12.13  (a) The twinning partial dislocations are emitted from a GB segment AB in nanocrystalline sample with GB disclinations of strength ±ω. The emission occurred in the region (bounded by dashed contour) where the shear stress of the disclination dipole reaches its highest level. The combined action of the external shear stress τ and the disclination stress field causes the emission and glide of partials along the adjacent slip planes. Most of the partials reach the opposite GB at its segment A‘B’. The overlapping stacking faults (generated behind the emitted partials) form the deformation twin lamella AA‘B’B. (b) Dependence of the critical external shear stress τc on the number n of emitted partials in nanocrystalline Cu (solid curves) and Al (dashed curves), for disclination strength ω = 0.5 (curves 1, 1‘), 0.4 (2, 2‘), and 0.3 (3, 3‘).

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intermediate stage of local flow of a NCM on a scale of one nanograin. In all stages, τc depends strongly on ω; indeed, a decrease in ω results in a sharp increase in τc. When studying the dependence of the equilibrium position peq of a twinning dislocation on its ordinal number n, we found the shape of the DT front (Fig. 12.14).177 Depending on the orientation of the disclination-dipole arm, the longitudinal section of DT lamella is close to a rectangle or a blunted wedge, which agrees well with the results of aforementioned experimental observations. The estimated DT thicknesses (5.6–7.0 nm for Al and 5–6 nm for Cu)177 are also consistent with the experimental data.47,160,161 The model of DT lamella nucleation at an extrinsic GB dislocation aside of a crack tip (Fig. 12.15 (a) ) has given similar results.94 It was shown that, if the external shear stress τ and the crack length L are sufficiently large, no energy barrier exists for the nucleation of a DT. Such values of τ and L fall in the ranges typical of the NCMs under study. For example, in nc-Al with d ≈ 30 nm the critical stress τc required for the nucleation of the first twinning dislocation at L = 20d = 600 nm is approximately 0.25 GPa (Fig. 12.15 (b) ). For a micro-crack with L = 200d = 6 µm, the critical stress decreases to approximately 15 MPa. With

12.14  Dependence of the equilibrium position peq of a twinning dislocation on its ordinal number n in nanocrystalline (a, c) Al and (b, d) Cu for the disclination-dipole strength ω equal to 0.3, 0.4, and 0.5. The dipole arm is oriented (a, b) along or (c, d) normal to the grain boundary.

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12.15  (a) Generation of a deformation-twin lamella at an extrinsic grain-boundary edge dislocation in the vicinity of a mixed I and II mode crack of length L. (b)–(c) The critical external shear stress τc and the equilibrium position peq of a twinning dislocation via its ordinal number n in nc–Al, for various values of the normalized crack length: L/d = 3, 10, 20 and 200.

raising the DT thickness, the critical stress of the emission of new twinning dislocations first grows, then saturates, and again grows, as is the case with DT generation in the disclination stress field.176,177 In all the stages, the critical stress τc strongly depends on the crack length L. A decrease in L results in an increase in τc. The curves peq(n), which determine the shape of the DT lamella, also depend on L (Fig. 12.15 (c) ). Depending on L, the longitudinal section of DT lamella is close to a rectangle or a trapezoid. The DT thickness was found to vary from 3.5 to 9.4 nm in nc-Al. The lower (higher) limit corresponds to the maximum (minimum) length L of the crack under discussion and the minimum (maximum) value of the applied critical stress τc. The main conclusion is that microcracks can stimulate the nucleation of thick DT lamellae far from the crack tip. Recently Fischer et al.178 have developed a similar micromechanical model and come to the same conclusion.

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12.3.3  Rotational deformation The principal structural features of NCMs, such as nanoscale grains, high volume fraction of grain boundaries and their triple junctions, and a high density of GB defects (see Section 12.2.2), provide many opportunities for development of rotational plastic deformation.78,132 Rotational modes of plasticity include stressand strain-driven formation of misorientation bands and new boundaries, change in GB misorientation angles and grain rotation, which are the processes of local reorientation of crystalline lattice.66,78,132,191 These processes are realized through the collective behavior of lattice and/or GB dislocations that is effectively described in terms of partial disclinations.27,29,64–67,78,102,132,191–193 Experimental evidence of rotational plasticity in deformed NCMs has been demonstrated in many works.194–205 Recent direct HRTEM observations of Murayama et al.195 have approved the existence of partial wedge disclinations in severely deformed nc-Fe. Ke et al.194 observed in situ GB sliding and grain rotation near the tips of opening cracks in nc-Au films. Shan et al.196–198 and Wang et al.203 reported on evident grain rotation in nc-Ni films deformed by in situ TEM tensile straining. Similar observations were made by Sergeeva et al.199–201 in nc-Ni3Al. The authors also noted that the mechanism of cooperative grain boundary sliding, which dominates in superplastic deformation of NCMs, is associated with sliding and rotation of entire grain groups. Yagi et al.202 studied the surface morphology and the crystallographic texture of nc-Au and nc-Cu after creep deformation and concluded that grain rotation takes place along the localized grain boundary sliding during creep deformation. Wang et al.203 observed that rotation of an individual grain is accompanied by rotation and further coalescence of neighbouring grains, which resulted in grain growth. Zizak et al.204,205 irradiated nc-Ti layers at room temperature with Au ions and studied the bombardmentinduced texture changes. They registered that ‘during off-normal irradiation, the nanocrystals undergo grain alignment and rotation up to ~90° at the highest ion fluence’.204 Recent computer simulations have also manifested the rotational plastic deformation in NCMs with finest grains (average grain size from 5 to 7 nm).157,206–210 Both the molecular dynamics206 and quasicontinuum (molecular statics)207–209 methods were used to simulate the evolution of atomic structure of NCMs in nc-Au206 and nc-Al207–209 under spherical nanoindenter. Among some other mechanisms of plasticity, the authors have observed the GB sliding accompanied by grain rotation and coalescence. Shimokawa et al.157 evaluated the molecular dynamics simulation of nc-Al under tensile loading and also the fixed relative rotation of some neighbouring grains. Monk and Farkas210 used the same method for studying the deformation behavior of nc-Ni nanowires under tension. They observed grain growth accompanied by grain rotation and measured the rotation angle of a sample grain in the center of the nanowire as a function of time for different strain rates. Their ‘data show that the grain rotation speed varies

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significantly with strain rate, indicating again that it is not a time controlled thermal process and is mostly driven by the strain itself’.210 Summarizing the results of experiments and computer simulations, one can conclude that stress- and strain-driven grain rotation is a typical mechanism of plastic deformation in NCMs with finest grains, which is accompanied by GB sliding and can lead to grain coalescence. To date there are a number of theoretical models which describe the gradual change in GB misorientation angles in the course of grain rotation. The earlier models211–213 were aimed at the analyses of energetics of splitting of GB disclinations into smaller-strength GB disclinations. It was shown that the split arrangements are always more energetically preferable than the initial disclinations. However these models did not include any mechanism of disclination motion along GBs. Later it was suggested that motion of GB disclinations could be realized through emission of lattice perfect (Fig. 12.16) and partial (Fig. 12.10 (b) ) dislocations into adjacent grains.149,150,166,214,215 This

12.16  Stress-driven displacement of the wedge disclination (black triangle) with the strength +ω from its initial position (dashed triangle) by the distance l is accompanied by the emission of two lattice dislocations with Burgers vectors b1 and b2. The +ω-disclination moves along the grain boundary plane towards another disclination (white triangle) with the strength –ω. See Gutkin et al.150 for details.

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mechanism seems to be more appropriate for NCMs, which may contain only few lattice dislocations inside the grains, than the earlier proposed mechanism66,216 of GB disclination motion through absorption of lattice dislocations from adjacent grains, which is appropriate for microcrystalline metals216,217 containing a high density of lattice dislocations. The scheme that illustrated the contribution of grain rotation, which is realized through motion of GB disclination dipoles, to plastic deformation of a NCM, was presented by Ovid’ko.218 The above-mentioned theoretical models manifest interplay between the translational (glide of lattice dislocations) and rotational (motion of GB disclinations) modes of plastic deformation in NCMs. For the case where the translational mode is mainly represented by GB sliding (smallest nanograins and/or superplastic deformation), another model (Fig. 12.17) was suggested.219 Its main idea is as follows. GB sliding occurs via the glide of GB dislocations with Burgers vectors, which are parallel to the GB planes along which these dislocations glide (Fig. 12.17 (b) ). Triple junctions of GBs serve as obstacles for the GB dislocation motion. GB dislocations stopped at a triple junction are capable of being split into climbing GB dislocations (Fig. 12.17 (c) ). When this process repeatedly occurs at a triple junction, it results in the formation of two walls of GB dislocations climbing along the GBs adjacent to the triple junction. The climbing GB dislocation walls cause the rotational deformation, in which case the repeatedly occurring splitting of gliding GB dislocations at the triple junction provides the crossover from the GB sliding to the rotational deformation mode (Fig. 12.17 (c), (d) ). This process can be spread over the grain, which has to rotate on an angle as a whole (Fig. 12.17 (e) ). Thus, the stopped GB sliding can stimulate plastic rotation of the neighbouring grain. Obviously this mechanism may only be effective under the condition of intensive GB diffusion of vacancies, which must be capable of providing the necessary velocity of GB dislocation climb. Analysing this model from a thermodynamic point of view, the authors219 concluded that the transition from GB sliding to rotational deformation becomes energetically favourable when the external shear stress achieves its critical value, and this depends on the elastic properties of the NCM, the structure of its GBs, its grain size and its shape. Smaller grains require smaller critical stress to rotate. Recent progress in theoretical modeling of rotational deformation in NCMs is mainly related with elaboration of dislocation–disclination models of grain refinement of polycrystalline metals under severe plastic deformation,220–222 interplay between GB sliding and grain rotation223–225 leading to the inverse Hall–Petch relationship in the range of smallest grain sizes,223,224 and GB migration95,96,226–230 and the formation of immobile disclinations whose strengths gradually increase during deformation as a result of grain boundary sliding and diffusion,231 as special mechanisms of rotational plasticity. Some of these models220–224 have been reviewed extensively by Romanov and Kolesnikova.29 The models226–230 are considered in more detail in Section 12.3.5.

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12.17  Combined action of grain boundary sliding and rotational deformation mode. (a) Nanocrystalline specimen in a non-deformed state. (b) Grain boundary sliding occurs via motion of gliding grain boundary dislocations under shear stress action. (c) Gliding dislocations split at triple junction O of grain boundaries into climbing dislocations. (d) The splitting of gliding grain boundary dislocations repeatedly occurs causing the formation of walls of grain boundary dislocations whose climb is accompanied by crystal lattice rotation in a grain. (e) Climbing dislocations reach triple junction O´ where they converge into gliding dislocations causing further grain boundary sliding.

Alternative approaches to theoretical modeling of grain rotation in NCMs have been represented by Kim et al.232 and Yang and Yang.233 These authors consider the kinetics and size effects of GB sliding and grain rotation driven by both GB energy and external stress. Ignoring the underlying structural mechanisms of GB

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sliding and grain rotation, they operate with continuum mechanics in terms of viscous GB gliding and GB diffusion as accommodation mechanisms. Due to its relative simplicity and high effectiveness, this approach looks rather attractive and fruitful although it does not allow one to visualize the structural mechanisms of grain rotation.

12.3.4 Mechanisms of strengthening and softening under superplasticity The superplasticity of NCMs has attracted much attention in the past decade (see original papers234–241 and reviews99,101,108,118,121,122,242). It has been found that the superplasticity in these materials is reached at lower temperatures and higher strain rates, offering strong possibilities for industrial application of this effect. Moreover, it has been discovered that the strength of a material increases significantly in the course of superplastic deformation. The yield stress and the hardening effect become especially great during deformation of NCMs, with an average grain size of about 50 nm. In this case, the stress–strain curves are bell-shaped, and demonstrate the presence of well-defined long hardening and softening stages. Among the main mechanisms of plasticity operating in NCMs (see Fig. 12.3), the GB sliding (in combination with accommodation mechanisms, such as GB migration and lattice sliding near GBs) is believed to be the dominant mechanism of superplastic deformation in NCMs.101,241 Therefore, the unusual effects of NCM hardening in the initial stage of superplastic deformation and subsequent softening, as well as very high values of the yield stress, can be due to the specific features of GB sliding. These features were described in theoretical models.243–245 First, we considered a situation near an isolated triple junction of GBs along which GB dislocations glide under an external shear stress τ (Fig. 12.18). Following the models,243,244 numerous acts of transfer of GB dislocations across the triple junction results in an increase in the Burgers vector of the difference sessile dislocation in the triple junction, which increases the critical stress τc necessary for dislocation transfer across the triple junction and hence leads to local strengthening. At the same time, the accompanying local migration of GBs leads to an increase in the angle a between the GB planes (adjacent to the triple junction), which decreases τc and hence leads to local softening. The competition between the strengthening and the softening effects is capable of crucially influencing the deformation behavior of NCMs exhibiting high strainrate superplasticity. In particular, superplastic deformation regime is realized if the strengthening dominates over the softening during the first extensive stage of deformation (characterized by a plastic strain of hundreds of percent). This strengthening prevents the necking and is responsible for an increase of the flow stress that drives the movement of GB dislocations. With rising plastic strain, local GB migration arranges GB planes to be tentatively parallel to each other in some local regions of a loaded sample. As a result, local softening becomes

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12.18  Numerous acts of transfer of GB dislocations across a triple junction and accompanying local migration of GBs leads to an increase in the angle a. (a) Initial (0th) state of defect configuration; two gliding GB dislocations move towards the triple junction. (b) Sessile dislocation with the Burgers vector b is formed; triple junction is displaced by the vector b2 from its initial position. (c) Generation of two new gliding GB dislocations that move towards the triple junction. (d) New sessile dislocation is formed; the triple junction is transferred by the vector 2b2 from its initial position. (e) The nth generation of two new gliding GB dislocations that move towards the triple junction. (f) The nth sessile dislocation is formed; the triple junction is transferred by the vector nb2 from its initial position.

substantial, which causes gradual macroscopic softening inherent in the second stage of superplastic deformation of NCMs. Secondly, we expanded these models by taking into account the effect of neighbouring triple junctions and the possible accommodation of the GB defect structure via emission of lattice dislocations (Fig. 12.19).245 In the model used, perfect lattice dislocations are emitted from triple junctions when Burgers vectors of sessile triple-junction dislocations reach critical values. After the first emission of a perfect lattice dislocation, the strength of the sessile dislocation again increases gradually. When its Burgers vector reaches a new critical value, a lattice dislocation is emitted again. A detailed examination of these processes allowed us to numerically calculate the strain–stress dependence shown by the solid curve in Fig. 12.20,245 for Al with the grain size of 100 nm. The dashed line represents experimental data.239 It can be seen that the theoretical and experimental values are close to each other. The theoretical curve is serrated due to the contribution from lattice sliding to the superplastic strain. Each elementary event of lattice sliding causes a drop in the critical stress, thereby leading to local softening.

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12.19  Emission of lattice dislocations with the Burgers vector be from a sessile dislocation with the Burgers vector Bm–1 in a triple junction on the mth transfer of GB dislocations across the triple junction.

12.20  External stress σ as a function of the total plastic strain ε.

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Further theoretical investigation of defect structure evolution near triple junctions of GBs during GB sliding has been evaluated recently by Ovid’ko and Sheinerman.246 The authors have taken into account the formation of disclination dipoles near triple junctions and the partial relief of disclination stresses due to GB diffusion. As the first process increases the strain hardening, while the second one decreases it, these factors could also be used in further theoretical models of superplasticity.

12.3.5  Athermal stress-induced grain growth In recent years, particular attention has been focused on the grain growth during plastic deformation of ultrafine-grained247–253 and nanocrystalline72,203,249–269 metals and alloys at room72,203,249–269 and cryogenic253–255 temperatures. Experimental studies on ultrafine-grained pure Al247,249–252 and Cu248,253 and Al-Mg alloys250,251 and on nanocrystalline pure Al,249–252,259–261,269 Cu,253–255,267 Ni,203,256–258,267,268 Pd72 and Co-P263,264 and Ni-Fe264–266 alloys have shown that the grain growth is possible during nano-249–252,257 and micro-indentation253–255 of thin films and torsion of them under high pressure,72,256 during compression of powder,247 micropillars258 and macroscopic samples,248,265 during cold-rolling,268 and, finally, during uniaxial tension of thin films203,259–262,269 and bulk planar samples.263,264,266 For an understanding of the physical nature of this phenomenon, the following experimental facts are of importance: (i) (ii)

(iii) (iv)

(v)

(vi)

At cryogenic temperatures, grains grow more rapidly than at room temperature.254 The grain growth is the most intensive in the regions of a sample where the elastic stress and its gradient are the largest (e.g. under a nanoindenter249–252,257 or in the immediate vicinity of a microindenter,253–255 near the tip of a slowly developing crack,259,262 in the surface layer of a sample in the vicinity of a neck forming under tension,266 or near specially prepared holes under tension269). The grain growth is completely suppressed250 or reduced261,263–266 in the presence of impurities. During grain growth, not only the grain size but also the character of the grain size distribution are changed; the distribution is broadened and sometimes becomes bimodal,254,259,264 with larger submicron grains occupying up to 15% of the volume254 and fine nanograins surrounding them. The grain growth occurs at relatively low nanoindentation rates257 and during microindentation in the creep mode,253–255 at relatively high compression rates (~10–3–10–1 s–1 258 and 10–3 s–1 265), and at widely ranged tension rates (~10–5 s–1,259–261 10–3 s–1,260,263 10–5–10–2 s–1,264 10–2 s–1 266). The grain growth somewhat decreases the ultimate strength, but it significantly increases the ultimate tensile strain (up to 25% in pure nc-Al259 and up to 7.2% in the nc-Ni-Fe alloy266), which is accompanied by noticeable hardening and the formation of dislocation structures in coarse grains. In micropillars of pure nc-Ni under uniaxial compression, ultrahigh plasticity © Woodhead Publishing Limited, 2011



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(up to 200% of the true strain) was observed at a flow stress of 2.0–2.4 GPa, which was accompanied by softening (due to equiaxial grain growth) followed by hardening caused by the elongation of grown grains and the accumulation of dislocations and twins in them.258 (vii) With increasing duration of holding of a sample under indenter, the lowangle GBs were observed to increase in number, especially at cryogenic temperatures.255 In submicron-sized grains grown during severe plastic deformation, subgrains were observed, which, in turn, were filled with dislocation cells.256 The authors72,203,249–269 believe that the above results unambiguously indicate the athermic character of grain growth, which occurs under elastic stresses forming at earlier stages of plastic flow. The process of grain growth is inhomogeneous over a cross-section of the sample; indeed, the grains that are located in places of concentrated stresses and, in addition, have a favourable orientation, increase in size. When the growing grains become a few hundred nanometers in size, the plasticity mechanisms typical of low-temperature deformation of coarse-grained metals begin to operate in them. For example, in copper, dislocation glide and the formation of dislocation pile-ups were observed at room temperature, and deformation twinning at a cryogenic temperature (77 K).255 Thus, the grain growth during plastic deformation increases the plasticity of NCMs, while the flow stress remains high at low temperatures and relatively high loading rates, which is very important for practical applications.252 Recent computer simulations157,207,208,210,270–274 have shown that lowtemperature stress-induced grain growth in NCMs is athermal. Its basic mechanisms are found to be stress-induced migration of GBs and their triple junctions, GB sliding, grain rotation and coalescence (see also Section 12.3.3). In particular, all of these mechanisms were observed to operate simultaneously in model samples of nc-Al208 and Ni210 with a mean grain size of 7 and 5 nm, respectively, when nanograins rotated through GB sliding under nanoindentation208 or uniaxial tension.210 The atomic mechanisms of motion of high-angle GBs have been considered in a number of recent works.275–281 Also, stress-induced GB migration and athermal grain growth have been described theoretically with the aid of dislocation-disclination models.95,96,152–154,226–230,282 For example, Bobylev et al.152–154 have studied the dynamics and decay of a low-angle tilt boundary under an applied shear stress τ (see Section 12.3.1). It was shown that, as the stress τ increases, the tilt boundary is first bent and then shifts to a new position corresponding to the applied stress. At a certain critical stress proportional to the misorientation angle θ of the boundary, it becomes unstable and glides irreversibly. The decay of one such boundary significantly decreases the critical stress for decay of neighbouring lowangle boundaries. As a result, the chain decay of the neighbouring boundaries occurs and the grains separated by them coalesce. The static model of the escape of dislocations from an infinite straight dislocation wall developed by Li282 also © Woodhead Publishing Limited, 2011

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permits one to estimate the critical stress for boundary decay, which is proportional to θ. The stress at which an intrinsic dislocation of a low-angle boundary (with θ = 0.1 (≈ 5.7°)) breaks away from it (estimated from this model to be about 2 GPa for Fe)282 is not far greater than that obtained from dynamic calculations (1.53 GPa).152–154 The model of Li282 also gives lower values of the critical stress for the decay of a boundary in the case where a few intrinsic or extrinsic dislocations break away simultaneously from it. However, the description of the boundary decay assuming that only single dislocations move while the positions of the other dislocations remain unchanged seems incorrect. Gutkin and Ovid’ko226 proposed a continuum disclination model for describing the migration of an arbitrary tilt GB. A migrating GB was approximated by a biaxial dipole of partial wedge disclinations capable of moving under an applied shear stress τ in the elastic field of a similar disclination dipole of opposite sign that forms when the GB breaks away from the neighbouring GBs (i.e. at the moment when triple GB junctions transform into double junctions) (Fig. 12.21). It was shown that there are two modes of GB migration. When the applied stress reaches the first critical value:

[12.7]

where D = G/[2π (1–ν)], G is the shear modulus, ν is the Poisson ratio, ω is the disclination strength equal to the misorientation angle of the migrating GB, 2a is the length of the GB and b is the interatomic distance, the GB begins to migrate in the stable mode in which its equilibrium position is determined by a stress level τ ≥ τc1. When the stress τ reaches the second critical value: ,

[12.8]

the GB migration becomes unstable; the equilibrium position of the GB disappears, and the GB migration no longer depends on τ. For pure nc-Al with grain size d ranging from 30 to 100 nm, the stress τc1 ranges from 7.6 to 23.5 MPa for ω = 5° and from 46.5 to 144 MPa for ω = 30°. The stress τc2 proves to be far greater, namely, 0.4 GPa for ω = 5° and 2.5 GPa for ω = 30°, irrespective of the grain size. We note that, in thin nc-Al films under tension, grains begin to grow intensively over the range of true tensile stresses from 130 MPa for d ≈ 90 nm to 190 MPa for d ≈ 40 nm,259,260 which correspond to the maximum values of τ from 65 to 95 MPa lying in the range τ1c < τ < τc2 for GBs with a misorientation angle ω = 5° and in a part of this range for GBs with ω = 30°. Computer simulations of nanoindentation of nc-Al films with a mean grain size of 7 nm showed208 that the migration of a low-angle tilt boundary with a misorientation angle of 13.5° becomes unstable under local shear stresses exceeding the estimated value 0.7 GPa obtained from equation [12.8]. Recently the model226 has been extended to the case of collective migration of the two opposite boundaries of a grain.227,228 We have considered the stress-induced

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12.21  Stress-induced migration of a low-angle (a,b) or high-angle (c,d) grain boundary (GB3) as a mechanism of rotational deformation realized through the glide of a wall of lattice dislocations (b) or motion of a dipole of wedge disclinations (d), respectively.

grain growth in a model nc-sample under a tensile stress σ (Fig. 12.22) and analysed in detail the situation with one pair of interacting GBs (Fig. 12.23). We have shown that two critical stresses, τc and τm, control the behavior of migrating GBs. When the external shear stress τ reaches τc, opposite GBs start to migrate to each other, their migration is stable, and their equilibrium positions are determined by τ ≥ τc. When τ ≥ τm >> τc, the GBs meet. Then the following regimes of cooperative migration are possible at τ > τm, depending on τ level and GB characteristics: 1) GBs annihilate in the very partial case where their misorientations are equal by magnitude and opposite in sign, 2) one GB captures another GB and makes it migrate together in one direction under a moderate τ, 3) GBs coalesce and stand at a local equilibrium position, 4) GBs can overcome their mutual attraction and migrate in opposite directions under a very high τ. In all cases, GB migration leads to unstable growth of a grain by annexing parts of its neighbours.

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12.22  Grain growth through collective GB migration in a model NCM under uniaxial tension: (a) the initial state of tilt boundaries with misorientation angles ω and Ω at a low tensile stress σ1; (b) at a stress σ2 > σ1, the boundaries begin to migrate into grains I–IV and partial wedge disclinations with strengths ±ω and ±Ω appear in the remaining double junctions and form dipole and quadrupole structures; (c) at a higher stress σ3 > σ2, some boundaries annihilate partially (grain I) or completely (grain II), while others pass through each other and stop only near the next boundaries (grains III, IV); (d) smoothing of the boundaries of the enlarged grains I–IV at a stress σ4 ≥ σ3.

The model226 has also been extended to the cases of GB migration and grain nucleation near cracks.95,96,229 It was shown that these processes result in moderate enhancement of fracture toughness96 and in an increase in the equilibrium lengths of the cracks, thus diminishing the probability of their development.229 On the other hand, the stress concentration provided by cracks leads to a decrease in the critical stresses τc1 and τc2.95 Bobylev and Ovid’ko230 have considered GB migration in hexagonal grains and found that, depending on the angle between the mobile and immobile GBs, © Woodhead Publishing Limited, 2011



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12.23  Collective migration of (a, b) low-angle and (c, d) high-angle tilt boundaries separating grains G1–G3 under applied shear stress τ: (a, d) geometrical models and (b, c) dislocation and disclination models, respectively.

GBs migrate more easily (at a lower stress level) compared to the previously examined situation226 with rectangular grains. The difference in the stress may reach a value of ~20 to 30%. The authors230 have concluded that ‘geometry of triple junctions crucially influences their mobility and thereby controls the stress level needed to drive migration of GBs and their triple junctions in deformed nanocrystalline materials’.

12.4 Conclusions and future trends We have considered some analytical theoretical models that describe elastic strains and plastic deformation phenomena in NCMs. Most of these models are © Woodhead Publishing Limited, 2011

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based on the theory of defects, a unified concept that allows one to describe the structure, the elastic fields and the mechanisms of plastic deformation from a unique physical viewpoint. Based on the results of such theoretical modeling, one can formulate the following general conclusions: (i) Due to their structural and scale features, NCMs always contain many elastic-strain sources and stress concentrators that are capable of initiating various mechanisms of plastic deformation under external loading. Most of the stress sources and concentrators are defects localized at/near GBs. At the same time, most of these defects can act as carriers of plastic deformation. As a result, GB-mediated mechanisms of plasticity dominate over other possible mechanisms in fine-grained NCMs. (ii) The GB mediated mechanisms of plasticity are emissions of partial and perfect lattice dislocations and twins from GBs; mass transfer along GBs and their triple junctions; GB sliding, decay and migration; grain rotation, growth and refinement. The present review demonstrates that most of these deformation mechanisms can be analysed theoretically within a unified energy approach. In doing so, one can calculate and analyse some critical values of the applied stress, which control the barrier-less activation of the deformation mechanisms and their transition from the stable regime of development to its unstable regime. Using these results, one can sometimes conclude which deformation mode is preferable in given conditions. When possible, the comparison of theoretical estimates with available experimental data and results of computer simulations shows rather good accordance. (iii) Due to the distribution in grain size, different mechanisms of plastic deformation can dominate in different grains; these mechanisms can also compete within the same grains. Interplay between different mechanisms of plasticity commonly occurs in NCMs. Theoretical modeling of this interplay seems to be a good and important challenge at present. This chapter has concentrated mainly on quasistatic theoretical models. Meanwhile, there are a number of models developed for ultrafine-grained and nanocrystalline materials within the evolutional dislocation kinetics78,120,283,284 and discrete dislocation dynamics.285,286 It seems that incorporating GB dislocation and disclination terms to these models may be a future trend in this field. One more future trend is the wider use of elastic fields of defects calculated in the framework of the strain-gradient elasticity,30,31,84 which allows one to avoid the classical singularities in elastic fields of defects and their interactions. Some examples of applying this theory to dislocation behavior in freestanding287 and in/near embedded nanowires288,289 have recently been demonstrated. Future theoretical models are also expected to describe in more details the interplay between dislocation–disclination and GB diffusion modes of plastic deformation, and between the mechanisms of plasticity and fracture as well.

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12.5 Sources of further information and advice Further information on the topics under discussion in this chapter can be taken from monographs,78,131–133 reviews1,2,10,17–22,29,59,97–130 and other references listed in Section 12.7. The most useful sources of current information are such materials science and physical journals as Acta Materialia, Applied Physics Letters, Journal of Materials Research, Journal of Materials Science, Materials Science and Engineering A, Nature Materials, Philosophical Magazine, Philosophical Magazine Letters, Physical Review B, Physical Review Letters, Physics of Solid State, Progress in Materials Science, Reviews on Advanced Materials Science, Science, Scripta Materialia, etc.

12.6 Acknowledgements The work was supported by the Russian Foundation of Basic Research (Grant No. 08–02–00304-a). I am deeply thankful to my friends and colleagues E.C. Aifantis, S.V. Bobylev, A.A. Fedorov, A.L. Kolesnikova, K.N. Mikaelyan, N.F. Morozov, I.A. Ovid’ko, C.S. Pande, A.E. Romanov, A.G. Sheinerman and N.V. Skiba for helpful discussions and collaboration.

12.7 References   1    2    3    4    5    6    7    8    9

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213 Gutkin M.Yu., Mikaelyan K.N., Ovid’ko I.A. Phys Stat Sol B 1996;153: 337. 214 Gutkin M.Yu., Kolesnikova A.L., Ovid’ko I.A., Skiba N.V. J Metastable & Nanostruct Mater 2002;12: 47. 215 Gutkin M.Yu., Ovid’ko I.A., Skiba N.V. Tech Phys Lett 2002;28: 437. 216 Valiev R.Z., Langdon T.G. Acta Metall Mater 1993;41: 949. 217 Nyilas R.D., Kobas M., Spolenak R. Acta Mater 2009;57: 3738. 218 Ovid’ko I.A. Science 2002;295: 2386. 219 Gutkin M.Yu., Ovid’ko I.A., Skiba N.V. Acta Mater 2003;51: 4059. 220 Orlova T.S., Romanov A.E., Nazarov A.A., Enikeev N.A., Alexandrov I.V., Valiev R.Z. Tech Phys Lett 2005;31: 1015. 221 Orlova T.S., Nazarov A.A., Enikeev N.A., Alexandrov I.V., Valiev R.Z., Romanov A.E. Phys Solid State 2005;47: 845. 222 Enikeev N.A., Orlova T.S., Alexandrov I.V., Romanov A.E. Sol State Phenom 2005;101–102: 319. 223 Kolesnikova A.L., Ovid’ko I.A., Romanov A.E. Tech Phys Lett 2007;33: 641. 224 Romanov A.E., Kolesnikova A.L., Ovid’ko I.A., Aifantis E.C. Mater Sci Eng A 2009;503: 62. 225 Bobylev S.V., Mukherjee A.K., Ovid’ko I.A. Rev Adv Mater Sci 2009;19: 103. 226 Gutkin M.Yu., Ovid’ko I.A. Appl Phys Lett 2005;87: 251916. 227 Gutkin M.Yu., Mikaelyan K.N., Ovid’ko I.A. Scr Mater 2008;58: 850. 228 Gutkin M.Yu., Mikaelyan K.N., Ovid’ko I.A. Phys Solid State 2008;50: 1266. 229 Ovid’ko I.A., Sheinerman A.G., Aifantis E.C. Acta Mater 2008;56: 2718. 230 Bobylev S.V., Ovid’ko I.A. Rev Adv Mater Sci 2009;22: 39. 231 Ovid’ko I.A., Sheinerman A.G. Scr Mater 2008;59: 119. 232 Kim B.N., Hirada K., Morita K. Acta Mater 2005;53: 1791. 233 Yang F., Yang W. Scr Mater 2009;61: 919. 234 Mishra R.S., Valiev R.Z., Mukherjee A.K. Nanostruct Mater 1997;9: 473. 235 Mishra R.S., Valiev R.Z., McFadden S.X., Mukherjee A.K. Mater Sci Eng A 1998;252: 174. 236 McFadden S.X., Misra R.S., Valiev R.Z., Zhilyaev A.P., Mukherjee A.K. Nature 1999;398: 684. 237 Islamgaliev R.K., Valiev R.Z., Mishra R.S., Mukherjee A.K. Mater Sci Eng A 2001;304–306: 206. 238 Mishra R.S., Stolyarov V.V., Echer C., Valiev R.Z., Mukherjee A.K. Mater Sci Eng A 2001;298: 44. 239 Mishra R.S., Valiev R.Z., McFadden S.X., Islamgaliev R.K., Mukherjee A.K. Phil Mag A 2001;81: 37. 240 Valiev R.Z., Song C., McFadden S.X., Mukherjee A.K., Mishra R.S. Phil Mag A 2001;81: 25. 241 Padmanabhan K.A., Gleiter H. Mater Sci Eng A 2004;381: 28. 242 Padmanabhan K.A. J Mater Sci 2009;44: 2226. 243 Gutkin M.Yu., Ovid’ko I.A., Skiba N.V. J Phys D: Appl Phys 2003;36: L47. 244 Gutkin M.Yu., Ovid’ko I.A., Skiba N.V. Acta Mater 2004;52: 1711. 245 Gutkin M.Yu., Ovid’ko I.A., Skiba N.V. Phys Solid State 2005;47; 1662. 246 Ovid’ko I.A., Sheinerman A.G. Acta Mater 2009;57: 2217. 247 Haber J.A., Buhro W.E. J Am Chem Soc 1998;120: 10,847. 248 Valiev R.Z., Kozlov E.V., Ivanov Yu.F., Lian J., Nazarov A.A., Baudelet B. Acta Metall Mater 1994;42: 2467. 249 Jin M., Minor A.M., Stach E.A., Morris Jr J.W. Acta Mater 2004;52: 5381.

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250 Soer W.A., De Hosson J.Th.M., Minor A.M., Morris Jr J.W., Stach E.A. Acta Mater 2004;52: 5783. 251 De Hosson J.Th.M., Soer W.A., Minor A.M., Shan Z., Stach E.A., Syed Asif S.A., Warren O.L. J Mater Sci 2006;41: 7704. 252 Jin M., Minor A.M., Morris Jr J.W. Thin Solid Films 2007;515: 3202. 253 Zhang K., Weertman J.R., Eastman J.A. Appl Phys Lett 2004;85: 5197. 254 Zhang K., Weertman J.R., Eastman J.A. Appl Phys Lett 2005;87: 061921. 255 Gai P.L., Zhang K., Weertman J. Scr Mater 2007;56: 25. 256 Liao X.L., Kilmametov A.R., Valiev R.Z., Gao H., Li X., Mukherjee A.K., Bingert J.F., Zhu Y.T. Appl Phys Lett 2006;88: 021909. 257 Pan D., Nieh T.G., Chen M.W. Appl Phys Lett 2006;88: 161922. 258 Pan D., Kuwano S., Fujita T., Chen M.W. Nano Lett 2007;7: 2108. 259 Gianola D.S., Van Petegem S., Legros M., Brandstetter S., Van Swygenhoven H., Hemker K.J. Acta Mater 2006;54: 2253. 260 Gianola D.S., Warner D.H., Molinari J.F., Hemker K.J. Scr Mater 2006;55: 649. 261 Gianola D.S., Mendis B.G., Cheng X.M., Hemker K.J. Mater Sci Eng A 2008;483– 484: 637. 262 Legros M., Gianola D.S., Hemker K.J. Acta Mater 2008;56: 3380. 263 Fan G.J., Fu L.F., Qiao D.C., Choo H., Liaw P.K., Browning N.D. Scr Mater 2006;54: 2137. 264 Fan G.J., Fu L.F., Choo H., Liaw P.K., Browning N.D. Acta Mater 2006;54: 4781. 265 Fan G.J., Wang Y.D., Fu L.F., Choo H., Liaw P.K., Ren Y., Browning N.D. Appl Phys Lett 2006;88: 171914. 266 Fan G.J., Fu L.F., Wang Y.D., Ren Y., Choo H., Liaw P.K., Wang G.Y., Browning N.D. Appl Phys Lett 2006;89: 101918. 267 Brandstetter S., Zhang K., Escuadro A., Weertman J.R., Van Swygenhoven H. Scr Mater 2008;58: 61. 268 Kulovits A., Mao S.X., Wiezorek J.M.K. Acta Mater 2008;56: 4836. 269 Rupert T.J., Gianola D.S., Gan Y., Hemker K.J. Science 2009;326: 1686. 270 Hasnaoui A., van Swygenhoven H., Derlet P.M. Acta Mater 2002;50: 3927. 271 Schiøtz J. Mater Sci Eng A 2004;375–377: 975. 272 Farkas D., Frøseth A., van Swygenhoven H. Scr Mater 2006;55: 695. 273 Sansoz F., Molinari J.F. Thin Solid Films 2007;515: 3158. 274 Dupont V., Sansoz F. Acta Mater 2008;56: 6013. 275 Cahn J.W., Mishin Y., Suzuki A. Acta Mater 2006;54: 4953. 276 Zhou L., Zhou N., Song G. Phil Mag 2006;86: 5885. 277 Zhang H., Srolovitz D.J., Douglas J.F., Warren J.A. Acta Mater 2007;55: 4527. 278 Ivanov V.A., Mishin Y. Phys Rev B 2008;78: 064106. 279 Mompiou F., Caillard D., Legros M. Acta Mater 2009;57: 2198. 280 Caillard D., Mompiou F., Legros M. Acta Mater 2009;57: 2390. 281 Mishin Y., Asta M., Li J. Acta Mater 2010;58: 1117. 282 Li J.C.M. Phys Rev Lett 2006;96: 215506. 283 Malygin G.A. Phys Solid State 2008;50: 1032. 284 Malygin G.A. Phys Solid State 2009;51: 1814. 285 Lefebvre S., Devincre B., Hoc T. J Mech Phys Solids 2007;55: 788. 286 Li Z., Hou C., Huang M., Ouyang C. Comp Mater Sci 2009;46: 1124. 287 Shodja H.M., Davoudi K.M., Gutkin M.Yu. Scr Mater 2008;59: 368. 288 Davoudi K.M., Gutkin M.Yu., Shodja H.M. Scr Mater 2009;61: 355. 289 Davoudi K.M., Gutkin M.Yu., Shodja H.M. Int J Solids Structures 2010;47: 741.

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13 The mechanical properties of multi-scale metallic materials Y.H. ZHAO and E.J. LAVERNIA, University of California Davis, USA Abstract: Bulk nanostructured metallic materials with a multi-scale grain size distribution possess both high strength and good ductility, and therefore are expected to have important technological implications. This chapter introduces the basic concepts of bulk multi-scale, bimodal and multimodal metallic materials and discusses their development background and preparation methods, followed by a review of the experimental and numerical results of mechanical properties (primarily strength and ductility), and deformation and fracture mechanisms of bimodal and multimodal metallic materials, and ends with a final discussion on the potential technological impact and future work. Key words: bulk multi-scale metallic materials, bimodal and multimodal metallic materials, strength and ductility, deformation and fracture mechanisms.

13.1 Introduction In the case of polycrystalline materials, such as metals, alloys, ceramics and intermetallics, grain size (i.e. fraction of grain boundary volume) is one of the most important microstructural parameters that influence properties and deformation mechanisms. For instance, the mean grain size generally influences the low-temperature yield strength of polycrystals via the well-known Hall–Petch relationship. The grain size of conventional structural polycrystalline materials typically falls in what is widely described as the coarse-grained (CG) regime (>1 µm, see Fig. 13.1) which may include the fine-grained sub-regime (1–10 µm).1 Over the past couple of decades, nanocrystalline (or bulk nanostructured, <100 nm)2 and ultrafine-grained (UFG, <1 µm)3 metallic materials have emerged as a new class of materials and have been the subject of widespread research studies. By extending the grain size down to the nanometer regime (see Fig. 13.1), UFG materials provide us not only with an excellent opportunity to study structure–property relationships in polycrystalline materials, but also present us with an attractive potential for technological applications with their novel properties. Initially, fundamental interest in this class of materials was motivated by the question of whether the large volume fraction of grain boundaries (GBs, 50% for 5 nm grains, 30% for 10 nm grains) in UFG metallic materials will significantly alter their physical, mechanical and chemical properties in comparison 375 © Woodhead Publishing Limited, 2011

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13.1  Grain size regimes of nanocrystalline, fine-grained, ultrafinegrained, coarse-grained and multi-scale metallic materials.

with those of conventional CG metallic materials. For instance, with the validity of extending the Hall–Petch relationship down to at least a small threshold grain size value of about 10–20 nm,4 the strength of UFG metallic materials is typically 5–10 times that of conventional CG material of similar composition, and thus offers interesting possibilities related to structural applications. In the case of structural metallic materials, strength and ductility are two of the most important mechanical properties. A structure must support load, thus mechanical strength is an obvious requirement and quite often it is among the most important criteria of any metallic materials selection decision. In addition, good ductility is essential to avoid catastrophic failure in load-bearing applications and for many shaping and forming operations without tearing or fracturing. Ductility is usually defined as the extent to which a material can be deformed plastically and measured in uniaxial tension. It is desirable that structural metallic materials have both high strength and high ductility. However, strength and ductility are often achieved at a trade-off, i.e. increasing the strength sacrifices the ductility, and elevating the ductility typically lowers the strength. This strength–ductility dilemma also applies to CG and UFG metals and alloys: the former have good ductility but low strength, while the latter have high strength but low ductility.5 The low tensile ductility in UFG metallic materials can be

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attributed to the premature onset of plastic instability (necking), which is further caused by low strain-hardening capability.6 According to Considère’s criterion,7 strain hardening is required in order to delay the initiation of tensile necking. Strain hardening typically results from the interactions of dislocations as they glide and intersect with each other. Typically, CG grains provide adequate spacing for significant numbers of dislocation intersections during deformation, while in UFG grains, dislocations move and accumulate at opposing GBs directly, and thereby result in minimal hardening.4 Low ductility has become a seemingly insurmountable obstacle for the widespread technological applications of UFG metallic materials. Since the year 2000, many efforts have been put forth to develop strategies for improving poor ductility.8–12 For CG metallic materials, the ductility and yielding, as well as the working hardening behavior, is generally insensitive to the character of the grain size distribution, such as the Hall–Petch relationship that references only the mean grain size distribution. However, for UFG metallic materials, the grain size distribution becomes potentially more important so that there exists the opportunity for manipulating the grain size distribution to control mechanical behavior. With such a background, bulk multi-scale metallic materials were originally developed as an important strategy for ductility enhancement of UFG metallic materials. Bulk multi-scale metallic materials usually have a wide grain size distribution ranging from the UFG to the CG regions (Fig. 13.1). The grain size distribution histogram could have either a two-peak feature or a continuous log-normal feature, where the former distribution is terminated by a bimodal grain size distribution and the latter by a multimodal grain size distribution. Figure 13.2 (a) shows a transmission electron microscopy (TEM) image of Cu with a bimodal grain size distribution, prepared by dynamic plastic deformation (DPD) and a subsequent annealing treatment.13 Two grain size distribution peaks are observed: the peak at small grain size values, ranging from about 20 to 200 nm with a mean value of about 75 nm, corresponds to the as-deformed nanocrystalline Cu matrix, and the peak at large grain size values, ranging from 1 to 6 µm with a mean value of 2.2 µm, represents the CG grains formed by a secondary recrystallization (Fig. 13.2 (b)). Figure 13.3 shows an electron backscattering diffraction (EBSD) crystal orientation mapping and corresponding grain size distribution histogram for multimodal Ni prepared by cryomilling and powder consolidation.14 The grain size has a log-normal distribution ranging from about 100 nm to 10 µm and the mean grain size is about 1 µm. The increasing importance of grain size distribution for multi-scale metallic materials can be examined in terms of two competing effects. First, the UFG grains at the small end of the size distribution possess increasingly higher strength relative to their larger counterparts. Conversely, the CG grains at the large end of the distribution occupy a larger proportion of the microstructure on a volumetric basis, thus increasing their effect on the behavior of the aggregate, such as ductility. Thus, the multi-scale metallic materials have a good combination of

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13.2  (a) Bright-field transmission electron microscopy (TEM) image of a bimodal Cu sample annealed at 140°C for 10 min. The recrystallized coarse grains are surrounded by areas of nanograins and remaining nanotwin bundles outlined and labeled “T”. (b) Grain size distributions of the as-DPD Cu sample and as-annealed bimodal Cu samples.13

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13.3  Electron backscattering diffraction (EBSD) crystal orientation mapping (a) and corresponding grain size distribution histogram (b) for multimodal Ni prepared by cryomilling and powder consolidation technique.14 The inset indicates crystal orientations, and the black arrows point to twin boundaries.

strength and ductility in comparison with singular unimodal UFG or CG metallic materials. Careful inspection of the literature indicates that investigations of multiscale UFG metallic materials may be traced to their source in the late 1990s.

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In 2000, Legros et al.15 reported an attractive balance of some tensile ductility (2.1%) and yield strength (535 MPa) in a nanocrystalline Cu with a mean grain size of 26 nm and a multi-scale grain structure, while a nanocrystalline Ni, with a mean grain size of 28 nm and without the multi-scale grain structure (Fig. 13.4), experienced an entirely elastic deformation up to failure. The nanocrystalline Cu was prepared by inert-gas condensation2 and subsequent warm compaction at 150°C as well as annealing at 150°C for 240 min. As a result, the nanocrystalline Cu specimen had significant volume fractions of UFG and few highly twinned 1–5 µm recrystallized CG grains. These UFG and CG grains were determined by the authors to be the microstructural reason for the higher ductility and lower flaw sensitivity compared with the nanocrystalline Ni. In 2001, Tellkamp et al.16 employed cryomilling and subsequent degassing, hot isostatic pressing and extrusion techniques to produce bulk commercial nanocrystalline 5083 Al alloys with both high yield strength (334 MPa) and good tensile ductility (8.4%), as shown in Fig. 13.5 (a). Their TEM observation revealed large grains next to an area with several small grains (Fig. 13.5 (b) ), indicating a

13.4  Tensile stress–strain curves of nanocrystalline Cu and Ni with mean grain sizes of 26 and 28 nm, respectively. The dotted lines indicate the linear elastic response.15

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13.5  (a) Engineering tensile stress–strain curves of bimodal and coarse-grained 5083 Al alloys prepared by cryomilling and powder consolidation techniques. (b) Bright-field TEM image showing ultrafine grains (UFG) and coarse grains (CG).16

bimodal grain size distribution. A theory from the field of fracture mechanics was used to explain the good tensile ductility, as schematically shown in Fig. 13.6. A crack was initiated at an internal flaw and propagated rapidly through the UFG region with brittle precipitates at the GBs. The crack could be blunted by the

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13.6  Proposed fracture theory for enhanced ductility of bimodal 5083 Al alloys. Cracks propagate quickly through the brittle UFG grains but are blunted by a large, ductile grain.16

large, ductile and single-crystal grains since it must propagate along the appropriate slip system of the large grains, and therefore, created ductility on a macroscopic level. In 2002, Wang et al.17 prepared a bimodal Cu with both high yield strength (320 MPa) and high tensile ductility (65% comparable to that of the CG Cu and 30% uniform elongation before necking instability occurs) by using a thermomechanical treatment (see Curve E in Fig. 13.7 (a) ). The UFG Cu (Curve C) was prepared by cryorolling at liquid nitrogen temperature and had a vast majority of UFG grains. Annealing the as-rolled UFG Cu at 200°C for 3 min led to a bimodal grain structure with about 25% volume fraction of 1–3 µm CG grains embedded inside a UFG matrix with a mean grain size smaller than 300 nm. The CG grains were formed by abnormal grain growth (secondary recrystallization), and the UFG matrix was formed by a full primary recrystallization (Fig. 13.7 (b)). The pioneering work of the above three groups of researchers has allowed the multi-scale grain size structure, as a generic and effective strategy, to be frequently employed to enhance the poor ductility of UFG metallic materials, such as Al18,19 and Al alloys,20–30 Cu.31–35 Fe36 and steels,37–42 Ni,14,43–45 and Ti.46

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13.7  (a) Tensile stress–strain curves of coarse-grained Cu (curve A), ultrafine grained Cu (curves B–D) and bimodal Cu (curve E) prepared by thermo-mechanical technique.17 (b) Bright-field TEM image of the bimodal Cu sample showing recrystallized coarse grains embedded in UFG matrix.

13.2 Mechanical properties of multi-scale metallic materials Although a large amount of published work has qualitatively verified that the introduction of multi-scale grain structures can indeed improve the poor ductility of UFG metallic materials,13–46 there are few systematic investigations to

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quantitatively characterize the relationship between the mechanical properties (strength and ductility) and the multi-scale grain structures.13,17,22,25,47–55 These quantitative studies can be classified into two categories: experimental studies13,17,22,25 and numerical studies.47–55 The experimental approaches have inherent challenges in accurately controlling the multi-scale grain structures and their distributions. The numerical methods can more accurately yield carefully controlled grain size distributions; however, it is difficult to interpret the results and extrapolate the underlying mechanisms. The following section reviews the quantitative studies related to the mechanical properties of multi-scale metallic materials; first the experimental results and then the numerical results.

13.2.1  Experimental results As discussed in the introduction, multi-scale grain structures can be introduced by either abnormal grain growth via annealing-induced secondary recrystallization of UFG metallic materials13,17,22 or via the consolidation of mixtures of multiscale size particles.16,19,36 With the former technique, it is difficult to quantitatively control the multi-scale grain structures by controlling recrystallized nucleation sites and growth kinetics due to the highly unstable high-energy states of UFG microstructures.17,56 The latter method allows for more accurate control of the multi-scale grain structures by simply controlling the mixing ratio of differentsize particles. However, the processing artifacts, such as nano-pores and incomplete bonding that are sometimes introduced by the consolidation process, may obscure the intrinsic mechanical property–structure relationships.20,21 Inspection of the published literature related to the quantitative mechanical property–structure relationship of multi-scale metallic materials reveals a focus on bimodal metallic materials.13,17,22,25 The following section first discusses quantitative experimental results of bimodal metallic materials and then addresses the topic of qualitative experimental results of multimodal metallic materials.14,27,35,44 Strength and ductility of bimodal metallic materials The initial development and subsequent studies on multi-scale metallic materials discussed in the introduction inherently invoke a strategy of compromise: i.e. to achieve ductility, we must sacrifice strength. The question is: what is the relationship between the volume fraction of the components and the mechanical behavior? Can one predict the behavior of multi-scale metallic materials using simple weighted averages of the strength and ductility of UFG and CG components, i.e. following the rule-of-mixtures?57 In the published literature, both positive (i.e. improved) and negative (i.e. diminished) deviations from the rule-of-mixtures have been reported. In the discussion that follows, we designate the positive case as a good combination of strength and ductility which stands out from the usual strength–ductility trade-

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off dilemma and has an extra gain in toughness; the negative case as a poor combination of strength and ductility; and the case complying with the rule-ofmixtures as the neutral or usual compromise between strength and ductility. In addition, there is one exception case reported for bimodal Ni, which was prepared by annealing an electrodeposited nanocrystalline Ni sample.58 The bimodal Ni samples have both lower strength and ductility than the nanocrystalline Ni. It has been explained that the decrease in ductility of the bimodal Ni resulted from S and P impurity segregation at GBs, which caused GB de-cohesion and embrittlement.58 First, let us look at a good combination of strength and ductility that is better than the rule-of-mixtures (positive case). As described in the introduction, Wang et al.17 reported that the introduction of 25% volume fraction of CGs into the UFG Cu matrix resulted in a 30% uniform elongation and a comparable elongation to failure (65%) with that of the CG Cu counterpart (70%), while the yield strength was still maintained at about 5–6 times higher than that of the CG Cu (Fig. 13.7). This, in fact, is an excellent compromise, because the simultaneous high strength and high ductility, especially the very large uniform elongation, results in a notable gain in toughness (the area under the stress–strain curve). To establish reproducibility, Wang et al. also annealed UFG Cu prepared by equal-channel angular pressing (ECAP)59 and observed similar coexisting high strength and high ductility. Moreover, Wang et al. also reported further annealing beyond the bimodal structure shown in Fig. 13.7 (b) (i.e. 25% volume fraction of CGs) caused additional grain growth and larger uniform elongation, but with a large decrease in yield strength and no further gain in overall ductility. Wang’s work suggests that a maximum combination of strength and ductility may exist when small amounts of CGs are embedded inside a UFG matrix, and that the combination (i.e. the toughness) decreases rapidly when the volume fraction of CGs are increased due to the rapid decrease in yield strength. Similar results were reported by Jin et al.22 with a 5754 Al alloy. The UFG Al alloy with duplex grain size distributions was prepared by asymmetric rolling and annealing. By treating the CGs with a size larger than 4 µm, and the UFGs with a size smaller than 4 µm, Jin et al. found both yield strength (YS) and ultimate tensile strength (UTS) increased linearly with increasing volume fraction of UFGs complying with the rule-of-mixtures, while the ductility of the 5754 Al alloy with duplex grain size distributions was comparable to that of the CG counterpart (~25%) when the CG content is 20–45%. Unlike in Wang’s work, Jin et al. found that the ductility decreased with further increases of the CG content from 60 to 80%, and increased again to 25% when the CG content reached 100%. Except for the above two papers, which reported a good combinations of strength and ductility in bimodal metallic materials, most related literature reports a poor combination of strength and ductility, which still complies with the strength–ductility trade-off dilemma.13,19,25,32–34,36,43 Li et al.13 performed a systematic study on the influence of CG content on the strength and ductility of bimodal Cu, and found that with increasing volume fraction of CGs, the strength decreased, and the ductility increased gradually to reach the value of the CG Cu

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(42%), as shown in Fig. 13.8 (a). Yield strength and uniform elongation are inversely related, following a typical strength–ductility trade-off relationship (Fig. 13.8 (b)). Here, the nanostructured (ns) Cu was prepared by DPD at liquid nitrogen temperature and consisted of about 33 vol.% nanoscale twin bundles embedded in 80 nm nanograins. Different volume fractions of CGs were introduced by static recrystallization (SRX). For instance, after annealing at 140°C for 10 min, the recrystallized CGs with a size ranging from 1 to 6 µm and a peak value of 2.2 µm were about 45% in volume, and the untransformed matrix consisted of the nanosized grains with a mean size of about 75 nm with nanoscale twin bundles (Fig. 13.2). After annealing at 200°C for 10 min, most of the sample was composed of SRX coarse grains with a mean grain size of 2.4 µm. The UFG Cu that was prepared by quasi-static compression (QSC) has a mean grain size of 290 nm. Annealing formed larger recrystallization grains (5 µm in mean) in UFG Cu. Most importantly, an obvious increment in the uniform elongation was achieved only when the volume fraction of SRX grains exceeded about 80% (Fig. 13.8 (c)). This volume fraction value of CGs is much larger than the value reported by Wang et al. where 30% uniform elongation was seen when CGs reached 25 vol.%. For

13.8  Tensile engineering stress–strain curves of bimodal Cu prepared by combination of DPD and annealing (as indicated) in comparison with the CG Cu. Uniform elongation is indicated for each sample by open circles.13 (b) Plots of uniform elongation vs. yield strength for bimodal Cu samples prepared by annealing DPD,13 QSC 13 and cryorolled17 UFG Cu samples. (c) Variation of uniform elongation as a function of the volume fraction of SRX CG grains in various bimodal Cu samples.13

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13.8  Continued.

comparison purposes, the data from Wang et al.17 was also plotted in Fig. 13.8 (c). One can see that the data point of Wang et al. is far above the line of the rule-ofmixtures, suggesting positive deviation, while the data points from Li et al. are far below the rule-of-mixtures, suggesting a negative deviation.

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Similar results were also reported by Han et al. with a bimodal 5083 Al-Mg alloy prepared by cryomilling and subsequent consolidation techniques.25 An introduction of 30% volume fraction of CGs into UFG Al-Mg alloy matrix only extended the ductility to less than 3%, much smaller than the ductility of the CG Al-Mg counterpart (about 20%), suggesting a negative behavior. Here the bimodal Al-Mg alloys were produced by mechanically blending cryomilled UFG powders with 15 and 30% volume fraction of unmilled CG powders. The blended powders were then canned, consolidated by cold isostatic pressing, vacuum degassed and extruded at 550°C.25 As a result, the CG regions with a mean grain size of about 1 µm extend along the extrusion direction and form discrete narrow bands surrounded by the continuous UFG matrix with grain sizes ranging from 100 to 400 nm. It should be noted that the consolidation methods might generate porosity, incomplete bonding, etc., artifacts that are known to be detrimental to tensile ductility. Nevertheless, the gradual decrease in strength and increase in ductility with annealing were also reported by many other groups in bimodal Cu prepared by cryorolling (Fig. 13.9 (a))33 and ECAP (Fig. 13.9 (b)),32,34 bimodal Ni by cryorolling (Fig. 13.9 (c)),43 bimodal Fe by spark plasma sintering (SPS) of ball-milled powders,36 and bimodal Al by ECAP consolidation with back pressure.19 Although these papers did not report a quantitative relationship between strength/ductility and volume fraction of CGs, the strength– ductility combinations are either neutral or negative cases, rather than positive cases.

13.9  (a) Engineering stress–strain curves of bimodal Cu prepared by cryo-worked (CW) and annealing (as indicated).33 (b) Engineering stress–strain curves of bimodal Cu prepared by ECAP and annealing/ cyclic deformation + ageing.34 The ageing conditions are room temperature for 5 months. (c) Tensile stress–strain curves of bimodal Ni prepared by rolling at room temperature (RT) and liquid nitrogen (LN) and subsequent annealing (as indicated).43

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13.9  Continued.

In view of the fact that tensile ductility is sensitive to both extrinsic parameters (artifacts, temperature, strain rate) and intrinsic microstructures,12 it is best to control one set of factors in order to reveal the quantitative relationship of strength/ ductility and volume fraction of CGs in bimodal metallic materials. The data of

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bimodal metallic materials prepared by consolidation methods can be considered only when the processing artifacts are removed and ductility approaches an intrinsic value.25 However, both good and poor strength–ductility combinations were observed in fully dense bimodal metallic materials that were artifactfree.13,17,22 Possible reasons for the different results may be the differences in the detailed microstructures, such as the distribution of the UFG and CG grains, or grain size differences between the UFG matrix and CGs. As described in the introduction, multi-scale metallic materials have a wide grain size distribution, and the grain size distribution histogram, (i.e. volume fraction), is in fact not sufficient to describe the microstructures. For example, the connectivity of the large grains and small grains and their geometrical configurations are factors that need to be taken into consideration. They can be distributed homogeneously, as shown in Fig. 13.3 or heterogeneously, as shown in Fig. 13.2, which features a small-grain agglomerate and a large-grain agglomerate. The distribution of the grains may also have a significant influence on the mechanical properties. Therefore, systematic investigations are necessary to quantitatively reveal the mechanical properties and microstructure relationships of bimodal metallic materials. Strength and ductility of multimodal metallic materials The microstructure of bimodal metallic materials with double grain size distribution peaks is heterogeneous. The ductility of bimodal metallic materials is determined by the ductility of the UFG matrix, which has low strain hardening and plastic deformation capability. Therefore, cracks usually initiate in the UFG matrix or at the UFG and CG interface. In order to make the UFG matrix plastically deform continuously with the CG component and further increase the ductility, the concept of multimodal metallic materials with a continuous and wide grain size distribution is emerging as a variant of bimodal metallic materials.14,27,35,44 In fact, many bimodal metallic materials in the literature are multimodal metallic materials since it is challenging to prepare bimodal metallic materials with two totally distinct grain size distributions.13,15,22,25 Research papers on multimodal metallic materials are very few. Shekhar et al.35 reported a better combination of strength and ductility (yield strength 460 MPa and ductility 6%) in multimodal Cu than that in unimodal UFG Cu (yield strength 560 MPa and ductility 1.1%). The multimodal Cu was prepared by consolidating machined Cu chips and has a wide grain size distribution from UFG to several micrometers. Zhang et al. reported a larger ductility in multimodal 5083 Al (about 4%) than that in bimodal counterparts (3%).27 The multimodal 5083 Al alloy was prepared by thermal consolidation of powders that were cryomilled for different times and had wide grain size distributions ranging from about 100 nm to 2.1 µm. The gain in ductility of multimodal 5083 Al alloy was obtained by sacrificing strength. Shen et al.44 reported a better combination of strength and ductility in multimodal Ni than that in a bimodal Ni counterpart, which is correspondingly

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better than that in a unimodal Ni. The multimodal, bimodal and unimodal Ni were prepared by the electrodeposition method. The grain size in multimodal Ni ranged from about 10 nm to 160 nm.44 Recently, Zhao et al.14 prepared multimodal and bimodal Ni, with minimal processing artifacts, by quasi-isostatic Ceracon forging of cryomilled Ni powders, and found better strength–ductility combinations than the data reported in literature (Fig. 13.10 (b)). The multimodal Ni has a grain size distribution ranging from about 100 nm to 10 µm (Fig. 13.3), and the bimodal Ni from 100 nm to 30 µm (Fig. 13.10 (c)). Compared with the tensile data of the CG Ni (yield strength of 154 MPa and ductility of 48%), both multimodal and bimodal Ni have better strength and ductility combinations (471 MPa and 39%, 312 MPa and 49%, respectively), as shown in Fig. 13.10 (a). In summary, available results suggest that a multimodal grain size distribution benefits ductility by sacrificing strength. Moreover, multimodal metallic materials exhibit combinations of strength and ductility that are superior to those of their unimodal counterparts. At present, the available published literature, however, does not unequivocally support the hypothesis that multimodal or bimodal metallic materials exhibit improved combinations of strength and ductility.

13.2.2  Numerical results As discussed in the above section, although some progress has been documented, the challenge remains to synthesize samples that are defect-free and contain a priori design of multi-scale grain size distributions. Even the preparation of samples that contain a bimodal grain size distribution remains challenging because of mechanisms, such as grain growth, which are almost always operative. In an effort to circumvent these experimental challenges, while simultaneously providing insight into the operative mechanisms, numerical modeling is being widely applied to study multi-scale metallic materials. In the sections that follow, we review published numerical studies on the behavior of bimodal and multimodal metallic materials and compare and contrast the results.47–55 Strength and ductility of bimodal metallic materials Inspection of the published literature shows that numerical studies on bimodal metallic materials predict behavior that is consistent (e.g. normal), and improved (e.g. positive), over the results obtained from a rule-of-mixtures rationalization. One example of a study that predicts behavior representing an improvement over the rule-of-mixtures was published by Sevillano et al.,47 who used a onedimensional cellular automaton model to simulate the elastic and plastic deformation of bimodal metallic materials. Examples of studies that predict a strength–ductility behavior that is consistent (e.g. normal behavior) with the ruleof-mixtures were reported by Raeisinia et al.,55 who used a micromechanics polycrystalline model to simulate the monotonic plastic deformation of polycrystal

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with a bimodal grain size distribution, and by Joshi et al.49 who applied a secant mean-field approach that approximated a bi-modal polycrystal as being composed of a coarse-grained phase embedded in an ultrafine-grained matrix. In the following sections the simulation results from these three studies are considered. First we will address the case in which the strength–ductility relationship is predicted to exceed the trend anticipated from the rule-of-mixtures (e.g. the positive case). By using a one-dimensional cellular automaton model of gradientdependent plasticity, Sevillano et al.47 comparatively investigated the mechanical behavior of both unimodal and bimodal metallic materials. Figure 13.11 (a) shows several tensile true stress–strain curves calculated for a unimodal polycrystal with different mean grain sizes. The tensile uniform elongation, indicated on each curve by open circles, increases first slowly and then rapidly with increasing the mean grain size or decreasing strength. Here b is the Burgers vector modulus, and the mean grain size of = 500b is approximately 130 nm for Cu, and = 105b is about 25 µm. A narrow unimodal grain size distribution in the range of ± 0.1 was assumed for UFG metallic materials. For larger grain sizes (i.e. = 25 µm), the unimodal distribution was assumed to be wider ( ± 0.9). It is important

13.10  (a) Tensile engineering stress–strain curves of multimodal (Multi-Ni), bimodal (Bi-Ni) and CG Ni.14 The Multi-Ni was tested at three strain rates: 10–2, 10–3 and 10–4 s–1, as indicated in the figure. The inset shows the picture of the fractured tensile specimens. (b) Yield strength vs. tensile ductility of Ni samples prepared by different techniques.14 (c) EBSD crystal orientation mapping of bimodal Ni prepared by cryomilling and powder consolidation technique.14 The inset indicates crystal orientations, and the black arrows point at twin boundaries.

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to note the difference between unimodal grain size distribution and the multimodal grain size distribution. The latter has a much wider grain size distribution if one considers the range from UFG to CG region. For example, for the multimodal Ni as shown in Fig. 13.2, the average grain size = 1 µm, and the grain size

13.11  (a) Tensile true stress–strain curves calculated for polycrystals with unimodal grain size distributions of different mean grain sizes. Uniform elongations are indicated by open circles. (b) Tensile true stress–strain curves calculated for bimodal nanograin and coarse grain mixtures. Uniform elongations are indicated by open circles. Uniform elongations of unimodal polycrystals of similar strength (from a) fall on the dashed line. (c) Predicated uniform elongation of bimodal polycrystals vs. rule-of-mixtures approximation.47

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13.11  Continued.

distribution ranges from 0.1 to 10 where the large grain size is about two orders of magnitude larger than the small grain size. In contrast, the large grain size in a unimodal distribution is one order of magnitude of the small grain size, or both are at the same order of magnitude. Figure 13.11 (b) shows several tensile true stress–strain curves calculated for bimodal mixtures with different volume fractions of UFG matrix, as indicated in the figure. In this case the bimodal structures are randomly mixed with different (linear) fractions of the unimodal UFG structure ( = 500b, i.e. about 130 nm, uniform distribution in the range ± 0.1) and the unimodal CG structure ( = 105b, i.e. about 25 µm, uniform distribution between  ± 0.9). The uniform elongation values for each curve are indicated by an open diamond. For comparison purposes, the ultimate tensile stress vs. the uniform elongation corresponding to the unimodal grain size distribution shown in Fig. 13.11 (a) is also shown in Fig. 13.11 (b) and is indicated by a dashed line. Different from that of the unimodal grain size distribution, the uniform elongation of the bimodal distribution increases first rapidly and then slowly with decreasing strength (i.e. volume fraction of UFG matrix). This results in a marked improvement in uniform elongation and the overall ductility of bimodal metallic materials relative to those corresponding to unimodal metallic materials possessing the same strength, i.e. a significant gain in toughness is attained by moving the curves towards upper-right corner. Sevillano et al. further argued that such a gain was obtained at the cost of a strength loss with respect to the unimodal UFG metallic materials, for instance, 10% of CGs in an UFG matrix produces only a 12% strength decrease relative to the 100% UFG metallic materials but increases the uniform elongation from less than 10% to near 40%. As a result, the ductility of bimodal polycrystal exceeds the prediction of the rule-of-mixtures, as shown in Fig. 13.11 (c). Moreover, the

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author further discussed that higher proportions of coarse grains induced important strength losses, resulting in yield stress or ultimate tensile stress values that fell below the rule-of-mixtures prediction. Sevillano and Aldazabal’s numerical results discussed above are quite consistent with the experimental results reported by Wang et al.17 and Jin et al.22 In contrast with the above numerical results in which the strength and ductility relationship deviated from the rule-of-mixtures in a positive way, Raeisinia et al.55 and Joshi et al.49 reported normal strength–ductility behavior for bimodal metallic materials, consistent with the predictions of the rule-of-mixtures. Figure 13.12 (a) shows the predicted stress–strain curves of a number of bimodal polycrystals constructed from different proportions of 200 nm ultrafine grains and 3 µm coarse grains. The 0% and the 100% indicate polycrystals with unimodal grain sizes of 200 nm and 3 µm, respectively. Here please note that, unlike Sevillano and Aldazabal’s unimodal grain size distribution, which is in the range of ± 0.1, Raeisinia’s unimodal metallic materials have the same grain sizes without any size distribution range, i.e. ± 0.0. All curves in Fig. 13.12 (a) were plotted to the end of uniform elongation as determined by Considère’s criterion.7 By incorporating 3 µm grains to the 200 nm grain matrix, the uniform elongation of the bimodal metallic materials is gradually restored at

13.12  (a) Predicted von Mises equivalent stress–strain curves of bimodal polycrystals constructed from different proportions of 200 nm ultrafine grains and 3 µm coarse grains. The 0% and the 100% indicate polycrystals with unimodal grain sizes of 200 nm and 3 µm, respectively.55 The variation of (b) ultimate tensile strength and (c) uniform elongation as a function of the volume fraction of coarse grain constituents (1 and 10 µm) for bimodal polycrystals with 200 nm UFG matrix.55

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the expense of the strength. Figure 13.12 (b) shows the evolutions of the ultimate tensile strength and the uniform elongation of the bimodal metallic materials having 200 nm UFG matrixes as a function of the volume fraction of their 1 or 10 µm coarse grain constituents. For the bimodal material with 1 µm coarse grains, the uniform elongation is zero when the volume fraction of CGs is smaller than 10%, and increases linearly with increasing the CG volume fraction more than 10%. When the CG constituent is a 10 µm grain, the uniform elongation has approximately linear relationship with the CG volume fraction, following the rule-of-mixtures prediction. Moreover, the ultimate tensile strength of the bimodal metallic materials decreased approximately linearly with increasing CG volume fraction (Fig. 13.12 (b) ), also following the rule-of-mixtures. Raeisinia’s numerical results indicate that it is possible to benefit from both the strengthening of the ultrafine grains and the high strain hardening capability (uniform elongation) of the coarse grains at intermediate volume fractions. Moreover, the larger coarse grain constituent has a marked positive influence on the uniform elongation relative to that of the smaller coarse grain constituent. Nevertheless, the strength– ductility combination follows the rule-of-mixtures without any additional gain in toughness as reported by Wang et al.,17 Jin et al.22 and Sevillano et al.47 In addition, Joshi et al.49 modeled the mechanical response of 5083 Al alloy with a bimodal grain size distribution by using the secant Mori–Tanaka (M–T) meanfield approach, and also reported that the ultimate tensile stress and uniform elongation follow the rule-of-mixtures prediction. In summary, it is evident that there are significant differences in the predicted behavior of the strength–ductility relationship for bimodal metallic materials, which can be attributed in part to the various assumptions made in the development of the numerical models. What is perhaps more significant, however, is that the numerical results suggest that the strength–ductility relationship exhibits a marked dependence on the size, distribution and geometrical arrangement of the various constituent phases. Moreover, it is also evident that additional studies are required, which ultimately, with appropriate experimental verification, may be used to develop design principles that can be applied to multiscale metallic materials, including those with a bimodal grain size distribution. Strength and ductility of multimodal metallic materials In this section, we review the numerical results related to the influence of the grain size distribution dispersion on the mechanical behavior of polycrystals, including those with multimodal and unimodal grain size distributions. Numerical simulation results from different research groups indicate that the width of the log-normal grain size distribution has a significant influence on the yield stress, strain hardening and uniform elongation.52,60–62 In an earlier study, Kurzydlowski60 used a polycrystalline model based on the Hall–Petch relationship and the assumption that the portioning of plastic strain is proportional to the grain

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volume, to predict the influence of the dispersion of grain size distribution on the yield strength, and predicted that the slope of the Hall–Petch plot decreases with increasing degrees of dispersion. The prediction is consistent with a number of recent studies where numerical models that explicitly include a distribution of grain sizes and numerical approaches to partition stress and strain amongst the grains have been employed.52,55,61,62 In the following section, we discuss some of the simulation results from Raeisinia et al.55 who used a grain size dependent constitutive model within a viscoplastic self-consistent formalism to form a polycrystal with varying grain sizes and grain size distributions. The generated log-normal grain size distributions with varying widths are shown in Fig. 13.13 in terms of: (a) number fraction and (b) volume fraction of grains. Here the grain size values, d, are normalized by the average grain size, µ. σ0 is the standard deviation of the grain size distribution.55 The dispersion of σ0 /µ ≥ 0.8 has a grain size range of 0.1µ–10µ, so it could be treated as multimodal grain size distribution. Figure 13.14 shows the predicted yield strength as a function of square root of mean grain size for a variety of unimodal polycrystals with varying distribution widths. The Hall–Petch plot shows that increasing the width of the distribution results in a lowering of the yield strength, and the effect is stronger the smaller the mean grain size, resulting in a decrease in Hall–Petch slope. Figure 13.15 depicts how the width of grain size distribution affects the stress (σeq)–strain response (a and b) and the working hardening Θ behavior (c and d) of polycrystals with two different mean grain sizes of 700 nm (a and c) and 10 µm (b and d), respectively. The von Mises equivalent stress–strain curves were plotted to the end of uniform elongation as calculated with Considère’s criterion (Θ = σeq). As the width of the distribution is increased, the uniform elongation of the polycrystal increases with a concomitant loss of some strength. At the same time, the strain hardening rate Θ increases, which can be used to rationalize the increased uniform elongation. Polycrystals with a 10 µm mean grain size behave similarly to their 700 nm counterparts, but the effect of the width of the distribution is much smaller. A similar grain size distribution dispersion effect on yield strength and uniform elongation was also reported by Malgin,54 Morita et al.,61 and Berbenni et al.51,52 who used elastic–plastic formulations. In addition, by using a physical model, which includes Coble creep at fine grain sizes, Masumura et al.63 have also concluded that the slope of the Hall–Petch is dependent on the width of the grain size distribution. Moreover, Phaniraj et al.64 examined the influence of grain size distribution on the transition from grain boundary strengthening to grain boundary weakening in nanocrystalline metallic materials. This study reported that the transition becomes broader with an increase in the standard deviation of the grain size distribution. In summary, with increasing grain size distribution dispersion (i.e. multimodal metallic materials), the uniform elongation and strain-hardening rate of a

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polycrystal increase by sacrificing strength. This, in fact, verified the abovementioned experimental results reported for multimodal metallic materials.14,27,35,44 Comparison of bimodal and multimodal metallic materials The numerical simulation results discussed above suggest that both bimodal and multimodal grain size distributions have a similar effect on the mechanical behavior of a polycrystal; i.e. an improvement in ductility is accompanied with a decrease in strength. Therefore, it is meaningful to accurately compare which distribution (i.e. bimodal or multimodal) has a stronger influence. To that effect, in a recent study, Raeisinia et al.55 compared different bimodal, multimodal and unimodal polycrystals with one another, as plotted in Fig. 13.16 in terms of the ultimate tensile strength versus the uniform elongation.

13.13  Generated log-normal grains size distributions with varying widths shown in terms of (a) number fraction and (b) volume fraction of grains. The grain size values, d, are normalized by the average grain size, µ. σ0 is the standard deviation of the grain size distribution.55

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13.14  Predicted yield strength as a function of square root of mean grain size for a variety of unimodal polycrystals with varying distribution widths.

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13.15  Calculated von Mises equivalent stress–strain curves and strain hardening Θ plots of polycrystals with 700 nm (a, c) and 10 µm (b, d) mean grain size and varying widths of distributions. In (c) and (d), the Θ = σeq line correspond to the Considère criterion.55

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13.16  Tensile strength vs. uniform elongation predicted for bimodal, unimodal and multimodal (σ0/µ = 0.8) metallic materials. The bimodal metallic materials have 200 nm UFG matrix and either 1 or 10 µm CG constituents. The arrows on the dashed lines show direction of increase in the volume fraction of CG constituents of bimodal metallic materials. For unimodal and multimodal metallic materials, the mean grain size µ ranges from 100 nm to 50 µm for each distribution width.55

The multimodal/unimodal polycrystals are of different average grain sizes (µ values ranging from 100 nm to 50 µm) and grain size distributions (σ0/µ ratio varying from 0 to 0.8), while bimodal polycrystals all have 200 nm UFG matrix and varying volume fractions of either 1 or 10 µm grains as their coarse constituents. Arrows on the dashed lines show the direction of increase in the volume fraction of the coarse constituents of the bimodal polycrystals. In the case of the unimodal polycrystals, uniform elongation exhibits a dispersion at smaller values which results from the improvement observed in uniform elongation of unimodal UFG polycrystals when the width of their size distribution is increased (as shown in Fig. 13.14). With increasing mean grain size, the dispersion in uniform elongation caused by grain size distribution dispersion gradually diminishes. As compared with unimodal and multimodal polycrystals, the bimodal polycrystals populate new regions of the ultimate tensile strength-uniform elongation space by shifting the strength-uniform elongation envelope defined by unimodal and multimodal polycrystals favorably towards higher strength and elongation. This result indicates that the bimodal grain size distribution has a better strength–ductility combination than that of the multimodal distribution. Moreover, a larger coarse grain constituent (such as 10 µm) shows a better strength–ductility combination when compared to that of a smaller coarse grain constituent (1 µm). The values for bimodal polycrystals represent upper limit © Woodhead Publishing Limited, 2011



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13.17  Plot of ultimate tensile strength vs. uniform elongation for bimodal metallic materials having 100 and 300 nm UFG matrix and 1 and 10 µm CG constituents.55 The arrows on the solid and dashed lines show direction of increase in the volume fraction of CG constituents.

estimates, because only bimodal structures with same-size ultrafine and same-size coarse grains were considered and as the ultrafine and coarse grains start to develop size distributions, the values of bimodal polycrystals will tend towards the unimodal values. Raeisinia et al.55 further examined the effect of varying the size of the UFG constituent on the strength-uniform elongation combination, as shown in Fig. 13.17. The ultrafine grains are designated as 100 and 300 nm, respectively. Aside from shifting either of the lines towards higher strength and uniform elongation, a decrease in the size of the UFG constituent also tends to amplify the difference between 1 and 10 µm. This means that as the behavior of the ultrafine grains approaches that of the coarse grains, or in other words the strength effect of the ultrafine grains vanishes, there is less improvement to be obtained in the strength–ductility response. In summary, the results described above suggest that a bimodal grain size distribution has an advantage in improving the combination of strength and ductility relative to that attainable with a multimodal grain size distribution.

13.3 Deformation and fracture mechanisms of multi-scale metallic materials The mechanical properties of multi-scale metallic materials (such as ductility) depend on the relevant deformation and fracture mechanisms that are activated © Woodhead Publishing Limited, 2011

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during loading. An inspection of the published literature reveals that investigations on the deformation and fracture mechanisms of multi-scale metallic materials deal principally with microstructures that contain a bimodal grain size distribution, for both experimental studies as well as numerical simulations. In the sections that follow, we first introduce the deformation and fracture mechanisms that are active in metallic materials with a unimodal grain size distribution, and then discuss the mechanisms that relate to bimodal metallic materials.

13.3.1 Deformation and fracture mechanisms of unimodal metallic materials Figure 13.18 schematically shows the deformation mechanisms of a face-centered cubic polycrystal with medium- and high-stacking fault energy as a function of grain size. When the grain size falls in the nanometer regime (say <10 nm), a transition of the dominant deformation mechanisms from the usual dislocation-mediated

13.18  Schematic representation of deformation mechanisms of a face-centered cubic polycrystal with medium and high stacking fault energy versus gain size.

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plasticity to grain boundary-mediated processes takes place which corresponds to a transition in the slope of Hall–Petch relationship.4,65–70 The grain boundarymediated processes include grain boundary sliding, migration and grain rotation.71–84 The macroscopic plastic deformation capability of nanocrystalline metallic materials with grain boundary-mediated processes is usually very limited under conventional deformation conditions,73 unless under some specific conditions such as dynamic loading,84 miniature sample geometries,85–87 or deformed at elevated temperature88–90 which promote the activation of boundary process. In contrast, when the grain size falls in the micrometer regime (>1 µm), intragranular dislocation activity plays a dominant role in plastic deformation.1 Micrometer-sized grains generally provide sufficient space for dislocation activity, such as nucleation, dislocation tangling, cutting and propagation and as a consequence, the associated strain hardening results in a high tensile ductility. When the grain size is smaller than 1 µm and larger than about 10 nm, grain boundaries act as both dislocation sources and sinks, and they lead to the absorption of dislocations by grain boundaries as soon as the dislocations are emitted from the opposite boundaries.4 Since very few dislocations can accumulate within ultrafine grains, the resultant strain hardening is very low, resulting in limited tensile ductility. In related studies, it was experimentally shown that, under the right conditions, such as at a very low strain rate of 10–5 s–1 or elevated temperatures, grain boundary sliding could be activated in UFG metallic materials with a mean grain size larger than 100 nm.78,88–90,91,92 However, under normal deformation conditions, grain boundary sliding is limited and hence does not contribute to the poor ductility of UFG metallic materials with a unimodal grain size distribution. When the grain size is smaller than about 50 nm, deformation twinning has been frequently reported even in metallic materials with medium to high stacking fault energies such as Cu and Ni, and this has led to the suggestion that twinning is a major plastic deformation mechanism in UFG metallic materials.93–96 Systematic high-resolution TEM studies revealed that the deformation twinning in UFG metallic materials was formed by the emission of Shockley partial dislocations from grain boundaries.67,73 A more recent study indicates that further decreasing the grain size of UFG metallic materials actually impedes twinning (i.e. inverse grain size effect), which was explained using generalized planar fault energies and grain size effects on the emission of partial dislocations.97 In reference to fracture mechanisms, both ductile and brittle fracture processes are reported to occur in nanocrystalline metallic materials, and there are several examples showing ductile fracture in metallic materials with an average grain size in range from 20 to 100 nm.4,98–101 Most of these experiments provide support to the suggestion that in nanocrystalline metallic materials the nucleation of cracks occurs at grain boundaries and triple junctions. For example, Kumar et al. examined deformation mechanisms and damage evolution in nanocrystalline Ni

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prepared by electrodeposition.98,99 It was reported that dislocation emission at grain boundaries, together with intragranular slip and unaccommodated grain boundary sliding facilitate the nucleation of voids at boundaries and triple junctions. When exposed to extensive local plasticity, these voids, as well as those that may have existed prior to deformation, can behave as nucleation sites for dimples leading to fracture that do not occur preferentially along grain boundaries. Moreover, Ovid’ko et al.102 reported that plastic deformation in a nanocrystalline solid is strongly influenced by the presence of interfaces. In particular, grain boundaries hinder intragranular slip activated by lattice dislocations. These hindering mechanisms are related to the formation of disclination dipoles where nanocrack nucleation occurs. In the case of UFG metallic materials with a mean grain size larger than 100 nm, numerous available experimental studies reveal that they fracture in a ductile way.4,103

13.3.2 Deformation and fracture mechanisms of bimodal metallic materials Available published studies on the deformation and fracture mechanisms that are active in bimodal metallic materials provide useful fundamental insight into their strength and ductility behavior. Unfortunately, however, such studies are limited, and often only preliminary results are available. In the sections that follow, we introduce deformation and fracture mechanisms in bimodal metallic materials for both tension and compression conditions. Tension To provide insight into the mechanisms responsible for the excellent combination of strength and ductility reported for bimodal Cu, Wang et al. applied finite element modeling in combination with post-mortem TEM analysis.17 They reported that during deformation, the CGs that are embedded in the heterogeneous microstructure experience multi-axial stress state conditions, consisting of a complex strain field with a triaxial strain component, and very large strain gradients (Fig. 13.19). Under these stress state conditions, strain–gradient plasticity theory104 suggests that an excessively large number of geometrically necessary dislocations is required to accommodate the large strain gradients, thereby resulting in significant strain hardening and large uniform elongation. Moreover, deformation twinning was observed after straining for 6% inside most of all of the CGs (Fig. 13.20 (a)). High resolution TEM, as shown in Fig. 13.20 (a) lower-right corner, shows twin boundaries located preferentially near the extrusions of the surrounding UFGs into the softer CGs, suggesting that the constrained CGs plastically deform at high stresses, which results in twinning initiation presumably due to stress

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13.19  The finite element modeling of the bimodal Cu. (a) Micrometer-sized grains (AL) embedded inside UFG matrix (Anano). (b) The large strain gradient observed across CG and UFG grains.17

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13.20  (a) Transmission electron microscopy image of the CG in bimodal Cu sample after 6% plastic strain.17 The upper left inset shows the twin relationship, and the lower right inset shows high-resolution TEM image of the interface of CG (L) and UFG (S) matrix. (b) Transmission electron microscopy image of bimodal Cu after 30% uniform strain.17

concentration. Twin boundaries can be considered to be a special type of high angle boundary, and hence are known to effectively increase strain hardening via dislocation accumulation. In summary, the deformation of the bimodal Cu can be described as follows. During loading, the CGs accommodate the strains preferentially. By the time

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the overall uniform elongation has attained a value of approximately 30%, the large-grain CGs have accumulated large numbers of twin boundaries, dislocations and subgrain boundaries, such that their microstructure is refined to a level similar to that of the UFG matrix (Fig. 13.20 (b) ). Beyond this point, the post-necking deformation is similar with that of the unimodal UFG metallic materials. Therefore, these results suggest that the presence of a heterogeneous microstructure is required to attain good combination of both high strength and high ductility. Recently, Lee et al.30 investigated deformation and fracture mechanisms of a bimodal Al-Mg alloy containing 30% volume fraction of CGs prepared by cryomilling and subsequent powder consolidation techniques. The microstructures of the bimodal Al-Mg alloy are shown in Fig. 13.11. Room temperature tensile studies show a good balance between strength and ductility for the bimodal sample in comparison with the results for the unimodal UFG and CG counterpart metallic materials (Fig. 13.21). As shown in the inset fracture end cross-section in Fig. 13.21, the unimodal UFG sample exhibits a fully flat fracture and involves a brittle transgranular shear type separation, caused by incomplete bonding and possibly by the presence of some processing artifacts due to consolidation processing.

13.21  Tensile stress–strain curves of bimodal Al-Mg alloy with 30% volume fraction of CGs compared with unimodal UFG and CG counterparts.30 The insets are cross-sectional SEM images of tensilefractured specimens of the CG (upper one) and bimodal (lower one) Al-Mg alloys. Arrows indicated the extrusion and tensile directions.

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13.22  Void initiation in (a) schematic, (b) SEM and (c, d) TEM images.30

The fracture surface cross-section of the bimodal sample shows a mixed fracture mode: large shear lips with a flat central region. Scanning electron microscopy (SEM) revealed that voids near the tensile fracture surfaces tended to initiate both in the UFG matrix as well as at the UFG and CG interfaces (Fig. 13.22 (b)). TEM observations further revealed small voids of about 50 to 300 nm at the UFG region and at the interface of CG and UFG regions (Fig. 13.22 (c, d)). Lee et al.30 explained the above results as follows. Under tensile loading, the constrained ductile CG regions first undergo yielding and plastically deformed without fracture while the UFG matrix carried most of the tensile load elastically.105 As the load continued to increase, the strong UFG regions plastically deformed very briefly after yielding at a higher stress. The stress concentration in the UFG matrix due to yielding may be relaxed by void generation and growth and by transferring local loads to the softer CG regions. Moreover, the stress mismatch between the UFG and CG regions also increases with increasing quasi-static loading105 and leads to initiation of interfacial voids.

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13.23  (a, b) Schematic and SEM micrograph of crack blunting of the UFG at the CG region. (c, d) Deflecting and branching of a longitudinal crack in CG by schematic and SEM image.30

Lee et al.30 also observed evident cracks in the UFG 5083 matrix which were apparently arrested by the ductile CG regions. Figure 13.23 (a, b) shows a schematic of the crack blunting mechanism together with an SEM image of a similarly blunted crack in the UFG matrix sandwiched by CG bands. Figure 13.23 (c) shows a schematic of a crack that grew into a CG region, branched, and then stopped. A similar crack configuration was observed by SEM (Fig. 13.23 (d)). These results indicate that crack propagation in the UFG regions tend to arrest at the CG regions, and interface voids appear to coalesce by transgranular-shear type separation and remain in the UFG regions. The ductile CG region may sustain additional plastic deformation beyond that of the UFG regions. Figure 13.24 (a, b) illustrates a process by which CG bands can bridge cracks and inhibit abrupt fracture. Note also that interface delamination between UFG and CG regions perpendicular to the fracture plane is evident in Fig. 13.24 (c, d) at the regions near fractures. These results suggest that large deformation occurs at the interface during crack nucleation and propagation. In addition, the necking deformation and dimple morphology that are also observed in the CG regions

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13.24  (a, b) Schematic and SEM image of crack bridging and branching of CG. (c, d) Interface delaminating and extensive plastic deformation of CG.30

indicate significant deformation in the CG regions via a ductile bridging mechanism (Fig. 13.25).48 Compression Billard et al.18 performed a careful investigation on deformation and fracture mechanisms of bimodal Al under compression. The fully dense bimodal Al was prepared by hot isostatic pressing of commercial purity Al nano-powders at 550°C under a pressure of 200 MPa for 600 min. As shown in Fig. 13.26, a proportion of microcrystalline grains (>1 µm) are embedded in UFG matrix with a mean grain size of 150 nm. Some of the CGs contain few dislocations (d) and/or a fine dispersion of γ-Al2O3 (p). Room temperature compressive testing, as shown in Fig. 13.27, revealed the high yield strength of 440 MPa and a total strain of 20%. Contrasting with the large strain hardening in bimodal Cu as observed by Wang et al.,17 a very short strain hardening followed the elastic domain, then a plateau of the stress can be seen and is subsequently followed by linear work softening (beginning at 10% of true strain).

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13.25  Fractography of the bimodal Al-Mg alloys with (a) 15% and (b) 30% volume fraction of CGs.48

After mechanical testing, one main crack appears, forming an angle of 45° ± 10° with the compression axis (Fig. 13.28). Some coarse grains have been intersected by the crack and these grains act as blunting obstacles, which provide support to the explanation on the improved ductility by CGs by Lee et al.30 Careful observation on the CGs revealed one or two slip systems, depending on the grain orientation (Fig. 13.28 (b)). This result illustrates an intense

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13.26  Bright-field TEM images showing (a) micrometer-sized (mc) grains embedded in UFG matrix and (b) one mc grain containing a fine dispersion of second-phase particles (p) and individual dislocations (d) that are pinned by the dispersoids.18

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13.27  True stress–strain curves of both bimodal (ufg Al) and mc Al tested at room temperature by compression.18

plasticity-based dislocation activity inside the CGs. Post-mortem TEM observation further revealed that the CGs without the fine oxide dispersion were subdivided into equiaxed subgrains delimited by dense dislocation walls (Fig. 13.29 (a)). The subgrain interior is dislocation free, suggesting the occurrence of a dynamic reorganization process. This dislocation arrangement is typical of high stacking fault energy face-centered cubic metallic materials, which were subjected to large-scale deformation.106 For the CGs containing a fine dispersion of oxide phases, dislocations were pinned by obstacles and in some cases cut through by leaving small loops (Fig. 13.29 (b)). Twinning was not observed in the deformed CGs. As for the UFG matrix, deformation occurs within ‘band’ that are homo­ geneously distributed throughout the matrix (Fig. 13.30 (a)). Figure 13.30 (b) is a closer view of a band in the deformed UFG matrix by atomic force microscopy (AFM) technique. The traces of the two band systems are oriented at 55° and 60° to the compression axis. These features were interpreted as large groups of grains that are emerging from inside the sample, and roughly oriented along planes of

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13.28  SEM images of the surface of bimodal Al compressive specimen showing (a) a primary crack (B) stopped by a CG grain, and (b) multiple slip in a large grain as a consequence of extensive dislocation activity.18

maximum shear.18 Similar deformation shear bands were reported by Fan et al.28 in a study involving compression testing of a bimodal Al-Mg alloy. The above experimental and numerical results provide some insight into the deformation and fracture mechanisms that are activated in both UFG and CG regions, as well as UFG/CG interfaces of bimodal metallic materials, and reasonable explanations on both good and poor combinations of strength and ductility of bimodal metallic materials. Furthermore, they suggest that the factors required for attaining a combination of strength and ductility include: processing artifact-free metallic materials, uniform distribution of CGs in an UFG matrix, strong interfacial bonding between CG and UFG regions. However, inspection of the published literature also shows that systematic information on the precise mechanisms that govern microstructure evolution (such as grain orientation, for example) in the UFG region in bimodal metallic materials during large plastic

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13.29  Post-mortem TEM images showing deformation microstructures of CGs embedded in the UFG matrix. (a) Dislocation-free cell, and (b) dislocation pinning (arrowed).18

deformation remain poorly understood. For example, key questions such as how is deformation in the UFG region related to plastic flow in the CG regions, will require additional experimental and theoretical studies.

13.3.3 Deformation and fracture mechanisms of multimodal metallic materials Interestingly, there appears to be an almost complete absence of experimental studies focused on the deformation and fracture mechanisms that are active in multimodal metallic materials. There are, however, several numerical studies available, and these are discussed in the section that follows.

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13.30  (a) SEM image showing deformation patterns of the UFG matrix after 20% compression strain. Two sets of symmetrical bands are visible and marked by dashed lines. (b) AFM topographic image of the surface of a deformed UFG matrix showing a 25 µm wide and stepped band.18

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On the basis of a self-consistent approximation, Liu et al.107 performed a numerical study on the deformation and fracture behavior of nanocrystalline metallic materials with a multi-scale grain size distribution. They generated the multi-scale metallic materials following a log-normal grain size distribution. The average grain size is 23 nm with a standard variation of 100. Figure 13.31 (a) shows the numerical results of local strain status less than 5% macroscopic strain.

13.31  The status of local von Mises equivalent strains (a) and their grain size dependence (b) under uniaxial tensile at a macro von Mises equivalent strain of 5%.107

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The local strains are grain size dependent, and they are non-uniform with various grain sizes. Figure 13.31 (b) shows the plastic strains (subjected to tension) of grains with different grain sizes under macroscopic strain rate of 10–3 s.–1 It is evident that under these conditions plastic deformation of the multi-scale metallic materials is not homogeneous. The local strains of the grains smaller than 20 nm are higher than those corresponding to the overall grain size, indicating grain boundary mediated deformation mechanisms when the grain size decreases to a critical value. The local strain of grains larger than 40 nm increases with increasing grain size, and such an increasing tendency is consistent with the dislocation mediated deformation mechanisms that were discussed previously. Based on the theory that nanocracks nucleate at the interface between adjacent grains, Liu et al. explored the fracture behavior of multi-scale metallic materials. Figure 13.32 shows the behavior of fracture nucleation and plastic flow process under mechanical loading. During the early stages of loading, nanovoids are generated at the interface with relatively high local strains (a). With increasing plastic flow, more and more new nanovoids appear as a result of stress concentration. The initially formed nanovoids grow larger (b). The large nanovoids gradually transform into microvoids (c). At the same time, plastic flow is localized and gives rise to the necking formation (b and c). Subsequently, ductile fracture occurs through coalescence of microvoids (d). In related numerical studies, Raeisinia et al.55 comparatively studied the evolution of local strain and stress fields in UFG metallic materials with a mean grain size of 700 nm and different grain size distributions, and CG metallic materials with a mean of 10 µm and a wide grain size distribution, as shown in

13.32  Predicted ductile fracture in nanocrystalline metallic materials with (a) formation of nanovoids (b) growing of nanovoids and formation of local necking with stress concentration (c) formation of microvoids (d) coalescence of microvoids.107

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13.32  Continued.

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Fig. 13.33. For these plots, the grains of each polycrystal were divided into size classes and the volume-weighted average of the equivalent stress and strain of the grains in each of these classes was calculated at different deformation steps. The ratio of this value to the macroscopic equivalent stress and strain is plotted. The deformation of polycrystal with the narrow grain size distribution is more homogeneous, and this homogeneity increases as deformation progresses. The UFG grains of the polycrystal with wider grain size distribution tend to deform less and are under more stress than the average. As deformation advances, the polycrystals become less heterogeneous causing the strains and stresses in the grains to approach the far field average values. The polycrystal with the larger mean grain size loses this heterogeneity faster than the polycrystal with smaller mean grain size. In summary, the above available numerical studies, despite their inherent assumptions and limitations, provide valuable insight into the deformation and fracture processes in multimodal metallic materials. That is, plastic deformation of the multimodal metallic materials is not homogeneous. In case of multimodal metallic materials with a mean grain size smaller than 100 nm, the local strains of both small and large grains are higher than those corresponding to medium-sized grains. In the case of multimodal metallic materials with a mean grain size larger

13.33  Predicted local relative von Mises equivalent stresses (bottom row) and strains (top row) as a function of grain size for three model polycrystals at three different stages of deformation corresponding to macro von Mises equivalent strain of 0.01, 0.10 and 0.50. The mean grain size and grain size distribution width (σ0/µ) are indicated in the figures.55

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than 100 nm, the small grains tend to deform less and are under more stress relative to the conditions experienced by the average-sized grains. Clearly, experimental studies that can provide some degree of experimental verification are needed.

13.4 Future trends The discussion presented in the above sections confirms that, in terms of the strength–ductility space, both UFG and CG metallic materials are located at the two extreme poles, whereas multi-scale metallic materials tend to populate the central regime. Multi-scale metallic materials are of interest from both technological and fundamental perspectives. That is, in comparison with the behavior of unimodal UFG and CG metallic materials, multi-scale metallic materials offer improved combinations of strength and ductility and therefore, provide a pathway that should be exploited for technological applications that require toughness. In comparison with UFG metallic materials with more than 30 years of history, multi-scale metallic materials represent a relatively new class, only approximately 10 years old. From a fundamental perspective, multi-scale metallic materials pose many interesting questions. For example, our knowledge of the mechanisms that govern the synthesis and behavior of multi-scale metallic materials is in its infancy, and phenomena such plasticity mechanisms, thermal stability, fatigue properties,29,47,108 and dynamic properties of multi-scale metallic materials will require extensive additional studies.

13.5 Conclusions Since initially reported in the year 2000, multi-scale grain size distributions are emerging as an effective strategy to improve the poor ductility of nanostructured and ultrafine-grained metallic materials. This chapter has mainly concentrated on mechanical behavior, deformation and fracture mechanisms of bulk multi-scale metallic materials. In addition, the chapter introduced the basic concepts, development background and history as well as preparation methods of multiscale metallic materials in the introduction part. Finally the chapter discussed the potential technological implications and future investigations of this material. Compared with unimodal ultrafine-grained and coarse-grained counterparts, multi-scale metallic materials (including bimodal and multimodal metallic materials) have a better combination of strength and ductility. If we designate the strength–ductility combination complying with the rule-of-mixtures as neutral combination, both positive (i.e. improved) and negative (i.e. diminished) deviations from the rule-of-mixtures have been reported experimentally for bimodal metallic materials, which might be caused by the inherent challenge to synthesize ideal samples that are defect-free and contain a priori design of

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multi-scale grain size distributions. Numerical studies on bimodal metallic materials predict both neutral and improved combination of strength and ductility, which can be attributed in part to the various assumptions made in the development of the numerical models. Therefore, systematic investigations are necessary to quantitatively reveal the mechanical properties and microstructure relationships of multi-scale metallic materials from both experiments and simulations. The results of deformation and fracture mechanisms of bimodal metallic materials reasonably explained the positive and negative strength–ductility combinations. They also suggest that the factors required for attaining a balance of strength and ductility include: processing artifact-free metallic materials, uniform distribution of CGs in an UFG matrix, strong interfacial bonding between CG and UFG regions. However, systematic studies on the precise mechanisms that govern microstructure evolution in the UFG region in bimodal metallic materials during large plastic deformation are still necessary.

13.6 Acknowledgements Y.H. Zhao and E.J. Lavernia would like to acknowledge supports by the Office of Naval Research (Grant number N00014-08-1-0370) with Dr. Lawrence Kabacoff as program officer, and the Army Research Laboratory (W911NF-08-2-0028).

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54 Malygin G.A. Phys Solid State 2008; 50: 1056. 55 Raeisinia B., Sinclair C.W., Poole W.J., Tome C.N. Modelling Simul Mater Sci Eng 2008; 16: 025001. 56 Sano T., Rohrer G.S. J Am Ceram Soc 2007; 90: 211. 57 Laws V. J Mater Sci Lett 1983; 2: 527. 58 Prasad M.J.N.V., Suwas S., Chokshi A.H. Mater Sci Eng A 2009; 503: 86. 59 Valiev R.Z., Isamgaliev R.K., Alexandrov I.V. Prog Mater Sci 2000; 45: 103. 60 Kurzydlowski K.J. Scr Metall Mater 1990; 24: 879. 61 Morita T., Mitra R., Weertman J.R. Mater Trans 2004; 45: 502. 62 Zhu B., Asaro R.J., Krysl P., Zhang K., Weertman J.R. Acta Mater 2006;54: 3307. 63 Masumura R., Hazzledine P.M., Pande C.S. Acta Mater 1998; 46: 4527. 64 Phaniraj M.P., Prasad M.J.N.V., Chokshi A.H. Mater Sci Eng A 2007; 463: 231. 65 Chokshi A.H., Rosen A., Karch J., Gleiter H. Scripta Metall 1989; 23: 1679. 66 Shen T.D., Schwarz R.B., Feng S., Swadener J.G., Huang J.Y., Tang M., Zhang J., Vogel S.C., Zhao Y. Acta Mater 2007; 55: 5007. 67 Yamakov V., Wolf D., Phillpot S.R., Mukherjee A.K., Gleiter H. Nature Mater 2002; 1: 45. 68 Schiøtz J., Jacobsen K.W. Science 2003; 301: 1357. 69 Lu L., Chen X., Huang X., Lu K. Science 2009; 323: 607. 70 Cheng S., Spencer J.A., Milligan W.W. Acta Mater 2003; 51: 4505. 71 Swygenhoven H. Van, Derlet P.M.. Phys Rev B 2001; 64: 224105. 72 Moldovan D., Wolf D., Phillpot S.R. Acta Mater 2001; 49: 3521. 73 Swygenhoven H. Van. Science 2002; 296: 66. 74 Gutkin Y.M., Ovid’ko I.A., Skiba N.V. Acta Mater 2003; 51: 4059. 75 Shan Z., Stach E.A., Wiezorek J.M.K., Knapp J.A., Follstaedt D.M., Mao S.X. Science 2004; 305: 654. 76 Jin M., Minor A.M., Stach E.A., Morris J.W. Acta Mater 2004; 52: 5381. 77 Yamakov V., Wolf D., Phillpot S.R., Mukherjee A.K., Gleiter H. Nature Mater 2004; 3: 43. 78 Chinh N.Q., Szommer P., Horita Z., Langdon T.G. Adv Mater 2006; 18: 34. 79 Gianola D.S., Petegem S. Van, Legros M., Brandstetter S., Swygenhoven H. Van, Hemker K.J. Acta Mater 2006; 54: 2253. 80 Legros M., Gianola D.S., Hemker K.J. Acta Mater 2008; 56: 3380. 81 Wang Y.B., Li B.Q., Sui M.L., Mao S.X. Appl Phys Lett 2008; 92: 011903. 82 Wang Y.B., Ho J.C., Liao X.Z., Li H.Q., Ringer S.P., Zhu Y.T. Appl Phys Lett 2009; 94: 011908. 83 Rupert T.J., Gianola D.S., Gan Y., Hemker K.J. Science 2009; 326: 1686. 84 Cheng S., Zhao Y.H., Guo Y., Li Y., Wei Q., Wang X.L., Ren Y., Liaw P.K., Choo H., Lavernia E.J. Adv Mater 2009; 21: 5001. 85 Pan D., Kuwano S., Fujita T., Chen M.W. Nano Lett 2007; 7: 2108. 86 Zhao Y.H., Guo Y.Z., Wei Q., Dangelewicz A.M., Xu C., Zhu Y.T., Langdon T.G., Zhou Y.Z., Lavernia E.J. Scripta Mater 2008; 59: 627. 87 Zhao Y.H., Guo Y.Z., Wei Q., Troy T.D., Dangelewicz A.M., Zhu Y.T., Langdon T.G., Lavernia E.J. Mater Sci Eng A 2009; 525: 68. 88 Sergueeva A.V., Mukherjee A.K. Rev Adv Mater Sci 2006; 13: 1. 89 Sergueeva A.V., Mara N.A., Mukherjee A.K. J Mater Sci 2007; 42: 1433. 90 Sergueeva A.V., Mara N.A, Valiev R.Z., Mukherjee A.K. Mater Sci Eng A 2005; 410–411: 413.

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91 Sabirov I., Estrin Y., Barnett M.R., Timokhina I., Hodgson P.D. Acta Mater 2008; 56: 2223. 92 Vinogradov A., Hashimoto S., Patlan V., Kitagawa K. Mater Sci Eng A 2001; 319–321: 862. 93 Liao X.Z., Zhao Y.H., Zhu Y.T., Valiev R.Z., Gunderov D.V. J Appl Phys 2004; 96: 636. 94 Liao X.Z., Zhao Y.H., Srinivasan S.G., Zhu Y.T., Valiev R.Z., Gunderov D.V. Appl Phys Lett 2004; 84: 592. 95 Wu X.L., Zhu Y.T. Appl Phys Lett 2006; 89: 3. 96 Wu X.L., Ma E. Appl Phys Lett 2006; 88: 3. 97 Wu X.L., Zhu Y.T. Phys Rev Lett 2008; 101: 4. 98 Kumar K.S., Suresh S., Chisholm M.F., Horton J.A., Wang P. Acta Mater 2003; 39: 3257. 99 Kumar K.S., Swygenhoven H. Van, Suresh S. Acta Mater 2003; 51: 5743. 100 Cheng S., Ma E., Wang Y.M., Kecskes L.J., Yousef K.M., Koch C.C., Trociewitz U.P., Han K. Acta Mater 2005; 53: 1521. 101 Yousef K.M., Scattergood R.O., Murty K.L., Koch C.C. Appl Phys Lett 2005; 87: 091904. 102 Ovid’ko I.A., Sheinerman A.G. Rev Adv Mater Sci 2007; 16: 1. 103 Zhao Y.H., Li Y., Topping T.D., Liao X.Z., Zhu Y.T., Valiev R.Z., Lavernia E.J. Int J Mater Res 2009; 100: 1647. 104 Gao H.J., Huang Y. J Mech Phys Solids 1999; 47: 1239. 105 Lee Z., Lee J., Lavernia E.J., Nutt S.R. MRS Symp Proc 2004; 821:9. 11. 106 Dirras G.F., Duval J.L., Swiatnicji W. Mater Sci Eng A 1999; 263: 85. 107 Liu Y.G., Zhou J.Q., Ling X. Mater Sci Eng A 2010; 527: 1719. 108 Simchi H., Simichi A. Mater Sci Eng A 2009; 507: 200.

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14 Enhanced ductility and its mechanisms in nanocrystalline metallic materials I.A. OVID’KO, Russian Academy of Sciences, Russia Abstract: This chapter summarizes the considerable information now available on tensile ductility, from recent experiments, computer simulations and theoretical models addressing enhanced tensile ductility at room temperature and its mechanisms in single-phase and composite nanocrystalline metallic materials. Particular attention is paid to optimizing the strength and tensile ductility of nanocrystalline metals, with the sensitivity of these mechanical characteristics to specific structural features taken into account. Key words: nanocrystalline metals, ductility, deformation, fracture.

14.1 Introduction Nanocrystalline (nano-grained) metallic materials show the outstanding mechanical properties opening a range of new structural applications.1–10 These outstanding properties are due to the interface and nanoscale effects associated with structural peculiarities of nanocrystalline materials where the volume fraction occupied by grain boundaries is extremely large, and grain size does not exceed 100 nm. Nanocrystalline metallic materials commonly exhibit superior strength and hardeness that are 2–10 times larger than those of their coarsegrained counterparts.1–10 However, in most cases, nanocrystalline metallic materials show superior tensile strength and hardeness at the expense of low tensile ductility, which significantly limits their applications. At the same time, there are several examples of substantial tensile ductility11–30 of super-strong nanocrystalline metallic materials at room temperature. (Besides, nanocrystaline metallic materials can exhibit superplasticity at higher flow stresses, higher strain rates and lower temperatures, compared to those characterizing superplasaticity of microcrystaline metallic materials with the same chemical composition; for a review, see Mukherjee31.) Nanocrystalline metallic materials with unique combinations of very high strength and good ductility at room temperature could be considered to be ideal materials for a wide range of applications in aerospace and automotive industries, medicine, energy, sport products, etc. In order to investigate the fundamental science of nanostructured materials and develop them for high-technology applications, it is very important to understand the underlying micromechanisms of enhanced ductility in nanocrystalline metallic structures, as experimentally revealed examples11–30 take into consideration. The main aim of this chapter is to give a brief overview of key concepts (based on experimental 430 © Woodhead Publishing Limited, 2011



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data, computer simulations and theoretical models) on ductility of nanocrystalline metallic materials. Particular attention will be paid to the sensitivity of the tensile ductility of nanocrystalline metallic materials to their specific structural features.

14.2 General aspects concerning the tensile ductility of materials Tensile ductility of a solid is controlled by competition between plastic deformation and fracture processes as well as its resistivity to plastic flow localization. In general, fracture processes involve nucleation, growth and coalescence of cracks/ voids in a solid, causing its separation into two or more pieces under the action of mechanical stress. On the other hand, brittle fracture occurs without apparent plastic deformation, in a dramatic way involving fast nucleation of cracks, their convergence and/or growth of a large brittle crack. These processes are also called brittle crack nucleation and propagation instabilities, and they result in low tensile ductility of solids. In nanocrystalline materials specified by large volume fractions occupied by grain boundaries and their triple junctions, brittle cracks tend to nucleate and grow along grain boundaries (Fig. 14.1); for a review, see Ovid’ko32. The brittle behavior is commonly undesired in materials exploited in structural and other applications. Ductile fracture is preceeded by essential plastic deformation. Ductile fracture behavior is typical for materials (e.g. coarse-grained polycrystalline metals) showing high tensile ductility which is attractive for practical applications. Ductile fracture occurs through a relatively slow nucleation, growth and coalescence of voids (Fig. 14.2), in which case dimpled structures are observed at fracture surfaces. After extended stage of homogeneous deformation, a necking develops, which enhances the growth and coalescence of voids (Fig. 14.2). Besides the slow ductile fracture (Fig. 14.2), fast ductile fracture associated with plastic strain instability can occur in solids under tensile load. In this situation, plastic flow is unstable relative to its dramatic localization in shear bands and neck formation (Fig. 14.3). The neck formation is followed by both stress concentration and fast ductile fracture (through fast nucleation, growth and coalescence of voids) within the neck region (Fig. 14.3). When a plastic strain instability comes into play, a solid shows low tensile ductility characterized by low overall strain-to-failure, though local plastic strain in the neck region is comparatively large, and dimpled structures are observed at fracture surfaces. Most nanocrystalline metallic materials exhibit low tensile ductility at room temperature.1–10 In order to explain the experimental results, one can consider the two key factors that suppress tensile ductility in nanocrystalline materials:10,16,24,33–35 1) brittle crack nucleation and propagation instabilities; and 2) plastic strain instability (dramatic localization of plastic flow). The former factor dominates in nanocrystalline metallic materials with finest grains having grain size d smaller than a critical value dc = 10–30 nm (depending on material and structure © Woodhead Publishing Limited, 2011

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14.1  Brittle fracture in nanocrystalline specimen occurs through fast nucleation of nanoscale flat cracks, their convergence and/or growth along grain boundaries.

characteristics). Plastic strain instability is treated to be the main factor causing low tensile ductility of nanocrystalline metallic materials with intermediate grains (grain size ranging from dc to 100 nm). For nanocrystalline materials, the crack nucleation instability means that plastic flow is suppressed in a nanocrystalline specimen characterized by high strength, and the applied stress rapidly reaches the level close to the critical stress needed to initiate cracks near local stress sources/concentrators. Such ‘dangerous’ stress sources/concentrators are either fabrication-produced flaws or defects generated due to very limited, local plastic deformation. The crack propagation instability is related to the fact that the conventional toughening mechanisms (first of all, lattice dislocation emission from crack tips) are suppressed in brittle nanocrystalline materials, which thereby show low resistivity to crack growth. When a nanoscale

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14.2  Ductile fracture occurs through a relatively slow nucleation, growth and coalescence of voids. Neck formation, after extended homogeneous deformation, may accompany growth and coalescence of voids.

14.3  Plastic strain instability in specimen under tensile load.

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crack nucleates in a brittle nanocrystalline solid, its growth cannot be effectively blunted through lattice dislocation emission at the crack tip.36 As a corollary, the crack with its sharp tip (which provides high stress concentration) rapidly grows and transforms into a catastrophic crack. The brittle crack nucleation and propagation instabilities are typically responsible for the low tensile ductility that exists in nanocrystalline metallic materials with the finest grains. Plastic strain instability (dramatic localization of plastic flow in shear bands and neck formation; see Fig. 14.2) in a solid occurs in the absence of the pronounced strain-hardening and strain rate hardening. The onset of necking is followed by fast ductile fracture occurring through fast nucleation, growth and coalescence of voids within the neck region (Fig. 14.2). In these circumstances, dimpled structures (with dimple sizes being much larger than grain size) are observed at fracture surfaces. As shown in many experiments, the deformation behavior associated with plastic strain instability is typical for most ultrafinegrained materials (with grain size ranging from 100 to 300 nm) and nanocrystalline metallic materials with intermediate grains (with grain size ranging from dc to 100 nm).16,24 In terms of the macroscopic characteristics (flow stress σ, . plastic strain degree ε, plastic strain rate ε) of plastic deformation of a solid under tensile load, its resistivity relative to the necking is described by Hart’s criterion:16,24

σ –1(∂σ/∂ε) ε. + m > 1.

[14.1]

The first term on the left-hand side of Hart’s criterion [14.1] describes the strainhardening, and m is the strain rate sensitivity (or strain rate hardening) defined as: . m = {∂ log σ /∂ ln ε}ε,T. [14.2] If Hart’s criterion [14.1] is valid, a solid under tensile load is stable relative to the necking. Commonly Hart’s criterion [14.1] in nanocrystalline metallic materials with intermediate grains is violated, and these materials are not stable against the necking.16,24 At the same time, there are several examples of enhanced tensile ductility of nanocrystalline metals,11–30 in particular, those with intermediate grains. In most nanocrystalline metallic materials with good ductility, the crucial suppression of plastic strain instability is due to strain hardening, while the role of strain rate hardening (characterized by m) is negligibly small. Thus, nanocrystalline metals are capable of exhibiting good tensile ductility when plastic strain, crack nucleation and propagation instabilities are suppressed in the metals. In order to understand the origin of these instabilities in nanocrystalline metallic materials, it is very important to identify the grain size effects on plastic flow and fracture mechanisms operating in these materials. Sections 14.3–14.5 briefly discuss the specific features of plastic flow and fracture mechanisms in nanocrystalline materials with a particular attention being paid to their sensitivity to the grain size.

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14.3 Plastic flow mechanisms in coarse-grained metallic polycrystals, ultrafine-grained metals and nanocrystalline metals with intermediate grains First, let us discuss the effects of grain size on plastic flow mechanisms operating in coarse-gained polycrystalline, ultrafine-grained and nanocrystalline metallic materials with intermediate grains. It is well known that the dominant deformation mechanism in conventional coarse-grained polycrystalline metals is lattice dislocation slip occurring in the large grain interiors.37 Its carriers are perfect lattice dislocations generated and stored in the form of dislocation cells/subgrains in the grain interiors during plastic deformation. Grain boundaries serve as obstacles for the movement of lattice dislocations, in which case they influence the level of the yield stress. This effect of grain boundaries in coarse-grained polycrystalline metals is described by the following classical Hall–Petch relationship between the yield stress τ and grain size d:38,39

τ = τ0 + kd –1/2,

[14.3]

with τ0 and k being constant parameters. However, in general, the mechanical behavior of coarse-grained polycrystalline metals is crucially affected by evolution of lattice dislocations in grain interiors, but not grain boundaries. For instance, the deformation-induced storage of lattice dislocations in grain interiors in coarsegrained polycrystalline metals is responsible for strain hardening. It means that the flow stress increases with rising plastic strain. This standard deformation behavior is exhibited by most coarse-grained polycrystalline metals with grain size d being larger than 300 nm. With grain refinement, the lattice dislocation slip shows deviations from its standard behavior due to both the nanoscale grain size and grain boundary effects. For illustration, let us consider ultrafine-grained metals (d ranges from 100 to 300 nm) and nanocrystalline metallic materials with intermediate grains (d ranges from dc to 100 nm). The lattice dislocation slip is still dominant in such materials. However, in contrast to the situation with conventional coarse-grained polycrystals, lattice dislocations are not intensively stored in grain interiors. In ultrafine-grained metals and nanocrystalline metallic materials with intermediate grains, the flow stress is crucially affected by the dislocation storage and annihilation at grain boundaries.16 The lattice dislocations are generated and move under the applied stress within the grain interiors. Then the lattice dislocations reach grain boundaries where they are transformed into grain boundary dislocations. This process leads to the dislocation storage at grain boundaries. The dislocation storage provides the strain hardening of a metallic material during plastic deformation. At the same time, grain boundary dislocations with opposite Burgers vectors tend to move towards each other and annihilate each other (when they meet). The dislocation annihilation at grain boundaries provides the strain softening (decrease in the flow stress with rising plastic strain) of a material during plastic deformation. Following

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Wang et al.,16 after some initial stage of deformation, the above opposing reaction rates reach an equilibrium by canceling each other. That is, such an equilibrium causes a steady state in which the dislocation generation rate is completely compensated by the dislocation annihilation rate. The steady state is characterized by an approximately constant flow stress, in which case strain hardening of the material during plastic deformation is practically absent. In this circumstance, the first term on the left-hand side of Hart’s criterion [14.1] is approximately 0. The conventional lattice dislocation slip typically results in the strain rate sensitivity m less then 0.1. Therefore, in nanocrystalline metallic materials with intermediate grains deformed by mostly the lattice dislocation slip, Hart’s criterion [14.1] is violated, and these materials under tensile load are unstable leading to the necking (Fig. 14.2). As shown in many experiments, this deformation behavior is typical for most ultrafine-grained materials and nanocrystalline materials with intermediate grains.16

14.4 Plastic flow mechanisms in nanocrystalline metals with the finest grains In nanocrystallin e metallic materials with finest grains (with grain size lower than dc = 10–30 nm), the lattice dislocation slip is very limited or even completely suppressed,1–10 because of the two factors. First, grain boundaries (of which there are many) stop gliding lattice dislocations in nanocrystalline materials. Second, the generation of dislocations by Frank–Read and other sources in nanoscale grains requires extremely high stress, which may initiate cracks.7 At the same time, alternative deformation modes such as grain boundary sliding, Coble creep, triple-junction diffusional creep, rotational deformation and nanoscale twin deformation effectively operate in nanocrystalline metals.1–10 Of primary importance to the ductility of nanocrystalline metallic materials with finest grains is the role of grain boundary sliding in plastic flow. This deformation mode means a relative shearing of neighboring grains, which is localized in the boundary between the grains. Since grain boundaries end at triple junctions, such junctions serve as natural geometric obstacles for grain boundary sliding. In this situation, the unfinished plastic shear (or, in terms of grain boundary dislocations, the dislocation Burgers vector) associated with grain boundary sliding is accumulated at triple junctions, which thereby serve as stress sources. There are several ways to accommodate of the unfinished plastic shear at the triple junctions in nanocrystalline materials: the emission of lattice dislocations from triple junctions (Fig. 14.4), diffusional accommodation, rotational deformation and void formation (Fig. 14.4 (c) ).40–46 The emission of lattice dislocations from triple junctions seems to be a rather widespread process in various nanocrystalline materials.45,46 Grain boundary sliding accommodated by such a dislocation emission process is characterized by creep strain rate:45,46

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437 [14.4]

where b denotes the lattice parameter, τ the applied shear stress, M the stress concentration factor (at triple junction), kB Boltzmann’s constant, and T the absolute temperature. Following papers,45,46 equation [14.4] is valid in a wide temperature interval, including room and ambient temperatures. (At the

14.4  Grain boundary sliding and its accommodation through lattice dislocation emission from triple junctions. (a) Grain boundary sliding occurs through the movement of grain boundary dislocations along grain boundaries. Grain boundary dislocations are accumulated near triple junctions. (b) Grain boundary dislocations transform into lattice dislocations that are emited from triple junction B and glide within grain I. These processes are accompanied by formation of dipole of wedge disclinations (full and open triangles) A and B. (c) The lattice dislocations reach grain boundary CD where they transform into grain boundary dislocations that climb along this grain boundary. The distance between wedge disclinations A and B increases due to grain boundary sliding. (d) The distance between wedge disclinations A and B increases more due to grain boundary sliding. Nanocrack nucleates in the stress field of the dipole of wedge disclinations A and B.

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same time, there is a restriction concerning grain growth that may destroy the nanocrystalline structure. That is, the temperature should be lower than the temperature at which intensive grain growth starts to occur in a nanocrystalline metal.) According to estimates45,46 for nanocrystalline Ni, strain rate sensitivity m is typically lower than 0.05 (except for regimes with extra low strain rate . ε  ≤ 10–8 s–1). Besides, grain boundary sliding produces dipoles of wedge disclinations – defects associated with crystal lattice orientation incompatibilities – at and near triple junctions (Fig. 14.4).47–49 (More precisely, a wedge disclination represents a rotational line defect located at either a grain boundary or a triple junction, and is characterized by the disclination strength or, in other words, the rotational misfit.50 For instance, a wedge disclination at a tilt grain boundary is the line dividing grain boundary fragments with different tilt misorientation angles, whose difference is the disclination strength. A wedge disclination exists at a triple junction of tilt boundaries if the sum of tilt misorientation angles of these boundaries is non-zero.50 The non-zero sum (angle gap) serves as the disclination strength). Figure 14.4 schematically shows formation of wedge disclination dipoles (two connected arrow signs in the figure) due to grain boundary sliding in a nanocrystalline specimen; for more details, see Ovid’ko and Sheinerman.47,49 Following,47,49 wedge disclination dipoles appearing in nanocrystalline metallic materials during grain boundary sliding create very pronounced strain hardening, and this factor can positively influence ductility of such materials (see Section 14.6). Now let us briefly discuss diffusional creep modes operating in nanocrystalline metallic materials with finest grains. The diffusion coefficient Dtj along triple junctions is much larger than the grain boundary diffusion coefficient Dgb,51 which, in its turn, is by several orders larger than the bulk diffusion coefficient Dbulk.52 Also, the volume fractions occupied by triple junctions and grain boundaries rapidly increase (at the expense of the volume fraction occupied by grain interiors) with decreasing the grain size d in nanocrystalline materials53 (Fig. 14.5). In these circumstances, the contributions of Coble creep and triple junction diffusional creep are enhanced with decreasing the grain size d54,55 more rapidly than that of the Nabarro–Herring creep (bulk diffusional creep). This tendency is . . reflected in various strain rates, Nabarro–Herring creep (ε bulk), Coble creep (εgb) . and triple junction diffusional creep (εtj), all of which are grain size dependent: . ε bulk ∝ Dbulk · d –2 σ, . εgb ∝ Dgb · d –3 σ, . εtj ∝ Dtj · d –4 σ, [14.5] where σ is the applied tensile stress. Since the diffusional mass transfer is enhanced with rising temperature, grain boundary and triple-junction diffusional

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14.5  Volume fractions of grain boundaries, triple junctions and interfaces (grain boundaries + triple junctions of grain boundaries + quadruple nodes of triple junctions) as a function of grain size d, for nanocrystalline metals with grain boundary thickness = 1 nm. Source: Reprinted from Scripta Materialia with permission from Elsevier.53

creep modes are capable of significantly contributing to plastic flow in nanocrystalline metallic materials with finest grains at intermediate and high temperatures (Tgbd < T < Tgg, where Tgbd ≈ 0.3 Tm is the minimum temperature at which intensive grain boundary diffusion occurs, Tgg ≈ (0.5–0.6) Tm is the minimum temperature at which intensive grain growth (destroying the nanocrystalline structure) occurs, and Tm is the melting temperature).54,55 Rotational deformation in coarse-grained and nanocrystalline solids is defined as plastic deformation accompanied by crystal lattice rotations within grains.50,56,57 Rotational deformation is commonly carried out by moving dipoles of grain boundary wedge disclinations.50,56,57 Disclination dipole movement in coarsegrained polycrystals occurs through rearrangement of lattice dislocations in grain interiors.50 In nanocrystalline metallic materials where the number of pre-existing lattice dislocations in grain interiors is very limited, rotational deformation occurs through 1) the emission of perfect lattice dislocations from grain boundaries and their absorption at opposite grain boundaries;57 2) stress-driven migration of grain boundaries;58 and 3) slip and climb of grain boundary dislocations.42,59 In the latter case, the rotational deformation can be effectively initiated by preceding grain boundary sliding and serve as its accommodating mechanism.42 The representations on rotational deformation are well supported by experimental observations of crystal lattice rotations within grains in deformed nanocrystalline metallic materials.40,60–64 Partial dislocations that carry partial dislocation slip and twin deformation have been experimentally observed in nanocrystalline metals with finest grains.65–72 In

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particular, pairs of partial dislocations emitted from grain boundaries and connected by wide stacking faults have been experimentally observed in nanocrystalline Al,69 whereas their formation in coarse-grained Al is commonly hampered due to high values of the specific stacking fault energy. The results of these experiments are indicative of the strong nanoscale and interface effects that enhance the partial dislocation slip. Also, twin deformation has been experimentally observed in nanocrystalline metals like Al, Cu, Ni and Ta.65–72 Twin deformation plays an important role, in particular, in nanocrystalline metals deformed at high strain rates and low temperatures, in which case grain boundary sliding and grain boundary diffusion are suppressed. Thus, grain boundary sliding, grain boundary diffusional creep, triple junction diffusional creep, partial dislocation slip, rotational and twin deformation modes effectively operate in nanocrystalline metallic materials with finest grains. These deformation mechanisms are characterized by very high values of the flow stress, which are much larger than those characterizing the lattice dislocation slip in conventional coarse-grained polycrystals and ultrafine-grained materials.1–10 At the same time, super-strong nanocrystalline metals with finest grains commonly show low tensile ductility, in particular, due to crack nucleation and propagation instabilities (Fig. 14.1). In doing so, the nanocrystalline structure is responsible for the action of specific crack nucleation and growth mechanisms operating in nanocrystalline metallic materials. This subject will be considered briefly in the next section.

14.5 Specific features of crack nucleation and growth processes in nanocrystalline metallic materials As it has been mentioned earlier, nanocrystalline metals can exhibit either ductile or brittle fracture behavior, depending on both their structural characteristics and the conditions of mechanical loading. In particular, there are several experimental reports on nanocrystalline metallic materials having an average grain size in the range of around 20 to 100 nm and showing slow ductile fracture with preceding neck formation and dimpled structures at fracture surfaces.18–23,40 The size of the dimples is commonly considerably larger than the grain size, and ductile fracture is believed to occur through the coalescence of microvoids. At the same time, there are nanocrystalline metallic materials showing the brittle fracture. For instance, nanocrystalline Ni-15%Fe alloy with an average grain size of around 9 nm under tensile test at room temperature18,19 and nanocrystalline Ni specimens with an average grain size of around 30 nm under fatigue test (tension–tension cyclic deformation) at room temperature73 exhibit intergranular brittle fracture. In these cases, the main brittle crack is believed to be formed through the multiple generations of intergranular nano/micro-scale cracks and their convergence.

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Brittle and ductile fracture processes in nanocrystalline metallic materials are crucially influenced by their structural features: nanoscale sizes of grains and large amounts of grain boundaries. In particular, grain boundaries serve as preferable places for nanocrack nucleation and growth because the atomic density is low, and interatomic bonds are weak at grain boundaries compared to the grain interior. In the case of ductile fracture carried by microvoid growth and coalescence in nanocrystalline metals, the microvoid growth by vacancy diffusion mechanism is enhanced in nanocrystalline metals due to the large amounts of grain boundaries characterized by high diffusivity. Besides, the extra energy of grain boundaries contributes to the driving force for intergranular fracture with cracks propagating along such boundaries and releasing the extra energy, compared to intragranular fracture with cracks propagating through grain interiors. At the same time, grain boundaries are short and curved at numerous triple junctions in nanocrystalline metallic materials. Therefore, if cracks tend to nucleate and grow along grain boundaries, crack propagation can be deflected from the axis of highest stress to less efficient orientations directed by curved grain boundary surfaces. This leads to increased fracture energy through increased fracture surface area and lower driving forces due to the reduced resolved normal stresses at the crack tip as a result of the deflection of the crack tip away from the most efficient (Mode I) loading orientation. As was noted in Section 14.4, plastic deformation in nanocrystalline metallic materials with finest grains occurs at very high stresses, and grain boundary sliding serves as one of its dominant deformation mechanisms. In the context discussed, one expects that crack nucleation and growth processes in nanocrystalline metals with finest grains are influenced by grain boundary sliding. This statement is confirmed by experiments, computer simulations and theoretical models. In particular, it was theoretically revealed that the enhanced generation of nanocracks in deforming nanocrystalline materials with finest grains can occur at triple junctions with defects produced by intergrain sliding, such as dislocations,43–46 disclination dipoles47,49 (Fig. 14.4 (c) ) and dislocation– disclination configurations48 serving as dangerous stress concentrators. Such nanocracks in the vicinities of triple junctions have been observed by Kumar et al. in in situ experiments using nanocrystalline Ni with an average grain size of around 30 nm.40 Also, molecular dynamics simulations74 show nanocracks being generated at triple junctions of grain boundaries near tips of pre-existing large cracks in nanocrystalline Ni with grain size ranging from 5 to 12 nm. With these experimental data, computer simulations and theoretical results, one expects that nanocracks at triple junctions of grain boundaries serve as typical elemental carriers (plate-like cracks of smallest size) of brittle fracture in nanocrystalline metallic materials with finest grains. Also, the unique structural features (nanoscale sizes of grains and large amounts of grain boundaries) of nanocrystalline metallic materials cause the specific features of crack growth in these materials. In most cases, super-strong

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nanocrystalline materials are characterized by low tensile ductility and low fracture toughness at room temperature.1–10 In particular, some nanocrystalline face-centred cubic (fcc) metals exhibit a ductile-to-brittle transition with decreasing grain size.18,19,23 In contrast, good ductility is typically inherent to coarse-grained fcc metals where the emission of lattice dislocations from cracks causes effective crack blunting and thus suppresses their growth. In the light of the discussed difference in the fracture behavior between nanocrystalline and coarse-grained fcc metals, of particular interest is the nature of the sensitivity of the crack-blunting process to nanocrystallinity. In paper,36 a theoretical model was suggested in describing the grain size effect on crack blunting through the emission of lattice dislocations from cracks in nanocrystalline metallic materials (Fig. 14.6 (a) and 14.6 (b) ). Within this model, grain boundaries serve as structural elements that hinder the movement of lattice dislocations emitted from cracks and thereby the blunting of cracks in nanocrystalline materials. In these circumstances, if the grain size of a polycrystalline solid is sufficiently large, the emitted dislocations move far enough from the crack tip and do not significantly hinder the motion of new dislocations until the number of the emitted dislocations becomes large enough (Fig. 14.6 (c) and 14.6 (d) ). As a result, the dislocation emission along one slip plane can induce significant blunting of the crack tip. Following,75,76 the significant blunting by lattice dislocations stops crack growth and makes the solid ductile. At the same time, in nanocrystalline materials with finest grains, the emission of even one dislocation and its immobility at the nearest grain boundary hinders the emission of the succeeding dislocations along the same plane due to dislocation repulsion (Fig. 14.6 (a) and 14.6 (b) ). In doing so, the dislocation emission does not induce significant crack blunting. As a corollary, the nanocrystalline solid tends to show low crack growth resistance. This conclusion is in good agreement with the experimental findings that most nanocrystalline materials with finest grains are brittle. On the other hand, the experiment77 showed enhancement of crack growth resistance of nanocrystalline Ni with grain size of around 20 nm, compared to that in coarse-grained Ni. These experimental data, as well as similar data78–81 on enhancement of crack growth resistance of nanocrystalline ceramics, are naturally explained within the theoretical concept82–86 that specific toughening micromechanisms can operate in nanocrystalline materials, which are not effective in coarse-grained polycrystals. Such micromechanisms are suggested to be nanoscale deformation twinning,82 Ashby–Verall creep carried by grain boundary sliding accommodated by grain boundary diffusion and grain rotations,83,84 stressdriven migration of grain boundaries85 and nucleation of nanoscale grains86 near crack tips. However, in most cases, as it has been previously noted, nanocrystalline materials with the finest grains exhibit brittle fracture.

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14.6  Grain size effect on crack blunting through emission of lattice dislocations from crack tips. (a) and (b) Emission of even one dislocation and its stop at the nearest grain boundary hinder the emission of subsequent dislocations along the same plane due to dislocation repulsion. As a result, the dislocation emission does not induce significant crack blunting in nanocrystalline specimen. (c) and (d) If the grain size of the solid is sufficiently large, the emitted dislocations move far enough from the crack tip and do not significantly hinder the motion of new dislocations until the number of the emitted dislocations becomes large enough. As a result, the dislocation emission along one slip plane can induce significant blunting of the crack tip in coarse-grained polycrystalline specimen.

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14.6 Enhanced ductility of artifact-free nanocrystalline metals with narrow grain size distributions Although most nanocrystalline metallic materials show disappointingly low tensile ductility at room temperature, several experimental examples have revealed substantial tensile ductility at room temperature.11–30 Of particular interest are experimental results20–22,27 that support the evidence of enhanced tensile ductility of single-phase nanocrystalline metallic materials with narrow grain size distributions and without artifacts, because these results are indicative of intrinsic ductility of the ‘pure’ nanocrystalline structures. (In such materials, ‘extrinsic’ factors like composite structures, bimodal/multimodal grain size distributions, pre-existent pores and contaminations do not operate.) In the experiments,20–22 artifact-free bulk nanocrystalline Cu and Al-5%Mg alloy with mean grain sizes of around 23 nm and 26 nm, respectively, were fabricated by in situ consolidation during mechanical alloying at liquid nitrogen temperature. These artifact-free nanocrystalline materials showed both ultrahigh strength and good tensile ductility20–22 (Fig. 14.7). (Similar good plastic properties were exhibited by the artifact-free nanocrystalline Cu specimens with narrow grain size distributions in the miniaturized disc bend test.87) They showed strainhardening and ductile fracture mechanism with ductile dimples at fracture surfaces.20–22 The lattice dislocation slip was reportedly active in artifact-free nanocrystalline Cu and Al-5%Mg alloys. With these data, Youseff et al.20–22 attributed the ductile behavior to both the strain hardening and thereby good

14.7  A typical tensile stress–strain curve for the bulk in situ consolidated nanocrystalline Cu sample in comparison with that of a coarse-grained polycrystalline Cu sample (an average grain size larger than 80 µm) and a nanocrystalline Cu sample prepared by an inert gas condensation and compaction technique (with a mean grain size of 26 nm). Source: Reprinted with permission from Applied Physics Letters.20

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ductility of the materials by lattice dislocation storage in grain interiors. However, this explanation did not take into account the microscopic mechanisms of generation and storage of lattice dislocations in interiors of fine grains. At the same time, this aspect of the dislocation behavior at the nanoscale level is of crucial importance because, in most cases, the lattice dislocation generation and storage in finest nanoscale grains are very limited or even completely suppressed. In particular, conventional lattice dislocation sources (like Frank–Read sources) do not operate in nanoscale grains.1–10 Besides, even if the lattice dislocations are generated in nanoscale grains, they tend to move toward grain boundaries (where these dislocations are absorbed) due to the image forces.88–91 The experimental data20–22 on simultaneously high strength and good tensile ductility of nanocrystalline metallic materials with narrow grain size distributions can be naturally explained within the approach49 focusing on the optimization of grain boundary sliding and diffusion processes. More precisely, grain boundary sliding in nanocrystalline materials results in the emission of lattice dislocations from triple junctions and produces wedge disclination dipoles at triple junctions of grain boundaries10,47,49 (Fig. 14.4). The wedge disclination dipoles create very pronounced strain hardening. The calculated strain hardening47,49 appeared to be so high that it leads to the experimental values of the ultimate stress (the peak stress at the experimental stress–strain curve) at very small values of plastic strain. For instance, the calculated stress reaches the value of 0.23 GPa (approximately equal to the experimental ultimate stress), at plastic strain = 0.01, for Cu, and the value of 0.61 GPa (approximately equal to the experimental ultimate stress) at plastic strain = 0.02, for Ni.49 Therefore, one can assume that such dramatic strain hardening (created by grain boundary sliding), although suppressing plastic strain instability to necking, commonly induces early fractures associated with intensive formation and growth of cracks. Nevertheless, experimentally detected examples of substantial tensile ductility20–22 of nanocrystalline metallic materials showing moderate strain hardening are naturally attributed to the strain hardening caused by grain boundary sliding, if it is relieved by some accommodation mechanisms. In particular, grain boundary diffusion can significantly reduce or even completely remove the disclination stresses and the associated strain hardening in nano­ crystalline materials. Following Ovid’ko and Sheinerman,49 diffusion processes are capable of suppressing crack nucleation and growth and thus result in good tensile ductility of nanocrystalline metallic materials at certain conditions that optimize grain boundary sliding and grain boundary diffusion process. The optimization in question means that, for a specified strain rate, the rate of diffusion should be high enough to decrease strain hardening and suppress nucleation of crack but, at the same time, small enough to suppress plastic strain instability. At the same time, for a specified strain, there exists an interval of strain rates and temperatures at which a nanocrystalline specimen is stable to necking and catastrophic fracture.49 With an increase of strain, this interval of strain rates and temperatures shrinks, and at some critical strain it disappears. Above this critical

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strain, a nanocrystalline specimen can no more be stabilized with respect to failure by either necking or fracture through the optimization of its deformation regime. Also, grain boundary sliding results in the emission of lattice dislocations from triple junctions (Fig. 14.4), and these dislocations cause the following two effects. First, lattice dislocations are absorbed by grain boundaries where they could glide and climb, enhance grain boundary sliding and produce grain boundary vacancies that enhance grain boundary diffusion, respectively.5,10 Second, lattice dislocations emitted from triple junctions can be stored in grain interiors due to Lomer–Cottrell locking92 and/or elastic interaction with other dislocations and grain boundary defects. For instance, intergrain sliding produces the wedge disclination dipoles of wedge disclinations which strongly interact with the lattice dislocations and prevent their movement toward grain boundaries; and thus are capable of enhancing the lattice dislocation storage in grain interiors. In this case, the experimentally observed lattice dislocations, as noted by Youseff and co-workers,20 can contribute to the strain hardening. However, it should be noted that, in the experiments,20 the lattice dislocation storage was observed near growing crack tips. At the same time, the conditions for lattice dislocation generation and storage in regions near crack tips (where extremely high local stresses operate, and the stress screening effects of crack free surfaces are pronounced) are much softer compared to those in nanoscale grain interiors located far from crack tips. Therefore, the lattice dislocation activity may be suppressed in the regions far from crack tips, and its contribution to the strain hardening of nanocrystalline metallic materials with narrow grain size distributions may be insignificant. Thus, the concept49 on the optimization of grain boundary sliding and diffusion process gives at least a semi-quantitative explanation of the experimentally observed20–22 good tensile ductility of artifact-free nanocrystalline metallic materials with narrow grain size distributions. Representations of this concept are also relevant to the description of experimentally observed superplasticity shown by nanocrystalline materials at higher strain rates and lower temperatures,31 compared to their coarse-grained counterparts. In the case of superplasticity, however, one should take into consideration several additional factors like grain growth, strain rate hardening, and formation of mesoscopic sliding surfaces.

14.7 Enhanced ductility of nanocrystalline metals due to twin deformation and growth twins There are experimental data indicating on the special role of twin deformation in an increase of strain-to-failure of nanocrystalline metals under tensile load. For instance, Karimpoor and co-workers14 experimentally revealed both high strength and enhanced tensile ductility of electroplated nanocrystalline Co (hexagonal close-packed) (containing 0.09 wt.% S and 0.07 wt.% C) with the mean grain size d = 12 nm at room temperature. These fully dense nanocrystalline Co specimens exhibited both moderate strain hardening approximately specified by the

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dependence σ = Kε n, where n = 0.4, and good tensile ductility characterized by strain-to-failure ranging from 0.06 to 0.09. Also, the nanocrystalline Co specimens are characterized by the yield and tensile strength, which are about 2–3 times higher than those of coarse-grained polycrystalline Co.14 In doing so, the yield and tensile strength increase as the plastic strain rate decreases from 2.5 10–3 s–1 down to 10–4 s–1. Since such a response is typical for a material in which the twin deformation mode is dominant,93 Karimpoor with co-workers14 postulated that enhanced tensile ductility of nanocrystalline Co occurs due to the dominant twin deformation that provides moderate strain hardening. Similar deformation behavior of electroplated nanocrystalline Co was reported in a paper.24 Further, a very high density of extremely thin twins was observed in the nanocrystalline Co specimens after tensile load. With these experimental data, the twin deformation mode associated with moderate strain hardening can serve as a micromechanism for enhancing tensile ductility in nanocrystalline Co and, probably, for other metals with low stacking fault energy. In recent years, particular attention has been paid to the unique combination of high strength and enhanced ductility of nanotwinned copper.17,28–30 Nanotwinned copper specimens have ultrafine-grained structure with a high density of nanoscale growth twins.17,28–30 Thus, the structure at the nanoscale level is composed of nanoscale elements – twins – divided by coherent twin boundaries serving as obstacles for moving lattice dislocations. Coherent twin boundaries have much lower energy (per unit area) and thereby are more stable against migration in nanotwinned materials, compared to high-angle grain boundaries in nanocrystalline materials with the same chemical composition.17,28–30 (The basic driving force for the migration of twin and grain boundaries is related to a decrease in the boundary energy. In this context, the boundaries with low energy (per unit area) are more stable against such a migration compared to those with large energy.) In the experiments,17,28–30 it is found that nanotwinned Cu specimens show high strength and good ductility. For instance, Lu and co-workers29 reported that nanotwinned copper (with the average twin lamella thickness of around 15 nm) exhibited good tensile ductility (strain-to-failure εf = 0.14), high values of the yield stress (900 MPa) and the ultimate tensile stress (1068 MPa). These strength values are at least one order of magnitude larger than those characterizing coarse-grained copper. Nanotwinned copper, with an average twin lamellar thickness of 4 nm, shows very good tensile ductility (strain-to-failure εf = 0.3), but at the expense of the ultimate tensile stress (around 700 MPa).29 Stress–strain curves of nanotwinned Cu specimens under tensile load are indicative of strain hardening.17,28–30 From the microstructural viewpoint, plastic deformation in nanotwinned metals occurs by lattice dislocation slip, which results in strain hardening due to accumulation and transformations of lattice dislocations in twin interiors and at twin boundaries.28–30 With decreasing of the average twin lamellar thickness, the hardening by the interaction between dislocations and twin boundaries increases and becomes dominant over the

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contribution from the hardening by the dislocation–dislocation interaction within twin interiors.29 In this context, of particular interest are the specific features of the dislocation behavior at twin boundaries in nanotwinned metals and its difference from the dislocation behavior at high-angle grain boundaries in nanocrystalline materials. When lattice dislocations reach coherent twin boundaries, they either keep their identity as lattice defects or transfer across twin boundaries into adjacent crystallites, in which case the residual dislocations are formed at coherent twin boundaries.28–30 As a result, the dislocations are accumulated at twin boundaries during plastic deformation and thus significantly contribute to the strain hardening. (This behavior is contrasted to that of lattice dislocations when they reach conventional high-angle grain boundaries in nanocrystalline materials under the action of the image forces and/or the external stress. The lattice dislocations are commonly absorbed by high-angle grain boundaries where they transform into grain boundary dislocations that intensively climb (due to enhanced diffusivity along high-angle grain boundaries), or glide and come into annihilation reactions or undergo other transformations reducing their density at grain boundaries.5,10 As a result, their accumulation is very limited or even completely suppressed at grain boundaries in nanocrystalline materials.) This activity of lattice dislocations within twin interiors and at coherent twin boundaries can serve as a micromechanism for enhancing the tensile ductility of nanotwinned copper and, probably, other metals with high densities of nanoscale growth twins.

14.8 Enhanced ductility of nanocrystalline metals due to strain rate hardening In papers,16,24 it was noted that enhanced tensile ductility of nanocrystalline and ultrafine-grained metallic materials can be achieved due to strain rate hardening, if it is characterized by large strain rate sensitivity (m = 0.5 or larger, as with conventional superplasticity of microcrystalline materials; e.g.94,95). This idea was indirectly illustrated by experimental data16 on simultaneously good ductility (strain-to-failure εf = 0.14) and high strength of ultrafine-grained Cu specimen under room temperature tensile tests at a low strain rate of 10–6 s–1. Also, Champion and co-workers13 fabricated nanocrystalline Cu that has large grains with size of around 200 nm divided into subgrains (with low-angle boundaries) whose typical sizes are between 50 and 80 nm. The Cu showed near-perfect elastic–plastic behavior with no strain hardening, absence of neck formation and strain-to-failure of 14% in a tensile test at a low strain rate of 10–6 s–1. However, in the experiment13 there are no direct experimental measurements of the strain rate sensitivity m, while Wang and Ma16 reported low values of the strain rate sensitivity (m = 0.025 or lower). In these circumstances, the enhancement of tensile ductility of nanocrystalline metallic materials through pronounced strain hardening rate needs further experimental and theoretical examinations.

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In general, strain hardening rate is high (m = 0.5–1) in nanocrystalline materials deformed by diffusional creep mode and grain boundary sliding. In particular, it is the case of creep in which grain boundary deformation processes can provide significant contribution to plastic flow. For instance, Coble creep (grain boundary diffusional creep) mode was recognized as the dominant deformation mechanism in tensile creep test of nanocrystalline Ni specimens (with grain size of around 30 nm) at room temperature.96 However, during the room temperature test, creep rates of these nanocrystalline Ni specimens very quickly diminish to very low . values (ε ≤ 10–9 s–1) under the applied stress close to the yield stress. Such low strain rates hardly allow one to reach reasonable degrees of plastic strain or, in other terms, good ductility at room temperature.

14.9 Enhanced ductility of single-phase nanocrystalline metals with bimodal structures One of the most effective strategies in achieving high strength in materials without loss of ductility is to fabricate single-phase metallic materials with bimodal structures composed of nanoscopic and comparatively large grains11,15 (Fig. 14.8). Such nanomaterials have two peaks in grain size distribution, one in the nanometer range, and the other in the submicrometer range. Although the micromechanisms responsible for combining high strength and good ductility of nanomaterials with bimodal structures in the course of their plastic deformation are still under discussion,11,15,97–99 the general assumption is that the presence of large grains suppresses crack formation and/or propagation (Fig. 14.8) and provides strain-hardening necessary for good ductility while the nanocrystalline matrix provides high strength and hardness. Apparently, the first experimental investigation of metallic nanomaterials with bimodal structures was performed by Tellcamp et al.,11 who fabricated a nanostructured Al alloy with an average grain size of 30 to 35 nm. The nanostructured alloy has been found to have a 30% increase in both yield strength and ultimate strength without the corresponding decrease in elongation. Such enhanced ductility has been attributed to the presence of larger Al grains in the bimodal grains. It is logical to assume that dislocation activity in these grains could blunt the propagating cracks and thereby enhance plasticity.11 In the experiment,15 crystallization of an initially amorphous metallic alloy – Fe-based metallic glass of the FINEMET type (Virtroperm) – was used as a method of obtaining a nanocrystalline material with a bimodal structure free from pores and contamination. Specimens with different grain size distributions were fabricated: 1) nanocrystalline specimens with a narrow grain size distribution (characterized by the mean grain size 15 nm), 2) specimens with a bimodal structure where distinct, large grains (with a grain size of around 200 nm) are randomly distributed in a nanocrystalline matrix (with a mean grain size of around 15–20 nm), and 3) specimens with a bimodal structure where large grains (with a

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14.8  Deformation and fracture processes in a specimen with bimodal structure. Large grains suppress crack propagation and provide strain hardening (related to lattice dislocation accumulation) necessary for good ductility while the presence of the nanocrystalline matrix results in high strength and hardness.

grain size of 100–200 nm) are arranged in groups randomly distributed in a nanocrystalline matrix (with a mean grain size of around 15 nm). These specimens showed different deformation behaviors under tensile tests at temperature T = 600°C and strain rate of 10–4 s–1. Nanocrystalline specimens with a narrow grain size distribution are characterized by high strength, low ductility, no strain hardening and strain rate sensitivity m = 0.5. Grain boundary sliding specified by m = 0.5 is supposed to dominate in these materials. Homogeneous nanocrystalline specimens show low tensile ductility when grain boundary sliding initiates nucleation of nanocracks at triple junctions that grow rapidly.15 Specimens with a bimodal structure containing distinctly separated large grains showed high strength (characterized by the ultimate tensile stress = 1.7 GPa), strain hardening and good tensile ductility (characterized by strain-to-failure εf = 0.15). The lattice dislocation activity seems to be responsible for strain accommodation, strain-

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hardening and good ductility, while the nanocrystalline matrix is responsible for the high strength.15 Specimens with a bimodal structure containing groups of large grains are characterized by comparatively low strength and intermediate ductility with poor resistance to plastic flow localization. The group of large grains most likely deforms by dislocation creep at low stresses. Plastic deformation by the lattice dislocation creep in large grains arranged in groups seems to control low strength and is responsible for neck formation in these materials.15 This approach – fabrication of materials with bimodal grain size distributions to obtain a combination of high strength and good ductility – has been extended to other alloys with bimodal structures consisting of large grains embedded into ultrafine-grained matrixes16,100–105 as well as the alloys with multimodal structures with several peaks in grain size distribution.106,107 For instance, Wang and co-workers16,100 fabricated copper specimens with a bimodal structure where large grains are embedded into an utrafine-grained matrix. To do so, they used equal-channel angular pressing followed by cryo rolling, i.e. cold rolling at a low temperature, and recrystallization at 200°C. The obtained bimodal structure showed both good plastic behavior, a high tensile strain-to-failure (about 65% in terms of engineering strain), and a high yield stress of more than 300 MPa, several times greater than the yield stress of coarse-grained Cu.

14.10 Enhanced ductility of nanocrystalline metallic composites with second-phase nanoparticles, dendrite-like inclusions and carbon nanotubes Another strategy in enhancing the ductility of high-strength nanocrystalline metallic materials is to fabricate a composite form of nanocrystalline materials. For instance, nanocrystalline Al alloys with second-phase nanoparticles are found to show high strength, strain hardening and enhanced tensile ductility.26 In the experiment,26 the 7075 Al alloy was solution-treated to obtain a coarse-grained polycrystalline solid solution. This coarse-grained specimen was cryogenically rolled into a nanocrystalline-structured sheet with a mean grain size of around 100 nm. Finally, the specimen was aged at a low temperature. This procedure produced a nanocrystalline structure with second-phase nanoparticles of a high density distributed within grain interiors.26 The mean interpacing between the nanoparticles was around 25 nm. The following three categories of nanoparticles were distinguished: 1) nanoscale spherical Guinier–Preston zones with coherent boundaries, 2) the same crystal lattice as the matrix and a Zn/Mg atomic ratio of about 1:1; plate-shaped nanoparticles of the metastable hexagonal η’ phase with semicoherent boundaries and a Zn/Mg atomic ratio of about 1.5:1; and 3) equiaxed nanoparticles of the stable hexagonal η phase with incoherent boundaries and a Zn/Mg atomic ratio of about 2:1. In tensile load test, the nanocrystalline Al alloy with second-phase nanoparticles exhibited high-yield strength, 615 Mpa, and functional tensile ductility

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characterized by the uniform elongation 7.4%.26 The yield stress value is larger than the yield stress values, 550 MPa and 145 MPa, characterizing nanocrystalline specimens without nanoparticles and coarse-grained specimens of the Al alloy under examination.26 The uniform elongation 7.4% of the nanocrystalline Al alloy with second-phase nanoparticles is larger than that (3.3%) of this alloy without nanoparticles. Such deformation behavior of the nanocrystalline Al alloy is crucially affected by second-phase nanoparticles. From a microstructural viewpoint, plastic deformation in the alloy occurs by lattice dislocation slip hampered by nanoparticles. After plastic deformation, a large number of lattice dislocations are located at nanoparticle boundaries and in their vicinity, whereas, before the tensile test, very few dislocations are found near nanoparticles.26 With this observation, Zhao and co-workers concluded that the composite structure is responsible for the experimentally documented difference in the deformation behavior between pure nanocrystalline Al alloy and the same alloy with nanoparticles. In particular, the presence of nanoparticles results in strain hardening (characterized by the dependence σ = Aε n, where n = 0.15) due to accumulation of lattice dislocations at and near nanoparticle boundaries.26 Also, enhanced ductility was shown by Ti-based nanocrystalline alloys with large dendrite-like inclusions of the second phase under compressive load. In these metallic nanocomposites, plastic flow is localized in shear bands propagating within the nanocrystalline matrix. Large dendrite-like inclusions of the second phase stop shear bands and cause the strain hardening that prevents dramatic localization of plastic flow. The discussed effect of the composite structure enhances compressive ductility up to strain-to-failure 14%.108,109 Very recently, the enhanced ductility of nanocrystalline Cu reinforced by multiwalled carbon nanotubes under compressive load has been reported.110 The nanocomposite consists of a nanocrystalline Cu matrix with the mean grain size d = 22 nm and 1% wt. carbon nanotubes which were located within grain interiors and at grain boundaries. In the experiment,110 the compression test of nanocomposite pillars showed good ductility (strain-to-failure εf = 0.28), strain hardening and the high yield stress (1125 MPa). Li and co-workers110 noted that the lattice dislocation slip is dominant in these nanomposites, while carbon nanotubes serve as the structural element hampering the dislocation motion. In this case, lattice dislocations tend to be accumulated at interfaces between the nanocrystalline Cu and carbon nanotubes, and this accumulation causes the strain hardening and, thereby, enhances compressive ductility.

14.11 Conclusions and future trends Thus, owing to the specific structural features of nanocrystalline metallic materials, the set of deformation mechanisms in these materials is richer than that in conventional coarse-grained polycrystals. In particular, such deformation mechanisms – grain boundary sliding, grain boundary diffusional creep, triple-

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junction diffusional creep, twin and rotational deformation modes – effectively operate in nanocrystalline metals with finest grains. Plastic deformation carried by grain boundary processes in nanocrystalline metallic materials with finest grains is characterized by very high values of the flow stress. Such plastic deformation very quickly leads to intensive nanocrack generation (at local stress sources and concentrators) and growth instabilities followed by macroscopic fractures (Fig. 14.1). The deformation behavior of nanocrystalline metallic materials with intermediate grains is controlled by grain boundaries operating as active sources and sinks of lattice dislocations. Plastic deformation carried by lattice dislocations in nanocrystalline materials with intermediate grains is characterized by the absence of strain hardening and low strain rate hardening, in which case it very quickly leads to plastic strain instability followed by fast ductile fractures (Fig. 14.3). The above factors – the absence of the strain hardening and low strain rate hardening in nanocrystalline materials with intermediate grains as well as very high flow stresses in nanocrystalline materials with finest grains – effectively explain numerous experimental data1–10 that are indicative of low tensile ductility exhibited by most nanocrystalline metallic materials at room temperature. At the same time, several experiments revealed substantial tensile ductility at room temperature.11–30 Of particular interest for understanding the fundamental micromechanisms of the intrinsic ductility of ‘pure’ nanocrystalline metals are experimental results20–22,27 giving evidence of enhanced tensile ductility of artifact-free nanocrystalline metallic materials with narrow grain size distributions. These results can be explained within the concept49 that is based on the optimization of grain boundary sliding and diffusion processes that cause moderate strain hardening and suppression of dangerous stress sources during extended plastic deformation of nanocrystalline materials. Also, enhanced tensile ductility comes into play in nanocrystalline metallic materials due to strain hardening provided by deformation-induced twins,14,24 pre-existent (growth) twins17,28–30 and secondphase nanoparticles.26 In addition, nanocrystalline metals with bimodal structures show good tensile ductility,11,15 because large grains embedded in nanocrystalline matrixes in these materials both provide strain hardening and stop crack growth due to crack tip blunting. Besides, dendrite-like inclusions and carbon nanotubes in nanocrystalline metallic composites serve as structural elements causing strain hardening effects that may enhance (at least, compressive) ductility of such nanocomposites.108–110 In general, a systematic attempt to obtain a combination of high strength and good tensile ductility in nanocrystalline metallic materials at widely ranged conditions (chemical compositions, structural parameters, conditions of mechanical load) represents a very important unresolved problem in nanomaterials science. This problem is of large significance for development of structural applications of nanocrystalline materials. In the context discussed, experimental identification, computer modeling and theoretical description of micromechanisms enhancing

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tensile ductility of super-strong nanocrystalline metals as well as determination of their structural characteristics and fabrication parameters that control/optimize ductility are the future critical directions of research in this area. In conclusion, let us outline the key points that are of particular interest for the future research of ductility of nanocrystalline metallic materials: (1) Development of methods for systematic fabrication of artifact-free metallic materials with narrow grain size distributions and various chemical compositions (in extension of the research efforts20–22,27). (2) Experimental identification and theoretical description of plastic flow, fracture and enhanced ductility micromechanisms operating in artifact-free metallic materials with narrow grain size distributions as those having “pure” nanocrystalline structures. (3) Experimental identification and theoretical description of new micromechanisms for suppression of plastic strain instability in nanocrystalline metallic materials with intermediate grains. (4) Experimental identification and theoretical description of new micromechanisms for suppression of crack nucleation and growth instabilities in nanocrystalline metallic materials. (5) Enhancement of ductility of nanocrystalline metallic materials with the aid of methods (e.g. fabrication of materials with multimodal grain size distributions,108,109 deformation at cryogenic temperatures111) found to be effective in ductilization of ultrafine-grained materials. (6) Experimental identification and theoretical description of the influence of stress-driven grain growth on tensile ductility of nanocrystalline metallic materials. (7) With results of (1)–(6) used as input, determination of structural characteristics and parameters of fabrication and processing that control and optimize strength and tensile ductility of nanocrystalline metallic materials with various structures and chemical compositions.

14.12  Sources of further information and advice Papers16,33,34 discuss the key factors – plastic strain instability as well as crack nucleation and growth instabilities – for suppressing tensile ductility of nanocrystalline metallic materials. Micromechanisms of plastic deformation and their sensitivity to the specific structural features of nanocrystalline metallic materials are considered in detail in reviews1–9 and Koch et al.10 An overview of experimental data, computer simulations and theoretical models concerning fracture processes in nanocrystalline materials, with the interface and grain size effects taken into account, is presented in Ovid’ko’s paper;32 see also Koch et al.10 Various strategies for enhancement of ductility in such materials are briefly reviewed in Ma’s paper.24 Experimental data on enhanced tensile ductility of

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artifact-free nanocrystalline metallic materials with narrow grain size distributions are presented in papers.20–22,27 Ductility enhancement in nanocrystalline metallic materials due to strain hardening is the subject of several papers focusing on the roles of deformation-induced twins,14,24 pre-existent (growth) twins,17,28–30 second-phase nanoparticles26 and bimodal grain size distributions.11,15 The effects of the composite structure on ductility of metallic nanocomposites are experimentally examined in papers.108–110

14.13 Acknowledgements This work was supported, in part, by the Russian Foundation of Basic Research (Grant 08–01–00225-a), Russian Academy of Sciences Program “Fundamental studies in nanotechnologies and nanomaterials”, and the Ministry of Education and Science of the Russian Federation.

14.14 References   1 Mohamed F.A., Li Y. Mater sci eng A 2001;298: 1.   2 Kumar K.S., Suresh S., Van Swygenhoven H. Acta mater 2003;51: 5743.   3 Wolf D., Yamakov V., Phillpot S.R., Mukherjee A.K., Gleiter H. Acta mater 2005;53: 1.   4 Ovid’ko I.A. Rev adv mater sci 2005;10: 89.   5 Ovid’ko I.A. Int mater rev 2005;50: 65.   6 Meyers M.A., Mishra A., Benson D.J. Progr mater sci 2006;51: 427.   7 Dao M., Lu L., Asaro R.J., De Hosson J.T.M., Ma E. Acta mater 2007;55: 4041.   8 Pande C.S., Cooper K.P. Progr mater sci 2009;54: 689.   9 Padilla II H.A., Boyce B.K. Exp mech 2010;50: 5. 10 Koch C.C., Ovid’ko I.A., Seal S., Veprek S. Structural nanocrystalline materials: Fundamentals and applications. Cambridge: Cambridge University Press, 2007. 11 Tellkamp V.L., Melmed A., Lavernia E.J. Metall mater trans A 2001;32: 2335. 12 Lu L., Li S.X., Lu K. Scr mater 2001; 45: 1163. 13 Champion Y., Langlois C., Guerin-Mailly S., Langlois P., Bonnentien J-L., Hytch M. Science 2003;300: 310. 14 Karimpoor A.A., Erb U., Aust K.T., Palumbo G. Scr mater 2003;49: 651. 15 Sergueeva A.V., Mara N.A., Mukherjee A.K. Rev adv mater sci 2004;7: 67. 16 Wang Y.M., Ma E. Acta mater 2004;52: 1699. 17 Lu L., Shen Y., Chen X., Qian L., Lu K. Science 2004;304: 422. 18 Li H., Ebrahimi F. Appl phys lett 2004;84: 4307. 19 Li H., Ebrahimi F. Adv mater 2005;17: 1969. 20 Youssef K.M., Scattergood R.O., Murty K.L., Horton J.A., Koch C.C. Appl phys lett 2005;87: 091904. 21 Cheng S., Ma E., Wang Y.M., Kecskes L.J., Youssef K.M., Koch C.C., Trociewitz U.P., Han K. Acta mater 2005;53: 1521. 22 Youssef K.M., Scattergood R.O., Murty K.L., Koch C.C. Scr mater 2006;54: 251. 23 Ebrahimi F., Liscano A.J., Kong D., Zhai Q., Li H. Rev adv mater sci 2006;13: 33. 24 Ma E. J mater 2006;54: 49.

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65 He J.H., Lavernia E.J. J mater res 2001;16: 2724. 66 Liao X.Z., Zhou F., Lavernia E.J., Srinivasan S.G., Baskes M.I., He D.W., Zhu Y.T. Appl phys lett 2003;83: 632. 67 Chen M.W., Ma E., Hemker K.J., Sheng H.W., Wang Y.M., Cheng X.M. Science 2003;300: 1275. 68 Liao X.Z., Zhao Y.H., Srinivasan S.G., Zhu Y.T., Valiev R.Z., Gunderov D.V. Appl phys lett 2004;84: 592. 69 Liao X.Z., Srinivasan S.G., Zhao Y.H., Baskes M.I., Zhu Y.T., Zhou F., Lavernia E.J., Hu H.F. Appl phys lett 2004;84: 3564. 70 Wang Y.M., Hodge A.M., Biener J., Hamza A.V., Barnes D.E., Kiu K., Nieh T.G. Appl phys lett 2005;86: 101915. 71 Wu X., Zhu Y.T., Chen M.W., Ma E. Scr mater 2006;54: 1685. 72 Li B.Q., Sui M.L., Li B., Ma E., Mao S.X. Phys rev lett 2009;102: 205504. 73 Moser B., Hanlon T., Kumar K.S., Suresh S. Scr mater 2006;54: 1151. 74 Farkas D., Van Swygenhoven H., Derlet P.M. Phys rev B 2002;66: 060101. 75 Rice J.R., Thompson R.M. Philos mag 1974;29: 73. 76 Rice J.R. J mech phys sol 1992;40: 239. 77 Mirshams R.A., Xiao C.H., Whang S.H., Yin W.M. Mater sci eng A 2001;315: 21. 78 Bhaduri S., Bhaduri S.B. Nanostruct mater 1997;8:755. 79 Pei Y.T., Galvan D., De Hosson J.T.M. Acta mater 2005;53: 4505. 80 Kaminskii A.A., Akchurin M.Sh., Gainutdinov R.V., Takaichi K., Shirakava A., Yagi H., Yanagitani T., Ueda K. Crystallogr rep 2005;50: 869. 81 Zhao Y., Qian J., Daemen L.L., Pantea C., Zhang J., Voronin G.A., Zerda T.W. Appl phys lett 2004;84: 1356. 82 Gutkin M.Yu., Ovid’ko I.A., Skiba N.V. Philos mag 2008;88: 1137. 83 Yang F., Yang W. Int j solids struct 2008;45: 3897. 84 Yang F., Yang W. J mech phys solids 2009;57: 305. 85 Ovid’ko I.A., Sheinerman A.G., Aifantis E.C. Acta mater 2008;56: 2718. 86 Ovid’ko I.A., Skiba N.V., Mukherjee A.K. Scr mater 2010;62: 387. 87 Youssef K.M., Scattergood R.O., Murty K.L, Koch C.C. Appl phys lett 2004;85: 929. 88 Gryaznov V.G., Kaprelov A.M., Romanov A.E. Scr metall 1989;23: 1443. 89 Gryaznov V.G., Polonsky I.A., Romanov A.E., Trusov L.I. Phys rev B 1991;44: 42. 90 Evans A.G., Hirth J.P. Scr metall mater 1992;26: 1675. 91 Romanov A.E. Nanostruct mater 1995;6: 125. 92 Wu X.L., Zhu Y.T., Wei Y.G., Wei Q. Phys rev lett 2009;103: 205504. 93 Christian J.W., Mahajan S. Progr mater sci 1995;39: 1. 94 Padmanabhan K.A., Davies J.J. Superplasticity. Berlin: Springer-Verlag, 1980. 95 Nieh T.G., Wadsworth J., Sherby O.D. Superplasticity in metals and ceramics. Cambridge: Cambridge University Press, 1997. 96 Yin W.M., Whang S.H., Mirshams R.A., Xiao C.H. Mater sci eng A 2001;301: 18. 97 Ovid’ko I.A., Sheinerman A.G. Rev adv mater sci 2007;16: 1. 98 Pozdnyakov V.A. Tech phys lett 2007;33: 1004. 99 Malygin G.A. Phys sol state 2008;50: 1032. 100 Wang Y., Chen M., Zhou F., Ma E. Nature 2002;419: 912. 101 Zhang X., Wang H., Koch C.C. Rev adv mater sci 2004;6: 53. 102 Han B.Q., Lavernia E., Mohamed F.A. Rev adv mater sci 2005;9: 1. 103 Han B.Q., Lee Z., Witkin D., Nutt S.R., Lavernia E.J. Metall mater trans A 2005; 36: 957. 104 Han B.Q., Huang J.Y., Zhu Y.T., Lavernia E.J. Acta mater 2006;54: 3015.

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15 The mechanical behavior of nanostructured metals based on molecular dynamics computer simulations V.I. YAMAKOV, National Institute of Aerospace, USA Abstract: The major advances of the past two decades in the atomistic simulation of the fundamental deformation mechanisms in nanocystalline metals are presented in this chapter. The discussion focuses on an overview of work that has contributed to our understanding of the mechanical behavior of these important emerging materials while also noting several disputed and controversial issues that remain to be resolved. The chapter includes a discussion of the properties of grain boundaries, grain-boundary deformation mechanisms, dislocation processes, grain growth and structure evolution in nanocrystalline metals as seen from the perspective of molecular dynamics simulations. Key words: nanocrystalline metals, molecular dynamics simulation, nanocrystalline deformation.

15.1 Introduction More than 25 years since the first nanocrystalline (NC) materials were synthesized, there is still very little consensus on their characteristic mechanical properties (for recent reviews see References 1–4). Suggestions range from greatly enhanced ductility5–7 to dramatically increased strength and hardness.8,9 In this state of controversial findings, computer simulations performed at the atomistic level, such as molecular dynamics simulations, are able to provide key insights on the underlying deformation mechanisms in these materials. Though in many cases the outcome of these simulations is no less controversial than the experimental results, the ability to study a fully characterized model to the extent of knowing the microscopic state of each atom with machine precision is invaluable for better understanding of the deformation process. Among the various atomic-level simulation approaches developed during past decades, including lattice statics, lattice dynamics, Monte Carlo and molecular dynamics (MD), the latter has proven particularly useful for the investigation of plastic deformation. Based on the solution of Newton’s equations of motion for a system of atoms interacting through a prescribed interatomic potential function, MD simulations are capable of exposing the real-time behavior during deformation at atomic resolution. In addition to studying equilibrium configurations, MD simulations can explore the transient responses of the system as it probes and traverses complex, often unanticipated saddle-point configurations in the 459 © Woodhead Publishing Limited, 2011

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deformation path (for an overview, see Allen and Tildesley10). A particular feature of MD simulations is that the operating deformation mechanisms emerge from the interatomic forces, and are not a prescribed input of the simulation model (such as they are in mesoscale models11). This capability allows not only the study of the anticipated deformation processes, but also the observation of new ones as they appear during simulation. Like any simulation method, MD simulations have inherent limitations and constraints that should always be considered in the interpretation of their results. These limitations are well known. One such limitation is the modeling of systems of relatively small nanometer dimensions. The small system size may introduce substantial finite-size effects and an increased interference of the boundary conditions on the system behavior. Another limitation is the very short time period of a few nanoseconds over which the dynamics of the system can be probed. This short time duration is of particular consequence for the simulations of plastic deformation. As a result, such simulations usually involve extremely high strain rates (of typically >107/s, corresponding to 1% strain in 1 ns) that are many orders of magnitude higher than in conventional experiments. To make the deformation observable within such a short time window, very high stresses, exceeding substantially the experimentally known yield stress, have to be applied. The reliability of the interatomic potentials used is also of a major concern. The interatomic force descriptions used in most MD simulations are of empirical or semi-empirical origin.12 While the empirical force representation has the advantage of being computationally efficient, it is unable to fully capture the many-bodied nature of electron bonding, particularly the complex, self-consistent electron density variation as a function of local structure and chemistry in the vicinity of defects. As a consequence of these limitations, deducing the relationship between simulation predictions and experimental observations is not always straightforward, and has to be extrapolated on the basis of a rigorous theoretical analysis. In spite of their limitations, MD simulations have brought significant advances in understanding the peculiar mechanical properties of NC materials. In NC metals, MD simulations have revealed the intrinsic relationship between various deformation modes. Specifically, MD simulations have shown that the unique mechanical properties demonstrated by NC metals are a result of the competition between intergranular deformation modes, such as grain-boundary sliding13–15 and diffusion,16,17 and transgranular deformation modes, such as dislocation slip,18,19 deformation twinning,19–21 and in some cases, lattice diffusion.22 While this competition has long been suspected and suggested,23 it has been fully revealed in simulations,24–26 and experiments are still verifying most of the processes seen in the simulations.2–4 Often, simulations are becoming a guiding tool for experimentalists by helping them to identify and decouple the various deformation phenomena observed under the microscope. Examples include the studies of dislocation structures in nanograins;27,28 full dislocation emission versus partial

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dislocation emission29 leading to high concentration of stacking faults in the grain interior in face-centered cubic (fcc) NC metals; the unexpected role of deformation twinning in nanograins;30,31 grain-boundary diffusion as a plausible deformation mode and its connection to the observed grain-boundary sliding.32 The purpose of this chapter is to give a brief overview of the recent advances in MD simulations of NC metals. The material is presented in several sections summarizing focus areas of the MD simulations. In Section 15.2, a discussion on MD studies on the structure and properties of grain boundaries in view of their governing role in the overall mechanical behavior of NC metals is presented. In Section 15.3, the deformation mechanisms operating in nanosized grains are summarized. Section 15.4 is devoted to the microstructure evolution in NC metals, discussing grain growth and recrystallization, which are very active in these materials and strongly influence their mechanical behavior with time. Concluding discussions are presented in Section 15.5.

15.2 The structure and properties of grain boundaries in nanocrystalline (NC) metals by molecular dynamics (MD) simulation It is widely acknowledged that grain boundaries (GB) define to a great extent the mechanical properties of NC metals. Grain boundary-mediated processes, such as GB diffusion and sliding, are responsible for the observed inverse Hall–Petch behavior at grain sizes smaller than 20 nm. At grain sizes between 20 and 100 nm, GBs become active sources for dislocations and serve as nucleation sides for deformation twins, thus triggering intragranular deformation modes. Understanding of these processes begins with the structure and properties of GBs. Considering the existence of a vast amount of literature on GB structure and properties (see Mishin et al.33), this section will focus mainly on the specifics of the GBs in NC metals.

15.2.1  Grain boundary structural model for NC metals Two key questions related to the role of GBs in NC materials that have evolved from experimental studies and have become a focus of MD simulations are: (1) To what extent can the atomic structure of the GBs in NC materials be extrapolated from those of coarse-grained polycrystalline materials and bicrystals? (2) What is the structural and thermodynamic relationship between NC materials and amorphous solids? The significant body of atomic-level simulations suggests important similarities34,35 as well as some differences36,37 between the GBs in coarse-grained polycrystalline microstructures and NC microstructures. A series of studies by Swygenhoven et al.,

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based on a MD model of NC Ni of grain sizes from 5.2 to 15 nm,34 and 20 nm,35 showed that the GB structural types present in coarse-grained fcc metals are also found in NC metals, without major differences. However, this conclusion was based on a polycrystalline model prepared using Voronoi tessellation, which is known to result in a random, but non-equilibrated GB topology. Contrary to that conclusion, Phillpot et al.36,37 argued that the most important differences between GBs in NC and coarse-grained metals arise from the severe microstructural constraints present in NC materials. GBs in NC materials are strongly constrained by the grain morphology (shape, size and misorientation) of the surrounding nanograins. At nanometer dimensions, the discrete atomic structure starts to affect the grain morphology. For example, constraining the grain size to a whole number of interplanar lattice spacings leads to the appearance of so-called incompatibility strain inside the grains. Because of this constrained morphology, GBs in NC materials cannot achieve their minimum-free-energy thermodynamic state within a nanocrystal as in the coarse-grained materials or bicrystal interfaces, which at 0 K are of a crystalline structure. Grain boundaries in MD simulations36,37 where NC microstructures were synthesized by modeling a recrystallization process in a super-cooled Lennard– Jones melt, into which small crystalline seeds of random orientations had been inserted, showed the structural and dynamic characteristics of a frozen liquid, similar to the well known Rosenhain’s ‘amorphous-cement’ GB model.38 In Phillpot et al,36,37 GB energy was found to be uniform for all GBs and independent of the misorientation. Even when the grain seeds were oriented to form a coherent twin boundary, which is the interface between two twins in a fcc lattice and is expected to have a perfectly ordered crystalline atomic structure, the resulting GBs again showed a highly disordered structure of high excess energy. This disorder arises from the highly constrained NC microstructure, in which the rigidbody translations of the grains parallel to the GB plane cannot be fully optimized, by contrast with an unconstrained GB in a bicrystal interface. The extension of the work on fcc metals to silicon39 further elucidated the connection between the GBs present in NC and coarse-grained microstructures. The simulations of NC Si,39 involving grain sizes of up to about 7 nm, revealed the presence of highly disordered GBs of a uniform thickness. Similar simulations for NC Pd40 using a many-body embedded atom method (EAM) interatomic potential41 yielded qualitatively identical results. Therefore, while NC and coarse-grained polycrystalline microstructures appear to contain the same structural types of GBs (synthesis and processing dependent), the most important measure of their differences probably lies in their GB-energy distribution functions. Whereas coarse-grained materials usually exhibit a broad distribution of GB energies, the severe microstructural constraints present in NC microstructures seem to have the effect of significantly increasing the fraction of high-energy GBs at the expense of the low-energy boundaries: It appears that the more severe the microstructural constraints become (e.g. by decreasing the grain

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size or by the use of a highly non-equilibrium synthesis route), the larger is the fraction of the high-energy boundaries in the system. Grain-boundary structure changes with temperature. Many of the earlier simulations of high-temperature GB structure predicted ‘premelting’ at the GBs, i.e. GB disordering below the bulk melting point, Tm (for a critical review, see42). By contrast with thermodynamic melting, in which a liquid phase forms at T = Tm, the GB premelting takes place through the formation of a liquid-like GB layer at T < Tm. This liquefied layer is characterized by increased structural disorder and by enhanced diffusion within it. The width of the layer gradually diverges as T → Tm. A series of more recent simulations (reviewed in2) suggested that the highly disordered high-energy GBs in Si39 and Pd43 undergo a continuous reversible structural and dynamical transition at elevated temperatures. Upon heating from 0 K to melting, the high-energy GBs in the polycrystal undergo a transition from a low-temperature, semi-crystalline solid GB structure to a mixed vitrified solid with liquefied confined volumes of higher diffusivity at high temperature.43 Above a certain transition temperature, Tc (Tc < Tm), which depends on the GB energy, a small fraction of liquefied volume is formed within the highly disordered, solid GB until, at T → Tm, the liquefied volume fills the entire, still highly confined, GB region. Possibly, the closest analogy of Tc can be made with the temperature of vitrification, Tg, in amorphous solids. Finally, for T ≥ Tm, the highly confined liquid GB layer spreads to induce thermodynamic melting.43 From a thermodynamic standpoint this behavior can be explained in terms of heterophase fluctuations, as suggested by Suzuki and Mishin44 based on an independent MD simulation of GB solid–liquid transition in Cu.

15.2.2  Grain-boundary diffusivity Grain-boundary diffusivity is directly related to GB structure and energy. In general, high-energy GBs of more disordered amorphous-like structure have higher and more isotropic diffusivity compared to the low-energy dislocation GBs with a pipeline diffusivity along the dislocation cores, or the low-energy special GBs45 with almost crystalline structure and very low diffusivity. Molecular dynamic simulations have been extensively used to study GB diffusivity as dependent on structure, energy and temperature in both flat bicrystalline GBs and GBs in NC microstructures. The microscopic mechanisms of GB diffusion at the atomic level in a flat GB interface in Cu have been thoroughly investigated by Suzuki and Mishin.44 At low temperature, GB diffusion occurs through individual vacancies and interstitials that can move by a large variety of diffusion mechanisms, including the collective motion of small clusters. At high temperature, GB premelting substantially changes the diffusion mechanism, which becomes, to a great extent, independent of the GB structure. There is still no clear picture of the exact atomistic mechanisms of diffusion in a premelted GB layer.44

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15.1  Schematic diagram, adapted from,43 illustrating the transition in the GB diffusivity, D, at the temperature of premelting Tc, dependent on the grain-boundary energy, EGB , and at the melting temperature Tm. Note that at Tc, D is continuous, while at Tm it is discontinuous.

Macroscopically, the change of the GB-diffusion mechanism at high temperatures is revealed by a jump in the diffusion activation energy at a critical temperature Tc < Tm (Fig. 15.1).43 This change of the diffusion mechanism correlates with the appearance of a liquid phase in the GB layer as discussed in the previous subsection 15.2.1.43 It is important to emphasize that while the diffusion coefficient at T < Tc is specific for each GB, at T > Tc GB diffusivity was found to be independent of the GB structure and becomes a universal property of the material.43 This universality has been widely exploited in follow-up MD simulation studies of GB diffusion creep as it allows the construction of a polycrystalline-microstructure model with GBs of uniform diffusivity.

15.2.3  Grain-boundary mobility Grain boundary mobility governs grain growth and microstructure evolution in NC materials at elevated temperatures. A large number of MD simulations on GB mobility46–49 have been performed using different types of microstructure models, exploring different types of GB-migration driving forces, such as elastic-driven or curvature-driven migration. A central point of all of these studies was to relate GB mobility to GB diffusion following the experimental knowledge that GB diffusion governs GB mobility. In the first of these studies, Schoenfelder et al.46 used elastic anisotropy to drive the migration of a flat, high-angle (001) φ = 43.60° (Σ 29) twist GB in an elastically strained Cu bicrystal. Later, this study was repeated and extended to cover the whole spectrum of (001) twist GBs.47 Both studies found a clear qualitative correlation between GB migration and diffusion that shows a similar transition from slow to fast migration/diffusion due to

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high-temperature premelting. Quantitatively though, the activation energy for migration was two to three times lower than that of diffusion. Similar results were reported for capillarity-driven migration of curved tilt boundaries in aluminum, first in two-dimensional,48 and later in three-dimensional49 simulation models. These simulation studies lead naturally to the conclusion that the mechanism of GB migration is not based on diffusion. In Schoenfelder et al.46 it was found that the estimated migration activation energy is close to the latent heat of fusion, supporting a GB migration mechanism proposed half a century earlier by Mott.50 According to Mott,50 GB migration involves local disordering, or ‘melting’, of small groups of atoms at the boundary, thereby enabling atoms belonging to one grain to reshuffle collectively while aligning themselves with the opposite grain. Compared to experimental results, the simulations of a family of (001) twist GBs in Cu47 reproduced the observed dependence of the GB mobility on GB misorientation, although the activation energies from the simulations were consistently much lower than the experimental ones. In situ experiments on elastic-strain-induced GB migration in Zn bicrystals51 revealed distinct activation energies of low-angle vs. high-angle <112> and <111> symmetric tilt GBs. While low-angle GBs exhibited values close to the activation energy of volume diffusion, high-angle GBs exhibited a value close to that of GB diffusion. A possible explanation for the role of diffusion in the experimental findings51 was that the impurities, always present in the experimental samples, cause a drag on the migrating GBs, thus increasing the activation energy to that for GB or volume diffusion, depending on the GB type. The finite mobility of GB vertices,52 which is diffusion governed, may also be a factor that connects GB diffusion to GB migration. In conclusion, while MD simulations have revealed many details of the structural properties of GBs, the full picture is far from complete. There is still no consensus on the difference between GBs in NC materials and their coarsegrained equivalents. The details of the atomistic mechanisms of GB diffusion and migration and their relation at elevated temperatures are not yet clear and require more studies. A thermodynamic picture of GB melting based on heterophase fluctuations in a constrained system has yet to emerge.

15.3 Deformation mechanisms in nanoscale grains Most of the deformation mechanisms known to operate in coarse-grained metals are also found in NC metals. What is notable though, is the striking difference in the regimes at which these mechanisms operate in a nanograin compared to a large micron-size grain, and in the intrinsic relation and competition between these mechanisms, which result in unique mechanical properties. The key to the mechanical behavior of NC metals lies in their specific microstructure consisting of small grains of crystalline matter embedded inside a dense GB network. Consequently, the intragranular processes such as dislocation slip or lattice

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diffusion are suppressed or have to compete with the enhanced GB-mediated mechanisms such as GB sliding and GB diffusion. Benefitting from the small grain size of NC metals, MD simulations proved to be very efficient in capturing the mechanical properties of these materials and in the study of their specific deformation mechanisms at atomic level.

15.3.1  Grain sliding Grain sliding is found in a large number of MD simulations of NC metals both at low temperatures (T < 0.3Tm)24,26,53 and at elevated temperatures (T > 0.5Tm).17 At present, there is a firm consensus among researchers that GB sliding is an important deformation mode in NC metals, but the debate continues regarding its nature and the underlying atomistic mechanism. Two opinions have been introduced: 1) GB sliding is a result of ‘atomic shuffling’ and ‘stress-assisted free-volume migration’,53 and 2) GB sliding is due to GB diffusion,17 which at low T involves individual movement of vacancies and interstitials or collective motion of small clusters of atoms.44 At high T, sliding is assisted by volume diffusion through the premelted GB layer.17 The difference between 1) and 2) is that while diffusion is a randomwalk process, the stress-assisted migration is a directed movement in response to the applied load. The latter is mostly reported in low- or room-temperature models where diffusion is too slow to accommodate deformation at the extremely high strain rates of 107 s–1 inherent in MD simulations.53 Sliding through GB diffusion (Fig. 15.2) has been unambiguously demonstrated in simulations performed at high temperatures as an accommodation mechanism for Coble creep.17 In coarse-grained metals, this type of GB sliding is known as Lifshitz sliding.54 The focus of debate is how reliably the diffusion-governed GB sliding at high temperatures can be extrapolated to low temperatures and low strain rate of the order of the typical experimental values of 10–1 to 102 s–1. It is still a challenge for MD simulations to probe low-temperature–low-strain-rate regimes and to give a definitive answer to this question.

15.3.2  Diffusion creep The role of diffusion creep as a possible deformation process in NC materials is currently under debate, with several conflicting reports arising from both the experimental and computer simulation communities. Gleiter,55 who first proposed this notion, rationalized that the abundance of GBs together with the absence of conventional dislocation activity would result in plasticity localized in the GB regions, namely diffusion and sliding, even at ambient temperatures. So far, MD simulation findings on diffusion creep in NC metals were reported only at temperatures that are close to the melting point of the material (T > 0.8 Tm).16,17 Simulations at lower temperatures24,26,53 report GB sliding as a dominant deformation mode.

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15.2  Atomic structure simulation snapshot of 8 nm size grains at 4% deformation during Coble creep at T = 1200 K in Pd. Strips of black lines, initially drawn in parallel at the beginning of the simulation, are used to monitor the deformation. The line offsets, seen at the GBs indicate GB sliding that has taken place to accommodate the diffusion creep. For clarity, only the GB and the strip atoms are visualized.

Molecular dynamics (MD) simulations of Si16 and fcc Pd17 on idealized threedimensional microstructures have clearly captured steady-state Coble creep. The microstructures for these simulations were carefully chosen to consist of grains with uniform size and shape thus eliminating the topological driving force for grain growth. The grains were randomly misoriented to form high-energy, structurally disordered GBs of uniform diffusivity as discussed in Section 15.2.2. During uniaxial loading, Coble creep was evidenced by several key signatures including: 1) equal activation energies for both the strain rate and GB diffusion, 2) the deformation was homogeneous over the entire simulation cell, and 3) observation of the accommodating Lifshitz-sliding mechanism54 (Fig. 15.2). The strain rate dependence on stress and grain size was also consistent with the Coble creep formulation56 after taking into account the finite width of the diffusive GB layer.17 Recent MD simulations22,57 in NC Mo (of body-centered cubic (bcc) structure) showed the unexpected result of creep via lattice diffusion (Nabarro–Herring

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creep58) and enhanced by GB-assisted vacancy nucleation. The observation of bulk self-diffusion facilitated by GB-nucleated vacancies opens up interesting possibilities for future atomistic studies of the role of vacancies and interstitials on the mechanical properties of materials that have traditionally been thought of as inaccessible by MD simulation.

15.3.3  Dislocation slips The role of dislocations in the deformation of NC metals has been a central focus of interest. This interest was mainly driven by the numerous, and in many cases controversial, reports on the break down of the Hall–Petch hardening effect at grain sizes below 20 nm, which is replaced by softening, known as an inverse Hall–Petch effect (as reviewed in3). It is believed that a modified dislocation–GB interaction mechanism in NC metals is responsible for reversing of the Hall–Petch effect. In MD simulations of fcc metals (Cu,13,14 Ni34) of very small grain sizes < 20 nm, dislocations were found in the form of Shockley partial dislocations emitted from the GBs and that produce faults behind, irreversibly destroying the crystal lattice. At this grain size, dislocations contribute less than 30% to the total deformation, which is dominated by GB sliding. MD simulations were used to study the structural changes in the GBs during dislocation emission and absorption and the atomistic mechanisms of dislocation nucleation from GBs. It was reported that the atomistic activity at the GB during emission of dislocations is similar to that during GB sliding.34 This finding suggests that dislocation emissions may be a possible mechanism for GB sliding, and that GB sliding can be accommodated by dislocation slip. Typical of all of the early simulations for NC fcc metals performed at grain sizes below 20 nm (such as13,14,34) is that dislocations were found only in the form of single partial dislocations. Since single partial dislocations are not common in coarse-grained fcc metals, which at low temperatures deform through slips of dissociated full dislocations, it is logical to expect a transition grain size, where the partial dislocation slip transforms into a full dislocation slip. The main difference between a full and a partial dislocation is that the Burgers vector of a partial dislocation is only a part of the lattice period. Thus, a partial dislocation produces a stacking fault in the crystal lattice that extends between the dislocation and its source of nucleation. This stacking fault carries an energy penalty – the stacking fault energy (SFE) per length – preventing the dislocation from traveling away from its source. The created stacking fault also presents an obstacle for other dislocations. By contrast, a full dislocation does not leave a stacking fault, but fully restores the crystal lattice after gliding away. This energetic and structural difference between a partial dislocation and a full dislocation can result in a substantial change in the mechanical behavior of the NC metals at the transition from a partial to a full dislocation slip. To find a regime of full dislocation nucleation in NC polycrystals, a special MD model has been constructed.18 Aluminum was selected as a material model

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because of its high SFE and small splitting distance, r (of 1–2 nm), between the two Shockley partials when joined in a full dislocation.59 The choice of aluminum proved to be crucial for the success of the simulation, as it was shown later60 that the ability to form full dislocations is strongly dependent on the generalized stacking fault energy curve, defined by the interatomic potential used in the MD models. An additional factor that restricts the formation of full dislocations is that the inherently high MD stress of deformation generally increases the splitting distance, which may become 10 to 20 times larger than its equilibrium value. To achieve a sufficiently large grain size to accommodate a full split dislocation under high stress a columnar model microstructure was chosen. This type of structure18 may be only a few nm thick in the columnar z-direction, allowing the simulation cell to be extended in the x-, and y-directions to simulate polycrystals of up to 100 nm grain size (achieved in Yamakov et al.21). The first results of these simulations in a system of four grains of up to 45 nm in size18 found full dislocation emission in grains of over 30 nm in size. As expected, the transition to full dislocation nucleation resulted in increased dislocation activity inside the grains due to the elimination of the stacking faults as obstacles for dislocation motion. This dramatically changed the deformation behavior of the material, triggering various types of intragranular dislocation– dislocation interaction processes19 such as cross-slip lock formations, stackingfault splitting, deformation twinning and formation of twin networks.20,21 The transition from partial to full dislocation nucleation in NC fcc metals introduces the splitting distance as an additional length scale in the deformation process. Since the splitting distance, r, depends on the local resolved shear stress acting on the dislocation, this length scale is a dynamic quantity and depends on both the SFE, ESF, and the applied stress, σ ; r = r(ESF, σ). Follow-up simulations on fully three-dimensional microstructures of varying d and ESF studied in more detail the role of this length scale on the deformation processes.25,61 The results are illustrated in four selected snapshots of intragranular deformation in nanograins shown in Fig. 15.3. Grains with d/r >> 1 are active in generating dislocations using GBs as nucleation sites (Fig. 15.3 (a)) and deformed mainly through dislocation slip. As the grain size approaches the size of the splitting stacking fault, d/r ≈ 1 (Fig. 15.3 (b)), the dislocation activity decreases. Grains with d/r < 1 (Fig. 15.3 (c)) soon become saturated by stacking faults which suppress dislocation motion and prevent further dislocation nucleation. These grains continue to deform mainly through GB mechanisms. Figure 3 (d) presents partial dislocation emission in a larger grain of a material of very low SFE, characterized by d/r < 1. The situation is similar to Fig. 15.3 (c). After saturating the grains with stacking faults, the dislocation activity ceases. Taken together, Figs. 15.3 (c) and 15.3 (d) illustrate the parallel between the deformation modes in small grains of high SFE (Fig. 15.3 (c)) and large grains of low SFE (Fig. 15.3 (d)). This parallel suggests the notion of the splitting distance as a length scale parameter.

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d = 32; ESF = 120

15.3  Atomistic snapshots revealing dislocation processes in a nanocrystalline simulation model of grains of different size, d (in nm), and stacking fault energy, ESF (in mJ/m2). (a) Continuous GB emission of full dislocations (1) governs the deformation in a large grain. (b) In grains of size approaching the size of the splitting stacking fault (2), which separates the two partial dislocations (1a) and (1b), the dislocation slip is suppressed. In (c) and (d) an analogy between a material of small d and high ESF, and a material of large d and low ESF is demonstrated.

The concept of the splitting distance as a length scale in the deformation properties of NC fcc metals was generalized in a deformation-mechanism map61 in terms of reduced units of stress, σ/σ∞, vs. inverse grain size, ro/d. The parameters, σ∞ and ro, are the theoretical shear strength limit and the equilibrium splitting distance of the material. The deformation map captures the transition from dislocation to GB-based deformation processes and the transition from conventional to partial slip as observed in the simulations.

15.3.4  Deformation twinning One important result from MD simulation studies of the deformation behavior of NC Al that was corroborated by experiments was the initiation of deformation twinning.19–21 Twins start to appear in nanograins of size larger than 40 nm at relatively high strain (>8%). Two mechanisms of twin nucleation were initially identified: heterogeneous nucleation from GBs by coordinated emission of partial dislocations and homogeneous nucleation by overlapping of stacking faults confined by the dense GB network in the nanocrystal.20 © Woodhead Publishing Limited, 2011



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In view of the classic understanding of deformation twinning (see62) as a phenomenon limited to relatively large grain size (>10 µm) and materials with relatively low SFE, such as Cu,63 these observations for NC Al were very unexpected. However, previous simulations for NC Cu had already shown the emission of extrinsic stacking faults from GBs early in the deformation process,64 but they did not show the development of deformation twinning during the later stages of the deformation because of the small grain size to which these simulations were limited. Deformation twinning in NC Al has been confirmed experimentally,30,31 and several additional twinning mechanisms in NC metals have been recently found.65 Similar findings have been reported for other fcc metals, such as Cu66 and Ni.67 Of particular interest is the report by Rösner et al.68 of similar deformationtwinning processes in another high-SFE fcc metal, Pd. A comparison between the Al30 and Pd68 experiments with the Al MD simulations19–21 showed similarities in the way that deformation twins formed. However, in contrast to the MD simulations, in both Pd and Al, twins were found to form on only one slip plane per grain; thus, the twins were always coplanar within each grain. As one slip plane is not enough to accommodate a general deformation, an additional deformation mechanism is required. Rösner et al. suggested that grain rotation would allow the grains to orient their active twin plane along the principal shear direction. By contrast, the MD simulations21 indicated the appearance of twin networks where two twin planes operate on an equal basis. A possible reason for this might be the much higher strain rates in the MD simulations compared to the experimental studies. The effect of twinning on the mechanical properties of NC metals can be twofold. During early deformation, when the grain interiors are practically free of dislocations, twinning can facilitate deformation by additional slip systems or by assisting the transfer between existing slip systems through dislocation–twin reactions. Once twins have formed, they can repel certain types of gliding dislocations and give rise to pile-ups with consequent strain hardening of the material.

15.3.5 The strongest size: competition between different deformation modes The well known and almost universal Hall–Petch relation, stating that the yield strength of a polycrystal is inversely proportional to the square root of the grain size, suggests that NC materials should acquire very high strength approaching the theoretical strength of a perfect crystal. Though in general, NC metals show much higher strength than their coarse-grained versions – more than an order of magnitude in some cases – theoretical strength is never attained. The reason is the breakdown of the Hall–Petch hardening effect observed below a certain grain size. The underlying reason for this breakdown is the increased role of the GB-mediated deformation processes. Ultimately, the overall strength is a result of

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a competition between intragranular deformation mechanisms that provide hardening, and intergranular mechanisms that provide softening of the material. This reasoning, formulated by S. Yip,23 leads to the conclusion of the existence of a characteristic length at which both softening and hardening mechanisms are equally strong. A polycrystal of that grain size, ‘the strongest size’,23 would have the highest practically achievable mechanical strength. Two MD simulation studies on fully 3D microstructures25,26 have been performed to capture the full range of grain sizes over which the crossover from dislocation to GB mediated deformation takes place and, thus, to elucidate the nature of the ‘strongest grain size’, dc, in NC fcc metals. The first of these studies,25 considered NC Al microstructures consisting of four grains in a periodically repeated simulation cell. This simple setup enabled exploration of a range of grain sizes from 7–32 nm, thus incorporating sizes below and above dc for Al, and allowing the transition from GB-dominated processes (for d < dc) to dislocation-dominated processes (for d > dc) to be probed. These simulations have demonstrated directly the coupling between the crossover in the deformation mechanism and the resulting mechanical behavior. In addition to yielding a value of dc ~ 18 nm for Al, these simulations showed unambiguously that the crossover in the mechanical behavior is, indeed, due to a transition in the dominant deformation process. These simulations, also, related dc to the splitting distance, r, as discussed in the previous section (15.3.4). In the second study, Schiotz and Jacobsen26 determined the flow stress of NC Cu with grain sizes ranging between 5 and 50 nm. These simulations revealed the expected crossover in the flow stress, from normal to inverse Hall–Petch behavior, at a value of dc ~14 nm for Cu. As in Yamakov et al.,25 this crossover in the mechanical behavior was accompanied by a change in the underlying mechanism from dislocation-mediated plasticity, dislocation slip and deformation twinning, to GB sliding.

15.4 Grain growth and microstructure evolution in NC metals Due to the extremely small grain size, NC metals are inherently unstable against grain growth (GG). In these materials, GG is not limited to high-temperature conditions but can occur even at relatively low temperature.69 Since the mechanical properties of NC metals are strongly dependent on the grain size, they are very sensitive to GG. For this reason, it is of significant practical importance to study GG and to determine the factors that have an influence on it. Experimental studies on NC GG are difficult to perform because of the substantial problems in fully characterizing NC microstructures and their evolution. For example, Malow and Koch70 have studied GG in NC Fe using X-ray diffraction to determine the grain size by the broadening of the diffraction peaks. To ensure that the internal lattice strain, which also causes peak broadening,

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does not affect the measurements, the estimated grain size had to be confirmed by TEM. Since thin metallic films make it easier to measure grain size, NC GG experiments are mostly performed on NC thin films.71,72 Theoretical studies of GG encounter considerable complexities in fully accounting for the dynamic topological features of evolving microstructures. These difficulties have led to extensive simulation studies on grain growth. The need to include large number of grains in statistically representative simulated systems required the use of mesoscale types of models (Potts models, front-tracking models, phase-field models, etc. reviewed in11), which consider the microstructure at the level of grains and GBs rather than at the level of atoms. While highly computationally efficient, these models require an input of prescribed parameters such as GB and vertex mobility, GB energy, etc. that may not be known a priori. The unaccounted effects of additional GG mechanisms or GG driving forces, not incorporated in the mesoscale models, may lead to qualitatively false predictions. The ability of atomistic simulations to generate GG driving forces through atomic interactions provides a fundamental understanding of the GG processes, which is not possible in the mesoscale models. The combined effect of a relatively small number of atoms per grain and a high driving force due to extremely small grain size, makes the observation of GG at MD time and length scales possible. At present, NC materials are the only systems where GG can be studied by MD simulations.

15.4.1  Grain growth due to grain-boundary migration As in coarse-grained metals, curvature-driven grain-boundary migration, i.e. the motion of GBs towards the center of their curvature,73,74 is also a dominant GG mechanism in NC metals. The driving force for such GG is proportional to the GB curvature, which for a given grain diameter, d, is of the order of 1/d. This makes GG very active in NC materials. In idealized, fully dense and impurityfree microstructures at temperatures close to the melting point where GB mobility is maximal, GG is fast enough to be observed and successfully studied by MD simulations on a timescale of 1 to 10 ns. This has been demonstrated in a series of papers by Haslam et al.75–78 in NC Pd. A system of 25 grains of average d = 15 nm75 has been simulated at T = 0.95 Tm for the period of 10 ns system evolution time. As a result of the GG, only 9 grains remained at the end of the simulation. The MD model has been reproduced by a mesoscale kinetic Monte Carlo GG simulation,76 where the GB mobility and GB energy parameters were extracted from the MD simulation. The good agreement between the two models in reproducing similar topological patterns in the microstructure evolution confirmed the GG mechanism through curvature-driven migration. This provides an example of a bottom-up multiscale approach where an atomistic simulation is used to provide parameters for a continuum-level model. In addition, the MD simulation revealed a series of processes taking place at the GBs and in the grain interiors

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during GG. Some of these processes, such as production of residual dislocations in the grains from GB disintegration, were a result of GG.77 Others, such as grain rotation and grain coalescence,75,76 present additional mechanisms of GG, which will be discussed in the next subsection. An important question to be addressed by MD simulations is ‘What is the activation energy of GG?’ The expected answer, based on experimental evidence that relates the activation energy of GG to that of GB or lattice diffusion, may not be trivial in view of the findings for the GB-migration activation energy in impurity-free MD simulations. As discussed in Section 15.2.3, the activation energy of GB migration was found to be substantially lower than that of GB diffusion, suggesting non-diffusion-related GB migration mechanisms.46,47 To address this issue and to evaluate the activation energy of curvature-driven GG, an idealized MD model of a polycrystal of bimodal grain size distribution was used.79 In this model, four-sided square grains were embedded between eight-sided octagonal grains. At high temperature, T > 0.8 Tm, all GBs were of uniform diffusivity and mobility, representing an isotropic system. As expected from the von Neumann–Mullins rule,80 the octagonal grains grow at the expense of the square grains. The activation energy of the grain growth process was found to be equal to the GB diffusion activation energy. This result suggested that while migration of a single GB may not involve diffusion, GG in a polycrystal is diffusion assisted. One possible role of diffusion is to accommodate the excess free volume generated during GG (because of the decreasing GB network, the density of the polycrystal increases). Alternatively, GB diffusion might be related to the vertex mobility, which can be the rate limiting mechanism for GG.52

15.4.2 Grain growth due to grain rotation and grain coalescence A novel mechanism for GG, specific for NC materials and shown by MD simulations, is grain coalescence due to grain rotation. In this mechanism, the driving force results from the dependence of the GB energy on the misorientation angle. This dependence creates a torque to rotate the grain to form less energetic GBs. When two grains assume the same orientation, they coalesce to form a single larger grain. This process is found in NC materials81,82 due to their extremely small grain size, resulting in relatively high grain mobility towards rotation.83 The mechanism of grain-rotation coalescence results in a power-law grain growth with time t, given as d ~ tν, with a universal scaling exponent, ν. A combined theoretical and simulation study84 demonstrated that the value of this exponent depends on the assumed mechanism by which the grain rotations are accommodated, being ν = 1/4, for GB diffusion, or ν = 1/3, for lattice diffusion accommodated grain rotation, respectively. For comparison, the growth exponent for isotropic curvature-driven GG is ν = 1/2.

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15.4.3  Deformation-driven grain growth Experimental studies on superplastic deformation of both metallic85,86 and ceramic87 materials have shown that high-temperature deformation of fine-grained polycrystals generally enhances the rate of GG compared to that at thermal annealing. This enhancement phenomenon is known as dynamic GG. As an extreme case of fine-grained materials, NC materials were also found to experience dynamic GG under various conditions including uniaxial tension88,89 and compression,90 high-pressure torsion91,92 and nanoindentation.93 A comprehensive MD simulation analysis of the relation between GG and deformation has been performed in two consecutive papers by Haslam et al.77,78 The first paper,77 described the effect of deformation on the enhancement of the GG in a 25 grain NC model of Pd as compared to GG in the same microstructure under thermal annealing.75,76 The second paper,78 considered the converse effect of GG on deformation, identified as Coble creep in this particular model. Based on the analysis, detailed in,77,78 mechanisms of deformation-accelerated GG were found to be: stress-enhanced GB migration, stress-induced grain rotation, dislocationassisted grain rotation, and dislocation emission due to grain coalescence. An example of the relationship between some of these mechanisms is presented in Fig. 15.4. The combined operation of GB-diffusion creep and GB-diffusion-assisted grain rotation resulted in splitting a grain in two parts, followed by a grain switching

15.4  Overall evolution of a MD-simulated Pd microstructure at σ = 0.6 GPa and T = 1200 K performed by Haslam et al.77,78 (unpublished figure). (a) Initial configuration. (b) Diffusion creep elongates grain B. (c) Stress-induced grain rotation separates grain B in two. (d) Neighborswitching event between grains A, B1, B2, and C is taking place according to the Ashby–Verrall mechanism.94

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event of Ashby–Verrall type.94 Independently, grain-rotation-driven dynamic GG has been found in MD simulations by Sansoz and Dupont,95 while stress-induced GB migration was reported by Farkas et al. in a similar simulation set-up.96 An interesting scenario for coupling between GG and deformation was found in.78 Monitoring the strain rate in these simulations showed that the deformation mechanism operating in this case, Coble creep, experienced enhancement in the first stages of GG before being slowed down by the increased grain size. This enhancement correlated with enhancement in the overall diffusion in the system, while the GB volume decreased. Further analysis showed that the diffusion was enhanced due to realignment of migrating high-energy GBs with respect to the deformation field. This realignment increased the diffusion flow through the GB network and maximized the work of deformation done by the external load. Another interesting example of a relation between deformation and GG was found as a coupling between GB sliding and GB migration of a tilt GB.78 This coupling has been investigated in detail by Cahn et al.97 for a symmetric tilt GB in Cu (MD simulation), and a theoretical model and criteria for the sliding/ migration relation have been derived. Experimental evidence for this mechanism has been reported recently.98,99

15.5 Conclusions The purpose of this by no means exhaustive review is to present the substantial advancement in understanding of the underlying deformation mechanisms in NC metals that has been achieved through MD simulations. As a result, in spite of the many seemingly controversial MD findings, an overall picture of the mechanical behavior of NC materials has emerged. Recognizing that GBs play a major role in these materials, MD researchers began with detailed investigations of the GB structural and dynamic properties. Researchers gained many valuable insights that would probably not otherwise have emerged given the difficulty in studying this field experimentally. Important among these insights are those regarding the nonequilibrium constrained GB structure present in NC materials, which have been seen to exhibit specific dynamic properties such as premelting and universal diffusivity at high temperature. In addition, a number of MD studies have revealed the role of GBs as dislocation sources during deformation, suggesting that GBs play a governing role in the dislocation dynamics of the nanograins. Understanding the competitive relation between GB-mediated and dislocation-governed deformation helped to uncover the mechanism of the crossover in the Hall–Petch effect, from hardening to softening, as the grain size decreases below 20–30 nm in the idealized fully dense simulated microstructures. The ‘strongest size’ has been explained as the smallest grain size at which the dislocation activity is suppressed, but at which the GB network is not yet dense enough for the GB deformation processes to take over. These simulation findings have triggered a wave of experimental research. As a result, many of the major MD results have met experimental supports, although

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in many cases, in regimes far different from the simulation models. Nevertheless, the experimental efforts have been inspired and directed by the simulation findings. Examples include: the role of GBs as dislocation sources in nanograins; deformation twinning as a viable deformation mode at nanoscale; suggestions for a possible contribution of GB-diffusion creep, in support of earlier speculations on its role in the deformation of NC materials; grain rotation as another deformation mode and grain-rotation-induced grain growth; coupling between deformation and grain growth, etc. There are still many unresolved issues in the global picture of NC material deformation. In many cases, MD simulations brought more questions than answers. The reported findings were sometimes counterintuitive or contradictive to the current experimental wisdom. For example, the finding in simulations of discrepancy between the activation energies for GB migration and GB diffusion is still an experimental puzzle. Another experimentally unexpected, but subsequently confirmed, result was the ability of fcc NC metals to deform through twinning. The controversial simulation findings whether GB mediated deformation is based on GB diffusion (Coble creep) or GB sliding still lacks a definitive experimental resolution. The fundamental question, whether there is a relation between NC materials and amorphous matter as a limiting state (when the grain size approaches zero), remains unanswered even after exhaustive efforts from MD researchers and the numerous theoretical models presenting NC materials as two-phase amorphouscrystalline systems. The thermodynamic state of such a system is unclear and escapes the ability of the MD models, limited in size and time scale, to probe it. The majority of MD simulations of NC metals to date have been focused on fcc metals. The reason for this is mostly due to the lack of reliable and computationally efficient interatomic potentials for bcc and hexagonal close-packed metals. As the skill in creating more accurate potential for atomistic simulations is constantly improving, MD studies are already broadening to other types of structures (for example, see Millett et al.22,57 for bcc NC Mo) thus giving a more complete picture on the deformation properties of NC metals. Definitely, there is a lot of room for further research and, as computing power continues to follow Moore’s law, many more exciting discoveries are awaited in the near future.

15.6 Acknowledgement V. Yamakov is sponsored through NASA cooperative agreement NCC-1-02043 with the National Institute of Aerospace.

15.7 References   1 Gleiter H. Acta mater 2000;48: 1.   2 Wolf D., Yamakov V., Phillpot S.R., Mukherjee A., Gleiter H. Acta mater 2005;53: 1, doi:10.1016/j.actamat.2004.08.045.

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  3 Meyers M.A., Mishra A., Benson D.J., Progress in mat sci 2006;51: 427, doi:10.1016/j. pmatsci.2005.08.003.   4 Dao M., Lu L., Asaro R.J., De Hosson J.T.M., Ma E. Acta mater 2007;55: 4041, doi:10.1016/j.actamat.2007.01.038.   5 Karch J., Birringer R., Gleiter H. Nature 1987;330: 556.   6 McFadden S.X., Mishra R.S., Valiev R.Z., Zhilyaev A.P., Mukherjee A.K. Nature 1999;398: 684.   7 Kim B.N., Hiraga K., Morita K., Sakka Y. Nature 2001;413: 288.   8 Nieh T.G., Wadsworth, J. Scripta metall 1991;25: 955.   9 Siegel R.W., Materials science forum 1997;235–238: 851. 10 Allen M.P., Tildesley D.J. Computer simulation of liquids. Oxford science publications: Oxford, 1987. 11 Frost H.J., Thompson C.V., Current opinion in solid state & materials science 1996;1: 361. 12 Brener D.W. Phys stat sol 2000;217: 23. 13 Schiotz J., Di Tolla F.D., Jacobsen K.W. Nature 1998;39: 561. 14 Schiotz J., Di Tolla F.D., Jacobsen K.W. Phys rev B 1999;60: 11,971. 15 Swygenhoven H.V., Spaczer M., Caro A., Farkas D. Phys rev B 1999;60: 22. 16 Keblinski P., Wolf D., Gleiter H. Interface sci 1998;6: 205. 17 Yamakov V., Wolf D., Phillpot S.R., Gleiter H. Acta mater 2002;50: 61. 18 Yamakov V., Wolf D., Salazar M., Phillpot S.R., Gleiter H. Acta mater 2001;49: 2713 19 Yamakov V., Wolf D., Phillpot S.R., Mukherjee A., Gleiter H. Nature mater 2002;1: 45, doi:10.1038/nmat700 20 Yamakov V., Wolf D., Phillpot S.R., Gleiter H. Acta mater 2002;50: 5005. 21 Yamakov V., Wolf D., Phillpot S.R., Gleiter H. Acta mater 2003;51: 4135, doi:10.1016/ S1359-6454(03)00232-5. 22 Millett P.C., Desai T., Yamakov V., Wolf D. Acta mater 2008;56: 368, doi:10.1016/j. actamat.2008.04.004. 23 Yip S. Nature 1998;391: 532. 24 Schiotz J., Di Tolla F.D., Jacobsen K.W. Nature 1998;391: 561. 25 Yamakov V., Wolf D., Phillpot S.R., Mukherjee A.K., Gleiter H. Phil mag lett 2003;83: 385, doi:10.1080/0950083031000120891. 26 Schiotz J., Jacobsen K.W. Science 2003;301: 1357. 27 Li H., Ebrahimi F. Acta mater 2006;54: 2877, doi:10.1016/j.actamat.2006.02.033. 28 Zhou F., Liao X.Z., Zhu Y.T., Dallek S., Lavernia E.J. Acta mater 2003;51:2777, doi:10.1016/S1359-6454(03)00083-1 29 Liao X.Z., Zhou F., Lavernia E.J., Srinivasan S.G., Baskes M.I., He D.W., Zhu Y.T. Appl phys lett 2003;83: 632, doi:10.1063/1.1594836. 30 Chen M., Ma E, Hemker KJ, Sheng H, Wang Y, Cheng X. Science 2003;300: 1275, doi:10.1126/science.1083727 31 Liao X.Z., Zhou F., Lavernia E.J., He D.W., Zhu Y.T. Appl phys lett 2003;83: 5062, doi:10.1063/1.1633975. 32 Chokshi A.H. Mat sci eng A 2008;483–484:485, doi:10.1016/j.msea.2006.10.197. 33 Mishin Y., Asta M., Li J. Acta mater 2010;58: 1117, doi:10.1016/j.actamat.2009.10.049. 34 Swygenhoven H.V., Farkas D., Caro A. Phys rev B 2000;62: 831. 35 Swygenhoven H.V., Derlet P.M., Hasnaoui A. Phys rev B 2002;66: 024101. 36 Phillpot S.R., Wang J., Wolf D., Gleiter H. Mat sci eng A 1995;204: 76. 37 Phillpot S.R., Wolf D., Gleiter H. Scripta metall mater 1995;33: 1245.

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74 Atkinson H.V. Acta metall 1988;36: 469. 75 Haslam A.J., Phillpot S.R., Wolf D., Moldovan D., Gleiter H. Mater sci eng A 2001; 318: 293. 76 Haslam A.J., Moldovan D., Phillpot S.R., Wolf D., Gleiter H. Comp mater sci 2002;23: 15. 77 Haslam A.J., Moldovan D., Yamakov V., Wolf D., Phillpot S.R, Gleiter H. Acta mater 2003;51: 2097, doi:10.1016/S1359-6454(03)00011-9. 78 Haslam A.J., Yamakov V., Moldovan D., Wolf D., Phillpot S.R., Gleiter H. Acta mater 2004;52: 1971, doi:10.1016/j.actamat.2003.12.048. 79 Yamakov V., Moldovan D., Rastogi K., Wolf D. Acta mater 2006;54: 4053, doi:10.1016/j.actamat.2006.05.004. 80 Mullins W.W. J app phys 1956;27: 900. 81 Harris K.E., Singh V.V., King A.H. Acta mater 1998;46: 2623. 82 Nichols C.S., Mansuri C.M., Townsend S.J., Smith D.A. Acta metall mater 1993;41: 1861. 83 Moldovan D., Wolf D., Phillpot S.R. Acta mater 2001;49; 3521. 84 Moldovan D., Yamakov V., Wolf D., Phillpot S.R. Phys rev lettrs 2002;89: 206101, doi:10.1103/PhysRevLett.89.206101. 85 Ghosh A.K., Hamilton C.H. Metall trans 1979;10A: 699. 86 Senkov O.N., Myshlyaev M.M. Acta metall 1986;34: 97. 87 Seidensticker J.R., Mayo M.J. Acta metall. 1998;46: 4883. 88 Fan G.J., Fu L.F., Choo H., Liaw P.K., Browning N.D. Acta mater 2006;54: 4781. 89 Gianola D.S., Petegem S.V., Legros M., Brandstetter S., Swygenhoven H.V., Hemker K.J. Acta mater 2006;54: 2253, doi:10.1016/j.actamat.2006.06.016. 90 Fan G.J., Wang Y.D., Fu L.F., Choo H., Liaw P.K., Ren Y., Browning N.D., Appl phys lett 2006;88: 171914, doi: 10.1063/1.2200589. 91 Liao X.Z., Kilmanetov A.R., Valiev R.Z., Gao H.S., Li X.D., Mukherjee A.K., Bingert J.F., Zhu Y.T. Appl phys lett 2006;88: 021909, doi:10.1063/1.2159088. 92 Wang Y.B., Ho J.C., Liao X.Z., Li H.Q., Ringer S.P., Zhu Y.T. Appl phys lett 2009;94: 011908, doi:10.1063/1.3065025. 93 Zhang K., Weertman J.R, Eastman J.A. Appl phys lett 2005;87: 061921 doi:10.1063/1.2008377. 94 Ashby M.F., Verrall R.A. Acta mater 1973;21: 149. 95 Sansoz F., Dupont V. Appl phys lett 2006;89: 111901, doi:10.1063/1.2352725. 96 Farkas D., Froseth A., Swygenhoven H.V. Scripta mater 2006;55: 695, doi:10.1016/j. scriptamat.2006.06.032. 97 Cahn J.W., Mishin Y., Suzuki A. Acta mater 2006;54: 4953, doi:10.1016/j. actamat.2006.08.004. 98 Gorkaya T., Molodov D.A., Gottstein G. Acta mater 2009;57: 5396, doi:10.1016/j. actamat.2009.07.036. 99 Rupert T.J., Gianola D.S., Gan Y., Hemker K.J. Science 2009;326: 1686, doi:10.1126/ science.1178226.

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16 The surface deformation and mechanical behavior of nanostructured alloys L.L. SHAW, University of Connecticut, USA Abstract: Many mechanical properties such as fatigue and wear resistance are highly sensitive to the surface condition and properties of the material. As such, processes based on surface deformation are important methods for improving mechanical properties. The latest development of surface severe plastic deformation (S2PD), namely a family of processes that entail repeated impacts against the workpiece surface by a stream of high-energy balls, has resulted in significant progress in this direction. In this chapter the fundamentals and mechanical properties derived from S2PD processing are reviewed. The topics discussed include development of deformation fields, formation of the nanocrystalline surface layer, evolution of the work-hardened surface region, profiles of macroscopic residual stresses, presence of the microstructure gradient, evolution of surface roughness, enhancements in mechanical properties (i.e., tensile properties, fatigue limits, and wear resistance), and mechanisms associated with the improved mechanical properties. The perspectives of future developments are also discussed. Key words: surface severe plastic deformation, surface mechanical attrition treatment, severe plastic deformation, surface nanocrystallization, nanostructured alloys.

16.1 Introduction Surface severe plastic deformation (S2PD) is a relatively new family of processes that have been developed with the aim to create a nanocrystalline (nc) surface layer.1–4 These processes, pioneered by K. Lu and J. Lu,5 rely on severe plastic deformation induced by impacts of high-energy balls, hammer peening, surface rolling, laser shock treatment, or machining to produce a nc surface layer. The common feature of these processes is S2PD. Among various methods, highenergy ball impact processes have received most of the attention because of their versatility in processing complex-shaped parts. Several different names have been used for this group of processes, including ultrasonic shot peening (USSP),6,7 high-energy shot peening (HESP),8 surface mechanical attrition treatment (SMAT),9–11 surface nanocrystallization and hardening (SNH),12–14 and particle impact processing (PIP).15,16 Differences among these processes stem mainly from the approach via which the high velocity of balls is generated. In USSP the movement of balls is generated through collision between balls and a vibrating chamber driven by an ultrasonic generator. For SMAT, HESP and SNH processes, the movement of balls is also generated through collision between balls and a vibrating chamber. However, the vibration of the chamber is driven by 481 © Woodhead Publishing Limited, 2011

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Table 16.1  Typical parameters of balls and shots used in SP and S2PD processes Process

Diameter of balls or Impact velocity (m/s) shots (mm)

Kinetic energy of balls or shots# (J)

SP USSP SMAT* SNH PIP

0.25–1.0 0.4–3.0 4.0–8.0 4.0–8.0 4

9.2 × 10–6–0.01 0.0001–0.02 <0.018 0.0063–0.43 1.88

20–150 <20 2–3 5–15 120

Source: From Dai and Shaw, 2007.14 With permission. Notes: * HESP has the same kinetic energy as SMAT because similar equipment is used. # Kinetic energy is also dependent of the density of the ball and shot used, which is not listed here.

an electric motor. PIP, in contrast, is done through a high-pressure light-gas gun, which accelerates particles to a desired impact speed. Different devices invented for generating high-speed balls offer a wide range of kinetic energies to produce various degrees of surface plastic deformation. Table 16.1 lists typical values for the sizes and speeds of balls and shots and their corresponding kinetic energies reported in the literature. It can be seen that PIP has the highest kinetic energy, followed by SNH and then SMAT. In what follows, S2PD will be used to stand for the entire group of high-energy ball impacting processes. Shot peening (SP), which was developed in ~1920s and has been widely used ever since to improve the fatigue life of metallic components17–21 and can sometimes produce a nc surface layer,18,20 is also included in Table 16.1 for comparison. SP is similar to S2PD in the sense that both processes entail the impact of a stream of spherical shots or balls against a workpiece. However, the kinetic energies of these two processes are quite different with S2PD typically larger than SP by 50 to 180 times.14 As shown in Table 16.1, the difference stems from the size of the impacting media. The shots used in SP are typically about 0.2 mm, whereas the balls used in S2PD are in the range of 5 to 10 mm in diameter. As a result, S2PD has a kinetic energy much higher than SP, thereby readily generating a nc surface layer. For a Ni-base C-2000 alloy processed with S2PD, a nanograined surface layer as thick as 50 µm has been observed,1,22 which has never been achieved by SP in any material.

16.2 Mechanics aspects during surface severe plastic deformation Many studies of analytical and numerical approaches have been conducted to establish the deformation field of the workpiece induced by high-energy shots and balls.23–25 The analytical approaches are mainly based on the Hertz theory of elastic contact between a sphere and a semi-infinite solid. The normal pressure © Woodhead Publishing Limited, 2011



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over the contact area upon impact and the stress field within the deformed solid can be calculated if the following two rules are allowed: 1) The stress field generated by elastic impact (with moderate velocities) is identical to that generated by elastic contact;26 and 2) The normal force upon impact is due to the deceleration of the moving ball.27 With these two rules, dynamic loading can be approximated by static contact, and the distribution of the normal pressure, P(r), over a circular contact area of radius, a (Fig. 16.1), can be calculated with the aid of:27

[16.1]

where r is the distance from the center of the contact circle and P0 is the maximum pressure in the circle of contact and given by:27

[16.2]

where R is the radius of the ball, EH is the equivalent modulus related to Young’s moduli and Poisson’s ratios of the ball and impacted solid (i.e. workpiece), and Fn is the maximum normal force upon impact. The maximum normal force upon impact is related to the deceleration of the impacting ball, and can be calculated via:27

[16.3]

where vb is the impact velocity of the ball, ES is the elastic modulus of the solid, and ρ is the ball density. This maximum normal force can be treated as a concentrated load and used to compute the stress field within the impacted solid, as described by Shaw and DeSalvo.28 Figure 16.1 (a) shows schematically the distribution of the normal pressure, P(r), over a circular contact area and the plastic–elastic boundary within the impacted solid, while Fig. 16.1 (b) shows the contours of the maximum shear stress within the impacted solid normalized by the maximum pressure in the circle of contact. Based on the maximum shear Tresca yield criterion, plastic flow of the impacted solid will start at the point where τ /p0 = 0.63, and the plastic zone will expand following the contours defined in Fig. 16.1 (b) as the impact load increases. The depth of plastic zone, h, has been calculated for an elastic, perfectly plastic solid to be 1.816a where a is the radius of the contact circle,28 and can be related to the parameters of shot peening and high-energy ball impact processes with the aid of:23

[16.4]

– where P is the mean normal pressure in the circle of contact and equal to 2/3 P0. R, ρ and vb have been defined before. The depth of plastic zone estimated from © Woodhead Publishing Limited, 2011

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16.1  (a) Schematic of the distribution of Hertz pressure during ball impact; the area within the dash line represents the plastic zone in the deformed solid. (b) Schematic of the contours of the maximum shear stress within the deformed solid, normalized by the maximum pressure in the circle of contact.

Eq. (16.4) does not include work hardening, strain rate sensitivity, and thermal effects. Nevertheless, Eq. (16.4) has been shown to be adequate in estimating the depth of plastic zone when compared with experiments.23,28 Even more importantly, Eq. (16.4) defines the relationship between the depth of plastic zone and the parameters of ball impact processes. Since the mean normal pressure is proportional to the hardness of the workpiece, Eq. (16.4) reveals that the depth of plastic zone increases with ball size, density and velocity, and decreases with an increase in the hardness of the workpiece. Based on these relationships, it can then be concluded that the depth of plastic zone increases with the kinetic energy of balls.

16.3 Changes in the microstructure and stress states induced by surface severe plastic deformation Severe plastic deformation at the surface region will change the surface microstructure and properties of the workpiece dramatically. The predictions from the analysis described in Section 16.2 have been confirmed by finite element modeling (FEM) as well as experiments. Furthermore, experiments offer microstructural evolution that cannot be predicted from the analytical analysis. In the following the prediction from FEM on the surface deformation will be described first and then the experimental results will be presented.

16.3.1 Plastic deformation zone predicted via finite element modeling (FEM) The depth of plastic zone is one of the most important parameters because it determines the thickness of the work-hardened layer as well as the thickness of the surface layer within which residual compressive stresses are present. Finite element modeling has shown that the depth of plastic zone coincides with the © Woodhead Publishing Limited, 2011



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thickness of the surface layer with residual compressive stresses.29 Table 16.2 lists the depth of plastic zone for several ball-impact processes, computed via finite element modeling of dynamic impact of a WC/Co ball on a nickel-based C-2000® Hastelloy plate using LS-DYNA commercial code.14 The C-2000 alloy is a single-phase material with a face-centered cubic crystal structure and a nominal chemical composition of (in percentage by weight): 23Cr, 16Mo, 1.6Cu, 0.01C, 0.08Si, and balance Ni. As expected, the depth of plastic zone increases with the kinetic energy of the balls. Additionally, the finite element modeling also reveals that the depth of the plastic zone increases with the ball size for a given kinetic energy. Such a conclusion is in good accordance with the prediction obtained from the analytical formula by combining Eq. (16.2), (16.3) and (16.4). Thus, an important conclusion is that high-energy ball impact processes can produce a deeper plastically deformed layer than shot peening because of the larger kinetic energy offered by S2PD. Interestingly, this conclusion still holds even when balls and shots in S2PD and SP have the same kinetic energy, as revealed in Table 16.2. Table 16.2 also lists the maximum effective plastic strain induced by impacts of balls. The location of the maximum effective plastic strain is found not to be at the very impacted surface, but slightly below that surface.14 As expected, the maximum effective plastic strain increases with the kinetic energy of balls. However, it is interesting to note that for a constant kinetic energy smaller balls generate larger effective plastic strain than large balls, even though the depth of plastic zone is smaller. A large plastic strain is necessary for the formation of nanograins.15,16 Thus, the finite element simulation suggests that for a given kinetic energy smaller balls are quicker in creating a nc surface layer than larger balls, whereas larger balls are more effective in creating a thicker nc surface layer than smaller balls. Figure 16.2 compares the effective plastic strain profiles within the workpiece of the C-2000 alloy generated via one impact and 770 random impacts of the S2PD process. The profiles are derived from FEM, and reveal that the depth of plastic zone is not sensitive to the number of impacts.14 Thus, Eq. (16.4), derived from the simplified analysis based on the Hertz theory, can be used to estimate the depth of plastic zone since this parameter is insensitive

Table 16.2  Results of finite element simulation of S2PD and SP processes Process

Ball Ball diameter density (mm) (g/cm3)

Impact velocity (m/s)

Kinetic energy (J)

Depth of plastic zone (mm)

Maximum effective plastic strain

S2PD SP Hypo*

7.86 0.3 0.3

5 50 670

0.0476 0.000265 0.0476

1.6 0.15 1.2

0.18 0.00175 0.315

15 15 15

Note: *A hypothetical case which has the same kinetic energy as S2PD, but with an extremely high impact velocity and a shot size equal to that in SP.

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16.2  The effective plastic strain profiles within the workpiece of the C-2000 alloy after one impact and 770 random impacts for the S2PD process. These profiles are generated via FEM. Source: From Dai and Shaw, 2007.14 With permission.

to the number of impacts. Figure 16.2 also provides insights into how the effective plastic strain field changes with the number of impacts. Note that the maximum effective plastic strain after 770 random impacts is 0.478, which represents more than 100% increase over that (~0.186) resulting from the single impact event. In fact, if the maximum effective plastic strain is plotted against the number of impacts (not shown here), the maximum effective plastic strain exhibits a continuous increase with the number of impacts. The maximum effective plastic strain is an important parameter because previous studies15,16 have shown that exceeding a critical plastic strain is necessary for the formation of nanograins in the severe plastic deformation process. Thus, as the processing time increases, the thickness of the surface nc layer increases. This is exactly observed in experiments.2

16.3.2  Work-hardened profiles Different extents of plastic deformation at different locations in the surface region will result in different work hardening at different locations. Figure 16.3 compares the Vickers microhardness profiles of the C-2000 alloy treated with S2PD and SP.1 As shown in Fig. 16.3, the depth of the work-hardened zone is only about 200 µm for the SP-processed sample, while it is about 800 µm for the S2PD-processed sample representing a fourfold increase. This is in good agreement with the prediction from the analytical analysis and FEM (see Table 16.2), i.e. the plastic deformation zone generated is much deeper with S2PD than with SP. However, it © Woodhead Publishing Limited, 2011



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16.3  The Vickers hardness of the C-2000 alloy with SP and S2PD processing as a function of the position measured from the processed surface. The hardness profile of an untreated sample is also included for comparison. Source: From Shaw et al., 2010.1 With permission.

is interesting to note that the Vickers hardnesses at the impacted surfaces of the S2PD- and SP-processed samples are very similar. This phenomenon is due to the formation of nc grains at the impacted surface of both materials.1 Figure 16.4 shows the nanoindentation hardness profile of the C-2000 alloy as a function of the position measured from the impacted surface.22 With the aid of transmission electron microscopy (TEM), the thickness of the nc surface layer for this particular processing condition has been identified as 50 µm. Therefore, one of the conclusions is that the hardness of the nc surface layer is a simple extension from the hardness of the work-hardened region. Thus, the hardness of the nc surface layer of C-2000 can be regarded as the simple extension of the work-hardened region. However, this is not the case for all materials. In fact, it has been shown that a sudden jump in the hardness is present for steels when the grain size changes from micrometers to nanometers (i.e. <100 nm).15 Figure 16.5 shows how the hardness profile of the C-2000 alloy as a function of the position alters with the S2PD processing time. Similar to the hardness profiles shown in Fig. 16.3 and 16.4, the hardness decreases gradually as the location moves away from the impacted surface. Clearly, the decrease in hardness is due to the reduced plastic deformation as the position moves deeper into the solid. However, the most interesting phenomenon to be noted in Fig. 16.5 is the surface hardening saturation, i.e. no additional hardening is obtained beyond 30-minute processing of the C-2000 alloy because the hardness curves of 30-minute and 180-minute processing are overlapped. Such a phenomenon has also been observed with an Al-5052 alloy (not shown here). Surface hardening saturation has important implications in process optimization © Woodhead Publishing Limited, 2011

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16.4  Berkovich nanoindentation hardness profile of the C-2000 alloy as a function of the position measured from the impacted surface after S2PD-processing for 180 min. The nanograined surface layer in the S2PD-processed sample is 50 µm thick. The nanoindentation hardness profile of an untreated sample is also included for comparison. Source: From Shaw et al., 2008.22 With permission.

16.5  Vickers hardness profiles of the C-2000 specimens treated with the S2PD process for various periods of time.

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because prolonged processing does not result in surface hardening, instead could lead to surface contamination of the workpiece by impacting balls.30 Another interesting phenomenon is how little change occurs in the hardness with 5-minute processing. Processing times exceeding 5 minutes are needed to attain the uniform and discernible hardness increase. The limited change in hardness with 5-minute processing is due to the incomplete coverage of the surface of the workpiece by ball impacts. Complete impact coverage of the entire surface is necessary for uniform and discernible hardness increase at the surface region.

16.3.3  Residual stress profiles Surface plastic deformation causes stretching of the top layer of the workpiece. Upon unloading, the elastically stressed sub-surface layers tend to recover their original dimensions, but the continuity of the material in both zones, the elastic and the plastic, does not allow this to occur. As a result, a residual compressive stress field followed by a tensile field is expected to form in the impacted workpiece. Figure 16.6 compares the residual stress profiles of C-2000 processed with S2PD and SP.1 The residual stress profiles shown in Fig. 16.6 are measured via X-ray diffraction in conjunction with material removal layer by layer. It is noted that the values of residual stresses at the impacted surface are similar for SP- and S2PD-processed samples. Furthermore, the maximum compressive

16.6  Residual stresses on the plane parallel to the impacted surfaces of SP- and S2PD-processed samples as a function of the position measured from the impacted surface, determined based on the X-ray diffraction combined with material removal layer by layer. Source: From Shaw et al., 2010.1 With permission.

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stress is not at the impacted surface, but at the sub-surface. However, the maximum compressive stress introduced is about 18% higher with S2PD (~1,020 MPa) than with SP (~860 MPa) and, in addition, occurs at a deeper location. These results are consistent with the predication of FEM, i.e. S2PD can lead to larger residual stresses than SP.14 The thicker surface layer with compressive residual stresses for the S2PD-processed sample than the SP-processed sample is also in good accordance with the predication of FEM since prior studies29 have shown that the depth of the compressive stress region is close to the depth of the plastic deformation zone.

16.3.4  Microstructure gradients It is well known that severe plastic deformation can result in grain refinement. Since S2PD leads to different degrees of plastic deformation at different locations in the surface region, it is expected that a microstructure gradient will be generated by S2PD. This expectation has been confirmed by many studies.1,4,6–11 Figure 16.7 shows how the microstructure gradient changes with the S2PD processing time for the C-2000 alloy. Note that there are many deformation markings (i.e. straight and bent lines) near the processed surface. These markings are confined within individual grains and their densities increase as the distance to the processed surface diminishes. These deformation markings have been identified as deformation twinning.2 As shown in Fig. 16.8, the selected area diffraction (SAD) pattern, exhibiting two sets of diffraction patterns that are symmetrical with each other with respect to the

16.7  Optical micrographs of the cross-sectioned C-2000 specimens, processed using S2PD for (a) 30 minutes, (b) 70 minutes, and (c) 180 minutes. Source: From Villegas and Shaw, 2009.2 With permission.

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16.8  Transmission electron microscopy bright-field images of the twin arrangement in the C-2000 alloy processed using S2PD for 30 minutes: (a) intersection of deformation microtwins and the corresponding SAD pattern, and (b) a closer view of micro- and nanotwins with trapped dislocations between them. Source: From Villegas and Shaw, 2009.2 With permission.

{111} plane, confirms that the microstructural features are indeed deformation twins. In the proximity to the surface, these deformation twins populate entire grains (Fig. 16.7), suggesting that structural refinement in the C-2000 alloy proceeds by the intersection of the twins, which subdivide micrometer-size grains into domains that are a fraction of the size of the parent grain. Twin-dislocation interactions, however, play a critical role at the later stage of grain refinement for the C-2000 alloy, which has very low stacking fault energy (~1.22 mJ/m2).2 Another important feature noticeable in Fig. 16.7 is that the depth at which high densities of deformation twins become so substantial that they surpass grain boundaries as the dominant microstructural feature, grows with the processing time. This depth is of the order of 250 µm at 30 minutes of processing, 300 µm at 70 minutes, and 450 µm at 180 minutes. However, careful observation of the specimens processed reveals that the greatest depth at which any indication of plastic deformation in the form of deformation twins is approximately 800, 824, and 963 µm in the 30-, 70- and 180-minute processed samples, respectively.2 These results are in good agreement with FEM (Fig. 16.2), predicting that the depth of plastic zone is insensitive to the number of impacts (i.e. the processing time), but the effective plastic strain at a given location within the plastic zone increases with the processing time. It is interesting to note that nanograins (<100 nm) are formed in all the C-2000 alloy samples processed using S2PD for 30, 70 and 180 minutes, as shown in Fig. 16.9.2 Although nanograins are formed at the impacted surfaces of these samples, the difference among these samples is obvious. Specifically, the 180-minute processed sample exhibits finer grain sizes, sharper grain boundaries, © Woodhead Publishing Limited, 2011

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16.9  Transmission electron microscopy bright-field and dark-field micrographs of equiaxed nanograins at the impacted surface of the C-2000 alloy processed using S2PD for: (a) and (b) 30 minutes; (c) and (d) 70 minutes; (e) and (f) 180 minutes, respectively. Source: From Villegas and Shaw, 2009.2 With permission. © Woodhead Publishing Limited, 2011



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and more uniform grain sizes. In contrast, 30-minute and 70-minute processed samples display larger grains and more diffuse diffraction contrast between individual grains. These phenomena are consistent with the expected strain gradient and how the strain field alters with the processing time, as predicted from FEM.14

16.3.5  Evolution of surface roughness and contamination Since S2PD relies on repeated impacts of balls on the surface of the workpiece, it is expected that surface roughness will increase after high-energy ball impacts. This is indeed the case. Detailed studies13,31,32 indicate that surface roughening in high-energy ball impact processes can be explained by the indentation process of impacting balls, and the surface roughness evolution can be divided into three stages: the roughness increase stage, the roughness decrease stage, and finally the steady-state stage. These three stages are related to different stages of the surface coverage by indents generated by impacting balls.31 The steady-state stage corresponds to the impact coverage of the entire surface multiple times, and the surface roughness at the steady-state increases with the ball size.32 If cold adhesion between balls and the workpiece takes place during processing, the subsequent separation of balls from the workpiece will result in surface contamination and may lead to continued increases in surface roughness beyond the steady-state.32 This will inevitably degrade the properties and performance of the workpiece. Many studies have indeed revealed that optimization in the SP and S2PD time is necessary; otherwise, the fatigue resistance of the impacted workpiece decreases rather than increases.19,30

16.4 Tensile properties of metals with a nanocrystalline surface and hardened layer The tensile properties of metals subjected to S2PD have been studied by several authors.8,33,34 Since S2PD processes only alter surface properties, it is expected that these processes cannot change the tensile strength of bulk materials significantly. Nevertheless, when bulk materials are in a plate form, a 35% improvement in the tensile yield strength of mild steels has been shown.8 Improvements in the tensile yield strength by 65–85% for the C-2000 alloy have also been demonstrated.33 However, in all of these cases some reduction in the elongation has been observed.8,34 Furthermore, it is found that the elastic modulus in tensile tests for the S2PD-processed sample is different from that without S2PD processing.33 These phenomena and the associated mechanisms are reviewed below.

16.4.1  Elastic modulus in tensile tests Figure 16.10 shows the tensile stress–strain curves of C-2000 plates of 3.2-mm thick with and without S2PD processing on both sides of the plates.33

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16.10  Tensile stress–strain behavior of the C-2000 plates with and without S2PD processing as indicated: (a) overall stress–strain curves and (b) the blow-up of the stress–strain behavior at the early stage of deformation. The origins of the tensile stress–strain curves in (b) have been shifted slightly to facilitate the observation of the slopes of the stress–strain curves. Source: From Tian et al., 2008a.33 With permission.)

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It is clear that both the 0.2% offset yield strength and ultimate tensile strength have been improved via S2PD processing. Additionally, it is noted that the elastic modulus of the specimen, as gauged from the slope of the stress–strain curve at the elastic deformation range, has decreased after S2PD processing (Fig. 16.10 (b)). With the aid of FEM, it is found that the reduced modulus is induced by residual compressive stresses at the surface region introduced by S2PD processing.33 Because of the presence of residual compressive stresses at the surface region, the central region of the plate is in residual tension. Thus, during tensile loading the central region deforms plastically first. The localized yielding of the specimen expands from the central region towards the surface region as the external loading increases. The global yielding of the entire specimen, however, does not occur until the entire cross-section of the specimen deforms plastically. Thus, the ‘elastic deformation’ shown in Fig. 16.10 is actually plastic deformation at the central region constrained by the elastic deformation at the surface region, leading to an overall reduced ‘elastic modulus.’

16.4.2  Tensile yield strength As shown in Fig. 16.10, both the 0.2% offset yield strength and ultimate tensile strength of C-2000 plates have been improved via S2PD processing. Specifically, the 0.2% offset yield strength has been increased by ~65% and ~84% for the 30- and 180-minute processed samples, respectively, over the annealed sample. Intuitively, the improvement can be directly related to the formation of the nc surface and the work-hardened surface region. Quantitative analysis via FEM, however, offers the relative contribution of each factor, and reveals that residual compressive stresses at the surface region also contribute to the improved yield strength.33 For the 3.2-mm thick C-2000 plates shown in Fig. 16.10, the simulation of FEM reveals that 40% of the increase in the apparent yield strength shown in Fig. 16.10 comes from residual stresses and 60% from the presence of the nc surface and work-hardened surface region induced by S2PD. Residual stresses contribute to the increase in the apparent yield strength of the specimen with S2PD processing for the following reasons.33 The global yielding of the entire specimen, which determines the apparent yield strength, will not occur until 1) residual compressive stresses at the surface region have been overcome and 2) tensile stresses at the surface region have been subsequently built up to reach the yield stress. By the time the tensile stress at the surface region has reached the yield stress of the material, the central region has plastically deformed and work hardened further. Thus, as a result of the work hardening of the central region, the specimen will yield at a higher stress than the specimen without residual stresses. The contribution of the presence of the nc surface and work-hardened surface region to the increase in the apparent yield strength of the specimen is straightforward, and can be related to the increase in the local yield strength at the

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surface region, which pushes the global yielding the entire specimen to a higher stress level.33 However, the relative contributions of the nc surface and workhardened surface region depend on the materials system. In addition to this general conclusion, the quantitative analysis of FEM does reveal an unexpected outcome, that is, the contribution from residual stresses is a substantial portion of the increase, and thus their effects cannot be ignored when considering the apparent yield strength of the specimen with S2PD processing.

16.4.3  Tensile ductility In spite of the improvements in the tensile yield and ultimate strength, S2PD processing typically results in a decrease in the tensile elongation.8,34 As shown in Fig. 16.10, the tensile elongation decreases from about 60% for the annealed sample to 40% and 30% for the samples with 30- and 180-minute processing, respectively. For steels the 35% enhancement in the tensile yield strength is accompanied by a 4% reduction in the elongation.8 Detailed analysis of experimental data34 reveals that S2PD processing also leads to decreases in the strain-hardening coefficient, the uniform true strain, and the reduction of area. The overall fracture morphology of tensile specimens has also been changed from the cup-and-cone fracture for the annealed sample to the shear fracture for S2PD-processed samples. Figure 16.11 shows the fracture surface of the annealed C-2000 sample, which is consistent with the observed cup-and-cone fracture morphology,34 i.e. the central region exhibits extensive equiaxed dimples, indicating substantial plastic deformation of the boundaries between micro-voids before local separation of the void boundaries. At the edge region where oblique shear rupture occurs at the ‘cone’ portion of the fracture, slightly elongated dimples with a much-reduced depth are present. Figure 16.12 shows that the equiaxed dimples observed in the annealed sample have become elongated dimples after 30 minutes of S2PD processing. This change is consistent with the shear fracture mode found for S2PD processed samples. For the samples with 180 minutes of S2PD processing, further changes in the fracture surface are noted, that is, dimples with shallow depth appear in the central region of the samples. The decreased depth of dimples from 30- to 180-minute processed samples is a reflection of the decreased plastic deformation of the boundaries between microvoids before local separation of the void boundaries. Such a change in the fracture surface is in good accordance with the decrease in the tensile elongation and the reduction of area. The fracture surfaces at the edge regions for 30- and 180-minute processed samples are similar, showing slightly elongated dimples with very shallow depth. The analysis via FEM 34 reveals that the fracture morphology change from the cup-and-cone to shear fracture is due to higher tensile stresses at the surface region than those at the central region of the specimen because of the presence of the nanograined surface and the work-hardened surface region created via S2PD processing.

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16.11  Fracture surfaces of the annealed C-2000 sample with (a) from the center and (b) from the edge of the specimen. Source: From Tian et al., 2008b.34 With permission.

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16.12  Fracture surfaces of C-2000 samples with S2PD processing: (a) from the center of the 30-min processed sample, (b) from the center of the 180-min processed sample, and (c) from the edge of the 180-min processed sample. Source: From Tian et al., 2008b.34 With permission.

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The presence of larger tensile stresses at the surface region than those in the central region results in the change in the initiation site of the fatal crack from the central region for the annealed sample to the specimen surface for the S2PD-processed samples. For the annealed sample in which tensile stresses are uniformly distributed over the entire cross-section during the stage of uniform strain, fine cavities form at the center of the specimen under a triaxial state of stress when necking occurs. These cavities grow and coalesce into a central crack, which leads to the final fracture of the specimen. In contrast, for the S2PD-processed samples the high tensile stress at the processed surface results in the initiation of the fatal crack at the surface even though there is a triaxial state of stress at the center of the specimen due to necking. Once the fatal crack is formed at one of the S2PD processed surfaces, it propagates along shear planes at roughly 45° to the tensile axis towards the other surface of the specimen, thereby leading to the observed shear fracture.34 The reduced tensile ductility is thus attributed to the presence of the nanograined surface and the work-hardened surface region created via S2PD.34 Both the nanograined surface and the work-hardened surface region result in a decrease in the strain-hardening coefficient and at the same time lead to higher tensile stresses at the surface region. Therefore, fatal cracks initiate at the surface prematurely, resulting in a decrease in the tensile elongation and the fracture mode change from the cup-andcone to shear fracture. The residual compressive stresses at the surface region created via S2PD, however, are found to have little influence on the tensile ductility of the specimen. The same conclusion holds for the surface roughness of S2PD-processed samples, i.e. surface roughness does not have much influence on the ductility.34

16.5 Fatigue resistance of metals with a nanocrystalline surface and hardened layer Fatigue properties of metals are highly sensitive to the surface condition and properties of the materials. Thus, it is expected that S2PD can have substantial impact on fatigue properties. This is indeed the case. Several recent studies12,30,35,36 have shown that S2PD can improve the fatigue limits of stainless steels, carbon steels, and nickel-based C-2000 alloys. A recent study1 further shows that S2PD is more potent in improving the fatigue limit than SP. The mechanism responsible for the improved fatigue resistance has also been investigated with the aid of FEM coupled with experiments.3 The key findings from these studies are briefly summarized below.

16.5.1  Improvement in the fatigue limit Figure 16.13 compares the S-N curves of the C-2000 alloy with SP and S2PD processing.1 The annealed sample is also included as the baseline for comparison. It is quite clear that both SP and S2PD processing have led to improvements in the fatigue endurance limit.

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16.13  S-N curves for annealed, shot peened, and S2PD-processed C-2000 samples, showing the S2PD-processed sample has the highest fatigue endurance limit, followed by the SP-processed sample. Source: From Shaw et al., 2010.1 With permission.

The result is consistent with the well-known phenomenon that SP improves the fatigue resistance over samples without the treatment.18–21 Moreover, Fig. 16.13 reveals that S2PD is more potent in enhancing the fatigue limit than SP. However, it should be emphasized that the comparison made in Fig. 16.13 is carried out for the processing conditions that provide the improvements in the fatigue resistance for both SP and S2PD. Thus, the conclusion derived from Fig. 16.13 should not be generalized to include broad processing conditions. In fact, it is well known that ‘over-processing’ could occur with SP, leading to the degraded fatigue resistance rather than improvements.19 The same is true for S2PD, as shown recently with the prolonged processing of S2PD exhibiting a decrease in the fatigue resistance rather than an increase.30

16.5.2  Mechanism of the improved fatigue resistance In order to understand the contributions of the nc surface, residual compressive stresses, and work-hardened surface region to the observed improvement in the fatigue limit, FEM has been performed.1,3 In those studies the individual contribution of each factor (i.e. the nc surface, the work-hardened surface region, and the residual compressive stresses) to the improved fatigue limit has been evaluated based on their effects on the stress and strain values at the specimen surface as well as the stress and strain profiles within the specimen when subjected to a four-point-bend fatigue test. The FEM analysis3 reveals that the nc surface © Woodhead Publishing Limited, 2011



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and work-hardened surface region play a significant role in enhancing the fatigue limit of the C-2000 alloy with S2PD processing. In contrast, even though residual compressive stresses also contribute to the improved fatigue limit, less contribution is provided by residual compressive stresses. The FEM analysis1 also sheds light on why S2PD can provide better improvement in the fatigue limit than SP, as shown in Fig. 16.13. It is concluded that S2PD produces a thicker nc surface layer and a larger work-hardened surface region with higher residual compressive stresses than SP. It is these differences that make S2PD more effective in improving the fatigue properties than SP.1 It is noted that Fig. 16.13 shows a crossover among the annealed, SP-processed and S2PD-processed C-2000 samples in the low cycle fatigue regime. The mechanism for this phenomenon is likely related to the fact that plastic deformation has occurred at the surface region for all of these samples in the low cycle fatigue regime. The yield strength of the annealed C-2000 sample is only 400 MPa.14 Based on this, it is proposed that the crossover is likely due to the low ductility of the nanograined surface at the SP- and S2PD-processed C-2000 samples and fading of the residual compressive stresses, both of which can promote the formation of fatigue cracks at the surface. This hypothesis appears to be consistent with the fact that S2PD-processed samples display a stronger tendency for the crossover than SP-processed samples because the former have a thicker nanograined surface layer than the latter. However, it should be emphasized that the crossover phenomenon is not present in other materials. When stainless steels and carbon steels are treated with S2PD, no crossover is observed.35,36 Therefore, additional work is needed to clarify the crossover mechanism observed in the C-2000 alloy.

16.6 Wear resistance of metals with a nanocrystalline surface and hardened layer Both friction and wear are surface-contact dominated processes, and thus S2PD is expected to have dramatic impacts on friction properties and wear resistance. A recent study37 has indeed confirmed such an expectation. It is shown that the friction coefficient of a low carbon steel is reduced by ~50% after S2PD processing. The abrasive wear resistance of the same low carbon steel against a diamond stylus has been improved as well. The improvements in both friction and wear properties have been attributed to the formation of a nc surface layer of 10 µm thick induced by S2PD.37 It is proposed that the increased hardness associated with the nc surface layer has resulted in shallower penetration of the diamond stylus into the low carbon steel, and therefore the lower friction coefficient as well as the less wear volume loss due to less plowing and micro-cutting.37 A more complicated situation is found recently with high-carbon steels, which are less ductile than low-carbon steels.38 It is shown that after S2PD processing the high carbon steel exhibits a similar wear resistance to that of the counterpart without S2PD processing, in spite of the formation of a nc surface layer of ~60 µm thick in © Woodhead Publishing Limited, 2011

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the S2PD-processed steel. However, the wear resistance is markedly enhanced after thermal annealing of the S2PD-processed steel at different temperatures to induce grain growth. Annealing at 650°C results in growth of ferrite grains from 8 nm to 32 nm, and is particularly effective in enhancing the wear resistance.38 Annealing at temperatures higher than 650°C leads to significant grain growth and the improved wear resistance starts to decrease. These interesting phenomena have been rationalized based on the modified empirical Archard equation38 [16.5]



where W is the wear rate with an applied pressure P, H is the material’s hardness, and K is a pre-factor relative to the material’s ductility. The high-carbon steel at the S2PDprocessed condition has a high hardness with low ductility. As a result, microcracking is relatively easy, leading to a high K value and the increased material removal during abrasive wear. After proper annealing at 650°C, the surface of the steel has a lower hardness than the steel in the S2PD-processed condition, but with better plasticity. As such, the steel annealed at 650°C exhibits the best wear resistance because of the proper combination of sufficient hardness and moderate plasticity. In contrast, the steel annealed at temperatures higher than 650°C is too soft to resist the abrasive wear and thus has the decreased wear resistance.38 Friction and wear properties of the nickel-based C-2000 alloy with S2PD processing have also been examined. Shown in Fig. 16.14 are three-dimensional wear tracks of the annealed, shot-peened, and S2PD-processed C-2000 alloy. It is clear that the annealed C-2000 alloy has the deepest groove and thus the worst wear resistance, while the S2PD-processed C-2000 alloy has the best wear resistance because it exhibits a negligible worn track. Quantitative analysis of the worn track reveals that the wear rate of the annealed C-2000 alloy against Si3N4 balls is 1 × 10–5 mm3/N.m. The shot peening treatment has reduced the wear rate by one order of magnitude to 1 × 10–6 mm3/N.m, whereas the wear rate of the S2PD-processed sample is negligible because the wear volume is too small to be measurable with accuracy under the testing condition investigated. It should be mentioned that improved wear resistance has been reported previously by many studies on shot-peened samples, and the improvement has been related to one or all of the following mechanisms: (a) the presence of residual compressive stresses, (b) increased hardness, (c) decreased coefficient of friction, and (d) altered surface roughness. However, detailed studies of the contribution from each factor listed above in conjunction with the presence of a nc surface layer have not been carried out yet for S2PD-processed materials. Systematic studies in this area are anticipated in the near future.

16.7 Conclusions The latest developments in high-energy ball impact processes, which have higher kinetic energies than shot peening, have offered new opportunities for surface © Woodhead Publishing Limited, 2011



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16.14  Three-dimensional wear tracks of the C-2000 alloy with a Si3N4 ball as the antagonist: (a) the annealed, (b) the shot-peened, and (c) the S2PD-processed sample. The wear test was conducted in a pin-on-disk configuration under ambient laboratory conditions (20°C and 45% relative humidity) and a load of 4.9 N without lubrication. Note that the deepest groove is created in the annealed sample, while the surface of the S2PD-processed sample remains almost the same as that before the wear test. © Woodhead Publishing Limited, 2011

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deformation processes. Because of their high kinetic energies, high-energy ball impact processes can produce a thicker plastically deformed layer with higher residual compressive stresses and a thicker nc surface layer than shot peening. Experimental studies have demonstrated that the more pronounced microstructural and stress-state changes induced by high-energy ball impact processes can offer better improvements in the tensile strength, fatigue properties, and wear resistance than shot peening can achieve. However, more direct comparisons between S2PD and SP are still needed to further quantify the benefit of S2PD. Systematic studies in this area are anticipated in the near future. Fundamental studies on separating individual contributions of residual compressive stresses, a work-hardened layer, and surface nanograins have been pursued and revealed that each of these factors plays a role in enhancing the tensile strength and fatigue resistance. However, further studies along this line are expected to be active in the near future because the understanding developed from such studies is essential for process optimization and full utilization of the potential of S2PD. Integration of high-energy ball impact processes with other treatments, such as annealing, carburizing and nitriding, can provide new avenues for strengthening materials. S2PD processing followed by annealing to enhance the wear resistance of high carbon steels is a good example of this kind.38 A recent work39 has demonstrated that the nc surface of a pure iron plate created via S2PD can greatly enhance the nitriding reaction so that nitriding can be accomplished at 300°C rather than 500°C used in conventional nitriding processes. Such a trend in integrating several processing approaches into one to achieve synergy is expected to continue.

16.8 Acknowledgements The author would like to thank his former students, Dr Juan C. Villegas, Dr Kun Dai, and Mr Misael Manjarres for their significant contributions to the work present here. The collaboration with and contributions from Professor Peter K. Liaw and Dr Jiawan Tian at the University of Tennessee, Professor Angel L. Ortiz at the Universidad de Extremadura, Spain, Professor Ruiming Ren at Dalian Jiaotong University, China, and Dr Dwaine L. Klarstrom at Haynes International are greatly appreciated. Financial support from the National Science Foundation through Grant No. DMR-0207729 is acknowledged.

16.9 References   1 Shaw L., Tian J.W., Ortiz A.L., Dai K., Villegas J.C., Liaw P.K., Ren R. and Klarstrom D.L. (2010), ‘A direct comparison in the fatigue resistance enhanced by surface severe plastic deformation and shot peening in a C-2000 superalloy’, Mater Sci Eng A, 527, 986–994.   2 Villegas J.C. and Shaw L. (2009), ‘Nanocrystallization process and mechanism in a nickel alloy subjected to surface severe plastic deformation’, Acta Mater, 57, 5782–5795.   3 Dai K. and Shaw L. (2008), ‘Analysis of fatigue resistance improvements via surface severe plastic deformation’, Int J Fatigue, 30, 1398–1408.

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  4 Ortiz A.L., Tian J.W., Villegas J.C., Shaw L. and Liaw P.K. (2008), ‘Interrogation of the microstructure and residual stress of a nickel-base alloy subjected to surface severe plastic deformation’, Acta Mater, 56, 413–426.   5 Lu K. and Lu J. (1999), ‘Surface nanocrystallization (SNC) of metallic materials – presentation of the concept behind a new approach’, J Mater Sci Technol, 15, 193–198.   6 Tao N.R., Sui M.L., Lu J. and Lu K. (1999), ‘Surface nanocrystallization of iron induced by ultrasonic shot peening’, Nanostruct Mater, 11, 433–440.   7 Wu X., Tao N., Hong Y., Xu B., Lu J. and Lu K. (2002), ‘Microstructure and evolution of mechanically induced ultrafine grain in surface layer of Al-alloy subjected to USSP’, Acta Mater, 50, 2075–2084.   8 Liu G., Wang S.C., Lou X.F., Lu J. and Lu K. (2001), ‘Low carbon steel with nanostructured surface layer induced by high-energy shot peening’, Scripta Mater, 44, 1791–1795.   9 Tao N.R., Wang Z.B., Tong W.P., Sui M.L., Lu J. and Lu K. (2002), ‘An investigation of surface nanocrystallization mechanism in Fe induced by surface mechanical attrition treatment’, Acta Mater, 50, 4603–4616. 10 Zhang H.W., Hei Z.K., Liu G., Lu J. and Lu K. (2003), ‘Formation of nanostructured surface layer on AISI 304 stainless steel by means of surface mechanical attrition treatment’, Acta Mater, 51, 1871–1881. 11 Zhu K.Y., Vassel A., Brisset F., Lu K. and Lu J. (2004), ‘Nanostructure formation mechanism of a-titanium using SMAT’, Acta Mater, 52, 4101–4110. 12 Villegas J.C., Shaw L., Dai K., Yuan W., Tian J.W., Liaw P.K. and Klarstrom D.L. (2005), ‘Enhanced fatigue resistance of a nickel-based Hastelloy induced by a surface nanocrystallization and hardening process’, Phil Mag Lett, 85, 427–438. 13 Dai K., Villegas J. and Shaw L. (2005), ‘An analytical model of the surface roughness of an aluminum alloy treated with a surface nanocrystallization and hardening process’, Scripta Mater, 52, 259–263. 14 Dai K. and Shaw L. (2007), ‘Comparison between shot peening and surface nanocrystallization and hardening processes’, Mater Sci Eng A, 463, 46–53. 15 Umemoto M., Todaka K. and Tsuchiya K. (2004), ‘Formation of nanocrystalline structure in carbon steels by ball drop and particle impact techniques’, Mater Sci Eng A, 375–377, 899–904. 16 Todaka K., Umemoto M. and Tsuchiya K. (2004), ‘Comparison of nanocrystalline surface layer in steels formed by air blast and ultrasonic shot peening’, Mater Trans, 45, 376–379. 17 Fuchs H.O. (1986), Mechanical Engineer’s Handbook, New York, Wiley. 18 Martin U., Altenberger I., Scholtes B., Kremmer K., Oettel H. (2004), ‘Cyclic deformation and near surface microstructures of normalized shot peened steel SAE 1045’, Mater Sci Eng A, 246, 69–80. 19 Wagner L. (1999), ‘Mechanical surface treatments on titanium, aluminum and magnesium alloys’, Mater Sci Eng, A263, 210–216. 20 Altenberger I., Scholtes B., Martin U., Oettel H. (1999), ‘Cyclic deformation and near surface microstructures of shot peened or deep rolled austenitic stainless steel AISI 304’, Mater Sci Eng A, 264, 1–16. 21 Cao W., Fathallah R. and Castex L. (1995), ‘Correlation of Almem arc height with residual stresses in shot peening process’, Mater Sci Technol, 11, 967–973. 22 Shaw L., Villegas J., Huang J.Y. and Chen S. (2008), ‘Strengthening via deformation twinning in nickel alloys’, Mater Sci Eng A, 480, 75–83. 23 Al-Obaid Y.F. (1995), ‘Shot peening mechanics: experimental and theoretical analysis’, Mech Mater, 19, 251–260.

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24 Guagliano M. (2001), ‘Relating Almen intensity to residual stresses induced by shot peening: a numerical approach’, J Mater Proc Technol, 110, 277–286. 25 Fathallah R., Inglebert G. and Castex L. (1998), ‘Prediction of plastic deformation and residual stresses induced in metallic parts by shot peening’, Mater Sci Technol, 14, 631–639. 26 Love A.E.H. (1934), Mathematical Theory of Elasticity, Cambridge, Cambridge University Press. 27 Davies R.M. (1949), ‘The determination of static and dynamic yield stresses using a steel ball’, Proc R Soc London, 197A, 416–432. 28 Shaw M.C. and DeSalvo G.J. (1970), ‘On the plastic flow beneath a blunt axisymmetric indenter’, Trans ASME, J Eng Ind, 92, 480–493. 29 Meguid S.A., Shagal G., Stranart J.C. and Daly J. (1999), ‘Three-dimensional dynamic finite element analysis of shot-peening induced residual stress’, Finite Elem Anal Design, 31, 179–191. 30 Tian J.W., Villegas J.C., Yuan W., Fielden D., Shaw L., Liaw P.K. and Klarstrom D.L. (2007), ‘A study of the effect of nanostructured surface layers on the fatigue behavior of a C-2000 alloy’, Mater Sci Eng A, 468–470, 164–170. 31 Dai K., Villegas J., Stone Z. and Shaw L. (2004), ‘Finite element modeling of the surface roughness of 5052 Al alloy subjected to a surface severe plastic deformation process’, Acta Mater, 52, 5771–5782. 32 Villegas J.C., Dai K. and Shaw L. (2003), ‘Surface roughness evolution in the surface nanocrystallization and hardening (SNH) process’, in Srivatsan T and Varin R, Processing and Fabrication of Advanced Materials: XII, Materials Park, OH, ASM International, 358–372. 33 Tian J.W., Dai K., Villegas J., Shaw L., Liaw P.K., Klarstrom D.L. and Ortiz A.L. (2008), ‘Tensile deformation behavior of a nickel alloy subjected to surface severe plastic deformation’, Mater Sci Eng A, 493, 176–183. 34 Tian J.W., Shaw L., Liaw P.K. and Dai K. (2008), ‘On the ductility of a surface severely plastically deformed nickel alloy’, Mater Sci Eng A, 498, 216–224. 35 Roland T., Retraint D., Lu K. and Lu J. (2006), ‘Fatigue life improvement through surface nanostructuring of stainless steel by means of surface mechanical attrition treatment’, Scripta Mater, 54, 1949–1954. 36 Li D., Chen H.N. and Xu H. (2009), ‘The effect of nanostructured surface layer on the fatigue behaviors of a carbon steel’, Appl Surf Sci, 255, 3811–3816. 37 Wang Z.B., Tao N.R., Li S., Wang W., Liu G., Lu J. and Lu K. (2003), ‘Effect of surface nanocrystallization on friction and wear properties in low carbon steel’, Mater Sci Eng A, 352, 144–149. 38 Zhou L., Liu G., Han Z. and Lu K. (2008), ‘Grain size effect on wear resistance of a nanostructured AISI52100 steel’, Scripta Mater, 58, 445–448. 39 Tong W.P., Tao N.R., Wang Z.B., Lu J. and Lu K. (2003), ‘Nitriding iron at low temperatures’, Science, 299, 686–688.

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17 Fatigue behaviour in nanostructured metals H.W. HÖPPEL and M. GÖKEN, Friedrich-Alexander University of Erlangen-Nuremberg, Germany Abstract: Nanocrystalline materials are very promising for modern lightweight engineering applications due to their extraordinary mechanical properties under monotonic as well as under cyclic loading. In particular, the fatigue properties of nanostructured metals and alloys are one of the key issues for the successful use of this new class of materials in engineering applications. As the fatigue behaviour of nanocrystalline materials cannot simply be explained by the Hall–Petch effect, several aspects such as microstructural stability, shearbanding or grain size distributions have to be considered. Starting with some general findings on the fatigue behaviour and fatigue lives of nanostructured materials, the fatigue behaviour of aluminum, magnesium and titanium alloys as well as of steels are discussed in detail. Strategies for optimizing the fatigue lives and the cyclic deformation behaviour are also formulated. Key words: ultrafine-grained (UFG) materials, nanocrystalline materials, severe plastic deformation, ECAP, fatigue behaviour, fatigue life, aluminium alloys, titanium alloys, magnesium alloys, steels, copper microstructure, damage mechanisms.

17.1 Introduction and motivation Nanostructured metals and alloys exhibit extraordinary mechanical properties under monotonic loading. Thus, this new class of material is very promising for modern lightweight engineering applications, which is also reflected in the growing number of publications in that field. Besides the monotonic mechanical properties, fatigue life and cyclic deformation behaviour are key features for the successful use of nanostructured materials in many potential engineering applications. Although many attempts have been made to understand the mechanical behaviour of nanostructured metallic materials, research activities on the fatigue properties of this new class of materials are still limited. There is a broad variety of processes for producing nanostructured materials, using either the bottom-up or the top-down approach. In this chapter, focus is laid on materials that can be produced in quantities suitable for potential engineering applications. This includes materials produced by severe plastic deformation processes, like Equal-Channel Angular Pressing (ECAP), Accumulative Roll Bonding (ARB) or High-Pressure Torsion (HPT). In this context, the expression ‘nanostructured materials’ refers to materials with grain sizes above 100 nm and below 1 µm, usually denoted as ultrafine-grained (UFG) materials. The progress that has been made in the last two decades in the field of Severe Plastic Deformation (SPD) processing, cf.,1,2,3 forms the basis for the potential 507 © Woodhead Publishing Limited, 2011

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use of nanostructured materials in engineering applications. Besides the increased quality of SPD-processed specimens, good progress has also been made in tailoring the properties of nanostructured materials during SPD processing,4 as well as in processing hard-to-deform materials, like steels,5 magnesium6 and titanium alloys.7,8 Besides, emphasis has been placed on scaling-up SPDprocessing of nanostructured materials for potential industrialization. Current research on continuous SPD techniques, like ECAP-Conform,9 continuous confined strip shearing (C2S2),10 as well as on up-scaling the ARB-process11 also reflect the great innovation potential of these materials (compare12). It is well known that UFG metals exhibit very promising mechanical properties under monotonic loads: high specific strength is paired with a relatively high ductility. For particular UFG materials it was also found that ductility (elongation to failure) is significantly higher than for the conventional grain-sized (CG) counterpart. This enhanced ductility paired with a significant increase in strength, introduced as the ‘paradox of strength and ductility’, has been found so far for ECAP-processed Cu and Al13,14,15 as well as for ARB-processed UFG Al,16 AA601616 and also for ARB-processed AA8011.17 In all these cases, the ductility increases as the strain rate decreases, indicating that enhanced strain rate sensitivity is the governing issue for the occurrence of the high ductility and strength of UFG materials. Although this paradox has been proven for different materials, the relevant deformation mechanisms are still being discussed. It is suggested that the enhanced ductility of UFG materials is due to thermally activated recovery of dislocations at the grain boundaries.18,19 As the volume fraction of grain boundaries is significantly increased in UFG materials, pipe diffusion processes along the grain boundaries will govern the deformation behaviour even at moderate homologous temperatures. Hence, gliding dislocations from the grain interior can easily annihilate at the grain boundaries by thermally activated climb processes and consequently, ductility is enhanced. By a simple calculation the strongly increasing fraction of the grain boundary volume relative to the volume of the grain interior can be derived. Considering cubes with a (grain) size of 100 µm for the CG condition or, respectively, a (grain) size of 100 nm for the UFG condition, and taking into account that the grain boundary itself or the grain boundary affected zone has a thickness of 3 nm, the volume fraction of the grain boundaries amounts to 0.01% for the CG condition whereas for the UFG condition, it amounts to 9.27%. Besides thermally activated recovery processes, grain boundary sliding at low temperatures20,21 and the generation of partial dislocations and twinning22 are also discussed to be the relevant deformation mechanisms explaining the enhanced ductility. More generally, it seems to be important to evaluate carefully the microstructural details of the materials investigated. As shown by Vevecka et al.,23 the strain rate sensitivity and hence the ductility significantly depends on the microstructure obtained by different ECAP processing. Although these principal questions still remain open, nanostructured metallic materials have a rather high potential for innovative applications where a high

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standard of fatigue properties are required. Generally speaking, nanostructured/ UFG materials exhibit significantly increased fatigue lives in a Wöhler (S-N) plot. In the following, some general findings on the fatigue behaviour of UFG materials, and in particular the fatigue behaviour of UFG steels and of UFG light metals, are reported in detail.

17.2 General findings on the fatigue behaviour and the fatigue lives of nanostructured model materials 17.2.1  Fatigue lives Discussing fatigue life, the most commonly used measure is the classical Wöhler (S-N) plot, in which the fatigue life is plotted with regard to the stress amplitude. As a rule of thumb it is known that increased strength under monotonic loading will also lead to an increase in fatigue life in a Wöhler (S-N) plot. In contrast, elongation to failure in a tensile test, often denoted as ductility, is known to affect fatigue life when the plastic strain becomes dominant. Thus, discussing the fatigue behaviour of nanostructured materials both aspects, strength and ductility, have to be considered. First investigations on the cyclic deformation behaviour of UFG single-phase model materials like pure copper, nickel or aluminium were performed by Rabinovich and Markushev,24 Vinogradov et al.25 and Agnew and Weertman60 more than a decade ago. So far, several groups of researchers have carried out only a limited number of systematic investigations on the fatigue behaviour of UFG copper,26–38 UFG nickel39,40 and UFG aluminium.34,35,41,42 All the results published for UFG model materials so far show significantly increased fatigue lives in a Wöhler (S-N) plot compared to their CG counterparts. These findings can easily be explained by the increased strength of the nanostructured materials, which is due to a much higher athermal stress component and thus, their fatigue lives are also superior compared to that of the CG counterparts. This statement is applicable not only to model materials in the low cycle fatigue (LCF) and high cycle fatigue (HCF) regime, but also to the alloyed and multiphase materials investigated so far. In this context, it became evident that the higher the increase in fatigue life at a given amplitude, the higher the stress amplitude. This behaviour can be explained as follows: Due to the significantly enhanced ultimate tensile strength (UTS) of UFG materials compared to the CG counterparts, the sustainable stress level at a given fatigue life is markedly increased in the LCF regime. As the stress amplitude decreases, the plastic strain amplitude decreases and work hardening as an additional hardening mechanism is reduced. Hence, in the HCF regime the sustainable stress levels of the UFG materials at a given fatigue life are still superior to those of the CG condition, but the differences are not as high as in the LCF-regime. These explanations are also supported by the obtained micro-yielding and work-hardening behaviour of nanostructured materials

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(compare References 15, 16 and 42). Thus, the difference in HCF fatigue lives between UFG and CG materials is due to their significantly different microyielding behaviour, (compare References 30, 34 and 42) which is schematically indicated in Fig. 17.1 by ∆σ MYS . When considering the very high cycle fatigue (VHCF) regime, where the number of cycles to failure is higher than 107, the fatigue lives of the UFG condition remain superior to that of the CG specimen, as it was shown for UFG copper and UFG aluminium.43,61 In contrast, UFG microstructures are disadvantageous when the plastic strain amplitude is the relevant quantity of the design. As suggested by Mughrabi and Höppel,28 a crossover of the fatigue life curves of CG and UFG materials in a

17.1  Schematic Wöhler (S-N) diagram showing the influence of an UFG microstructure on fatigue life.

17.2  Schematic total strain fatigue life diagram reflecting the crossover of the fatigue life curves of CG and UFG conditions, as suggested in Reference 28.

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total strain fatigue life diagram takes place, see Fig. 17.2. According to Morrow44 and Landgraf,45 the total strain fatigue life is given by the combination of the well-known empirical laws from Coffin46 and Manson,47 as well as Basquin48 (see Eq. (17.1)).

[17.1]

According to Eq. (17.1), the fatigue life for a given total strain amplitude ∆εt /2 can be calculated from the combination of the Coffin–Manson and Basquin laws. Based on Morrow’s44 investigations of plain carbon steel at different microstructural states and based on his principal considerations derived therefrom, total strain fatigue life is significantly influenced by the strength and the ductility of the material (see Fig. 17.3). A strong material is beneficial in the HCFregime, whereas in the LCF regime, where the Coffin–Manson law governs fatigue life, a ductile material should be preferred. To achieve satisfying fatigue properties for a broad range of strain amplitudes it is important to balance both strength and ductility of the material. In this context it becomes apparent that improving fatigue life over a broad range of total strain amplitudes has to shift the point of transition to high total strain amplitudes. UFG materials exhibit a drastically reduced fatigue ductility coefficient εf' of the Coffin–Manson law while the fatigue strength coefficient σf' of the Basquin law is significantly increased, both compared to the CG condition. The exponents (b and c) for both laws remain more or less unchanged (compare References 49,

17.3  Schematic total strain fatigue diagram for a strong, ductile and tough material. Please note the transition point marked in the diagram for a strain amplitude of 1% was derived for different states of a plain carbon steels. After Morrow.44

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50 and 51). Consequently, in the HCF regime, i.e. in the regime of small plastic strain amplitudes, which is usually studied in stress-controlled tests and which is primarily governed by the Basquin law, the increased fatigue strength coefficient σf' accounts for the enhancement in fatigue life. On the other hand, in the LCF regime, i.e. in the regime of intermediate-to-high plastic strain amplitudes, in which usually strain-controlled experiments are performed and which is primarily governed by the Coffin–Manson law, the decreased fatigue ductility coefficient εf' will lead to a deterioration of the fatigue life.28–30,34,52 The crossover of the fatigue life curves (compare Fig. 17.2), is observed for all UFG materials except for titanium and titanium alloys, see for example References 32, 53, 54 and 68. As it seems that the crossover in the fatigue life curves of nanostructured and conventional grain size materials is unavoidable, focus should be laid on the transition point. For a successful use of UFG materials for prospective engineering applications, the transition point should be shifted to rather high strain amplitudes (and simultaneously to a low number of cycles to failure) as most of the fatigue loads during service are far below these amplitudes.

17.2.2  Influence of grain size To understand the fatigue properties of nanostructured materials, the influence of the grain size on the Wöhler (S-N) fatigue life diagram needs to be discussed in more detail. The influence of the grain size on fatigue behaviour and damage is summarized in a very detailed overview by Zhang and Wang.55 According to early works from Thompson and Backofen56 as well as Lukáš and Kunz,57 the influence of the grain size (in the range from some micrometers up to some millimetres) on fatigue lives is strongly related to the dominating glide character of the material. If the material exhibits a wavy glide character (which is supposed to be mainly influenced by the ease of cross slip) as in the case of aluminium and copper, only a small influence of the grain size is detectable in the lower LCF regime (intermediate-to-short fatigue lives), while in the upper LCF and the HCF regime no grain size effect for the CG states is found. When the glide character is planar, as for example in α-brass, a pronounced grain size effect on the fatigue lives is found throughout the complete fatigue life range. Regarding UFG materials, this situation changes drastically. As shown by Thiele et al.40,62 and Klemm39 for nickel, the cyclic saturation stress is affected by the grain size. If the grain size becomes smaller than about 4 µm, the cyclic saturation stress increases, following a Hall–Petch type relationship, as shown in Fig. 17.4, for a given plastic strain amplitude of 2 × 10–3. Due to the small grain size, the back stresses of the boundaries can either affect the source stress for emitting a gliding dislocation or the gliding stress itself. With this assumption a grain or even a subgrain boundary will affect the fatigue behaviour due to either a direct interaction of a moving dislocation with the boundaries or an interaction between the stress field of the boundary and the dislocation source.

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17.4  Cyclic saturation stress σs,GB (grain boundary contribution) vs. the inverse square root of the grain size D (Hall–Petch plot) for nickel deformed cyclically at ∆εpl /2 = 2 × 10–3. After Klemm39 and Thiele et al.62 as modified in Mughrabi et al.34 Note: FG: fine-grained, MC: microcrystalline, RT–ECAP and ET–ECAP refer to ECAP at room and at elevated temperature.

These findings can also explain the changes in fatigue life diagrams. Irrespective of the glide character there is a strong grain size dependence of the fatigue lives ranging from the LCF to the HCF regime. In UFG materials with a grain size below 1 µm, the grain size lies in the range of the slip distance of the dislocations. In contrast, in CG materials the gliding distance of dislocations are much smaller than the grain size for intermediate-to-low plastic strain amplitudes. Only pile-up effects of dislocations moving on a particular glide plane, like in-planar glide materials, will lead to a grain size effect on the fatigue properties. With increasing plastic strain amplitudes, the slip distances of the gliding dislocations increase and consequently, at high plastic strain amplitudes the gliding dislocations will interact with the grain boundaries even for wavy slip materials. In other words, the probability of gliding dislocations interacting with grain boundaries or grain boundary dislocations is much higher for UFG materials than for CG materials. In this context, it should be stated that the term grain size is used irrespective of the angle of misorientation between the adjacent (sub)grains. Although the characters of the boundaries are different, the hardening effects of subgrains or grains are supposed to be qualitatively similar. According to the Hall–Petch relationship, the hardening effect is inversely proportional to the square root of the grain size while for subgrains the hardening effect is inversely proportional to the grain size. Based on these observations, improvement of fatigue life cannot simply be explained by the well-known Hall–Petch58,59 relationship. Fatigue life is always strongly related to the question of the dominating cyclic deformation mechanisms. For monotonic, as well as for cyclic loading, the principal

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deformation mechanisms may vary from material to material and depend on the pre-processing in order to obtain a nanostructured metal or alloy. In particular, under cyclic loading it has turned out that for nanostructured materials microstructural stability is one of the key issues.38,60–62 Other issues that have to be considered carefully are the strain rate dependence of the fatigue behaviour, the effect of testing conditions (load/strain control) on the stability and the influence of the microstructure on the localization of deformation and on the crack formation and propagation. Moreover, very promising fatigue properties in the LCF as well as HCF regimes can be achieved by introducing so-called bimodal grain size distributions, where the microstructure consists of two distinctive grain size distributions: one group of grain size distributions belongs to the nano-scale range and the other to the microscale range. 28,29,35

17.2.3  Cyclic deformation behaviour In order to understand the fatigue properties of UFG materials, cyclic deformation behaviour and related damage mechanisms have to be considered. For more pure single-phase UFG materials, pronounced cyclic softening is often observed.26,29,31,60 In this context, systematic investigations on UFG Cu31 reveal that the microstructural stability is a key feature governing the cyclic deformation behaviour. For high-purity UFG copper in the LCF regime it was reported that dynamic grain growth occurs at a low homologous temperature of 0.22 followed by the formation of macroscopic shear bands.28,31 More specifically, grain growth and, related to that, the cyclic softening ratio, were found to be time- and temperature-dependent. Moreover, the plastic strain amplitude also affects the grain growth in a particular way (see Fig. 17.5). In the case of less pure singlephase materials, like commercial grade copper61,63 and commercial purity UFG Al,30,41,67 the reduced purity leads to drastically reduced dynamic grain coarsening, which is also reflected in a significantly different cyclic deformation behaviour, as shown in Fig. 17.6. Thus, it becomes apparent that the purity of single-phase materials has a strong influence on the cyclic deformation behaviour. Generally speaking, UFG materials of commercial purity are cyclically more stable than high-purity UFG materials, which usually show severe cyclic softening. In this context, the instability of the microstructure and, related to that, the grain boundary mobility, appear to be the relevant microstructural issue. It has also to be mentioned that the fatigue test conditions affect the occurrence of cyclic softening. According to the work of Kunz et al.,38 under stress-controlled conditions neither pronounced grain coarsening nor cyclic softening were detected, whereas for fatigue tests performed under strain control, pronounced cyclic softening was obtained. For the time being, it has to be stated that the relevant mechanisms leading to cyclic softening, grain coarsening and shear band formation are not yet clearly understood. In this context, the enhanced strain rate sensitivity (SRS) of UFG materials also has to be considered. The influence of

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17.5  Cyclic softening ratio vs. plastic strain amplitude for UFG copper and representative microstructures after fatigue loading until failure. Note: Please note the pronounced maximum in the cyclic softening ratio and the related very intensive grain coarsening observed. The cyclic softening ratio is calculated by using the materials response (stress or stress amplitude) at the beginning of the fatigue test divided by the materials response at half of the number of cycles to failure.31

17.6  Cyclic deformation curves of UFG high purity 99.99 OFHC-copper and UFG Al-99.5 fatigued at the same plastic strain amplitude of 1 × 10–3. Pronounced cyclic softening for UFG high-purity copper is clearly visible, whereas for UFG CP Al-99.5 cyclic softening is absent.

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the increased SRS on the fatigue life and the deformation behaviour of UFG Al was investigated in total strain controlled fatigue tests using different strain rates ranging from 5 × 10–3 s–1 to 5 × 10–5 s–1.64,77 The strain rate has a clear influence on the Wöhler (S-N) fatigue life as well as on the cyclic deformation behaviour (see Fig. 17.7). At lower strain rates, the UFG material is softer for approximately the first hundred cycles and the fatigue life is reduced by roughly a factor of two. After the first hundred cycles, pronounced hardening took place at all amplitudes applied. The corresponding stress amplitudes for the tests performed at the lower strain rates slightly exceeded the levels of the experiments performed at the higher strain rates. Such an influence was not found for the swaged CG condition. As mentioned earlier, there is an ongoing discussion on the dominating mechanism leading to the enhanced SRS. As localization of plastic deformation is always a prerequisite for fatigue crack nucleation and propagation, special emphasis should be put on the mechanisms leading to the crack formation in UFG materials. Based on

17.7  Cyclic deformation curves of UFG Al and swaged CG Al, respectively, fatigued at different constant total strain amplitudes and at two different strain rates; solid lines: 5 × 10–3 s–1 and dotted lines: 5 × 10–4 s–1. For an amplitude of ∆εtot /2 = 3.8 × 10–3 an additional test at a strain rate of 5 × 10–5 s–1 was also performed, indicated by an asterisk. Courtesy of D. Amberger.64

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the findings on UFG copper31,32,38,63 and other UFG materials like aluminium and titanium alloys,52,54,67,97 it can be concluded that the onset of macroscopic shear banding is mostly regarded as the relevant localization mechanism.28,33,65 Up to now, there has been an ongoing discussion about whether the shear bands are inherently formed during the ECAP process, whether they form due to a strain-path change from ECAP shear deformation to symmetrical push–pull deformation, or whether they form as a consequence of the local onset of grain coarsening.28,35,66,67 Based on the investigations made so far, it seems that the dominating mechanisms for the formation of macroscopic shear bands depends on the particular material properties (for instance the stacking fault energy and others), on the kind and degree of impurities, on the SPD processing parameters leading to strongly different microstructures, and also on the cyclic deformation conditions. More detailed aspects on the cyclic deformation behaviour and on the fatigue lives of nanostructured materials are summarized for example in.35,38,68,69 Unless these manifold results obtained so far on the fatigue properties of UFG materials, the relevant processes taking place in UFG materials under cyclic loading are not clear yet and need to be investigated systematically in more detail. Nevertheless, UFG materials provide a high potential for prospective engineering applications and appear to be one of the keys for designing more sustainable and energy saving high potential/lightweight materials. Hence, the following paragraphs address the fatigue behavior of UFG steels and UFG light metal alloys in more detail.

17.3 Light metal alloys Light metals, in particular aluminium and its alloys, are the most frequently used materials for producing nanostructured materials by SPD. From an engineering point of view nanostructured light metal alloys are excellent candidates for future lightweight construction concepts, as these materials exhibit excellent specific mechanical strength under monotonic loading. As the UFG structure leads to a strong increase in the yield strength and the ultimate tensile strength, the fatigue lives in a Wöhler (S-N) diagram are normally also significantly improved (compare also the overview article of Estrin and Vinogradov69). Hence, in the following the fatigue lives, cyclic deformation behaviour and damage mechanisms of the most prominent lightweight UFG materials, namely aluminium and titanium as well as aluminium, magnesium and titanium alloys, are presented.

17.3.1 Ultrafine-grained (UFG) aluminium and aluminium alloys Aluminium and its alloys are the most prominent lightweight materials. Nanostructured aluminium of commercial purity (CP) exhibits a significant increase in the monotonic strength as well as a very high elongation to failure

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compared to the CG counterpart. Owing to the enhanced strain rate sensitivity an elongation to failure of up to 190% at elevated temperatures was obtained.19 Regarding the fatigue strength of CP aluminium with an UFG microstructure, an extraordinary large improvement in fatigue life is obtained from the LCF regime up to the HCF and even to the very high cycle fatigue (VHCF) regime (Fig. 17.8). Similar behaviour could be observed in technologically more interesting aluminium alloys. Introducing an UFG microstructure in aluminium alloys can significantly improve the fatigue life of these materials. This was shown for the AA5056 alloy,70 for Al-0.7% Cu,71 for Al-Mg-Sc-Zr72,73 alloys, for the AA2124 alloy processed with back-pressure during ECAP 74 and for the Al-Mg system.67,75 For the latter system, the Mg content was systematically varied between 0.5% and 2% in order to investigate the influence of the amount of the solutes/impurities on the fatigue strength as well as on the microstructural stability. In a Wöhler (S-N) diagram the fatigue lives of the UFG conditions of the Al-Mg alloys are superior to the CG counterparts, throughout all the Al-Mg alloys and the whole range of fatigue lives investigated (see Fig. 17.9). Even the fatigue life of the highest alloyed Al-2% Mg alloy in the CG condition is inferior to the fatigue life of the UFG condition of the Al-0.5% Mg alloy. In other words, introducing an UFG

17.8  Wöhler (S-N) diagram for CP aluminum in the CG and UFG condition ranging from the LCF to the VHCF regime.43

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17.9  Significantly enhanced fatigue lives in a Wöhler (S-N) diagram of fatigue lives of UFG AlMg0.5, AlMg1, AlMg1.5 and AlMg2 and corresponding CG conditions. From May.67

structure will provide the possibility of reducing (or even removing) alloying elements without any cost to the fatigue strength. Moreover, it is apparent that in the LCF regime the improvement of an UFG microstructure is stronger than in the HCF regime. In the same work, it was also shown that the number of ECAP passes has a very strong effect on the fatigue lives in the Wöhler (S-N) diagram of the AlMg0.5 alloy (Fig. 17.10). The application of only four passes of ECAP leads to a very considerable improvement in the fatigue life curve, compared to the CG counterpart. A further increase in the number of ECAP passes to eight significantly enhances the fatigue strength again – whereas 12 ECAP passes result in only a moderate increase in the fatigue strength compared to the eight-pass condition. The volume fraction of high-angle grain boundaries determined by the number of ECAP passes seems to govern the achievable improvement under fatigue loading. It is also noteworthy that the cyclic deformation behaviour depends strongly on the number of passes. As shown in Fig. 17.11 (a), a pronounced cyclic softening is observed for the materials processed with four ECAP passes, while the specimens processed with eight or 12 ECAP passes exhibit a rather stable cyclic deformation curve with a distinct regime of cyclic saturation. Moreover, it is shown by a systematic variation of the alloying content that with increasing magnesium content from 0.5 wt.% to 1 wt.% the cyclic stability increases significantly (Fig. 17.11 (b)).

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17.10  Wöhler (S-N) diagram for AlMg0.5 in the CG condition and after 4, 8 and 12 ECAP passes, Route Bc. A significant increase of the fatigue strength with number of ECAP passes is clearly visible.67

As already shown in Fig. 17.2, in a total strain fatigue life diagram a crossover of the fatigue life curves of the CG and UFG condition is predicted and was found also for the AlMg0.5 alloy (Fig. 17.12 (a)), as well as for AlMg2.0, (Fig. 17.12 (b)). When the total strain amplitude is the relevant design criteria, UFG materials show significantly improved fatigue lives in the HCF regime compared to their CG counterparts. In contrast, in the LCF regime, when the plastic strain amplitude-based Coffin–Manson law governs the fatigue life, fatigue lives deteriorate compared to their CG counterparts. For both UFG materials the fatigue ductility coefficient εf ′ is significantly reduced, whereas the fatigue strength coefficient from the Basquin law is significantly enhanced, when compared to their CG counterparts. It is also worth pointing out that for the alloy AlMg0.5 the relative increase in the fatigue strength coefficient is much higher than in the case of the AlMg2.0 alloy. Moreover, for the latter alloy exponents of both the Coffin–Manson and Basquin laws also change by introducing an UFG structure. It is also important to have a closer look at the point of transition where the fatigue life of the UFG materials becomes equal to that of the CG condition. As reported in67 the point of transition can be significantly shifted to lower numbers of cycles to failure (in the left direction) by approximately one decade when regarding the alloy AlMg2.0. Hence, one way to improve the fatigue properties of UFG materials is to shift the point of transition by alloying specific elements.

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17.11  (a) Influence of number of ECAP-passes on the cyclic deformation curves of AlMg0.5 deformed at a total strain amplitude of 3.8 × 10–3. The pronounced cyclic stability after 8 and 12 ECAP passes should be noted. (b) Influence of alloying content on cyclic stability for different AlMg alloys fatigued at a total strain amplitude of 3.8 × 10–3.67

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17.12  Total strain fatigue life diagrams for (a) AlMg0.5 and (b) AlMg2.0 for the UFG and the CG conditions. Note the crossover of the fatigue life curves for both alloys and the pronounced shifting of the transition point.67,76,77

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Distinct differences in cyclic deformation behaviour can be observed when different ECAP routes are applied. As described in detail by Iwahashi et al.,78 the ECAP rods can be turned in a particular manner (route) after each ECAP pass, which leads to pronounced differences in the microstructure. Thus, it was observed that ECAP Route A leads to larger improvements of the fatigue performance than ECAP Route Bc (see Fig. 17.13 (a)). This difference in fatigue life is explained by the influence of different textures. Route Bc produced a weak texture, whereas Route A ended up yielding a pronounced <110> texture, which is the elastically strong direction. Consequently, in a Coffin–Manson diagram, where only the plastic amplitudes are plotted, the influence of the ECAP processing route is completely missing (see Fig. 17.13 (b)). Another influence of ECAP processing parameters should be discussed. According to the work of Lapovok et al.68,74,79 on the commercial aluminium alloy AA2124, the material processed with eight ECAP passes exhibits a higher fatigue resistance than the CG material over the whole range of fatigue lives investigated. The considerable improvement of the fatigue properties and the absence of the crossover reported above most probably result from the employment of back-pressure during ECAP processing. Although these results reveal that applying back-pressure is beneficial for fatigue life, a microstructurally based explanation for this behaviour is necessary in order to identify the relevant mechanisms and to make them usable for further improvements. Switching to heat-treatable commercial aluminium alloys, the benefit of an UFG microstructure has to be discussed in more detail. For the AA6061 alloy an improvement of the fatigue life in a Wöhler (S-N) plot was reported by Chung et al.80 It was also shown that with increasing the number of ECAP passes, there is less improvement in fatigue life compared to the T6 CG counterparts. In other works,81,82 where an overaged condition of the AA6061 alloy was ECAP-processed, it was shown that the introduction of an UFG structure lead to a moderate improvement in fatigue life compared to the T6 CG condition (see Fig. 17.14). Comparing the fatigue lives for the commercial alloys AA6061 from Kautz et al.81,83 and AA6082 from Böhner,84 which both contain about 1% Mg, with the results of the binary alloy AlMg1 from May,67 it becomes obvious that introducing a nanostructure in the solid solution-hardened material will lead to a well-pronounced increase in fatigue life compared to the CG counterpart (Fig. 17.14). In contrast, when considering precipitation-hardened aluminium alloys like AA6061, only a moderate benefit for the fatigue lives can be found by introducing an UFG structure. As to the cyclic deformation behaviour, a significant enhancement of the cyclic stress response is observed compared to the overaged CG condition (see Fig. 17.15). Unfortunately, loaded with the same plastic strain amplitude the fatigue life of the UFG state deteriorates compared to the CG counterpart. Promising ways to improve strain-related fatigue lives in UFG materials include applying an appropriate recovery heat-treatment and/or introducing a bimodal microstructure (by heat-treatment) (compare References 29, 30 and 51). Referring to the work of

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17.13  (a) Influence of ECAP route on the fatigue life in a Wöhler (S-N) diagram for AlMg1.5. Route A leads to an improved fatigue life compared to Route Bc both after 8 ECAP passes. (b) The results of the same fatigue tests of UFG specimen plotted in a Coffin–Manson diagram. The influence of the ECAP route applied becomes negligible.67

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17.14  Wöhler (S-N) diagram of AlMg1, AA6061 and AA6082 alloys in UFG and CG conditions. Courtesy of J. May.67

17.15  Cyclic deformation curves of alloy AA6061 in different microstructural conditions, fatigued at a constant mean plastic strain rate of ε̇ pl = 1 × 10–3 s–1and at a constant plastic strain amplitude of ∆εpl /2 = 5 × 10–3.81

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Cavaliere and Cabibbo,85 a sound improvement of the fatigue life of an AA6106 alloy that was modified with small contents of Zr and Sc was achieved when, in addition to 4 ECAP passes, a subsequent annealing treatment was applied. To understand the fatigue properties of UFG metallic materials, cyclic crack growth behavior must be investigated and the results need to be analysed. According to the early work of Rabinovich et al.24 it was shown for an Al-Mg-Mn alloy that an UFG structure will unfortunately lead to a reduced threshold value of the stress intensity factor ∆ K. The influence of ECAP processing and subsequent annealing treatment was investigated recently by Hockauf et al.86 for the alloy AA6060. As depicted in Fig. 17.16, with an increasing number of ECAP passes the threshold values for the stress intensity factor ∆ K th becomes significantly smaller. For other UFG aluminum alloys or for CPAl (compare References 87–90), a similar behavior was found. In all cases the fatigue threshold was reduced for the UFG condition compared to the CG counterpart. Furthermore, crack propagation rates close to the threshold are higher for UFG conditions than for the CG condition. Applying an appropriate post-ECAP annealing heat treatment after only one ECAP pass will significantly improve the ∆ K thvalue.86 In the same paper it was also shown that an annealing treatment after two ECAP passes also positively

17.16  Cyclic crack growth rate vs. stress intensity factor range ∆ K for AA6060. Strongly reduced threshold values of the stress intensity factor, ∆ K th, for ECAP-processed conditions. Please note the improvement of ∆ K th by a post-ECAP annealing treatment. Source: After Hockauf.86 Courtesy of K. Hockauf.

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17.17  Fatigue threshold ∆ K th vs. load ratio R. With increasing R-ratio the fatigue threshold is decreasing. Please note again the improvement of ∆ K th by a post-ECAP annealing treatment. Source: After Hockauf.86 Courtesy of K. Hockauf.

affects the fatigue life in a Wöhler (S-N) plot. The fatigue threshold ∆ K this further reduced when the stress ratio R, defined by the ratio of the minimum stress to the maximum stress, increases (see Fig. 17.17). Moreover, a post-ECAP annealing treatment leads again to an improved fatigue threshold value.

17.3.2  Deformation and damage mechanisms Looking at the deformation and damage mechanisms an ambivalent picture has to be drawn. For CP Al-99.5 macroscopic shear banding oriented at 45° to the ECAP-pressing and fatigue-loading axis was found to take place, paired with grain rotation and a moderate grain coarsening within the shear band. Microhardness measurements revealed a loss in strength of 20% within the shear band. In contrast, for Al-0.5Mg, which has nominally the same amount of solutes/ impurities as CP Al-99.5, the fatigue cracks always form along the last ECAP shear plane. Microstructural investigations revealed that with increasing Mg content, shear band formation during ECAP processing becomes more pronounced and hence fatigue failure will take place predominantly along these pre-induced shear bands.67 In fact, the influencing factors governing failure mechanisms in UFG materials during fatigue are difficult to define. In particular, the interaction

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17.18  Macroscopic shear band that has formed during fatigue loading of CP Al-99.5 at RT. The shear band is declined at 45° to the stress and ECAP-pressing axis. Please note the rotated grain orientation and the moderately increased grain size within the shear band.42

of solute atoms with the matrix will have a strong effect. Stacking fault energy and grain boundary mobility are supposed to be decisive quantities.

17.3.3  UFG magnesium alloys There have also been some studies of fatigue properties of UFG magnesium alloys. Unfortunately, no clear picture of the influence of an UFG structure on the fatigue properties of magnesium alloys can be drawn up to now. For AM60,91 a significant enhancement of fatigue strength and endurance limit was achieved in which the authors varied the ECAP processing temperature between 150°C and 350°C. By reducing the ECAP processing temperature the microstructure became more uniform and homogeneous and the grain size was reduced down to approximately 1 µm. The grain size obtained by the different ECAP processing temperatures affects the fatigue endurance limit, as plotted in Fig. 17.19. As it becomes apparent from Fig. 17.19 the fatigue endurance limit of the AM60 alloy strictly follows the Hall–Petch relationship. In this context it has to be mentioned that the grain size of the AM60 alloy after ECAP processing at 150°C was reported to be rather uniform with a size of 1 µm, the smallest grain size range obtained in this investigation. In contrast, for AZ31,92 no positive effect of an UFG structure introduced by ECAP processing was found. As reported by the authors, softening due to texture anisotropy seems to over-compensate the strength enhancement due to grain refinement in the latter case.

17.3.4  UFG titanium and titanium alloys Results on the fatigue behaviour of commercially pure titanium with an UFG microstructure were first reported by Stolyarov et al.93 in 1999 and later by

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17.19  Dependence of the fatigue endurance limit of the AM60 alloy on d –1/2, where d is the mean grain size. The two additional data points indicated by the open symbols are from an Mg alloy with similar contents of Al and Mn but with Zn in addition.91

Vinogradov et al. in 2001.32,94 A strong dependence of obtained fatigue lives in a Wöhler (S-N) diagram on SPD processing parameters has been found. Qualitatively similar results were also obtained by Kim et al.95 The combination of ECAP processing with a subsequent cold rolling process leads to a further increased fatigue strength, almost reaching the fatigue strength of the Ti-6Al-4VELI (extra-low interstitials) alloy in the CG condition (see Fig. 17.20 and compare also69 for other alloys). It also becomes apparent that for the Ti-6Al-4V-ELI alloy with an UFG microstructure a significant improvement of the fatigue strength is obtained, which make these materials very promising for potential use for medical implant materials with improved durability.97 Fatigue tests using a rotating bending machine show qualitatively similar results for Ti-6Al-4V (compare Reference 53). Both investigations on UFG Ti-6Al-4V53,97 revealed that nano­ structuring this material resulted in strongly improved endurance limits determined at 1 × 106 cycles of about 35 MPa or 70 MPa, respectively. In the case of CP titanium, the endurance limit was increased by 230 MPa by an UFG structure.32 In contrast, it also becomes obvious that the benefit from an UFG structure depends strongly on the microstructural (and also other material-specific) details. Hence no generalized quantitative prediction can be made on how much fatigue strength can be improved by introducing a nanostructure.

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17.20  Wöhler (S-N) diagram for CP-Ti and Ti-6Al-4V ELI alloy in CG and UFG conditions: Data from References 32, 94 and 96. (UFG1: 2 ECAP passes, Bc; UFG2: 4 ECAP passes, Bc).97

In the total strain fatigue life diagram, as already mentioned earlier, titanium and its alloys do not show the typical crossover of the fatigue life curves of the CG and UFG conditions. For CP titanium it was shown by Vinogradov and Hashimoto32 that the fatigue ductility coefficient εf ′ from the Coffin–Manson law was not affected by an UFG structure at all. Hence, the fatigue life of the UFG condition is superior to that of the CG counterpart throughout the whole range of total strain amplitudes. For Ti-6Al-4V the situation is a little more complex, as this material is known for a two-fold Coffin–Manson regime, as already reported by Vittemant et al.98 for different CG microstructures. Similar behavior was found for CG Ti-6Al-4V ELI by Saitova et al.97 (see Fig. 17.21). The total strain fatigue life of the Ti alloy with an UFG structure is superior throughout the whole regime investigated. In contrast, CP titanium with an UFG structure exhibits a slightly reduced fatigue life in the Coffin–Manson plot, whereas under the Basquin law fatigue life is significantly improved, both compared to the CG counterpart. Consequently, in a total strain fatigue life diagram the UFG condition exceeds the fatigue lives of the CG conditions. The cyclic deformation behaviour of UFG Ti-6Al-4V ELI appears to be cyclically rather stable at intermediate-to-low plastic strain amplitudes; whereas, at a high plastic strain amplitude of 5 × 10–3 it exhibited pronounced cyclic softening.97 Figure 17.22 shows the microstructure of UFG Ti-6Al-4V ELI before and after fatigue loading. By X-ray diffraction peak broadening analysis it

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17.21  Total strain, plastic strain and elastic fatigue life diagrams for Ti-6Al-4V ELI with a CG and UFG microstructure (UFG1: 2 ECAP passes, Bc; UFG2: 4 ECAP passes, Bc). Please note the knee point in the Coffin–Manson plot for the CG condition.97

17.22  Microstructure of Ti-6Al-4V ELI UFG condition (a) in the initial state and (b) after fatigue loading at a plastic strain amplitude of 5 × 10–3.97

could be shown that the dislocation density as well as the cell/grain size is slightly increased after fatigue loading (see also Saitova et al.99). Compared to the pronounced grain coarsening found for high-purity copper (compare Fig. 17.5), the microstructure of the highly alloyed Ti-6Al-4V can be regarded as rather stable. Similar to the behavior reported for aluminum and its alloys, the cyclic crack growth rate of UFG titanium deteriorated compared to the CG counterpart. As

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shown by Hanlon et al.90 for UFG titanium (grade 2) processed by ECAP the fatigue threshold ∆Kth was reduced and the crack growth rates da/dN were higher than for the CG condition. Like the observations made for AA6060,86 for UFG titanium the fatigue threshold is reduced further when increasing the stress ratio R. According to Hanlon et al.,90 which also considered the crack growth behavior for nanocrystalline nickel and Al-7.5Mg, it is apparent that when grain size is reduced to the UFG/NC level the tortuosity of the crack paths decreased. Nanocrystalline nickel as well as UFG titanium exhibit comparatively straight crack paths, both relative to their CG counterparts. Similar observations were reported by Saitova et al.97 for UFG Ti-Al6-4V ELI. Hence, it is generally assumed for NC/UFG materials that with a reduction in grain size the effective driving force for crack propagation will be increased stemming from a reduced contribution to crack deflection and asperity contact. Although fatigue crack growth rates and fatigue thresholds deteriorate, fatigue lives in a Wöhler (S-N) plot are superior to the CG counterparts, indicating that the number of cycles for crack initiation has to be significantly increased in UFG/NC materials.

17.4 Fatigue behaviour and life of nanostructured steels Although steels are the most important engineering materials, fatigue data on nanostructured steels can be found rather sparely. Although the ECAP process was invented in 1981100, it took until 2001 for the first results on the fatigue properties of low-carbon steel with an ultrafine-grained structure to be reported by Park et al.101 and later by Kim et al.102 Both papers mainly addressed the influence of the UFG structure on cyclic crack growth rates. Compared to their CG counterparts, reduced fatigue threshold values ∆ K th as well as increased cyclic crack growth rates were found in nanostructured low-carbon steels. Unfortunately, no cyclic deformation curves or fatigue life diagrams were found in these papers. Di Schino et al.103,104 showed for the AISI304L austenitic stainless steel that the fatigue lives in a Wöhler (S-N) plot were significantly improved by reducing the grain size from 47 µm down to 1 µm. Although the grain size investigated is at the upper limit of the UFG regime, it is worth pointing out that due to the described reduction of grain size the fatigue limit was improved by 30%. The most detailed work was performed by Niendorf et al.105,106 on an interstitial-free micro-alloyed steel. It is shown that fatigue lives as well as the cyclic deformation behaviour are significantly affected by the number of ECAP passes and the ECAP routes applied. Depending on the particular ECAP processing parameters, the cyclic stress response of the UFG state at a given total strain amplitude of 2.8 × 10–3 is more than doubled compared to the as-received counterpart (Fig. 17.23). Moreover the number of cycles to failure is also improved by a factor of 2. As shown by detailed analysis of the microstructure, the grain size significantly changes when the number of ECAP passes increases from 1 to 4. In contrast, the grain size is not

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17.23  Cyclic deformation curves for IF steel in the as-received condition and after different ECAP passes and routes fatigued at a total strain amplitude of 2.8 × 10–3. Source: Niendorf et al.106

affected by further ECAP processing. Besides, there is a strong dependence of the cyclic stress response on the ECAP route applied. Pronounced cyclic softening is observed for the IF-steel ECAP-processed with less than four passes. Cyclic softening was reduced when four ECAP passes were applied. Fatigue life and cyclic deformation behaviour are also influenced by the ECAP route applied. Cyclic stability seems to be increased when Route C and Route E are used, whereas Route A leads to a more pronounced cyclic softening. It should also be pointed out that Route C leads to higher cyclic stress responses than Route E. Niendorf et al.105 also showed that increasing the number of ECAP passes from four to eight using Route C leads to a further improvement in cyclic stress response as well as to an increase in fatigue life. Furthermore, it was found that the ECAP-processed IF steel (four and eight passes, Route C) shows nearly perfect Masing behaviour, indicating that during cyclic loading the same microstructure forms independently from the stress amplitude applied. Regarding the fatigue life of IF steels, a crossover of the CG and UFG conditions is observed and can be explained by the principal considerations on the fatigue lives of UFG materials according to Mughrabi and Höppel,28 shown in Fig. 17.2. From the total strain fatigue life diagram (see Fig. 17.24), it is apparent that an UFG microstructure leads to a deterioration of the fatigue lives in the LCF regime, i.e. where the plastic strain amplitude governs the fatigue life. In contrast, when the elastic strain amplitude becomes dominant (HCF regime) the IF steel in an UFG condition is superior to the CG counterpart. When applying a moderate post-ECAP heat treatment a bimodal microstructure can be introduced, which leads to improved fatigue lives in the LCF regime. In contrast, in the HCF regime

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17.24  Total strain fatigue life diagram for CG and UFG IF steel. The UFC specimens were ECAP-processed using 8 passes, Route C. In addition, fatigue data for specimens with a bimodal microstructure heat-treated after ECAP processing are also plotted. Source: Data from Niendorf et al.105 Courtesy of T. Niendorf.

the fatigue lives are slightly reduced compared to the as-ECAP condition, but still superior to the CG counterpart. Höppel et al.107 first reported a beneficial effect of a bimodal grain structure on the fatigue properties in bimodal copper.

17.5 Consequences and strategies for optimizing fatigue lives and cyclic deformation behaviour Based on the aspects of the fatigue properties of different nanostructured materials described above, the following general conclusions can be drawn: • Nanostructured engineering materials exhibit excellent fatigue properties. In particular the fatigue lives of UFG metals with a grain size below 1 µm in a Wöhler (S-N) plot are significantly enhanced making this kind of material very promising for prospective applications such as structural materials for light-weight design. • Although some UFG materials exhibit an extraordinary strength paired with an improved ductility, for many nanostructured materials a reduced ductility of UFG materials under monotonic loading is reported. Consequently, the fatigue life will deteriorate when large plastic strain amplitudes dominate, whereas when the elastic strain amplitude governs the (total strain) fatigue life the high strength of the UFG materials experience a distinct improvement. Thus, with the exception of titanium and its alloys, in a total strain fatigue life

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diagram a crossover of the fatigue life curves of the UFG and CG conditions takes place. However, the crossover typically appears at high plastic/total strain amplitudes, which are not relevant for most engineering applications. • Fatigue lives depend on the ECAP routes, during which different microstructures and textures are introduced into the UFG material. The enhanced strain rate sensitivity of UFG materials also affects the fatigue life and the cyclic deformation behaviour. • Localization of plastic deformation as a prerequisite for crack initiation and propagation in UFG/NC materials is triggered by microstructural instabilities like grain coarsening, grain rotation and macroscopic shear banding. The experimental results reported so far reveal that different mechanisms have to be considered for shear band formation. Shear banding might occur as a consequence of microstructural instability, as a consequence of the strain path change when changing the deformation conditions from ECAP shearing to cyclic loading, or can inherently be generated during ECAP processing depending on the materials’ properties. In the latter case cyclic deformation is localized along the last ECAP-shear plane. In all cases, shear banding is reported to be a dominant phenomenon in UFG materials and hence has a significant influence on the fatigue damage mechanisms. • Post SPD processing heat treatment allows the possibility of recovering the microstructure without triggering recrystallization and hence of increasing the ductility of the material, with a positive effect on its fatigue life. Introducing a bimodal grain size distribution by appropriate post SPD processing heat treatments offers another way to improve the fatigue properties of UFG materials. Unfortunately, a bimodal microstructure cannot simply be introduced in every material selected for the design. Therefore, the following strategies for improving fatigue properties of UFG materials appear to be most promising. Figure 17.25 provides a schematic overview on potential improvement strategies and on the key issues affecting the fatigue life of UFG materials: • One way to improve the fatigue properties of UFG materials is to shift the transition point of intersection in a total strain fatigue life diagram (as described above) to even lower numbers of cycles to failure. This can be achieved by a further increase of the athermal stress component leading to an increase in the fatigue strength coefficient of the Basquin law. Possible strategies for achieving this goal are optimizing ECAP parameters, for example pressing temperature, pressing speed etc. and, most promising, applying back-pressure during ECAP processing. Moreover, an appropriate selection of the kind and amount of alloying elements can improve the fatigue strength. These activities should also affect the cyclic stability of the microstructure positively and also reduce or avoid the formation of shear bands during ECAP processing.

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17.25  Key issues affecting fatigue life of ultrafine-grained materials and derived improving strategies.

• Reducing the disposition of UFG structures to form macroscopic shear bands is another way to enhance cyclic stability and fatigue life. As long as the shear bands are not inherently formed during the SPD processing, measures to improve microstructural stability will help to retard or to avoid shear band formation during cyclic deformation. Microstructural stability is significantly influenced by the amount and by the kind of impurities and also by the SPD processing parameters, leading to different grain structures and textures. In this context, grain boundary mobility and stacking fault energy seem to play a key role governing the microstructural stability and the shear band formation in UFG materials. In particular, the latter point is supposed to influence the occurrence of shear band formation during ECAP processing. • Increasing the ductility of the UFG material is another strategy to improve the fatigue properties of UFG materials, in particular in the LCF regime when the plastic strain amplitudes dominate the fatigue life. The ductility of UFG materials can be enhanced by an appropriate recovery heat treatment after SPD processing, leading to a reduced dislocation density and a more relaxed and stable grain boundary configuration. Moreover, cyclic crack propagation is positively influenced by a recovery heat treatment. • Another way to improve ductility is to introduce a bimodal grain structure, where larger grains in the micrometer range are embedded in a matrix of

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ultrafine grains. Bimodal grain structures will improve the fatigue properties in the LCF regime when the plastic strain amplitude becomes dominant. Although, there will be a loss in fatigue strength compared to the as-processed UFG counterpart. • In all cases, post SPD processing heat treatment, leading either to a recovery of the microstructure or to a bimodal grain size distribution, has the potential to improve the fatigue strength of UFG materials as well as the fatigue threshold. • Another possibility is to vary the grain size as the limiting factor for the slip length of dislocations. In UFG materials under cyclic loading the grain size range of above 100 nm and below 1 µm is in the range of the slip length of the dislocations. Hence, adjusting the grain size to a more moderate, but still ultrafine-grained level will allow improvement of the fatigue ductility coefficient from the Coffin–Manson law and hence increase the fatigue properties further. Of course, it should be clear that by increasing the grain size, the fatigue strength coefficient from the Basquin law could deteriorate. Hence, the key challenge is to balance both effects in order to obtain an optimum fatigue resistance. The grain size can be adjusted either by a post SPD heat treatment or by selecting appropriate SPD processing parameters. Although there are some disadvantages like reduced fatigue thresholds and deteriorated fatigue lives in a Coffin–Manson plot, the general benefit of an UFG microstructure is best represented when the stress amplitude-related fatigue lives in a Wöhler (S-N) diagram are considered. For all the UFG materials investigated so far, a pronounced increase of the stress amplitude-related fatigue lives was obtained. Moreover, the fatigue limits, the most important quantity for an engineering design under fatigue loading, are significantly higher. Thus, UFG materials exhibit a very high potential for successful use in engineering applications in which high fatigue strength is required.

17.6 References   1 Valiev R.Z., Islamgaliev R.K, Alexandrov I.V. Progr in Materials Science 2000;45: 103.   2 M. Zehetbauer, R.Z. Valiev (eds.), Proc of 2nd Int Conf on Nanomaterials by Severe Plastic Deformation Nanospd 2, Wiley-VCH, Weinheim, 2004.   3 Estrin Y., Maier H.J. Proc of 4th Int Conf on Nanomaterials by Severe Plastic Deformation Nanospd 4; Materials Science Forum, 2008.   4 Hausöl T., Maier V., Schmidt C.W., Winkler M., Höppel H.W., Göken M. Adv Eng Materials 2010, Tailoring materials properties by ARB, accepted for publication.   5 Shin D.H., Kim W.G., Ahn J.Y., Park K.T., Kim Y.S. Mater Sci Forum 2006; 503–504: 447.   6 Estrin Y., Hellmig R., Ek M.J., Lamark T.T., Zuberova Z., Lapovok R., Popov M.V. TMS Annual Meeting 2006:381.   7 Stolyarov V.V., Zhu Y.T., Alexandrov I.V., Lowe T.C., Valiev R.Z. Mater Sci Eng A 2003; 343: 43.

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  8 Ko Y.G., Lee C.S., Shin D.H., Semiatin S.L. Metall Mater Trans A 2006;37: 381.   9 Raab G.J., Valiev R.Z., Lowe T.C., Zhu Y.T. Mat Sci Eng A 2004;382: 30. 10 Lee J.C., Seok H.K., Han J.H., Chung Y.H., Mat Res Bul 2001;36: 997. 11 Tsuji N., Kamikawa N., Kim H.W., Minamino Y. Ultrafine-Grained Materials III 2004: 219. 12 Valiev R.Z., Zehetbauer M.J., EstrinY., Höppel H.W., Ivanisenko Y., Hahn H., Wilde G., Roven H.J., Sauvage X., Langdon T.G. Adv Eng Materials 2007;9: 527. 13 Valiev R.Z., Alexandrov I.V. J Mater Res 2002; 17(1): 5. 14 Höppel H.W., May J., Eisenlohr P., Göken M.Z. Metallkunde 2005;96: 566. 15 May J., Höppel H.W., Göken M., Mater Sci Forum 2006;503–504: 781. 16 Höppel H.W., May J., Göken M. Adv Eng Materials 2004; 6: 781. 17 Kim H.S., Ryu W.S., Janacek M., Baik S.C., Estrin Y. Adv Eng Materials 2005;7: 43. 18 Höppel H.W., May J., Göken M. Adv Eng Materials 2004;6: 781. 19 May J., Höppel H.W., Göken M. Scripta Mater 2005;53: 189. 20 Chinh N.Q., Szommer P., Horita Z., Langdon T.G., Adv Mater 2006;18: 34. 21 Chinh N.Q., Szommer P., Csandi T., Horita Z., Langdon T.G. Mater Sci Eng 2006;A434: 326. 22 Zhu Y.T., LiaoX.Z., Srinivasan S.G., Lavernia E.J, J. Appl Phys 2005;98: 034319. 23 Vevecka-Priftaj A., Böhner A., May J., Höppel H.W., Göken M., Mater Sci Forum 2008;584–586: 741. 24 Rabinovichj M.K., Markushev M.V., J Mater Sci 1995;30: 4692. 25 Vinogradov A., Kaneko Y., Kitagawa K., Hashimoto S., Valiev R.Z., Mater Sci Forum 1998;269–272: 987. 26 Agnew S.R., Vinogradov A., Hashimoto S., Weertman J.R., J Electronic Materials 1999;28: 1038. 27 Mughrabi H. In: Lowe T.C., Valiev R.Z. (eds.). Investigations and applications of severe plastic deformation, Kluwer Academic Publishers, 2000, p.241. 28 Mughrabi H., Höppel H.W. In: Farkas D., Kung H., Mayo M., v. Swygenhoven H., Weertman J. (eds.). Structure and mechanical properties of nanophase materialstheory and computer simulation vs. experiment, Mat Res Soc Symp Proc, Vol. 634, Warrendale (PA): Materials Research Society; 2001, p. B 2.1.1. 29 Höppel H.W., Brunnbauer M., Mughrabi H., Valiev R.Z., Zhilyaev A.P. in: Proc of Werkstoffwoche 2000, http://www.materialsweek.org/proceedings, 2001. 30 Mughrabi H., Höppel H.W., Kautz M., Scripta Mater 2004;51: 807. 31 Höppel H.W., Zhou Z.M., Mughrabi H., Valiev R.Z. Phil Mag 2002;A82: 1781. 32 Vinogradov A., Hashimoto S., Mater Trans 2001;42: 74. 33 Vinogradov A., Hashimoto S., in: Zehetbauer M., Valiev R.Z. (eds.), Proc of 2nd Int Conf on Nanomaterials by severe plastic deformation Nanospd 2, Wiley-VCH, Weinheim, 2004, p.663. 34 Mughrabi H., Höppel H.W., Kautz M. In: Zhu Y.T., Varyukhin V. (eds.), Nanostructured Materials by High-Pressure Severe Plastic Deformation NATO ARW, Springer, 2006, p.209. 35 Höppel H.W., Kautz M., Xu C., Murashkin M., Langdon T.G., Valiev R.Z., Mughrabi H. Int J Fatigue 2006,28: 1001. 36 Maier H.J., Gabor P., Karaman I. Mat Sci Eng 2005; A410–411: 457. 37 Kunz L., Lukáš P., Svoboda M. Mat Sci Eng 2006;A424: 97. 38 Kunz L., Lukáš P., Svoboda M. Kovove Materialy 2009; 47:1. 39 Klemm R. Doctorate Thesis. Technische Universität Dresden, 2004.

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40 Thiele E., Bretschneider J., Hollang L., Schell N., Holste C. In: Lowe T.C., Valiev R.Z. (eds.). Investigations and applications of severe plastic deformation. Dordrecht: Kluwer Academic Publishers, 2000, p.173. 41 Kautz M. Doctorate Thesis. Universität Erlangen-Nürnberg, 2005. 42 Höppel H.W., Xu C., Kautz M., Barta-Schreiber N., Langdon T.G., Mughrabi H.: In: Zehetbauer M., Valiev R.Z. (eds.), Proc of 2nd Int Conf on Nanomaterials by severe plastic deformation Nanospd 2, Wiley-VCH, Weinheim, 2004, p.677. 43 Höppel H.W., May L., Prell M., Göken M. Int J Fatigue, 2011;33: 10, accepted for publication. 44 Morrow J.D. In: Internal Friction, Damping and Cyclic Plasticity, ASTM STP 378, American Society for Testing Materials, Philadelphia, PA, 1965, p. 45. 45 Landgraf R.W. In: Achievement of High Fatigue Resistance in Metals and Alloys, ASTM STP 467, American Soc for Testing and Materials, Philadelphia, PA, 1970, p.3. 46 Coffin L.F., Trans ASME 1954;76: 9310. 47 Manson S.S. NACA 1953;TN-2933. 48 Basquin O.H., Proc ASTM 1910;11: 625. 49 Patlan V., Higashi K., Kitagawa K., Vinogradov A., Kawazoe M.. Mater Sci Eng 2001;A319–321: 587. 50 Hashimoto S., Kaneko Y., Kitagawa K., Vinogradov A., Valiev R.Z., Mater Sci Forum 1999;312–314: 593. 51 Höppel H.W., Valiev R.Z. Z Metallkunde 2002;93: 641. 52 Mughrabi H., Höppel H.W., Kautz M. In: Zhu Y.T., Langdon T.G., Horita Z., Zehetbauer M., Semiatin S.L., Lowe T.C. (eds.), Ultrafine-grained materials IV, TMS, Warrendale, PA, USA, 2006, p.47. 53 Zherebtsov S., Salishchev G., Galeyev R., Maekawa K. Mater Trans 2005; 46(9): 2020. 54 Saitova L.R., Höppel, H.W., Göken M., Semenova I.P., Valiev R.Z. Int J Fatigue 2009;31: 322. 55 Zhang Z.F., Wang Z.G. Progress in Materials Science 2008;53: 1025. 56 Thompson A.W., Backofen W.A. Acta Metall 1971;19: 597. 57 Lukáš P., Kunz L. Mater Sci Eng 1987;85: 67. 58 Hall E.O. Proc Phys Soc 1951;B64: 747. 59 Petch N.J. Iron Steel Inst 1953;174: 25. 60 Agnew S.R., Weertman J.R., Mater Sci Eng 1998;A244: 145. 61 Lukáš P., Kunz L,, Svoboda M. In: Proc of 9th Int Fatigue Congress, Fatigue 2006, FT62. 62 Thiele E., Holste C., Klemm R. Z Metallkd 2002;93: 730. 63 Lukáš P., Kunz L., Svoboda M. Mater Sci Eng 2005;A391: 337. 64 Amberger D. Diplomarbeit(Master Thesis). Universtät Erlangen-Nürnberg, 2005. 65 Wu S.D., Wang Z.G., Jiang C.B., Li G.Y., Alexandrov I.V., Valiev R.Z. Mat Sci Eng 2004;A387–389: 560. 66 Iwahashi Y., Horita Z., Nemoto M., Langdon T.G. Acta Mater 1988;46: 3317. 67 May J. Doctorate Thesis, University Erlangen-Nürnberg, 2008. 68 Mughrabi H., Höppel H.W. Int J Fatigue 2010;32 :1413. 69 Estrin Y., Vinogradov A., Fatigue behaviour of light alloys with ultrafine grain structure. In: Proc of 17th European Conference on Fracture (ECF 17), Int J Fatigue 2010;32: 898. 70 Patlan V., Vinogradov A., Higashi K., Kitagawa K. Mater Sci Eng 2001;A300: 171.

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71 Zhang Z.F., Wu S.D., L Y.J., Liu S.M., Wang Z.G. Mater Sci Eng A 2005;412: 279–286. 72 Vinogradov A., Washikita A., Kitagawa K., Kopylov V.I. Mater Sci Eng 2003; A349: 318. 73 Meyer L., Sommer K., Halle T., Hockauf M. J Mater Sci 2008;43: 7426. 74 Lapovok R., Loader C., Dalla Torre F., Semiatin S.L. Mater Sci Eng 2006;A425: 36. 75 Höppel H.W., May J., Göken M. Mat Sci Forum 2008;584–586: 840. 76 Höppel H.W., May J., Göken M. In: Portella P.D., Beck T., Okazaki M., editors. In: Proc of 6th Int Conf on Low Cycle Fatigue (LCF6). DVM, Berlin, Germany: 2008, p.325. 77 Höppel H.W. Mater Sci Forum 2006; 503–504: 259. 78 Iwahashi, Y., Horita, Z., Nemoto, M., Langdon, T., Acta Mater 1998;46: 3317. 79 Lapovok R.Y. Mater Sci Forum 2006; 503–504: 37. 80 Chung C.S., Kim J.K., Kim H.K., Kim W.J. Mater Sci Eng 2002;A337: 39. 81 Kautz M., Höppel H.W., Xu C., Langdon, T.G., Mughrabi H., Fatigue lives and cyclic deformation behaviour of ultrafine-grained materials; in: 5th Int Conf on Low Cycle Fatigue Behaviour (LCF 5), Portella P., Sehitoglu H. and Hatanaka K. (eds.), DVM, Berlin, 2004, p.113. 82 Höppel H.W., Kautz M., Mughrabi H. in: Proc of 9th Int Fatigue Congress, Fatigue 2006, FT207. 83 Kautz M., Doctorate Thesis. University of Erlangen-Nürnberg, 2004. 84 Böhner A. Private communication, University of Erlangen-Nürnberg, 2010. 85 Cavaliere P., Cabibbo M. Mater Character 2008;59: 197. 86 Hockauf K., Meyer L.W., Halle T., Hockauf M. Mat-wiss. u. Werkstofftechnik 2009;40: 493. 87 Vinogradov A., Patlan V., Kitagawa K., Kawazoe M. Nanostruct Mater, 1999;11: 925. 88 Hübner P., Kisseling R., Biermann H., Hinkel T., Jungnickel W., Kawalla R., Höppel H.W., May J. Metall Mater Trans 2007;38A: 1926. 89 Kiessling R., Hübner P., Biermann H., Vinogradov A. Int J Mater Res 2006;97: 1566. 90 Hanlon T., Tabachnikova E.D., Suresh S., Int J Fatigue 2005;27: 1147. 91 Kulyasova O., Islamgaliev R., Mingler B., Zehetbauer M. Mater Sci Eng A 2009;503: 176. 92 Kim H.K., Lee Y-I., Chung C-S. Scripta Mater 2005;52: 473. 93 Stolyarov V.V., Alexandrov I.V., Kolobov Yu.R., Zhu M., Zhu T., Lowe T. in: Wu X.R., Wang Z.G. (eds.), Fatigue’99, vol. 3. PR China: Higher Education Press; 1999. p.1435. 94 Vinogradov A.Y., Stolyarov V.V., Hashimoto S., Valiev R.Z. Mater Sci Eng A 2001;318: 163. 95 Kim W.J., Hyun C.Y., Kim H.K. Scripta Mater 2006;54: 1745. 96 Turner N.G., Roberts W.T. Transitions of the metallurgical society of AIME 1968;242: 1223. 97 Saitova L.R., Höppel, H.W., Göken M., Semenova I.P., Valiev R.Z. Int J Fatigue 2009;31: 322. 98 Vittemant B., Thauvin G. in: Proc of 6th World Conference on Titanium, vol. 1; 1988. p.319. 99 Saitova L.R., Höppel H.W., Göken M., Kilmametov A.R., Semenova I.P., Valiev R.Z. Mater Sci Forum 2008;584–586: 827. 100 Segal V.M., Reznikov V.I., Drobyshevskiy A.E., Kopylov V.I. Russian Metallurgy (Engl Transl) 198;1: 115.

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101 Park K.T., Kim Y.S., Shin D.H. Met Trans 2001;A32: 2373. 102 Kim H.K., Choi M.I., Chung C.S., Shin D.H. Mat Sci Eng 2003;A340: 243. 103 Di Schino A, Kenny JM, Materials Letters 2003;57: 3182. 104 Di Schino A., Barteri M., Kenny J.M. J Mater Sci 2003;38: 4725. 105 Niendorf T., Canadinc D., Maier H.J., Karaman I., Sutter S.G. Int J Mater Res 2006;97: 1328. 106 Niendorf T., Canadinc D., Maier H.J., Karaman I., Sutter S.G. Met Mat Trans 2007;A38: 1946. 107 Höppel H.W., Brunnbauer M., Mughrabi H. Cyclic deformation behaviour of ultrafine grain size copper produced by equal channel angular extrusion; in: Materialsweek 2000 – Proceedings, Werkstoffwoche-Partnerschaft (ed.), Frankfurt, 25–28 Sept 2000, at http://www.materialsweek.org/proceedings, 2001.

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18 Superplastic deformation in nanocrystalline metals and alloys A. SERGUEEVA, The Nanosteel Company, USA and A. MUKHERJEE, University of California Davis, USA Abstract: This chapter presents theoretical predictions of the superplastic behavior of metallic materials with decreasing grain size down to nanoscale, and experimental observations on their deformation behavior at elevated temperatures. General trends and specific features of elevated temperature behavior are discussed in terms of evolutionary microstructure during processing. Based on experimental observations, as well as predictions from molecular dynamic simulation (MDS) approaches, possible deformation mechanisms in nanocrystalline materials at elevated temperatures are outlined. Key words: nanometallic materials, deformation, superplasticity.

18.1 Introduction Superplasticity (SP) has been a subject of scientific interest and industrial application for many years. Indeed, the word superplasticity first appeared in the English language in 1947 as a direct translation of the Russian word sverhplastichnost meaning ultrahigh plasticity. Nevertheless, it was only in 1991, following demonstrations of superplasticity in a very wide range of different materials, that a precise definition of SP was first put forward:1 SP is the ability of a polycrystalline material to exhibit, in a generally isotropic manner, very high tensile elongations prior to failure (usually more than 200%). SP is being investigated nowadays both for its intrinsic merit in the context of fundamental flow and failure mechanisms and for its technological significance in forming operations. There are considerable savings in material costs and in labor-intensive machining costs in this near-netshape forming process. It is not the intent to present here an exhaustive review of the phenomenon of micrograin SP. Several books and reviews for general reading have appeared over the past few years.2 SP is a close cousin of creep, and in fact, it is one of the various elevated temperature micromechanisms of deformation. The constitutive equation for elevated temperature crystalline plasticity was given by Mukherjee, Bird and Dorn (MBD) in 1968 and 1969.3–5 In generalized form, this equation can be written as: , 542 © Woodhead Publishing Limited, 2011

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. where ε is the steady-state strain rate, D is the appropriate diffusivity (lattice or grain boundary), G is the shear modulus, b is the Burger vector, k is the Boltzmann constant, T is the test temperature, d is the grain size, p is the grain size exponent, σ is the applied stress, and n is the strain rate sensitivity of the flow stress. SP obeys the general formalism of the correlation depicted by Eq. (18.1), with values of n = 2, p = 2–3 and an activation energy usually equal to the activation energy for grain boundary (GB) diffusion and occasionally equal to that for volume diffusion typical for thermally activated deformation behavior. One of the dominant microstructural features in SP is the role played by grain-boundary sliding (GBS). The grain compatibility during GBS is maintained by concurrent accommodation processes, which may involve GB migration, grain rotation, diffusion or dislocation motion. Most of the models proposed in the literature (for a review, see Reference 6) for SP generally consider one or the other accommodation process in conjunction with GBS. The accommodation mechanisms considered can be divided into three general groups: (a) diffusional accommodation, (b) accommodation by dislocation motion and (c) combined models having elements of both dislocation and diffusional accommodation. The rate equations (correlating flow stress, strain rate, grain size, and test temperature) derived from different models have essentially the same form. This is true despite the differences in the detailed concepts associated with individual models.7 In this chapter, theoretical prediction on SP behavior of materials with decreasing grain size down to nanoscale is discussed in Section 18.1. Section 18.2 presents experimental observations on deformation behavior at elevated temperature of different nanocrystalline (NC) metals and alloys prepared by severe plastic deformation (SePD), nanocrystallization (NC) from amorphous state, electrodeposition (ED) and by powder consolidation (PC). Specific features of their behavior are pointed out in Section 18.3. Based on experimental observations, as well as molecular dynamic simulation (MDS) approaches, possible deformation mechanisms in NC materials at elevated temperatures are discussed in Section 18.4.

18.2 Theoretical predictions Nanochrystalline materials contain a very large density of GB, causing them to differ structurally from crystals and glasses with the same chemical composition. Based on the classical scaling laws developed for conventional microcrystalline (MC) materials (grain size, d > 10 µm), expected behavior would include very high yield strength, σy at low temperature, due to constraints on dislocation motion (e.g. the Hall–Petch model predicts σy ∝ d –1/2) and low strength/high . ductility at higher temperatures due to short diffusion paths (e.g. the strain rate, ε . in Coble creep scales as ε ∝ d –3).

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Deformation behavior of NC materials at room temperature was intensively investigated, However, very little is known about creep behavior and the actual diffusional accommodation at elevated temperatures. It is expected that due to the ultrafine grain size and the large fraction of intergrain areas in NC materials, Coble creep (diffusional creep along GB) would become important in these materials when crept at low temperatures. Room temperature diffusional creep, however, predicted to be appreciable in NC samples was not confirmed in subsequent investigation.8 At the smallest grain sizes the significant volume associated with triple points must also become important. However, according to a model proposed by Suryanarayana et al.,9 when the grain size is about 30 nm, the volume fraction of triple junctions is less than 1% while the fraction of GB is about 10% by assuming GB thickness of 1 nm. Based on this information, the triple junction process is likely to be important when the grain size is less than 10 nm. Another important prediction for NC materials is their high ability for SP deformation. The two basic requirements for the observation of structural SP are (a) a temperature greater than about one-half of the melting temperature, Tm and (b) a fine and equiaxed grain size (<10 µm) that does not undergo significant growth during high-temperature deformation. In addition to these two requirements, GB need to be mobile, high-angled, and able to resist tensile separation. SP in MC materials is well established as a grain size dependent phenomenon described by the constitutive Eq. (18.1) for conventional SP. Behavior described by this equation has been observed for metals, intermetallics and ceramics materials. According to this relationship between grain size, SP strain rate, and SP temperature, a shifting of the optimum strain rate to higher values and/or the optimum temperatures to lower values with microstructural refinement has been predicted. Both aspects happen to have attractive technological significance and were extensively studied. For example, mechanically alloyed aluminum alloys having a typical grain size of 0.5 µm exhibit SP at strain rates > 1 s–1, comparable to conventional hot forming rates. In comparison, the SP strain rates of material with a typical grain size of 15 µm are 10–4 – 10–3 s–1. The relationship between grain size and optimum strain rate of aluminum alloys is shown in Fig. 18.1 (a) (data taken from Mishra et al.10) while Fig. 18.2 (b) shows the variation of SP temperature with grain size (data taken from Valier et al.11 and Mishra et al.12). From these figures, it is clear that by manipulating the grain size it is possible to (a) increase the SP strain rate, and (b) decrease the SP temperature. From Eq. (18.1) at constant temperature, it is evident that forming rates can be increased by decreasing the grain size. In addition, at a constant strain rate, the decrease in grain size from micrometer to nanometer scale can lead to lowering of the SP forming temperature. This effect is buried in the strongly temperature dependent Arrhenius expression for diffusivity in Eq. (18.1). Such lowering of temperatures allows for decreased grain growth, as well as leading to the ability to lower forming temperatures into ranges suitable for conventional tooling.

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18.1  The relationship between grain size and (a) optimum strain rate or (b) superplastic temperature.

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18.2  Variation of normalized yield stress with temperature for CP Ti in microcrystalline state and after HPT.

18.3 Superplasticity in nanocrystalline metals and alloys 18.3.1 Nanocrystalline materials produced by severe plastic deformation Severe plastic deformation (SePD) has been demonstrated to be an effective technique for the production of truly bulk, fully dense and contamination-free metals with nano- or near nanostructures.13 This technique includes such methods as equal-channel angular pressing (ECAP),14 high-pressure torsion (HPT),14 multiple forging (MF)15 and friction stir processing (FSP).16 In this section, experimental observations on SP behavior of metallic and intermetallic materials subjected to SePD by HPT are presented. These methods provide the finest microstructure that might be obtained by deformation processes nowadays. Ti-based alloys Titanium alloys represent one of the successful examples of application of SP forming. However, although significant progress has been made in understanding deformation mechanisms of Ti and its alloys, all these efforts have focused on the MC state. Extensive grain growth in metals at elevated temperatures prevents the

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possibility of evaluating the grain size dependence of its deformation behavior at low length scale. However, a number of metallic materials including Ti-based alloys have demonstrated relatively high thermal stability after SePD 14 that makes it possible to study mechanical behavior of nanostructures at elevated temperatures. Pure Ti HPT of commercially pure (CP) titanium results in microstructure with a mean grain size of 120 nm.17 Annealing the SePD Ti showed that the grain size of the material remains particularly stable at temperatures up to 0.4Tm. Increase in annealing temperatures led to rapid grain growth. A number of tensile tests at temperatures between 20° and 650°C and at strain rates of 10–4. . .10–2 s–1 revealed a dramatic decrease in yield stress with increasing temperature up to T  0.4Tm (Fig. 18.2) at all strain rates. At the same time, the flow stress of NC Ti was higher than that for MC Ti at all temperatures (Fig. 18.2). The experimental data on MC CP Ti was taken from.18 Despite titanium’s18 reputation as a relatively low-strain-hardening material, high stresses and extensive strain hardening were observed after HPT at temperatures below 0.4Tm and all strain rates in the investigated range. At higher temperatures (T > 0.4Tm) a transition to steady-state flow (550°C data) has been revealed (Fig. 18.3). However, the power-law behavior with stress exponent n = 5.8 (corresponding to stress strain sensitivity m = 1/n ~ 0.2) was estimated

18.3  True stress–true strain curves at two temperatures for CP Ti after HPT.

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18.4  Microstructure of CP Ti produced by severe plastic deformation and deformed at (a) 350°C and (b) 600°C.

with the apparent activation energy of 270 kJ/mol.19 This mechanism of deformation, namely five-power-law creep, seems to be also operative in Ti in the NC range at temperatures higher than 0.4Tm and at ‘conventional’ strain rates (10–4. . . 10–2 s–1).20 Apparent activation energy for both MC and NC states seems to be higher than that for lattice diffusion reported for CP Ti (153 kJ/mol20). Figure 18.4 presents the microstructure of Ti produced by SePD and deformed at 350°C (a) and 600°C (c) to a strain of 65 and 190%, respectively. It is seen that despite such high elongations the grains remain equiaxed in both cases. Twinning was not observed during deformation at 350°C (Fig. 18.4 (a)), while at 600°C twins were formed (Fig. 18.4 (b)). As shown by analysis of stress–strain rate data, the rate controlling deformation mechanism in the investigated range of strain rates and temperatures is dislocation glide controlled by dislocation climb. Ti-6Al-4V alloy HPT of Ti-6Al-4V alloy leads to the formation of a microstructure with high internal stresses and elastic distortions of the crystal lattice typical of SePD materials.14 Mean grain size estimated from dark-field transmission electron microscopy (TEM) images was 100–200 nm.21 Typical true stress–strain curves observed during the tensile tests at 650 and 725°C and different strain rates are shown in Fig. 18.5. It is seen that the flow curve at 650°C and strain rate of 10–4 s–1 (Fig. 18.5 (a)) has a relatively stable flow with low stress values, which is typical for SP deformation. However, the maximum elongation was observed at higher strain rate (10–3 s–1) when some strain hardening occurred. An increase in the strain rate to 10–2 s–1 leads to extensive hardening during deformation and lower tensile elongations. The extensive hardening was also observed at 725°C but it decreases with the decreasing strain rate from 10–1 to 10–3 s–1 (Fig. 18.5 (b)). Significant elongation of more than 500% was observed (Fig. 18.6 (a)). Moreover, this alloy has shown

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18.5  Typical stress–strain curves for the Ti-6Al-4V alloy after HPT at (a) 650°C and (b) 725°C and different strain rates. Source: Sergueeva et al.21 (reprinted with permission from Elsevier Ltd).

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18.6  (a) A view of samples before and after deformation.21 Source: (reprinted with permission from Elsevier Ltd); (b) correlation between DSC data and superplastic flow of Ti-6Al-4V alloy.

an elongation of more than 200% even at a strain rate 10–1 s–1 at 725°C that is three orders of magnitude higher than the strain rate for SP deformation of this alloy in the MC state. Strain rate sensitivity m was estimated to be 0.5 at 725°C and 0.4 at 650°C21–23 with the activation energy of 312 kJ mol–1, which is higher than that of lattice self-diffusion. Figure 18.6 (b) shows a correlation between DSC data and tensile elongation of the alloy as a function of temperature. Deformation at elevated temperatures leads to microstructural changes in the alloy when GB become better defined (Fig. 18.7). Some grain growth to a mean value of 300 nm was observed in the

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18.7  Bright-field TEM images of Ti-6Al-4V alloy after deformation at (a) 650°C (568%), (b) 725°C (504%). Source: Sergueeva et al.21 (reprinted with permission from Elsevier Ltd).

specimen tested to an elongation of 568% at 650°C but despite the high elongation of samples, the grains remained equiaxed. A mean grain size of specimen deformed at 725°C to 504% was about 1 µm. Also, there is dislocation activity inside grains (separate dislocations showed by arrows in Fig. 18.7 (b)). In the case of deformation only to 50% at the same temperature, microstructural changes are not so evident but enough to change the properties of the alloy. It is important to note that particles of the β-phase at a size of 100–200 nm appeared after SP deformation and they were located mostly on the GB and in triple points (Fig. 18.7). However, the volume of these particles was very small (less than 5% even after deformation at 725°C).

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Another feature of the alloy after SP deformation is the absence of any voids, and we could not detect any cavitations after high elongation even before fracture. NiTi alloy In NiTi shape memory alloy, deformation behavior at elevated temperatures is generally not considered as being very important, and has therefore received only limited attention in the literature.24 High-pressure torsion of the NiTi alloy leads to the amorphization of the material25 and microstructures with different grain sizes in the nanoscale range can be formed by subsequent annealing. The details of the structural evolution with temperature are reported in Sergueeva et al.25 Annealing of SePD NiTi at 200°C for 1 h results in a uniform crystalline structure with a mean grain size of 20 nm.19 The tensile tests of this NC NiTi were carried out at temperatures between 400° and 650°C and at strain rates from 10–5 to 10–1 s–1. The yield and flow stress exhibited a strong dependence on temperature and strain rate. A temperature effect on deformation behavior of the NC NiTi at constant strain rate is demonstrated in Fig. 18.8 (a). It is seen that at 400°C this material shows high ultimate strength (UTS = 1900 MPa) but the fracture occurs by extensive necking immediately following the UTS. At lower strain rates, a transition to steady-state flow with some linear strain hardening was observed. At 500°C a steady-state flow with substantial linear strain-hardening after yielding was revealed at strain rates as high as 10–2 s–1.25 Maximum elongation of 250% has been obtained at 500°C and at strain rate 10–3 s–1. A correlation between the temperature for microstructural instability and the onset of enhanced plasticity was observed (Fig. 18.8 (b)). Further increase in temperature leads to a decrease in ductility, primarily to grain growth, although a steady-state flow without strain hardening has been detected at all strain rates in the investigated range. At 650°C strain hardening was not observed at the investigated strain rates, and the flow stress seems to be independent of grain size. Although there was a great disparity between grain size of the initial rod (30 µm) and after HPT (30 nm), this material showed almost similar elongation and a similar rate of strain hardening at the same test conditions (Fig. 18.8 (a), 650°C data). From the experimental data, stress exponents at a steady state flow were calculated to be equal to 3 (m = 1/n ~ 0.3). Strain-rate jump tests at constant temperature also yield n-value equal to 3 in the investigated range of strain rates. The apparent activation energy in the range where it is independent of stress was evaluated and was found to be 210 kJ/mol24 assuming that the activation energy for viscous glide, which is controlled by Darken interdiffusivity, is close to volume self-diffusivity in this case. Microstructures of NC NiTi after annealing and after deformation at 400°C are shown in Fig. 18.9. The additional spots on the selected area electron diffusion (SAED) pattern for microstructure of the deformed specimen revealed the

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18.8  (a) True stress–true strain curves for NiTi in MC and NC states. (b) Combined plots showing variations of DSC signal and elongation with temperature.

occurrence of precipitations while there is no evidence of precipitations after annealing at the same temperature. Grain size was in the range of 20–30 nm in both cases. Despite the fact that the grain size of this material is on the nanometer scale, and the volume fraction of GB is therefore significant, it seems that GBS or operation of Coble creep is suppressed in NiTi. One plausible reason for this behavior could be related to stress-induced nano-precipitation observed in this material during deformation at temperatures of 400°C and higher. These

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18.9  Microstructure (with SAED as insert) of NiTi (a) after annealing at 400°C for 1 h; (b) after deformation at 400°C and 10–5 s–1.

nanoscaled precipitates at GB seem to have been able to suppress GBS and also the manifestation of SP in this NC material. Al-based alloys The widespread use of SP forming of aluminum alloys is hampered by the slow optimum strain rate for SP, particularly in commercial aluminum alloys. In addition, elaborate thermomechanical processing is needed to obtain a microstructure conducive to SP deformation. The optimum strain rate for SP deformation of 7075 Al alloy was shown to be 8.3 × 10–4 s–1 at 510°C after microstructure refinement by the thermomechanical processing26 that is an order of magnitude slower than desirable for widespread use of SP forging/forming of components in automotive industries.27 Al-1420 alloy Commercial Al-1420 alloy had a microstructure with the average grain size of 83 ± 33 nm after HPT at room temperature. The grains had mostly an equiaxed shape. However, the contrast within the grains was not uniform and often changes in a complex way, indicating that the grains were highly distorted. Several primary particles of impurity elements, such as Fe-based intermetallics, were also observed with a typical size of 3–5 µm.28 Figure 18.10 (a) shows the stress–strain curves at 250°C. All these specimens showed SP elongations, with a minimum of about 330% (true strain, 1.46) at 1 × 10–1 s–1 and a maximum of about 440% (true strain, 1.69) at 1 × 10–2 s–1. Figure 18.10 (b) shows the stress–strain curves at 300°C for different strain rates. All specimens showed SP elongation. The elongation at the strain rate of 5 × 10–1 s–1 was about 420%. An important feature is the difference between the shapes of the flow curves at 250 and 300°C. At 300°C, all the flow curves show significant strain hardening.28 The strain-hardening slope is higher at higher strain © Woodhead Publishing Limited, 2011



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18.10  The variation in stress with strain in NC Al-1420 alloy as a function of strain rate at (a) 250°C and (b) 300°C. Source: Mishra et al.28 (reprinted with permission from Taylor & Francis Group).

rates. The specimens before and after testing at various temperatures are shown in Fig. 18.11 (a). The specimens show neck-free elongation that is characteristic of SP flow. At 250°C, the apparent stress exponent n was about 4.5 (m ~ 0.22) at low strain levels and dropped to about 2.7 (m ~ 0.37) at higher strain levels. On the other hand, the apparent stress exponent at 300°C was about 2.5 (m ~ 0.4) at low strain levels and drops to about 2.0 (m ~ 0.5) at high strain levels. An analysis of the temperature dependence gives an apparent activation energy of about 118 kJ/mol at lower temperatures and a significant increase in the temperature range 250–300°C.28 The correlation between DSC signal for thermal stability and increase in ductility is shown for SePD-processed Al-1420 alloy in Fig. 18.11 (b). The onset of grain growth was independently established by analysing the video recording

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18.11  (a) Nanocrystalline Al-1420 alloy specimens before and after deformation. Source: Mishra et al.28 (reprinted with permission from Taylor & Francis Group). (b) Combined plots showing variation of DSC signal and elongation with temperature.

of in situ TEM heating. The current authors believe that the onset of grain growth itself can be an accommodation mechanism for stress concentrations at triple points as a result of GBS. At grain growth, a set of triple points is continuously replaced by a coarse set of triple points leading to stress relaxation. Figure 18.12 (a) shows a dark-field micrograph of a specimen tested to an elongation of 385% at 250°C. The average grain size had grown to about 300 nm. The microstructural features of particular importance are dislocations within the grains and in the grain boundary. Figure 18.12 (b) shows a dark-field image of a specimen deformed to an elongation of 775% at 300°C. The average grain size had grown to about 1 µm. In contrast with the specimen deformed at 250°C, this specimen showed a very high dislocation activity. The

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18.12  Dark-field TEM images of microstructure of Al-1420 alloy specimens deformed at (a) 250°C and (b) 300°C. Source: Mishra et al.28 (reprinted with permission from Taylor & Francis Group).

grains had 40–50 nm particles (probably AI-Li precipitates) and frequent dislocation–particle interactions were observed. Ni-based alloys Ni3Al alloy The boron doped Ni3Al was subjected to HPT, which resulted in formation of a NC structure with mean grain size of 50 nm.29 The stress–strain behavior of this NC material at a strain rate of 1 × 10–3 s–1 and 650 and 725°C is shown in Fig. 18.13 (a). The total elongations for as-processed specimens were 380 and 560% at 650 and 725°C, respectively. The flow showed an extensive hardening period at both temperatures. At 650°C, failure occurred soon after the peak stress © Woodhead Publishing Limited, 2011

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18.13  (a) The variation of true flow stress with elongation for NC Ni3Al alloy at 650 and 725°C and a strain rate of 1 × 10–3 s–1; (b) specimens before and after deformation. Source: Islamgaliev et al.63 (reprinted with permission from Elsevier Ltd).

was achieved. On the other hand, the flow curve at 725°C showed significant strain softening before failure. Figure 18.13 (b) shows a set of specimens before and after testing. The stress exponent n of 2.6 (m ~ 0.38) for the alloy was estimated from strain rate jump tests performed at 650°C.30

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In Fig. 18.14 (a) the DSC results are overlaid with elongation as a function of temperature.31 It is apparent that the onset of SP deformation coincided with the onset of grain growth. Figure 18.14 (b) shows the microstructure of NC Ni3Al alloy after testing at 650°C to 380% elongation. Although some grain growth is evident in the deformed sample, most of the grains are still in NC range around 100 nm. The dislocation activity appears to be quite limited. A few lattice dislocations were visible, as marked in Fig. 18.14 (b). It is interesting to note that

18.14  (a) Correlation between DCS results and superplastic deformation for NC Ni3Al alloy; (b) a bright-field transmission electron micrograph of a Ni3Al specimen superplastically deformed at 650°C to an elongation of 380%. Some of the lattice dislocations are marked by arrows.

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dislocation ‘2’ has one end in the grain boundary. The appearance of this type of dislocation suggests the grain boundaries as sources of dislocations. A twin formation was also observed in post-deformed samples.32 In fact, most of the MC Ni3Al alloys show a ductility minimum in the temperature range of 600–750°C.33 The much-enhanced ductility along with high flow stresses in the NC Ni3Al alloy are characteristics that are very different from that manifested by MC Ni3Al alloy.

18.3.2 Nanocrystalline materials crystallized from amorphous precursor Among the many methods of producing NC materials, devitrification of amorphous solids offers some attractive advantages. For example, with the correct chemistry, devitrification allows for a wide range of microstructures to be evolved by simply changing annealing conditions without the problems of contamination or residual porosity that are inherent to other processing methods such as electrodeposition or inert-gas condensation. With the right type of chemical composition, as long as the annealing is carefully carried out, the retention of unwanted amorphous or other phases can be minimized in a primary crystallization range, and grain sizes as low as 20 nm can be generated.34 Fe-based alloys A commercially available metallic glass (Vitroperm, Fe73.5Cu1Nb3Si15.5B7) was crystallized into a single-phase structure of α-Fe with a grain size of approximately 15 nm by annealing at 600°C for 1 h.35 In order to verify the absence of the residual amorphous phase at the grain boundaries, HRTEM investigation was carried out that showed no evidence of a residual amorphous phase and appeared clean of contamination by other phases.36 When tested at 600°C at varying strain rates, this NC material showed limited ductility and high strength values as shown in Fig. 18.15 (a). It is to be noted that the strain rate sensitivity value, m, for these testing conditions was estimated to be 0.5. The microstructure of the sample after testing at 600°C and at strain rate 1 × 10–4 s–1 shows little grain growth, and retention of the original single-phase microstructure (Fig. 18.15 (b)). In contrast, the behavior at 725°C at the same strain rate is very different. Plasticity is enhanced, steady-state flow is reached, and flow stress values are much lower as seen in Fig. 18.16 (a). A strain rate sensitivity m of 0.2 was determined from a number of strain rate jump tests at temperatures above 675°C.35 This m-value is usually associated with power-law creep; a mechanism that depends on dislocation climb and lattice diffusion to accommodate the plastic flow, and may result in elongation of the deformed grains in the absence of grain rotation. However, the grains have remained remarkably equiaxed, considering that they

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18.15  (a) True stress–true strain curve for Vitroperm after 600°C 1 h anneal, tested at 600°C at different strain rates; (b) TEM image of microstructure of Vitroperm alloy after tensile testing at 600°C and strain rate of 10–4 s–1.

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18.16  (a) True stress–true strain curve for Vitroperm tested at 725°C; (b) a bright field image of Vitroperm microstructure after tensile testing at 725°C to an elongation of 65%.

have undergone 65% elongation (Fig. 18.16 (b)). From the selected area electron diffraction pattern and corresponding bright and dark field images, it is clear that a second phase has nucleated at some of the triple points, and the larger grains have grown to ~125 nm in diameter. An activation energy of the deformation process

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was estimated to be 455 kJ/mol for this NC material, which is higher than any literature values for lattice self-diffusion or the other elements present in α-Fe. A definite change in mechanism from the tests at 600°C and those at 675°C and above were observed in this NC material.36 At 600°C, m = 0.5 was estimated, which corresponds to GBS as a deformation mechanism. But at this temperature the material shows very limited plasticity (Fig. 18.15 (a)). For the ductile specimens above 675°C, a strain rate exponent of 0.2 was determined that is usually associated with power-law creep; a mechanism that depends on dislocation climb and lattice diffusion to accommodate the plastic flow, and may result in elongation of the deformed grains in the absence of grain rotation. We did not see elongation of grains that could correspond, for example, to 65% ductility in TEM micrographs of the post-tested material (Fig. 18.16 (b)). Electron Energy Loss Spectroscopy (EELS) and Energy Dispersive Spectroscopy (EDS) analyses revealed the segregation of Nb in the small particles at the triple points.35 Other authors have found that in FINEMET, another Fe-based metallic glass, Nb tends to reside at the grain boundaries in the as-crystallized structure and will pin the boundaries, leading to a structure that is quite stable at high temperatures.37 This coincides with the above results, in that the grain size is very stable up to a certain point. With Nb migration from a-Fe grain boundaries and segregation in a newly forming second phase, grain growth in the material quickly proceeds. Furthermore, if the 15 nm grains are too small to have dislocation activity to accommodate the deformation at triple points, it is logical that once the grains have grown sufficiently to allow dislocation motion, the strength should drop, while the plasticity should increase. This is, in fact, exactly the trend that was revealed in the data above. If dislocation-free grains are formed at stress concentrations such as triple points through the diffusion of Nb-containing phases, the growth of these phases could explain the accommodation of the strain seen in the tensile tests.

18.3.3 Nanocrystalline materials produced by electrodeposition Pure Ni Nanocrystalline Ni with mean grain size of 35 nm was obtained by electro­ deposition.38 Tensile samples geometry before and after deformation at 350°C, which is 0.36 of the melting point of this material, are shown in Fig. 18.17 (a), which demonstrates the large uniform elongation and absence of localized necking. Stress–strain curves obtained at a constant strain rate of 1 × 10–3 s–1 are shown in Fig. 18.17 (b). An important transition in mechanical behavior occurred above 280°C, indicated by the 350°C curve that shows yielding and strong strain hardening with a large increase of deformation into the SP regime of greater than 200% elongation. This transition from low plasticity to large plasticity coincided with an exothermic peak in the DSC curve as shown in Fig. 18.18, where

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18.17  (a) Tensile specimens in the as-machined geometry and deformed at a strain rate of 10–3 s–138. Source: McFadden et al.38 (reprinted with permission from Elsevier Ltd). (b) Stress–strain curves show a transition in mechanical behavior from low plasticity to superplasticity in NC Ni above 280°C.

elongation, as a function of test temperature, is combined with a plot in the DSC curve. A maximum elongation of 895% was obtained at 420°C and at a strain rate of 1 × 10–3 s–1. An elongation of 295% was obtained at 350°C and at a strain rate of 1 × 10–3 s–1. Strain rate sensitivity values, calculated from strain rate jump test data were estimated to be about 0.25–0.28 at initial straining and increased to 0.4–0.5 with strain.38

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18.18  Increase in ductility coincides with the onset of grain growth in NC Ni as indicated by a strong exothermic peak in the DSC signal. Source: McFadden et al.38 (reprinted with permission from Elsevier Ltd).

18.3.4 Nanocrystalline materials produced by powder consolidation Pure Zn Nanocrystalline Zn samples were produced by ball-milled (BM) powder consolidation by compression at room temperature. Grain size varied with ballmilling time.39 Grain size distribution in the range of 5–80 nm was observed for Zn samples from powder that was ball-milled for 25 h. Ball-milled powder was then compressed to disks at room temperature by uniaxial pressure. True stress–true strain curves for Zn with different average grain sizes are plotted in Fig. 18.19 (a). Yield stress increased, while elongation decreased with the decrease in the average grain size. Maximum elongation of 110% was observed in NC Zn with an average grain size of 240 nm.40 Tensile sample before and after deformation is shown in Fig. 18.19 (b). The stress exponent n of deformation process for NC Zn was calculated to be 6.6 (m ~ 0.15) with activation energy value of 60 J/mol.39 A typical TEM image in the region near the fracture surface of the NC Zn after 110% elongation is shown in Fig. 18.20. Grains remain equiaxed despite such large strain. The interior of these equiaxed grains has fewer dislocations than seen in the grains before the tensile test. There are no visible changes in the average grain size before and after deformation.

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18.19  (a) Stress–strain curves for NC Zn with different grain size tested at room temperature. Source: Zhang et al.39 (reprinted with permission from Elsevier Ltd). (b) A view of the tensile sample before and after deformation. Source: Zhang et al.40 (reprinted with permission from American Institute of Physics).

The m-values for BM 3h Zn tested at 20 and 40°C were both around 0.15, which indicates that there was basically no SP at this strain rate, although a 110% elongation was observed at 20°C tested at a strain rate of 10–3 s–1. The activation energy for plastic deformation in NC Zn was around 60 kJ mol–1.39 This is close to the activation energy for GB self diffusion in pure Zn, which is about 59 kJ mol–1.41 TiAl alloy Nanocrystalline γ-TiAl alloy has been synthesized by hot isostatic pressing (HIP) of mechanically alloyed powders.42 The average grain size was estimated to be in the range of 25–50 nm. The presence of a small volume fraction of Ti3Al phase was detected by X-ray analysis as well as a number of small, unidentified phases. No porosity was detected in the as-consolidated specimen. The stress–strain behavior of NC TiAl at 1 × 10–4s–1 and 750°C is shown in Fig. 18.21.

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The flow stress is stable and after a true compressive strain of 0.9, no edge cracking was observed. The stress exponent for deformation in the range of temperatures (750–950°C) and strain rates (10–5 – 10–5 s–1) was estimated to be ~6 (m ~ 0.16).

18.20  Bright-field TEM image of NC Zn after deformation to elongation ~110% at room temperature. Source: Zhang et al.40 (reprinted with permission from American Institute of Physics).

18.21  The stress–strain behavior of the NC TiAl alloy at 750°C. Source: Mishra et al.42 (reprinted with permission from Elsevier Ltd).

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18.4 Specific features of superplasticity in nanocrystalline materials 18.4.1  Microcrystalline vs. nanocrystalline plasticity Figure 18.22 represents a summary of experimental data on grain size dependence of maximum elongation observed in different SePD materials tested in tension at optimal conditions.43 It can be seen that despite a theoretical prediction for advanced SP in NC materials, tensile elongation continuously decreases with decreasing grain size in MC range. In addition, Al alloys have demonstrated a greater propensity for SP flow than other metals (solid symbols in Fig. 18.22). But it was noticed that superplasticity in ultrafine-grained materials is achieved only when precipitates or other obstacles are present to restrict the GB migration, and therefore the occurrence of grain growth, at these elevated temperatures. In general, in the most intensively investigated NC materials produced by SePD, deformation at microstructurally stable temperature ranges results in a slight increase in ductility but is far from predicted SP response. In the last ten years, we have observed SP in a number of NC materials (Section 18.2). The nature of SP in NC materials appears to be quite different from that in MC materials. The results on NC materials that did undergo SP deformation have

18.22  Grain size dependence of maximum elongation at optimal deformation conditions in SePD materials. Source: Sergueeva et al.43 (reprinted with permission from Elsevier Ltd).

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established a number of general trends of their mechanical behavior at elevated temperatures such as excessive strain hardening during tensile tests, high-flow stresses (compared to MC materials at comparable temperature and strain rate), a correlation between microstructural instability (in terms of onset of grain growth) and SP, absence of cavitations, which will be discussed below. Some NC metals and alloys did demonstrate high strain superplasticity (HSRS) and lowtemperature superplasticity (LTSP) with elongation of more than 100%. High flow stresses Figure 18.23(a) shows a comparison of the flow curves during SP in a Ni3Al alloy. This alloy was tested in both MC 44 and NC 45 states (Fig. 18.23 (a)). The highflow stresses during SP of NC Ni3Al alloy are apparent. This was unfortunately unavoidable. We could not compare them at the same temperature. At 1050°C where the 6 µm material was optimally SP, the grains of the 50 nm specimen would have grown enormously. Conversely, the 6 µm grain material is not SP at 725°C where the 50 nm material is optimally so. The overall ductility in both cases happens to be similar, which is purely coincidental and is not being emphasized here. A TEM study of the SP-deformed Ni3Al alloy with a 6 µm grain size had shown significant intragranular dislocation activity.45 Low-flow stress is one of the features of conventional SP in MC material. The observation of SP with high-flow stresses in NC materials needs a new approach to explain the origin of such high-flow stresses. First, the starting flow stress in Ni3Al in Fig. 18.13 (a) (Section 18.2.1) is around 170 MPa. Second, after significant strain hardening, the flow stress reaches the level of 780 MPa at 725°C. At 650°C, the flow stress values are even higher (Section 18.2.1, Fig. 18.13 (a)). According to models,46 some grains throughout the sample will have a statistical probability of being unfavorably oriented for sliding, then, a sample with more grains through the thickness will have a greater probability of encountering such an unfavorably oriented grain. Therefore, the flow stresses will be higher in order to provide a driving force for reorientation of these grains, or for dislocation motion (which at these length scales will be difficult at best) to shear across the grain. However, a test of the samples in the NC and MC states with an approximately similar number of grains through their thickness (Fig. 18.23 (b)) has shown that this is not the issue. Figure 18.24 shows the variation of flow stress with temperature and grain size compensated strain rate for the NC and MC Ni3Al alloy where d is a grain size and DL is lattice diffusivity. The observation of SP with high-flow stresses and high-strain hardening in NC material needs a new approach in order to explain the origin of such high-flow stress. Any explanation for the high-flow stress, therefore, has to be linked to the grain size effect rather than an alloy-specific explanation. For example, Ni3Al alloys exhibit anomalous strengthening with peak stress in the temperature range

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18.23  (a) A comparison of flow curves for Ni3Al alloy in microcrystalline and nanocrystalline state; (b) a comparison of flow curves for Ni3Al alloy in MC and NC states with approximately equal number of grains through sample thickness.

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18.24  The variation of flow stress with temperature and grain size compensated strain rate for Ni3Al alloy. The flow stresses are higher in NC Ni3A1 as compared to MC alloy at the same compositions.

of 600–750°C.33 This temperature range is similar to the temperature range of the present work. An explanation of high-flow stresses on the basis of anomalous strengthening in Ni3Al would not be able to explain the results on other alloys. Further, there is a basic difference between the MC alloy and the NC alloy. In fact, most of the MC Ni3Al alloys show a ductility minimum in the temperature range of 600–750°C.33 The much-enhanced ductility along with high-flow stresses in NC Ni3A1 alloy are characteristics that are very different from those manifested by the MC Ni3Al alloy. The data on Al-1420 alloy (Fig. 18.25, where Dg is grain boundary diffusivity) shows a similar trend for high-flow stresses in NC state. The data for the three other lower temperature tests, where NC grain size can be maintained (Section 18.2.1), showed higher-flow stresses in normalized coordinates. However, the data at 573K (300°C) correlated well with existing data from the literature on MC specimens as well as with the predictions of theoretical models for such MC SP. It should be noted that the grain growth in this alloy became substantial at temperatures of 300°C and over. The observed higher-flow stress for NC material suggests a transition in micromechanism or additional difficulty in GBS. This is also valid for SP in NC Zn-Al eutectoid47 where the superplastic flow is GB diffusion-controlled. Therefore, regardless of GB- or lattice-diffusion-controlled GBS, the flow stresses for SP in NC materials are higher. This is the opposite of some of the earlier expectations of enhanced SP in NC materials.

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18.25  A comparison of the experimental stress–strain rate data with the empirical correlation and theoretical models for the Al-1420 alloy. Note that while the data for microcrystalline and submicrocrystalline starting grain size merge, the low temperature data with nanocrystalline state shows higher-flow stresses. Source: Mishra et al.28 reprinted with permission from Taylor & Francis Group.

Excessive strain hardening Experimental results on deformation behavior of Al-1420 and Ni3Al alloys, CP Ti, Ti-6Al-4V and NiTi alloys subjected to HPT have revealed an excessive strain hardening when their grain are about 100 nm in size and smaller (Section 18.2). Intensive grain growth at high temperatures or low testing strain rate leads to dramatic change in the deformation flow and no strain hardening was observed. It is important to note that the strain hardening in the Al-1420 alloy (Section 18.2.1) and Ti-6Al-4V alloy (Section 18.2.1) increases with increasing strain rate. We have observed a similar trend in other SePD processed materials such as ZnAl and Al-2124 alloys48,49. These observations establish a trend. There is some grain growth in these NC during SP deformation. Because of the grain size dependence in the constitutive relationship for SP flow, strain hardening during SP has been conventionally explained in terms of grain growth. However, grain growth alone cannot account for the entire strain hardening in all these materials. For example, such an explanation would not predict higher strain hardening at higher strain rate. With reference to Eq. (18.1), at constant temperature, the stress dependence n, and grain size dependence p, have been experimentally determined for NC Ni3Al.50 Both of these values are equal to 2. An examination of Eq. (18.1) will

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. reveal that at constant T and constant ε : σ ∝ (d)p/n, with n = 2 and p = 2, σ ∝ d, i.e. the increase in stress should be directly proportional to increase in grain size. However, the results on Ni3Al alloy at 650°C and 1 × 10–3 s–1 strain rate shows a flow stress increase by a factor of ~5 where the grain size increased only by a factor of ~2. Similar extensive strain hardening was detected during elevated temperature deformation of NC materials produced by nanocrystallization from amorphous state (Section 18.2.2) and by electrodeposition (Section 18.2.3). Nanocrystalline materials produced, however, by sintering of NC powders did not show a trend for such strain hardening (Section 18.2.4). Correlation between microstructural instability and superplasticity The driving force for grain growth is quite high in NC materials because of the high interfacial area per unit volume. We have observed a nice correlation between the temperature for microstructural instability and onset of SP in these materials (Section 18.2). In some ways this is expected because both GB migration and GBS involve diffusion. An important implication of this is that one needs to establish the narrow temperature range in which there is enough thermal activation for GBS but the grain growth rate is relatively low. This is important for observing the GBS regime without significant influence of grain growth, particularly from the viewpoint of obtaining parametric dependencies for constitutive modeling. We have investigated the microstructural instability by three different ways: differential scanning calorimetry (DSC), in situ TEM heating and TEM of heat-treated specimens. The correlation between the DSC signal for thermal stability and an increase in ductility was observed for SePD-processed Ti-6Al-4V (Fig. 18.6 (b)), Ni3Al (Fig. 18.14 (a)), Al-1420 (Fig. 18.11 (b)) and NiTi (Fig. 18.8 (b)) alloys as well as in electrodeposited Ni (Fig. 18.18). The onset of grain growth was independently established by analysing the video recording of in situ TEM heating. The results show that the DSC can work as a very good tool to establish the optimum SP temperature for NC materials. Absence of cavitations All MC SP materials have shown clear evidence for intergranular cavitation. This includes observation on Al-Cu-Li-Zr alloy51 and Ni3Al alloy.52 However, our investigation on NC materials fails to reveal any evidence of cavitation. In an analysis of cavity nucleation in SP,51 the authors have proposed a competition between the characteristic relaxation time for GBS leading to the development of stress concentration at ledges. Cavities may nucleate at these sites, if the incubation period for cavity nucleation is less than the characteristic time for the relaxation of stress concentration by localized diffusion creep. The analysis yields a quantitative cavity nucleation map in terms of normalized stress versus normalized

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cavity height/spacing. The analysis also suggests that in such NC materials, it is possible for cavities to nucleate under some rather limited experimental conditions. Low-temperature superplasticity Related to GBS is a grain size effect that is manifested as a decrease in superplastic temperature (Section 18.2). For technological applications, the reduction of SP forming temperature in TiAl and Ni3Al alloys is desirable. For example, a Ni3Al alloy (Table 18.1) with a 6 µm grain size shows SP at 1050°C.45 This temperature is higher than the current industrial practice of ∼900°C as an upper temperature limit for SP forming of superalloys. The decrease in SP temperature (to 725°C in NC Ni3Al alloy) brings it within the conventional SP forming range and, therefore, current die and tooling methods can be used. A decrease in SP temperature for the NC state as compared to MC state is ~200°C for titanium alloys, ~325°C for Ni3Al alloys, ∼400°C for pure nickel, and ~200°C for aluminum alloys (Section 18.2). These reductions in SP temperature represent a significant drop in terms of homologous temperatures. Pure nickel is SP at temperatures as low as 0.36 Tm (where Tm is the melting point). This is even lower than the conventional understanding of minimum homologous temperature for the onset of diffusion-controlled deformation processes. High-strain superplasticity The NC materials were found to be SP at a strain rate of 10–1 s–1 (Section 18.2). Table 18.2 shows that by refining the grain size in Al-1420 alloy from 6 µm to 100 nm, the strain rate for SP flow can be increased from 10–3 to 5 × 10–1 s–1, i.e. an increase of 500 times. Table 18.1  Low-temperature superplasticity in NC Ni3Al Parameters

50 nm grain size

6 µm grain size

Elongation (%) Temperature (°C) Strain rate (s–1) Reference

560 725 1 × 10–3 [29]

560 1050 6 × 10–4 [44]

Table 18.2  HSRS in nanocrystalline Al-1420 alloy Parameters

100 nm grain size

6 µm grain size

Elongation (%) Temperature (°C) Strain rate (s–1) Reference

420 300 5 × 10–1 [28]

400 450 1 × 10–3 [45]

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However, the results on Al-2124 were not so dramatic.54 The difference between Al-1420 and Al-2124 shows the role of alloy composition on the effectiveness of NC structure on SP behavior. Nevertheless, the kind of improvements in SP conditions observed so far are likely to have a significant impaction on the SP forming of aluminum alloys.

18.4.2  Effect of processing The ability of NC materials to SP flow seems to be strongly dependent on the method of their synthesis.55 In many cases the data on mechanical properties of NC materials show contradictory trends. A possible reason for this is the expected difference in structure (porosity, density gradients, contaminations, internal stresses, defects including microcracks, etc.) of samples, prepared in different laboratories even for the same grain size. Often this difference in structure is due to uncertain processing history and/or lack of proper control of process variables. Thus, a number of NC materials produced by powder consolidation procedure did not demonstrate any SP.56,57 They have often revealed shear banding during deformation.57 Such deformation behavior, typical of a noncrystalline matrix, suggests that perhaps exceptionally small and finely dispersed impurities (oxides, carbides, etc.) in the microstructure, picked up during the processing steps, may be responsible for this behavior. Nanocrystalline metals and alloys, produced by utilizing cold deformation (ECAP, HPT, cold rolling, etc.) have shown a potential for enhanced plasticity under appropriate loading constraints. Cold deformation leads to a high density of dislocations. It is widely accepted that GBS occurs by the glide of extrinsic GB dislocations and their excess should enhance GBS. As a result, overall material plasticity will increase under such a process, while dislocation-free GB will lead to localized shear.58 It was shown, for example, that deformation to large strains at room temperature (high dislocation density) of coarse-grained Cu results in an enhanced value of strain-rate sensitivity of 0.0159 suggesting an increased role of GB in deformation processes. Results on electrodeposited NC Ni indicated that SP was obtained in this material in the presence of sulfur. The effect of sulfur at an elevated temperature was to inhibit grain growth and to promote grain boundary sliding. Nanocrystalline Ni electrodeposited from a sulfamate bath contained less than 0.002 wt.% S was not SP.60

18.4.3  Effect of microstructural features Grain size distribution effect A significant increase in plasticity of the NiTi alloy with bimodal grain size distribution was observed at 500°C (Fig. 18.26).61 The overall ductility

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18.26  True stress–true strain tensile curves at 500°C for NiTi alloy after HPT and annealing.

of the sample with initial bimodal grain size distribution was more than twice of that for the sample with homogeneous NC structure (170% vs. 367%, Fig. 18.26). Such increase in ductility might be related to the initiation of an additional mechanism such as dislocation creep in larger grains, especially in the beginning of the deformation process.62 Moreover, the presence of these larger grains seems to slow down the grain growth process. The sample with bimodal grain size distribution exhibited higher ductility and although it was affected by elevated temperature for a much longer time, the mean grain size was about 300 nm in both samples after deformation. At the same time, the difference in mechanical behavior of the samples at 400°C was insignificant.61 The presence of grains of 100–200 nm in a NC matrix (d < 100 nm) leads to the material yielding at significantly lower stresses with more pronounced strain hardening at a temperature of 0.4 Tm or lower, as compared to the deformation behavior of the same material with a homogeneous NC structure. Similar behavior was detected in NC Fe-based alloy, in which large non-equiaxed grains (100–200 nm in length) were embedded in NC matrix with mean grain size of 15 nm.61 This material yielded at a stress value that is three times lower than yield stress of NC material with homogeneous structure (dm = 15 nm). The ductility of the alloy was also relatively low in both states as compared to NC Ni3Al.

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Phase morphology effect A clear example of the phase morphology effect, for example, is shown in Fig. 18.27. After annealing at 600°C for 100 h, the (Fe0.8Cr0.2)81B17W2 alloy shows much higher yield stress and considerably lower ultimate strength and a garland of fine phase distributed along the boundaries of equiaxed grains (Fig. 18.27, curve B) as compared to the equiaxed grained structure with approximately the same grain sizes as in curve A (Fig. 18.27). In this case, a test temperature was chosen that was higher than annealing conditions for both states of the alloy microstructure.62 These results have clearly demonstrated the influence of annealing conditions on the nature of crystallization products and, as a result, on the mechanical behavior of the alloy. Hence, depending upon the microstructure that is produced and the deformation conditions that are chosen, a wide variety of strength/ elongation properties can be generated for various potential applications. The real promise of this approach is to separate out the physical mechanisms governing strength and hardness from those governing toughness and ductility, and then subsequently and independently optimize both to overcome the existing inverse relationship between strength and toughness found in conventional materials.

18.27  Stress–strain curves and microstructures of the (Fe0.8Cr0.2)81B17W2 alloy crystallized by different thermal treatments.

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18.28  The effect of heat treatment on stress-elongation behavior of the NC Ni3Al alloy. Note the change in the shape of the curve as well as the drop in total elongation after heat treatment.

18.4.4  Effect of annealing Short annealing of SePD-processed NC Ni3Al does not change the grain size significantly, but it has a dramatic effect on the flow behavior (Fig. 18.28). The initial flow stress increases and the shape of the flow curve changes. The overall ductility reduces from 350% in the as-received condition to ~100% after the short anneal. The likely explanation may lie in the annealing out of dislocations, particularly mobile dislocations at GB initially present in as-prepared SePD alloy, due to annealing treatment.63

18.5 Deformation mechanisms The unique deformation behavior of NC materials is considered to be caused by suppression of conventional lattice dislocation slip (which dominates in MC materials) and effective action of alternative deformation mechanisms mostly occurring in GB. Such mechanisms as GB sliding, GB diffusional creep and triple-junction diffusional creep become increasingly important. Most of the experimental data have been interpreted by extrapolating one of the deformation mechanisms to smaller grain sizes, generally leading to the idea that the limited ductility is an intrinsic property of the nanostructure. There are,

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however, some experimental results suggesting that trying to understand the deformation mechanism demands more than extrapolation of equations derived for coarse-grained material. For example, the rapid decrease in the slope of NC stress–strain curves before failure is usually interpreted in terms of a lack of work hardening leading to plastic instability. However, some deformation tests under both tensile and compression conditions showed a considerable amount of elongation before failure and without evidence of necking.64,65 Moreover, other deformation techniques, such as grinding and cold rolling, demonstrate the existence of considerable plastic deformation.66,67 Therefore, the early failure might be a result of internal flaws, such as porosity, and impurities.

18.5.1  Dislocations in nanocrystalline materials Slip accommodation is an important feature in SP deformation of MC metallic materials. Most of the SP models incorporate this feature6,68 and transmission electron microscopy does indicate intragranular dislocation activity. On the other hand, deformed NC materials have shown very little intragranular dislocation activity and the theoretical calculations69,70 appear to support this lack of such dislocation activity. An increasing role of GB in NC materials, especially as sources/sinks of mobile dislocations, was clearly demonstrated by MDS.71 The authors observed generation of dislocations at GB in high stacking fault energy metal with a grain size of 45 nm after 12% strain at room temperature. Such dislocation motion has been captured by video camera at room temperature in Ni3Al ordered matrix (Fig. 18.29 (a)).2 Figure 18.29 (b) depicts such behavior in MDS of room temperature deformation of Al that shows trends very similar to those depicted in Fig. 18.29 (a) from in situ TEM tests of Ni3Al.

18.5.2  Diffusional creep With the large volume fraction of GB in NC materials, initial publications on the deformation of NC materials suggested the presence of diffusional creep at room temperature.72 These experimental data demonstrate the 4–6 orders of magnitude increase in the GB diffusion coefficient of copper in NC nickel in comparison with the MC nickel. Similarly enhanced diffusivity in GB permeability has been found in other NC SePD materials73,74 providing additional evidence suggesting the importance of specific fundamental characteristics of the boundaries, including enhanced free volume, excess energy, and long-range stresses.75 The emerging experimental trend suggests that some rethinking on the applicability of the diffusional-creep model is needed. Important issues include the influence of the nature of GB/interfaces and the level of strain at which the theory–experiment comparison is made. At low strain levels, transient deformation mechanisms are observed, and this should be taken into consideration for a meaningful interpretation of mechanisms.

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18.29  (a) In situ tensile testing of Ni3Al at room temperature. Note: Observe dislocation “A” in nanosized grain. (b) Dislocation in an Al NC-grain (light grey: fcc, black: hcp, dark grey: other atoms) partially travels away from the GB to be absorbed in the opposite GBs.

18.5.3  Grain boundary sliding In SP materials undergoing strains of hundreds and even thousands of percent, the operation of a specific large-scale mechanism of deformation is needed. Under conditions of microstructural stability, cooperative grain boundary sliding (CGBS) is shown to be responsible for such elongations in MC materials (with grain size from one-half to tens of microns). This mechanism is associated with sliding and rotation of entire grain groups along common sliding surfaces and it was experimentally observed and analysed in detail for MC materials. The most valuable evidence for occurrence of this mechanism in MC materials is the existence of steps along shear planes on a surface of post-deformed materials. However, this relies on observation of surface phenomenon and the actual process of sliding has never been observed in action. Direct observation of CGBS in MC materials by TEM is unattainable, mostly because of specific sample features

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when a ‘bamboo’ structure (with width of one or two grains only) is formed in the viewable area of the thin foil. Such structures eliminate mechanisms, such as CGBS, active in three-dimensional (3D) volumes. Advances in fabrication of NC materials (with grain size smaller than 100 nm) allow retention of a 3D structure even in thin foils acceptable for TEM observations. When the current authors analysed by SEM the pre-polished surface of Ni3Al alloy after deformation at an elevated temperature to high elongation, specific features similar to that observed previously in MC materials76,77 were revealed. Initially straight reference marks (Fig. 18.30 (a)) were showing a clear deviation from linear direction and offsets (Fig. 18.30 (b), marked by arrows) after deformation. Such features are usually attributed to a CGBS. The geometrical size of the

18.30  SEM images of the NC Ni3Al sample surface (a) in initial state; (b) after deformation at 750°C to 450%. Source: Sergueeva et al.78 (reprinted with permission from Taylor & Francis Group).

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offsets is a few orders of magnitude larger than the mean grain size of the material, suggesting that large groups of grains were involved in the sliding process. The bright-field micrographs in Fig. 18.31 (a) are in a frame extracted from a real-time video during in situ tensile straining in TEM at 750°C. During straining, a consistent change in grain contrast was observed in the observation area in the 81-second video frame up to the moment when CGBS occurred.78 The formation of sliding surfaces (or stringers) is evidently seen in Fig. 18.31 (a) (marked by arrows). The large dark feature in the upper left corner is debris in a TEM specimen used for a reference. A similar sliding surface along few grains was also observed in post-deformed NC Pd.79

18.31  (a) TEM image of NC Ni3Al extracted from a real-time video of an in situ tensile test at 750°C. Sliding surfaces are pointed by arrows. (b) Possible mechanisms of the formation of the sliding surface for CGBS in microcrystalline materials: I – dislocation glide; II – grain rotation; II-III – grain boundary sliding; IV – grain boundary migration. Source: Sergueeva et al.78 (reprinted with permission from Taylor & Francis Group).

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To make such mesoscopic cooperative sliding possible, a number of boundaries must cooperate to form a planar interface. Interconnection of this interface with other similar planar interfaces can provide an opportunity for a long-range sliding until it is stopped by an insurmountable barrier, e.g. an extralarge grain or a coarse precipitate. The driving force for planar interface formation is the reduction in the overall GB energy through a reduction in the GB area in the direction of sliding. To create a plane interface, the peaks and troughs of the mesoscopic GB plane must be removed, i.e. the GB area along the mesoscopic glide plane must be minimized to an acceptable degree. In those cases when part of the GB are oriented non-favorably for the realization of sliding with respect to operating stresses, the transfer of deformation from one GB to another might occur via intergranular dislocation glide (grain I, Fig. 18.31 (b)). Another possibility is the localization of migration of GB and their fine adjustment along the common surface (grain IV, Fig. 18.31 (b)). Moreover, such mechanisms as local GBS and grain rotation are also likely to occur (grains II and III, Fig. 18.31 (b)). It can be suggested that this alignment is a preparation step for forming the sliding surface for the following CGBS event to take place along this surface. These processes are relatively slow and create the situation when the local applied stress at the GB plane surface exceeds the threshold stress for sliding. Once these small adjustments have been made, the long-range deformation of CGBS transpires in less than one second until it is stopped by any obstacle such as particles, variations in grain orientation that make such sliding difficult, etc. After this relaxation event, the threshold stress for sliding becomes higher than the applied stress and the process starts again, but in another area of the gage. Changes in the local stress state form a new CGBS surface, since there exists an opportunity to select from a continuum of orientations, represented by a sufficiently high density of GB at varying orientation, and not from a finite number of slip systems as in intracrystalline plasticity. The expression ‘slip system’ in this instance refers to sliding by shear: not intragranular sliding along slip planes, but along intergranular sliding surfaces.

18.5.4  Grain rotation Local grain sliding and rotation was observed in NC Ni80 and Al-1420 alloy13 during in situ straining. For example, in situ deformation of NC Al-1420 alloy revealed clear evidence of grain rotation under applied strain (Fig. 18.32). No dislocations were observed inside the grains at this stage of the experiment. Because of the nanometer size of the grains, it was not possible to conduct SAED (selected area electron diffraction) to track individual grain orientation as a function of strain. To get information on the accommodation processes at hand, as well as a stronger affirmation of grain boundary rotation, more precise analysis is needed including high-magnification imaging of grain boundary regions and triple points during high-temperature straining.

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18.32  (a) An image of NC Al-1420 alloy microstructure during in situ tensile test; (b) an image of the same place after 5 seconds of straining; (c) overlapping contours of grains 1 and 2 corresponding to their position in (a) and (b). Note a rotation of grain 1.

18.5.5  Parametric dependences For SP, it is customary to evaluate the stress exponent, activation energy and grain size exponent in Eq. (18.1), which indicate the dominant deformation mechanism. The determination of the grain size exponent is a very complicated and timeconsuming procedure and was not performed for most investigated NC materials at this point. The summary of our observations on the mechanical behavior of NC materials at elevated temperatures is listed in Table 18.3. Grain growth during mechanical tests at elevated temperatures remains a major obstacle in establishing the high-temperature deformation mechanisms. For example, the values of stress exponent, grain size exponent, and activation energy are influenced by concurrent grain growth in a complex manner. The extent to which the results summarized below are influenced by concurrent grain growth is not clear. There is a significant variation in stress exponent values and the activation energy in some cases is significantly higher than the activation energy for grain boundary diffusion. This is intriguing, because, with the abundance of GB in NC materials, an activation energy value is expected to correspond to GB-related deformation mechanisms at elevated temperatures. In general, deformation mechanisms and overall response of polycrystalline materials, especially at the nanoscale are very sensitive not only to grain size but also

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CP Ti (HPT) 120 1 × 10–4 450 550 Ti-6Al-4V (HPT) 100–200 1 × 10–3 650 725 Ti-6Al-4V (HPT) 100–200 1 × 10–1 725 Ti-6Al-4V (HPT) 70 1 × 10–3 575 NiTi (HPT) 20 1 × 10–3 500 Ni3Al (HPT) 100 1 × 10–1 650 725 Al-1420 100 1 × 10–1 250 300 Vitroperm (NC) 15 1 × 10–4 600 725 Ni (ED) 35 1 × 10–3 350 420 Zn (PC) 60 1 × 10–3 RT 240 TiAl (PC) 25–50 1 × 10–4 750 Pb-Sn (HPT) 100 6.1 × 10–3 RT 4.8 × 10–4 Zn-22Al (HPT) 80 5 × 10–4 120 130 120 75 40 140 165 300 460 270 106 33 300 120 70 20 160 120 140 30 11 18

330 120 160 120 360 – 900 1530 790 154 146 1270 140 380 60 180 120 140 33 11 –

Activ. energy (kJ/mol)

90 5.8 0.2 270 95 568 2.5 0.4 – 676 2.0 0.5 240 2 0.5 – 215 – – – 250 3 0.3 210 380 2.6 0.38 – 560 330 3.6 0.28 118 775 2.6 0.38 20 2 0.5 455 65 5 0.2 295 4 0.25 – 895 2 0.5 45 6.6 0.15 60 110 – 6 0.16 – 120 2.2 0.46 – 300 230 2.7 0.37 –

Stress (MPa) Material Grain Strain Temp. Elong. Stress SRS m size (nm) rate (s–1) (°C) ε = 0.1 Max. (%) exp. n



Table 18.3  Elevated temperature behavior of nanocrystalline materials

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[46]

[42] [46]

[40]

[38]

[35]

[28]

[21] [53] [19] [29,30]

[21]

[19]

Ref.

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to structural characteristics (grain size distribution, grain shapes, etc.), GB structure (misorientation, density of GB dislocations, etc.), and atomic scale structure (type of lattice, stacking fault energy, etc.). Depending on these and concurrent deformation conditions (temperature, strain rate, stress level), one mechanism might dominate with accommodation by one or a few other simultaneously acting mechanisms. As a result, NC materials exhibit particular parametric dependences of deformation flow. It is vital to document the distribution of grain size precisely in order to interpret the deformation mechanisms responsible for the observed deformation in such NC materials. Moreover, the mechanical response of NC materials to the production process can also be very sensitive (Section 18.3.2).

18.5.6  Molecular dynamic simulations Unfortunately, there is still a lack in technological approaches that can allow the production of high-quality NC materials with grains under 20–30 nm in a volume large enough for appropriate mechanical testing. The most important and significant results on the physical and mechanical processes occurring during plastic deformation of NC metals have been obtained by MDS. This technique is well suited to the study of NC metals where a volume of only approximately 1 m–3 can be tested. For conventional polycrystals, such a volume would not be representative of the material. These simulations provide very helpful information for GB structure81 as well as analysis of the deformation processes82 involved in NC materials. Many of the experiments on plastic behavior of NC materials are often conducted using hardness measurements: these (as well as a few creep studies) are performed in the temperature regime corresponding to Coble creep and Nabarro– Herring creep. Such processes involve atomic diffusion and, hence, take place in a timescale that is large compared to atomic vibrations. Computer simulation experiments are restricted to much shorter time scales and, consequently, have to be done at much higher stress levels, in order to keep the time factor within tractable dimensions. Furthermore, the atomic interaction used within MDS is derived from an empirical model. Its quantitative prediction capabilities, when extrapolated far from the region where it was fitted, as in the case of disordered interfaces, have to be considered with care. However, the technique has the power of highlighting the physical processes involved, and careful interpretation of the data can provide a quantitative evaluation of the parameters controlling the temperature, stress, and grain-size dependencies, which have been the central focus of this manuscript. Additionally, the approach can yield simulated data at a very low grain size range where experimentalists cannot easily conduct their studies yet. The capability of supercomputers is increasing ever so rapidly in terms of processing speed and memory. It should be possible in the not-too-distant future to investigate the complex interplay of GBS, GB migration and grain rotation,

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and GB diffusion-controlled creep mechanisms by MDS in comparatively larger nanoscale grains. These are all essential inputs to the understanding of superplastic behavior of fine-grained microstructures in metals and ceramics. When that point is reached, it will no longer be necessary to restrict MDS to idealized and artificially stabilized NC microstructure. Predictions from MDS experiments in NC plasticity can then be compared directly with real-life experiments and each approach will be able to complement the other. Molecular dynamic simulation was used for the first time to study diffusion creep by Keblinski et al.83 Working with pure silicon, with uniform grain size (25 nm) and identical grain shape, they were able to show the operation of Coble creep. Their simulation results yielded activation energy equal to that for GB diffusion, a three-power grain size dependence and (at low stresses) a one-power stress dependence of the strain rate. An increasing role of GB in NC materials, especially as source and sink of mobile dislocations, was also demonstrated by MDS.84 The authors observed GB generation of dislocations in a 45 nm grain size high stacking fault energy metal (12% strain) at room temperature. Such dislocation motion has already been captured by video camera at room temperature in Ni3Al ordered matrix (Section 18.4.1). More detailed information can be found in Mukherjee.85 Recently, Yamakov et al.84 investigated the dislocation processes involved in the deformation of face-centered cubic NC materials. This large-scale MDS of NC Al elucidates the intricate, highly nonlinear atomic-level mechanism controlling complex defect-lattice interaction in the deformation of nanocrystals. These simulations have now advanced to a level where they provide a powerful new tool for describing the atomic-level mechanism controlling dislocation processes and also the response of the grain boundary network to internal and external stresses. Collective shuffling of a few tiny grains on a shear plane has also been predicted in computer simulations.86 MDS also lends support to the above observations87 showing a formation of common shear planes during deformation. With the formation of local shear planes, some grains can move collectively relative to some others. The authors87 also showed that due to the presence of GB that are resistant to sliding (i.e. special low-angle GB or misorientation close to a twin boundary), local shear planes can concentrate around these grain boundaries creating a cluster of grain embedded in a sliding environment.

18.6 Conclusions Although NC materials are a subject of intensive investigation nowadays, there are no systematic data on their SP behavior. SP is a much more complex physical process than just an ability of fine-grained polycrystalline materials to exhibit high elongations prior to failure. Experimental data demonstrates that SP of NC metals and intermetallics follow the general trend of the constitutive relation but with important differences in the level of stress and strain hardening rates

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[Section 18.2]. However, from the evaluation of the behavior of NC materials, it is clear that a NC grain size does not appear to be a sufficient condition for SP. A number of metals and alloys with grain sizes below 100 nm did not exhibit classical SP (Table 18.3). The effect of short annealing on deformation behavior (Section 18.3.4) has clearly demonstrated that microstructural features other than grain size can play a considerable role. Moreover, the ability of NC materials to SP flow seems to be strongly dependent on the method of their synthesis (Section 18.3.2). A direct observation of CGBS in the NC material that did deform superplastically is a confirmation that this deformation mechanism is common to MC and NC materials during SP. Under the conditions of microstructural stability, sliding surface formation with subsequent CGBS is believed to be responsible for such elongations. Such a deformation mechanism is common in MC and NC materials to the point where dislocation or diffusion accommodation can support it, and is considered as SP flow. When considerable grain growth is observed during deformation, the formation of sliding surface and CGBS is restrained. Despite the fact that these NC materials show enhanced plasticity, their deformation is more likely to occur by dislocations or diffusional creep rather than by grain boundary sliding responsible for SP flow in NC materials with a stable microstructure. Thus, ductility of NC materials and some specific features of their behavior at elevated temperatures should be attributed to microstructural stability as well as to the probability of formation of sliding surfaces, sliding distance, and related accommodation mechanisms. One of the open questions on the micromechanism of SP in such materials is the possible mechanism (or mechanisms) for GBS accommodation. As noted earlier, the MC materials do show significant intragranular dislocation activity and these dislocation features are interpreted as evidence for slip accommodation. On the other hand, deformed NC materials have shown rather limited dislocation activity. Moreover, an analysis of experimental data on mechanical behavior of NC materials under different conditions clearly demonstrates that some microstructural features other than just grain size (grain boundary structure; grain size distribution, phase morphology, etc.) can also be responsible for the material behavior (Section 18.3). The specific indications of SP are caused by the special deformation mechanism related mainly to the intergranular character of deformation. Notwithstanding the many discussions on the relative contributions of diffusion, dislocation motion and GBS to optimal SP flow, by the 1990s it was realized that nearly 100% of the external deformation strain resulted from GBS. However, there is evidence for limited amounts of diffusion and dislocation activity during optimal SP flow (Section 18.4). Thus, a viable physical picture would be that GBS is responsible for the measured external strain, while diffusion and dislocation motion are mostly accommodation processes essential for the continual operation of GBS in polycrystalline materials. In the absence of classical intragranular slip, GBS in NC materials is controlled by such mechanisms as specialized intragranular slips

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(mostly partial dislocation emission and twining) and grain boundary diffusion (thermal and/or athermal by atomic shuffling). In order for GBS to be activated and, as a result, for NC materials to show an enhanced plasticity, there are a number of specific requirements for microstructural characteristics and for testing conditions. First of all, a NC material must have high-angle GB and mobile triple junctions. Any impurities that lock GB and triple junctions need to be avoided. The ideal temperature range for deformation process should be in the narrow temperature range in which there is enough thermal activation for GBS but where the grain growth rate is relatively low. The cases where NC material exhibits very high strain rate sensitivity but limited ductility suggest that GB processes alone are not able to support stable homogeneous deformation. Accommodation either by dislocation motion or by diffusion is needed to alleviate the extreme brittleness of NC materials at low temperatures. The presence of isolated relatively large grains (bimodal grain size distribution) in a NC matrix has a beneficial effect on plastic behavior of NC materials, while maintaining the high-strength characteristics of the material. The crucial feature of this structure is the isolation of large grains from each other within a finer-grained matrix. When these grains combine in groups, a dramatic drop in strength and ductility (but still higher than that for a uniform nanostructure) was revealed (Section 18.3.3). The analysis of deformation mechanisms at extremely diminished length scale appears to be a very complicated task. The simultaneous occurrence of multiple independent processes that might support the deformation flow, such as dislocation glide and climb, GB migration, GBS and grain rotation, new phase formation at triple points, twinning, shear banding, etc., makes it difficult to isolate a particular controlling mechanism in NC materials at particular conditions. It should be suggested that in most cases of deformation of NC materials, a few independent processes are active simultaneously and result in a wide range of parametric values. Molecular dynamic simulations have now advanced to a level where they provide a powerful new tool for describing the atomic-level mechanism controlling dislocation processes and also the response of the GB network to internal and external stresses. The experimental data (Table 18.3) indicate that the stress exponent and activation energy for SP flow is similar for MC and NC materials, although the details are not clear at this stage. The initial results in the last few years have established a number of trends: excessive strain hardening, high-flow stresses, a strong annealing effect on flow behavior and a correlation between microstructural instability and SP (Section 18.3). Based on the limited data, the kinetics of SP flow is suggested to undergo a transition at a critical grain size. The key points that are interesting for the future theoretical studies of plastic deformation processes and associated phenomena in NC materials are: • a theoretical description of the critical grain size at which the general equations for SP deformation will break down;

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• a theoretical analysis of the specific features of plastic flow in NC materials; • a development of the generalized model that will describe the combined action of different deformation mechanisms (such as lattice dislocation motion in grain interiors, grain boundary sliding, grain rotation, and diffusion-based plasticity mechanisms associated with grain boundary diffusion and triple-junction diffusion) whose contribution to plastic flow in NC materials is dependent on the material characteristics, grain size distribution and conditions of loading.

18.7 Acknowledgments The authors acknowledge the contribution of their student and post-doctoral colleagues over many years and also the support from the Division of Materials Research, US National Science Foundation. The authors also acknowledge collaboration with Professor C.C Koch, Dr X. Zhang, Professor R.Z. Valiev and Dr D. Branagan.

18.8 References   1 Langdon T.G. In: Hori S., Tokizane M., Furushiro N., editors. Superplasticity in Advanced Materials, Japan Society for Research on Superplasticity, Osaka, 1991, p. 3.   2 Mukherjee A.K., Mater Sci Eng A 2002;322: 22.   3 Mukherjee A.K., Bird J.E., Dorn J.E. The role of climb in creep processes. In: Eyre B.L., editor. The Interactions Between Dislocations and Point Defects, vol. II, Part III, United Kingdom Atomic Energy Authority, Harwell, UK, 1968, p. 422.   4 Mukherjee A.K., Bird J.E., Dorn J.E. Trans Am Soc Metals 1969;62: 155.   5 Bird J.E., Mukherjee A.K., Dorn J.E. Correlation between high temperature behavior and substructure. In: Rosen A., editor. Int Conf Quantitative Relation Between Properties and Microstructure, Haifa, Israel, 1969, p. 255.   6 Mukherjee A.K. Superplasticity in Metals, Ceramics and Intermetallics. In: Mughrabi H., editor. Plastic Deformation and Fracture of Materials, vol. 6, VCH, Weinheim, 1993, p. 407.   7 Suery M., Mukherjee A.K. Creep Behavior of Crystalline. Solids. In: Wilshire B., editor. Superplasticity – Correlation Between Structure and Properties in Creep Behavior of Crystalline Solids, Pineridge Press, Swansea, UK, 1985, p. 137.   8 Nieman G.W., Weertman J.R., Siegel R.W. J Mater Res 1991;6: 1012.   9 Suryanarayana C., Mukhopadhyay D., Patankar S.N., Froes F.H. J Mater Res 1992;7: 2114. 10 Mishra R.S., Bieler T.R., Mukherjee A.K., Acta Metall Mater 1995;43: 877. 11 Valiev R.Z., Korznikov A.V., and Mulyukov R.R., Mater Sci Eng A 1993;168: 141. 12 Mishra R.S., Lee W.B., Mukherjee A.K., Kim Y-W. Mechanism of superplasticity in gammaTiAl alloys. In: Kim Y-W., Wagner R., and Yamaguchi M., editors. International Symposia on Gamma Titanium Aluminides, TMS, 1995, p.571. 13 Sergueeva A.V., Mara N.A., Mukherjee A.K. Microstructure/mechanical properties relationship in SePD materials. In: Altan B.S., editor. Severe Plastic Deformation: Towards Bulk Production of Nanostructured Materials, Nova Science Publishers, 2005, p. 84.

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14 Valiev R.Z., Islamgaliev R.K., and Alexandrov I.V. Prog Mater Sci 2000;45: 103. 15 Salishchev G.A., Galeyev R.M., Malisheva S.P., Valiakhmetov O.R. Mater Sci Forum 1997; Vols.243–245, p.585. 16 Mishra R.S., Mahoney M.W., McFadden S.X., Mara N.A., Mukherjee A.K. Scripta Mater 2000;42: 163. 17 Sergueeva A.V., Stolyarov V.V., Valiev R.Z., Mukherjee A.K. Scripta Mater 2001; 45: 747. 18 Weiss I., Semiatin S.L. Mater Sci Eng A 1999;263: 243. 19 Sergueeva A.V., Mukherjee A.K. The elevated temperature stress–strain behavior of Ti and TiNi alloy produced by high-pressure torsion. In: Mishra R.S., Earthman J.C., Raj S.V., editors. Creep Deformation: Fundamentals and Applications, TMS, 2002, p. 137. 20 Konstantidinis D.A., Aifantis E.C., Nanostr Mater 1998;10: 1111. 21 Sergueeva A.V., Stolyarov V.V., Valiev R.Z., Mukherjee A.K. Mater Sci Eng A 2002;323: 318. 22 Mishra R.S., Stolyarov V.V., Echer C., Valiev R.Z., Mukherjee A.K. Mater Sci Eng A 2001;298: 44. 23 McFadden S.X., Sergueeva A.V., Mukherjee A.K. Mater Sci Forum 2001; Vols. 357–359, p. 499. 24 Mukherjee A.K. Applied Physics 1968;39: 2201. 25 Sergueeva AV., Song C., Valiev R.Z., Mukherjee A.K. Mater Sci Eng A 2003;339: 159. 26 Jiang X.,Wu Q., Cui J., Ma L. Metall Trans A 1993;24: 2596. 27 Basic Research Needs for Environmentally Responsive Technologies of the Future, Workshop Report, 1996, New Orleans, Jan 4–6. 28 Mishra R.S., Valiev R.Z., McFadden S.X., Islamgaliev R.K., Mukherjee AK. Phil Mag A 2001;81: 37. 29 Mishra R.S., Valiev R.Z., McFadden S.X., Mukherjee A.K. Mater Sci Eng A 1998; 252: 174. 30 McFadden S.X., Valiev R.Z., Mukherjee A.K. Mater Sci Eng A 2001;319–321: 849. 31 McFadden S.X., Sergueeva A., Mukherjee A.K. Mater Sci Forum 2001; Vols. 357– 359: 499. 32 Mara N.A., Sergueeva A.V., Mara T.D., McFadden S.X., Mukherjee A.K. Mater Sci Eng A 2007;463: 238. 33 Stoloff N.S. Inter Mater Rev 1989;34: 153. 34 Liu X-D. Met Trans 1998;39: 783. 35 Sergueeva A.V., Mara N.A., Mukherjee A.K. Rev Adv Mater Sci 2004;7: 34. 36 Mara N.A., Sergueeva A.V., Mukherjee A.K., Mater Sci Eng A 2004;374: 244. 37 Kulik T.J. Non-cryst Solids 2001;287: 145. 38 McFadden S.X., Zhilyaev A.P., Mishra R.S., Mukherjee A.K. Mater Lett 2000;45: 345. 39 Zhang X., Wang H., Scattergood R.O., Narayan J., Koch C.C., Sergueeva A.V., Mukherjee A.K., Acta Mater 2002;50: 4823. 40 Zhang X., Wang H., Scattergood R.O., Narayan J., Koch C.C., Sergueeva A.V., Mukherjee A.K. Appl Phys Lett 2002;81: 823. 41 Wadja E.S. Acta mater 1954;2: 184. 42 Mishra R.S., Mukherjee A.K., Mukhopadhyay D.K., Suryanarayana C., Froes F.H. Scripta Mater 1996;34: 1765. 43 Sergueeva, A.V., Mara, N.A., Valiev, R.Z., Mukherjee, A.K. Mater Sci Eng A 2005;410–411: 413. 44 Mukhopadhyay J., Kaschner G., Mukherjee A.K. Scripta Metall Mater 1990; 24: 857.

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45 McFadden S.X., Mishra R.S., Valiev R.Z., Jilayev A.P., Mukherjee A.K. Nature 1999;398: 684. 46 Kaibyshev O.A. Mater Sci Eng A 2002;324: 96. 47 Mishra R.S., Mukherjee A.K. Superplasticity in nanomaterials. In: Ghosh A.K., Bieler T.R., editors. Superplasticity and Superplastic Forming, The Mineral, Metals and Materials Society, PA, 1998, p. 109. 48 Mishra R.S., Valiev R.Z., Mukherjee A.K., Nanostr Mater 1997;9: 473. 49 Mukherjee A.K., Mishra R.S., Bieler T.R., Acta Mater 1997;45: 561. 50 Mishra R.S, McFadden S.X., Valiev R.Z., Mukherjee A.K. JOM 1999, January, p. 37. 51 Chokshi A.H., Mukherjee A.K. Mater Sci Eng A 1989;110: 49. 52 Mukhopadhyay J., Kaschner G.C., Mukherjee A.K. Superplasticity and cavitation in boron doped Ni3Al. In: Superplasticity in Aerospace, TMS-AIME, Warrendale, 1990, p. 33. 53 Kaibyshev O.A. Superplasticity of alloys, intermetallics and ceramics, Springer, Berlin, 1992, p. 151. 54 Mishra R.S., Mukherjee A.K. (unpublished research 1998). 55 Mohamed F.A., Li Y. Mater Sci Eng A 2001;298: 1. 56 Sanders P.G., Rittner M., Kiedaisch E., Weertman J.R., Kung H., Lu Y.C., Nanostr Mater 1997;9: 433. 57 Carsley J.E., Fisher A., Milligan W.W., Aifantis E.C., Met Mater Trans A 1998; 29: 2261. 58 Lloyd D.J., Court S.A., Gatenby K.M., Mater Sci Tech 1997;13: 660. 59 Zehetbauer M., Seumer V., Acta Metall Mater 1993;41: 577. 60 McFadden S.X., Mukherjee A.K. Mater Sci Eng A 2005;395: 265. 61 Sergueeva A.V., Mara N.A., Mukherjee A.K. Mater Res Soc Symp Proc 2004; Vol. 821, p.9.8.1. 62 Sergueeva A.V., Mara N.A., Branagan D.J., Mukherjee A.K. Mater Lett 2007;61: 1465. 63 Islamgaliev R.K., Valiev, R.Z., Mishra, R.S., Mukherjee, A.K. Mater Sci Eng A 2001;304–306: 206. 64 Champion Y., Langlois C., Guerin-Mailly S., Langlois P., Bonnentien J-L., Hytch M.J. Science 2003;300: 310. 65 Jia D., Wang Y.M., Ramesh K.T., Ma E., Zhu Y.T., Va1iev R.Z. App Phys Lett 2001; 79: 611. 66 Wang Y., Chen M., Zhou F., Ma E., Nature 2002;419: 912. 67 Markmann J., Bunzel P., Liu K.W., Padmanabhan K.A., Birringer R., Gleiter H., Weissmuller J. Scripta Mater 2003;49: 637. 68 Sherby O.D., Wadsworth J. Prog Mater Sci 1989;33: 169. 69 Gryaznov V.G., Polonsky I.A., Ramanov A.E., Trusov L.I. Phys Rev B 1991;44: 42. 70 Romanov A.E.. Nanostr Mater 1995;6: 125. 71 Yamakov V., Wolf D., Phillpot S.R., Mukherjee A.K., Gleiter H., Nature Mater 2002;1: 45. 72 Karch J., Birringer R., Gleiter H. Nature 1987;330: 556. 73 Valiev R.Z., Razumovskii I.M., Sergeev V.I. Phys Stat Sol A 1993;139: 321. 74 Würschum R. Ann Chim Science des Materiaux 1996;21: 471. 75 Valiev R.Z. Nanostr Mater 1995;6: 73. 76 Zelin M.G., Dunlap M., Rosen A., Mukherjee A.K. J Appl Phys 1993;74:4972. 77 Zelin M.G., Mukherjee A.K., Acta Metall Mater 1995;45: 2359. 78 Sergueeva A.V., Mara N.A., Krasilnikov N.A., Valiev R.Z., Mukherjee A.K. Phil Mag 2006;86: 5797. 79 Markmann J., Bunzel P., Rosner H. Scripta Mater 2003;49: 637.

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80 Shan Z., Stach E.A., Wiezorek J.M.K., Knapp J.A., Follstaedt D.M., Mao S.X. Science 2004;305: 654. 81 Phillpot S.R., Wolf D., Gleiter H. Scripta Metall Mater 1995;33: 1245. 82 Wolf D., Yamakov V., Phillpot S.R., Mukherjee A.K., Gleiter H. Acta Mater 2005; 53: 75. 83 Keblinski P., Wolf D., Gleiter H. Interface Science 1998;6: 205. 84 Yamakov V., Wolf D., Phillpot S.R., Mukherjee A.K., Gleiter H. Nature Mater 2002; 1: 45. 85 Mukherjee A.K. Elevated temperature crystalline plasticity at diminished length scales, in: Mishra R.S., editor. Creep Deformation: Fundamentals and Applications, TMS-AIME, Pittsburgh, PA, 2002, p. 3. 86 Hasnaoui A., Van Swygenhoven H., Derlet P.M. Phys Rev B 2002;66:184112. 87 Van Swygenhoven H. Mater Sci Forum Vols. 447–448, 2003, p. 1.

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19 Creep and high-temperature deformation in nanostructured metals and alloys W. YIN, Williams Advanced Materials, USA Abstract: This chapter discusses the unique creep behavior and hightemperature deformation of nanostructured metals and alloys. First the findings from the investigations on the deformation and creep mechanism in pure nanostructured metals are reviewed followed by further discussion on singlephase nanostructured alloys. It also summarizes the latest experimental results on creep and high-temperature deformation of nanostructured alloys and composites as well as the results from the atomistic simulations and theoretical modeling on these subjects. Key words: creep, high-temperature deformation, grain boundary, diffusion, nanostructured materials.

19.1 Introduction One of the most remarkable phenomena that nanostructured materials exhibit is the time-dependent deformation, or creep, at ambient temperature, though creep occurs typically at high temperature in conventional coarse-grained materials. Significant progress on this subject has been made in the past decade thanks to the success in synthesizing high-quality bulk nanostructured materials in addition to atomic simulations aided by advanced computing technology. Nevertheless, experimental investigations on creep and high temperature deformation in nanostructured metals and alloys are still limited in scope and quantity1–3 in contrast to the well-established physics of creep in coarse-grained materials. Although the mechanical properties have been explored for a long period of time,4 often the experimental results of different investigators were not consistent with each other. The extrinsic effect of the complications is related to defects introduced in the fabrication process, including high porosity level, large distribution of grain size and different impurity level. The intrinsic high activity due to the large volume of intercrystalline components (grain boundary, triple junction, etc.) leads to unique deformation behavior that may involve multiple mechanisms, and a single model may not be sufficient to interpret the deformation process. Although there is no doubt that grain boundary plays an important role in this process, interpreting the experimental results is not as simple as grain boundary diffusion or sliding. In addition, most experimental studies on creep have been limited to a small range of testing temperatures because of the stability of grain structure. The grain growth during creep at elevated temperatures further 594 © Woodhead Publishing Limited, 2011



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complicates the creep mechanisms. Furthermore, the extrinsic effect might be significant because of defects introduced in fabrication process, including high porosity level, large distribution of grain size and different impurity level. It is a challenge to produce fully densified nanostructured materials through powder metallurgy processes, and therefore the porosity in this kind of material may lead to premature failure during deformation. In the meantime, oxides most likely exist in bulk nanostructured metals prepared by this method and might increase creep resistance by pinning grain boundaries. On the other hand, computer simulations5 at atomic and molecular levels have been a promising approach not only to interpret the experimental results, but also to investigate deformation mechanisms and defect structures in extreme testing conditions (strain rate or temperature) and fine grains (<10 nm). The combination of computer simulations and experimental research are proved to be an effective tool for studying creep and high-temperature deformation in nanostructured metals and alloys. Despite the fact that some contradicting results among different investigators or between experimental results and atomic simulations have brought some confusion to the scientists, progress in understanding creep behavior in nanostructured metals and alloys is substantial. Particularly in the past decade, significant progress has been achieved in the areas of mechanical testing, microstructure characterization and computer simulation. This chapter will focus on the latest results on creep and high-temperature deformation in nanostructured metals and alloys with a typical grain size in the range of 10 to 200 nm in the hope that this will provide some insights in these areas.

19.2 Temperature-dependent deformation in fine-grained pure metals 19.2.1  Deformation at elevated temperatures Plastic deformation at elevated temperature received little attention during earlier experimental investigations when the focuses were a ‘negative’ Hall–Petch effect and superior strength at ambient temperature. This has been changed since the late 1990s when porosity-free and uniform-grained nanostructure metals were successfully produced through advanced synthesis processes such as the electrodeposition (ED) technique and severe plastic deformation (SPD). The different process techniques offer the opportunity to study the intrinsic as well as processrelated extrinsic deformation behavior in these metals. The mechanical behavior of ED nanostructured nickel has been investigated and the experimental results showed that the nanostructured nickel exhibited unique deformation behavior, different from the counterpart coarse-grained nickel.6 In nanostructured nickel, the temperature effect on tensile strength is pronounced between 290 K and 473 K.7,8 The ultimate tensile strength of nanostructured nickel was as high as 1.5 GPa at room temperature, five times that

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of conventional coarse-grained nickel, but the strength dropped to 740 MPa at 473 K. The tensile tests and cyclic tests showed strain hardening in nanostructured nickel (Fig 19.1).8 The work hardening rate dropped sharply with increasing tensile strain before it became exhausted at a few percent of true strain. The curves of work hardening rate vs. true strain at room temperature, 373 K and 473 K, coincide with each other, suggesting that the deformation mechanism remains the same in the tested temperature range. On the contrary, nanostructured Zinc exhibits a different deformation mechanism at an elevated temperature from that at room temperature.9 The strain hardening decreases with an increase of testing temperature and ceases to occur at 200°C. Wang et al.10 observed additional evidence for the high activation energy and small activation volume in nanocrystalline Ni, which suggests that the thermally activated process in this material is different from the conventional forest dislocation cutting mechanism. Instead, the experimental findings and their analyses suggest strong interaction between dislocation and grain boundaries, which dominates the creep deformation. However, grain boundary diffusion and sliding are suggested in a similar material deformed at room temperature. Extremely fine grain structure makes nanostructured metals highly prone to recover grain growth at elevated temperatures, particularly for the materials processed by severe plastic deformation (SPD). Pure, ultrafine-grained (UFG) Cu produced by equal-channel angular pressing at ambient temperature was deformed in uniaxial compression at elevated temperatures up to 418 K.11 The

19.1  Work hardening in nanostructured nickel. Source: Yin et al.8

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deformation was accompanied by softening as shown in Fig. 19.2. The softening has been related to the intrinsic nature of pure nanostructured metals at an elevated temperature. Metallurgical study indicates that homogeneous growth of the subgrains occurred at elevated temperatures and eventually reached a steady state. The stable subgrain size in the UFG materials depends on the applied stress as in

19.2  Work softening phenomenon in UFG material showing decrease in defect density at high-angle boundaries (thin arrows) and deformation-induced coarsening of subgrains and grains (thick arrows). Source: Blum et al.11

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conventional materials. Blum et al.11 proposed a dislocation model to explain the softening behavior in the UFG materials. In addition, recrystallization also results in local structure coarsening and produces bimodal grain structures. Therefore it leads to strong softening when the temperature is sufficiently high. Numerical modeling isolates the microstructure instability with a capability to focus on mechanical behavior. The deformation of nanostructured aluminum at temperatures of 0.8–0.97 Tm appears to be controlled by grain boundary mechanisms.12 Following yielding, both the flow stress and grain size are developed to steady states that depend on the deformation temperature. Although this is well known for dynamic recrystallization induced by diffusion-controlled dislocation climb in conventional coarse-grained materials, this study suggests that there is negligible dislocation activity in the nanostructured grain size range considered. The activation energies for grain boundary-based deformation mechanisms were comparable to the apparent activation energy derived for hot working. This suggests that the flow stress and grain size are primarily controlled by grain boundary sliding, migration and rotation, rather than diffusion-based dislocation climb. The negligible degree of dislocation activity observed is consistent with the deformation microstructures observed in materials produced by high strain rates near the melting point.

19.2.2  Creep behavior Despite their excellent high tensile strength, nanostructured metals are prone to exhibit room temperature creep. The available experimental results of creep tests on nanostructured materials are still limited due to the difficulty of preparing high-quality samples with relatively uniform grain size, full density and free of grain boundary impurities. Furthermore, grain growth occurs at much lower temperatures in nanostructured metals than that in the coarse-grained counterpart. This limitation sets an upper bound of testing temperatures in creep tests, which are below 300°C for most nanostructured metals and alloys. Low temperature (~0.24–0.33 Tm) creep13 in nano-Cu and Pd with a grain size of 10 nm to 55 nm is two to four orders of magnitude slower than the theoretical values of Coble creep rate. The creep tests6,14 show that the model of grain boundary sliding aided by grain boundary diffusion fits the experimental data well at ambient temperature. Also, the results showed that grain size has a strong influence on creep rate and the stress exponent.6 With the exception of the stress exponent of 1.18 for the finest grained sample (6 nm), the creep rate is proportional to the second power of the applied stress at room temperature for nanostructured nickel with average grain size of 20–40 nm. Wang et al.6 suggested that enhanced grain boundary diffusion in the finest grain sample might account for the difference in the stress exponent. For as-deposited nano-Cu, the stress exponent of unity15 was observed, whereas it was equal to 2 for cold-rolled nano-Cu. Lu and co-workers16 observed the superplastic extensibility at room temperature in the

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nanostructured pure copper. The average grain size remained unchanged after cold rolling, whereas the micro-strain in the sample and the average misorientation angle of grain boundaries increased in the early stage of rolling and saturated in the later stage. These experiments suggest that the deformation mechanism depends on several factors including grain size, grain boundary misfit and testing conditions: stress and temperature. A series of systematic experiments is necessary to clarify the roles of individual factors in the creep mechanism. Yin et al.7 noticed that the primary creep of nano-Ni at room temperature has been prolonged remarkably compared to conventional creep tests of coarsegrained nickel at high temperatures. The primary creep lasts more than 200 hrs at 700 MPa at room temperature, as shown in Fig 19.3. The primary stage drops sharply to around 40 hrs at 700 MPa at 373 K. It should be noted that the previous creep experiments were restricted to very short periods of time.6,14 As a result, this approach may raise the uncertainty in the results on the steady state creep. Therefore it makes more sense to perform longer-term creep tests to achieve more reliable experimental results. Despite the variation of composition, the activation energy for creep was found to be around 90 kJ/mol in nano-Ni.8 This value is close to the activation energy for grain boundary diffusion, 107 kJ/mol, in coarse-grained Ni.17 A similar result was obtained in nano-Cu.14 The similarity of the activation energy for creep to the activation energy for grain boundary diffusion suggests that grain boundary sliding or grain boundary diffusion may dominate the creep deformation in this material.

19.3  Primary creep of nanostructured nickel with a grain size of 30 nm at room temperature. Source: Yin et al.7

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19.2.3  Grain boundary relaxation Ke,18 Cordea and Spretnak19 observed grain boundary relaxation phenomena in conventional polycrystalline metals and alloys. The research started with the effort to demonstrate the viscous behavior of pure polycrystalline metals with planar and flat grain boundaries. The study on grain boundary relaxation of nanostructured materials at ambient temperatures may help understanding of their mechanical response, especially for creep behavior. Numerous investigations have been conducted to study this relaxation process in nanostructured metals such as nano-Pd,20 nano-Au,21 nano-Cu,22 nano-Ni23 and nano-Al.24 The reversible boundary shear was first described by Zener25 and studied extensively by Ke.26 The initial anelastic sliding along the planar parts of the boundary is blocked by the grain edges and triple junctions, and the local stress is concentrated on these locations so that a counter stress is built up. Thus, the initial sliding rate depends on the intrinsic viscosity of the planar grain boundary. Thus the longer the planar grain boundary is, the larger the total viscous slip would be. However, irregularities such as serrations, ledges, impurities and precipitates may act as obstacles to the grain boundary sliding. As a result, anelastic relaxation should be less than the Zener calculation. Anelasticity measurements have been performed on several nanostructured metals prepared by different techniques.24 The internal friction of nanostructured metals has been highly enhanced at low temperatures whereas conventional polycrystalline materials exhibit very low damping. Internal friction of nanostructured aluminum prepared by mechanical attrition was measured as a function of temperature. A broad internal friction peak was found at 501 K with a frequency of 3 Hz in this material. An exponential-like background damping is observed at higher temperatures (>500 K). Compared to the grain boundary relaxation in coarse-grained aluminum, the peak temperature for the nanostructured Al with grain size of 40 nm shifted by 31 K. The peak temperature further decreased to 461 K for the nano-Al with grain size of 20 nm.25 The peak temperature also depends on the frequency of the test. According to the relationship of peak temperature and test frequency, the activation energy for internal friction, 1.65 eV, can be obtained. This value is close to the activation energy of grain boundary diffusion. Therefore, this process can be attributed to grain boundary relaxation because of the above similarities. The internal friction measured with a frequency range of 0.1–1.0 Hz in nanostructured nickel is much higher than that in coarse-grained nickel.8 The background intensity of internal friction increases with decreasing grain size from 30 nm to 15 nm. The strength of internal friction peak at 700 K in nanostructured nickel is two orders of magnitude higher than that in coarse-grained nickel. The calculated activation energy for this process, 92 kJ/mol, is close to the activation energy of grain boundary diffusion in nickel. The fact that a high volume fraction of intercrystalline components exists in nanostructured nickel, and the similar values of the activation energy between anelastic deformation and grain boundary © Woodhead Publishing Limited, 2011



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diffusion, indicates that grain boundary sliding accommodated by grain boundary diffusion must be the main source of the anelasticity. The internal peak observed in nano-Ni together with the corresponding measured peak parameters including activation energy of the relaxation and specific relaxation time, hints at the presence of an anelastic relaxation process rate-limited by single-atom jumps at the interfaces. The samples of nano-Fe with an initial grain size of 15 nm display higher damping than the samples with a grain size of 40 nm.24,25 However, the internal friction of nano-Ni with grain size of 20 and 40 nm does not show an appreciable difference. The relaxation also strongly depends on processing which may introduce defects during sample preparation. Compared to nano-Ni prepared by ball milling, the electrodeposited nano-Ni exhibits higher damping, especially at temperatures above 600 K. This is probably due to the particles and oxides that may have formed along grain boundaries during ball milling and the following compaction. This contamination will lower internal friction by inhibiting grain boundary sliding. Grain boundary sliding will operate more easily at high temperatures than it does at room temperature. Therefore, the pinning effect of the particles becomes more pronounced at high temperatures. Some impurities may result from the contamination with the chemical solution in electron-deposition processing: these impurities also may reduce the internal friction. For instance, the relaxation strength in boron-doped nano-Ni is much lower than that in pure nano-Ni.

19.3 Creep and high-temperature deformation in nanostructured alloys While extensive research has been carried out on the deformation mechanisms in pure nanostructure metals, the effects of alloy additions to nanostructured matrices are poorly understood. Alloying or introduction of additional phases may lower diffusion or reduce grain boundary activity, which will result in higher tensile strength and enhanced creep resistance.

19.3.1 Plastic deformation and creep in nanostructured alloys The tensile behavior of nanocrystalline Mg-3%Al alloy has been investigated at temperatures ranging from room temperature to 250°C.31 The strain hardening decreases rapidly with increasing temperature in the fine-grained specimens and this causes plastic instability at elevated temperatures. This effect is so pronounced for the nanocrystalline sample that the strain to failure decreases at temperatures higher than room temperature. A similar effect has been recorded for ultrafinegrained Al-7.5%Mg alloys by Han and Lavernia,32 who observed that necking predominates at lower temperatures for finer-grained samples due to increased interfacial sliding. Mishra et al.33 studied high-temperature deformation behavior

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of a gamma TiAl alloy. The stress exponent for deformation is approximately 6 in the strain rate range of 10–5–10–3 s–l and 1023–1223 K. Therefore the authors suggested that a climb-controlled dislocation mechanism, rather than grain boundary sliding dominates in the nanocrystalline gamma-TiAl alloy. There are many metal–metal systems with a miscibility gap in the liquid state, particular in Al and Pb systems, which are immiscible in the solid state and have a wide miscibility gap in the liquid state.27 The large size difference between the Al and Pb atoms can promote segregation or precipitations near the grain boundary. There have been several studies that show the effects of Pb additions to Al. The melting behavior of nanosized Pb particles can be higher or lower than the bulk value.28 The studies on effects of Pb on the mechanical properties of nanocrystalline Al yielded conflicting results. In one case significant strengthening was observed,29 while in the other case a pronounced softening was observed.30 Using melt spinning and ball milling, Sheng et al.29 produced nanocrystalline Al-Pb alloys up to 30 wt.% Pb. Incoherent Pb particles in the size range 5–30 nm with large Pb particles were observed in this alloy using electron microscopy. The hardness increased by 50% at 5 wt.% Pb compared to the pure nanocrystalline Al prepared using the same process. The authors attributed the increase to the strengthening effect of fine Pb particles. Rajulapati et al.30 used ball milling to produce nanocrystalline Al-Pb alloys ranging from pure Al to pure Pb. No increase in hardness was observed. Addition of 5 wt.% Pb produced a 45% drop in hardness. Lead particles ranging from nanoscale to submicron sizes were observed. Z-contrast high-resolution electron microscopy indicated that Pb segregated to grain boundaries during the initial additions of Pb. These authors hypothesized that the decrease in hardness was due to segregated Pb atoms that affected the interplay between dislocation and grain boundary modes of deformation. Fabrication processes such as cryomilling, which introduces oxides and nitrides during the preparation of alloys, exhibit a significant effect on the deformation of nanostructured alloys.34,35 The creep behavior of cryomilled Al 5083 alloy at 0.61– 0.66 Tm34 shows that neither the apparent stress exponent nor the apparent activation energy is a constant; instead they decrease with increasing applied stress. Chauhan et al.34 introduced a threshold stress that could be attributed to the potential grain boundary segregation or nano scale dispersion inside grains. The introduction of threshold stress yielded a true stress exponent of about 2 and true activation energy close to that anticipated for boundary diffusion in Al. These values of the true stress exponent and the true activation energy suggest that the rate controlling process is related to grain boundary sliding.

19.3.2 The effects of dual and multiple phases on hightemperature deformation Stable microstructure at an elevated temperature is essential to maintain the unique mechanical properties of nanostructured materials. However, the superior

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mechanical properties of nanostructured materials may vanish at elevated temperatures as the microstructure becomes unstable. The effective approach to prevent the grain structure from coarsening is to introduce secondary phase and/ or oxides dispersion. Fine and uniform oxide dispersoids can significantly stabilize grain structure and improve mechanical properties at elevated temperatures in nanostructured alloys. A total of 5 vol.% of TiC, ZrO2 or a combination of the two dispersoids leads to a strong reinforcing effect and keeps the creep resistance in compression up to 773 and 1123 K.36 Oxide-dispersion strengthened (ODS) ferritic steel 14YWT (Fe-14.2%Cr-1.95%W-0.22%Ti-0.25%Y2O3)34 has a fine grain size, typically 50–200 nm, which is stable even after annealing at 1000°C for several hours. The fine grains contain many Ti-rich nanoscale oxide clusters based on 3D atom-probe results, and these clusters have been proposed as the reason for the superior creep resistance of the 14YWT steel by Hayashi et al.37 The 14YWT alloy maintains a stable grain structure when annealing at 1000°C for 1 h followed by creep testing at 800°C with an applied stress of 250 MPa. Remarkably, in spite of the very fine grain size, the alloy exhibits excellent creep resistance. This suggests that there is no significant grain boundary sliding even for the very fine grain size (approx. 100 nm) structure. Fine grains are observed in both samples of 1 h as-annealed and 1 h annealed/crept. Moreover, there is no significant difference in dislocation structures in the fine grains. A prolonged annealing (120 hours) resulted in extensive anomalous grain growth from a few hundred nanometers to over 10 microns. The minimum creep rates of the 14YWT samples annealed for various times at 1000°C are similar, even though they possess vastly different grain structures. In the coarse grains, the dislocations are strongly impeded by the presence of Ti-rich oxide nanoclusters that may contribute to the retention of creep strength even after anomalous grain growth has occurred.

19.4 Deformation mechanisms and modeling In order to evaluate the stress dependence, the minimum creep rate could be normalized with respect to temperature and grain size. The data employed in the normalization are listed in Table 19.1.

Table 19.1  The parameters for creep rate normalization

Grain boundary (GB) thickness W, nm

GB diffusion Db0, m2/s

GB activation energy Q, eV

Burger vector b, nm

Cu Ni

0.5 0.5

3×10–9 7×10–6

0.82 0.94

0.249 0.256

Sources: Sanders et al.;13 Yin and Whang.7

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19.4  The plot of the true tress vs the normalized minimum strain rate , showing the stress exponents at/above ambient temperature. Source: Yin and Whang, 2005.7

The stress dependence on minimum strain rate for nano-Cu13,14 and nano-Ni6,8 at and above room temperature is shown in Fig. 19.4. The plot indicates that the minimum strain rate at room temperature is approximately second power to the applied stress for nano-Ni, whereas it is difficult to obtain the value for nano-Cu14 due to its narrow range of the applied stress. Above ambient temperature, the stress exponent constant was about 4 for both nano-Ni8 and nano-Cu.13 This indicates that grain boundary sliding may be a dominant factor in the room temperature creep, while the mechanism at higher temperatures appears to be complex. The results of tensile creep tests showed the reduced minimum creep rate in nanostructured Ni-0.06 at.% S compared to the nano-Ni-0.03 at.% S at room temperature.8 Boron and sulfur are effective additives in improving the creep resistance of nano-Ni at ambient temperature. These elements play an even more important role as grain boundary segregants in the creep above room temperature. In situ transmission electron microscopy observations reveal that dislocations glide exists in large grains (70 nm) of nano-Ni sample with an average grain size of 40 nm.38 Deformation is instigated by the emission of dislocations at grain boundaries whereupon voids and/or wedge cracks form along grain boundaries and triple junctions as a consequence of transgranular slip and unaccommodated grain boundary sliding as shown in Fig 19.5. Ex situ and in situ deformed

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19.5  A schematic illustration depicting creep fracture mechanism. Source: Kumar et al.38

specimens exhibit similar fracture surface features that primarily reveal the occurrence of dimpled rupture. The dimples nucleated by the voids grow to some six to ten times the average grain size. The in situ experiments also reveal the formation of twins. Such twinning in the present face-centered cubic metal could be envisioned as a possibility since the local resolved shear stress could easily exceed a critical value, approximately 300 MPa, in the nanostructured Ni. Due to the instability of microstructure at high temperatures and intrinsic high strength, the creep tests for nanostructured metals may be carried out in a small regime of high stresses and near-room temperatures. According to the deformation mechanism map proposed by Ashby39 for coarse-grained nickel, there are five regions dominated by different deformation mechanisms including grain boundary sliding, diffusion creep and dislocation creep. However, the map would not be adequate for nanostructured nickel where a large volume fraction of grain boundaries is highly thermally activated. In general, the creep deformation could be attributed to many micro-mechanisms. Therefore, the plastic strain in a tensile creep consists of the contributing components:

ε = εgb + εd + (εdg + εn),

[19.1]

where εgb, εd εdg, and εn are grain boundary sliding, stress-directed diffusion of vacancies, the strains caused by dislocation glide, and non-conservative motion of dislocations, respectively.

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In practice, it is difficult to evaluate the grain boundary sliding (GBS) in nanostructured materials by employing marker lines as have been used in the polycrystalline specimens. Alternatively, computer simulations have been one of the useful tools for investigating creep mechanisms. In nanostructured palladium with grain size of 7.6 nm, the GBS at 1200 K and 400 Mpa, was investigated by molecular dynamic simulations.40 To overcome the well-known limitations associated with the relatively short time interval used in the MD simulation (typically <10–8 s), Yamakov et al.40 performed simulations at elevated temperatures where the distinct effects of GB diffusion are clearly identifiable. In order to prevent grain growth and thus to enable steady-state diffusion creep to be observed, the input microstructures were tailored to 1) have a uniform grain shape and a uniform grain size of nm dimensions and 2) contain only high-energy GBs that are known to exhibit rather fast, liquid-like self-diffusion. The simulations showed a linear dependence of the creep rate with the applied stress. The grainsize scaling of the Coble creep is found to decrease from d–3 to d–2 when the grain diameter becomes the order the GB width. It was also observed that GBS acts as an accommodation mechanism for the Coble creep. Keblinski and his co-workers found that the creep rate of nanostructured Si increased as a non-linear function of the applied stress,41 which is contrary to their earlier study. This discrepancy probably stems from the assumption made in the Coble equation, where 2sinh(σΩ/kT) was simplified to σΩ/kT by assuming σΩ << kT. This assumption works well for most conventional coarse-grained materials where creep occurs at high temperatures and low stresses. Nevertheless, the assumption may become invalid for creep near ambient temperature and at high stresses. Therefore, the non-linear relationship between the strain rate and the high-applied stress at ambient temperature must be explored from this viewpoint. It is widely accepted that neither Coble creep nor GBS is an independent deformation mechanism, and they are both integral parts of the deformation mechanism in the absence of dislocation mechanisms. Nevertheless, the atomic simulations have not been successful in identifying which mechanism, GB diffusion or GBS, plays the dominant role. In these simulations,42 strain rates as high as ~107 s–1 were used to meet the capacity of the computation. It is not known whether the results of such simulations at unusually high temperatures and high stresses can extend to the realistic deformation of nanostructured metals at low/intermediate temperatures. The strain rate of nano-nickel with grain size of 10 nm under a tensile stress of 2.6 GPa at 300 K was found to be 3 × 107 s–1 while it would be 3 × 105 s–1 at 26 MPa at the same temperature assuming the linear relationship holds.40 Arzt, Ashby and Verrall43 proposed a model of two-dimensional GB for creep based on GB dislocations. A square grain is acted on by equal and opposite normal stresses σn. The grain boundaries contain an array of straight, parallel GB dislocations of spacing h between two neighboring dislocations. It is well known that GB dislocations have different Burgers vectors from those of lattice

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dislocations, and therefore they are constrained to remain in the boundaries during gliding. In this model, the GB dislocation glide causes GBS whereas its climb results in GB migration. It is also assumed that the number of dislocations per grain is conserved. In other words, at the steady state, if one corner of the grain loses one dislocation, another corner would gain a new dislocation. The cores of the boundary dislocations are a perfect source or sink for vacancies. This intrinsic Lifshitz model of GBS ends up with the classic Coble creep equation. Nevertheless, in this case, there is inconsistency between computer simulations or analytical model and experiments. For example, the computer simulations yield the linear relation between the steady strain rate and the true stress, whereas the experiments resulted in stress exponents of 2. Langdon44 proposed a model of GBS for determining the climb velocity of an isolated dislocation in an infinite crystal, and obtained the strain rate as a function of the second power of stress. Spingarn and Nix’s slip band model45 predicted a creep process that is controlled by GB diffusion, whose exponents vary from 1 to 5. However, these models could not be applied to nanostructured metals and alloys because both models require lattice dislocations to accommodate GBS. For an intrinsic creep model, the important assumption is that the surface density of grain boundary dislocations is independent of the applied stress. This model might work well for the creep at high temperatures and low stresses. But, it may not work equally well at high stresses and low temperatures in nanostructured metals where GBS is the dominant deformation mechanism.43 Suppose the density of GB dislocations being ρ = Aσ/d, and the strain rate to be ε̇ = ρbgbυ/d, the creep rate is given as:

[19.2]

where C(= A ⋅ B), A and B are constants; d and δ are grain diameter and grain boundary thickness, respectively. This model may explain the second power relationship of the creep rate vs. stress in the current experiments at room temperature. Another issue to be addressed is that the nominal stress exponent increased from unity to as large as five at higher temperatures. In coarse-grained metals, the large stress exponent (n > 3) has been attributed to the presence of precipitates on grain boundary. In the studied nano-nickel, neither precipitates nor lattice dislocations were observed in the specimens tested at 373 K and 473 K. Therefore, further research is desired to elucidate whether the lattice dislocations become active during creep testing above ambient temperature. When the creep test temperature increases from room temperature to 373 K, the enhanced GB diffusion rate will promote GBS by two orders of magnitude. The extensive GBS would inevitably encounter the resistance of triple junctions. In other words, the elastic strain may accommodate the internal stress for creep deformation at room temperature, whereas the plastic strain has to occur near the grain boundary and at triple junctions for creep deformation at 373 K.46,47 As a

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result, the applied stress will reduce to an effective stress, σeff = σapp – σb, where σb is the resistant stress. Therefore, equation (19.2) may be modified to:

[19.3]

In nanostructured materials, the activity of dislocations is limited because of very high required stress for nucleation of dislocations in nanograins. Therefore sulfur should have little effect on grain deformation, since the dislocation activity in the grains is negligible, needless to mention the dilute concentration of sulfur in the grains. Thus, the role of sulfur as a segregant to the grain boundaries in deformation should be pronounced in the grain boundaries, where the deformation occurs through GBS and high diffusion. Yin and Whang8 shows that the nano-nickel with 0.06 at.% sulfur exhibited improved creep resistance. The molecular dynamics simulations using the embedded-atom-method (EAM) have been performed to study the segregation behavior of phosphorus at grain boundaries in Ni.48 The results showed that phosphorus reduced the number of micro-voids near the grain boundaries, which implies that the phosphorus may increase GB cohesion. The fluctuation of sulfur along grain boundaries was also confirmed by the high-resolution electron microscopy in nano-Ni containing 0.29 at.% sulfur.49 Such compositional fluctuation may be explained using the ‘disordered-atom group’ model for GB by Ke,18 in which the grain boundaries are presumed to consist of many disorderedatom groups, which are separated by regions of good fit. It is reasonable to assume that the solutes tend to stay in the cores of disordered-atom groups as the cores have larger excess free volume. From the plot of the segregation fluctuation along the grain boundary,49 the zone with high sulfur content can be measured to be around 10 nm. Considering the factor due to impurity segregation at GB, the back stress consists of two components, i.e.:

σb = σb,Ni + σb,imp,

[19.4]

where σb,Ni, σb,imp are back stress from pure Ni grain boundaries and the incremental back stress due to the impurity segregation in grain boundaries. It is estimated that the back stress for nano-Ni ranges from 200 MPa to 400 MPa.8 This indicates that the impurities at GB play a significant role in increasing back stress. Howell and Dunlop50 have observed experimentally that the main obstacles to the motion of GB dislocations are particles situated at GBs and triple junctions. These obstacles contributed to the back stress for GBS. The particle-induced back stress could be as high as 270 MPa for nanostructured Y-SZP 51 with grain sizes of 40 nm and 60 nm at 1373 K. During deformation, matrix dislocations interact with GBs that constitute very strong barriers to dislocation glide processes. Some dislocations may enter the GB, giving rise to extrinsic GB dislocations that disturb the intrinsic GB structure. Gleiter52 suggested that extrinsic GB

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dislocations might be important for the emission and absorption of vacancies. Stress relaxation associated to extrinsic GB dislocations must occur for the plastic deformation to go on and for the GB to return to equilibrium. In nanostructured copper, the back stresses were obtained for as-deposited and cold-rolled conditions. The back stress increased dramatically from 130 MPa for the as-deposited copper to 340 MPa for the cold-rolled copper.14 While one creep deformation mechanism often dominates in traditional polycrystalline materials, multiple mechanisms may operate simultaneously in nanostructured materials. Grain size varies in nanostructured materials and size distribution plays an important role in controlling creep deformation. GB processes take place in finer grains and the transition to dislocation-based deformation mechanism may occur in larger grains. Particularly for pure nanostructured metals, grain structure becomes unstable at a temperature not much higher than ambient temperature. Therefore an extended creep deformation at elevated temperatures may result in grain growth, which must be taken into consideration in the analysis of plastic deformation. Millett et al.53 have used molecular dynamics simulations to demonstrate and characterize diffusionaccommodated creep deformation in a body centered cubic nanocrystalline metal, Mo, using the Finnis–Sinclair potential. An idealized columnar microstructure with uniform grain size and hexagonal shape was designed to study the creep deformation at temperatures ranging from 2300 K to 2900 K. A uniaxial stress was applied in a wide range from 0.2GPa to 0.8GPa so that the magnitude of the applied stress was sufficiently small in order to prevent dislocation nucleation on the GBs and thus ensure that all deformation was attributable to diffusion processes. The observed creep rates exhibited linear-stress dependence for the studied grain size of 8 nm to 20 nm, and a grain-size scaling factor that deviates from d–3 to d–2 as the grain size is increased. This, together with a positive curvature in the Arrhenius diagram for the creep rates, provides evidence for a combination of Coble and Nabarro–Herring creep operating in parallel.

19.5 Conclusions This chapter has summarized various reports concerning the high-temperature deformation and creep behavior in nanostructured metals and alloys. Although the deformation and fracture mechanisms in these materials have been better understood in the last ten years, there are too many unanswered questions. Significant progress has been made in the past decade on understanding creep deformation mechanism and yet much more work is still needed. In particular, experimental study in nano-grains less than ~10 nm is a challenging task due to the specimen preparation and the influence of artifacts. Nevertheless, current the remarkable progress in materials fabrication offers extraordinary opportunities for studying the mechanical properties of nanostructured materials in the future.

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19.6 References   1   2   3   4   5   6   7   8   9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 25 26 27 28 29 30 31 32 33 34 35 36 37 38

Gleiter H. Prog Mater Sci 1989;33: 223. Gryaznov V.G., Trusov L.I. Prog Mater Sci 1993;37: 289. Meyers M.A., Mishra A., Benson D.J. Progress in Materials Science, 2006;51: 427. Suryanarayana C., Froes F.H. Met Trans A 1992;23: 1071. Wolf D., Yamakov V., Phillpot S.R., Mukherjee A., Gleiter H. Acta Mater 2005;53: S.1. Wang N., Wang Z.R., Aust K.T., Erb U. Mater Sci Eng A 1997;237: 150. Yin W.M., Whang S.H. Scripta Mater 2001;44: 569. Yin W.M., Whang S.H. JOM 2005;1: 63. Zhang X., Wang H., Scattergood R.O., Narayan J., Koch C.C., Sergueeva A.V, Mukherjee A.K. Acta Mater 2002;50: 4823. Wang Y.M., Hamza A.V, Ma E. Acta Mater 2006;54: 2715. Blum W., Li Y.J., Durst K. Acta Mater 2009;57: 5207. Gerlich A.P., Yue L., Mendez P.F., Zhang H. Acta Mater 2010;58: 2176. Sanders P.G., Eastman J.A., Weertman J.R. Acta Mater 1997;10: 4019. Cai B., Kong Q.P., Cui P., Lu L., Lu K. Scripta Mater 2001;45: 1407. Cai B., Kong Q.P., Lu L., Lu K. Scripta Mater 1999;41: 755. Lu L., Sui M.L., Lu K. Science 2000;287: 1463. Kaur I., Gust W., Kozma L. Handbook of Grain and Interphase Boundary Diffusion Data, Ziegler Press, Stuttgart, 1989. Ke T.S. Metall Mater Trans A 1999; 30A(9) 2267. Cordea J.N., Spretnak J.W. Trans of the Metall Society of AIME, 1966;236: 1685. Weller M., Diehl J., Schaefer H.E. Phil Mag A 1991;63: 527. Okuda S., Tang F., Tanimoto H., Iwamoto Y. J Alloys Comp 1994;211–212: 494. Mulyukov R.R., Schaefer H.E., Weller M., Salimonenko D.A. Mater Sci Forum 1994;170–172: 159. Bonetti E., Pasquini L., Sampaolesi E. Nanostr Mater 1998;10: 437. Bonetti E., Pasquini L. J Electron Mater 1999;28: 1055. Bonetti E., Campari E.G., Bianco L.D., Pasquini L., Sampaolesi E. Nanostr Mater 1999;11: 709. Zener C. Phys Rev 1941;60: 906. Ke T.S. Phys Rev 1947;71: 533. Jang S., Purohit Y., Irving D.L., Padgett C., Brenner D., Scattergood R.O. Acta Mater 2008;56: 4750. Zhang D.L., Walker H. Mater Sci Eng A 2004;375: 985. Sheng H.W., Zhou F., Hu Z.Q., Lu K. J Mater Res 1998;13: 308. Rajulapati K., Scattergood R.O., Murty K.L., Duscher G., Koch C.C. Scripta Mater 2006;55: 155. Mallick A., Vedanta S., Lu L. Mater Sci Eng A 2009;515: 14. Han B.Q., Lavernia E.J. Mater Sci Eng A 2005;410–411: 417. Mishra R.S., Mukherjee A.K., Mukhopadhyay D.K., Suryanarayana C., Froes F.H. Scripta Mater 1996;34: 3765. Chauhan M., Roy I., Mohamed F.A. Mater Sci Eng A, 410–411, 24–27. Hayes R.W., TellKamp V.L., Lavernia E.J. J Mater Re 2000: 15. Palma R.H., Sepulveda A., Espinoza R., Dianez M.J., Criado J.M., Sayagues M.J. Mater Sci Eng A 2005;391: 60. Hayashi T., Sarosi P.M., Schneibel J.H., Mills M.J. Acta Mater 2008;56: 1407. Kumar K.S., Suresh S., Chisholm M.F., Horton J.A., Wang P. Acta Mater 2003;51: 387.

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39 40 41 42 43 44 45 46 47 48 49 50

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Ashby M.F. Acta Metall 1972;20: 887. Yamakov V., Wolf D., Phillpot S.R., Gleiter H. Acta Mater 2002;50: 61. Keblinski P., Wolf D., Gleiter H. Interface Sci 1998;6: 205. Swygenhoven H.V., Spaczer M., Caro A. Acta Mater 1999;47: 3117. Arzt E., Ashby M.F., Verrall R.A. Acta Metall 1983;31: 1977. Langdon T.G. Philos Mag 1970;22: 689. Spingarn J.R., Nix W.D. Acta Metall 1979;27: 171. Yin W.M., Whang S.H., Mirshams R.A, Xiao C.H. Mater Sci Eng A 2001;301: 18. Yin W.M., Whang S.H., Mirshams R.A. Acta Mater 2005;53: 383. Liu X., Liu H., Dong J., Xie X. Scripta Mater 2000;42(2): 189. Klement U., Erb U., El-Sheik A.M., Aust K.T. Mater Sci Eng A 1995;203A: 177. Howell P.R., Dunlop G.L. In Proc 1st Int Conf Creep and Fracture of Engineering Materials and Structures, Wilshire B. and Owen D.R.J., editors, Pineridge Press Swansea p.127, 1981. 51 Gutierrez-Mora F., Dominguez A., Jimenez-Melendo M., Chaim R., Hefetz, M. Nanostruct Mater 1999;11: 531. 52 Gleiter H. Acta Metall 1979;27: 187. 53 Millett P.C., Desai T., Yamakov V., Wolf D. Acta Mater 2008;56: 3688.

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20 Processing nanostructured metal and metal-matrix coatings by thermal and cold spraying G.E. KIM, Perpetual Technologies Inc., Canada, V.K. CHAMPAGNE and M. TREXLER, US Army Research Laboratory AMSRD-ARL-WM-MC, USA and Y. SOHN, University of Central Florida, USA Abstract: This chapter provides an overview of the development and application of nanostructured coatings, with an emphasis on the latest results on metal-base materials. Thermal spray processing of nanostructured ceramic coatings have been successfully implemented in Navy and industrial applications. Thermal and cold spray processes have been used to deposit dense, oxide-free nanostructured coatings from metal-base feedstock. Different approaches for manufacturing nanostructured metal and metal-matrix composite feedstocks have been presented. Thermal and cold spraying of nanostructured metal-base coatings show promise in better protecting components that are exposed to high temperatures, to corrosion, and to wear. Key words: metal-base coatings, nanostructured, cold spray, thermal spray, HVOF.

20.1 Introduction This chapter provides an overview of the development and application of nanostructured metal-base coatings. The search for improved wear and corrosionresistant coatings has recently focused on developing nanostructured materials such as alumina-titania and tungsten carbide-cobalt. Applications that may benefit from nanostructured metal-base coatings include oxidation and hot corrosionresistant alloys, electronics, bioengineering and anti-fretting applications. To incorporate metal-base nanostructured coatings on a commercial scale, a cost-effective, scaleable powder feedstock processing method is required. Amongst several approaches for the processing of nanostructured powder, noncryogenic milling (NCM) has recently emerged as a promising option. Noncryogenic milling can process larger quantities of metal-base powder in a relatively short duration, at a lower cost than competing processes. The use of nanostructured coatings also requires an appropriate method of application. Starting with the first research in this area in 1997 at the United States Office of Naval Research (ONR),1 thermal spray processes have been successfully used to deposit nanostructured coatings of metals, ceramics, and their composites. A range of these coatings is reviewed in this chapter. 615 © Woodhead Publishing Limited, 2011

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When spraying nanostructured coatings, there are particular requirements in preserving the functionality of the feedstock powder in the final coating. This is especially true when depositing temperature sensitive and readily oxidizing materials such as carbides, nitrides, and metals. For these materials, the goal is to replace most, if not all, of the thermal energy (i.e. flame temperature) with kinetic energy (i.e. particle velocity) so as to retain the nanostructure without contributing to coating oxidation or porosity. The introduction of a relatively new deposition process, referred to as the cold spray process, is particularly suited to meet the low-temperature, high-velocity criteria for the deposition of dense, oxide-free metal-base nanostructured coatings. The cold spray process demonstrates the ability to deposit dense, oxide-free, nanostructured aluminum alloy coating that may improve resistance against localized corrosion and wear. In addition to coatings applications, the same approach may be further developed to spray-form nanostructured metal-base components. Cold spray of nanostructured metal-base materials may also contribute to stronger near net-shape spray nanostructured forms, and better repair of worn/damaged components. This chapter reviews key developments in the manufacture of nanostructured metal-base feedstock, including high-energy ball milling (HEM), the use of cryomilling and the development of new techniques that do not require the use of liquid nitrogen. It goes on to discuss the use of thermal spray techniques for applying a broad range of coatings and the application of the cold spray process to more sensitive materials as a way of achieving coatings with the required functionality.

20.2 Nanostructured metal-base feedstock As with the processing of bulk nanomaterials and nanoparticles, the processing of nanostructured powders can be top-down, bottom-up, and a combination of the two. In the top-down approach, nanostructured powders can be produced by refining coarse-grained materials. A common top-down approach is via severe plastic deformation (SPD) techniques such as ball milling. In the bottom-up approach, nanostructured particles can be assembled from atoms, molecules and/ or nanoparticles. An example of the bottom-up approach to forming nanostructured powder is the spray drying of nanoparticles. High-energy ball milling (HEM) is a commercially available, relatively lowcost approach that has been fairly widely used to produce nanostructured powder.2,3,4 There are numerous types of HEM systems, including shaker mills, Simoloyer® high-energy mills, planetary grinding mills, vertical attritors, and drum mills. In addition to microstructure refinement of metal-base powder, the very high energy transfer of HEM systems can be used to activate chemical reactions (i.e. reactive milling, mechanical alloying), to reduce particle size of hard and brittle materials, and to produce metal matrix composite (MMC) powder with uniformly distributed reinforcing particles within a very fine metal matrix. In

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addition to its relatively low cost, HEM systems are scalable to meet commercial demands. When working with relatively ductile and elastic materials like many metals, milling in cryogenic temperatures (cryomilling) embrittles the powder, making it grindable. In addition, the extremely low temperature suppresses recovery and recrystallization, thereby resulting in finer grain structure. In addition to rapid grain refinement, the liquid nitrogen environment serves to mitigate oxidation, promote fracturing, and form nanodispersoids of nitrides and/or oxy-nitrides within the metal powder. The latter helps strengthen the metal matrix. It is important to note, however, that cryomilling is not economically viable for commercial applications in many cases due to the high cost of liquid nitrogen. In 2003, n-WERKZ Inc was created to focus on developing a new approach to processing nanostructured metal-base powders with the potential for larger scale production and at competitive costs. A study carried out by Ye et al.5 provides an insight into the high cost associated with the need for liquid nitrogen when cryomilling metal powders into nanostructure form. In 2003, n-WERKZ received partial funding from ONR to study the feasibility of processing AA5083 (Al 4.0-4.9 Mg 0.4-1.0 Mn 0.4 Si 0.4 Fe 0.25 Zn 0.15 Ti 0.1 Cu 0.05-0.25 Cr in wt%) and NiCrAlY powders into nanostructure form without the use of liquid nitrogen. After three and a half years of experimentation, a new design and fabrication of customized equipment finally led to the successful processing of nanostructured metal powders with equiaxed particles. The general approach to compensating for the absence of liquid nitrogen was to increase the strain rate exerted onto the particles during milling. Details of the customized equipment and the processing parameters are confidential to n-WERKZ Inc. The company has disclosed that, even without the use of liquid nitrogen in their processing, the milling time is shorter than cryomilling for similar powder characteristics. The spray drying of nanoparticles to form oral drug delivery systems has also been developed successfully.6,7 A similar approach has been successfully used for processing nanostructured ceramic powders, which were then used to deposit thermal sprayed nanostructured ceramic coatings.8,9 Figure 20.1 shows a scanning electron microscope (SEM) view of a spray-dried nanostructured TiO2 particle from Altair (Reno, Nevada) used to deposit a nanostructured coating. Spray drying has also been used to agglomerate nanoparticles of WC with Co as shown in Fig. 20.2.10 Agglomerates of metal nanoparticles have also been spray dried.

20.3 Thermal spray processing Thermal spray is by far the most versatile modern surfacing method in terms of economics, range of materials, and scope of applications. It consists of projecting molten or semi-molten particles of metals, ceramics, or their composites from powder, solution/suspension, or wire feedstock (Fig. 20.3).11 A general rule of

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20.1  Spray-dried nanostructured TiO2 particle from Altair.

20.2  Agglomerated nanostructured WC-12Co powder.

thumb is that any material that has a stable molten phase and can be processed into the appropriate feed specifications can be thermal sprayed. The heat source used to heat and accelerate the feedstock is generated either chemically via oxygenfuel combustion, or electrically via an arc. The hot molten or semi-molten particles impinge and solidify on the surface forming a layered, lamellar structure. Depending on the desired thickness of the deposit, single or multiple passes of the torch at any given region can be carried

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20.3  Agglomerated nanostructured WC-12Co powder.

out. A typical thermal sprayed monolithic coating will consist of inherent nonhomogeneous features, including very fine grains, splat boundaries, pores, oxide inclusions, and partially melted or unmelted particles. Even with this nonhomogeneous structure, a well-applied thermal spray coating will provide reliable protection against many wear, corrosion and thermal conditions. It is important to note, however, that thermal sprayed coatings are not often used as a corrosion barrier without the aid of a sealant. Each thermal spray process has a unique combination of requirements and capabilities. The most important requirements are generally the type of feedstock material (e.g. powder, solution/suspension, or wire) and the type of energy source (e.g. liquid fuel or electricity). In addition, factors such as the melting temperature of the feedstock, the type of substrate, the particle size distribution, the target microstructure of the coating (e.g. porosity, grain size, chemistry, oxide content), and the available budget, can be useful in narrowing the spectrum of thermal spray processes that may be appropriate for a given application. In working with nanostructured metal-base materials to produce a coating, the process requirements and capabilities are quite particular. Typically, the desired coating is dense, with low thermal degradation (e.g. oxidation, decarburization) and limited grain growth. In addition, although there are different forms of attainable nanostructured metal-base feedstock, nanostructured powders seem to have the best combination of characteristics to produce a good final coating. In terms of capabilities, thermal spray processes may be differentiated from one another by focusing on two main parameters: • the typical flame temperature; • particle velocity. Out of all the types of thermal spray processes available, the High-Velocity OxyFuel (HVOF) process has made a significant impact in the application of metal-base coatings. As with other combustion spray processes, the HVOF

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process uses liquid fuel. However, its torch design incorporates a nozzle that dramatically increases gas acceleration. The combination of high gas velocities in the range of 1500 to 2000 m/s and relatively low gas temperatures in the order of 3000°C is ideal for depositing temperature-sensitive, dense coatings. A large proportion of HVOF applications are for temperature-sensitive carbide composites such as WC-Co and Cr3C2-NiCr. The process capabilities that make HVOF ideal for spraying carbides – namely high velocities at reduced temperatures – are also beneficial for spraying nanostructured metal-base coatings. An operating HVOF is presented in Fig. 20.4.12

20.4  Operating high velocity oxyfuel system.

20.4 Thermal spray processing of nanostructured coatings: tungsten carbide-cobalt (WC-Co) coatings Results from research carried out by different institutions on thermal sprayed nanostructured WC-Co coatings have lacked reproducibility and did not show any clear advantage over conventional WC-Co coatings.13–15 This seems to have been due to variations in the parameters for thermal spray processing by each applicator, and to the susceptibility of the carbide nanoparticle within the cobalt matrix to undergoing accelerated and extensive decarburization. There are, however, several studies that show favorable wear, microhardness, fatigue, and corrosion results for nanostructured WC-base coatings when compared directly to conventional coatings of the same composition.16–22 The US Office of Naval Research (ONR) research program has focused on the processing of nanostructured oxide and tungsten carbide-cobalt (WC-Co) coatings mainly for wear and corrosion applications. The goal was to fabricate coatings that exhibit hardness, toughness, abrasion resistance, and reduce ongoing

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maintenance costs by extending the service life of ship machinery and assets. The program has been a huge success, with estimated annual cost savings approaching $100 million for the US Navy. Some of the coatings developed under this program are discussed in the following sections.

20.5 Thermal spray processing of nanostructured coatings: alumina-titania (n-AT) coatings Research by Gell et al.23,24,25 at the University of Connecticut (UCONN) within the ONR program has resulted in the development of a nanostructured aluminatitania (n-AT) coating. This novel coating has shown unique and superior properties compared to a conventional coating of the same composition. These properties included double the bond strength, up to four times the abrasive resistance, and enhanced toughness. The very favorable test results of the n-AT coating have resulted in its application on numerous Navy components. Examples of components with n-AT coating include:26 • • • •

titanium submarine doors bolted to steel frames and immersed in saltwater; ball valves that regulate water flow in submarines; pump components that control submarine diving and resurfacing; 80-ton air conditioner components on ships.

Among the numerous Navy components with the n-AT coating, one application clearly stands out as benefiting from the unique attributes of this coating. This application involves the main propulsion shafts of mine countermeasure (MCM) ships. Since modern mines are triggered not only by collision, but also by sound or magnetic signature of a ship, every effort is made to minimize the use of materials that trigger a magnetic resonance. Hence, the MCM shafts, for example, cannot be fabricated from ferrous material like steel, and are replaced by nonmagnetic nickel aluminum bronze (NAB), which is considerably softer than steel. NAB shafts have suffered from excessive wear in the stern tube and bearing strut areas due to bio-growth between the bearing staves. In addition to the cost of repair for the shafts, replacing these shafts also requires dry-docking the ships. Figure 20.5 shows a dry-docked MCM and a view of the main propulsion shaft. Due to the significant levels of torque, bending, and fatigue experienced by the shafting, conventional brittle ceramic coatings were never feasible for this application. Instead, n-AT coatings were applied by Norfolk Naval Shipyard under a NAVSEA Engineering for Reduced Maintenance project. Currently, the majority of the MCMs in the Navy Fleet operate with n-AT coated shafts. In February 2009, one of the ship sets was removed and evaluated at a Navy shipyard. After seven years in service, there were no signs of spallation resulting from wear and/or corrosion. In fact, over 80% of the coating showed no visible signs of degradation. Considering a repair cost of $75 000 per ship set with the new thermal spray of n-AT approach, compared to the former OEM repair cost of

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20.5  View of the main propulsion shaft region of a mine countermeasures ship.

$275 000 per ship set, this new approach is very attractive. The original estimate of return on investment cost avoidance, based on an improvement of two-fold service life with the nanostructured coating, was over $34 000 000 over the remaining life of these components for the fleet of MCMs. Latest in-service results point to a four-fold life-extension improvement, thus further increasing the return on investment by a considerable amount.

20.6 Thermal spray processing of nanostructured coatings: titanium oxide coatings In April 2000, with the permission of the US Navy, Perpetual Technologies set out to develop thermal spray nanostructured ceramic coatings for industrial application. Within a month, a collaborative agreement with Mogas Industries and FW Gartner was established to develop a nanostructured titanium oxide (n-TiO2) coating customized for use for severe-service ball valves. The objective was to produce a novel coating that would extend the service-life of ball valves exposed to very extreme conditions found in nickel/cobalt high-pressure acid leach (HPAL) process, including high temperatures (~265°C); high pressures (4700 to 5500 kPa); high sulfuric acid concentrations (>95%); and high solids concentrations (>20 wt%). The choice of titanium oxide was based on the knowledge that titanium was one of the materials that show reasonable chemical resistance to this harsh environment.

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The n-TiO2 coating possessed increased hardness and superior wear resistance. Figure 20.6 provides the results of abrasion and slurry erosion tests conducted on conventional and n-TiO2 coatings. The dramatic reduction in volume loss of the abraded n-TiO2 coating compared to that of the conventional coating was not due solely to the increase in microhardness. It was the unique combination of increased hardness along with the increased toughness that led to this drastic enhancement in abrasive wear resistance.27,28,29 Although the increased toughness was not measured quantitatively, numerous qualitative features validate the presence of increased toughness in the nanostructured coatings. Common knowledge in the study of erosion states that ductile materials undergo higher erosion loss at low-impingement angles relative to the substrate surface. The opposite is true for harder materials, in that they undergo higher erosion loss at high-impingement angles. The n-TiO2 coatings samples showed a reduction in volume loss at both high- and low-slurry impingement angles compared to the conventional coating samples. This result is unique and attributable to the nanostructured coating possessing increased hardness and toughness characteristics.

20.6  Abrasion (top) and slurry erosion (bottom) wear test results on TiO2 coatings.

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The second feature that revealed the superior toughness of n-TiO2 coatings is shown in Fig. 20.7. This figure provides views of the indented (with 500g load) regions of each coating cross-section. It is clearly apparent that the n-TiO2 coating had lower degrees of crack density, width, and length, as compared to the conventional coating.

20.7  Conventional (top) and nanostructured (bottom) TiO2 coating cross-sections following 500 g Vickers indent.

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In addition to the increased toughness, i.e. resistance to crack propagation, the depth of indentation at the same load for both coatings reveals a harder nanostructured coating. Closer examination of the region around the cracks in the nanostructured coating revealed an interesting connection between the presence of nano-porous, unmelted or partially melted particles and crack propagation. These fine-pored agglomerates seemed to deflect the crack and/or blunt the crack tip, thus hindering its propagation. The same effect was not observed on dense unmelted particles found in the commercial coating. The third feature was demonstrated by the scars left on the surface of the coatings following abrasion tests, low-impingement slurry erosion tests, and high-impingement slurry erosion tests. It was evident from SEM views of both types of coating surfaces (Fig. 20.8) that, in all three tests, the scars left on the n-TiO2 coating were smoother

20.8  Scars on conventional TiO2 coating following abrasion (a), low-impingement angle erosion (b), high-impingement angle erosion (c) and nanostructured TiO2 coating following abrasion (d), lowimpingement angle erosion (e), high-impingement angle erosion (f).

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and possessed physical characteristics of ductile wear, i.e. microploughing, microcutting, plastic deformation, directional scarring (at low-impingement angles). On the other hand, the surfaces of the conventional samples were rougher and possessed the physical characteristics of brittle wear, i.e. microcracking, spallation (especially along the splat boundaries), very little directional scarring at lowimpingement angle slurry erosion. Based on these very promising laboratory results, the n-TiO2 coating was first applied onto field components in late 2001. Although hundreds of ball valve components were coated with n-TiO2 coating, it was only in 2003 that a direct comparison between n-TiO2 and the previously incorporated coating of chromium oxide blend was carried out at Lihir mines in Papua New Guinea. Figure 20.9

20.9  Ten-inch titanium balls with chromia-blend (top) and nanostructured (bottom) TiO2 coatings after ten months of service.

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provides photographs of the ball surface following 10 months of parallel service between two identical ten-inch valves, each with a different type of coating. It was clearly evident that the n-TiO2 coating was in a far superior state when compared to the non-nanostructured Cr2O3-blend coating. The surface of Cr2O3-blend coated ball had large regions without coating, which led to slurry leakage. In contrast, the n-TiO2 coated ball had a few isolated regions without coating and was returned into service without rework. In 2007, a mine in Western Australia applied and tested the n-TiO2 coating on lab scale impeller blades against slurry erosion. The results indicated a more than two-fold increase in coating life with the n-TiO2 coating when compared to the coating that was being previously applied. On the basis of this result, over 46 field impeller blades have been coated with the nanostructured coating. There are currently ten or more installations around the world with n-TiO2 coated ball valves.

20.7 Thermal spray processing of nanostructured coatings: MCrAlY and NiCrAlY coatings In 2001, researchers at Perpetual Technologies Inc and National Institute of Standards and Technology (NIST) approached ONR with an idea to develop and study nanostructured MCrAlY bond coats for high temperature applications. The general approach was to process nanostructured MCrAlY powder using cryomilling technique, to thermal spray the powder to form nanostructured coating samples, and to evaluate the samples and compare test results to those of conventional MCrAlY coating samples. The tests were carried out with samples as single-layer MCrAlY only and as a thermal barrier coating (TBC) duo layer of MCrAlY bond coat and yttria partially stabilized zirconia (YPSZ) top coat.

20.7.1 Manufacturing MCrAlY and NiCrAlY coatings by cyromilling In 2001, Perpetual Technologies Inc, NIST, and UCD started a three-year program to cryomill conventional MCrAlY powder to form nanostructured powder and to deposit this transformed feedstock powder into coating form using conventional thermal spray processes. NI-343 powder from Praxair (Ni-22Cr10Al-1Y in wt%) was the first alloy studied in detail within this program.30,31,32 Cryomilling took place for eight hours in a Model 1-S attritor mill where the stainless steel milling media and NiCrAlY powders were submersed in liquid nitrogen.33 The powders were characterized using X-ray diffraction (XRD), transmission electron microscopy (TEM), chemical analysis, and thermal analysis. Conventional and nanostructured NiCrAlY powders were sprayed using thermal spray techniques typically used by gas turbine engine original equipment manufacturers (OEMs). The two thermal spray processes used to deposit NiCrAlY coatings in this program were HVOF and LPPS. The coatings underwent

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microhardness, nanoindentation, XRD, SEM, and TEM evaluations. Static oxidation and thermal cycling experiments were conducted on NiCrAlY-only and NiCrAlY with YPSZ top coat samples, respectively. The results for samples with nanostructured NiCrAlY coating were compared directly to those with conventional NiCrAlY coating. Figure 20.10 provides an SEM view of the as-received, conventional and the nanostructured NiCrAlY powders. The cryomilled powder had a larger average

20.10  As-received conventional and cryomilled NiCrAlY powder.

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20.11  X-ray diffraction spectra for as-received and cryomilled NiCrAlY powders.

particle of about 40 µm as compared to about 21 µm for the conventional powder. The high degree of grain refinement in the cryomilled powder was qualitatively indicated by peak broadening observed in the corresponding XRD spectrum as compared to that of the as-received conventional powder (Fig. 20.11). Klug et al.34 and Suryanarayana35 provide details of how peak broadening is associated with the small grain size structure of the powder and microstrain introduced into the material during processing. Although the XRD spectra provided a good indication that cryomilling of NiCrAlY powder produced fine microstructure, e.g. grain size, TEM analysis more accurately revealed the actual grain size, as well as other micro- or nano-scopic features, e.g. dislocations, stacking faults, etc. (Fig. 20.12, top). The TEM results indicated an average grain size of 26 ± 8 nm within the cryomilled powder. An important feature in milled powder was the in-situ formation of dispersoids.36–40 In addition to the presence of phases from the NiCrAlY, the diffraction pattern from the TEM analysis revealed the presence of Al2O3 and AlN (Fig. 20.12, bottom). These two phases represented dispersoids that were formed when aluminum present in the alloy reacted with oxygen in the system, e.g. gaseous oxygen, or within the passivated layer of the particles, and nitrogen in liquid form. The iron phase also present in the cryomilled powder was contamination from the stainless steel milling media and chamber wall. The DJ 2700 (Sulzer Metco) HVOF system was used to deposit coating samples from cryomilled powder (Fig. 20.13). The coating had a fairly low porosity level at less than 1% and an average microhardness of approximately 440 HV 0.3. The backscattered electron image of the nanostructured NiCrAlY coating

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20.12  Transmission electron microscopy micrograph of cryomilled NiCrAlY powder (top) and diffraction pattern and indexing results (bottom).

20.13  Cross-section of HVOF-applied nanostructured NiCrAlY coating.

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20.14  Backscattered electron image of HVOF applied nanostructured NiCrAlY coating.

showed a structure composed mainly of two phases γ (Ni solid solution) and γ' (Ni3Al), as in Fig. 20.14. The bright and dark regions correspond to the γ and γ' phases, respectively. Figure 20.15 provides the TEM analyses of the nanostructured coating. The two notable features were that there were no longer any signs of AlN phase and that the grain size was not uniform. The absence of AlN in the nanostructured coating was likely a result of its decomposition and oxidation during HVOF processing. The grain size distribution in the nanostructured NiCrAlY coating was ‘multimodal’ in structure, nano-grained regions (approximately 75 nm), ultrafine-grained regions (100–550 nm), and submicron-grained regions (<1 µm). The static oxidation test at 1000°C yielded notable differences in the type of thermally grown oxide (TGO) that formed on the surfaces of the conventional and nanostructured NiCrAlY-only coating samples. It became apparent that the nanostructured coating quickly formed a continuous, stable, and preferred α-Al2O3 TGO layer, which mitigated further oxidation of the coating surface (Fig. 20.16). On the other hand, the conventional coating quickly formed a TGO consisting of non-continuous α-Al2O3 layer with protrusions of mixed oxides (Fig. 20.17). It is well accepted within the TBC community that delaying the formation of mixed oxides, which is associated with higher growth rate, is an important factor in extending the life of TBCs.41,42 After 95 hrs, the formation of mixed oxides was observed on the nanostructured coating samples (Fig. 20.18). A re-oxidation test was carried out on nanostructured coating samples that had already been exposed to the 1000°C static oxidation test. As a result of having been exposed to high temperatures, these samples’ grain size had increased to the

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20.15  Transmission electron microscopy micrograph of nanostructured NiCrAlY coating (top) and diffraction pattern and indexing results (bottom).

range of as-sprayed conventional coatings. The objective of this test was to determine whether or not the preference for the nanostructured coating to form a α-Al2O3 TGO layer was linked to the bond coat’s fine grain structure. Interestingly, the static re-oxidation test results showed similar affinity for the formation of α-Al2O3 TGO layer (Fig. 20.19). The isolated regions where mixed oxide protrusions were visible corresponded to areas where the aluminum content was depleted prior to carrying out the re-oxidation test. These results indicated that the origins for preferential α-Al2O3 TGO layer formation were not, at least solely, a result of fine grain structure. Current hypothesis is that the preference in nanostructured NiCrAlY coatings towards the formation of an α-Al2O3 TGO layer is linked to the presence of the previously mentioned alumina dispersoids

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20.16  TGO formation on nanostructured NiCrAlY coating – top (top) and cross-sectional (bottom) views.

that are formed during cryomilling and retained in the coating after spraying (Fig. 20.20). Wu et al.43 have observed the same response when an Al2O3 second phase was incorporated into NiCrAlY coatings obtained by plasma-laser technique. It seems that the Al2O3 dispersoids act as nucleation sites and/or hinder the diffusion of Ni and Cr to the coating surface when exposed to high temperatures.

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20.17  TGO formation on conventional NiCrAlY coating – top (top) and cross-sectional (bottom) views.

To compare thermal cycling performances between TBC samples with nanostructured and conventional bond coats, 25 mm diameter by 3 mm thick Hastelloy X substrates were prepared. Each sample consisted of an HVOF or LPPS sprayed (100–150 µm thick) NiCrAlY bond coat with an APS sprayed (250–300 µm thick) YPSZ top coat. The TBC samples were then heat treated in

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20.18  TGO formation on nanostructured NiCrAlY after 95 hrs at 1000°C.

20.19  Top view of TGO formation on re-oxidized nanostructured NiCrAlY coating.

vacuum at 1080°C for four hours prior to undergoing the thermal cycling test. The TBC samples with nanostructured bond coat outperformed those with conventional bond coat by more than 50%, with TBCs with LPPS nanostructured bond coat leading the way (Fig. 20.21). The majority of the TBC samples showed the

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20.20  Dispersoids in nanostructured NiCrAlY coating.

20.21  Thermal cycling results for TBC samples with conventional and nanostructured NiCrAlY bond coats.

presence of mainly α-Al2O3 TGO with a small amount of discrete yttrium aluminum oxide particles. There was an obvious difference in TGO growth rate for TBC samples with LPPS applied conventional and nanostructured NiCrAlY, with the latter showing a notably slower rate and longer cycles to failure (Fig. 20.22).44 There was no obvious link between TGO growth rate and number of cycles to failure for TBC samples with HVOF bond coats; hence, there may be other mechanism(s) affecting these TBC samples’ performance.

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20.22  TGO of failed TBC samples with conventional (top) and nanostructured (bottom) bond coats following thermal cycle testing.

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The presence of the fine- or nano-dispersoids may enhance the life of TBCs by one or more of the following mechanisms: • enhanced alumina formation and lower TGO growth rate; • a better coefficient of thermal expansion (CTE) match between top and bond coats; • increased bond coat creep resistance; • slower diffusion of Ni and Cr to the coating surface; and • reduced interdiffusion between bond coat and substrate. Anyone who has studied TBCs knows how complex the system is with regards to failure mechanisms and life prediction. The experience gained with nanostructured NiCrAlY bond coats shows promising results; however, there needs to be much greater detailed evaluation to understand and further optimize the mechanisms that exist in this new approach.

20.7.2 Manufacturing MCrAlY and NiCrAlY coatings by non-cryogenic milling (n-WERKZ powder) Since its inception in 2003, n-WERKZ Inc has developed a non-cryogenic milling (NCM) means of processing nanostructured metal powders, including NiCrAlY. Based on the availability of this new commercially viable powder, a new effort to deposit and evaluate the n-WERKZ NiCrAlY powders for TBC applications was initiated in 2007. The goal was to determine whether or not an n-WERKZ nanostructured NiCrAlY powders would be able to form coatings with enhanced oxidation and thermal cycling characteristics, similar to those of cryomilled powder. NiCrAlY with and without top coats were deposited using HVOF. All the top coats were applied via APS. Characterization of n-WERKZ powders and coatings as well as thermal tests on coating samples was carried out. The n-WERKZ NiCrAlY powder had an average particle size of 34 µm as compared to the as-received average particle size of 21 µm. Figure 20.23 provides a magnified view of the n-WERKZ powders. As expected, there is a strong resemblance in powder morphology when compared to the same powder that has undergone the cryomilling process. The XRD analyses (Fig. 20.24) results show refinement in the grain structure of the n-WERKZ powder. The Jet Kote HVOF system from Deloro Stellite was used to deposit coating samples from n-WERKZ and conventional powders (Fig. 20.25). The spray parameters corresponded to coating quality qualified by a major gas turbine engine original equipment manufacturer (OEM) for this material; no optimization of the spray parameters was made for the n-WERKZ powder. The coatings had fairly low porosity levels at less than 1% and an average microhardness of approximately of 515 and 522 HV 0.3 for the conventional and n-WERKZ coatings, respectively. The static oxidation test at 1000°C yielded comparative results, similar to the conventional and cryomilled NiCrAlY samples, between the TGO formed on the

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20.23  Non-cryogenically milled (NCM) NiCrAlY powder.

20.24  X-ray diffraction spectra for the as-received and NCM NiCrAlY powders.

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20.25  Cross-sectional view of HVOF-applied conventional (top) and NCM nanostructured (bottom) NiCrAlY coatings.

surfaces of the conventional and n-WERKZ NiCrAlY-only coating samples. A continuous, stable, and preferred α-Al2O3 TGO layer formed on the surface of the n-WERKZ coating after 95 hrs of exposure time (Fig. 20.26, bottom); whereas the conventional coating formed a TGO consisting of a non-continuous α-Al2O3

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layer with protrusions of mixed oxides (Fig. 20.26, top). It is noteworthy that even after 95 hrs, the n-WERKZ coating did not form mixed oxides, as compared to the cryomilled coating, which eventually formed a mixed oxide TGO after exposure to the same conditions and time.

20.26  Cross-sectional view of HVOF-applied conventional (top) and NCM nanostructured NiCrAlY coating after 95 hrs heat treatment (bottom).

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TBC samples with n-WERKZ and conventional bond coats were processed onto 25 mm diameter by 3 mm thick Hastelloy X substrates. Each sample consisted of a Jet Kote sprayed (100–150 µm thick) NiCrAlY bond coat with an APS sprayed (250–300 µm thick) YPSZ top coat. The TBC samples were tested as-sprayed, without post-spray heat treatment. The average of three TBC samples with n-WERKZ bond coat outperformed the best performing conventional bond coat by approximately 50% (Fig. 20.27). Failure analyses of the thermal cycle samples were carried out at the US Naval Academy. As often observed in thermal sprayed TBCs, failure occurred mostly within the YPSZ top coat layer adjacent to the TGO layer (Fig. 20.28). The notable differences between failed TBC samples with n-WERKZ bond coat and those with conventional bond coat consisted of the following: • n-WERKZ NiCrAlY had thicker and more continuous α- Al2O3 TGO layer, and very few and isolated regions consisting of mixed oxide; • conventional NiCrAlY had duo layers consisting of Al2O3 and mixed oxide TGO layers with an overall thickness that seemed lower (note that these samples failed at least 30% sooner) upon failure. At the present time, it is believed that the presence of the fine- or nano-dispersoids, i.e. Al2O3, formed during the n-WERKZ process, was the source of the enhanced thermal properties of the n-WERKZ nanostructured NiCrAlY coating. The presence of the dispersoids may positively influence the thermal performance of the nanostructured coatings by accelerating the formation of a protective α-Al2O3 TGO that will mitigate the further oxidation of the NiCrAlY coating. This in turn may decrease the coefficient of thermal expansion (CTE) of the bond coat to

20.27  Thermal cycling test results for TBCs with conventional and NCM nanostructured NiCrAlY bond coats.

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20.28  TGO of failed TBC samples with conventional (top) and NCM nanostructured (bottom) bond coats following thermal cycle testing.

reduce its mismatch with the YPSZ top coat in a TBC system, increasing bond coat creep resistance, and slowing down interdiffusion between bond coat and substrate. As noted in the previous section, more detailed study of these new coatings is required to better understand the mechanisms associated with nanostructured MCrAlYs. Professor Brochu and his group at McGill University have carried out parallel efforts in the processing and testing of nanostructured NiCoCrAlY for petrochemical applications.45,46 The results from their study support the findings presented in this chapter. Table 20.1 shows the type of TGO growth observed on nanostructured and conventional-microstructured CoNiCrAlY powders. As observed in NiCrAlY coatings, the cryomilled nanostructured CoNiCrAlY

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Nanostructured metals and alloys Table 20.1  Oxide scale at different temperature as a function of the starting grain size

Starting grain size 30–40 nm

500°C α-Al2O3 800°C α-Al2O3 1000°C α-Al2O3

3–4 µm Cr2O3 Cr2O3 Al2O3•Cr2O3 Cr2O3 Al2O3•Cr2O3

powder formed the favorable a-alumina TGO, as opposed to chromia and mixed oxide TGO formed on the conventional CoNiCrAlY powder. This data shows similar attributes between the coatings sprayed using non-cryogenically milled powder and their cryomilled counterpart. The advantages of the NCM process are lower cost, shorter processing time, and easier scalability.

20.8 The cold spray process Cold spray is a materials deposition process whereby combinations of metallic and non-metallic particles are consolidated to form a coating or freestanding structure by means of ballistic impingement upon a suitable substrate.47,48,49 The particles utilized are in the form of commercially available powders, typically ranging in size from 5 to 100 µm, which are accelerated from 300 to 1500 m/s by injection into a high-velocity stream of gas. The high-velocity gas stream is generated via the expansion of a pressurized, preheated, gas through a converging– diverging de Laval rocket nozzle. The pressurized gas is expanded to supersonic velocity, with an accompanying decrease in pressure and temperature.50,51,52 The particles, initially carried by a separate gas stream, are injected into the nozzle either prior to the throat of the nozzle or downstream of the throat. The particles are subsequently accelerated by the main nozzle gas flow and are impacted onto a substrate after exiting the nozzle (Fig. 20.29). Upon impact, the solid particles deform and create a bond with the substrate.53,54 As the process continues, particles continue to impact the substrate and form bonds with the consolidated material resulting in a uniform deposit with very little porosity and high bond strength. The term ‘cold spray’ has been used to describe this process due to the relatively low temperatures (–250 to –100°C) of the expanded gas stream that exits the nozzle. This is illustrated in Fig 20.30, which uses a cold spray model developed by Helfritch et al.55 to calculate the temperature of the gas as it expands from the nozzle as a function of inlet temperature and pressure. The temperature of the gas stream is always below the melting point of the particulate material during cold spray, and the resultant consolidated material is

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20.29  Schematic of cold spray system.

20.30  Gas exit temperature calculated with nitrogen and helium gas as a function of temperature of 400°C and with a main gas pressure of 400 psi using a cold spray nozzle.

formed in the solid state. Since the adhesion of the powder to the substrate, as well as the cohesion of the deposited material, is accomplished in the solid state at low temperatures, the characteristics of the cold spray material are quite unique in many regards. The low temperatures associated with the cold spray process are desirable when nanostructured powders are used as feedstock because the risk of grain growth and phase transformation is minimal or nonexistent. In addition, particle oxidation is avoided, as well as deleterious tensile stresses that occur

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during thermal contraction. Therefore, cold spray has the potential to produce nanostructured coatings with a bond strength superior to that of the substrate. With further advancement of techniques to manufacture “cold spray” powders, greater cohesive strength should be possible when compared to conventional thermal spray and powder metallurgy processes. Cold spray is often compared to traditional thermal spray processes. Although there are certain similarities, it is important to recognize the fundamental differences between the two approaches in order to determine which technique is best suited for the development of nanostructured materials. Cold spray technology is the logical choice for applications where the high temperatures associated with conventional thermal spray technology can result in undesirable metallurgical transformations, including grain growth, as well as oxidation that can have detrimental effects on bond strength and porosity. Cold spray incorporates very high particle velocities (300–1500 m/s) to achieve consolidation, and gas temperatures can be adjusted to avoid undesirable transformations in the feedstock, the resultant deposit, and the substrate, yielding a deposit with low porosity, high bond strength and increased cohesive strength. One of the most deleterious effects of depositing materials at high temperatures is the tensile residual stress that develops, especially at the substrate-coating interface, which is the result of the thermal contraction of the molten particles upon solidification. This can become a particular concern in an application where a layer of nanostructured material is to be deposited onto the surface of another material. These stresses often cause delamination, and limit the maximum deposit thickness that can be achieved. This problem is compounded when the substrate material is different from the coating material in terms of hardness and density and there is a significant variation in the coefficient of thermal expansion. In contrast, there is very little thermally induced dimensional change of the cold spray material since consolidation of the particles takes place in the solid state. Also, the significantly high impact velocities of the solid particulates are very effective at peening the underlying material and producing deposits that are typically in a state of compressive stress.56 In addition, interfacial instability due to differing viscosities, along with the resulting interfacial roll-ups and vortices, promote interfacial bonding by increasing the interfacial area, giving rise to material mixing at the interface and providing mechanical interlocking between the two materials.57 Adhesion of thermal spray coatings relies primarily upon the surface finish referred to as the anchor tooth profile of the substrate. The molten particles or ‘splats’, which are propelled onto the substrate penetrate and subsequently solidify, locking themselves mechanically within the valleys of the surface profile. Except for some of the HVOF coatings that contain carbides or extremely hard particles, there is a significant difference between the bonding mechanism of thermal spray and cold spray. In comparison with conventional thermal spray techniques, the materials produced by cold spray are typically less porous, with higher hardness and

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conductivity and lower oxide concentration. The Young’s moduli of cold-sprayed deposits have been reported to be greater than 80% of bulk values.58 The Army Research Lab (ARL) has developed a cold spray process for depositing 6061 aluminum that has achieved an ultimate tensile strength, yield point and Young’s modulus greater than what has been reported in literature for wrought 6061-T6, which is solutionized, quenched and tempered, while the properties of the cold spray coating were taken in the as-sprayed condition. These characteristics are achieved because cold particles are less susceptible to oxidation, and a high velocity impact creates dense, well-consolidated material. The superior qualities of cold-sprayed materials are required by certain applications. For example, the high heat transfer coefficient and electrical conductivity of cold spray materials favor their use in electronic applications.59 Good corrosion protection is also achieved by dense, impermeable, cold-sprayed coatings.

20.9 Characteristics of cold spray material Nanostructured materials as defined within the context of this section are those materials whose grain size has dimensions in the 1 to 100 nm range.60 Osmotic consolidation, pressure filtration, and tape casting have been used to produce consolidated nanostructured materials with limited thickness. Cold spray has been investigated to produce nanostructured coatings, as well as nanostructured bulk materials. The typical particle size of stock powders used for cold spray ranges between 5 and 100 µm. Particles that are <5 µm do not have enough momentum to leave the gas stream and impact on the substrate and are simply swept away as the gas flows over the substrate. Hence, nanoparticles cannot be deposited using cold spray. Instead agglomerated nanoparticles or nanostructured powder within the feasible size range is used. The deposition thickness produced by a single pass of the cold spray nozzle can vary from 0.01 to 1.0 mm, depending on the powder feed rate, nozzle traverse speed, and deposition efficiency. Multiple coating layers can result in deposits several centimeters thick and some materials appear to have no limitation in the thickness that can be achieved. The width of a single pass of a conventional nozzle is approximately 5 mm, and large surfaces can be coated through multiple, slightly overlapping, parallel sweeps. Nitrogen can be used as the accelerating gas to produce a fully dense copper deposit, with several passes resulting in a coating that was approximately 2 mm thick. The individual copper particles consolidate into a dense, uniform deposit, which adheres tightly to the aluminum substrate. The copper is actually mechanically mixed with the aluminum at the interface. The microstructure resulting from the interaction of impacting particles and the substrate is analogous to materials that have been explosively bonded. Ceramics can also be considered as a suitable substrate for cold spray, and nitrogen can be used as the accelerating gas to deposit copper powder onto a silicon carbide substrate. Single traces of low oxide copper are deposited forming

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a uniform and continuous coating. Ceramics such as alumina, silicon carbide, and aluminum nitride have been successfully coated onto by the cold spray process, as well as some composite and polymeric materials.

20.10  Cold-sprayed processing of WC-Co Cold spray has been used successfully to deposit cermets such as WC-Co61,62 and also nanostructured WC-Co.63 The combination of WC and metallic cobalt as a binder is well suited for sintering and results in a system that has desirable properties. Nanostructured feedstock of WC-Co has been produced by dispersing nano-sized WC particles in a suitable solvent with a cobalt binder precursor and spray dried under a controlled atmosphere to form spheroid particles. WC has high solubility in cobalt at elevated temperatures, and, in combination with the ability of liquid cobalt to wet the WC, superior densification can be achieved during sintering. The binder precursor forms small crystals, coating the nanoparticles, and fills in the gaps interconnecting them, making the resultant agglomerate conducive to the cold spray process, which requires a certain degree of plasticity for adequate consolidation. The cobalt binder serves to contain the WC, and the resultant agglomerate, which is approximately 5–50 µm in diameter (Fig. 20.31), has a good combination of high strength, toughness and hardness. The agglomerates have adequate ductility and deform during the cold spray process upon impact, allowing the buildup of material.

20.31  Agglomerated WC-Co powder.

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Figure 20.32 represents an example of the WC-12Co feedstock powder used for cold spray, which consisted of agglomerated submicron particles of WC encapsulated with cobalt. Figure 20.33 shows a cold spray deposit of WC-12Co that was achieved using helium as the accelerating gas. Microstructural characterization of the WC-Co feedstock powder and the resultant cold spray

20.32  Submicron particle of WC held together with a cobalt binder.

20.33  Cross-sectional view of cold spray WC-Co coating using helium as accelerating gas.

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deposits by SEM and X-ray diffraction revealed that there did not appear to be any evidence of phase transformation or decarburization of the WC during cold spray deposition and the original morphology of the submicron particles was unchanged. These are advantages of the cold spray process over thermal spray. Hardness values of 1315 Vickers were also achieved but the resultant coating contained small microcracks. An attempt to mitigate the occurrence of microcracks was undertaken by incorporating nitrogen as the accelerating gas. Figure 20.34 shows a micrograph of a cross-section of a cold spray deposit using nitrogen. The hardness values were approximately the same, 1300 Vickers, but the overall bond strength of these coatings was lower than those achieved using helium. This was substantiated by the fact that a more aggressive grit blast had to be performed during the surface preparation stage prior to spraying when using nitrogen and the through-thickness hardness values were lower. A 24 grit size alumina had to be used when attempting to cold spray onto hardened (HRC35) 4340 steel, as compared to 60 grit alumina, which was used during the original helium cold spray trials. The differences in through-thickness hardness was attributed to the fact that nitrogen would result in lower impact velocities, and therefore the particle-toparticle bond would not be as great as that which was achieved using helium, since helium would have much higher impact velocities. In addition, it was determined that there was a greater concentration of WC on the surfaces of those samples produced using nitrogen as the accelerating gas than on those produced using helium because the higher impact velocities associated with helium would also cause an

20.34  Interface of cold spray WC-Co coating deposited onto aluminum using nitrogen as accelerating gas.

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erosion problem during the cold spray process. This problem could be alleviated by producing feedstock powder that was comprised of WC particles fully encapsulated by a cobalt binder. The feedstock used in this study contained WC particles that were not always adequately coated with cobalt and the exposed areas would erode away the surface of the previous deposit during the cold spray process. In summary, there has to be more work by powder producers concentrating on the production of ‘cold spray’ powders to alleviate such problems as erosion during the cold spray process.

20.11 Cold-sprayed processing of non-cryogenically milled n-WERKZ AA5083 The cold spray process was used to consolidate non-cryogenically milled (NCM) AA5083 powder produced by n-WERKZ at the US Army Research Laboratory. The cold spray process operates at temperatures that can exceed 800°C with corresponding pressures greater than 650 psi. Therefore predictive models were used to develop the optimized process parameters that would maintain the nanostructured microstructure. It must be understood that although the cold spray gas temperature may be set well below any critical transformation temperature for AA5083, the kinetic energy of accelerating particles are transferred into thermal energy upon impact. Continuous particle impact events can increase the temperature of the coating/deposit as well as the substrate locally, especially when attempting to build up thick deposits. In addition, aluminum and its alloys also present another challenge with regard to nozzle clogging, which is related primarily to operating temperature. Various nozzle materials have been investigated over the years by ARL and others to mitigate clogging of low temperature materials. A thermally stable amorphous thermoplastic polymer was chosen for this effort. The predictive models developed by ARL can be used to determine the impact velocity of accelerating particles as well as the ‘critical’ impact velocity. The critical impact velocity can be defined as that which results in adequate consolidation of the particles. The exact amount of plastic deformation that each particle must undergo to result in an adequate consolidated deposit is still very much under debate, but as Fig. 20.35 indicates, the critical impact velocity is approximately 650 m/s. Incorporating the cold spray process parameters used in this study with the accelerating gas set at a temperature of 400°C and a main gas pressure of 400 psi, a 20 µm particle would achieve an impact velocity of 1438 m/s with helium and 697 m/s in a nitrogen gas stream, (Fig. 20.35). The average particle size for the AA5083 was 56.7 µm, as the data presented in the particle analysis shows (Fig. 20.36). However, this analysis also shows a larger percentage of particles that are >100 µm. The corresponding impact velocity for the average particle size was approximately 850 m/s, as calculated for the accelerating gas set at a temperature of 400°C and a main gas pressure of 400 psi. However, the impact velocity of some of the larger agglomerates (>120 µm) cannot be achieved using

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20.35  Critical impact velocity calculated with the helium accelerating gas set at a temperature of 400°C and with a main gas pressure of 400 psi.

20.36  Particle analysis of the n-WERKZ AA5083 showing the average particle size as approximately 56.7 µm. Note the larger percentage of particles >100 µm.

the process parameters described. This would explain the random voids observed within the structure of the cold spray deposit. The best operating process parameters were selected based upon several primary factors, including maximum temperature, deposition efficiency, density and nozzle clogging. Helium was used as the accelerating gas at a temperature of approximately 400°C with a pressure of 400 psi. Figure 20.37 shows an as-polished cross-section

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of the resultant deposit. Note the ‘splat’ or particle boundaries and the complete consolidation that was achieved using these process parameters. There were random voids observed within the structure that were later attributed to large agglomerates found in the original feedstock powder (Fig. 20.38). These agglomerates were in excess of 100 µm, and as such would not completely deform during impact, leaving

20.37  Optical microscope view of cold spray deposit of n-WERKZ nanostructured AA5083.

20.38  Original n-WERKZ nanostructured AA5083 feedstock with large agglomerates.

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behind these occasional defects. An attempt was made to sieve the feedstock powder using a 325-mesh sieve, which would remove any particle having a diameter greater than approximately 44 µm. The particle size analysis of the sieved powder shows new mean particle size of 33.9 µm, with no particles larger than 65 µm (Fig. 20.39). Additional spray trials were conducted and results indicated the elimination of these voids in the structure of the AA5083 cold spray deposit (Fig. 20.40).

20.39  Particle analysis of the sieved n-WERKZ AA5083 showing the average particle size as approximately 33.9 mm.

20.40  Optical microscope view of cold spray deposit of sieved n-WERKZ nanostructured AA5083.

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A typical bright-field TEM micrograph from cold-sprayed AA5083 is presented in Fig 20.41. Very little porosity and oxide inclusion were observed. Deformation of face-centered cubic (fcc) Al from high particle velocity deposition resulted in elongated grains with aspect ratio ranging from 2~3 to 1. Mean grain size was approximated at 100 ± 35 nm. Between nano-grains, excellent chemical bonding without deleterious voids or inclusions was observed as demonstrated by the high-resolution TEM micrograph in Fig. 20.42. However, inclusions and voids

20.41  Bright-field TEM micrograph of cold-sprayed AA5083.

20.42  High-resolution TEM micrograph of grain boundary in coldsprayed AA5083.

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were occasionally observed at splat (e.g. prior particle) boundaries as presented in Fig. 20.43. At the interface between AA5083 cold-sprayed coating and AA6061 substrate, excellent bonding was observed as presented in Fig. 20.44. Certainly, inclusions of oxides were observed but not as a continuous layer since they were

20.43   Bright-field TEM micrograph showing decohesion (white region) and inclusions (dark spots) observed at the splat boundary of cold-sprayed AA5083.

20.44  Bright-field TEM micrograph of coating-substrate interface.

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20.45  X-ray diffraction patterns from cold-sprayed AA5083 and uncoated bottom surface of AA6061 substrate.

broken apart due to the deformation of impinging particle associated with high velocity impact. Thus, a majority of the coating/substrate interface consisted of fcc-Al bonding between AA5083 and AA6061. Figure 20.45 presents X-ray diffraction patterns from cold-sprayed AA5083 and annealed AA6061 (e.g. uncoated bottom surface). While both patterns correspond to fcc-Al (i.e. also confirmed by electron diffraction from TEM), a noticeable compressive strain, estimated at 0.31% was observed for the cold-sprayed AA5083 coating.

20.12 Future trends The low temperature and high kinetic energy associated with the cold spray process allow for the retention of fine/nano-grain structure, absence of phase change, capability for thick deposits, and promotion of compressive residual coating stress. These capabilities make the cold spray process an ideal approach to depositing nanostructured metal-base coatings. In addition to the nanostructured metal-base coatings presented in this chapter, potential nanostructured coating applications may include: MCrAlY coatings for high temperatures; CuCr for oxidation protection; Al and Zn sacrificial cathodic protection coatings; Al- or Cu-base metals or their MMCs for thermal management; Al, Cu, and steel for electronics; Ti and Ta for bioengineering and corrosion protection; and CuNiIn for anti-fretting.

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In addition to applications revolving around nanostructured coatings, cold spray of nanostructured metal-base materials may also contribute to stronger near-net-shape spray nanostructured forms, and better repair of worn/damaged components.

20.13 Sources of further information and advice Additional sources of information pertaining to thermal-sprayed nanostructured metal-base coatings can be found in technical journals relating to thermal spray and/or materials science.

20.14 Acknowledgements We wish to thank Dr Lawrence T. Kabacoff (ONR), Ken Scandell (NAVSEA), and Linda K. Jensen (Juridica, Inc.) for their constructive contributions towards the preparation and the review of this manuscript. Special thanks should be given to Jimmy Walker and FW Gartner Thermal Spraying Co. for their contribution of industrial thermal spray processing photographs. As well, we would like to thank Professors Angela L. Moran (US Naval Academy) and Julie Schoenung (UC, Davis), as well as Dr Virgil Provenzano (NIST) for their technical contributions to portions of this chapter.

20.15 References   1 Kabacoff L.T., Nanoceramic Coatings Exhibit Much Higher Toughness and Wear Resistance than Conventional Coatings. The AMPTIAC Newsletter, Spring 2002, Volume 6, Number 1.   2 Shaw L., Luo H., Villegas J., Miracle D. Thermal Stability of Nanostructured Al93Fe3Cr2Ti2 Alloys Prepared via Mechanical Alloying. Acta Materialia 51 (2003), p. 2647.   3 Eigen N., Klassen T., Aust E., Bormann R., Gartner F. Production of Nanocrystalline Cermet Thermal Spray Powders for Wear Resistant Coatings by High-Energy Milling. Materials Science and Engineering A356 (2003) p. 114.   4 Chen Y., Li C.P., Chen H., Chen Y. One-Dimensional Nanomaterials Synthesized using High-Energy Ball Milling and Annealing Process. Science and Technology of Advanced Materials 7 (2006), p. 839.   5 Ye J., Schoenung J.M. Technical Cost Modeling for the Mechanical Milling at Cryogenic Temperature (Cryomilling). Advanced Engineering materials 2004, 6, No. 8, p. 656.   6 Beck R.C.R., Lionzo M.I.Z., Costa T.M.H., Benvenutti E.V., Re M.I., Gallas M.R., Pohlmann A.R., Guterres S.S. Surface Morphology of Spray-Dried NanoparticleCoated Microparticles Designed as an Oral Drug Delivery System. Brazilian Journal of Chemical Engineering, 2008, Vol. 25, No. 02, April–June, p. 389.   7 Chaubal M.V., Popescu C. Conversion of Nanosuspensions into Dry Powders by Spray Drying: A Case Study. Pharmaceutical Research 2008, Vol. 25, No. 10, October, p. 2303.

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  8 Jordan E.H., Gell M. Nano Crystalline Ceramic and Ceramic Coatings Made by Conventional and Solution Plasma Spray. In Nanomaterials Technology for Military Vehicle Structural Applications, Meeting Proceedings RTO-MP-AVT-122, Paper 9. Neuilly-sur-Seine, France, 2005, pp. 9–19.   9 Wang D., Tian Z., Shen L., Liu Z., Huang Y. Preparation and characterization of nanostructured Al2O3-13wt.%TiO2 ceramic coatings by plasma spraying. Rare metals 2009, Vol. 28, no. 5, October, p. 465. 10 Marple B.R., Voyer J., Bisson J.F., Moreau C. Processing and Characterization of Nanostructured Cermet Coatings. Proceedings of the International Thermal Spray Conference (ITSC 2001), Singapore, May 28–30, 2001, p. 343. 11 Bernecki T. Surface Science. In Davis J.R., editor. Handbook of Thermal Spray Technology. ASM International, Materials Park, OH, USA, 2004, p. 14. 12 F.W. Gartner Thermal Spraying Co. 13 Qiao Y., Liu Y.R., Fischer T.E. Sliding and Abrasive Wear Resistance of ThermalSprayed WC-Co Coatings. Journal of Thermal Spray Technology, Vol. 10(1), March 2001, p. 118. 14 Guilemany J.M., Dosta S., Miguel J.R. Study of the Properties of WC-Co Nanostructured Coatings Sprayed by High-Velocity Oxyfuel. Journal of Thermal Spray Technology, Vol. 14(3), September 2005, p. 405. 15 He J., Ice M., Dallek S., Lavernia E.J. Synthesis of Nanostructured WC-12 Pct Co Coating Using Mechanical Milling and High-Velocity Oxygen Fuel Thermal Spraying. Metallurgical and Materials Transactions A, Vol. 31A, February 2000, p. 541. 16 Ibrahim A., Berndt C.C. Fatigue and Mechanical Properties of Nanostructured WC-Co Coatings. Proceedings of the International Thermal Spray Conference, May 10–12, 2004, Osaka, Japan, p. 878. 17 Morks M.F., Shoeib M.A., Ibrahim A. Comparative Study of Nanostructured and Conventional WC-Co Coatings. Proceedings of the International Thermal Spray Conference, May 10–12, 2004, Osaka, Japan, p. 857. 18 Zha B., Wang H., Su X., Nano Structured WC-12Co Coatings Sprayed by HVO/AF, Proceedings of the International Thermal Spray Conference, May 10–12, 2004, Osaka, Japan, pp. 881–881. 19 Liu S., Sun D., Fan Z., Yu H.Y., Meng H.M. The influence of HVAF powder feedstock characteristics on the sliding wear behaviour of WC-NiCr coatings. Surface & Coatings Technology 202 (2008), p. 4893. 20 Kim H.J., Lee C.H., Hwang S.Y. Superhard nano WC-12%Co coating by cold spray deposition. Materials Science and Engineering A 391 (2005), p. 243. 21 Smirnov N.I., Prozhega M.V., Smirnov N.N. Study of Tribological Properties of Detonation Nanostructured WC-Co-Based Coatings. Journal of Friction and Wear 2007, Vol. 28, No. 2, p. 200. 22 Zhu Y.C., Yukimura K., Ding C.X., Zhang P.Y. Tribological properties of nanostructured and conventional WC-Co coatings deposited by plasma spraying. Thin Solid Films 388 (2001), p. 277. 23 Jordan E.H., Gell M., Sohn Y.H., Goberman D., Shaw L., Jiang S., Wang M., Xiao T.D., Wang Y., Strutt P. Fabrication and Evaluation of Plasma Sprayed Nanostructured Alumina-Titania Coatings with Superior Properties, Mater Sci Eng, A301, 2001, p. 80. 24 Gell M., Jordan E.H., Sohn Y.H., Goberman D., Shaw L., Xiao T.D. Development and Implementation of Plasma Sprayed Nanostructured Ceramic Coatings, Surface and Coatings Technology,’ vol. 146–147, 2001, p. 48.

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25 Goberman D., Sohn Y.H., Shaw L., Jordan E.H., Gell M. Microstructure Development of Al2O3-13 wt%TiO2 Plasma Sprayed Coatings Derived from Nanocrystalline Powders. Acta Materialia, 50, 2002, p. 1141. 26 Papparado J. U.S. Navy Finding New Applications for Advances in Nanotechnology. National Defense Industrial Association’s Business & Technology Magazine. Available from: http://www.nationaldefensemagazine.org/issues/2004/oct/US_Navy_Finding. htm [accessed 14 December 2006]. 27 Williams J., Kim G.E., Walker J. Ball Valves with Nanostructured Titanium Oxide Coatings for High-Pressure Acid-Leach Service: Development to Application. Proceedings of Pressure Hydrometallurgy 2004, Banff, Alberta, Canada, October 23–27, 2004. 28 Kim G.E., Walker J. Successful Application of Nanostructured Titanium Dioxide Coating for High-Pressure Acid-Leach Application. Journal of Thermal Spray Technology, Volume 16(1), March 2007, p. 34. 29 Kim G.E. Thermal Sprayed Nanostructured Coatings: Applications and Developments. Chapter 3 of Nanostructured Materials Processing, Properties, and Applications – 2nd edn, Koch C.C, editor. William Andrew Publishing, 2007. 30 Kim G.E. Proven and Promising Applications of Thermal Sprayed Nanostructured Coatings. Proceedings of the International Thermal Spray Conference, Seattle, USA, May 15–18, 2006. 31 Schoenung J.M., Tang F., Ajdelsztajn L., Kim G.E., Provenzano V. Processing and Characterization of Thermal Barrier Coatings with Cryomilled Bond Coats. Materials Forum, Vol 29, pp. 414–419, 2005. 32 Ajdelsztajn L., Picas J.A., Kim G.E., Bastian F.L., Schoenung J.M., Provenzano V. Oxidation behavior of HVOF sprayed nanocrystalline NiCrAlY powder. Materials Science and Engineering, A338, 2002, p. 33. 33 Ajdelsztajn L., Tang F., Kim G.E., Provenzano V., Schoenung J.M. Synthesis and Oxidation Behavior of Nanocrystalline MCrAlY Bond Coatings. Journal of Thermal Spray Technology, Volume 14(1), March 2005, p. 23. 34 Klug H.P., Alexander L.E., X-Ray Diffraction Procedures: For Polycrystalline and Amorphous Materials, 2nd Edition, New York, NY: Wiley, 1974, p. 643. 35 Suryanarayana C., Mechanical Alloying and Milling, New York, NY: Marcel Dekker, 2004, p. 110. 36 Ur S.C., Choo H., Lee D.B., Nash P. Processing and Properties of Mechanically Alloyed Ni(Fe)Al-Al2O3-AlN. Metals and Materials, Vol. 6, No. 5 (2000), p. 435. 37 Dymek S., Dollar M., Hwang S.J., Nash P. Deformation mechanisms and ductility of mechanically alloyed NiAl. Materials Science and Engineering A152 (1992), p. 160. 38 Lee D.B., Kim G.Y., Park S.W., Ur S.C. High temperature oxidation of mechanically alloyed NiAl-Fe-AlN-Al2O3. Materials Science and Engineering A329–331 (2002), p. 718. 39 Dollar M., Dymek S., Hwang S.J., Nash P. The Role of Microstructure on Strength and Ductility of Hot-Extruded Mechanically Alloyed NiAl. Metallurgical Transaction A, Volume 24A, September 1993, p. 93. 40 Whittenberger J.D., Eduard A., Luton M.J. 1300 K compressive properties of a reaction milled NiAl-AlN composite. Journal of Materials Research, Volume 5, Issue 12, December 1990, p. 2819. 41 Evans A.G., Mumm D.R., Hutchinson J.W., Meier G.H., Pettit F.S. Mechanism controlling the durability of thermal barrier coatings. Progress in Materials Science, Volume 46, Issue 5, 2001, p. 505.

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42 Wright P.K., Evans A.G. Mechanisms governing the performance of thermal barrier coatings. Current Opinion in Solid State and Materials Science, Volume 4, Issue 3, June 1999, p. 255. 43 Wu Y.N., Qin M., Feng Z.C., Liang Y., Sun C., Wang F.H. Improved oxidation resistance of NiCrAlY coatings. Materials Letters 57 (2003), p. 2404. 44 Tang F., Ajdelsztajn L., Kim G.E., Provenzano V., Schoenung J.M. Effects of variations in coating materials and process conditions on the thermal cycle properties of NiCrAlY/ YSZ thermal barrier coatings. Mater Sci Eng A425 (2006), p. 94. 45 Mercier D., Kim G.E., Brochu M. Surface Oxide Selectivity of Nanostructured CoNiCrAlY and NiCoCrAlY Materials. Oral presentation at 2009 TMS Annual Meeting & Exhibition, February 15–19, 2009: San Francisco, CA. 46 Kaplin C., Mercier D., Brochu M. Nanostructured MCrAlY Coatings for High Temperature Oxidation in Petrochemical Applications. Oral presentation at Materials Science & Technology 2009, October 25–29, 2009: Pittsburgh, PA. 47 Papyrin A. Cold Spray Technology. Advanced Materials & Processes, September, 2001, p. 49. 48 Van Steenkiste T.H. Kinetic Spray Coatings. Surface and Coatings Technology, 1999, 111, p. 62. 49 Stoltenhoff T., Kreve H., Richter H. An Analysis of the Cold Spray Process and Its Coatings. Journal of Thermal Spray Technology, 2002, Vol. 11(4), p. 542. 50 Dykhuizen R., Smith M. Gas Dynamic Principles of Cold Spray. Journal of Thermal Spray Technology, 1998, 7(2), p. 205. 51 Kosarev V.F., Klinkov S.V., Alkhimov A.P., Papyrin A.N. On Some Aspects of Gas Dynamic Principles of Cold Spray Process. Journal of Thermal Spray Technology, 2003, Vol. 12(2), p. 265. 52 Grujicic M., Zhao C.L., Tong C., DeRosset W.S., Helfritch D. Analysis of the Impact Velocity of Powder Particles in the Cold-Gas Dynamic-Spray Process. Materials Science and Engineering A368, 2004, p. 222. 53 Dykhuizen R.C., Smith M.F., Gilmore D.L., Neiser R.A., Jiang X., Sampath S. Impact of High Velocity Cold Spray Particles. Journal of Thermal Spray Technology, 1999, Vol. 8(4), p. 559. 54 Grujicic M., Saylor J.R., Beasley D.E., Derosset W.S., Helfritch D. Computational Analysis of the Interfacial Bonding between Feed-Powder Particles and the Substrate in the Cold-Gas Dynamic-Spray Process. Applied Surface Science, Vol. 219, 2003, p. 211. 55 Helfritch DJ, Champagne VK. Optimal Particle Size for the Cold Spray Process. Presented at the International Thermal Spray Conference, May, 2006. 56 Champagne V., editor. The Cold Spray Materials Deposition Process: Fundamentals and Applications. Woodhead Publishing Limited, Abington Hall, Abington, Cambridge CB21 6AH, England, 2007, p.57. 57 Grujicic M., Saylor J.R., Beasley D.E., Derosset W.S., Helfritch D. Computational Analysis of the Interfacial Bonding between Feed-Powder Particles and the Substrate in the Cold-Gas Dynamic-Spray Process. Applied Surface Science, Vol. 219, 2003, p. 211. 58 Amateau M.F., Eden T.J. High Velocity Particle Technology. iMast Quarterly, 2000, p. 3. 59 McCune R.C., Donlon W.T., Popoola O.O., Cartwright E.L. Characterization of Copper Layers Produced by Cold Gas-Dynamic Spraying. Journal of Thermal Spray Technology, 2000, Vol. 9(1), p. 73. 60 Moriarty P. Nanostructured Materials. Reports on Progress of Physics, 64 (2001), p. 297.

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61 Shukla V., Elliott G.S., Kear B.H. Nanopowder deposition by supersonic rectangular jet impingement. Journal of Thermal Spray Technology, Vol. 9(3), 2000, p. 394. 62 Lima R.S., Karthikeyan J., Kay C.M., Lindemann J., Berndt C.C. Microstructural Characteristics of Cold-Sprayed Nanostructured WC-Co. Thin Solid Films, 416 (2002) p. 129. 63 Kim H.J., Lee C.H., Hwang S.Y. Superhard Nano WC-12%Co Coating by Cold Spray Deposition. Materials Science and Engineering A391 (2005), p. 243.

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21 Nanocoatings for commercial and industrial applications J.L. McCREA, G. PALUMBO, I ntegran Technologies, Canada and U. ERB, University of Toronto, Canada Abstract: Recent advances in the development of bulk nanocrystalline materials have paved the way for a multitude of commercial and industrial applications whereby novel nanostructured coatings have either replaced conventional technologies or have enabled new technologies ultimately leading to new products. In this chapter, the unique functional and structural properties of various nanostructured materials are highlighted/reviewed along with several current and emerging commercial and industrial applications for nanostructured metal coatings. Key words: nanostructured materials, structure–property relationships, commercialization, chrome replacement, nanometal polymer hybrids, magnetic shielding, nanometal carbon fiber composite hybrids.

21.1 Introduction While the field of nanotechnology has developed rapidly over the last decade, the principle upon which it is based – nanoscale features resulting in unique properties – has existed in nature and engineered materials long before the term ‘Nanotechnology’ was defined.1 A good example of nature exploiting the distinct features of nanotechnology can be found in the moth’s eye. As a result of hexagonally arranged protrusions a few hundred nanometers tall and apart (smaller than the wavelength of light), the moth’s eye surface has a very low reflectance, thereby absorbing more light, which allow moths to see much better in the dark than humans.2 In the engineering world, nanometer size precipitates in age-hardened aluminium alloys have been responsible for significant increases in the alloy’s strength, long before the characterization equipment was available to positively identify these nanometer size structures.1,3 With the advent of sophisticated materials characterization techniques, such as high-resolution TEM, SEM, high-resolution SPM, etc., came the ability to effectively identify and characterize nanometer sized structures and features in materials. With these techniques, materials engineers now had the tools to study structural features of materials on the nanometer scale. With the revelation of the uniqueness of nanostructured materials4,5 and the development of various synthesis techniques to intentionally create these materials, engineers and scientists quickly worked to effectively characterize these structures, and establish direct correlations between the structure and the properties. 663 © Woodhead Publishing Limited, 2011

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As will be reviewed in Section 21.2, the outstanding structural and functional properties of nanostructured materials have resulted in the identification of numerous potential applications. However, as a result of multiple entry barriers for new materials in the commercial and industrial world, only a few of these applications have been successfully implemented in industry on a wide scale (i.e. commercialized). In Section 21.3, a quick overview of some of these barriers will be discussed and Section 21.4 will then highlight various applications of nanostructured coatings focusing on a few specific case studies where the market entry barriers have been overcome and new nanostructured materials were successfully introduced into the market.

21.2 Overview of nanostructured metals and alloys As already outlined in previous chapters (Chapter 5 in particular), the properties of a nanostructured material can differ significantly from those of a conventional material of equivalent composition. This is a direct result of the significant increase in the number of interfaces, or grain boundaries, in the material as the grain size decreases below 100 nm.6 It is the enhancement of many of these properties that make nanostructured materials very attractive for use in various commercial and industrial applications. Figure 21.1 shows a schematic diagram of a number of properties that are enhanced (or otherwise affected) by grain refinement to the nanometer scale along with a several potential applications that have been identified in the literature.7 The figure links each property to each application that it influences. With the large number of multiple correlations between properties and applications, the figure emphasizes the importance of the multifunctional nature of nanostructured materials, which is at the heart of the enabling proposition for many of the applications, which will be discussed in more detail later in this section. For simplicity, the material properties listed in Fig. 21.1 are separated into two broad categories: structural and functional. Structural properties include those that are critical for applications in which the nanostructured material will bear load, whereby the mechanical properties (for example: yield strength, elastic limit, ductility, thermal shock resistance) are critical. Functional properties are defined as those that bring additional function to the application and are unique to the nanostructured material, such as excellent wear resistance, lower friction, increased catalytic activity, excellent soft magnetic properties and high electrical resistivity, as well as many others. Rarely does one property alone dictate the use of a material for a specific application. With so many outstanding properties, nanostructured materials by definition are extremely multifunctional, wherein a combination of properties can create a synergistic effect, which essentially enables many applications. A good example of this multifunctional nature is in the fabrication of micro–electrical– mechanical (MEMS) devices. A process has recently been developed to make

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21.1  Enabling properties of nanostructured materials and the correlated applications.7

nanocrystalline nickel, nickel-iron and cobalt for microsystem component applications.8 The ultra-fine, equiaxed, grain structure of the nanocrystalline microcomponents results in outstanding isotropic mechanical properties that provide considerable enhancements of several performance indicators compared to conventional metals, including: higher elastic storage capacity (resilience) and thermal shock resistance. The high wear resistance and lower friction further increases the components’ functionality by significantly improving the tribological performance, and the enhanced electrical and soft magnetic properties, enable many electromagnetic applications for components operating at high frequency by lowering core loss and reducing eddy currents. Another good example of multiple properties coming together to enable an application is the structural reinforcement of polymer portable electronic component housings with excellent electromagnetic shielding performance.9,10,11

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For some applications, the properties of nanostructured materials are not always synergistic; in some cases they can be counter productive, in which case the evaluation and prioritization of the competing objectives must be considered. A good example of this is in the application of nanocrystalline metal coatings on copper wire to greatly enhance the strength-to-weight ratio of electrical conductors in wiring systems, in particular for aircraft applications.12 While a decrease in grain size significantly increases the tensile strength, it also increases the electrical resistivity, which is undesirable for electrical conductors. Potential compromises are therefore 1) to optimize the grain size to achieve an acceptable strength at an acceptable penalty to the overall conductivity, or 2) to design such that the nanocrystalline coating bears the majority of the mechanical load, while the copper core carries the majority of the electrical load. By following the latter approach, wires with ultimate tensile strengths of 1070 MPa were fabricated while retaining an overall conductivity of 57%IACS,12 thereby exceeding the strength-to-weight performance of the incumbent Cu-Be wires. The enhanced properties of nanostructured materials enable many applications where conventional materials would not work, however, it is critical that a comprehensive understanding of the full structure–property relationships exist, such that the synergies and/or trade-offs between them can be fully optimized. As will be shown in the next section, this understanding along with the ability to produce high-quality nanostructures (with predictable material properties), using low-cost production methods helps to minimize implementation risks and overcome the multiple entry barriers these new materials face during commercialization.

21.3 Commercialization of nanostructured materials Most early-stage research and development of new materials is performed in government research labs or universities.13 While the research pushes the boundaries of technology and is extremely innovative, fundamental science is typically the focus, and scaling the technology beyond lab-scale prototypes is usually of secondary importance. As a result, the technology transfer from research to product development can carry cumbersome process development costs that make it difficult for the technology to be commercially viable, regardless of how attractive the properties are. Returning to the moth’s eye as an example, multiple research groups are currently investigating recreating the nanostructured morphology found in the moth’s eyes in materials of various electronic devices (LEDs, lens) with very promising results. However, techniques that can scale beyond laboratory prototypes into cost-effective industrial processes have not yet been defined.14 By no means does this demean the importance, quality or value of the research, it is meant simply to emphasize one of the many hurdles new technology must overcome during commercialization: that of moving the technology out of the lab and into industry in a cost-effective manner. It is

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absolutely essential that the high introductory cost of new materials and processes be offset by compelling end-customer benefit. A common measure used by many of the world’s major companies and agencies (e.g. US DoD, NASA, etc.) to assess the maturity of evolving technologies is the Technology Readiness Level (TRL). Figure 21.2 shows a schematic of the TRL rating scale used by NASA.15 Basic research and technology development covers TRL levels 1 through 5. Before new technology can be effectively implemented in industry, the technology must pass through extensive technology demonstration and system level validation testing (TRL 6 through 8), which has been referred to as the ‘valley of death’.16 The term ‘valley of death’ alludes to the difficulty in maturing technologies through this demonstration and validation stage due to a number of barriers, which ultimately lead to a failure to transfer many new technologies to industry. Bringing new technology through the ‘valley of death’ is one of the most costly stages of development. Costs associated with extensive component level demonstration/validation testing, capital investment, redefinition of codes and standards, as well as others can be overwhelming and prohibitive. Aside from costs, another main barrier is risk aversion of the eventual end-user or of the party responsible for the development costs.

21.2  Technology Readiness Level (TRL): a rating scale commonly used by NASA and the United States Department of Defense to assess the maturity of evolving technologies [after Mankins15].

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There are many risks involved with the implementation of new materials, including: 1) market/product risk, 2) latent liability risk, 3) manufacturing risk, and 4) time to market risk.17 With new materials comes uncertainty, and as a result designers are reluctant to select a new material until it is extensively evaluated in service. However, this presents a chicken-and-egg scenario, as a new material cannot be evaluated in service until a designer selects it. This is a good example of risk adverseness with respect to market/product risk. There is no guarantee to investors/stakeholders that materials will find product acceptance and thus in order to minimize risk, ‘materials must find applications quickly or else lose user interest’.17 In general, the risk of the public’s reluctance to embrace innovative technology without real safety data or products is one of a few of the bottlenecks facing early-stage nanotechnology commercialization.18 The uncertainty factor comes into play again with respect to liability risk. Without the historical data to back long-term use, early adopters assume significant latent liability and warranty risk for the lifetime of the product. As previously mentioned, manufacturing risk (the risk that materials can be cost-effective in large-scale production) is also a significant barrier to the successful implementation of nanostructured materials. Another chicken-and-egg scenario exists here, in that the new materials do not gain market acceptance until their costs decrease (or cost-effectiveness is demonstrated on a large scale), but costs will not decrease until the material gains market acceptance and is produced on a large scale. Most materials advancements that occurred in the twentieth century required 20 years to move from research stage to full commercialization.17 Also known as the ‘20-year barrier’, this represents one of the biggest risks with regard to investing in new materials. The development time, however, can depend on the industry into which the material is being introduced (for example materials in aerospace and defense typically involve longer development times than in sporting goods or consumer electronics), as well as the manner in which it is being introduced. Table 21.1 shows typical development times for new materials in aerospace components depending on how it is being implemented.19 Only a handful of commercial companies exist today with the sole mandate to introduce new nanostructured materials into various industrial and commercial applications. Figure 21.3 shows a graph (the Lux Innovation Grid20), which compares different companies based on technical value and business execution. While the technical value of most companies is rated favorably, only a few of the companies are rated as mature with regards to business execution, thereby showing their relative infancy of the area of technology. As was shown in this section, nanostructured materials face many entry barriers and risks during development and commercialization. Through the use of costeffective production processes and risk mitigation, however, nanostructured materials have penetrated these barriers and have been effectively introduced into various applications across many industries, including: aerospace, defense, automotive, consumer electronics and sporting goods. In the following section,

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Table 21.1  Typical development times for new materials19 Development phase

Development time

Modification of an existing material for a non-critical component

2 to 3 years

Modification of an existing material for a critical structural component

Up to 4 years

New material within a system for which there is experience

Up to 10 years – includes time to define the material’s composition and processing parameters

New material class

Up to 20 years and more – includes time required to develop design practices that fully exploit the performance of the material and establish a viable industrial base

21.3  ‘Lux Innovation Grid’ comparing the technical value and business execution of various commercial nanomaterials companies.20

several current and emerging applications are reviewed and where possible the factors that led to market penetration in light of the aforementioned barriers will be highlighted.

21.4 Current and emerging applications Some of the earliest systematic studies on the use of electrodeposition to produce nanocrystalline materials occurred in the 1980s.21,22 The first large-scale structural

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application for nanostructured materials was introduced in 1993 (the Electrosleeve process for nuclear steam generator repair),23,24,25 which was followed shortly by some of the earliest issued US patents in the field of nanotechnology.26,27 Nearly 20 years have now passed since this first industrial application and patents were issued, and true to the ‘20-year barrier’, nanostructured materials are now starting to see widespread use in a variety of industrial and commercial applications. The following sections present some several case studies of current and emerging applications of nanostructured metal coatings, highlighting the value proposition and market entry in light of the risks described in the previous section.

21.4.1  Hard chrome replacement Commercial hard chrome plating from hexavalent chromium plating solutions has been around since the early part of the twentieth century.28 As a result of their intrinsic high hardness (600 to 1000 VHN) and low coefficient of friction (<0.229) hard chrome coatings (0.00025" to 0.010" thick) are used extensively for imparting wear and erosion resistance to components in both industrial and military applications,30,31 including: aircraft landing gear, hydraulic actuator rods and cylinders, gas turbine engines, helicopter dynamic components and propeller hubs, as well as many others. As a well-established process, the properties and performance of chrome coatings are well known, and as a result designers typically specify chrome as the protective coating on many parts based on legacy, as it presents the option with the least risk. In some cases hard chrome may not be the optimal coating for a particular application; it may just be the coating with the most available historical data. While hard chrome coatings are hard and wear resistant, there are significant process and performance drawbacks associated with their use. For example: hard chrome plating processes have a relatively low electrolytic efficiency, resulting in low deposition rates, extraneous energy consumption and mist formation of toxic hexavalent chromium. Moreover, the intrinsic brittleness of hard chrome deposits invariably leads to micro- or macro-cracked deposits. These cracks do not compromise wear and erosion resistance, but they are wholly unsuitable for applications where corrosion resistance is required and invariably lead to a fatigue debit for high strength steels. Even with the drawbacks described above, designers still specify chrome. Alternative coating technologies that have been considered as hard chrome alternatives include: thermal spray,32 plasma vapor deposition,33 and other Cr-free coatings applied by electrolytic or electroless plating techniques.34,35 Over the last 10 years, high velocity oxygen-fuel (HVOF) thermally sprayed WC-Co and WC-CoCr coatings have been validated by the Hard Chrome Alternatives Team (HCAT) and have generally been adopted within the North American aerospace industry36 and for other low-volume, high-added-value line-of-sight coating applications.37 For non-line-of-sight deposition and high-volume, low-added-value

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production, electroplating technologies have proved more suitable and cost effective. Traditionally, most of these have been based on Ni, including both electroless (Ni-P and Ni-B) and electrolytic (Ni-W, Ni-Co, Ni-Mo, etc.) coatings. As Ni is listed by the Environmental Protection Agency (EPA) as a priority pollutant38 and is listed among the 14 most toxic heavy metals, it is evident that a non-Ni based electroplating technology would provide an environmentally acceptable alternative. Although alternative coating technologies may decrease manufacturing time, lead to longer service life, and reduce overall ‘cradle-to-grave’ lifecycle costs, near-term switching costs and potential technical risks may discourage and/or delay the adoption of the new technology, unless a further impetus is present – such as the elimination of a toxic substance from worksites. Health risks associated with the use of hexavalent chromium (Cr6+) baths have been recognized since the early 1930s.39 The US Department of Labor’s Occupational Safety and Health Administration (OSHA) recently reduced the permissible exposure limit (PEL) for hex chrome and all hexavalent chromium compounds from 52 to 5 µg/m3 as an eight-hour time-weighted average, effective May 30, 2006. The rule also includes provisions for employee protection such as preferred methods for controlling exposure, respiratory protection, protective work clothing and equipment, hygiene areas and practices, medical surveillance, hazard communication, and record keeping. More recently (April 8, 2009) the Under Secretary of Defense for Acquisition, Technology and Logistics in the United States issued a memorandum for secretaries of all US DoD Military departments to take significant action to minimize the use of hexavalent chromium. The memo states that the Defense Acquisition Regulation Council will prepare a clause for defense contracts prohibiting the use of hexavalent chromiumcontaining materials in all future procurements unless specifically approved by the US Government. As a direct result of these restrictions, regulatory burdens and lifecycle costs associated with hard chrome plating will continue to increase, providing significant incentive/need for the industry to identify a suitable alternative. With high hardness and excellent wear properties, nanostructured coatings make an obvious candidate as an alternative to hard chrome coatings. Nanostructured materials can be made using a variety of different methods, including physical and chemical vapor deposition, inert-gas condensation, highpressure severe plastic deformation, and electrodeposition, as well as others. However, the one method that stands out against the others for the particular application as a replacement for hard chrome is electrodeposition. With funding from the US Department of Defense Strategic Environmental Research and Defense Program (SERDP) and Environmental Security Technology Certification Program (ESTCP) as well as from the Technology Partnership Canada (TPC) program, Integran Technologies developed Nanovate-CR™: an electrodeposited nanocrystalline cobalt-phosphorus alloy as an alternative to hard

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chrome, based on their patent-protected technology regarding the synthesis of nanostructured materials via electrodeposition.26,27 As an electrodeposition process, Nanovate CR allows for a true ‘drop-in’ replacement, capable of using existing infrastructure for chrome plating, with the only major capital expense being a pulse plating power supply. As a result of the nanostructured grain size, the material has high hardness, high strength, good ductility and excellent wear resistance40,41 (see Table 21.2 below). Figure 21.4 shows an image of a hydraulic actuator rod coated with a ~0.010" thick Nanovate CR™ coating along with an optical micrograph showing the cross-section through the thickness of the coating.42

Table 21.2  Comparison of nanovate CR and electrolytic hard chrome properties

Nanovate CR

EHC

Hardness, HVN Ductility Wear volume loss, mm3/Nm Coefficient of friction Pin wear Corrosion resistance*

530–600 (as-deposited) 600–680 (heat treated) 5–7% 6–7 × 10–6 0.4–0.5 Mild 8

Min 600 – <0.1% 9–11 × 10–6 0.7 Severe 2

Note: *ASTM B 537 protection rating after 1 000 hr salt-spray exposure per ASTM B 117 (rating out of 10, higher = better performance).

21.4  High strength steel rod coated with Nanovate CR along with an optical micrograph of a cross-section of the coating showing a fully dense, crack-free deposit [after McCrea42].

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The figure demonstrates that the coating is not microcracked, which ultimately results in superior corrosion resistance over hard chrome when tested in the standard salt-spray environment. There are also significant advantages associated with the process: the overall plating efficiency is greater than 90%, compared to less than 35% for hard chrome, thus leading to 1) significant reductions in energy consumption, and 2) deposition rates ranging from four to eight times faster than hard chrome, which leads to substantial increases in throughput during manufacturing. The Nanovate CR™ process is now in the early commercialization stage with several industrial installations. The first non-industry demonstration/validation installation was in an old chrome-plating tank at NAVAIR JAX (a US Navy Repair and Overhaul Depot for Navy Aircraft), and is currently going through an extensive demonstration/validation test program on various retrofitted aerospace components. Enduro Industries, Inc. of Hannibal Missouri (a subsidiary of PTC Alliance) has also recently installed the process at their facility. Enduro Industries is a major manufacturer of hard chrome steel bars and tubes for the fluid power industry and has entered into a license agreement with Integran, with limited exclusivity for the use of Nanovate-CR™ for the fluid power steel bar and tube outside diameter coating market, and is currently supplying Nanovate-CR™ coated steel bars for various customers.

21.4.2 Lightweight nanometal polymer hybrids for automotive applications There is a significant driving force to decrease vehicle weight and increase fuel economy in the automotive industry. Enabled by its excellent structural properties, one of the latest application areas involves nanocrystalline metal/polymer hybrid technology used to manufacture strong yet extremely lightweight components.43 Morph Technologies, Inc. recently partnered with DuPont Engineered Plastics to launch Metafuse™, a nanocrystalline metal/polymer hybrid technology that can be used to manufacture extremely lightweight components with the strength and stiffness of metal combined with the design flexibility, lightweight benefits and low cost of injection-molded high-performance thermoplastics. The technology involves precisely applying a thin high-strength nanostructured metal layer to molded components made of DuPont Engineering Polymers to create lightweight complex-shaped components with high stiffness, high strength, and which possess a highly wear-resistant surface. Bending stresses and stiffness are proportional to the distance from the neutral axis, therefore by applying the nanometal coating at the outermost edges of the molded polymer component (furthest from the neutral axis), the coating is in the optimal location to increase stiffness and bear the majority of the load, both in axial bending and in torsion. Figure 21.5 shows a comparison of room temperature properties of a 25% glass-reinforced Zytel PA66 injection-molded polymer coated with 100 µm of nanostructured nickel-iron alloy against the uncoated polymer, both

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21.5  Room temperature properties of the nanometal/plastic hybrid compared to plastic alone in three properties: Bending stiffness, impact strength and tensile strength [after Day43].

in the shape of ISO tensile bars. The figure compares the bending stiffness (measured by flexural modulus), impact strength (measured by multi-axial impact) and tensile strength (measured in uniaxial tension). The data shows typical increases in flexural modulus and impact strength of two to four times that of the plastic alone. As the properties of metals are far less temperature sensitive than those of polymers, the nanometal/polymer hybrids have been shown to maintain excellent structural properties in temperature ranges where polymers exhibit significant losses due to relative low glass-transition temperatures. Dynamic mechanical analysis (DMA) has shown that the hybrid structures retain 70 to 80% of initial modulus at temperatures exceeding the glass transition temperature, thereby effectively extending the working temperature range of polymer parts by 50 to 75°C, which can be of considerable interest for automotive applications involving ‘under the hood’ components. A specific example of a nanometal/polymer component in an automotive application is the Grille Guard.9 In this application, a truck grille guard made from 6 mm thick blow-molded polycarbonate (PC)/acrylnitrile-butadiene-styrene (ABS) did not meet the deflection (deflection of less than 25 mm under an applied load of 250 lbs) and vibration requirements (a first natural frequency of above 30 Hz). Analysis of the design revealed that increasing the plastic thickness to achieve the required stiffness resulted in a thickness beyond the limitations of the blow-molded process. While a formed steel bracket, screwed onto the back plate, could be used to meet the stiffness requirements, the increase in cost and weight was undesirable. By applying a 25 µm thick nanostructured Ni-Fe alloy coating to the polymer part, substantial reinforcement was observed. The stiffness increased such that the part now met the required deflection (<25mm under a 250 lbf load) and frequency (>30 Hz) requirements, all while adding only 153 grams of weight to the part, keeping it well below the 20 lb weight limit. While other metallic coatings would add the same stiffness, due to a similar Young’s modulus (see Table 21.3), none would be able to withstand the high stresses at full deflection (>900 MPa under the 250 lbf load). Although numerous design iterations were considered (see Table 21.4) only the one using the nanostructured Ni-Fe alloy coating met all of the performance criteria.

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Table 21.3  Yield strength comparison of selected metallic materials9 Metallic coatings

Elastic modulus (GPa)

Yield strength (MPa)

Conventional Ni Sulfamate Ni Nicoloy Nanostructured NiFe

185 185 185 185

220 <550 <1000 1785

Table 21.4  Summary of design iterations9 Part Plastic Static def. thickness (specification: <25 mm)

1st natural Part mass frequency (specification >30 Hz)

PC/ABS PC/ABS + steel   brackets Stiff PC/ABS Stiff PC/ABS   with 25 µm Nano   NiFe coating

4 mm 6 mm

>100 mm 36 mm

16 Hz 30 Hz

5.2 kg 9.5 kg

6 mm 6 mm

33 mm 24.6 mm

26 Hz 30.3 Hz

7.8 kg 8.0 kg

Nanometal/polymer hybrid materials are expected to have enormous impact in the automotive and aerospace sectors, enabling significant weight reductions in numerous components. Examples of potential automotive applications include: grille-guards, brake, gas or clutch pedals, fuel rails, running boards, spoilers, muffler tips, wheels, vehicle frames and structural brackets9 among many others.

21.4.3  Electromagnetic applications Considerable changes in the magnetic behavior of a ferromagnetic material can occur when the average grain size approaches critical magnetic length scales (such as the domain wall thickness or the ferromagnetic exchange length) found in polycrystalline materials. For example, when the average grain size is reduced to the extent that it is comparable to the domain wall thickness, the coercivity, Hc (the critical field strength required to flip the direction of magnetization), is found to dramatically decrease.44,45 Contrary to the strong grain size dependence of coercivity, the saturation magnetization, Ms (or magnetic flux density, Bs) has been shown to be relatively insensitive to grain size.46–49 As a result, soft ferromagnetic materials, with an average grain size less than 20 nm, typically have low coercivity, high permeability and a predictable magnetic flux density determined by the composition of the alloy.

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Due to these attractive properties, nanostructured soft magnetic alloys have slowly started to replace conventional materials in certain niche applications. For example, novel high magnetic moment CoNiFe thin films have been developed to replace conventional permalloy films in magnetic recording heads.50 The nanocrystalline grain structure of the thin films allows for high permeability and low coercivity, while the high saturation magnetization, which is relatively unaffected by grain size, is mainly governed by the alloy composition. Nanostructured soft magnetic foils made from the recrystallization of Fe-Si-B amorphous alloys containing Nb and Cu (made by the rapid solidification/melt spun technique) have good soft magnetic properties with saturation flux density (Bs) of 1.2 to 1.4T and high permeability.51 The high alloy content of these materials, however, limits the amount of iron and thus the flux density is much lower that that of silicon steels (~1.8–2.0T). Recent advances with Fe-M-B alloys, where M is selected from the group of Zr, Hf or Nb have produced nanostructured materials with higher flux density (as high as 1.64 T52). Nanostructured alloys made from recrystallized amorphous precusors are commercially available and marketed under various trademarks, such as: Metglas®, Vitroperm™, and Finemet™. Applications of these materials include tape-wound and laminated magnetic cores for specialized applications such as: transfomers for pulse current sensitive earth leakage circuit breakers, current transformers with small errors in phase angle and amplitude, common mode radio frequency interference (RFI) chokes for electromagnetic compatibility (EMC) and high-frequency power transformers.53 Another emerging application for nanostructured ferromagnetic materials is in the area of shielding of low-frequency electromagnetic interference (EMI). Sensitive electrical instrumentation typically requires protection from external magnetic fields. While thin high-conductivity metallic coatings are effective at shielding high-frequency magnetic fields, high-permeability ferromagnetic alloys, such as Permalloy, are typically used for shielding from low-frequency magnetic fields, which can be emitted from sources such as switches, motors, power supplies and transformers. The high permeability of nanostructured soft magnetic materials makes them ideal for shielding sensitive electrical instrumentation from low frequency EMI. Figure 21.6 shows a schematic of the advantages and drawbacks of various commercially available shielding solutions to low-frequency EMI.11 Historically, Permalloy (a high permeability nickel-iron alloy) foils have been the most common material used for low-frequency EMI shielding. As Permalloy is soft and ductile, it can be formed into shapes to fit into mildly complex geometries components. The deformation induced into the microstructure during forming, however, significantly compromises the permeability and a hightemperature annealing step is required to restore the magnetic properties. Nanostructured recrystallized amorphous foils can also be laid up into devices to provide shielding; however, the foils are difficult to form, which limits them to

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21.6  Advantages and drawbacks of existing commercially available shielding solutions to low frequency EMI.11

relatively simple geometries. Other solutions include metal injection molding of specialty ferromagnetic powders and pure metal components, but these solutions to not offer the same degree of shielding as with high permeability materials. With recent developments in nanocrystalline ferromagnetic coatings, an alternative solution is to apply a high magnetic permeability coating directly to the surface of a part11 using low-cost deposition techniques that are amenable to manufacturing large volumes of components.26,27 Direct coating provides excellent design flexibility and processing benefits. More complex components can be effectively coated, than protected with foils, and with the direct coating technique steps associated with forming heat treatments and joining are eliminated, reducing both part count and labor, thereby decreasing cost. The true value of the nanostructured coating, however, comes from the multifunctional nature of the coating when the high strength and stiffness is also leveraged. Complex parts made from low-cost injection-molded polymers can be effectively coated with nanostructured ferromagnetic coatings, thereby providing the polymeric component with: 1) high stiffness, 2) high strength, 3) high surface hardness, 4) good wear resistance, and 5) excellent magnetic shielding performance. Figure 21.7 shows a complex polymer housing for a portable electronic device coated with a high permeability nanocrystalline ferromagnetic coating. To demonstrate the enhanced strength and stiffness of a nanometal/polymer hybrid electronic housing, an injection-molded polyamide-based cellular telephone

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21.7  Complex polymer housing for a portable electronic device coated with a high permeability nanocrystalline ferromagnetic coating.11

frame was coated with a 50 µm thick, nanostructured nickel coating following the methods described in US Patents 5,352,266 and 5,433,797, and US Patent Publication No. 2006/0135282.10 The nickel-coated frames were then tested for ‘torsional’ and ‘flexural’ stiffness and compared to uncoated frames. The flexural force required for the nanometal-coated frames was roughly 3 to 3.5 times that of the uncoated frames, while the torsional force required to twist from 0° to 2° was twice that required for the uncoated frames, thereby clearly demonstrating that even a thin layer of nanostructured coating can significantly increase the stiffness of an injection-molded polymer frame.

21.4.4  Lightweight nanometal composite hybrid tooling Boeing’s newest aircraft, the 787 (Dreamliner), as well as the US Department of Defense’s new fighter jet, the Joint Strike Fighter (the F-35 Lightning II) are good examples of the recent trend in both the commercial and military aerospace industries towards producing larger and more complex structural components out of lightweight carbon fiber-reinforced plastic (CFRP) composites.54,55,56 The high specific strength and design flexibility of the CFRP structures allow for lighter and more aerodynamic designs that can significantly increase fuel economy and decrease operating costs. Boeing’s 787, which had its first test flight in 2009, is comprised of over 50% CFRP and represents the first large commercial aircraft in which the primary structure (wings and fuselage) is fabricated from CFRP instead of aluminum.57 Following suit, Airbus’s A350 will also be fabricated from over 50% CFRP material, which is scheduled for release in mid-2013.58

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CFRP components are fabricated by laying-up carbon fiber cloth, typically pre-impregnated with a thermosetting resin (pre-preg), on the surface of a tool (also known as a mold), which is then cured at elevated temperature (~125 to 250°C) to create components with excellent stiffness to weight characteristics. In order to meet the precise dimensional tolerances required for the CFRP components, the tools used to fabricate the parts must have a coefficient of thermal expansion (CTE) that is closely matched to the CFRP part material. The tooling/molds required for the fabrication of large composite parts, however, are a challenge.59 Invar (a NiFe Alloy) tools are the most extensively used for production because of their low thermal expansion and durability. Their main drawbacks are: the long lead time and expense required to fabricate the tool, the high physical weight of the tool, the large thermal mass of the tool (long heating/ cooling cycles) and the relative softness of Invar (low scratch/dent tolerance). The sheer weight of metallic tools required for the large aircraft components may exceed the limitations of the existing manufacturing infrastructure (overhead cranes, automatic fiber placement machines), and may severely limit the extent to which Invar tools can be used for these applications. Alternatively, tooling made from CFRP is lightweight, of lower cost and lower thermal mass, and can be manufactured more quickly, but does not have the long-term durability that is required for production tooling and is therefore typically only used for prototype tools. Although progress continues to be made on improving the lifespan and manufacturability of CFRP tooling, poor surface durability and vacuum integrity problems limit the ultimate lifespan of the tools to a fraction of the lifespan of solid metal tools. A low thermal expansion nanostructured Invar-alloy coating has recently been developed60 that has been applied to the surface of composite tools to improve the durability and increase the lifespan of composite tools. Figure 21.8 shows the hardness of the low-CTE nanostructured nickel iron alloy compared to other materials commonly used for the production of composite tools. Due to the ultrafine grain size of the nanostructured alloy, a significant increase in hardness and strength relative to their coarser-grained counterparts (Invar36 and Alloy42) is observed, which renders the coating ideally suited for applications requiring wear resistance and structural reinforcement. Figure 21.9 shows a section of a small CFRP tool coated with high strength nanometal, and Figure 21.9 (b) and 21.9 (c) show scanning electron micrographs of cross-sections of a carbon epoxy substrate that has been coated with approximately 150 µm of nanostructured FeNi and thermally cycled multiple times (× 5) from room temperature (20°C) to liquid nitrogen (–196°C). The micrograph shows that no debonding occurred between the coating and the carbon epoxy composite substrate. The multifunctional nature of the nanostructured coating is what enables this application. The high strength and ductility of the nanostructured coating provides a very durable surface that can take severe abuse from the operators throughout the lifetime of the tool. The low friction of the nanometal surface allows for good part release after curing. The high wear and scratch resistance provide increased

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21.8  Graph showing the superior hardness of low-CTE nanostructured nickel-iron (Nanovar™) compared to conventional low-CTE metals and carbon fiber composite.60

21.9  (a) CFRP tool section coated with low-CTE nanostructured nickel-iron, (b) and (c) scanning electron micrographs of cross-sections of the coated CFRP after thermal cycling. Source: Integran Technologies.

performance and durability compared to both Invar and CFRP tools, and the matched CTE of the coating to the CFRP surface, along with excellent adhesion allows for excellent thermal cycling performance without debonding and/or distortion. What will add real value to the technology, however, will be the ability to scale the coating process to the large components being manufactured for the © Woodhead Publishing Limited, 2011



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large commercial and military aircraft programs. While the current process to deposit the low-CTE nanostructured coating has been demonstrated on a tool of moderate geometry measuring approximately 5 ft by 5 ft in size, similar manufacturing techniques have previously been used to manufacture conventional nickel molds measuring 32 ft long by 12 ft wide.61

21.4.5  Sporting goods The global sports equipment market is forecast to have a value of $81.7 billion by 2013. It is therefore not surprising that there is a large driving force to introduce new material technologies into the sporting goods market. With the constant turnover of new products and an industry where hype and marketing play almost as big a role as actual verified performance data, the sporting good industry is the ideal low-risk industry to introduce new material technologies. Nanostructured materials exhibit a desirable set of characteristics for sports equipment, including high strength, high strength-to-weight ratio, high resilience (e.g. defined as R = s2/2E, where s is the yield strength and E is the elastic modulus), high fracture toughness, high elasticity, high vibration damping, high hardness, high ductility, high wear resistance and low friction.62 As a result of the low risk involved in market entry, the high potential pay-off and the highly desirable properties, nanostructured materials can be found in many of today’s sporting good products, with actual measureable performance enhancements. Some recently commercialized products include: 1) the ‘Epic Golf Shaft’ by Grafalloy, a lightweight nanometal-coated graphite epoxy golf shaft with excellent accuracy due to increased torsional stiffness (Fig. 21.1063), 2) the

21.10  The ‘Epic Golf Shaft’ by Grafalloy, a lightweight nanometalcoated graphite epoxy golf shaft with excellent accuracy due to increase torsional stiffness.63

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‘Exit AB Bat’ by Combat and the ‘Nanotek Bat’ by Anderson, both nanometalcoated aluminum baseball bats with unprecedented strength, improved feel and twice the effective hitting area (Fig. 21.11), 3) the ‘iN® Ping Putter’, a putter with a lightweight yet strong nanometal/polymer hybrid insert that increases forgiveness and improves roll (Fig. 21.12), and 4) ‘Metallix’ tennis and squash racquets by Head, which employ high-strength nanometal stabilizers resulting in a lighter,

21.11  The ‘Exit AB Bat’ by Combat, and the ‘Nanotek Bat’ by Anderson, both nanometal-coated aluminum baseball bats with unprecedented strength, improved feel and twice the effective hitting area.63

21.12  The ‘iN® Ping Putter’, a putter with a lightweight yet strong nanometal polymer hybrid insert that increases forgiveness and improves roll.63

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21.13  The ‘Mettalix’ tennis racquet by Head, which employs high strength nanometal stabilizers resulting in a lighter, stronger and more powerful racquet.63

stronger and more powerful racquet (Fig. 21.13). All of the above applications are enabled by the nanometal technology provided by Powermetal Technology, Inc. of Carlsbad, California.

21.5 Conclusions The excellent properties of nanostructured materials have enabled many new applications whereby the nanomaterials are providing performance previously unattainable with other materials. As 20 years have now past since the benefits of nanostructured materials were first reported, nanomaterials are now found to be gaining steady market acceptance in various industries. Even with a very strong value proposition, pushing new technology through the market barriers rarely succeeds in effective commercialization in a short time period; it is far more

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effective if the technology is pulled through by a clear and present market need, as has been shown by the need to replace hazardous hard chrome coatings and the need to increase fuel efficiency in the automotive and aerospace industries. The true potential of these multifunctional nanomaterials is now starting to emerge in novel hybrid material designs. With further development and testing, new nanometal/polymer and nanometal/composite structures are sure to evolve, leading to significant advances in lightweight engineered structures, which may also see their industrial adoption accelerated by demands for lightweight components for the transportation sector (aerospace, automotive, etc.) in the continuing drive to improve fuel efficiency and reduce greenhouse gas emissions.

21.6 References   1 Koch C.C. Preface, in Koch CC (Ed.), Nanostructured Materials, 2nd ed., Norwich, NY: William Andrew; 2007.   2 http://www.sciencedaily.com/releases/2007/11/071126115318.htm (accessed February 13, 2010) Cardiff University. “Engineers Give Industry A Moth’s Eye View.” Science Daily, November 28, 2007.   3 Hornbogen E. Precipitation Hardening—The Oldest Nanotechnology, in Lightweight Alloys for Aerospace Application, K. Jata et al. (Eds.) Warrendale, PA: TMS; 2001.   4 Gleiter H. Progress in Materials Science 1989;33: 1   5 Gleiter H., in Deformation of Polycrystals: Mechanisms and Microstructures, Proc 2nd Risφ Int Symp On Metallurgy and Materials Science, Risφ National Laboratory, Roskilde Denmark (1991) Vol. 15.   6 Palumbo G., Thorpe S.J., Aust K.T. Scripta Metall Et Mater 1990;24: 134.   7 Erb U., Aust K.T., Palumbo G. Electrodeposited nanocrystalline metals, alloys and composites, in Koch C.C. (Ed.), Nanostructured Materials, 2nd ed., Norwich, NY: William Andrew; 2007.   8 Erb U., Baglibanan M.R., Cheung C., Palumbo G., in Processing and Fabrication of Advanced Materials XII, Srivatsan T.S. and Varin R.A. (Eds.), Materials Park, OH: ASM International; 2004, p.301.   9 Palumbo G., McCrea J., Tomantschger K., Brooks, I., Jeong D., Panagiotopoulos K., Erb U., Wang A. Article containing a fine-grained metallic material and a polymeric material. US Patent # 7,553,553 B2. 10 Elia A., Robertson C.K., Hazel M., Palumbo G., Wang A., Giallonardo J.D., Limoges D. Metal Coated Structural Parts for Portable Electronic Devices. International Patent Application # WO 2009/04531 A1. 11 Emrich R., Wang A. Low Frequency Magnetic Shielding: An Integrated Solution, Interference Technology, EMC Directory & Design Guide 2009 (2009) 120. 12 Winfield I., Brooks I., Yokley E.M., Heard R., Palumbo G., Wire J Int 2009;42(4): 102–106. 13 Bement A., El-Rahaiby S.K., Campbell C.X. Bringing Advanced Materials to Market, A Supplemental Report to the 1995 DOD/DOE/NASA Workshops on the US Advanced Composites Industrial Base. Ceramics Information Analysis Center Report 8. April 1995. 14 Rodriguez A., Echeverría M., Ellman M., Perez N., Yuri K.V., Peng C.S., Berthou T., Wang Z., Ayerdi I., Savall J., Olaizola S.M. Microelectronic Engineering, 2009; 86(4–6): 937–940.

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15 Mankins J.C. Technology Readiness Levels: A White Paper. NASA, Office of Space Access and Technology, Advanced Concepts Office. April 6, 1995. 16 Committee on Accelerating Technology Transition, National Research Council, Accelerating Technology Transition: Bridging the Valley of Death for Materials and Processes in Defense Systems, Washington, DC: National Academies Press; 2004. 17 Musso C.S. Beating the System: Accelerating Commercialization of New Materials. PhD Thesis, Department of Technology, Management, and Policy at the Massachusetts Institute of Technology, February 2005. 18 Bawa R. Nanotechnology Law and Business 2004;1 (1). 19 Schafrik R. GE Aircraft Engines, Technology Transition in Aerospace Industry, briefing presented at the Workshop on Accelerating Technology Transition, National Research Council, Washington, DC, November 24, 2003. 20 Lux Research, The Wizards of Nanointermediates: Assessing Catalysts, Coatings, and Composites on the Lux Innovation Grid, September 2, 2009. 21 McMahon G., Erb U. Microstr. Sci 1989;17: 447. 22 McMahon G., Erb U. J Mat Sci Lett 1989;8: 865. 23 Gonzalez F., Brennenstuhl A.M., Palumbo G., Erb U., Lichtenberger P.C. Mat Sci Forum 1996;225–227: 831. 24 Palumbo G., Gonzalez F., Brennenstuhl A.M., Erb U., Shmayda W., Lichtenberger P.C. Nanostr Mater 1997;9: 737. 25 Palumbo G., Lichtenberger P.C., Gonzalez F., Brennenstuhl A.M. US patents 5,527,445 (1996); 5,516,415 (1996); 5,538,615 (1996). 26 Erb U., El-Sherik A.M. US Patent No. 5,352,266 (1994). 27 Erb U., El-Sherik A.M., Cheung C., Aus M.J. US Patent No. 5,433,797 (1995). 28 Mandich N.V., Snyder D.L. In Schlesinger M., Paunovic M. Modern Electroplating, (Eds.), Toronto: Wiley & Sons; 2000, p. 289. 29 Gawne D.T. J Vac Sci Tech 1985;A3(6): 2334. 30 DOD-STD-2182 (January 29, 1985). 31 MIL-P-19419A (August 21, 1989). 32 Legg K.O., Graham M., Chang P., Rastegar F., Gonzales A., Sartwell B. Surface and Coatings Technology 1996; 81: 99–105. 33 Navinsjek B., Panjan P., Milosjev I. Surface and Coatings Technology 1999;116–119: 476–487. 34 Brooman E.W. Metal Finishing 2004;102 (9): 75–82. 35 Brooman E.W. Metal Finishing 2004;102 (10): 42–54. 36 Legg K. Adoption of Thermal Spray Coatings as Hard Chrome Alternatives by the North American Aerospace Industry and Other Industry Sectors. Presentation at the 3rd Int Conf On Hard and Decorative Chromium for the 21st Century, Saint-Etienne, France (2001). 37 Rastegar F., Richardson D.E. Surface and Coatings Technology 1997;90(1–2): 156–163. 38 National Recommended Water Quality Criteria: 2002 (EPA-822-R-02–047), Environmental Protection Agency (2002). 39 UK Chromium Plating Regulations 1931 (amended in 1973), HMSO (1073). 40 Facchini D., McCrea J.L., Gonzalez F., Tomantschger K., Palumbo G. Products Finishing (Cincinnati) 2009;73(7): 14–18. 41 Facchini D., McCrea J.L., Gonzalez F., Palumbo G., Tomantschger K., Erb U. Galvanotechnik. 2009; 100(3): 523–534. 42 McCrea J.L. Surface Engineering 2010;26 (3): 149–152.

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43 Day M. Nanometal-Polymer Hybrid, in Advanced Materials & Processes 2008, April, pp. 25–27. 44 Herzer G. in Handbook of Magnetic Materials (Vol. 10, Chap 3 p. 415), Bushchow K.H.J. (ed.) Amsterdam: Elsevier Science; 1997. 45 McHenry M.E., Laughlin D.E. Acta mater 2000;48: 223–238. 46 Aus M.J. Ph. D. Thesis, Queen’s University, Kingston, Ontario, Canada (1999). 47 Aus M.J., Cheung C., Szpunar B., J Mat Sci Lett 1998;17: 1867. 48 Aus M.J., Szpunar B., Erb U., Palumbo G., Aust K.T. MRS Symp Proc 1993;318: 173. 49 Aus M.J., Spzunar B., El-Sherik A.M., Erb U., Palumbo G., Aust K.T. Scripta Metall 1992; 27: 1639. 50 Osaka T., Takai M., Hayashi K., Ohashi K., Saito M., Yamada K. Nature 1998;392: 796. 51 Inoue A., Makino A., Bitoh T. Magnetic Properties of Nanocrystalline Materials, in Koch C.C. (ed.), Nanostructured Materials, 2nd ed., Norwich, NY: William Andrew; 2007, pp 487–536. 52 Makino A., Bitoh T., Kojima A., Inoue A., Masumoto T. J Magn Magn Mater 2000;215– 216:288–292. 53 Petzold J. J Phys IV France 08 (1998) Pr2–767-Pr2–770. 54 Russell J.D. Advanced Materials & Processes 2007;165.6(4):29. 55 Gapper J. A cleverer way to build a Boeing, Financial Times, London (UK) (July 9, 2007) p. 11. 56 Cameron D. Spotlight: Boeing 787 Dreamliner – ‘Green’ plastic airliner takes off, Financial Times, London (UK) (July 2, 2007) p. 32. 57 Michels J. Aviation Week & Space Technology 2007;166(16): 36. 58 Kingsley-Jones M., Bicheno T. Flight International 2007; 118. 59 Black S. New metal coating to optimize composite tooling. High Performance Composites, May 2009, pp. 76–79. 60 McCrea J.L., Emrich R., Gonzalez F., Palumbo G. Nanotechnology Enabled Low Thermal Expansion Metal Coatings to Enhance the Durability of Composite Tooling. Proc 39th ISTC, Cincinnati, OH, Oct 29–Nov 1, 2007. 61 Nickel Electroforming: Processes and Applications. Copyright Inco Limited 1991. 62 Palumbo G., Davidson W.F., McCrea J.L., Tomantschger K. Brooks I. Limoges D. Panagiotopoulos K., Erb U. Sports Articles Formed Using Nanostructured Materials, US Patent Application, Pub. No.: US 2006/0160636 A1. 63 Source: Integran Technologies, Inc.

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22 Applying nanostructured steel sheets to automotive body structures Y. OKITSU and N. TSUJI, Honda R&D Co., Ltd., Japan Abstract: In this chapter, the results of studies on application of nanostructured steel sheets to automotive body structures are introduced. A new route to fabricating nanostructured/ultrafine ferritic microstructures without severe plastic deformation is presented. The preparation and evaluation of two kinds of steel sheets, Ultrafine-grained (UFG) ferrite-cementite (FC) steel and UFG multi-phase (MP) steel are also presented and discussed. The UFG-FC steel showed large strain rate sensitivity in flow stress, while the UFG-MP steel showed a good combination of high strength and large work hardening rate, which improved the dynamic collapse properties of hat columns. It is shown that UFG steels would help further weight reduction of automotive body structures. Key words: ultrafine grain, steel sheets, multi-phase, strain rate sensitivity, dynamic collapse.

22.1 Introduction In recent times, reducing the body weight of automobiles has been considered one of the important criteria in auto manufacturing for reducing CO 2 emissions as well as improving the fuel efficiency of automobiles. Steels have been the most popular and indispensable material for automotive body structures in the past, and recently in particular, various kinds of high-strength steels (HSS)1 have been developed and applied to the body structures, which has contributed to a weight reduction. In order to achieve further weight reduction, new HSS are required. As described in the next section, nanostructured or ultrafine-grained (UFG) steels are expected to become one of the new HSS.2 However, it is still difficult to apply the UFG steel sheets to automobile body parts. This is owing to the limited dimensions of the UFG steels fabricated by severe plastic deformation (SPD) processes such as equal-channel angular extrusion (ECAE),3 high-pressure torsion (HPT),4 and accumulative roll bonding (ARB),5–7 which require very high plastic strain. Recently the authors showed a new route to fabricate UFG steel sheets through conventional rolling and annealing procedures,8 which made it possible to overcome the dimensional problem, and evaluate the properties and performances required for automotive body structures systematically. Based on this processing route, UFG steel sheets with various microstructures such as ferrite-cementite (FC)8,9 and multi-phase (MP) structures10 were fabricated. In this chapter, future trends of automotive body engineering and demands for UFG steels are described first. Secondly, the new route to fabricate UFG steel 687 © Woodhead Publishing Limited, 2011

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sheets without SPD and the properties of the fabricated UFG-FC steel sheets are shown. Next, UFG-MP steel sheets developed in order to improve the work hardening rate of UFG microstructures are described. Finally, there is an illustration of the crash-worthiness of the UFG steel sheets, which is one of their important properties as body materials.

22.2 The potential demand for nanostructured steels for automotive body structures Nowadays, improving the fuel efficiency of automobiles is a very important subject, which comes from global demands for reducing CO 2 emissions. For this purpose, it is necessary not only to improve the fuel efficiency of the engines, but also to reduce body weight, rolling drag force, friction, etc. However, the actual body weight of automobiles has increased mainly due to the demands for improving the crash-worthiness of the body structures during a collision. For this reason, considerable efforts have been made to suppress any weight increase. The applications of HSS in automobiles have increased significantly since the 1990s.11 As a result, more than 50% of the body parts are made of HSS 12 in recent cars. Although low-density metals such as aluminium and magnesium are also applied, low-carbon steels are still widely used for manufacturing various kinds of cars due to their high cost performance. The ULSAB (UltraLight Steel Auto Body) project showed that a significant weight reduction could be achieved by applying AHSS (advanced high strength steels) and advanced manufacturing methods. A review of such projects is seen in the appendix to this chapter. In order to achieve further weight reductions by extending the application of HSS, new steels with new microstructures and superior properties have been widely studied.13 An example is high-Mn TWIP (twinning-induced plasticity) steels,14,15 which have austenite microstructures and a combination of superior tensile strength and elongation. This steel is classified as ‘second-generation AHSS’.2 A recent target, so-called ‘third-generation AHSS’,2 is steels with intermediate elongation between conventional HSS and TWIP steels but fewer alloy elements than the TWIP steels. Grain refinement down to submicrometer grain sizes is thought to be one of the important microstructural controlling methods that will contribute to third-generation AHSS.2 Up to now, the improvement of automotive steels has been discussed in terms of formability. However, in order to achieve further weight reduction, other points of view are being considered. Generally the parts in an automotive body structure are classified roughly into two groups having different functions. The one is the parts in crushable zones, i.e. the front and rear frame sections, which deform heavily in car collision and should absorb impact energy. The other is the parts making up the passengers’ cabin, which deform little and prevent the passengers from injury during a collision. Ultra high strength steels (UHSS) with tensile strength of over 1000 MPa are applied to the parts for making up the passengers’

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Applying nanostructured steel sheets to automotive body structures 689 cabin.16 However, if UHSS are applied to the parts in the crushable zones aiming for further weight reduction, other mechanical properties must be preferentially considered. For example, when UHSS are applied to the crushable parts, their deformation mode tends to become unstable, which reduces the efficiency of energy absorption.10 This is caused by the decreased work hardening rate of the material already highly strengthened.17 The authors10 have shown using labfabricated UFG-MP steel that a large work hardening rate (n-value) was effective in achieving a stable deformation in axial collapse. In the following sections, the practical results of evaluating microstructures, mechanical properties and crashworthiness using the fabricated UFG steel sheets are shown and discussed.

22.3 Fabricating nanostructured low-C steel sheets 22.3.1 A new route to fabricate nanostructured steel sheets without severe plastic deformation It has been already reported that UFG ferritic steels have superior properties such as high strength,18 high fracture toughness at around –190°C19 and high strain rate sensitivity in flow stress.20,21 Severe plastic deformation processes are generally applied in order to fabricate nanostructured or UFG steels. However they do not seem to adapt to the conventional mass production routes for steels. In this section, firstly, the concept of the new route to fabricating UFG steel sheets without SPD is described. The distinguishing feature of the process is conventional rolling of a duplex microstructure composed of soft ferrite and hard martensite. The key factor in the process is strain distribution between soft and hard phases. When such a duplex microstructure is deformed, a larger strain is introduced in the soft phase (ferrite), while a strain that is not so heavy but sufficient for final microstructural refinement is introduced in the hard phase (martensite). As a result, a number of recrystallization nuclei form uniformly from both ferrite and martensite, and uniform UFG microstructures are obtained after subsequent annealing. Table 22.1 shows the chemical composition of the UFG-FC steel studied. This steel is made by adding Nb and B to a low C steel. Figure 22.1 shows schematic illustration describing the fabricating process and conditions. The fabricating process consists of conventional hot-rolling, cold-rolling and annealing as indicated in Fig. 22.1. An ingot was hot-rolled to a thickness of 6.8 mm at austenite region, air-cooled to 540°C, which corresponded to the intercritical region of ferrite and austenite, and water-cooled to room temperature for obtaining a duplex microstructure of ferrite and martensite. The hot-rolled sheets were cold-rolled at room temperature with lubricant. Specimens having various total cold-rolling reductions from 85 to 94% were prepared. The cold-rolled sheets were annealed at various temperatures ranging from 525 to 700°C for 120 seconds in a salt bath. Annealed sheets that

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Table 22.1  Chemical composition (mass%) of the UFG-FC steel C

Si

Mn

P

S

Al

Nb

B

N

0.10

0.01

2.00

0.002

0.0013

0.035

0.022

0.0015

0.0007

22.1  Schematic illustration describing the fabricating conditions of the UFG-FC steel.

were 150 mm wide and 0.4 to 1.0 mm thick were obtained. Microstructural observations were carried out by optical microscopy and scanning electron microscopy (SEM). An optical micrograph (OM) of the hot-rolled steel sheet observed from the transverse direction (TD) of the sheet is shown in Fig. 22.2. The hot-rolled sheet showed a duplex microstructure composed of a ferrite matrix (bright region) and martensite islands (dark region). The mean intersect lengths along the normal direction (ND) of the both regions, measured using the OM, were 5.55 µm in the ferrite and 2.46 µm in the martensite. The area of martensite was 42% of the whole. Transmission electron microscopy (TEM) observation has confirmed that the martensite present was ‘lath-martensite’ including a high density of dislocations. Cementite particles were not observed in the as-quenched martensite. Figures 22.3 (a), 22.3 (d) and 22.3 (g) show SEM microstructures of the specimens cold-rolled to reductions of 85%, 91% and 94% in thickness, respectively. The ferrite matrix (dark gray region) exhibited a wavy microstructure elongated roughly to the rolling direction (RD) and bent along the martensite islands (light gray region). It was indicated that complex plastic flow occurred and higher strain was introduced in the softer ferrite matrix owing to the existence of hard martensite phase. TEM observation8 of the 91% cold-rolled specimen confirmed a fine lamellar structure with a mean spacing of 0.14 µm in the ferrite region. It was also confirmed by selected area diffraction that this region contained various crystal

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22.2  Optical micrograph of the hot-rolled sheet of the UFG-FC steel. Observed from TD.

orientations.8 It is noteworthy that the fine structure including large misorientations, which had been found in SPD-processed materials, already existed at the coldrolled state in spite of the relatively low plastic strain of 2.8. It is well known that the hard second particles increase the rate of formation of high angle grain boundaries (HAGB) in the matrix through inhomogeneous deformation in twophase metals and alloys.22 The large local misorientation is caused by local lattice rotations in the vicinity of the hard particles. In addition, the shear strain should be closely related to the significant grain refinement of ferrite matrix. Kamikawa et al.23 have reported that redundant shear strain introduced at sheet subsurface regions owing to high friction in rolling accelerates the microstructure refinement in the ARB of IF (interstitial-free) steel. The wavy-shaped ferrite and diamondshaped martensite in Fig. 22.3 suggested that large plastic strains including shear strain components were introduced to the ferrite grains. On the other hand, the martensite islands were also deformed to some extent in the cold-rolling and showed diamond shapes. Table 22.2 summarizes the coldrolling reduction and the mean thickness ratio, t/t0, of the martensite islands in the microstructures measured using the OM of the hot-rolled sheet and the SEM micrograph of the cold-rolled specimens. Here, t and t0 are the mean intersect lengths of the martensite islands along ND after and before the cold-rolling, respectively. The reduction of the martensite islands was much smaller than the reduction of the specimen, which indicated that a larger strain was introduced to the ferrite grains. By TEM analysis in the © Woodhead Publishing Limited, 2011

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22.3  Scanning election microscope (SEM) microstructures of (a) (d) (g) cold-rolled specimen, (b) (e) (h) specimens annealed at 600°C after cold-rolling and (c) (f) (i) specimens annealed at 650°C after cold-rolling. The cold-rolling reductions are (a) (b) (c) 85%, (d) (e) (f) 91% and (g) (h) (i) 94%. Observed from TD. Table 22.2  Cold-rolling reduction and mean thickness ratio of the specimens and the martensite islands of the cold-rolled UFG-FC specimens Cold-rolling reduction t/t0 of the specimen of the specimen (%)

Mean t/t0 of the martensite islands

85 91 94

0.47 0.32 0.27

0.15 0.09 0.06

previous study,8 large local misorientations in the deformed martensite regions were also confirmed in spite of the smaller strain in martensite. Ueji et al.24 have reported that 50% cold-rolled low-carbon martensite exhibited fine lamellar structure involving large misorientations, which was equivalent to the microstructure in SPD processed steels. This is thought to be attributed to the complex and fine microstructure of the as-transformed martensite, also involving a high density of dislocations. They also showed equiaxed UFG microstructure

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Applying nanostructured steel sheets to automotive body structures 693 after annealing of the 50% cold-rolled specimen with a single phase of martensite. It can be concluded therefore that the strain applied to martensite in the present study was not very large but probably enough to introduce large local misorientations and to form UFG microstructure through subsequent annealing. Figure 22.3 (b), 22.3 (e) and 22.3 (h) show the microstructures of the coldrolled sheets after annealing at 600°C. In the 85% cold-rolled and annealed specimen (Fig. 22.3 (b)), both equiaxed fine ferrite grains and elongated ferrite grains located in an arc-like row (in the lower part of Fig. 22.3 (b)) were observed. The fine equiaxed ferrite grains seemed to be formed by continuous coarsening of the finely subdivided regions in the cold-rolled microstructure together with recovery.8 It was difficult to distinguish clearly which area in Fig. 22.3 (b) was originally ferrite or martensite, but according to the supposed mechanism discussed before, the ultrafine ferrite grains could originate from both ferrite and martensite. On the other hand, some coarse grains in an arc-like row seen were probably formed mainly by recovery of the ferrite regions such as the elongated and bent ferrite seen in the upper and left part of Fig. 22.3 (a). Those ferrite regions in the cold-rolled microstructure seem to be deformed to a smaller plastic strain because of the relatively low density of surrounding martensite islands. Also the fact that the coarse ferrite grains in the annealed microstructure contained few cementite particles suggests that they were originally ferrite. When the coldrolling reduction was more than 91%, the specimens were filled mostly with equiaxed ultrafine ferrite grains (Fig. 22.3 (e) and 22.3 (h)). This seemed to be because the spacing of the martensite islands as seen in Fig. 22.3 (d) and 22.3 (g) decreased due to the larger cold-rolling reductions. When the specimens were annealed at 650°C, significant grain growth occurred in all the specimens. Fine cementite particles dispersed in ferrite grains were also observed in all annealed specimens in Fig. 22.3. Figure 22.4 shows the relationship between the annealing temperature and mean ferrite grain size measured on the SEM micrographs by the mean intersection method along the RD and ND. The larger the cold-rolling reduction was, the smaller the obtained ferrite grain size became. The sizes of the equiaxed ultrafine ferrite grains shown in Fig. 22.3 (b), 22.3 (e) and 22.3 (h) were not so different. However, due to the existence of the elongated and arc-like ferrite grains the average ferrite grain size in the specimen 85% cold-rolled and annealed at 600°C (Fig. 22.3 (b)) was slightly larger than that in other specimens having larger cold-rolling reductions (Fig. 22.3 (e) and 22.3 (h)). On the other hand, the effect of the annealing temperature on the ferrite grain size was more significant as shown in Fig. 22.4. The 85% cold-rolled specimens annealed at 600 and 625°C contained some recovered ferrite grains as shown in Fig. 22.3 (b). The minimum grain size of the homogeneous grain structures obtained was 0.43 µm in the specimen 94% cold-rolled and then annealed at 600°C (Fig. 22.3 (h)). The UFG ferrite formed throughout the specimens by large cold-rolling reductions followed by low annealing temperatures. In order to clarify the process

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22.4  The relationship of annealing temperatures and mean ferrite grain sizes measured by the mean intersect method of the UFG-FC steels.

22.5  Scanning electron microscopy microstructure of the UFG-FC steel that was 94% cold-rolled and annealed at 525°C.

of fine-grain formation, Fig. 22.5 shows the microstructure of a specimen that was 94% cold-rolled and subsequently annealed at 525°C for 120 seconds. The dotted lines roughly delineate the former martensite islands that had already changed to fine-grained ferrite and cementite. In the ferrite matrix, UFG

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Applying nanostructured steel sheets to automotive body structures 695 ferrite also formed along the wavy microstructure in the vicinity of the former martensite. Finer equiaxed grains of ferrite were seen around the former martensite islands. The result suggests that a larger strain was introduced into the ferrite/ martensite interface regions through cold-rolling. Therefore, in order to reduce the cold-rolling reductions required, it seems to be effective to decrease the spacing of martensite islands in the starting microstructure before cold-rolling.

22.3.2 The mechanical properties of nanostructured ferrite-cementite steel sheets The tensile properties of nanostructured ferrite-cementite steels were investigated using a high-speed servo-hydraulic material test system produced by Saginomiya Inc. equipped with a special load-sensing block.25,26 With this machine, stress– strain (s–s) curves at a wide range of strain rates from quasi-static to dynamic deformations can be obtained. Figure 22.6 shows the appearance of the prepared tensile specimen having a gauge length of 6mm and a width of 2mm.

22.6  Schematic drawing of the test piece for dynamic and quasi-static tensile tests.

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The tensile direction was parallel to RD. Tensile tests were operated at various strain rates ranging from 10–2s–1 to 103s–1 at room temperature. Total elongation of the specimens was measured from the difference in the gage length before and after testing. Fabricating conditions, microstructures and quasi-static mechanical properties measured at a strain rate of 10–2s–1 are summarized in Table 22.3. UFG-FC A, B, C and FCM specimens were prepared by 91% cold-rolling of the same hot-rolled sheet as shown in Fig. 22.2 and subsequent annealing at 620, 635, 670 and 700°C for 120 seconds, respectively. The mean ferrite grain sizes indicated in Table 22.3 were calculated by the EBSD (electron backscatter diffraction) data measured on the TD sections. The UFG-FC steels showed microstructures of ultrafine ferrite and cementite, while the FCM specimen showed a microstructure composed of ferrite, cementite and martensite. The FCM specimen contained about 14% of martensite in the microstructure. The Ac1 transformation temperatures of the UFG-FC steel measured by a dilatometer was approximately 700°C, so that the FCM specimen contained both ferrite and austenite during the annealing at 700°C and the austenite transformed to martensite during the subsequent water-cooling. Figure 22.7 shows s–s curves at strain rates of 10–2, 102 and 103 s–1. Figures 22.7 (a), 22.7 (b), 22.7 (c) and 22.7 (d) correspond to the test results of the UFG-FC steels A, B, C and the FCM steel listed in Table 22.3. Both UFG-FC and FCM steels showed the yield drop phenomenon. The flow stress increased whereas the uniform elongation significantly decreased as the ferrite grain size in the UFG-FC specimens decreased (Figs. 22.7 (a), 22.7 (b) and 22.7 (c)). The same behavior has been reported for the UFG IF steel sheets prepared by ARB and the annealing process.18 On the other hand, as shown in Fig. 22.7 (d), the work hardening increased when martensite was introduced in the microstructure. The flow stress significantly increased when the strain rate increased in the UFG-FC steels. In order to investigate the strain rate dependence of the flow

Table 22.3  Microstructures and quasi-static tensile properties of the fabricated UFG steels and FCM steel for tensile tests

Annealing Microstructure Mean ferrite 0.2% offset Tensile Total temperature grain size stress strength) elongation (°C) (µm) (MPa) (MPa (%)

UFG-FC A 620 UFG-FC B 635 UFG-FC C 670 FCM 700

F-C F-C F-C F-C-M

0.49 0.62 0.95 1.0

966 816 636 515

Note: F: ferrite, C: cementite, M: martensite.

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966 820 638 753

8.4 11.3 23.4 28.0

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22.7  Nominal stress–strain curves of UFG-FC steel specimens 91% cold-rolled and annealed at (a) 625°C, (b) 640°C, (c) 670°C and (d) 700°C.

stress, the difference in tensile flow stress at 5% nominal strain between the strain rates of 103 s–1 and 10–2 s–1, ∆σ, was evaluated. Figure 22.8 shows the relationship between the ∆σ and the quasi-static flow stress of the fabricated UFG-FC steels and other conventional steels referred from previous studies (some were evaluated at slightly different strains). The present UFG-FC includes additional data not listed in Table 22.3. The ∆σ of the UFG-FC steels with sub-micron grain sizes were as large as that of the mild steels27,28 with a single ferrite phase. However, the conventional high-strength steels (HSS)27–29 showed a lower ∆σ. The FCM specimen fabricated in this study had a similar ∆σ value to the conventional HSS. In Fig. 22.8 the data of the UFG-FC steels reported by Tsuchida et al.21 are plotted as well. The ∆σ values by Tsuchida et al. were close to that of the present work. This result indicates that the grain refinement of FC microstructure to sub-micron size did not decrease the ∆σ. It is expected that the large ∆σ value promotes high dynamic energy absorption due to the large dynamic flow stress. Generally in most metals and alloys the flow stress increases with an increasing strain rate.30–33 This is explained in terms of the thermally activated process of the dislocation motion against short-range obstacles such as Peierls potential. The higher the strain rate, the higher the external stress required for the dislocation motion. During the deformation, the thermal vibration of iron atoms can help the

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22.8  Relationship of the difference in flow stress, ∆σ and quasi-static flow stress of the fabricated UFG-FC steels and other steels in references.

dislocations to overcome the obstacles. As the strain rate is increased, the assist by the thermal vibration will be less effective because there is less time available to overcome the obstacles. Therefore, at higher strain rates, the required external stress for dislocation motion will be increased. The component of flow stress that is related to the thermal activation process is called thermal stress, while the other component, which is independent of the strain rate and temperature, is called athermal stress. When alloy elements are added, the strain rate sensitivity decreases.33 Among commercial steels, mild steels show the highest strain rate sensitivity in flow stress and it decreases gradually when the steels are strengthened by alloy addition (solution hardening) or the introduction of second phases (precipitation hardening).27,28,34,35 This is understood in terms of the increase of the activation volume in the thermally activated process of dislocation motion owing to alloy elements, precipitates and second phases.36 On the other hand, it has been shown that the UFG-FC microstructure does not decrease the strain rate sensitivity in flow stress.9,20,21 It means that ultra grain refinement influenced mainly the athermal component of flow stress rather than the thermal component.

22.3.3 Further requirements for nanostructured ferrite-cementite steel sheets In the previous section, it was shown that ultra grain refinement increased strength significantly while keeping a large strain rate sensitivity in flow stress. The strain rates of the material through the dynamic axial collapse of square columns exceed 102 s–1,37 therefore the dynamic strength of the material is

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Applying nanostructured steel sheets to automotive body structures 699 important for automotive body parts in the crushable zones. Dynamic collapse tests of hat columns confirmed good performance of the fabricated UFG-FC steel sheets. However, ultra grain refinement reduced the uniform elongation of the steel (Fig. 22.7). This is due to the insufficient work hardening rate in the UFG single-phase microstructures.38,39 Based on the plastic instability condition in tensile tests, the highly strengthened material requires a greater work hardening rate to keep the uniform deformation. The work hardening rate of the present UFG-FC steels seemed insufficient, resulting in early necking (early plastic instability) in the tensile test. Considering the stamping process of the automotive body parts, adequate uniform elongation is required. Therefore in order to apply UFG steels widely to automotive body parts, the uniform elongation should be improved. In order to meet this demand, the best solution seems to be an introduction of hard second phases to the UFG microstructure.40 Generally duplex microstructures, for example dual-phase (DP) or multi-phase (MP) microstructures, show improved uniform elongation by the enhanced work hardening rate. Also in the case of fine-grained steels, a calculation using the ‘secant method’41 has shown that significant improvement could be expected by an introduction of a hard phase. In the next section, the concept of improving the uniform elongation in the UFG steels is shown, and the test results using the fabricated UFG-MP steels are described and discussed.

22.4 Improving elongation in nanostructured steel sheets 22.4.1 Introduction of hard second phases to nanostructured ferritic microstructures In order to improve the uniform elongation of nanostructured or UFG ferritic steels, one of the potential ways is to introduce of hard phases.40 A recent study on UFG-DP steels using ECAP and subsequent intercritical annealing42 has shown that the UFG-DP microstructure with a mean ferrite grain size of 0.8 to 1.2 µm improved tensile strength without loss of uniform elongation compared with a coarse grained DP steel. In the present work, as shown in Table 22.3, introducing martensite by increasing the final annealing temperature improved both the tensile strength and elongation. However, the obtained tensile strength was not so high because the ferrite grain size was around 1 µm, owing to the grain growth. The potential competitor of the UFG steels is modern UHSS, which has higher tensile strengths than 1000 MPa.1,13 In this section, we show the concept of introducing hard second phases while keeping the ultrafine ferrite matrix. In order to avoid grain growth, the transformation temperature of the steel was decreased by Mn addition, which could decrease the intercritical annealing temperatures. Table 22.4 shows the chemical compositions of the steels used in this section.

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Table 22.4  Chemical composition (mass%) of the UFG-MP steels Steel

C

Si

Mn

P

S

Al

Nb

N

UFG-MP1

0.21

0.01

3.0

0.002

0.001

0.022

0.046

0.0013

UFG-MP2

0.15

1.42

4.0

0.001

0.001

0.026

0.054

0.0021

22.9  Schematic illustration describing the fabricating conditions of (a) the UFG-MP1 steel and (b) the UFG-MP2 steel.

The Ac1 transformation temperatures of the UFG-MP1 and UFG-MP2 steels measured by a dilatometer were 690 and 650°C, respectively. The transformation temperatures were significantly lower than that of the UFG-FC steel (approximately 700°C in the UFG-FC steel). The fabricating process of the UFG-MP1 and UFG-MP2 steels are shown in Figs. 22.9 (a) and 22.9 (b), respectively. For the UFG-MP1 steel, after hot-rolling to a thickness of 6 mm, the sheet was immediately cooled to room temperature by water, followed by intercritical annealing at 730°C for 90 minutes in order to obtain a duplex microstructure of ferrite and martensite. After mechanical grinding, the hot-rolled sheets of the UFG-MP1 steel were coldrolled from 5 to 1.5 mm in thickness at room temperature. The total reduction through the cold rolling was 70%. The cold-rolled sheets were annealed for 120 seconds at 675 or 700°C followed by water-cooling to room temperature. The annealing temperature of 700°C corresponded to the intercritical region of ferrite

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Applying nanostructured steel sheets to automotive body structures 701 and austenite. On the other hand, as shown in Fig. 22.9 (b), the UFG-MP2 steel was air-cooled to room temperature after hot-rolling to a thickness of 5 mm. The air-cooling rate was sufficient to obtain a complex structure composed of soft ferrite and hard phases in the UFG-MP2 steel due to the higher Mn content. The hot-rolled sheets of the UFG-MP2 steel were heated at 500°C for 1 hour in order to reduce the hardness, and then rolled from 3.5 to 1.2 mm in thickness without reheating. The total reduction through the warm-rolling was 66%. The warm-rolled sheets were annealed for 120 seconds at intercritical temperatures of 685 or 700°C, followed by subsequent annealing at 400°C for 300 seconds. The austenite amounts of the specimens after the final annealing were estimated by X-ray diffractometry using Co-Kα radiation. The austenite volume fraction was calculated using the integrated intensities of (110)α, (200)α, (211)α, (111)γ, (200)γ and (220) γ diffraction peaks. Fig. 22.10 (a) shows the OM after the intercritical annealing of the hot-rolled sheet of the UFG-MP1 steel. A fine duplex microstructure of ferrite (light gray regions) and martensite (dark gray regions) was observed. The mean intersect lengths of each phase in the hotrolled microstructure, t0, were measured using the OM of the hot-rolled sheet shown in Fig. 22.10 (a). As summarized in Table 22.5, the t0 values along ND of the ferrite and martensite regions were 1.65 and 1.73 µm, respectively. The area of ferrite region in the hot-rolled microstructure measured by point counting method was 30%. Figure 22.10 (b) shows the SEM microstructure of the specimen after cold-rolling. It was shown that the ferrite grains (dark regions) were elongated and had wavy shapes, which meant that large and complex plastic deformation was introduced in the ferrite. The martensite (gray regions) was also deformed roughly along the RD. The features are the same as those in the cold-rolled microstructure of the UFG-FC steels shown in Fig. 22.3.

22.10  (a) Optical micrograph of the hot-rolled and annealed sheet (before the cold-rolling) of the UFG-MP1 steel observed from TD. (b) Scanning electron microscopy microstructure of the cold-rolled sheet of the UFG-MP1 steel observed from TD.

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Table 22.5  Mean intersect lengths before the cold-rolling (t0), after the cold-rolling (t) and the mean thickness ratios (t/t0) of both ferrite and martensite regions in the UFG-MP1 steel Phase

Mean intersect length before cold-rolling, t0

Mean intersect length after cold-rolling, t

Mean thickness ratio, t/t0

Ferrite

1.65

0.18

0.11

Martensite

1.73

0.52

0.30

Table 22.5 also summarizes the mean intersect lengths after the cold-rolling (t) and the mean thickness ratios (t/t0) of both the ferrite and martensite regions. The t values were measured using the SEM micrograph of the cold-rolled specimen shown in Fig. 22.10 (b). The t/t0 of the martensite regions was approximately 0.3, which was close to the t/t0 of the specimen. On the other hand, the t/t0 value of 0.11 in the ferrite regions was much smaller than that of the specimen. This result indicates that the plastic strain concentrated to the ferrite region through cold rolling. Figure 22.11 shows SEM microstructures after the final annealing of the cold/ warm-rolled sheets of the UFG-MP1 (Fig. 22.11 (a) and 22.11 (b)) and UFG-MP2 (Fig. 22.11 (c) and 22.11 (d)). The intercritical annealing temperatures of the specimens in Fig. 22.11 (a), (b), (c) and (d) are 675, 700, 685 and 700°C, respectively. In both steels, the volume fraction of the second phases (the light gray regions in Fig. 22.11) increased with the annealing temperature. Here, ‘second phases’ means austenite, bainite and martensite which appear as light gray islands in the SEM micrographs. Table 22.6 summarizes the ferrite grain size, the area share of the second phases in the SEM micrograph and the retained austenite content measured by X-ray diffraction. The rest of the second phases should be bainite and/or martensite as observed in low-C TRIP (transformation-induced plasticity) steels;43,44 however, those phases were not distinguished clearly in the SEM micrograph. It was shown that a considerable amount of hard second phases were introduced by keeping the ferrite grain size less than 1 µm, owing to the decreased Ac1 transformation temperatures in the UFG-MP steels with relatively high Mn content. Also it is noteworthy that UFG microstructures were obtained in spite of the relatively lower cold-rolling reductions (70% in the UFG-MP1 steel). As summarized in Table 22.5, in the UFG-MP1 steel the mean intersect length of the ferrite region before the coldrolling was 1.65 mm, which was much smaller than that of the UFG-FC steel (5.55 µm). It seemed that the reduction of 70% was sufficient to concentrate the plastic strain to the ferrite regions due to the small intersect length. This result indicates that the grain refinement of the starting microstructure is effective in reducing the required cold-rolling reduction for the formation of UFG microstructures through the subsequent annealing.

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Applying nanostructured steel sheets to automotive body structures 703

22.11  SEM microstructures of the fabricated UFG-MP steels. (a) UFG-MP1 steel annealed at 675°C, (b) UFG-MP1 steel annealed at 700°C, (c) UFG-MP2 steel annealed at 685°C and (d) UFG-MP2 steel annealed at 700°C. Observed from TD.

Table 22.6  Annealing temperature and microstructural parameters of the fabricated UFG-MP steels Steel

Annealing temperature (°C)

Mean ferrite grain size (µm)

Fraction of second phases (%)

Austenite fraction (%)

UFG-MP1 UFG-MP1 UFG-MP2 UFG-MP2

675 700 685 700

0.58 0.51 0.49 0.41

17 36 44 50

13 16 12 22

22.4.2 Mechanical properties of nanostructured multi-phase steel sheets Tensile properties were investigated at a nominal strain rate of 10–2 s–1 at room temperature using the specimens shown in Fig. 22.6. The tensile direction was parallel to RD. Figure 22.12 shows s–s curves of the fabricated UFG-MP steels with various annealing temperatures. Yield drop with Lüders elongation was observed in all the specimens.

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22.12  Nominal stress–strain curves of (a) the UFG-MP1 steel and (b) the UFG-MP2 steel corresponding to Fig. 24.11. The temperatures in the figure indicate the intercritical annealing temperatures.

However, significant work hardening was observed after the Lüders elongation, except for the UFG-MP1 steel annealed at 675°C, which resulted in a good combination of high strength and large uniform elongation. The mechanical properties are summarized in Table 22.7. Here, the n-values, which represent the work hardening rate of the steels, were calculated assuming that s–s curves at a strain range of 0.05 to 0.1 could be approximated by:

[22.1]

where σ, K and n are true stress, a constant, and a work hardening component (n-value), respectively.

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Applying nanostructured steel sheets to automotive body structures 705 Table 22.7  Annealing temperature, thickness and quasi-static mechanical properties of the fabricated UFG-MP steels Steel Annealing Thickness 0.2% Tensile n-value Uniform Total temperature (mm) offset strength (5–10%) elongation elongation (°C) stress (MPa) (%) (%) (MPa) UFG-MP1 UFG-MP1 UFG-MP2 UFG-MP2

675 700 685 700

1.5 937 1.5 719 1.2 1034 1.2   840

937 1050 1155 1380

0.056 0.324 0.205 0.321

0.6 13 17 13

32 25 28 22

The n-values of the fabricated steels were calculated by:

[22.2]

where σ2 and σ1 are true stress at plastic strains of ε2 and ε1, respectively. In this case plastic tensile strains (true strain) of 0.05 and 0.1 were chosen. The UFG-MP steels, except for the UFG-MP1 steel annealed at 675°C, had fairly larger n-value than recent UHSS.1,45,46 The significant work hardening of the UFG-MP steels seemed to be caused by strain-induced martensitic transformation of the retained austenite, since the austenite fraction after 15% tensile strain was less than 1% in the UFG-MP1 steel annealed at 700°C. In fact, it has been reported that low-carbon steels containing 5 to 7% Mn show good a combination of strength and elongation47–51. In Merwin48, a multi-phase microstructure of the 7% Mn steel composed of fine ferrite and hard phases has been shown. The concept of this microstructure is close to that of the UFG-MP steels in the present study. However, the strength–elongation balance in the present UFG-MP steel containing 4% Mn was better than that of the 5% Mn steels in the previous studies.47–50 The difference seems to be caused by the difference of the annealing conditions. In the present annealing process shown in Fig. 22.9 (b), the heating rate was high (10 to 25°C s–1) and the holding time at the intercritical region was short (120 seconds), due to the heating with salt bath. On the other hand, in the previous studies47–49 ‘batch-annealing’ was employed. For example, the heating rate was 0.16°C s–1 and the holding time was 1200 seconds.50 The rapid heating and short holding time in the present study were effective to suppress the grain growth, which seemed to improve the combination of strength and elongation. In addition, the dynamic tensile tests were carried out also for the UFG-MP steels using the same equipment described in Section 22.3.2. The ∆σ value (the difference in tensile flow stress at 5% nominal strain between the strain rates of 103 s–1 and 10–2 s–1) was around 100 MPa in the UFG-MP1 steel. This value

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was close to that in the conventional HSS and not so large compared with that in the UFG-FC steels. In the UFG microstructure, the strain rate sensitivity in flow stress decreased by the introduction of hard second phases as well as in the conventional coarse-grained microstructure. This result suggests that the thermal activation process of dislocation motion was controlled mainly by the hard second phases as described in Section 22.3.2, even in the UFG microstructure.

22.5 Crash-worthiness of nanostructured steel sheets In order to evaluate the crash-worthiness for automotive body parts, dynamic collapse tests46 have been widely employed. In this study, dynamic axial collapse tests by using hat rectangular columns were carried out. Figure 22.13 shows the cross-section of the hat column, which is composed of a hat-shape part and a flat back plate. The hat-shape part, which was prepared by bending the steel sheet with a radius of 5 mm, was set with a back plate and then spot-welded at the center of the flanges. The same material was used for both the hat part and the back plate. The pitch of the spot-welding was 40 mm. Figure 22.14 shows a schematic illustration of the dynamic collapse test. A free-fall type collapse test machine was employed. A 110 kg weight was dropped from 11 m and hit the top end of the hat column fixed vertically on a steel plate by arc-welding. The weight displacement was measured by a laser-type displacement sensor, and the deformation load was measured by a load-cell set under the hat column. Two steel pipes were set beside the hat column in order to stop the falling weight at a collapse displacement of 160 mm. Two types of the UFG-MP steels, the UFG-MP1 and the UFG-MP2, were evaluated in the dynamic collapse tests. The chemical compositions of both steels

22.13  Schematic drawing of the cross-section of the hat column.

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Applying nanostructured steel sheets to automotive body structures 707

22.14  Appearance of the hat column for the dynamic collapse test.

were the same as those shown in Table.22.4 The process was basically the same as that shown in Fig. 22.9. The fabricating conditions of the steels are shown in Table 22.8. The FT, Ts and TOA in Table 22.8 mean the temperature after the hot-rolling, the temperature of the intercritical annealing and the holding temperature after the intercritical annealing, respectively. The CR and WR mean cold-rolling and warm-rolling, respectively. In warm-rolling, the hot-rolled sheets were heated at 500°C for 1 hour and then rolled to 1.2 mm in thickness without reheating. They are indicated in Fig. 22.9. In the UFG-MP1 steel, the intercritical annealing after the hot-rolling was replaced by direct air-cooling, and the thickness of the specimen after the cold-rolling was reduced to 1.2 mm. The UFG-MP2 specimens were prepared in almost the same conditions as those shown in Fig. 22.9 (b) except for the intercritical annealing temperature. For comparison, a commercially

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Table 22.8  Fabricating conditions of the UFG-MP steels used for axial collapse tests. The meanings of FT, TS, and TOA are the same as in Fig. 22.9 Steel FT Cooling CR/WR (°C) after HR

Thickness of CR/WRed sheet (mm)

CR/WR TS (°C) reduction (%)

TOA (°C)

UFG-MP1 UFG-MP2

1.2 1.2

76 66

– 400

780 840

AC AC

CR WR

700 690

Note: HR: hot-rolling, WQ: water-cooling, AC: air-cooling, CR: cold-rolling, WR: warm-rolling.

22.15  Quasi-static s–s curves of the steels evaluated in the dynamic collapse tests. The black line, the gray line and the dotted line represent the UFG-MP1, UFG-MP2 and DP steels. JIS No.5 specimens were used.

available DP steel sheet was also tested. Figure 22.15 shows quasi-static s–s curves of the evaluated steels obtained using JIS No. 5 specimens with a gauge length of 50 mm and a gauge width of 25 mm, of which the direction was parallel to the RD. The UFG-MP1 and MP2 steels showed steady work hardening up to tensile strains of 16–17%, while it saturated at the early stage of tensile deformation in the DP steel. Table 22.9 summarizes the mechanical properties of the steels. All steels had a tensile strength higher than 1000 MPa; however, the n-values in the UFG-MP steels were significantly larger than those of the DP steel. Figure 22.16 shows the appearance of deformed columns following dynamic collapse tests. The columns of UFG-MP steel were deformed in a compactmode,52,53 which means a stable deformation through the formation of a series of continuous folds like an accordion.

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Applying nanostructured steel sheets to automotive body structures 709 Table 22.9  Quasi-static tensile properties of UFG-MP steels and DP steel used for axial collapse tests. JIS No. 5 specimens were used Steel Thickness (mm)

0.2% offset Tensile n-value stress strength (5–10%) (MPa) (MPa)

UFG-MP1 UFG-MP2 DP

453 972 747

1.2 1.2 1.2

1005 1088 1064

Uniform Total elongation elongation (%) (%)

0.244 17 0.284 16 0.068   8

22 21 14

22.16  Photographs of the hat columns after dynamic collapse tests. (a) The UFG-MP1 steel, (b) the UFG-MP2 steel and (c) the DP steel.

This is the ideal deformation mode in the axial collapse for impact energy absorption. On the other hand, the column made of the DP steel did not form compact buckling but fell down due to the moment of rotation generated by the nondeformed straight region, and buckling near the bottom end of the column. Also fracture at the hat wall was observed. This is called ‘non-compact’52,53 mode, which means an unstable deformation through the formation-retaining straight regions in the column walls. The change in deformation mode from compact to non-compact, which reduces the efficiency of energy absorption, is caused by the decreased work hardening rate of the material highly strengthened.16,17 Commercially available UHSS generally has a low work hardening rate (n-value)45,46 because it has more hard phases such as martensite in the microstructure. Uenishi et al.17 showed by FEM (finite element model) simulation that a desirable compact-mode deformation of hat columns during axial collapse could be promoted by improving the work

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hardening rate of the material. The authors10 confirmed by FEM simulation that the high n-value promoted continuous strain distribution between buckling regions, which resulted in a continuous folding (compact mode), while strain concentration in the buckling areas was significant and resulted in non-compact folding in a material with low n-value. It was shown that the improved work hardening rate promoted the compact mode in the axial collapse. Figure 22.17 (a) shows the load-displacement curves of the two columns, made of the UFG-MP2 steel and the DP steel. In the case of these thin wall columns, the maximum load corresponds to the first peak load at the start of buckling. In both steels the deformation loads were almost

22.17  (a) Load-displacement curves and (b) absorbed energydisplacement curves obtained by dynamic collapse tests. Bold black lines represent the UFG-MP2 steel and narrow gray lines represent the DP steel.

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Applying nanostructured steel sheets to automotive body structures 711 Table 22.10  Axial collapse properties of UFG-MP steels and DP steel Steel Maximum load Average load Average (kN) (10–150 mm) load/maximum (kN) load

Absorbed energy (0–150 mm) (kJ)

UFG-MP1 UFG-MP2 DP

7.73 8.60 6.86

219 223 250

49.1 55.1 42.0

0.22 0.25 0.17

the same until the collapse displacement of 100 mm; however, the load dropped in the DP steel after displacement of about 100 mm. On the other hand, the deformation load of the UFG-MP2 column kept the same level until displacement of 160 mm. It was confirmed by the high-speed camera observation that the load drop in the DP column corresponded to the onset of the decline of the column. As a result, as shown in Fig. 22.17 (b), the absorbed energy saturated at the displacement of 100 mm in the DP steel. On the other hand, in the column of UFG-MP2 steel the absorbed energy increased continuously until displacement of 160 mm. This continuous energy absorption increment of UFG-MP2 steel is favorable for the front and rear frames in automotive body structures that are deformed along the longitudinal direction in a collision. Table 22.10 summarizes the results of the dynamic collapse tests. The maximum load of the DP column was the largest due to its highest yield strength. However, the average load and absorbed energy in the UFG-MP steels were fairly larger than those in DP steel. This is because of the steady deformation load brought about by an ideal compact-mode deformation in the UFG-MP steels. The ratio of the average deformation load to the maxim load was greater in the UFG-MP steels, which was also favorable in the axial collapse. The UFG-MP1 specimen for the collapse test exhibited Lüders elongation. The Lüders elongation was capable of causing irregularities such as local buckling or strain concentration in the axial collapse of the columns. However, the effect of the Lüders elongation on the deformation behaviour was not observed clearly. It could be concluded that work hardening at a tensile strain over 5% was important for promoting the compact mode. Furthermore, if new microstructures are obtained with both a large work hardening rate and a large strain rate sensitivity, they should be promising materials for automotive body structures.

22.6 Conclusions In this chapter the future demands for nanostructured or ultrafine-grained (UFG) steel sheets for automotive body structures were described first, and practical test results for evaluating the UFG steel sheets were presented. A new route to fabricating UFG steel sheets without severe plastic deformation was introduced.

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It was shown that the UFG ferrite-cementite (FC) steel showed large strain rate sensitivity compared with other high-strength steels (HSS), while uniform elongation was significantly decreased by ultra grain refinement. In order to improve the uniform elongation of the UFG ferritic microstructure, UFG multi-phase (MP) steels were developed. The UFG-MP steel sheets showed an improved strength–elongation balance. The large work hardening rate of the UFG-MP steels promoted a stable compact-mode deformation in dynamic axial collapse of a hat column, which should contribute to the improvement of the crash-worthiness and further weight reduction of automotive body structures.

22.7 References   1 Takechi H. JOM 2008;60 No.12: 22.   2 Matlock D.K., Speer J.G. Third generation of AHSS: microstructure design concepts. In: Haldar A., Suwas S., Bhattacharjee D., editors. Microstructure and Texture in Steels and Other Materials. London: Springer, 2009; p. 185.   3 Segal V.M. Mater Sci Eng A 1995:197: 157.   4 Valiev R.Z., Korznikov A.V., Mulyukov R.R. Mater Sci Eng A 1993:168: 141.   5 Saito Y., Tsuji N., Utsunomiya H., Sakai T., Hong R.G. Scripta Mater 1998:39: 1221.   6 Tsuji N., Saito Y., Utsunomiya H., Tanigawa S. Scripta Mater 1999:40: 795.   7 Saito Y., Utsunomiya H., Tsuji N., Sakai T. Acta Mater 1999:47: 579.   8 Okitsu Y., Takata N., Tsuji N. Scripta Mater 2009:60: 76.   9 Okitsu Y., Takata N., Tsuji N. J Mater Sci 2009:43: 7391. 10 Okitsu Y., Naito T., Takaki N., Sugiura T., Tsuji N. SAE Technical Paper 2010: 2010-01-0438. 11 Kuriyama Y., Takahashi M., Ohashi H. J Soc Automotive Eng Jpn 2001:55 No.4: 51. 12 Lüdke B., Pfestorf M. Functional design of a “Lightweight body in white” – How to determine body in white materials according to structural requirements. In: Hashimoto S., Jansto S., Mohrbacher H., Siciliano F., editors. International Symposium on Niobium Microalloyed Sheet Steel for Automotive Applications. Warrendale: TMS, 2006; p. 27. 13 World Steel Association, 2009. Advanced High Strength Steel (AHSS) Application Guidelines Version 4.1. Available from: http://www.worldautosteel.org [accessed 15 January 2010]. 14 Grässel O., Krüger L., Frommeyer G., and Meyer L.W. Int J Plast 2001:16: 1391. 15 Cornette D., Cugy P., Hildenbrand A., Bouzekri M., Lovato G. SAE Technical Paper 2005: 2005-01-1327. 16 Mallen R.Z., Odell J., O’Hara B. SAE Technical Paper 2009: 2009-01-0088. 17 Uenishi A., Kuriyama Y., Takahashi M. Nippon Steel Tech Rep 2000:81: 17. 18 Tsuji N., Ito Y., Saito Y., Minamino Y. Scripta Mater 2002:47: 893. 19 Tsuji N., Okuno S., Koizum Y., Minamino Y. Mater Trans 2004:45: 2272. 20 Jia D, Ramesh KT, Ma E. Acta Mater 2003:51: 3495. 21 Tsuchida N., Masuda H., Harada Y., Fukaura K., Tomota Y., Nagai K. Mater Sci Eng A 2007:488: 446. 22 Humphreys F.J., Hatherly M., Recrystallization and Related Annealing Phenomena, 2nd edn. Oxford: Elsevier, 2004. p. 457. 23 Kamikawa N., Sakai T., Tsuji N. Acta Mater 2007:55: 5873. 24 Ueji R., Tsuji N., Minamino Y., Koizumi Y. Acta Mater 2002:50: 4177.

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Applying nanostructured steel sheets to automotive body structures 713 25 Tanimura S., Mimura K., Umeda T. Journal de Phys IV 2003:110: 385. 26 Chuman Y., Kimura K., Tanimura S. Int J Impact Eng 1997:19: 165. 27 Takahashi M., Uenishi A., Yoshida H., Kuriyama Y. SAE Technical Paper 2003: 2003-01-2765. 28 Takagi S., Tokita Y., Sato K., Shimizu T., Hashiguchi K., Ogawa K., Mimura K., Tanimura S. SAE Technical Paper 2005: 2005-01-0494. 29 Moriau O., Tosal-Martinez L., Verieysen P., Degrieck J Int Conf on TRIP-Aided High Strength Ferrous Alloys, Aachen, 2002; p. 247. 30 Harding J. Acta Metall 1969:17: 949. 31 Campbell J.D., Ferguson W.G. Phil Mag 1970: 21: 63. 32 Harding J. Mater Tech 1977:4: 6. 33 Harding J. The effect of high strain rate on material properties. In: Blazynski, T.Z., editor. Materials at high strain rates. London: Elsevier, 1987; p. 133. 34 Miura K., Takagi S., Hira T., Furukimi O., Tanimura S. SAE Technical Paper 1998: 980952. 35 Bruce D.M., Matlock D.K., Speer J.G., De A.K. SAE Technical Paper 2004: 2004-01-0507. 36 Kato M. Introduction to the theory of dislocations. Tokyo: Shokabo, 1999; p. 102. 37 Otubushin A. Int J Impact Eng 1998:21: 349. 38 Ma E. Acta Mater 2004:52: 1699. 39 Tsuji N. Fabrication of bulk nanostructured materials by accumulative roll bonding (ARB). In: Zehetbauer M.J., Zhu Y.T., editors. Bulk nanostructured materials. Weinheim:WILEY-VCH, 2009; p. 246. 40 Tomota Y., Narui A., Tsuchida N. ISIJ Int 2008:48: 1107. 41 Tsuchida N., Tomota Y., Nagai K. Tetsu-to-Hagané 2003:89: 1170. 42 Son Y.I., Lee Y.K., Park K.T., Lee C.S., Shin D.H. Acta Mater 2005:53: 3125. 43 Jacques P.J., Ladrière J., Delannay F. Metall Mater Trans A 2001:32A: 2759. 44 Zaefferer S., Ohlert J., Bleck W. Acta Mater 2004:52: 2765. 45 Takakura K., Takagi K., Yoshinaga N. SAE Technical Paper 2006: 2006-01-1586. 46 Walp M.S. SAE Technical Paper 2007: 2007-01-0342. 47 Miller RL. Met. Trans 1972:3: 905. 48 Merwin M.J. SAE Technical Paper 2007: 2007-01-0336. 49 Merwin M.J. Iron & Steel Tech 2008 Oct: 66. 50 Huang H., Matsumura O., Furukawa T. Mat Sci Tech 1994:10: 621. 51 Furukawa T., Huang H., Matsumura O. Mat Sci Tech 1994:10: 964. 52 Mahmood H.F., Paluszny A. SAE Technical Paper 1981: 811302. 53 Reid S.R., Reddy T.Y., Gray M.D. Int J Mech Sci 1986:28: 295.

22.8 Appendix Lightweight automotive body structures by steels have been proposed through several projects. The recent projects are reviewed below.

ULSAB (UltraLight Steel Auto Body) This is the first organized lightweight steel body project from 1994 to 1998. It was operated through a consortium composed of 35 steel manufacturers representing

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18 countries. Targeting mid-sized four-door sedans, a practical concept body was constructed. Various kinds of HSS were applied to more than 90 percent of the body structure. Also several new manufacturing methods, i.e. tailored blanks (steel sheets assembled from a number of single sheets having various thickness and strength by laser welding), tubular hydroforming (forming of a steel pipe by hydro pressure applied to the inside of the tube) and laser-welding assembly were applied. A weight reduction of 25% compared with the benchmark cars was achieved. At the same time, other two projects, ULSAC (UltraLight Steel Auto Closure) and ULSAS (UltraLight Steel Auto Suspension) were carried out.

ULSAB-AVC (ULSAB-Advanced Vehicle Concepts) As a post-project of ULSAB, advanced lightweight steel bodies, which adapt to more variations of automobile safety assessments, were studied. AHSS (advanced high strength steels) including DP (dual-phase) and TRIP (transformation induced plasticity) -assisted steels were applied. Targeting European C-class cars and North American midsize-class cars, lightweight car concepts including the body structure, closure panels, chassis and power trains were proposed.

FSV (Future Steel Vehicle) This project started in 2008 targeting potential cars for mass production in 2020, i.e. BEV (battery electric vehicle), PHEV (plug-in hybrid electric vehicle) and FCEV (fuel cell hybrid electric vehicle). In those vehicles, the main body structure might be different from the conventional ones, i.e. a new structure supporting new power plants. Therefore significant weight reduction could be expected from the new concepts of structures and materials investigated through this project. Further information is available at the website of world steel association: http:// www.worldautosteel.org/.

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23 Production processes for nanostructured wires, bars and strips S. TORIZUKA, and E. MURAMATSU, National Institute for Material Science, Japan, T. KOMATSU, Komatsuseiki Koksakusho Co., Ltd., Japan and S. NAGAYAMA, Tokushu Kinzoku Excel Co., Ltd., Japan Abstract: Some commercially applicable processes for nanostructured steel wires, bars and strips are introduced in this chapter. They are warm multi-pass caliber rolling, warm continuous oval to square rolling, cold strip rolling including cladding, and repetition of cold strip rolling with reverse phase transformation. The basic idea of how to apply the amount of strain necessary for introducing a nanostructure differs depending on the product shape and material. Microstructures with a grain size of several hundred nanometers and the mechanical properties of these materials are presented.   Several application examples of these nanostructured steels such as small screws, orifice plates for liquid spray and shafts are explained. The advantage of nanostructured material is not only in strength but also in formability and machinability. The applications take advantages of these unique features of nanostructured steel properly and they are at the stage of mass production. Key words: caliber rolling, oval to square rolling, cladding, reverse phase transformation, orifice plates.

23.1 Introduction The process of manufacturing nanostructured or ultrafine-grained steels has, recently, become a hot topic for researchers all over the world. Nanostructure can be fabricated using the concept ‘high Z-large strain deformation’. Z expresses the Zener–Hollomon parameter.1–5 Based on this concept, various multi-pass, large strain deformation processing techniques have been developed such as equalchannel angular pressing (ECAP),6 accumulative roll bonding (ARB),7 multiple compression,8 ball milling and sintering,9 and warm multi-pass caliber rolling10 to produce nanostructured materials. In order to evolve a fine structure, large plastic strain deformation exceeding a true strain of more than 2 is generally required. A sub-micron ferrite structure can be formed by single-pass warm deformation of ferrite phase when the strain exceeds approximately 3.1–5 However, considering the capacity limitations of practical rolling and other processing equipment, this type of heavy single-pass deformation is not realistic for large bulk materials, which suggests that a study of multi-pass deformation processes is indispensable for industrial applications. Shin et al.11 have studied ultrafine-grained microstructures of low-carbon steels using ECAP and evaluated their mechanical properties. Storojeva et al.12 have 715 © Woodhead Publishing Limited, 2011

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studied heavy warm deformation of medium carbon steel to produce ferrite. Song et al.13 have reported the large strain warm deformation of 0.2%C-Mn steel for evolving ultrafine-grained ferrite microstructures, and studied their mechanical properties. However, all these studies were conducted on a laboratory scale and the full-scale impact properties of the resultant nanostructure were not reported. This is an important pending issue to be resolved because the strength–toughness combination of nanostructured materials has to be evaluated before any practical application of these materials can take place.

23.2 The production processes and properties of nanostructured steel bars 23.2.1  Warm multi-pass caliber rolling Torizuka et al.10,14–16 have developed the warm multi-pass caliber rolling technology to obtain a nanostructured steel bar. Figure 23.1 shows the schematic drawing of caliber rolling, which is a simple process for imposing a large strain using two-dimensional reduction. Any strain can be imposed theoretically into the material by selecting a suitable billet shape. For example, when a material with a section of 80 × 80 mm2 is deformed to 18 × 18 mm2, the imposed strain is calculated by equation [23.1]:

ε = ln(802/182) = 3.

[23.1]

It is obvious that a large strain can easily be introduced into a material by caliber rolling. The warm multi-pass caliber rolling process is shown schematically in Fig. 23.2. Steel billets with a carbon content of 0.02, 0.05, 0.15, 0.3 and 0.45 and 0.3Si, 0.5 or 1.5Mn are heated to 550°C, which is below the temperature of α → γ transformation. The billets are then warm rolled at 550°C for 21 passes from 80 × 80 mm2 to a final size of 18 × 18 mm2 (cumulative reduction in area 95%, cumulative strain 3.0). The appearance of the rolled bar is shown in Fig. 23.3. Figure 23.4 (a–h) shows the SEM (scanning electron micrographs) of the

23.1  Schematic drawing of caliber rolling.10

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23.2  Condition of warm multi-pass caliber rolling.

23.3  Appearance of rolled bar.

cross-sections of 0.15% C steel during and after completion of multi-pass warm caliber rolling at a temperature of 550°C.10 Cumulative reductions during warm rolling correspond to (a), (b) 75%; (c), (d) 87%; (e), (f) 91% and (g), (h) 95%. The left row ((a), (c), (e) and (g)) shows the microstructure at 1 mm deep from the surface near the corner of the cross-section of the specimen, while the right row ((b), (d), (f ) and (h)) shows the microstructure near the center of the cross-section. The microstructure, Fig. 23.4 (b), at the center where cumulative reduction in area is the smallest, reveals that the dark etching area is limited to the original ferrite grain boundaries, and only lightly etched sub-boundaries can be observed inside the original grains. The pearlite phase existed at the start of rolling is found to be fragmented. At a cumulative reduction of 87%, new nanostructure evolution has been noticed as shown in Fig. 23.4 (d). These newly generated ferrite grains are surrounded by clear grain boundaries and are indistinguishable from the original ferrite grains. The share of the area occupied by these nanostructured ferrite grains increases by cumulative reduction, but their average size remained substantially constant, showing no dependency on reduction in area. In the final specimen with a cumulated reduction in area of 95%, a microstructure with an average grain size

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23.4  Scanning electron microscopy (SEM) micrographs revealing the microstructures of caliber-rolled specimens at 823K with accumulative reduction of (a),(b) 75%; (c),(d) 87%; (e),(f) 91%; (g),(h) 95% in area.10

of 500 nm is obtained. At this stage the entire cross-section is covered with nanostructured ferrite grains as shown in Fig. 23.4 (h). Figure 23.5 shows the relationship between the Zener–Hollomon parameter (Z) and the nominal grain size of the newly formed nanostructured ferrite evolved through a single pass compression as well as warm multi-pass caliber rolling.4,10 It can be clearly seen that the data for a single-pass compression lie on a straight line of grain size decreasing with increasing Z parameter. Similar behavior is exhibited by the test data of multi-pass warm caliber-rolled specimens rolled at different temperatures. Although the temperature at the surface of the rolled material is maintained to the set temperature, it is not constant and fluctuates during rolling. The error bars in the Z parameter for the caliber-rolled specimens in Fig. 23.5 for grain size are due to the variation of the temperature during rolling

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23.5  Relationship between Zener–Hollomon parameter and the average size of newly evolved ultrafine ferrite grains.4,10

(±20K). Based on Fig. 23.5, it can be concluded that the grain size of nanostructured ferrite evolved by multi-pass warm caliber rolling is close to what would be predicted from the Z parameter for equivalent single-pass compressive deformation. This suggests that the influence of structural changes such as interpass grain growth would become impossible to ignore if the rolling temperature were increased further.

23.2.2  Variation of microstructures by carbon content Figure 23.6 (a–e) shows microstructures of caliber-rolled bars at a fixed strain of 3.0 for 0.02, 0.05, 0.15, 0.3 and 0.45% carbon content.17 It can be seen from these microstructures that some of the grains are slightly elongated to the direction of rolling and cementite is uniformly distributed in the ferrite matrix with better distribution by increasing carbon content. It is clear that the grain sizes of specimens with 0.02 and 0.05% C are slightly coarser, 700 nm and 600 nm respectively, while the grain sizes of specimens with carbon contents of 0.15, 0.30 and 0.45% are nearly the same, 500 nm. The average size of cementite particles in all specimens is in the range of 100–200 nm. Figure 23.7 shows the boundary maps of the 0.02% C steel at the center of the specimen in the L direction.17 Although some subgrains and ferrite grains elongated to the rolling direction have been retained, a large number of equiaxed nanostructured ferrite surrounded by high-angle grain boundaries were observed.

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23.6  Microstructure of ultrafine-grained steels with various carbon contents of (a) 0.02, (b) 0.05, (c) 0.15, (d) 0.3 and (e) 0.45% processed by warm multi-pass caliber rolling.17

23.7  Grain boundary map of ultrafine-grained steel bars with a carbon content of 0.02% processed by warm multi-pass caliber rolling.17

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The volume fraction of high-angle grain boundaries increases when a large plastic strain is introduced. More than 70% of the boundaries are high-angled ones, regardless of carbon content. Therefore, it is clear from these microstructures that caliber rolling produces bulk nanostructured materials with uniform microstructures consisting predominantly of high-angle grain boundaries.

23.2.3  Mechanical properties Figure 23.8 shows the nominal stress–strain curves of nanostructured steels with carbon contents in the range of 0.02 to 0.45%.17 When carbon content is 0.02%, yield strength is 700 MPa, which is the lowest among them, and the total elongation is as small as 5%. Uniform elongation for 0.02% C steel does not appear in the stress–strain curve. This indicates that immediately after yielding, plastic instability occurs. However, when carbon content is slightly increased to 0.05%, yield strength increases to 830 MPa and total elongation drastically increases to 14%. Further, uniform elongation of 3% appears in this stress–strain curve. For 0.05% C steel, no plastic instability was noticed immediately after yielding, in contrast with that observed for 0.02% C steel. This is attributed to strain hardening by cementite dispersion. When carbon content is 0.15%, strain hardening is evident, and it becomes more pronounced with a carbon content of 0.3%. Ultimate tensile strength is clearly observed in steels with a carbon content of 0.3% and 0.45%. The tensile strength of 1000 MPa and total elongation of 18% is obtained when the carbon content is 0.45%. The failure stress also increases monotonously with an increase in carbon content. The volume fraction of cementite is virtually zero in steel a with carbon content of 0.02%, resulting in

23.8  Nominal stress–strain curves of ultrafine-grained steel with carbon content in the range of 0.02 to 0.45wt%.17

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non-uniform elongation. The presence of cementite is clearly very effective in increasing uniform elongation. While several studies examined the tensile properties of nanostructured steels, Charpy impact testing was less commonly carried out due to the limitation in obtaining bulk samples prepared by severe plastic deformation processes.18,19 Warm multi-pass caliber rolling can produce bulk materials large enough to obtain a Charpy impact test specimen. Charpy impact fractures strongly depend on imposed strain.18 It is clear that a generation of new ultrafine grains surrounded by high-angle grain boundaries is responsible for the improvement of Charpy impact properties, ductile–brittle transition temperature and absorbed energy. This clearly indicates that work hardening is harmful for Charpy impact properties while new nanostructured grains with a high proportion of high-angle grain boundaries are beneficial.20

23.3 The production processes and properties of nanostructured steel wire 23.3.1  Warm continuous multi-directional rolling Although warm multi-pass rolling is effective in obtaining nanostructure ferritegrained steel bars, simple caliber rolling shown in Fig. 23.1 is not applicable to industrial mass production and, therefore, a more efficient method is required. A new continuous and compact rolling process, which is an improvement of caliber rolling, has been developed. By imposing a multi-direction compressive strain, more strain can be introduced into a material in spite of a smaller reduction ratio.21,22 As a forging type, multi-directional compressive deformation is not suitable for obtaining a long continuous product; developing a rolling-type multi-directional deformation is required. Caliber rolling with oval and square grooves is focused23–27 as is shown in Fig. 23.9. A bar material is flattened by rolling through an oval groove firstly, and then the material is deformed to the opposite direction by a square groove. Thus, the rolling process is equivalent to multidirectional deformation. It is verified theoretically and experimentally that this process introduces far more strain into materials than square–square grooves.25–28 A prototype rolling machine was designed and fabricated based on this concept in order to produce continuous long wire by warm rolling. Figure 23.10 shows the schematic drawing of the ‘continuous oval to square rolling system’, the design concept of which is as follows:23,24 • • • •

Coil to coil continuous rolling. Temperature controlled rolling by on-line heating. Two-tandem horizontal and vertical rolling. Multidirectional rolling with oval groove and square groove.

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Square caliber roll 2nd pass

23.9  Schematic drawing of multidirectional deformation rolling realized using oval-caliber and square-caliber rolling.27

23.10  Schematic drawing of a newly developed warm continuous oval to square rolling system.29–35

23.3.2 Rolling condition, microstructure and mechanical properties Steel wire coil with a diameter of 6 mm is used as a starting material. The chemical composition of the wire is 0.01C-0.3Si-0.2Mn. The wire is heated to 500°C, rolled by an oval–square roll and coiled. Then, the rolled wire is again heated and rolled by a set of different oval–square rolls and coiled. Finally, the same process was repeated with the other oval–square roll set to obtain a wire 3 mm in diameter. Though the apparent reduction in cross-section is only 75% (strain = 1.35), a strain that is larger than 4 is introduced in the material.25–27 The appearance of the rolled wire is shown in Fig. 23.11. Several hundred meters of wire were obtained.29–34

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23.11  Ultrafine-grained steel wire with a diameter of 3 mm.34,35

23.12  SEM micrograph and EBSD image of ultrafine-grained steel wire with a diameter of 3 mm in the L-direction.

Figure 23.12 shows the SEM image and EBSD (electron backscattered diffraction) image of the wire at the center region in the L-direction. The structure is occupied by fine equiaxed ferrite grains. This shows that oval–square rolling process generates nanostructure grains, although the apparent reduction is only 75%. Figure 23.13 shows tensile test results. The tensile strength of the starting material is 350MPa, and that of the nanostructure steel wire is 900MPa. Although total elongation decreases from 37 to 10%, the reduction in area decreases slightly from 89 to 77%. This wire has a good balance of tensile strength and reduction in area. Thus, warm continuous oval–square rolling realizes the industrial production of nanostructured steel wire.

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23.13  Nominal stress–strain curves of ultrafine-grained steel wire manufactured by warm continuous oval to square rolling.

23.4 The production processes and properties of nanostructured steel strips 23.4.1  Production processes and microstructure Two different methods have been investigated as candidates for manufacturing nanostructured steel strips. One is ‘introducing cladding in a cold rolling process’38 and the other is the repetition of plastic deformation and reverse phase transformation.39 Both of these methods are based on the cold rolling process. These two methods will now be introduced in detail. The first method, ‘introducing cladding in cold rolling process’, uses severe plastic deformation. It is well known that an equivalent strain (e) of more than about 4 is required to obtain nanostructured metals. But, in general, it cannot introduce sufficient equivalent strain for grain nanostructuring in a cold rolling process except in the case of very thin products, because the thickness of the starting strip is limited by the performances of rolling mills. For example, if the thickness of the product strip you need is 0.2 mm and the thickness of the starting strip is 2 mm, which is common for cold rolling, it is able to introduce an equivalent strain of only about 2.7 and you cannot obtain a nanostructured strip as it stands. In order to rectify this lack of equivalent strain, introducing cladding in a cold rolling process is effective. Cladding is a similar process to accumulative roll bonding (ARB 40). It can be used to bond two or more various kinds of metal plates or strips face-to-face41 and has been used for many years to manufacture composite materials that consist of multi-layered metals such as Fe, Ni, Cu and Al, etc.

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Figure 23.14 shows one of the manufacturing processes used to obtain nanostructured type 430 stainless steel strip. First, the starting strip is cold rolled until it has the moderate thickness required to progress. The number of coils should be sufficient for the next step. Secondly, the surface of each strip to be bonded is brushed by wheel brushes made of steel for the purpose of forming heavily deformed and hardened layers on the metal surfaces. Thirdly, the brushed surfaces are stuck to each other and rolled together, approximately 50% in one pass. The hardened layers are so hard that they are broken during rolling by the huge reduction. Consequently, virgin metal-faces appear through numerous cracks at the broken regions. The regions in the interface where the virgin metal-faces are stuck to each other are temporarily bonded, and the many strips become only one strip.41 This third step is the ‘cladding’. Although the brushing and the cladding are done only once in this example, it is possible to do them more often, depending on the necessity for grain nanostructuring. The fourth step is that the bonded strip is rolled by cold rolling until it becomes the required thickness for the final product. At this point, the interfacial joint strength is not strong enough for practical use, so the heat treatment process, which is carried out at a temperature just below the recrystallization temperature of the metal, is indispensable as the fifth step. In general, metals bonded by cladding should be heat-treated at a temperature higher than the recrystallization temperature to enhance their interfacial joint strength by active interdiffusion of their component elements at the interface. But it is impossible for nanostructured metal to be treated this way because of the risk of grain growth. To compensate for this insufficient heat treatment, the total rolling reduction of the third and fourth steps become greater, and the interfacial

23.14  Manufacturing process of nanostructured strip using the method of introducing cladding in the cold rolling process.

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joint strength becomes dramatically stronger. It appears that when the total rolling reduction exceeds about 80%, the interfacial joint strength reaches the strength of the matrix.42 Although the nanostructured strip has already been obtained by the fifth step, it is not strong enough because softening by restoration has occurred by this stage. So, as the sixth step, several more passes of cold rolling are necessary to enhance strength. This should be carried out depending on the mechanical properties required, and if necessary, the thickness of the strips after the fifth time has to be thicker than required product’s thickness. Figure 23.15 and 23.16 show the strip manufactured by this process and its nanostructure images analysed by EBSD respectively. The strip is 0.2 mm

23.15  Nanostructured type 430 stainless steel strip.

23.16  Nanostructure of type 430 strip analysed by EBSD. (a) Inverse pole figure map from rolling direction. (b) Grain boundary map. Note: ND: normal direction, RD: rolling direction.

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thick, 20 mm wide and 300 m long, and has the mean grain size of about 1300 nm. The nanostructure shows elongated grain structure toward the rolling direction, and has a high number of high-angle grain boundaries whose angles are greater than 15°. The share of its high-angle grain boundaries is about 72%. The second method, ‘repetition of plastic deformation and reverse phase transformation’, uses reverse phase transformation from the martensite (α’) phase to the austenite (γ) phase.43 This method can be applied to metastable austenitic stainless steels such as type 301 and type 304. In these materials, strain-induced martensitic transformation occurs when they are deformed by cold processes. The martensite phase is so hard that it is difficult to provide a giant equivalent strain for grain nanostructuring. So using the reverse phase transformation, which is conducted with appropriate heat treatment, is useful. It is known that if the material is preliminarily transformed to martensite phase by about 90% (ε = 2.66) cold rolling, a nanostructured material consisting of uniform γ phase is obtained after the reverse phase transformation. But actually, 90% cold rolling is difficult industrially because it makes the material so hard for deformation. Therefore, repetition of the reverse phase transformation after about 50 to 60% cold rolling (a common reduction in the cold rolling process) is applied. Figure 23.17 shows one of the manufacturing processes of nanostructured type 304 stainless steel strips by this second method. In this example, the cycle of reverse phase transformation after cold rolling is repeated four times, and it is confirmed that the nanostructure evolves with the number of the cycles (Fig. 23.18). It is thought that two effects are responsible for the evolution of this nanostructure. One is grain refining through the reverse phase transformation in

23.17  The process of manufacturing nanostructured strips using the ‘repetition of plastic deformation and reverse phase transformation’ method.

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23.18  Nanostructure evolution with the number of cycles analysed by EBSD, (a) after one cycle, (b) after two cycles, (c) after three cycles, (d) after four cycles. Note: ND: normal direction, RD: rolling direction.

the regions where the martensitic transformation is induced by cold rolling. The other is severe plastic deformation in the regions where retained γ phase still exists. The heat treatment temperature at which the reverse phase transformations occur is lower than the recrystallization temperature. Therefore, the strain introduced by cold rolling remains, and accumulates by repetition in the grain nanostructuring. Both of these effects make it possible to obtain nanostructured steel strips that have a uniform and comparatively equiaxial nanostructure. The heat treatment condition of the last cycle can be changed from the temperature of the reverse phase transformation to the recrystallization temperature in order to control the grain sizes and the mechanical properties of the strip. Figures 23.19 and 23.20 show the strip obtained by this process and its nanostructures analysed by EBSD respectively. It is 0.1 mm thick, 100 mm wide and 500 m long, and has the mean grain sizes of about 450–800 nm with comparatively large amounts of high-angle grain boundaries from 57 to 77%.

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23.19  Nanostructured type 304 stainless steel strip.

23.4.2  Properties of nanostructured steel strips The mechanical properties of the nanostructured steel strips compared with the conventional coarse-grained steel strips manufactured by cold rolling are shown in Table 23.1. The tensile stress–strain curves of the type 430 stainless steels are shown in Fig. 23.21 and the type 304 stainless steels are shown in Fig. 23.22. In the case of type 430 stainless steels, both the nanostructured and coarsegrained steels have almost equal Vickers hardness and tensile strength, but the ductility of the nanostructured one is higher than that of the coarse-grained one. It shows that the nanostructured type 430 stainless steel has better balance between strength and ductility. In the case of type 304 stainless steels, on the other hand, there is no significant difference between the nanostructured steels and the coarse-grained steels. It is thought that the reason why they have almost equal mechanical properties is that there are several kinds of hardening mechanisms such as the Hall–Petch relationship, dislocation strengthening and strain-induced martensitic transformation, and that their interaction in these steels is complicated. Although superior mechanical properties cannot be expected of nanostructured type 304 steels, it is shown that their nanostructure contributes to workability for pressing, especially for punching small holes, as is shown later in this chapter.

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23.20  The nanostructure of type-304 strip analysed by EBSD. (a1) Inverse pole figure map from normal direction (grain size is about 450 nm). (a2) Inverse pole figure map from normal direction (grain size is about 800 nm). (b1) Grain boundary map (grain size is about 450 nm).(b2) Grain boundary map (grain size is about 800 nm). Note: ND: normal direction, RD: rolling direction.

23.5 Applications of nanostructured steels and their features 23.5.1  Nanostructured steel wire for heading screws Figure 23.23 shows the relationship between the reduction in area and tensile strength of nanostructured steels with the carbon contents of 0.02 to 0.45%.17,35 The test data of conventional ferrite + pearlite steel, tempered martensitic steel and bainite steel are also plotted in Fig. 23.23 for the purpose of comparison. The balance of reduction in area and tensile strength for ultrafine-grain steels is far better than the conventional ferrite + pearlite steels, tempered martensite steels and superior to bainitic steels or acicular ferrite steels.

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Table 23.1  The mechanical properties of nanostructured stainless steel strips and coarse-grained stainless steel strips Vickers Hardness (HV) Type 430 Type 304

Nanostructured Coarse grained Nanostructured 1 Nanostructured 2 Coarse grained 1 Coarse grained 2

Ultimate tensile strength (MPa)

0.2% yield ductility (%) strength (MPa)

228   760   670 223   721   678 403 1265   914 340   962   880 385 1267 1078 302   968   744

12.4 4.1 13.5 43.0 21.6 44.6

Nanostructured 1: The mean grain size of 450 nm. Nanostructured 2: The mean grain size of 800 nm Coarse grained 1: Cold rolled for 40% after recrystallized to the mean grain size of 9 µm. Coarse grained 2: Cold rolled for 18% after recrystallized to the mean grain size of 9 µm.

23.21  Tensile stress–strain curves of type 430 stainless steel strips, nanostructured and coarse grained.

Reduction in area is a measure of formability as well as uniform elongation. Nanostructured ferrite + cementite steels are expected to have good formability. In order to demonstrate the formability, micro screws were formed, as are shown in Fig. 23.24, from nanostructured 0.02C steel wire. There are made by cold header and rolling. This indicates that the steel has a good formability for cold heading and rolling.35

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23.22  Tensile stress–strain curves of type 304 stainless steel strips, nanostructured and coarse-grained. (a) Nanostructured strip with a mean grain size of 450 nm compared with coarse-grained strip that was cold rolled to 40%. (b) Nanostructured strip that has the mean grain size of 800 nm compared with coarse-grained strip that was cold rolled to 18%.

23.5.2  Nanostructured steel strips for machinability Studies on the machinability of nanostructured steel are quite limited. The reasons are: (1) The supply of nanostructured steel is limited in size and volume.44 (2) Researchers and new material developers of nanostructured steels are mostly interested in their mechanical characteristics rather than machinability. © Woodhead Publishing Limited, 2011

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23.23  Reduction in area (RA) and tensile strength balance of ferrite + pearlite steel ( ■ ), bainite steel (▲), tempered martensite (●), and ultrafine-grained steel (◆).17

23.24  M1.7 micro screw (a), ultrafine-grained screw (b), normal-grained screw (c), appearance of ultrafine-grained screws (d).29–35

(3) Nanostructure creation by drilling or cutting at machined surface is more interested in than machinability of nanostructured steel for reason (1) above.45 As explained in the first part of this chapter, however, there are already solutions to the first problem, which means that studies on machinability are available.

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The benefit of a product is strongly connected with its material characteristics, including chemical factors, mechanical factors and factors of fabricability including machinability. These factors should be examined simultaneously. If the nanostructure has much positive influence on multiple factors, it has a high probability of adding new value to the product such as a long product life cycle, reasonably uniform quality, low cost and so on. The products could then offer multiple benefits both for producers and users, which makes them competitive in the market place. For the first time, the benefit of nanostructured steel for machinability was identified in a study on the material made by NIMS (National Institute for Material Science, Japan) of 0.2 mm thickness. It was cut by shearing, and the sheared surface was different in quality from that of steels with a normal grain size. Figure 23.25 explains the terminology of a typical sheared surface and Fig. 23.26 shows the photographs of the sheared surface. In the case of the nanostructured steel, the rollover was smaller and the surface roughness was flatter, especially on the fractured surface. Based on this result, we have proposed a hypothesis that ‘Nanostructure has an excellent influence on machinability’ (Torizuka & Komatsu’s hypothesis).46 Fine blanking, mostly for thicker metal plate, is known in stamping companies as one of the major processes for creating a small rollover (height and width) and a complete burnished surface. Shearing or barreling also creates an appropriate rollover and a complete burnished surface. These methods are difficult to employ for processing thinner strips, because the stamping clearance (gaps between the punch and the die) must be as narrow as possible and the surface of the blanked product is damaged by the high pressure of fine blanking. Nanostructured steel is, thus, suitable for thin material to produce a fine shearing surface.

23.25  Explanations of the terminology for a typical sheared surface.

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23.26  Samples of sheared surface: (a) nanostructured steel, (b) normal-grained steel.

Figure 23.27 shows the surface roughness of iron-based nanostructured steel and type 304 stainless steel after shearing with the same tool. The profile and surface roughness are measured by a non-contact 3D measuring machine. The burnished surface of nanostructured steel is equal to normal steel because the surface is burnished by the shearing punch and its surface roughness transfers to the sheared surface during the process (Fig. 23.28). The fractured surface has, however, a different tendency. A fractured surface of nanostructured steel ranges

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23.27  Difference of sheared surface between (a) nanostructured steel and (b) normal stainless (type 304).

from 290 to 330 nm. On the other hand, that of normal steel ranges from 350 to 390 nm. The difference could be caused by the grain size. Figure 23.29 (a) and (b) shows the profile of both steels and the result of measurement of depth in fractured surface. The depth of the nanostructured steel is from 8 to 10 µm, and that of normal steel is from 10 to 15 µm. Figure 23.30 shows the tool setting, and the clearance between punch and die is 10 µm. As the depth in the fractured surface of nanostructured steel is close to the clearance, it can reproduce the tool setting. On the other hand, the depth of normal steel is well

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23.28  Surface roughness difference between a sheared and a fractured surface.

23.29  Contour map of fractured surface: (a) normal stainless steel, (b) nanostructured steel.

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23.30  Description of clearance.

over the clearance. This means that the material is torn off at the processed area (red area in Fig. 23.30). The small depth that is a feature of the fractured surface makes nanostructured steel applicable for a precision straight hole. Figure 23.31 shows the piercing of holes of 0.42 mm in diameter on both nanostructured steel and normal-grained steels. The rollover of the nanostructured steel is clearly smaller than the normalgrained steel. Figure 23.32 shows the measurement results of the pierced hole diameter on the surface of the strips at punch entrance and exit side. The average diameter of holes for nanostructured steel is uniform for punch entrance and exit, which means that the hole is straighter. The shapes of small pierced holes must be uniform for orifices of liquid spray in order to obtain a stable flow volume of the liquid. Nanostructured steels are applied for the test of liquid spray. Orifices that have small punched holes are produced in nanostructured stainless steel (type 304 and 430) strips with thicknesses of 0.08~0.3 mm. The hole size has a range of 0.1~0.2 mm in diameter with slant angles. The conditions of the orifice are shown in Fig. 23.33. The rollover of normalgrained material is unstable and partially deformed; on the other hand, the nanostructured orifice has stable rollover and edge condition. The number of orifices with deformation over 5 µm at rollover is counted in 120 pieces after

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23.31  Difference in rollover between the normal-grained and nanostructured steel at piercing small holes.

23.32  Piercing hole diameter differences between entrance and exit side.

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23.33  Appearance of holes after 10 000 shots.

10 000 holes are pierced; there are 107 pieces with a deformation over 5 µm in normal material but none in the nanostructured orifice. The machinability advantage of nanostructured steel also influences the functions of orifices. Orifices require stable flow volume between the pieces. As the shape of the rollover is stable, liquid flow does not have to contend with obstacles such as deformations and cracks. Figure 23.34 shows the comparison

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23.34  Difference of flow volume variations between normal and nanostructured stainless steel.

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between normal-grained and nanostructured steels of liquid flow volume under same pressure of orifices that have multiple holes. The differences of liquid flow volume between MAX and MIN within the 60 orifices of nanostructure and normal are compared. When nanostructured steel is used for orifice applications, the variation of flow volume becomes 50% smaller than normal steel. If several orifices are used in a product, the nanostructured orifices will spray 50% more evenly than a normal orifice. The orifice is only one of the applicable examples of nanostructured steel. The machinability feature of nanostructured steel could be relevant to other stamping markets.

23.6 Future trends Nanostructured steel has been developed to increase strength, based on Hall– Petch. Its characteristics can be used in the shafts of a structure. Several nanostructured shafts are produced using 0.45C steel with heat treatment and 0.1C-1Cr-0.3Mo steel (Fig. 23.35)48 and compared to conventional shafts, indicating the benefits of applying nanostructured steel to shaft production. Because of the greater tensile strength and ductility, the product is stronger and shows improved wear resistance. Moreover, to obtain the required strength, nanostructured steel can be used for manufacturing shafts with precise dimensional tolerances, because the shafts are free from the deformation created by heat treatment. During the production of these shafts, the cutting force is measured and compared to similar-strength steel. The results are shown in Fig. 23.36. The cutting force of nanostructured steel is lower than other steels even though they have similar strength. Nanostructured steel is, therefore, applicable for products that need to reduce cutting force. In Japan, two national projects to develop ultrafine-grained steel were carried out: the Ultra-Steel Project and the Super-Metal Project.36 Nakayama steel produces and sells hot coils with a ferrite grain size of 2 µm, which is used for automobile parts and construction parts.37 Basic research is expected to deliver a deeper understanding of the processes by which ultrafine structures are formed through large strain deformation processes. At the same time, refining the grain structures of steel only in order to increase its strength is not sufficient to add value to industry. The pursuit of the mechanical properties inherent to nanostructure and the development of associated manufacturing processes are believed to be the key themes of future research. Finally, a technology transfer from research to commercial production is also needed.

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23.35  Shafts in nanostructured materials.

23.36  Comparative cutting force of nanostructured steel and normalgrained 0.15C-Cr-0.3Mo steel.

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23.7 Acknowledgements This work was supported by ‘FY2007-2009 subsidies for projects to promote the enhancement of manufacturing technology for small and medium enterprises(SMEs)’ sponsored by the Japanese Ministry of Economy, Trade and Industry (METI).

23.8 References   1 Ohmori A., Torizuka S., Nagai K., Yamada K., Kogo Y. Testu-to-Hagane 2002;88: 857–864.   2 Ohmori A., Torizuka S., Nagai K., Koseki N., Kogo Y. Mater Trans 2004;45: 2224–2231.   3 Murty S.V.S.N., Torizuka S., Nagai K., Koseki N., Kogo Y. Scr Mater 2005;52: 713–718.   4 Torizuka S. Ferrum 2005;10: 188–195.   5 Murty S.V.S.N, Torizuka S., Nagai K. ISIJ int 2005;45: 1651–1657.   6 Segal V.M., Reznikov V.I., Drobyshevskiy A.D., Kopylov V.I. Russian Metallurgy 1981; 1: 99–106.   7 Saito Y., Utsunomiya H., Tsuji N., Sakai T. Acta Mater 1999;47: 579–583.   8 Belyakov A., Sakai T., Miura H. Mater Trans JIM 2000;41: 476.   9 Kimura Y., Suejima S., Goto H., Takaki S. ISIJ Int 2000;40: S174. 10 Ohmori A., Torizuka S., Nagai K., Koseki N., Kogo Y. Tetsu-to-Hagane 2003;89: 781– 788. 11 Shin D.H., Kim B.C., Kim Y.S., Park K.T. Acta Mater 2000;48: 2247. 12 Storojeva L., Ponge D., Kaspar R., Raabe D. Acta Mater 2004;5: 2209. 13 Song R., Ponge D., Raabe D., Kaspar R. Acta Mater 2005;53: 845. 14 Ohmori A., Torizuka S., Nagai K. Tetsu-to-Hagane 2003;89: 765–772. 15 Ohmori A., Torizuka S., Nagai K. ISIJ int 2004;44: 1063–1071. 16 Torizuka S., Ohmori A., Murty S.V.S.N., Nagai K. Mater Sci Forum 2006: 503–504, 329–334. 17 Torizuka S., Muramatsu E., Murty S.V.S.N., Nagai K. Scr Mater 2006;55: 751. 18 Hanamura T., Yin F., Nagai K. ISIJ Int 2004;44: 610. 19 Tsuji N., Okuno S., Koizumi Y., Minamino Y. Mater Trans 2004;45: 2272. 20 Torizuka S., Ohmori A., Murty S.V.S.N., Nagai K. Scr Mater 2006;54: 563–568. 21 Torizuka S., Inoue T., Nagai K. Tetsu-to-Hagane 2000;86: 801–806. 22 Inoue T., Torizuka S., Nagai K. Mater Sci Technol 2001;17: 1329–1338. 23 Torizuka S., Muramatsu E. Proc 64th Conf Japan Soc for Heat Treatment 2007: 23–24. 24 Torizuka S., Muramatsu E. Proc 58th Conf Japan Soc for Technology of Plasticity 2007: 139–140. 25 Inoue T., Torizuka S., Nagai K. J Japan Inst Metals 2005;69: 934–942. 26 Inoue T., Torizuka S., Muramatsu E. and Nagai K. Tetsu-to-Hagane 2008;94: 164–172. 27 Torizuka S., Muramatsu E., Inoue T., Nagai K. J Japan Inst Metals 2008;72: 571–580. 28 Inoue T., Yin F., Kimura Y. Mater trans 2007;8: 2028–2035. 29 Torizuka S., Muramatsu E. CAMP-ISIJ 2007;20: 1395. 30 Torizuka S., Muramatsu E. CAMP-ISIJ 2008;21: 712, 1654. 31 Torizuka S., Muramatsu E. Steel Res 2010; 81: 258-261.

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32 Torizuka S., Muramatsu E. Proc 2008 Japanese Spring conf for the Technology of Plasticity 2008: 339–340. 33 Torizuka S., Muramatsu E. Proc 60th Japanese Joint Conf for the Technology of Plasticity 2009: 389–390. 34 Torizuka S., Muramatsu E. Mater Sci Forum 2009;638–642: 3543–3548. 35 Torizuka S. Materia Japan 2006;45: 438–443. 36 Etou M., Fukushima S., Sasaki T., Haraguchi Y., Miyata K., Wakita M., Tomida T., Imai N., Yoshida M., Okada Y. ISIJ Int 2008;48: 1142–1147. 37 Chikushi I., Torizuka S., Shintomi T., Ohtani T., Tsuzaki K. J Japan Soc Technology of Plasticity 2008;49: 216–220. 38 Nagayama S., Torizuka S., Komatsu T. Proc 2008 Japanese spring conf for the technology of plasticity 2008: 341. 39 Nagayama S., Terada D., Tsuji N. CAMP-ISIJ 2008;21: 1651. 40 Tsuji N. Boundary 2003;19: 8. 41 Vaidyanath L.R., Milner D.R. British Welding Journal 1960:1. 42 Nagayama S., Torizuka S., Komatsu T., Tsuji N. Proc. 2010 Japanese spring conf for the technology of plasticity 2010:61. 43 Takaki S. Ferrum 2007;12: 761. 44 Komatsu T., Torizuka S., Matsuzawa M., Watanabe Y. Proc 58th Japanese Joint Conf for the Technology of Plasticity 2007: 383. 45 Umemoto M. Formation of Nanocrystaline Structure by Severe Plastic Deformation, Ferrum 2007: 781. 46 Nagayama S., Torizuka S., Komatsu T. Proc 2008 Japanese Spring Conf for the Technology of Plasticity 2008: 46. 47 Komatsu T., Torizuka S., Muramatsu E., Nagayama S., Kobayashi H. Proc 2009 Japanese Spring Conf for the Technology of Plasticity 2009: 148. 48 Komatsu T., Torizuka S., Matsuzawa M., Watanabe Y. Proc 58th Japanese Joint Conf for the Technology of Plasticity 2007: 383.

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24 Nanostructured plain carbon-manganese (C-Mn) steel sheets prepared by ultra-fast cooling and short interval multi-pass hot rolling T. TOMIDA, K. MIYATA, and H. NISHIBATA, Sumitomo Metal Industries Ltd., Japan Abstract: This chapter describes the combination of an ultra-fast direct cooling process with short interval multi-pass hot rolling to produce nanostructured C-Mn steel sheets, and their mechanical and welding properties. Despite milling at high temperatures, plain carbon steel Fe-0.15%C–0.7%Mn exhibits grain refinement as fine as one micrometer in diameter by this new processing route. This grain refinement is caused by static transformation from austenite to ferrite with the enhanced nucleation owing to large frozen-in strain by ultra-fast direct cooling applied directly after short interval multi-pass rolling; the cooling rate is over 1000 K·s–1. The nanostructured sheet steel shows high strength, good local deformability and enough weldability, which are attractive ingredients for industrial applications. Key words: ultra-fast direct cooling, short interval multi-pass hot rolling, carbon manganese steel sheet, strain-induced static transformation.

24.1 Introduction Today the annual production of steel in the world exceeds 1.2 billion tons and is still increasing year by year. There is also a growing demand for high-strength steels that can be used to reduce the weight of various structures and components like vessels and bridges as well as automobiles, where specific strength plays an important role in reducing carbon dioxide emissions and in conserving natural resources in order to sustain modern lifestyles. In automobile industries, for instance, 30 to 60% more body parts are at present made of high-strength steel than in the 1990s. It requires costly alloying elements such as Nb, Ti and Mo, which are hard to recycle. Therefore there has been a strong motivation to develop steels that are largely strengthened by grain refinement without using those alloying elements, as described in the earlier chapters. This chapter describes the production of nanostructured plain low C-Mn steel sheets by ultra-fast direct cooling and short interval multi-pass hot rolling (UDCSMR), which may be applicable to commercial mass production in the near future. Currently the grain refinement of steel to a nanometer scale is most often investigated via heavy deformation at a low temperature, such as high-pressure 747 © Woodhead Publishing Limited, 2011

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torsion (HPT),1 equal-channel angular-pressing (ECAP)2 and accumulated roll bonding (ARB).3 However, the application of heavy deformation at a low temperature naturally increases deformation load and tends to decrease the productivity of the grain-refinement processes used. The complexity of those methods is another factor that hinders application to the mass production of nanostructured materials. On the other hand, the grain size of ferrite obtained by a hot strip mill (see Fig. 24.1 and 24.2), which is ideal equipment that has been used to mass-produce sheet steel for modern industry, is limited to over 5 µm for plain C-Mn steels. It is commonly agreed that this lower limit of grain size cannot be much decreased to below 3 µm, no matter how much deformation is exerted on the material during hot rolling (see Fig. 24.3). Therefore 3–5 µm is at present the practical lower bound of ferrite grain size in commercial plain C-Mn steels, to which a challenge has to be made. If the grain size can be reduced to below 1 µm by maintaining the rolling load of hot strip mills in a practical range, it may open new avenues for a variety of industrial applications. Historically the metallurgy in steel production using hot rolling and subsequent accelerated cooling in hot strip and plate mills has been studied as thermo-

24.1  Finishing train in a commercial hot strip mill at Kashima steel works of Sumitomo Metal Industries Ltd, Japan.

24.2  Layout of a hot strip mill.

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24.3  Deformation temperature of various grain refinement processes and ferrite grain diameters of plain C-Mn steel.

mechanical controlled processes (TMCP) for several decades. The reader might be referred to the literature about TMCP, for example, by Tamura et al.4 Grain refinement is part of the mechanism of improving the properties of steel by TMCP, which is explored in this chapter. Concerning UDCSMR, the present authors,5–9 Wakita et al.,10 Etou et al.11 and Fukushima et al.12 have given a series of papers in recent years. The following pages describe the process concept, grain refinement and its mechanism by UDCSMR, and the properties of nanostructured sheet steel thus obtained.

24.2 The concept of ultra-fast direct cooling and short interval multi-pass hot rolling (UDCSMR) and an experimental hot rolling mill This process was designed to greatly reduce the grain size of ferrite in C-Mn steel without much increase in the rolling load in hot strip mills. To maintain the rolling load within a practical range, the rolling temperature in UDCSMR is kept as high as that in conventional hot strip mills (see Fig. 24.3). If rolling is performed at a conventional high temperature range over 1100 K, the required rolling force would be acceptable in designing a commercial scale mill with increased reduction at each stand to about 50%.11,12 In such a temperature range the C-Mn steel under investigation is of thermodynamically stable austenite. Therefore transformation

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from austenite to ferrite is inevitable after hot rolling. Intense grain refinement may be expected to occur as enough nucleation sites for ferrite are introduced into austenite. However the question is of course how such a large number of nucleation sites can be introduced. A related notion might be found in the so-called strain-induced dynamic transformation (SIDT). In SIDT a super-cooled unstable austenite was deformed at lower temperatures than Ae3 to induce a dynamic (during deformation) transformation to fine ferrite. Many researchers, including Yada,13,14 Hodgson,15 Adachi,16 Hurley17 and Beladi,18 have reported a grain size of 1 to 2 µm for C-Mn steels by SIDT. It is believed that substructures such as dislocation cell structures or microbands that contain relatively high-angle boundaries are introduced into super-cooled austenite by heavy deformation at relatively low temperatures. As a result, the enhanced nucleation of ferrite by these substructures leads to grain refinement. Instead of lowering deformation temperature, high-speed multi-pass hot rolling and rapid cooling are combined with very short intervals between each step in order to enhance the build-up of strain in austenite in UDCSMR. Therefore the time interval between hot rolling passes, as well as that between the hot rolling and the subsequent rapid cooling, is reduced as much as possible. The rate of cooling to the temperature where ferrite quickly precipitates (the precipitation nose around 930 K) is increased to over 1000 K·s–1 to bypass recovery and recrystallization of austenite, and to promote the transformation to nanostructured ferrite (see Fig. 24.4). In other words, UDCSMR was designed to a cause the strain-induced static (post-deformation) transformation leading to a nanograin ferrite structure.

24.4  Schematic representation of a continuous cooling transformation diagram in C-Mn steel, cooling patterns in the present experiments and the effects of strain accumulation on ferrite precipitation.

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The experimental apparatus for UDCSMR is shown in Fig. 24.5 and 24.6. With three rolling stands in line, it can simulate hot rolling in a finishing train of commercial hot strip mills, whereas the commercial finishing train in general consists of six to seven rolling stands (see also Fig. 24.2). In the commercial mill, the time interval between rolling stands decreases as strips advance in the finishing train, and the minimal interval in today’s advanced commercial mill is around 0.3 s. In this experimental mill, the interval can be further decreased despite applying a larger reduction at each stand than in commercial mills. The distance between the F2 and F3 stands is particularly designed short to reduce the time interval to below 0.2 s with high-speed rolling. Immediately or directly after exiting from the last rolling stand, the 1 mm thick rolled steel strips are rapidly cooled by a device consisting of high-pressure water sprays at a rate up to 2000 K·s–1. The device is located so close to the final stand that the time interval between the end of rolling and the start of cooling can be reduced to below 0.1 s, while in commercial mills, this time interval is from

24.5  A photograph of apparatus for experimenting on UDCSMR.

24.6  Schematic representation of the experimental apparatus for UDCSMR.

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one-half to several seconds and the typical rate of cooling is from 30 to 200 K·s–1. Here we specifically define ∆t1 as the time interval that the steel strips take to run between the exit from final rolling and the place where the high-speed water stream first hits the strip surface (see Fig. 24.6). This time interval ∆t1 is a critical factor to obtain grain-refined structures in steel, as will be explained later. There is also a secondary cooling system that can simulate ordinary run-out cooling, as well as a cooling device to suppress deformation heating between the F2 and F3 stands as illustrated in Fig. 24.6. The specifications of the mill are listed in Table 24.1.

24.3 Nanostructured carbon-manganese (C-Mn) steel sheets produced by UDCSMR The steel compositions chosen for the experiment were two simple C-Mn steels. Their chemical compositions and Ae3 temperatures calculated by THERMOCALC 19 are listed in Table 24.2. Both steels are of 440 MPa tensile strength grades and of 5 to 7 µm in grain size, as they are produced by a conventional hot strip mill. First the influence of the interval between hot rolling and subsequent ultra-fast cooling, ∆t1, on ferrite grain size was investigated using 0.1%C-1%Mn steel. The small steel slabs, 70 mm in length, 100 mm in width and 30 mm in thickness, were hot-rolled to about 1500 mm × 110 mm × 1.2 mm strips with the thickness reductions of 40, 40 and 50% at the final three rolling passes. Subsequently, they were ultra-fast-cooled to the precipitation nose of ferrite (around 930 K) with various ∆t1 values as illustrated in Fig. 24.4. The hot rolling was finished at about 1100 K; the finishing temperature was measured at the exit of the final rolling pass using a pyrometer without applying ultra-fast cooling beforehand. This finishing Table 24.1  Specifications of experimental apparatus for UDCSMR

F1

F2

F3

Work roll diameter (mm) Work roll barrel length (mm) Maximum rolling load (kN) Maximum rolling speed (mpm)

200 400 3000 540

200 400 2500 360

220 400 2500 720

Table 24.2  Chemical compositions in mass percent and calculated Ae3 temperatures in K of steels used C

Si

Mn

P

S

Al

N

Nb

Ti

Ae3

0.10 0.15

0.05 0.01

1.11 0.75

0.018 0.020

0.003 0.002

0.017 0.022

0.0035 0.0022

trace trace

trace trace

1091 1091

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temperature lies at the calculated Ae3, and it is indeed close to the finishing temperature for steel of this kind in commercial mills. This also indicates that the hot rolling has been performed in a stable austenite region where transformation to ferrite hardly occurs during hot rolling. All the rolling pass intervals were over 0.6 s. Hence only the influence of ∆t1 on grain size was investigated with ordinary rolling pass intervals in the first experiment. The influence of ∆t1 on ferrite grain size is shown in Fig. 24.7 and 24.8. As ∆t1 is 0.5 s (around the lower limit of ∆t1 in conventional hot strip mills), the obtained ferrite grain size is still around the known lower limit of 3 µm, although the reduction at each rolling pass is as much as 40 to 50% and post-rolling cooling speed is as high as 2000 K·s–1. Therefore it is clear that the ultra-fast cooling device conventionally located (away from hot rolling stands) would not much influence the ferrite grain size in hot-rolled steel strips. Carrying out ultra-fast cooling on the run-out tables of hot strip mills was once intensively investigated in Europe in the 1990s by Simon20 and Neutjens21 et al., in which the cooling rate

24.7  Influence of ultra-fast direct cooling on the ferrite grain diameters of 0.1%C-1%Mn steel. Reducing the interval ∆t1 effectively reduces the grain diameter.

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24.8  Scanning electron micrographs of hot-rolled 0.1%C-1%Mn steel showing the reduction in grain size by ultra-fast direct cooling.

up to 1000 K·s–1 was attained with the cooling device at a more or less conventional position in commercial hot strip mills. They did not report an extensive grain refinement in plain C-Mn steel strips. However, as ∆t1 decreases to below 0.2 s, an extensive grain refinement appears. The grain size, particularly in the region from the sheet surfaces to a depth of onequarter of the sheet thickness, shows a large sudden drop as seen in Fig. 24.7. It decreases down to 1.3 µm in the subsurface region as ∆t1 reduces to 0.05 s. In this lower ∆t1 case, the water stream from spray nozzles hits the strip surface only about 10 cm from the rollers of the final stand so that the water stream surges to the rollers; i.e. complete direct cooling is practically attained. Although the grain refinement becomes less prominent in inner regions, it breaks the conventional

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lower bound of ferrite grain size and the average size becomes less than 2 µm as a result of the ultra-fast direct cooling. The ferrite grains thus obtained are markedly equiaxed and almost free from dislocations as seen in Fig. 24.9. This is evidence that these fine grains are due, not to dynamic transformation, but to static transformation after hot rolling, since dynamic transformation always implies some deformation of ferrite after transformation. There is a clear tendency that the finer grains found in shallower regions are more equiaxed than the coarser grains in the inner regions. On ferrite grain boundaries there are cementite (Fe3C) particles of the order of 100 nm in diameter in the subsurface region. Secondly, the combined effects of ultra-fast direct cooling and reducing the rolling pass interval were investigated using 0.15%C-0.7%Mn steel. The experimental procedures were mostly the same as those in the first experiment except for the final rolling pass interval (the interval between the rolling passes at F2 and F3 in Fig. 24.6). This interval, which we will call ∆t2 hereafter, has been varied from the ordinary duration of one second to less than two-tenths of a second, while ultra-fast direct cooling has been always applied (∆t1 was kept at 0.05 s). The results are presented in Fig. 24.10 to 24.12. As ∆t2 is over 0.5 s (the same as in the first experiment), the grain size of 0.15%C-0.7%Mn steel is approximately the same as that in the 0.1%C-1%Mn steel in the first experiment (compare Fig. 24.7 and 24.10). The grain size varies from 1.3 to slightly over 2 µm depending

24.9  Scanning electron micrographs of hot-rolled 0.1%C-1%Mn steel, showing the reduction in grain size produced by ultra-fast direct cooling.

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24.10  Influence of the reduction in rolling pass interval ∆t2 on ferrite grain diameter of 0.15%C-0.7% Mn steel.

24.11  Scanning electron micrographs of the nanostructured 0.15%C–0.7%Mn steels by UDCSMR (∆t1 = 0.05 s and ∆t2 = 0.17 s).

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24.12  Grain structures observed by electron backscattering diffraction for the nanostructured 0.15%C–0.7%Mn steel produced by UDCSMR.

on the depth from the sheet surfaces. However, as ∆t2 is reduced to 0.17 s, it effectively refines ferrite grains further. The grain sizes obtained at ∆t2 of 0.17 s are 0.9, 1.1 and 1.4 µm in subsurface, at a depth of one-quarter of the sheet thickness, and in the central regions respectively. Those fine grains are mostly surrounded by high-angle grain boundaries. For 90% of the boundaries, crystal rotation is more than 15 degrees. It is also interesting to note that the reduction in ∆t2 alone makes little contribution to the grain refinement, while ultra-fast direct cooling has greatly contributed to it. Hence the combination of ultra-fast direct cooling and short-interval multi-pass hot rolling is a key to attaining nanostructures in plain C-Mn steel.

24.4 Grain refinement mechanisms There were several possible mechanisms for explaining the present grain refinement, although strain-induced static transformation was originally expected for UDCSMR. The mechanism is important because it determines the applicability of the process to other steel alloys, and it gives us information on whether or not the process has a wide processing range for commercialization. The probable mechanisms are illustrated in Fig. 24.13. The first one is strain-induced static transformation, which operates in the conventional TMCP with the help of microalloying that retards the recovery of austenite. The second is SIDT and the last is dynamic recrystallization of austenite, in which fine recrystallized austenite grains provide ferrite necessary nucleation sites, leading to grain refinement. In what follows, several experiments that we have conducted to elucidate the mechanism are described.6 The first investigation was intended to understand the structure of steel sheets just before ultra-fast cooling. The ultra-fast cooling that was left off at about 930 K in the first rolling experiment presented in Fig. 24.7 and 24.8 was continued to

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24.13  Schematic representation of possible grain refinement mechanisms in UDCSMR.

room temperature with the other conditions being unchanged; i.e. the structure prior to ultra-fast cooling was thus quenched to room temperature. The micrographs shown in Fig. 24.14 show those quenched microstructures. It is seen that, in the central regions, the structure is quenched into martensite with a small amount of ferrite precipitating on the prior austenite grain boundaries irrespective of the value of ∆t1 (see Fig. 24.14 (d) to (f )). The prior austenite grains that are decorated by the small ferrite particles are obviously elongated in the rolling direction as indicated by white dashed lines. These results suggest that, in this central region, the nanostructured ferrite has emerged from a deformed austenite during the slow cooling after the ultra-fast cooling to 930 K. Hence the grain refinement is due to the strain-induced static transformation shown in Fig. 24.13 (a). The effect of reducing ∆t1 in this region, a gradual reduction in ferrite grain size as shown in Fig. 24.7, is likely to be due to an arrest of recovery of accumulated strain. In the subsurface region, the quenched microstructures are somewhat different from those in the central region. As ∆t1 is more than 0.3 s, the quenched microstructure is similar to that in the central region except that the prior austenite grains are not elongated but rounded as indicated by a white dashed line in Fig. 24.14 (b). However, as ∆t1 is 0.05 s, martensite has scarcely emerged and instead a fine-grained ferrite has appeared (see Fig. 24.14 (a)). The grain size of the

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24.14  Quenched microstructures after hot rolling in 0.1%C-1%Mn steel. Ultra-fast cooling was continued to room temperature with various ∆t1 conditions.

fine ferrite is as small as about 1 µm. It seemingly indicates that this fine ferrite, as well as that seen in Fig. 24.8 (a), appeared before the ultra-fast direct cooling. Therefore SIDT in Fig. 24.13 (b) may be the mechanism of grain refinement in the subsurface region. Nevertheless, since the quenched microstructure at ∆t1 of 0.3 s indicates the presence of rounded and somewhat coarsened prior austenite grains, as mentioned above, the structure 0.3 s after hot rolling (but before the ultra-fast cooling) should not be fine ferrite. The martensite structure shown in Fig. 24.14 (b) certainly conflicts with SIDT. To explain the structure in Fig. 24.14 (b), the mechanism based on SIDT requires a reverse transformation from the fine ferrite in Fig. 24.14 (a) to austenite as well as subsequent grain growth to the rounded austenite grains in Fig. 24.14 (b) during the short interval of 0.3 s. This is not likely to occur. Furthermore, the dislocationfree microstructure shown in Fig. 24.9 also suggests that grain refinement should not be caused by SIDT as mentioned earlier. Hence the fine ferrite shown in Fig. 24.8 (a) and 24.14 (a) is most likely to be due to a static transformation from deformed or dynamically recrystallized austenite. This static transformation is so fast that it cannot be bypassed by ultra-fast direct cooling to room temperature, leading to the formation of fine-grained ferrite shown in Fig. 24.14 (a) (see also Fig. 24.4).

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Then the second investigation was to distinguish, by texture analyses, whether the static transformation in the subsurface region is from deformed austenite (Fig. 24.13 (a)) or from dynamically recrystallized fine austenite (Fig. 24.13 (c)). The crystallographic texture of deformed austenite should be different from that in dynamically recrystallized austenite, although a difficulty exists in that the texture of prior austenite is destroyed by transformation to ferrite at a low temperature. The calculation method that Tomida et al.22,23 recently proposed was employed to overcome the difficulty. Based on the misorientation distribution function method (MODF),24 the texture of prior austenite can be deduced from that of the product ferrite, which is readily analysed by X-ray pole figure measurements. Tomida et al. introduced a new variant selection rule for Kurdjumov–Sachs (KS) orientation relationship: {111}γ  //{110}α and <110>γ  //<111>α25 into MODF; the variant selection rule is called the double KS relation. Then they showed that the texture change due to the transformation from austenite to ferrite after hot rolling could be quantitatively simulated by MODF combined with the variant selection rule. Thereby deduced textures of prior austenite are shown in Fig. 24.15 in the form of orientation distribution functions (ODF). The prior austenite textures in the subsurface regions at ∆t1 of 0.05 and 0.3 s were deduced using the measured ferrite textures for the samples shown in Fig. 24.8 (a) and 24.8 (b). For comparison, typical deformed and recrystallized face-centered cubic (fcc) textures in subsurface regions of hot-rolled Ni-30%Fe alloy are also shown; Ni-30%Fe is known as a model alloy of austenite, since it has a similar stacking fault energy to that of austenite and never transforms to body-centered cubic (bcc) on cooling.26 The texture of prior austenite at ∆t1 of 0.05 s is clearly different from that at 0.3 s. At ∆t1 of 0.05 s, the main components lie around {100}<011> to {322}<011> as well as around the {111} fiber located at 54.7° in F in the φ2 = 45° section of ODF, which is very similar to the texture observed in the deformed Ni-Fe model alloy (compare Fig. 24.15 (a) and 24.15 (c)). However, at ∆t1 of 0.3 s, the {100}<011> component completely disappears and a component around {410}<144> appears instead. This type of texture obviously corresponds to that of the recrystallized austenite (compare Fig. 24.15 (b) and 24.15 (d)). A broad {111} fiber seen in the φ2 = 45° section is perhaps a remnant of deformed austenite. Therefore it is concluded that the transformation in the subsurface region at ∆t1 of 0.05 s is not from recrystallized austenite but from deformed austenite. Recrystallization of austenite takes place in the subsurface region as ∆t1 is increased over 0.3 s. Hence the grain refinement mechanisms via ultra-fast direct cooling should be based on the strain-induced static transformation shown in Fig. 24.13 (a) regardless of the depth from sheet surfaces. Similar analyses under UDCSMR conditions have led us to the same conclusion. In UDCSMR, the reduction of the last pass interval perhaps suppresses the recovery and recrystallization of austenite, which otherwise occur during this interval, and therefore the even finer grain structures shown in Fig. 24.11 and 24.12 can appear due to the enhanced accumulation of strain.

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24.15  ODFs of the deduced textures of prior austenite at ∆t1 of (a) 0.05 s and (b) 0.3 s in 0.1%C-1%Mn steel and the (c) deformed and (d) recrystallized textures of hot-rolled Ni-30%Fe alloy in subsurface regions. The deduced textures were calculated from the measured textures for the microstructures shown in Fig. 24.8(a) and 24.8(b).



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If the mechanisms in both subsurface and central regions are similar, then what caused the large difference in grain size between the two regions? To clarify the reason for this, the deduced texture of prior austenite in the central region is shown in Fig. 24.16 along with a typical deformed fcc texture in the central region of hot-rolled Ni-30%Fe alloy. It is interesting to observe that the prior austenite texture in the central region, which is a deformation texture as expected, is totally different from that in the subsurface region (compare Fig. 24.15 (a) and 24.16 (a)). The texture in the subsurface region is known as a shear deformation texture that develops under strong influence of friction between the roller and sample surfaces. During hot rolling, large shear stress is exerted on materials because of the friction so that subsurface layers undergo additional shear deformation. Therefore the shallower the depth from the sheet surface, the larger the strain during hot rolling. Hence the finer grain structure in the subsurface region is mainly ascribed to this additional shear strain that increases towards the sheet surfaces and enhances nucleation of the ferrite. This increase in strain due to shear stress is also the reason why the

24.16  ODFs of (a) the deduced texture of prior austenite at ∆t1 of 0.05 s in 0.1%C-1%Mn steel and (b) the deformed texture of hot-rolled Ni-30%Fe alloy in the central region.

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recrystallization of austenite occurs in the subsurface region for the interval of 0.3 s, whereas it does not occur in the central region as seen in Fig. 24.14. In such a heavily deformed or work-hardened austenite, the increase in nucleation sites for ferrite has been discussed in relation with 1) an increase in high-angle grain boundary areas due to elongated grain shape in the rolling direction, 2) an increased nucleation potency at the grain boundaries because of the introduction of grain boundary ledges, and 3) additional nucleation sites due to deformation substructures.27 Therefore a study has finally been conducted, using the Ni-30%Fe model alloy, on what substructure evolves in austenite during UDCSMR. The model alloy is known to have a stacking fault energy similar to austenite as mentioned earlier. However it shows a somewhat slower self-diffusion rate than that of austenite at the same temperature; i.e. a slower recovery is expected. Therefore the model alloy was hot-rolled at a higher finishing temperature than that for C-Mn steels to attain comparable recovery rates. The finishing rolling temperature for the model alloy was 1173 K, whereas for C-Mn steels it was around 1100 K. The initial grain size was also carefully controlled so as to be comparable with the grain size of austenite in the C-Mn steel, which was about 50 µm. Grain elongation in the rolling direction is clearly seen in the orientationimaging map of hot-rolled Ni-30%Fe by electron backscattering diffraction (EBSD) as shown in Fig. 24.17. Since the initial grain size is about 50 µm, the small elongated grains seen in the subsurface region are indicative of recrystallization during rolling pass intervals and subsequent deformation probably at the final rolling, whereas little recrystallization is observed in the central region. On the grain boundaries some ledges, and particularly in the subsurface region, very small equiaxed grains that are mostly surrounded by highangle boundaries are observed. Within the grains, the boundaries or dislocation walls are aligned at an angle of about 30° with the rolling direction. Many of them

24.17  Orientation imaging map by EBSD for hot-rolled Ni-30%Fe sheets by UDCSMR at a finishing temperature of 1173 K.6

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have developed to high-angle boundaries and they are associated with the small equiaxed grains. Interestingly, there is a good correlation between the spacing between those boundaries (ds) in the model Ni-30%Fe alloy and the grain size of the nanostructured ferrite shown in Fig. 24.11 and 24.12. For instance, the average spacing between boundaries with a misorientation angle of over 10° in the Ni-30%Fe is 1.2 µm in the subsurface region and 2.1 µm in the central region (see Fig. 24.17), while that for the nanostructured ferrite is 0.9 and 1.4 µm respectively. Transmission electron micrographs in Fig. 24.18 reveal the details of such substructures; the planes of observation have been normal to the transverse direction (the same plane as in Fig. 24.17). Under transmission electron micrography, the structure in the subsurface layer appears to entirely consist of cellular arrays of dislocations or boundaries. This structure is similar to the cell structure that has been reported to appear in the early stages of deformation in fcc metals.28 However, unlike the conventional cell structure consisting of low-angle boundaries, these cellular arrays contain many high-angle boundaries over 20° in misorientation angle as indicated in Fig. 24.18. A similar cellular substructure has been reported by Hurley et al.29 in their study on SIDT. Probably, the equiaxed

24.18  Transmission electron micrographs of the hot rolled Ni-30%Fe sheets shown in Fig. 24.17.6 The numbers indicate misorientation angle in degrees.

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grains in Fig. 24.17 are the cellular structures that have developed to high-angle boundaries. In the central regions there are fewer cellular structures, and instead the band-like structure divided mostly by low-angle boundaries appears with some kind of kink (indicated by arrows in Fig. 24.18 (b). Therefore all three structural features mentioned above to enhance the nucleation of ferrite have been observed. Hence although the role of the small angle boundaries on nucleation is unclear, it is thought that those substructures with dense high-angle boundaries, which are frozen in by ultra-fast direct cooling, will provide static transformation with numerous nucleation sites to form the nanostructured ferrite.

24.5 Deformation characteristics The effect of grain size on the mechanical properties of materials is most commonly expressed in a series of constitutive equations comprising a Hall–Petch type of relationship,30,31 by which the properties are related proportionally to the reciprocal root of the grain size. For the yield stress σy of plain low-carbonmanganese steels, Pickering32,33 has proposed the following equation:

σy[MPa] = 15.4 (3.5 + 2.1·Mn + 5.4·Si + 23·Nf 1/2 + 1.13·d–1/2), [24.1] where Mn, Si and Nf are the amounts of silicon, manganese and free nitrogen in mass percent respectively, and d is the grain diameter in µm. It is expected that grain refinement down to 1 µm in grain size by UDCSMR can achieve yield strength over 700 MPa in simple chemical compositions such as 0.15%C-0.7%Mn. The mechanical properties of 0.15%-0.7%Mn steel sheets with a variety of grain sizes were evaluated by tensile tests. The grain size was controlled by changing the pass interval (∆t2) and cooling conditions (∆t1 and cooling rates) after hot rolling using the laboratory mill shown in Fig. 24.5 and 24.6. For samples with the smallest average grain size of 0.9 µm, small test pieces with gauge length, width and thickness of 8.1, 3.4, and 0.2 mm respectively were cut from the subsurface layer of the nanostructured steel sheet shown in Fig. 24.11 and 24.12, while the other samples were evaluated with the gauge length and width of 50 and 25 mm respectively, without thinning sheet thickness. The grain size averaged over the entire sheet thickness for the nanostructured steel sheet by UDCSMR is 1.2 µm. Figure 24.19 shows the stress–strain curves by tensile tests. It is obvious that the flow stress is significantly increased and then 440 MPa grade steel results in a highstrength grade with the upper yield strength at over 700 MPa by reducing the grain size to below 1 µm. The obtained yield strength is shown in Fig. 24.20 as a function of grain size, comparing it with some previous studies on plain C-Mn steels.34,35 The yield strength of steel with an average grain size of 0.9 to 5 µm agrees well with the equation [24.1] or more specifically the following Hall–Petch equation36 as shown in Fig. 24.20: σupper–y[Mpa] = 100 + 600 × d–1/2, © Woodhead Publishing Limited, 2011

[24.2]

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24.19  Stress–strain curves by tensile tests with various average grain sizes of 0.15%C-0.7%Mn hot-rolled sheets.11

24.20  Yield strength of 0.15%C-0.7%Mn steel sheet samples as a function of the grain size, compared with previous studies.

where σupper–y is upper yield strength. Therefore it has been confirmed that the strength of the present nanostructured steel by UDCSMR is related with grain size according to the conventional Hall–Petch relationship, and σupper–y increases to 700 MPa for the subsurface layers (measured for the thinned sample as abovementioned) and 650 MPa for the whole sheet. © Woodhead Publishing Limited, 2011



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On the other hand, tensile elongation is significantly reduced by grain refinement especially down to a grain size less than 2 µm. It is because uniform elongation greatly decreases due to an associated decrease in work hardening rates, by which Considère’s criterion37,38 for plastic instability is satisfied in an earlier stage of deformation. Large yield point elongation, or Lüders deformation, is another typical characteristic of deformation observed for the nanostructured steels. These tensile properties are consistent with those of other nanostructured materials.39,40,41,42,43 To further understand deformation in nanostructured steel, the evolution of Lüders bands has been observed using small tensile test pieces (8.1 × 3.4 × 0.2 mm3 in gauge dimensions), which have been cut from the subsurface region of coarse-grained and nanostructured steel sheets. The microstructures of both tensile specimens mostly consist of equiaxed ferrite grains in which the internal dislocation density is quite low as shown in Fig. 24.21. The evolution of Lüders bands during tensile tests can be clearly observed by the surface roughness created on electro-polished surfaces as shown in Fig. 24.22. In the coarse-grained specimen, the yielding is accompanied with the evolution of Lüders deformation,

24.21  Transmission electron micrographs of subsurface layers of 0.15%C-0.7Mn hot-rolled steels used for tensile tests.

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24.22  Evolution of Lüders deformation in small tensile test specimens of the nanostructured and coarse-grained 0.15%C-0.7%Mn steel.

which propagates throughout the gauge section, followed by uniform deformation with work hardening. In the nanostructured specimen, on the other hand, the development of Lüders band is interrupted due to the onset of necking. The necking develops in the Lüders bands by suppressing the propagation of the bands throughout the gauge section. In Fig. 24.23, an image quality (IQ) map by EBSD analysis for the Lüders bands is displayed. The plane of observation is the sheet surface and the observed area is the center of necked parts if it is necked. Elongation in the tensile direction of ferrite grains with deformation substructures is seen in the IQ maps. By considering the crystal rotation of initial grains due to the introduction of substructures, the elongation or strain of the initial grains in the tensile direction was roughly determined from the IQ maps as well as the crystal orientation distributions obtained at the same time. In Fig. 24.24, the average strain for ferrite grains is plotted against the ratio of the sheet thickness of the necked part to the

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24.23  IQ maps by EBSD showing deformation structures in the Lüders bands shown in Fig. 24.21.

initial thickness. Interestingly, the result obviously indicates that the local ductility of the nanostructured ferrite grains is almost equivalent to that of the coarsegrained ferrite. Local ductility at necked parts can be evaluated by obtaining the non-uniform elongation or necking elongation in tensile tests as well, which is defined as the difference between the total and uniform elongations. The uniform elongation in C-Mn steel, however, disappears as ferrite grains are refined to below 2 µm in diameter, as mentioned earlier. Therefore, instead of obtaining non-uniform elongation, total elongation under various gauge lengths has been measured to evaluate the local ductility. The necking elongation is sensitive to the specimen

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24.24  Grain elongation ratios as a function of necking strain.

shape, and if the gauge section is very short the necking elongation accounts for most of the elongation. Therefore the extrapolation of total elongation to the null gauge length allows us to compare the non-uniform elongations of two materials without obvious uniform elongation. Such comparison is shown in Fig. 24.25 for the nanostructured and coarse-grained steels. Indeed the elongation of the nanostructured steel becomes comparable to or may even exceed that of the coarse-grained steel at the lower limit of gauge length. As ferrite is grain-refined, the second phase, whether cementite or pearlite, is also finely dispersed. Then the formation of voids and their linkage to cause fracture (see Fig. 24.26) should be decelerated as strain increases to fracture levels. Therefore the finer grain structure may lead to better local ductility. Such local ductility is also known to bear strongly on endurance against fracture during the hemming, stretch-flanging and hole-expanding processes. Fig. 24.27 and 24.28 show the examples of those forming tests. Hemming tests have shown that the nanostructured steel sheets of 1.4 mm in thickness can be completely hemmed without rupture as seen in Fig. 24.27. The examination by SEM of microstructures after hemming barely indicated the presence of voids. Hole-expanding tests furthermore showed a greater hole expansion ratio than for coarse-grained steels, while the tensile strength for the nanostructured steel was largely increased by the grain refinement as shown in Fig. 24.28; the hole expansion ratio was defined as the increment of diameters of punched holes divided by the initial diameter of the holes, in which the holes were

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24.25  Total elongation of the nanostructured and coarse-grained 0.15%C-0.7%Mn steels measured with various gauge lengths.

24.26  Cross sectional microstructures of fractured regions by tensile tests in 0.15%C-0.7%Mn steel.

expanded by a conical punch until a fracture occurred. Hence although the uniform elongation in tensile tests in the nanostructured steel by UDCSMR is severely decreased due to the decrease in strain hardening rates, it shows much local ductility that may play an important role in various forming processes. A better

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24.27  Microstructures of the 0.15%C-0.7%Mn nanostructured sheet after a hemming test.10

24.28  Effects of grain size on hole expandability of 0.15%C-0.7%Mn steel sheets.

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balance between strength and local ductility is expected to extend the applications of the nanostructured steel to complex components such as automobile body parts.44

24.6 Welding and application to some prototype parts For applications such as manufacturing automobile bodies, weldability is an essential requisite for the steel used. Particularly in nanostructured steel, it has been long pointed out that fine grains grow quickly during heat cycles of welding,45 and this process causes severe softening in heat-affected zones (HAZ). Unless sufficient resistance to HAZ softening is attained, the material is practically unusable for the mass production of automobiles. Furthermore in recent years, so-called tailored welded blanking (TWB) has become one of the key technologies in auto body assembling.46,47 In TWB, pre-blanked and welded steel sheets are press-formed together into a final shape. Therefore the weld requires to be press-formable. Hence the HAZ softening and applicability to TWB of the nanostructured sheet steel by UDCSMR have been investigated via laser welding (LW) and plasma arc welding (PAW) as well as resistant spot welding (RSW), one of the most important welding methods in the automobile industry. A 0.15%C-0.7%Mn nanostructured sheet steel of 2 mm in thickness was prepared by UDCSMR, and its weldability was compared with those of two commercial steels. These commercial steels were used as comparative materials, since they showed good weldability under most conventional welding conditions. The chemical compositions and tensile properties of the steels are listed in Table 24.3. Although possessing a similar tensile strength slightly over 600 MPa, they are very different in chemistry since the commercial steels are mostly strengthened by solution and precipitation hardenings, unlike the present nanostructured steel. The grain sizes of the commercial steels are much larger than those of the nanostructured steel as seen in Fig. 24.29. Table 24.3  Chemical compositions, mechanical properties and Ceq of Steels used for welding tests

Chemical compositions (mass %)

Strength (MPa)



C

Si

Mn

others

YS

TS

Steel A   nanostructured steel Steel B Steel C

0.15

0.03

0.70

trace

633

656 0.186

0.15 0.10

0.02 0.94

1.34 1.70

Ti, Nb trace

474 392

604 0.234 625 0.230

Note: Ceq = C + Mn/6 + (Cr + Mo + V)/5 + (Ni + Cu)/15.

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24.29  Microstructures of steels A, B and C.

The carbon equivalent (Ceq) for hardenability,48 expressed by equation [24.3], is also listed in Table 24.3: Ceq = C + Mn/6 + (Cr + Mo + V)/5 + (Ni + Cu)/15,

[24.3]

where the element symbols on the right side indicate the amounts of elements in mass fractions. Welding produces a complex temperature environment at the joints, and it brings significant and detectable physical change. The physical change can be grain growth, tempering of the steel if it has been previously hardened, or hardening of the steel, depending upon various welding conditions. In particular, final microstructures and hardness are strongly related with cooling rates. Therefore microstructures and hardness distribution around welds using two different methods, LW and PAW, were first investigated. The cooling rates in LW and PAW are in the ranges of around 300 K·s–1 and 40 K·s–1 respectively, and these two cooling rates may result in rather different microstructures as depicted in the continuous cooling transformation diagram for a steel of 590MPa tensile strength grade in Fig. 24.30. When laser-welded, both the present grain-refined steel (steel A) and steel B exhibited similar hardness distributions as seen in Fig. 24.31 (a). One of the reasons is that the hardenability of both steels is great enough to transform into martensite and/or bainite in the welded metal at the cooling rate of LW (see Fig. 24.32). The slightly lesser hardness of the weld metal for steel A is due to the smaller number of alloying elements contained. The other important reason is that severe coarsening of ferrite grains has scarcely occurred in the HAZ of steel A (see Fig. 24.33). It is worth noting that the nanostructure in the present material is so stable against grain growth that HAZ softening hardly takes place during LW. The microstructure in the transition region from HAZ to the unaffected base metal of steel A consists of fine ferrite grains of which the grain size is equal to that of the base metal.

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24.30  Typical CCT diagram for a steel of 590MPa tensile strength grade and the cooling rates of various welding methods.

24.31  Cross-sections and hardness distributions of steels A and B. (a) Laser welded joint, (b) Plasma arc welded joint.

However, a softening of the HAZ has occurred in the plasma-arc-welded joint of the steel A. Since the slower cooling rate of PAW resulted in coarse proeutectoid ferrite and bainite in the welded metal and even coarser ferrite in its vicinity, the hardness in steel A showed a marked reduction in the region 2 to 4 mm away from the center of the weld as shown in Fig. 24.31 (b) and 24.34.

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24.32  Microstructures of welded metal.

24.33  Microstructures of a heat affected zone of laser-welded steel A.

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24.34  Microstructures of a heat-affected zone of plasma-arc-welded steel A.

The influence of cooling rates on microstructures and hardness is also seen in the HAZ simulation shown in Fig. 24.35. The heat schedules of the simulation are shown in Fig. 24.36. The heating rate is 100 K·s–1, and each specimen of steel A has been kept for 4 seconds at 1073 or 1173 K being followed by cooling at the rate of 500 or 40 K·s–1; the temperatures of 1073 and 1173 K are a ferrite and austenite dualphase temperature and an austenite temperature respectively. As the cooling rate was 500 K·s–1 to simulate LW, the microstructures consisting of martensite or a fine mixture of ferrite and martensite appeared, and a larger hardness than that of the non-annealed steel A was obtained at both annealing temperatures. On the other hand, as the cooling rate was 40 K·s–1 to simulate PAW, the microstructure consisting of coarse ferrite and pearlite emerged and hardness greatly decreased. Hence if heat inflow is sufficiently low and the speed of subsequent cooling is comparable to or faster than that in LW, HAZ softening is not likely to occur in the present nanostructured steel. Indeed no HAZ softening has been observed in RSW either. Then, to compare the TWB formability of the nanostructured steel by UDCSMR to that of the steel B, laser-welded or plasma-arc-welded sheets of 50 mm in width and 100 mm in length were subjected to dome-forming tests shown in Fig. 24.37; the diameter of the hemispheric punch was 50 mm, punching speed was 1 mm per second, and the holding pressure was 98 kN. The sheets with the weld lines, which were perpendicular (type A) or parallel (type B) to the long side, as well as those without weld lines, were stretched out by the punch until they

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24.35  Microstructures of a base metal and HAZ-simulated specimen.

24.36  Schematic representation of heat treatment in HAZ simulation tests.

fractured, and the final height of the dome was measured. A comparison has been made in the joint efficiency defined as the ratio of the dome height with the weld line to that without the weld line. The results of type A of the forming test are shown in Fig. 24.38 and 24.39. It is seen that, using LW, both steels A and B have ruptured in the base metal and the joint efficiency has been over 90%. However, under PAW, nanostructured steel A ruptured in the HAZ, and the joint efficiency greatly decreased since the HAZ

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24.37  Schematic representation and photographs of dome-forming specimens.

24.38  Schematic representation and photographs of dome-forming specimens.

softening caused a large concentration of deformation into the HAZ resulting in a marked decrease in dome height. On the other hand, steel B, which showed little HAZ softening, ruptured in the base metal showing good joint efficiency of over 90% under PAW. Therefore the HAZ softening in the nanostructured steel seen in Fig. 24.31 is certainly a crucial problem to its use in TWB as well as for many other purposes.

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24.39  Photographs of the fracture areas of formed specimens (type A).

Nevertheless it should be noted that the nanostructured steel A shows a certain superiority for TWB over conventional steel in type B of the forming test as shown in Fig. 24.40 and 24.41. In this test, steel A exhibited the comparable joint efficiencies from 80 to 90% to those in the type A forming test, whereas steel B showed decreased efficiencies of about 65% as compared to those in the type A test. Both of the steels A and B failed to rupture in welded metal under LW as well as PAW. This is because in the type B test, where the main load is parallel to weld lines, the ductility of welded metal directly influences the limit of forming. Therefore the material mostly fails to rupture in welded metal, of which the ductility is in general inferior to that of base metal, and the nanostructured steel A, which has softer and thus more ductile welded metal owing to less alloying elements (see Fig. 24.31), has shown superior formability in type B of the forming test. Hence if LW or a welding method with even higher cooling rates is employed, the nanostructured sheet steel with no HAZ

24.40  Results of forming tests of type B.

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24.41  Photograph of the fracture areas of formed specimens (type B).

softening might be as good as or even better a material for TWB than the conventional sheet steels; note that LW is the most used welding method in TWB at present. Weldability in RSW has furthermore been investigated using steels A and C, since RSW is the most used and the most important method in joining steel components in the automobile industry. Tension shear tests are commonly used in quality control of RSW joints.49 Therefore the test specimens as shown in Fig. 24.42 were prepared by overlapping two rectangle sheets and spot-welding in the center of the overlapped area with various weld currents. Then they were subjected to tensile tests to measure the strength of joints and the size of nuggets. The size of nuggets was examined by measuring the diameter of sheared sections or hollow parts of torn joints. The spot weld may fail in shear through or around welded nuggets. Generally the shear failure at weld nuggets results in lower strength, while higher strength is obtained as base metal is torn to rupture. As seen in Fig. 24.43 and 24.44, such behavior of joints is seen for both of nanostructured steel A and steel C. They also show approximately the same strength of joints with the size of nuggets being the same, since HAZ softening scarcely occurs for either steels in RSW as mentioned above. As the nugget diameter increases with the weld current, splashes of molten melt start occurring. Thus the weld current range is limited by this splash as well as the lower bound of the desired nugget size that is generally around two to four times the square root of the sheet thickness.49 In Fig. 24.43, thus-determined

24.42  Schematic representation of tension shear tests.

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24.43  Nugget diameters versus weld current for steels A and C under welding pressure and time of 3.9 kN and 0.5 s.

24.44  Joint strength versus weld current for steels A and C under welding pressure and time of 3.9 kN and 0.5 s.

appropriate weld current ranges are indicated; the lower bound indicated is four times the square root of the sheet thickness. Although the appropriate current range of the nanostructured steel is slightly shifted to a higher current because of lower electric resistance (caused by a smaller number of alloying elements), it shows a comparable range of appropriate weld current to conventional steel. Hence it is concluded that this nanostructured sheet steel has fairly good weldability and may be applicable to various steel components in industry. Finally, the two prototype components50,51 made of 0.15%C-0.7%Mn nanostructured steel sheets by UDCSMR are displayed in Fig. 24.45 and 24.46; the tensile strength, width and thickness of the sheets used were about 650 MPa, 300 mm and 1.5 mm respectively. Simple bending, punching, stretching as well drawing tests were first conducted to examine the forming limits of the material beforehand, and then the J-shaped and T-shaped components shown in the figures were designed taking front and center pillars in automobile bodies as models. In designing these components, the material was assumed to deform almost to its limit in the most severely deformed part (especially in the J-shaped component). The former was press-formed from a blanked sheet, while the latter was press-formed from two tailored blanked sheets

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24.45  J-shaped prototype component die-formed from the 0.15%C-0.7%Mn nanostructured steel sheet. Arrows indicate the portions fractured.

24.46  T-shaped prototype component die-formed from the TWB 0.15%C-0.7%Mn nanostructured steel sheets.50,51 Arrows indicate the necked portions and the welded joint by LW.

welded together by LW. The heights of flanged and embossed parts were 30 and 10 mm respectively in both cases. No fracture has occurred in the T-shaped component including the flanged LW-welded joint as seen in the photograph in Fig. 24.46, although slight necking has been observed in the part embossed into a triangular roof shape (indicated by the arrows A). For the J-shaped component, the most severely deformed portions underwent fracture as indicated by the arrows in Fig. 24.45, which had been expected by the numerical simulation during the designing; a similar fracture was also observed to occur in press-forming the

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same component using conventional 590 MPa grade steel sheets. Otherwise the forming tests were very successful. Hence these press-forming trials clearly indicated fairly good formability of the present nanostructured steel sheet, which is presumably enough for the material to be applied to practical parts for cars, machines and other structures.

24.7 Conclusions Although rolled at a high temperature over Ae3, which would ease industrial application, the steel (having a very simple chemical composition such as 0.15%C–0.7%Mn) can be made into the nanostructured material by a combination of ultra-fast direct cooling and short interval multi-pass hot rolling. The experiment using a laboratory rolling mill equipped with closely aligned rolling stands and cooling apparatus, in which extremely short intervals below 0.2 s as well as large cooling rates over 1000 K·s–1 are attained, has successfully shown that the ferrite grain diameter of plain C-Mn steel reduces to below 1 µm. This new route of nanograin refinement is due to an enhanced nucleation of ferrite in austenite with accumulated and frozen-in strain by UDCSMR. Since this transformation to fine ferrite is static (post-deformation), a relatively wide processing range of hot rolling operations would be expected on applying it to hot strip mills unlike dynamic transformation. The nanostructured material exhibits an attractive combination of high strength, high local ductility and good weldability. It has been particularly shown that, while the elongation in tensile tests is severely decreased due to the decrease in strain hardening rates, and HAZ softening occurs in welding with very slow cooling rates, the C-Mn sheet steel hardened by nanostructures exhibits large local deformability as well as excellent weldability in resistant spot and laser weldings. Indeed the present material could be applied to several prototype components made by various types of forming and welding processes. Thus UDCSMR may open a path to the industrial mass production and application of nanostructured steels. However the results described in this chapter are only concerned with plain C-Mn steel. Various other types of steel such as duplex-phase steel and transformation induced plasticity steel containing Si, Cr and more Mn have been developed and are in increasingly wide use in industry. The influence of UDCSMR on the microstructures and properties of such an advanced type of steel would be greatly worth investigating. The second phases contained in those steels, such as martensite, bainite and retained austenite, may dramatically the improve mechanical properties of the nanostructured steels. Those points need to be further investigated.

24.8 References   1 Variev R.Z., Ivanisenko Y.V., Rauch E.F., Baudelet B. Acta Mater 1996;44: 4705–4712.   2 Park K.T., Kim Y.S., Lee J.G., Shin D.H. Mater Sci Eng A 2000;293: 165–172.

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  3 Tsuji N., Saito Y., Lee S.H., Minamino Y. Adv Eng Mater 2003;5: 338–344.   4 Tamura I., Ouchi C., Tanaka T., Sekine H. Thermomechanical processing of high strength low alloy steels, London, Butterworths 1988.   5 Tomida T., Imai N., Yoshida M., Fukushima S. Mater Sci Forum 2007;539–543: 4708– 4713.   6 Tomida T., Imai N., Miyata K., Fukushima S., Yoshida M., Wakita M., Etou M., Sasaki T., Haraguchi Y., Okada Y. ISIJ International 2008; 48: 1148–1157.   7 Miyata K., Wakita M., Fukushima S., Etou M., Sasaki T., Shibahara T. Super short interval multi-pass rolling technology for manufacturing ultrafine-grained steel sheet. In: Proceedings of materials science & technology. ASM International, 2005: pp. 55–64.   8 Miyata K., Wakita M., Fukushima S., Etou M., Sasaki T., Tomida T. Mater Sci Forum 2007;539–543: 4698–4703.   9 Miyata K., Wakita M., Fukushima S., Tomida T. Microstructures and properties of ultrafine grained C–Mn steel sheets by super short interval multi-pass rolling. In: Proceedings of second international symposium on steel science. The Iron and Steel Institute of Japan, 2009: pp. 115–120. 10 Wakita M., Kawano K., Tomida T. Microstructures and mechanical properties of ultrafine-grained steel due to super short interval multi-pass rolling. In: Proceedings of ISUGS 2007. The Iron and Steel Institute of Japan, 2007: pp. 8–11. 11 Etou M., Fukushima S., Sasaki T., Haraguchi Y., Miyata K., Wakita M., Tomida T., Imai N., Yoshida M., Okada Y. ISIJ international 2008;48: 1142–1147. 12 Fukushima S., Sasaki T., Etou M., Shibahara T., Kawano K., Wakita M. Development of super short interval multi-pass rolling technology for ultrafine-grained hot strip. In: Proceedings of eighth ICTP. University of Padova, 2005: pp. 531–538. 13 Yada H., Matsumura Y., Senuma T. Massive type transformation induced by hot deformation in low carbon steels. In: Proceedings of international conference on martensitic transformation. Japan Institute of Metals, 1986: pp. 515–520. 14 Yada H., Matsumura Y., Senuma T. A new thermomechanical heat treatment for grain refining in low carbon steels. In: Proceedings of Thermec-88, vol. 1. Iron and Steel Institute of Japan, 1988: pp. 200–207. 15 Hodgson P.D., Hickson M.R., Gibbs R.K. Mater Sci Forum 1998;284–286: 63–72. 16 Adachi Y., Tomida T., Hinotani S. Tetsu to Hagane 1999;85: 620–627. 17 Hurley P.J., Hodgson P.D. Mater Sci Eng A 2001;302: 206–214. 18 Beladi H., Kelly G.L., Hodgson P.D. Mater Trans 2004;45: 2214–2218. 19 Sundman B., Jansson B., Andersson J-O. CALPHAD 1985;9: 153–190. 20 Simon P., Fishbach J-P., Riche P. Revue de Metallurgie-CIT 1996;93: 409–415. 21 Neutjens J., Harlet P., Bakolas T., Cantinieaux P. Processing and properties of a new hot-rolled high-strength fine-grained multi-phase steel. In: Proceedings of 40th mechanical working and steel processing conference. Pittsburgh, 1998. p. 311–320. 22 Tomida T., Wakita M., Yoshida M., Imai N. Quantitative prediction of transformation texture in hot-rolled steel sheets by multiple KS relation. In: Proceedings of 15th ICOTOM. American Ceramic Society, 2008. 23 Tomida T., Wakita M., Yoshida M., Imai N. Mater Sci Forum 2009;638–642: 2846– 2851. 24 Bunge H.J., Humbert M., Welch P.I. Textures and microstructures 1984;6: 81–96. 25 Kurdjumov G., Sachs G. Z Physik 1930;64: 325–343. 26 Charnock W., Nutting J. Mater Sci Journal 1967;1: 123–127. 27 Umemoto M., Hiramatsu A., Moriya A., Watanabe T., Nanba S., Nakajima N., Anan G., Higo Y. ISIJ International 1992;32: 306–315.

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28 Hirsch J., Lück K., Hatherly M. Acta Metall 1988;36: 2905. 29 Hurley P.J., Muddle B.C., Hodgson P.D. Formation of ultra-fine ferrite during strip rolling and analysis of potential ferrite nucleation sites within austenite. In: Proceedings of thermomechanical processing of steels. IOM communications, 2000: pp. 476–485. 30 Hall E.O. Proc Phys Soc London 1951;64B: 747–753. 31 Petch N.J. J Iron Steel Inst 1953;174 (Part 1): 25–28. 32 Pickering F.B. The effect of composition and microstructure on ductility and toughness. In: Toward improved ductility and toughness. Japan: Climax Molybdenum Development Co, 1971: p. 9. 33 Pickering F.B. Physical metallurgy and the design of steels. London: Applied Science Publishers Ltd; 1978: p. 37. 34 Morrison W.B. Trans. ASM 1966;59: 824–846. 35 Matsukura N., Nanba S. Tensile properties of fine grain steels through heavy deformation in alpha+gamma dual-phase region. In: Current advances in materials and processes, vol. 12. Iron and Steel Institute of Japan, 1999: pp. 373–376. 36 Takeda K., Nakada N., Tsuchida T., Takaki S. ISIJ International 2008;48: 1122–1125. 37 Morris Jr. J.W., Guo Z., Krenn C.R., Kim Y.H. ISIJ International 2001;41: 599–611. 38 Morris Jr. J.W. ISIJ International. 2008;48: 1063–1070. 39 Miller R.L. Metall Mater Trans 1978;3: 905–912. 40 Nagai K. J Mater Process Technol 2001;117: 329–332. 41 Tsuji N., Ito Y., Saito Y., Minamino Y. Scripta Mater 2002;47: 893–899. 42 Yu C.Y., Kao P.W., Chang C.P. Acta Mater 2005;53: 4019–4028. 43 Tomota Y., Narui A., Tsuchida N. ISIJ International 2008;48: 1107–1113. 44 JDDRG. Handbook on sheet metal forming severity (second edition). Nikkan Kogyo Shinbunsha, 1997: p. 423. 45 Mochizuki M., Shintomi T., Hashimoto Y., Toyoda M. Welding in the World 2004;48; n° 9/10: 2–12. 46 Yoshitake A. Application technologies for weight reduction, improving crashworthiness, and shortening of the development period for automobiles. In: JFE technical report 2004, vol. 4. JFE steel, 2004: pp. 1–8. Available from: http://www.jfe-steel.co.jp/en/ research/report/004/pdf/004-02.pdf#search=’ULSAB (Yoshitake). 47 Shibata K. J Japan Welding Soc 1999;68–4: 70–73. 48 IIW technical report. 1967; IIW document:IX-535–67. 49 Oikawa H., Murayama G., Sakiyama T., Takahashi Y., Ishikawa T. Resistance spot weldability of high strength steel (HSS) sheets for automobiles. In: Nippon steel technical report 2007, No. 95. Nippon Steel, 2007. Available from: http://www.nsc. co.jp/en/tech/report/pdf/n9508.pdf#search=’&039. 50 Kiuchi M. ISIJ International 2008;48: 1133–1141. 51 JRCM NEWS No. 249. Japan Research and Development Center for Metals, 2007. Available from: http://www.jrcm.or.jp/jrcmnews/0707jn249.pdf.

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Index

α-Al particles, 168–9 AA6061 alloy, 524 cyclic deformation curves, 525 accumulative roll bonding, 86, 179, 276, 278–81, 507, 687 bulk nanostructured metals and alloys, 40–57 change in microstructures during the process, 45–53 1100-Al microstructures, 50 commercial purity Ti microstructures, 52 subsequent heat treatments, 50–1, 52 mechanical properties, 53–7 1100-Al engineering stress–strain curves, 56 processed materials engineering stress– strain curves, 54 strength and ductility for ARB-processed materials, 55 nonequilibrium phases formation, 52–3 Cu + Zr multi-stacks microstructure, 53 principle, 41–2 schematic illustration, 41 processing details, 42–5 Al alloy sheets appearance, 44 material geometrical changes, 42 rolling mill, 42 ultrafine grains formation, 45–50 1100-Al micrograph and boundary misorientation map, 48 grain subdivision mechanism during plastic deformation, 49 IF steel boundaries misorientation distributions, 47 IF steel boundary misorientation maps, 46 single-phased materials microstructures, 47 activation energy, 474 AISI304L, 532 Al-1420 alloy, 554–7 high strain superplasticity, 574 in-situ tensile test, 584 variation in stress with strain, 555 Al 5083 alloy proposed fracture theory for enhanced ductility, 382 tensile stress–strain curves and TEM image, 381 Al-based alloy, 554–7

Al-Mg alloy fractography, 415 tensile stress–strain curves, 411 allotropic transformation, 68 alumina-titania coatings, 621–2 aluminium, 98, 469–70 deformation, 598 aluminium-based bulk glassy, 156 AM60 alloy, 529 amorphous phase bulk nanocrystalline and nanocomposite alloys production, 152–72 bulk metallic glassy alloys formation, 153–9 nano-quasicrystals formation, 165–7 nanocomposite alloys magnetic properties, 169–72 nanocomposite alloys mechanical properties, 167–9 nanostructure formation by crystallisation, 159–65 analytical continuum modelling, 335 anelasticity, 600 annealing, 50, 51, 55, 286–9, 578 annealing-induced hardening, 287–8 APT see atom probe tomography ARB see accumulative roll bonding Archard equation, 502 Archard’s law, 140 ARL see Army Research Lab Army Research Lab, 647 artifact-free nanocrystalline metals, 444–6 Ashby–Verrall mechanism, 475 ASTM standards, 136 athermal stress–induced grain growth, 359–65 applied shear stress in collective migration, 365 External stress σ as a function of the total plastic strain ε, 360 grain growth through collective GB migration in a model of NCM, 364 stress-induced migration of low- or high-angle GB, 363 atom probe field ion microscopy, 162, 170 atom probe tomography, 100 austenite, 89, 90, 110 automotive applications, 673–5 automotive body structures, 687–712

787 © Woodhead Publishing Limited, 2011

788

Index

bainite, 89, 90, 92 ball milling, 153 Basquin law, 511, 521 batch-annealing, 705 Berkovich nanoindentation hardness profile, 488 bimodal metallic materials, 408–19 Al 5083 alloys proposed fracture theory for enhanced ductility, 382 Al compressive specimen primary crack stopped by a CG grain, 418 Al-Mg alloy fractography, 415 tensile stress–strain curves, 411 bimodal Cu brightfield TEM image, 377–8 CG TEM image, 410 deformation, 411 engineering stress–strain curves, 388–9 finite element modelling, 409 tensile engineering stress–strain curves, 386–7 bimodal Ni yield strength vs. tensile ductility, 392 bimodal polycrystals predicted uniform elongation, 395 predicted von Mises equivalent stress– strain curves, 396 ultimate tensile strength and uniform elongation, 397 deformation and fracture mechanisms, 408–19 CGs deformation microstructures, 419 compression, 414–19 crack blunting, 413 crack bridging and branching, 414 micrometer-sized grains, 416 tension, 408–14 void initiation, 412 strength and ductility experimental results, 384–90 numerical results, 393–8 tensile strength vs. uniform elongation, 404 tensile true stress–strain curves for bimodal nanograin and coarse grain, 394 UFG Al and mc Al true stress-strain curves, 417 ultimate tensile strength vs. uniform elongation, 405 vs multimodal metallic materials, 403–6 bimodal microstructures, 194 blocky austenite, 92 boron, 170, 172 bottom-up approach, 59 brittle crack, 431 nucleation and propagation instabilities, 431 brittle fracture, 431, 432 bubble raft model, 214 buffers, 120 bulk glassy alloys, 153–9 casting technique, 154 defined, 152 bulk melting point, 463 bulk metallic glasses see bulk glassy alloys bulk nanocrystalline produced from amorphous phase, 152–72

bulk metallic glassy alloys formation, 153–9 magnetic properties, 169–72 mechanical properties, 167–9 nano-quasicrystals formation, 165–7 nanostructure formation by crystallisation, 159–65 bulk nanocrystalline metals and alloys processing by electrodeposition, 118–46 applications, 145–6 methods, 119–28 nanocrystalline electrodeposits corrosion properties, 141–3 nanocrystalline electrodeposits mechanical properties, 136–41 nanocrystalline electrodeposits other properties, 143–5 prepared nanocrystalline metals and alloys, 128–36 bulk nanostructured metals and alloys accumulative roll-bonding, 40–57 change in microstructures during the process, 45–53 mechanical properties, 53–7 principle, 41–2 processing details, 42–5 severe plastic deformation processing, 3–34 enhanced properties, 22–33 innovation potential, 33–4 new trends for effective grain refinement, 8–22 principles, 4–8 Burgers vector, 260, 264, 265, 468 C-2000 alloy fracture surfaces of the annealed sample from the centre and from the edge, 497 from the centre of 30 min and 180-min processed sample, 498 surface severe plastic deformation Berkovich nanoindentation hardness profile, 488 cross-sectioned specimens, 490 effective plastic strain profiles, 486 equiaxed nanograins at the impacted surface, 492 S-N curves, 500 twin arrangement, 491 Vickers hardness profiles, 487, 488 wear tracks, 503 Canadian CANDU, 119 carbide, 99, 100 carbide-free bainite, 100 carbon content, 719–21 carbon equivalent, 774 carbon fibre-reinforced plastic composites, 678 tool section coated with low CTE nanostructured nickel-iron, 680 carbon-manganese steel sheets nanostructured, UDCSMR, 747–84 concept and experimental hot rolling mill, 749–52 deformation characteristics, 765–73 deformation temperature of grain refinement processes, 749 grain refinement mechanisms, 757–65 UDCSMR, 752–7

© Woodhead Publishing Limited, 2011



Index

welding and application to some prototype parts, 773–84 carbon nanotubes, 451–2 cathodic reactions, 122, 123–4 electroformed product net-shape manufacturing, 123 nanocrystalline sheet/foil continuous electrodeposition, 124 CEC see cyclic extrusion and compression cementite, 89, 105 ceramics, 647 CFRP composites see carbon fibre-reinforced plastic composites CG see coarse-grained; conventional grain-sized Charpy impact testing, 722 CHT see continuous heating transformation cladding, 725 classical defect structures, 214–24 absent in nanograined metals, 221–4 classical structures absent, 221–2 cross-slip and slip transfer due to dislocation pile-up, 223 dislocation pile-up and dislocation emission, 222 missing structures effect on mechanical properties, 224 reasons for absence, 222–4 Al-Mg-Sc alloy dislocation structure, 216 crystalline lattices potential defect structures, 215 grain boundaries, 219–20 partial dislocations (stacking faults), 217–18 deformation map delineating the active deformation mechanism, 217 perfect dislocations, 216 point defects and resulting structures, 220–1 stacking-fault tetrahedra and dislocation loops, 221 twins, 218–19 deformation twin in Al near crack tip, 219 classical Gibbs–Kelvin equation, 126 classical theory of elasticity, 333, 337 coarse-grained metallic materials, 375, 425 grain size regimes, 376 coarse-grained metallic polycrystals plastic flow mechanisms, 435 coarse-grained metals, 224 cobalt, 98 Coble creep, 308, 309, 312, 337, 403, 438, 449, 466, 467, 476, 544, 606 atomic structure simulation snapshot at 4% deformation, 467 Coble creep rate, 598 Coble equation, 606 coefficient of thermal expansion, 679 coercivity, 675 Coffin–Manson law, 511, 521, 530 cold deformation, 575 cold rolling, 288, 289, 692 cold rolling reduction, 692 cold spray process, 644–7 gas exit temperature calculated with nitrogen and helium, 645 non-cryogenically milled n-WERKZ AA5083, 651–7 average particle size, 654

789

brightfield TEM micrograph, 655 coating-substrate interface, 656 cold spray deposit, 653 cold-sprayed and uncoated bottom surface XRD patterns, 657 critical impact velocity, 652 decohesion and inclusions, 656 grain boundary, 655 original n-WERKZ feedstock, 653 particle analysis, 652 sieved cold spray deposit, 654 schematic, 645 WC-Co, 648–51 agglomerated powder, 648 deposited onto aluminium using nitrogen, 650 helium as accelerating gas, 649 WC held together with a cobalt binder, 649 commercially pure aluminium, 517, 518 commercially pure titanium, 547–8 severe plastic deformation, 548 true stress–true strain curves, 547 complex partial dislocation structures, 218 complexing agents see ligands composite deposits, 120 compression, 414–19 Conform process, 9 Considère’s criterion, 377, 400, 767 continuous equal-channel angular-pressing, 9–12 continuous heating transformation, 164 continuous recrystallisation, 51 continuous shear drawing, 270 continuum disclination model, 362 conventional grain-sized, 508 copper, 29, 30, 647 core-and-mantle model, 302 Cottrell atmosphere, 103, 104 CP aluminium see commercially pure aluminium crack propagation instability, 432 creep, 594–609, 598–9 fracture mechanism, 605 creep rate, 607 normalisation parameters, 603 creep resistance, 603 creep tests, 598, 604, 605 cryomilling, 75, 602, 617, 627–38 CTE see coefficient of thermal expansion Curie temperature, 171 current efficiency, 122 cyclic deformation behaviour, 514–17, 524 consequences and strategies for optimising, 534–7 cyclic extrusion and compression, 40 cyclic softening, 514 cyclic softening ratio, 515 3D-atom probe, 19, 20 damage mechanisms, 527–8 decahedral nanoparticles, 332–3 deformation, 303 see also plastic deformation characteristics, 765–73 cross sectional microstructures of fractured regions by tensile tests in 0.15%C0.7%Mn steel, 771

© Woodhead Publishing Limited, 2011

790

Index

evolution of Lüders deformation in small tensile test specimens, 768 grain elongation ratio as a function of necking strain, 770 grain size effect on hole expandability of 0.15%C-0.7%Mn steel sheets, 772 IQ maps by EBSD, 769 microstructures of 0.15%C-0.7%Mn nanostructured sheet after hemming test, 772 stress-strain curves by tensile tests, 766 TEM of subsurface layers of 0.15%C0.7Mn hot-rolled steels, 767 total elongation of nanostructured and coarse-grained 0.15%C-0.7%Mn steel, 771 yield strength of 0.15%C-0.7%Mn steel sheets, 766 elevated temperatures, 595–8 mechanisms, 406–25, 440, 527–8 face-centred cubic polycrystal, 407 nanocrystalline metals and alloys, 578–87 in nanoscale grains, 465 mechanisms and modelling, 603–9 creep fracture mechanism, 605 creep rate normalisation parameters, 603 true stress vs the normalised minimum strain rate, 604 twinning, 349–52, 470–1 equilibrium position dependence, 351 model of DT lamella nucleation at an extrinsic GB dislocation, 352 twinning partial dislocations emission, 350 deformation-induced softening phenomenon, 287–8 deformation map, 470 deformation structures nanograined pure metals, 213–39 classical defect structures, 214–21 classical defect structures absent, 221–4 defects in historical perspective, 213–14 future trends, 236–9 initial microstructure effect, 230–6 novel defect structures, 224–30 dendrite-like inclusions, 451–2 devitrification process, 159, 160, 161 diffusion activation energy, 474 diffusion bonding, 52 diffusional creep, 438, 466–8, 544, 579 dimensionally stable anode, 124 direct current plating, 121, 126 disclination dipole movement, 439 disclinations, 229 dislocation emission, 345 dislocation loops, 220, 347–8 dislocation slips, 468–70 dislocation source-limited hardening, 288 dislocation–disclination models, 355, 361 dislocation–dislocation interactions, 222–3, 224 dislocations, 579, 580 DJ 2700 HVOF system, 629 DMA see dynamic mechanical analysis DP steel axial collapse properties, 711 hat columns after dynamic collapse tests, 709 DPD see dynamic plastic deformation 787 Dreamliner, 678

DSA see dimensionally stable anode ductile fracture, 431, 433 ductility, 376, 509 dynamic collapse test, 706 dynamic GG, 475 dynamic mechanical analysis, 674 dynamic plastic deformation, 378

ε-carbide, 100, 104, 105, 106 EBSD see electron backscattering diffraction ECAE see equal channel angular extrusion ECAP see equal channel angular pressing ECAP-Conform process, 12 EDX analysis, 56 elastic modulus, 218 elastic strains, 330–7 grain boundary sources, 335–6 grain boundary stress concentrators, 336–7 nanoparticles, 331–5 De Wit’s schematics of partial disclination formation, 332 Partial positive wedge disclinations of strength, 333 elasticity theory, 333 electrodeposition, 670 applications, 145–6 bulk nanocrystalline metals and alloys, 118–46 electrolyte composition and plating conditions for nanocrystalline Co-W alloy deposits synthesis, 132 electrolyte composition and plating conditions for nanocrystalline synthesis Ni deposits, 130 Ni-P alloy deposits, 128 Ni-SiC composites, 136 Zn-Ni deposits, 133 methods, 119–28 anodes, 124 cathodes and cathodic reactions, 123–4 conventional direct current plating diagrams, 120 conventional electrodeposits structure evolution, 125 electroformed product net-shape manufacturing, 123 electrolyte, 119–21 iron electrodeposit grain size and shape evolution, 125 nanocrystalline electrodeposits structure evolution, 125–8 nanocrystalline sheet/foil continuous electrodeposition, 124 over-potential/current density effect on critical crystal nucleation size, 126 power supplies in conventional electroplating, 121–3 pulsed current plating diagrams, 127 nanocrystalline electrodeposits, 136–145 corrosion properties, 141–3 mechanical properties, 136–41 other properties, 143–5 shapes and applications, 145 nickel electrodeposits diagram and cross-sectional micrograph, 131 saccharin concentration effect on grain size and sulphur content, 131

© Woodhead Publishing Limited, 2011



Index

prepared nanocrystalline metals and alloys, 128–36 benzamide, 132 cobalt-iron alloys phase fields, 135 list of metals, alloys and metal matrix composites, 130 Ni-5.2 at.% P brightfield and darkfield micrographs, 129 polycrystalline, nanocrystalline and amorphous Co-W alloys, 134 polycrystalline nickel surface structure micrographs, 131 electroforming, 123 electromagnetic applications, 675–8 electromagnetic interference, 676 shielding solutions advantages and ­drawbacks, 677 electromechanical shaping technology, 157 electron backscattering diffraction, 45, 206, 277, 378, 727, 763 crystal orientation mapping, 379, 392 electron-beam irradiation, 165 electroplating, 123 electrosleeve process, 119, 670 EMI see electromagnetic interference energy maps, 340 pure Al under external shear stress, 341 enthalpy, 64, 65, 72 Epic Golf Shaft, 681 equal channel angular extrusion, 9, 40, 687 equal channel angular pressing, 4, 5, 8, 86, 179, 276, 320, 507, 526, 528 nanostructured low-carbon steel, 243–72 continuous shear drawing, 270–2 grain refinement and microstructural modification, 268–70 mechanical response, 261–8 microstructural evolution, 244–61 technique, 6, 9 equilibrium distance, 331 excessive strain hardening, 572–3 Exit AB Bat, 682 external shear stress, 346 F-35 Lightning II, 678 face-centered cubic, 218 Faraday constant, 122 fatigue behaviour nanostructured metals, 507–37 nanostructured steels, 532–4 fatigue life, 509–12 consequences and strategies for optimisation, 534–7 nanostructured steels, 532–4 total strain fatigue life diagram AlMg0.5 and AlMg2.0 for UFG and the CG conditions, 522 CG and UFG IF steel, 534 crossover of fatigue life curves, 510 strong, ductile and tough material, 511 ultrafine-grained materials, 535–7, 536 Wöhler (S–N) diagram influence of ECAP route, 523–4 influence of UFG microstructure, 510 UFG AlMg0.5, AlMg1, AlMg1.5 and AlMg2 and CG conditions, 519 fatigue limit, 499–500

791

fatigue resistance, 499–501 fatigue threshold, 532 FCC see face-centered cubic FCM steel, 696 Fe-based alloys, 560–3 FE-SEM see field-emission type scanning electron microscope FEM see finite element modelling ferromagnetic alloys, 169 field-emission type scanning electron ­microscope, 45 field theory of elastoplasticity, 333 fine blanking, 735 fine grained metallic materials, 376 FINEMET, 449, 563 Finemet, 676 finite element method, 270 finite element modelling, 409, 484–6, 500–1 S2PD and SP processes, 485 Finnis–Sinclair potential, 609 Fleischer solution-hardening model, 319 forming test, 780 fracture mechanisms, 406–25 Frank–Read source, 302, 445 GB engineering see grain boundary engineering GBS see grain boundary sliding geometrically necessary boundaries, 49, 191 geometrically necessary dislocations, 269 GFA see glass-forming ability GG see grain growth Gibbs free energy, 71, 73, 92, 311 Gibbs–Thompson relationship, 260 glass-forming ability, 153 glass-transition, 158 glide character, 512 gliding dislocations, 508, 513 GNB see geometrically necessary boundaries GND see geometrically necessary dislocations Graffalloy, 681 grain boundary, 435, 461 sources, 335–6 stress concentrators, 336–7 structure and properties in nanocrystalline metals, 461–5 grain-boundary diffusivity, 463–4 grain-boundary mobility, 464–5 structural model, 461–3 grain boundary contribution, 513 grain boundary diffusion, 445, 543 grain boundary diffusional creep, 440 grain boundary diffusivity, 463–4, 571 transition, 464 grain boundary dislocations, 435, 513 grain boundary engineering, 28 grain boundary migration, 473–4 grain boundary mobility, 464–5, 514 grain boundary relaxation, 600–1 grain boundary sliding, 407, 436–7, 440, 445, 446, 466, 543, 580–3, 601, 604 grain coalescence, 474 grain growth, 472–6 deformation-driven grain growth, 475–6 grain-boundary migration, 473–4 grain rotation and grain coalescence, 474

© Woodhead Publishing Limited, 2011

792

Index

grain refinement, 17–18, 32, 56, 66, 435, 688 dual-phase LCS alloy, 269–70 steel SEM image with higher magnification, 269 enhanced tensile properties, 268–70 LCS alloy containing vanadium carbides, 268–9 nanoscale vanadium carbides existence image, 268 grain refinement mechanisms, 757–65 0.1%C-1%Mn steel microstructure, 759 ODFs of deduced textures austenite at 0.05s and 0.3s, 761 ODFs of deduced textures austenite at 0.05s 0.1%C-1%Mn steel, 762 orientation imaging map by EBSD for Ni-30%Fe sheets, 763 schematic representation of refinement mechanisms, 758 TEM of hot rolled Ni-30%Fe sheets, 764 grain rotation, 474, 583–4 grain rotation coalescence, 474 grain size, 375, 512–14, 544 distribution, 377, 575–6 as-DPD Cu sample and as-annealed bimodal Cu samples, 378 multimodal Ni, 379 unimodal, 396 unimodal vs multimodal, 393–4 influence on fatigue behaviour and fatigue lives, 512–14 grain sliding, 466, 583 grain subdivision, 49, 50 Grille Guard, 674 HAB see high-angle boundaries HAGB see high angle grain boundaries Hall–Petch equation, 300, 765–7 Hall–Petch hardening effect, 471 Hall–Petch model, 222, 300–3, 543, 595, 730, 743 Hall–Petch plot, 399, 400 Hall–Petch relationship, 22, 23, 27, 86, 217, 221, 304, 375–6, 377, 398, 408, 435, 471, 512, 513, 528 Hall–Petch rule, 23, 24 Hall–Petch strengthening, 289 hammer milling, 203 Hard Chrome Alternatives Team, 670 hard chrome replacement, 670–3 hard magnetic alloys, 171–2 hardenability, 774 hardening, 377 Hart’s criterion, 434, 436 HCAT see Hard Chrome Alternatives Team HCF see high cycle fatigue helium, 652 Helmholtz free energy, 311 HEM see high-energy ball milling Hemming tests, 770 Hertz theory, 482 HESP see high-energy shot peening hex chrome, 671 high-angle boundaries, 23 high angle grain boundaries, 321, 322, 691 high Curie temperature, 170 high cycle fatigue, 509, 514

high-energy ball milling, 616 high-energy shot peening, 481 high pressure torsion, 5, 8, 24, 40, 86, 179, 276, 320, 507, 687 high-rate superplasticity, 22 High Resolution Electron Microscopy, 305 high resolution transmission electron microscopy, 19, 162, 170 high strain superplasticity, 569, 574–5 high strength steels, 687, 697 high temperature deformation, 594–609 dual and multiple phases effects, 602–3 high velocity oxyfuel process, 619–20 operating system, 620 Hole-expanding tests, 770–1 hot rolling mill, 749–52 continuous cooling transformation diagram in C-Mn steel, 750 photograph of apparatus for experiment, 751 schematic representation of experimental apparatus, 751 HPT see high pressure torsion HRTEM see high resolution transmission electron microscopy HSRS see high strain superplasticity HSS see high strength steels Hume–Rothery phases, 158 HVOF process see high velocity oxyfuel process icosahedral nanoparticles, 333–4 icosahedral quasicrystalline phase, 165, 166 IDB see incidental dislocation boundaries IF steel see interstitial free steel image quality map, 768–9 iN Ping Putter, 682 in-situ consolidation, 77 incidental dislocation boundaries, 49 infrared thermographic, 184 intermetallic compounds, 67, 68, 163 interstitial free steel, 45, 276, 280–1 Invar, 679 Jet Kote HVOF system, 638 Joint Strike Fighter, 678 Kauzmann paradox, 158 Kikuchi-line analysis, 46 Kikuchi pattern analysis, 252, 253, 278 kinetic energy, 74 Kissinger analysis method, 164 Kolmogorov–Johnson– Mehl–Avrami general exponential equation, 160 Krudjumov Sachs, 760 LAB see low-angle cell boundaries LAGB see low-angle grain boundaries lamellar-type boundaries, 249 Large Strain Extrusion Machining, 186 laser assisted sintering, 75 lattice dislocation creep, 451 lattice dislocation slip, 444 lattice dislocations, 439, 446, 448 LCF see low cycle fatigue LCS see low-carbon steel Lifshitz model, 607 Lifshitz sliding, 466

© Woodhead Publishing Limited, 2011



Index

ligands, 121 lightweight nanometal polymer hybrids automotive applications design iterations, 675 room temperature properties, 674 yield strength comparison of selected metallic materials, 675 liquid nitrogen temperature, 77 local strains, 422 low-angle cell boundaries, 23 low-angle grain boundaries, 321, 322 low-carbon steel equal-channel angular pressing, 244–8 ECAP-deformed samples, 245 ferrite phase grains, 246 pearlite colonies, 247 ferrite phase annealing behaviour, 253–7 activation energy log plot, 256 grain size variation, 255 TEM and optical images, 254 fine cementite precipitates formation, 259–61 excess carbon concentration, 260 spheroidised pearlite colony, 259 grain refinement mechanism, 248–53 four-pass ECAPed LCS micrograph, 252 high-angle grain boundary formation, 252–3 Kikuchi patterns, 253 microstructural evolution, 244–61 pearlite structure annealing behaviour, 257–9 initial LCS sample without ECAP, 258 microstructure change of pearlite in ECAPed LCS samples, 257 post-ECAP annealing, 253–9 slip system, 248–52 ECAP first pass, 248–50 ECAP second pass, 250–2 first pass ECAPed LCS micrograph, 249 second pass ECAPed LCS micrograph, 250 two-pass ECAPed LCS micrograph, 251 low cycle fatigue, 509, 514 low-flow stress, 569 low temperature superplasticity, 4, 22, 569, 574 LSEM see Large Strain Extrusion Machining LTSP see low temperature superplasticity Lüders banding, 289 Lüders deformation, 767–8 small tensile test specimens, 768 Lüders elongation, 711 Lux Innovation Grid, 668, 669 machinability, 733–43 magnetic flux density, 675 magnetically hard alloys see hard magnetic alloys magnetically soft alloy see soft magnetic alloys MAM see modulation-assisted machining manufacture microelectromechanical system, 200 Marks–Ioffe disclination, 334 martensite, 86, 89, 92, 110 MBD equation see Mukherjee, Bird and Dorn equation MCrAlY coatings, 627–44 MD simulation see molecular dynamics simulation mechanical alloying, 63, 68–75

793

mechanical attrition future trends, 80–1 methods description, 60–1, 62 basic event, 62 nanocrystalline metals and alloys preparation, 59–81 nanocrystalline phase formation, 62–75 nanocrystalline powders consolidation, 75–80 in situ consolidated bulk nanocrystalline materials, 77 microstructure micrograph and diffraction pattern in in situ consolidated Cu, 78 tensile stress-strain curve for annealed and coarse-grained samples, 79 tensile stress-strain curve for in situ consolidated Cu, 79 phase mixtures mechanical alloying, 68–75 Al-Mg system free energy diagram, 72 composition effect on minimum grain size, 70 metastable phase formation basic principles, 73 milling intensity effect on phase ­transformation, 74 typical layered microstructure, 69 single-phase materials mechanical milling, 63–8 lattice strain for different mechanically milled fcc metals vs melting temperature, 64 minimum grain size, 64 pure metals and solid solutions minimum grain size, 66 stored enthalpy in mechanically milled Ni vs reciprocal grain size, 65 mechanical milling, 63–8 medium range order, 157 MEMS see manufacture microelectromechanical system metal ion complex, 121 metal matrix composite, 616 Metallix, 682, 683 Metglas, 676 Meyers–Ashworth models, 303 microcrystalline materials, 543 microstructure evolution, 472–6 microstructure gradients, 490–3 microvoids, 422 microwave assisted sintering, 75 migration activation energy, 474 milling process, 60–1, 200 Mine Countermeasures Ship, 622 misorientation distribution function method, 760 MMC see metal matrix composite modulation-assisted machining, 200 molecular dynamics modelling., 320 molecular dynamics simulation, 225, 459–61, 586–7 nanostructured metals mechanical behaviour, 459–77 deformation mechanisms in nanoscale grains, 465 grain boundaries structure and properties, 461–5 grain growth and microstructure evolution, 472–6 molybdenum, 93

© Woodhead Publishing Limited, 2011

794

Index

MRO see medium range order Mukherjee, Bird and Dorn equation, 542 multi-scale metallic materials, 375–426 deformation and fracture mechanisms, 406–25 bimodal metallic materials, 408–19 multimodal metallic materials, 419–25 EBSD crystal orientation mapping and grain size distribution histogram, 379 grain size regimes, 376 mechanical properties, 383–406 experimental results, 384–92 future trends, 425 numerical results, 393–406 tensile stress–strain curves and TEM image bimodal and coarse-grained 5083 Al alloys, 381 coarse-grained, ultrafine grained and bimodal Cu sample, 383 multimodal metallic materials, 390 deformation and fracture mechanisms, 419–25 local von Mises equivalent strains, 421 predicted ductile fracture, 422–3 predicted local relative von Mises equivalent stresses, 424 UFG matrix deformation patterns, 420 generated log-normal grains size distributions, 399 multi-Ni EBSD crystal orientation mapping and grain size distribution, 379 tensile engineering stress–strain curves, 391 strength and ductility experimental results, 390–2 numerical results, 398–403 tensile strength vs. uniform elongation, 404 volume fraction of grains, 400 vs bimodal metallic materials, 403–6 multimodal polycrystals, 404, 405 n-WERKZ, Inc, 617 n-WERKZ AA5083, 651–7 n-WERKZ powder, 638–44 NAB see nonmagnetic nickel aluminium bronze Nabarro–Herring creep, 308, 312, 467, 609 nano-beam, 53 nanocomposite alloys bulk metallic glassy alloys formation, 153–9 bulk glassy sample casting technique, 154 Ni60Pd30P20 alloy medium range order zones, 157 sintered specimen cross-section micrograph, 155 spark plasma sintering technique, 155 SPS compact dimensions, 156 magnetic properties, 169–72 Co-Fe-Ta-B glassy sample magnetisation curve, 169 hard magnetic alloys, 171–2 soft magnetic alloys, 169–71 nano-quasicrystals formation, 165–7 annealed Cu55Zr30Ti10Pd5 alloyTEM image, 166 nanostructure formation by crystallisation, 159–65 Al-based alloys differential scanning calorimetry traces, 160

annealed Fe40Co40Cu0.5Zr9Al2Si4B4.5 alloy, 162 Cu45Zr45Ag10 glassy alloy Avrami plot, 161 Hf55Co25Al20 glassy alloy X-ray diffraction pattern, 164 produced from amorphous phase, 152–72 mechanical properties, 167–9 nanocrystalline electrodeposits, 136–45 corrosion properties, 141–3 nickel cross-sectional corrosion morphologies, 142 mechanical properties, 136–41 hardness, yield strength and wear resistance, 138–40 nanocrystalline nickel Vickers hardness, 139 nickel hardness, yield strength, Young’s modulus and Taber wear resistance, 137 ultimate tensile strength and tensile ductility, 140–1 Young’s modulus, 138 other properties, 143–5 nickel electrical resistivity, saturation magnetisation, and thermal expansion coefficient, 143 nanocrystalline materials see also nanocrystalline metals and alloys crystallised from amorphous precursor, 560–3 Fe-based alloys, 560–3 deformation mechanisms, 578–87 diffusional creep, 579 dislocations, 579, 580 grain boundary sliding, 580–3 grain rotation, 583–4 molecular dynamic simulations, 586–7 parametric dependences, 584–6 elevated temperature behaviour, 585 produced by electrodeposition, 563–5 pure Nickel, 563–5 produced by powder consolidation, 565–7 pure Zinc, 565–6 TiAl alloy, 566–7 nanocrystalline metallic materials bulk in situ consolidated Cu tensile stress– strain curve, 444 crack nucleation and growth processes, 440–3 grain size effect on crack blunting, 443 Cu and Ni tensile stress–strain curves, 380 deformation mechanisms in nanoscale grains, 465 competition between different deformation modes, 471–2 deformation during Coble creep, 467 deformation twinning, 470–1 diffusion creep, 466–8 dislocation processes atomistic snapshots, 470 dislocation slips, 468–70 grain sliding, 466 enhanced ductility and its mechanisms, 430–54 artifact-free nanocrystalline metals, 444–6 crack nucleation and growth processes, 440–3 future trends, 452–4 plastic flow mechanisms, 435–6 second-phase nanoparticles, dendrite-like inclusions and carbon nanotubes, 451–2

© Woodhead Publishing Limited, 2011



Index

strain rate hardening, 448–9 twin deformation and growth twins, 446–8 grain boundaries structure and properties by MD simulation, 461–5 grain-boundary diffusivity, 463–4 grain-boundary diffusivity transition, 464 grain-boundary mobility, 464–5 structural model, 461–3 grain growth and microstructure evolution, 472–6 deformation-driven grain growth, 475–6 grain-boundary migration, 473–4 grain rotation and grain coalescence, 474 MD-simulated Pd microstructure overall evolution, 475 grain size regimes, 376 mechanical behaviour on molecular dynamics computer simulations, 459–77 plastic flow mechanisms in nanocrystalline metals with the finest grains, 436–40 grain boundaries volume fractions, 439 grain boundary sliding, 437 predicted ductile fracture, 422–3 single-phase metals with bimodal structures, 449–51 deformation and fracture processes, 450 tensile ductility, 431–4 brittle fracture, 432 ductile fracture, 433 plastic strain instability, 433 nanocrystalline metals elastic and plastic deformation, 329–66 elastic strains, 330–7 future trends, 365–6 plastic deformation, 337–65 strengthening mechanisms, 299–325 alternative deformation mechanisms at very fine grain sizes, 307–14 caused by solute, order, twin boundaries, 319–20 future trends, 324 Hall-Petch breakdown, 303–7 materials with ultrafine microstructure prepared by SPD, 320–4 polycrystals deformation, 300–3 second-phase particles, 314–19 nanocrystalline metals and alloys mechanical attrition, 59–81 future trends, 80–1 nanocrystalline phase formation, 62–75 nanocrystalline powders consolidation, 75–80 superplastic deformation, 542–90 deformation mechanisms, 578–87 superplasticity, 546–67 superplasticity specific features, 568–78 theoretical predictions, 543–6 nanocrystalline powders, 75–80 ‘nanodisturbances’ in Gum Metal, 338 nanograined pure metals classical defect structures, 214–24 absent in nanograined metals, 221–4 defects in historical perspective, 213–14 deformation structures, 213–39 future trends, 236–9 initial microstructure effect, 230–6

795

grain size and total numbers for annealing treatments, 232 microfabricated structure, 231 ratios derived from grain size distribution annealing treatments, 233 novel defect structures, 224–30 agglomerated grains, 224–8 Al-4Mg-0.3Sc alloy destruction, 228 Cu-16%Al dislocation structures, 227 disclinations, 229–30 nanocrystalline Fe powder, 230 proposed grain boundary migration mechanisms, 225 star twins, 228–9 twinned Au nanoparticle, 229 pulsed laser deposited Ni device fracture surface, 235 fracture surface produced by microfabrication, 237 still frame with migrating boundary, 234 nanoindentation, 361 nanoparticles, 331–5 De Wit’s schematics of partial disclination formation, 332 Partial positive wedge disclinations of strength, 333 nanoscale crystalline, 159, 167 nanostructure nickel see nickel nanostructured alloys creep and high temperature deformation, 601–3 effects of dual and multiple phases, 602–3 plastic deformation and creep, 601–2 production using severe plastic deformation, 178–207 bulk forms with ultrafine grained microstructure, 196–200 microstructure refinement study, 189–96 nanostructured particulate, 200–5 SPD mechanics, 179–89 surface nanostructuring, 205–7 surface deformation and mechanical behaviour, 481–504 fatigue resistance, 499–501 microstructure and stress states changes, 484–93 surface severe plastic deformation mechanics aspects, 482–4 tensile properties, 493–9 wear resistance, 501–2 nanostructured carbon-manganese steel sheets, 752–7 chemical composition and temperature, 752 experimental apparatus specifications, 752 grain structures observed by electron backscattering diffraction, 757 SEM of 0.1%C-1%Mn steel, 754 SEM of hot-rolled 0.1%C-1%Mn steel, 755, 756 SEM of nanostructured 0.15%C-0.7%Mn steel, 756 ultra-fast direct cooling effect on ferrite grain diameters, 753 nanostructured coatings cold spray process, 644–7 cold spray material characteristics, 647–8

© Woodhead Publishing Limited, 2011

796

Index

non-cryogenically milled n-WERKZ AA5083, 651–7 WC-Co, 648–51 commercial and industrial applications, 663–84 nanostructured materials, 666–9 nanostructured metals and alloys, 664–6 current and emerging applications, 669–83 CFRP tool coated with low CTE nanostructured nickel-iron, 680 hard chrome replacement, 670–3 lightweight nanometal composite hybrid tooling, 678–81 lightweight nanometal polymer hybrids, 673–5 low CTE nanostructured nickel-iron hardness, 680 sporting goods, 681–3 electromagnetic applications, 675–8 complex polymer housing for a portable electronic device, 678 shielding solutions to low frequency EMI, 677 nanostructured metal-base feedstock, 616–17 agglomerated nanostructured WC-12Co powder, 618, 619 spray dried nanostructured TiO2 particle, 618 sporting goods, 681–3 Epic Golf Shaft, 681 Exit AB Bat, 682 Metallix, 683 iN Ping Putter, 682 thermal and cold spraying, 615–58 future trends, 657–8 nanostructured metal-base feedstock, 616–17 thermal spray processing, 617–20 alumina-titania coatings, 621–2 MCrAlY and NiCrAlY coatings, 627–44 titanium oxide coatings, 622–7 WC-Co coatings, 620–1 nanostructured ferritic microstructures hard second phases, 699–703 mechanical properties, 703–6 nanostructured low-carbon steel continuous shear drawing, 270–2 proposed die used for CSD technique, 271 spheroidisation behaviour, 271 deformation mechanism, 263–8 dislocation cell sizes, 267 distribution and density of lattice dislocation, 266 tensile deformed sample, 266 ultrahigh strength, 263–4 grain refinement and microstructural modification, 268–70 lack of strain hardenability dislocation mean free length, 265–8 dynamic recovery, 264–5 mechanical response, 261–8 ferrite grain sizes and tensile properties, 263 microhardness plot vs pass number, 262 properties, 261–3 stress–strain curves, 263 tensile properties, 262 microstructural evolution during ECAP, 243–72

nanostructured materials, 153, 507 see also nanostructured metals and alloys commercialisation, 666–9 development times for new materials, 669 enabling properties and correlated ­applications, 665 nanostructured metals and alloys, 664–6 accumulative roll bonding, 278–81 nanostructured Al, 278–80 rolling reduction effect on strength and ductility of samples, 291 characteristic microstructures, 277–86 Al 1100 and IF steel structural parameters, 279 parameters, 277–8 chemical composition commercial purity Al, 277 commercial purity Ni, 277 creep and high temperature deformation, 594–609 deformation mechanisms and modelling, 603–9 fine-grained pure metals, 595–601 nanostructured alloys, 601–3 cyclic deformation curves alloy AA6061, 525 ECAP-passes, 520–1 IF steel in the as-received condition, 533 UFG Al and swaged CG Al, 516 UFG high purity 99.99 OFHC-copper and UFG Al-99.5, 515 fatigue behaviour, 507–37 motivation, 507–9 nanostructured steels, 532–4 optimising fatigue lives and cyclic deformation behaviour, 534–7 fatigue behaviour and fatigue lives, 509–17 cyclic deformation behaviour, 514–17 cyclic saturation stress vs inverse square root of grain size, 513 cyclic softening ratio vs. plastic strain amplitude, 515 fatigue lives, 509–12 grain size, 512–14 hardening by annealing and softening by deformation, 286–9 interstitial free steel chemical composition, 277 engineering stress–strain curves, 288, 289 microstructural parameters, 293 produced by accumulative roll bonding, 280–1 structural morphology and dislocation configurations image, 280–1 TEM microscopy structures, 292–3 light metal alloys, 517–32 cyclic crack growth rate vs. stress intensity factor range, 526 deformation and damage mechanisms, 527–8 fatigue endurance limit dependence, 529 fatigue threshold vs. load ratio, 527 macroscopic shear band formed during fatigue loading, 528 Ti-6Al-4V ELI UFG condition, 531 UFG magnesium alloys, 528 UFG titanium and titanium alloys, 528–32

© Woodhead Publishing Limited, 2011



Index

ultrafine-grained aluminium and aluminium alloys, 517–27 microstructure and mechanical properties optimisation, 289–90, 290, 291–2 nanostructured Al, 278–80 engineering stress–strain curves, 287 produced by accumulative roll bonding, 278–80 structural morphology and dislocation configurations, 279 tensile stress–strain curves, 287 nanostructured Ni by high-pressure torsion, 281–5 crystallites and deformation twins, 284 microstructure at a strain of 8.7, 282 observed lamellar structure, 283 pure Ni misorientation angles distribution, 285 prepared by plastic deformation, 276–94 Wöhler (S–N) diagram AlMg1, AA6061 and AA6082 alloys, 525 AlMg0.5 in the CG condition, 520 CP aluminium, 518 CP-Ti and Ti-6Al-4V ELI alloy, 530 nanostructured particulate, 200–5 nanostructured steel bars, 716–22 mechanical properties, 721–2 nominal stress–strain curves of ultrafinegrained steel, 721 microstructure variation by carbon content, 719–21 carbon contents of various ultrafine-grained steels, 720 grain boundary maps, 720 warm multi pass caliber rolling, 716–19 appearance of rolled bar, 717 caliber rolling, 716 condition of warm multi-pass caliber rolling, 717 SEM of microstructures of caliber rolled specimens, 718 Zener–Hollomon parameter and ferrite grain size, 719 nanostructured steel sheets automotive body structures application, 687–712 potential demand, 688–9 crash-worthiness, 706–11 axial collapse properties, 711 fabricating conditions for axial collapse tests, 708 hat column cross-section, 706 hat column for the dynamic collapse test, 707 hat columns after dynamic collapse tests, 709 load-displacement and absorbed energy displacement curves, 710 quasi-static s–s curves in dynamic collapse tests, 708 quasi-static tensile properties for axial collapse tests, 709 fabricating nanostructured low-C steel sheets, 689–99 annealing temperatures and mean ferrite grain sizes, 694 cold-rolled specimen, 692

797

cold-rolling reduction and mean thickness ratio, 692 flow stress and quasi-static flow stress, 698 further requirements, 698–9 mechanical properties, 695–8 microstructures and quasi-static tensile properties, 696 nominal stress–strain curves, 697 test piece for dynamic and quasi-static tensile tests, 695 without severe plastic deformation, 689–95 improving elongation, 699–706 hard second phases to nanostructured ferritic microstructures, 699–703 mechanical properties, 703–6 nanostructured steel strips, 725–31 machinability, 733–43 clearance, 739 contour map, 738 flow volume variations, 742 hole appearance, 741 piercing hole diameter, 740 rollover difference, 740 sheared surface sample, 736 sheared surface vs nanostructured steel and type 304, 737 surface roughness, 738 terminology for a typical sheared surface, 735 production processes and microstructure, 725–30 cladding in cold-rolling process, 726 EBSD analysed type-430 stainless steel strip, 727 EBSD analysis of nanostructure, 729 nanostructured type-430 stainless steel strip, 730, 731 repetition of plastic deformation and reverse phase transformation, 728 type-430 stainless steel strip, 727 properties, 730–1 mechanical properties, 732 tensile stress-strain curves of type-304, 733 tensile stress-strain curves of type-430, 732 nanostructured steel wires, 722–5 heading screws, 731–3 M1.7 micro screw, 734 reduction in area and tensile strength balance, 734 rolling condition, microstructure and mechanical properties, 723–5 SEM and EBSD image of ultrafinegrained steel wire, 724 stress-strain curves, 725 ultrafine-grained steel wire, 724 warm continuous multidirectional rolling, 722–3 multidirectional deformation rolling, 723 schematic drawing of oval to square rolling system, 723 nanostructured steels accelerating the bainite reaction at low temperatures, 98 bainite formation kinetics and austenite grain effect, 99 carbon atom map ferrite/austenite interface, 103

© Woodhead Publishing Limited, 2011

798

Index

microtwins in retained austenite, 105 and silicon in transformed NANOBAIN 2, 106 characterising nanocrystalline bainitic steels at the atomic scale, 98–106 austenite and bainitic ferrite carbon content, 101 austenite and ferrite carbon isoconcentration surface and concentration profiles, 102 carbon trapped in defects, 103–4 cementite formation in lower bainite, 104–6 solute distribution during transformation, 101–2 fatigue behaviour and life, 532–4 finest grain structures in steels, 86–9 logarithm plot of ferrite grain size vs free energy, 88 future trends, 113 NANOBAIN 3 and 4 steels quantitative microstructure results, 109 transformation temperature dependences and stress–strain curves, 107 NANOBAIN steel, 93–8 alloys compositions, 93 austenite and bainitic ferrite X-ray experimental data, 96–7 NANOBAIN 1 and 2 calculated TTT diagram, 95 NANOBAIN 2 microstructure, 94, 97 nanocrystalline bainitic steels mechanical properties, 107–13 bainitic microstructures curves obtained in NANOBAIN 3 steel, 111 ferrite dislocation density and carbon content, 109 steel ultimate strength vs fracture toughness, 112 strengthening contributions vs transformation temperature, 110 phase transformation theory, 89–93 alloy computed martensite-start, bainitestart and temperatures, 93 calculated phase boundaries for different steel grades, 91 processing by solid reaction, 85–113 nanostructured titanium oxide (n-TiO2), 622 nanostructures wires, bars & strips, production processes for, 715–44 applications and features, 731–43 comparative cutting force, 744 future trends, 743–4 shafts in nanostructured materials, 744 steel bars, 716–22 steel strips, 725–31 steel wires, 722–5 nanotechnology, 663 Nanotek Bat, 682 nanotwinned electrodeposits, 140 Nanovar, 680 Nanovate-CR, 671–2, 673 high strength steel rod, 672 vs electrolytic hard chrome properties, 672 nanovoids, 422 National Institute for Material Science, 735 NAVAIR JAX, 673

NCM see noncryogenic milling necking, 434 Nernst diffusion layer, 122 Ni3Al alloy, 557–60, 573 correlation between DCS results and superplastic deformation, 559 flow curves in microcrystalline and nanocrystalline state, 570 heat treatment on stress-elongation behaviour, 578 in-situ tensile testing, 580 low temperature superplasticity, 574 sample surface in initial state and after deformation, 581 sliding surfaces, 582 variation of true flow stress with elongation, 558 nickel, 595–6, 605 primary creep, 599 work hardening, 596 NiCrAlY coatings, 627–44 as-received and cryomilled powder, 628 x-ray diffraction spectra, 629 as-received and NCM powder, 639 dispersoids in nanostructured coating, 636 HVOF-applied conventional and NCM nanostructured coatings cross-sectional view, 640 cross-sectional view after 95 hrs heat treatment, 641 HVOF-applied nanostructured coating backscattered electron image, 631 cross-section, 630 non-cryogenically milled powder, 639 TEM micrograph cryomilled powder, 630 nanostructure coating, 632 TGO formation after 95 hrs at 1000°C, 635 conventional coating, 634 failed TBC samples, 637 nanostructured coating, 633 re-oxidised nanostructured coating, 635 TGO of failed TBC samples conventional and nanostructured bond coats, 637 conventional and NCM nanostructured bond coats, 643 thermal cycling results, 636 TBCs with conventional and NCM nanostructured bond coats, 642 NiTi alloy, 552–3 after annealing and deformation, 554 microstructure after annealing, 553 true stress–true strain curves after HPT and annealing, 576 microcrystalline and nanocrystalline states, 553 nitrogen, 647 non-compact mode, 709 noncryogenic milling, 615, 638–44 nonequilibrium eutectic, 158 nonmagnetic nickel aluminium bronze, 621 OFHC see oxygen-free high conductivity orientation distribution functions, 760 Orowan strengthening models, 315

© Woodhead Publishing Limited, 2011



Index

Orowan type process, 304 oxidation test, 631 oxygen-free high conductivity, 205 pancake shaped ultrafine grains, 43 partial dislocation, 468 particle image velocimetry, 181 particle impact processing, 481 pearlite wire, 86 Peierls potential, 697 PEL see permissible exposure limit Permalloy, 676 permissible exposure limit, 671 phase morphology effect, 577–8 phase transformation theory, 87, 89–93 PIP see particle impact processing PIV see particle image velocimetry plastic deformation, 87, 108, 164, 337–65, 484–6, 516, 535, 595 athermal stress–induced grain growth, 359–65 applied shear stress in collective migration, 365 External stress σ as a function of the total plastic strain ε, 360 grain growth through collective GB migration in a model of NCM, 364 stress-induced migration of low- or high-angle GB, 363 deformation twins generation, 349–52 equilibrium position dependence, 351 model of DT lamella nucleation at an extrinsic GB dislocation, 352 twinning partial dislocations emission, 350 dislocation generation mechanism, 338–49 critical stress, 347 2D model of NCM with positive and negative wedge GB disclinations, 346 decay of a GB with N = 15 dislocations in nanocrystalline Fe, 344 energy change, 345 energy change map, 341 evolution of high-angle GB with intrinsic dislocations, 345 low-angle tilt boundary decay, 343 new gliding DL generation, 348 two-dimensional representation of crystal lattice transformation, 339 nanostructured alloys, 601–2 nanostructured metals, 276–94 characteristic microstructures, 277–86 hardening by annealing and softening by deformation, 286–9 microstructure and mechanical properties optimisation, 289–90 rotational deformation, 353–7 grain boundary sliding and rotational deformation mode, 356 stress-driven displacement, 354 schematics of deformation mechanism, 338 strengthening/softening under superplasticity, 357–9 GB dislocation transfer, 358 lattice dislocations emission, 359 plastic flow mechanisms, 435–40 plastic instability, 56 plastic relaxation, 104 plastic strain, 605

799

plastic strain amplitude, 515 plastic strain instability, 431, 432, 433, 434 plating bath, 119 Poisson’s ratio, 260, 264 polycrystals deformation mechanisms, 407 von Mises equivalent stress–strain curves and strain hardening, 401–3 precipitation hardening, 698 premelting, 463 pure Nickel, 563–5 pure titanium, 547–8 QSC see quasi-static compression quasi-static compression, 386 quasicrystalline, 159 quasicrystalline materials, 73 repetition of plastic deformation and reverse phase transformation, 728 residual stress, 489–90 resistant stress, 608 roll-bonding, 41, 43 rolling, 41 rolling mill, 42–3 rotational deformation, 353–7, 439 grain boundary sliding and rotational deformation mode, 356 stress-driven displacement, 354 rule-of-mixtures, 385 saccharin, 121 SAD see selected area diffraction SAD pattern see select area diffraction pattern SAED see selected area electron diffraction saturation magnetisation, 675 scaling laws, 543 Scifer, 86 second generation AHSS, 688 second-phase nanoparticles, 451–2 select area diffraction pattern, 230 selected area diffraction, 490 selected area electron diffraction, 157, 246 SePD see severe plastic deformation severe plastic deformation, 40, 86, 153, 220, 507–8, 596, 616, 687 Al 6061-T6 particulate optical micrograph, 204 scanning electron micrographs produced by MAM, 202 bulk forms with ultrafine grained microstructure, 196–200 1080 steel pearlite microstructure, 198 bulk forms produced by LSEM, 197 hardness after deformation by machining, 199 micro-scale gears from Inconel 718 foil, 200 pure Ti micrographs, 198 bulk nanocrystalline materials processing, 14–17 rapidly-quenched Ti50Ni25Cu25 alloy, 15 SPD consolidation, 14 SPD-induced nanocrystallisation, 14–17 Ti50(Ni, Cu)50 alloy X-ray diffraction patterns, 16 Ti49.4Ni50.6 alloy after HPT and annealing, 17

© Woodhead Publishing Limited, 2011

800

Index

ECAP-Conform Al wire longitudinal section, 11 Al work piece, 11 set-up, 10 ECAP processing principle, 7 routes, 8 enhanced properties, 22–33 Al alloys in the form of Hall–Petch relation, 27 alloy 1570 UFG structured formed after HPT-processing, 25 contribution in flow stress for SPD-­ processed Ni, 25 strength and ductility at ambient temperature, 23–33 strength and ductility in metals subjected to SPD, 30 stress vs strain tensile plots, 32 tensile engineering stress–strain curves for Cu, 29 UFG alloys 1570 and 7475 engineering stress–strain curves, 26 Vickers microhardness variation, 31 yield stress as a grain size function for Ni, 24 grain size dependence of maximum elongation, 568 innovation potential, 33–4 assumed innovation probability in various sectors vs. specific strength, 33 mechanics, 179–89 constrained chip formation, 186–8 copper and titanium machining process, 183 copper velocity and strain rate field, 182 deformation field in SPD vs other methods, 188–9 large strain extrusion machining mechanics, 187 machining as an experimental platform, 189 plane-strain machining, 180 pure copper deformation conditions, 188 strain rate, 183–4 temperature, 184–5 texture, 186 Zener–Hollomon parameter, 185–6 microstructure refinement study, 189–96 copper at strain and deformation conditions, 190 copper deformation-microstructure map, 191 copper microstructure, 193 deformation-microstructure map, 196 deformation twinning, 192–3 discontinuous dynamic recrystallisation and bimodal microstructures, 193–4 evolution at small deformation rates, 191–2 fully recrystallised microstructures, 194 homogeneity, 194–6 orientation imaging microscopy analysis, 195 recrystallised grains optical micrograph, 195 nanocrystalline materials, 546–67 Al-based alloys, 554–7 Ni-based alloys, 557–60 Ti-based alloys, 546–54 nanostructured alloys production by machining, 178–207

nanostructured particulate, 200–5 method for making metallic fibres, 203 modulation-assisted machining schematic, 201 particulate consolidation, 203–4 nanostructures types, 18–22 alloy Al 6061 UFG structure, 22 HPT-processed 6061 Al alloy grain boundary segregations, 21 UFG Al-3%Mg alloy nonequilibrium grain boundaries, 19 UFG Cu after ECAP and cold rolling, 20 new trends for effective grain refinement, 8–22 basic rules for grain refinement, 17–18 principles, 4–8 illustration, 5 ultrafine-grained copper, 6 producing bulk nanostructured metals and alloys, 3–34 surface nanostructuring, 205–7 copper and brass strain variation, 206 techniques and routes development, 8–14 Al samples tensile mechanical properties, 12 combined SPD processing, 12–14 continuous equal-channel angular-pressing, 9–12 Grade 2 Ti microstructure, 13 Ti billets mechanical properties, 13 SFE see stacking fault energy shear banding, 575 sheaves of bainite, 99 Shockley dislocation, 344–5 Shockley partial dislocations, 218, 468 shot peening, 482 balls and shots parameters, 482 finite element simulation results, 485 silicon, 89, 100 simple twins, 331 SLF see slip line field slip accommodation, 579 slip line field, 182 SMAT see surface mechanical attrition treatment SNH see surface nanocrystallisation and hardening soft magnetic alloys, 169–71 solid reaction nanostructured steels processing, 85–113 accelerating the bainite reaction at low temperatures, 98 characterising nanocrystalline bainitic steels at the atomic scale, 98–106 finest grain structures in steels, 86–9 future trends, 113 NANOBAIN steel, 93–8 nanocrystalline bainitic steels mechanical properties, 107–13 phase transformation theory, 89–92, 93 solution hardening, 698 SP see shot peening; superplasticity SP strain rates, 544 spark plasma sintering, 75, 154, 156 SPD see severe plastic deformation S2PD see surface severe plastic deformation Spingarn and Nix’s slip band model, 607 splitting distance, 469, 470

© Woodhead Publishing Limited, 2011



Index

sporting goods, 681–3 SPS see spark plasma sintering SRS see strain rate sensitivity SRX see static recrystallisation stacking fault energy, 468 stacking fault tetrahedra, 220 star twins, 228–9 static recrystallisation, 386 strain hardening, 80, 111, 377 rate, 400, 448–9 strain-induced dynamic transformation, 750, 757 strain rate sensitivity, 516 strain rate sensitivity value, 560 strain–gradient plasticity theory, 408 strength-uniform elongation combination, 405 strength–ductility behaviour, 376, 390–2, 398–403 strengthening mechanisms alternative deformation mechanisms at very fine grain sizes, 307–14 classical deformation mechanisms, 308–9 inert-gas-condensed compacted-powder materials deformation analysis, 309 mechanical behaviour new experimental analysis, 311–13 other nanocrystalline materials deformation, 310–11 suggestions for new deformation mechanisms in nanocrystalline metals, 313–14 values of activation volume measured in Cu and Ni, 312 future trends, 324 Hall–Petch breakdown, 303–7 defective materials importance, 304–7 fine grain size limit to models, 303–4 hardness variation with grain size for nanocrystalline Ni-base samples, 306 materials with ultrafine microstructure prepared by SPD, 320–4 boundary misorientations distribution in Fe3Al, 321 hardening analysis during Fe/Fe3Al/FeAl cold working or milling, 324 hardening analysis during Fe3Al rolling, 323 nanocrystalline metals, 299–325 polycrystals deformation, 300–3 Cu yield stress variation, 301 milled Fe hardness variation, 301 second-phase particles, 314–19 Cu-bcc particle strengthening analysis, 315 dislocation–particle interactions in Cu-bcc particle materials, 316 Fe hardness milled with Al2O3 with Pb, 318 FeAl dislocation–particle interactions, 317 FeAl materials hardness, 317 solute, order, twin boundaries, 319–20 Super-Metal Project, 743 superplastic deformation nanocrystalline metals and alloys, 542–90 deformation mechanisms, 578–87 superplasticity, 546–67 superplasticity specific features, 568–78 theoretical predictions, 543–6

801

theoretical predictions, 543–6 grain size and optimum strain rate or superplastic temperature, 545 normalised yield stress variation, 546 superplasticity, 141, 157, 357–9, 542 effect of microstructural features, 575–8 grain size distribution effect, 575–6 phase morphology effect, 577–8 stress-strain curves and microstructures, 577–8 GB dislocation transfer, 358 lattice dislocations emission, 359 microcrystalline vs. nanocrystalline plasticity, 568–75 absence of cavitations, 573 excessive strain hardening, 572–3 experimental stress–strain rate data, 572 flow stress variation, 571 grain size dependence of maximum elongation, 568 high flow stresses, 569–72 microstructural instability and superplasticity, 573 nanocrystalline materials crystallised from amorphous precursor, 560–3 produced by electrodeposition, 563–5 produced by powder consolidation, 565–7 produced by severe plastic deformation, 546–60 nanocrystalline metals and alloys, 546–67 Al-1420 alloy specimens before and after deformation, 556 darkfield TEM images Al-1420 alloy specimens, 557 NC Ni increase in ductility, 565 tensile specimens in the as-machined geometry, 564 specific features in nanocrystalline materials, 568–78 effect of annealing, 578 effect of microstructural features, 575–8 effect of processing, 575 microcrystalline vs. nanocrystalline plasticity, 568–75 surface mechanical attrition treatment, 481 surface nanocrystallisation and hardening, 481 surface nanostructuring, 205–7 surface severe plastic deformation, 481 balls and shots parameters, 482 fatigue resistance of metals, 499–501 fatigue limit improvement, 499–500 mechanism, 500–1 mechanics aspects, 482–4 Hertz pressure distribution during ball impact, 484 microstructure and stress states changes, 484–93 finite element simulation results, 485 microstructure gradients, 490–3 plastic deformation zone predicted via FEM, 484–6 residual stress profiles, 489–90 residual stresses on the plane parallel to the impacted surfaces, 489 surface roughness and contamination evolution, 493

© Woodhead Publishing Limited, 2011

802

Index

Vickers hardness, 487 work hardened profiles, 486–9 tensile properties of metals, 493–9 C-2000 plates tensile stress–strain behaviour, 494 elastic modulus in tensile tests, 493–5 fracture surfaces of the annealed C-2000 sample, 497, 498 tensile ductility, 496–9 tensile yield strength, 495–6 wear resistance of metals, 501–2, 503 C-2000 alloy wear tracks, 503 Taber wear index, 137, 140 tailored welded blanking, 773 Taylor factor, 264 TBC see thermal barrier coating Technology Readiness Level, 667 temperature dependent deformation deformation at elevated temperatures, 595–8 work hardening in nanostructured nickel, 596 work softening phenomenon, 597 fine-grained pure metals, 595–601 creep behaviour, 598–9 deformation at elevated temperatures, 595–8 grain boundary relaxation, 600–1 tensile creep, 605 tensile ductility, 431–4, 496–9 tensile mechanical tests, 17 tensile uniform elongation, 393 tensile yield strength, 495–6 tension, 408–14 tension shear tests, 781 tension tests, 79 THERMOCALC, 752 texture angle, 186 thermal barrier coating, 627 thermal spray processing, 615, 617–20 alumina-titania (n-AT) coatings, 621–2 Mine Countermeasures Ship main propulsion shaft region, 622 MCrAlY and NiCrAlY coatings, 627–44 cryomilling, 627–38 non-cryogenic milling, 638–44 oxide scale, 644 titanium oxide coatings, 622–7 abrasion and slurry erosion wear test results, 623 conventional and nanostructured TiO2 coating, 624 scars following abrasion, 625 titanium balls with chromia-blend and nanostructured coatings, 626 WC-Co coatings, 620–1 thermal stress, 698 thermocouple methods, 184 thermomechanical controlled processes, 748–9, 757 third generation AHSS, 688 Ti-6Al-4V alloy, 529, 548–52 before and after deformation, 550 bright field TEM images after deformation, 551 typical stress–strain curves, 549 Ti-6Al-4V-ELI, 529

total strain, plastic strain and elastic fatigue life diagrams, 531 Ti-6Al-4V-ELI UFG, 531 Ti-based alloys, 546–54 Ti-Ni alloys, 15 TiAl alloy, 566–8 stress–strain behaviour, 567 time–temperature–transformation, 92, 95 titanium, 34 titanium oxide coatings, 622–7 TLDs see trapped lattice dislocations top-down approach, 59–60 total strain fatigue life, 530 trapped lattice dislocations, 265 Tresca yield criterion, 483 TriboMAM, 202 TRIP effect, 110 triple junction diffusional creep, 438–9, 440 TRL see Technology Readiness Level TTT see time–temperature–transformation tungsten carbide-cobalt coatings, 620–1 TWI see Taber wear index twin deformation, 440, 446–8 twinning induced plasticity, 688 TWIP steels, 688 UDCSMR see ultra-fast direct cooling, short interval multi-pass hot rolling UFG see ultrafine grained UFG aluminium and aluminium alloys, 517–27 UFG-FC steel, 689 94% cold-rolled and annealed at 525°C, 694 annealing temperatures and mean ferrite grain sizes, 694 chemical composition, 690 cold-rolling reduction and mean thickness ratio, 692 fabricating conditions, 690 flow stress and quasi-static flow stress, 698 hot-rolled sheet, 691 nominal stress–strain curves, 697 UFG-FC steel sheets, 688 UFG magnesium alloys, 528 UFG materials see ultrafine grained materials UFG-MP steel annealing temperature, thickness and quasi-static mechanical properties, 705 axial collapse properties, 711 chemical composition, 700 fabricating conditions, 700 fabricating conditions for axial collapse tests, 708 microstructures of fabricated steels, 703 quasi-static s–s curves in the dynamic collapse tests, 708 quasi-static tensile properties, 709 UFG-MP1 steel annealing temperature and microstructural parameters, 703 fabricating conditions, 700 hat columns after dynamic collapse tests, 709 hot rolled and cold-rolled sheet, 701 mean intersect lengths, 702 nominal stress–strain curves, 704 UFG-MP2 steel fabricating conditions, 700 hat columns after dynamic collapse tests, 709

© Woodhead Publishing Limited, 2011



Index

load-displacement and absorbed energy displacement curves, 710 nominal stress–strain curves, 704 UFG steels microstructures and quasi-static tensile properties, 696 sheets, 687 UFG titanium and titanium alloys, 528–32 UHSS see ultra high strength steels ultimate tensile strength, 509 ultra-fast direct cooling, short interval multi-pass hot rolling nanostructure plain carbon-manganese steel sheets, 747–84 concept and experimental hot rolling mill, 749–52 deformation characteristics, 765–73 deformation temperature of grain refinement processes, 749 grain refinement mechanisms, 757–65 hot strip mill in Kashima steel works, 748 layout of a hot strip mill, 748 UDCSMR, 752–7 welding and application to some prototype parts, 773–84 ultra high strength steels, 688–9 Ultra-Steel Project, 743 ultrafine grained, 4, 34, 40, 179, 196, 200 metallic materials, 375, 377, 425 grain size regimes, 376 micrometer-sized grains embedded in UFG matrix, 416 plastic flow mechanisms, 435 work softening phenomenon, 597 ultrafine grained materials, 508 see also specific types fatigue life, 535–7 key issues affecting fatigue life, 536 ultrafine lamellar boundary structures, 43 UltraLight Steel Auto Body project, 688 ultrasonic shot peening, 481 uniform–random distribution, 335 unimodal metallic materials, 406–8 polycrystals, 404 predicted yield strength as a function of square root of mean grain size, 401 tensile strength vs. uniform elongation, 404 US Patent 5,352,266, 678 US Patent 5,433,797, 678 US Patent Publication No. 2006/0135282, 678 US Pressurised Water Reactors, 119 USSP see ultrasonic shot peening UTS see ultimate tensile strength valley of death, 667 very high cycle fatigue, 510 VHCF see very high cycle fatigue Vickers hardness, 487, 488 Vickers microhardness, 486 Vitroperm, 449, 676 true stress–true strain curve after 600°C 1 h anneal, tested at 600°C, 561

803

tested at 725°, bright field image after tensile testing, 562 von Mises equivalent strain, 41–2, 278 von Mises equivalent stress–strain curves, 400, 401–2 von Neumann–Mullins rule, 474 vorticity, 18 warm multi pass caliber rolling, 716–19 Watts nickel plating bath, 119 WC-12Co, 618 wear resistance, 501–2 wedge disclinations, 438 welding application to prototype parts, 773–84 chemical composition, mechanical properties and Ceq of Steels, 773 steel microstructures, 774 base metal microstructure and HAZ-simulated specimen, 778 CCT diagram for a steel of 590MPa tensile strength grade and cooling rates, 775 cross-sections and hardness distribution of steels, 775 forming test results, 780 heat affected zone of laser-welded steel, 776 heat affected zone of plasma-arc-welded steel, 777 J-shaped prototype component die-formed from 0.15%C-0.7%Mn nanostructured steel, 783 joint strength vs. weld current for steels A & C under 3.9kN and 0.5s, 782 nugget diameter vs. weld current for steels A & C under 3.9kN and 0.5s, 782 photographs of fracture areas of formed specimens (type A), 780 photographs of fracture areas of formed specimens (type B), 781 schematic representation and photographs of dome-forming specimens, 779 schematic representation of heat treatment in HAZ simulation tests, 778 T-shaped prototype component die-formed from TWB 0.15%C-0.7%Mn ­nanostructured steel, 783 tension shear tests, 781 welded metal microstructures, 776 Widmanstätten ferrite, 90 work hardened profiles, 486–9 work hardening, 596 work softening, 597 yielding, 377 Young’s modulus, 138, 143, 144, 167, 260 yttria partially stabilised zirconia (YPSZ), 627 Zener–Hollomon parameter, 185–6, 715, 718 Zinc, 565–6 after deformation to elongation, 567 stress–strain curves, 566

© Woodhead Publishing Limited, 2011