Maraging Steels: Modelling of Microstructure, Properties and Applications

i

Maraging steels

ii

Related titles: Titanium alloys: Modelling of microstructure, properties and applications (ISBN 978-1-84569-375-6) Computer-based modelling of material properties and microstructure is a very fast growing area of research and the use of titanium is growing rapidly in many applications. The first part of the book reviews experimental techniques for modelling the microstructure and properties of titanium. A second group of chapters looks in depth at the physical models and a third group examines neural network models. The final section covers surface engineering products. Creep-resistant steels (ISBN 978-1-84569-178-3) Creep-resistant steels must be reliable over very long periods of time, at high temperatures and in severe environments. Their microstructures have to be very stable, both in the wrought and the welded states. Creep, especially longterm creep behaviour of these materials, is a vital property and it is necessary to evaluate and estimate long-term creep strength accurately for safe operation of plant and equipment. The first part of the book describes the specifications and manufacture of creep-resistant steels. Part two covers the behaviour of creep-resistant steels and a final group of chapters analyses applications. Fundamentals of metallurgy (ISBN 978-1-85573-927-7) As product specifications become more demanding, manufacturers require steel with specific functional properties. Fundamentals of metallurgy summarises the research in this area and its implications for manufacturers. With the overall emphasis on properties and processes, this applied text will appeal to both the academic and the steel-producing markets. Details of these and other Woodhead Publishing materials books can be obtained by: ∑ visiting our web site at www.woodheadpublishing.com ∑ contacting Customer Services (e-mail: [email protected]; fax: +44 (0) 1223 893694; tel.: +44 (0) 1223 891358 ext. 130; address: Woodhead Publishing Limited, Abington Hall, Granta Park, Great Abington, Cambridge CB21 6AH, UK) If you would like to receive information on forthcoming titles, please send your address details to: Francis Dodds (address, tel. and fax as above; e-mail: [email protected]). Please confirm which subject areas you are interested in.

iii

Maraging steels Modelling of microstructure, properties and applications Wei Sha and Zhanli Guo

CRC Press Boca Raton Boston New York Washington, DC

Woodhead publishing limited

Oxford    Cambridge    New Delhi

iv Published by Woodhead Publishing Limited, Abington Hall, Granta Park, Great Abington, Cambridge CB21 6AH, UK www.woodheadpublishing.com Woodhead Publishing India Private Limited, G-2, Vardaan House, 7/28 Ansari Road, Daryaganj, New Delhi – 110002, India www.woodheadpublishingindia.com Published in North America by CRC Press LLC, 6000 Broken Sound Parkway, NW, Suite 300, Boca Raton, FL 33487, USA First published 2009, Woodhead Publishing Limited and CRC Press LLC © 2009, Woodhead Publishing Limited 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 publishers cannot assume responsibility for the validity of all materials. Neither the authors nor the publishers, 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. Library of Congress Cataloging in Publication Data A catalog record for this book is available from the Library of Congress. Woodhead Publishing ISBN 978-1-84569-686-3 (book) Woodhead Publishing ISBN 978-1-84569-693-1 (e-book) CRC Press ISBN 978-1-4398-1877-0 CRC Press order number: N10125 The publishers’ 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 publishers ensure that the text paper and cover board used have met acceptable environmental accreditation standards.  Typeset by Replika Press Pvt Ltd, India Printed by TJ International Limited, Padstow, Cornwall, UK

v

Contents

Author contact details

viii

Preface

ix

Acknowledgements

xi

1

Introduction to maraging steels

1

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

What are maraging steels? Microstructure and mechanical properties Thermodynamic calculation Phase transformation kinetics and age hardening Overageing Precipitation hardening stainless steels Modelling correlations using an artificial neural network References

1 3 4 5 8 10 14 15

2

Microstructure of maraging steels

17

2000 MPa grade cobalt-free maraging steel 2400 MPa grade cobalt-free maraging steel 18Ni (350) cobalt-containing grade 2800 MPa cobalt-containing grade References

17 40 47 48 48

Mechanical properties of maraging steels

49

2000 MPa grade cobalt-free maraging steel 2400 MPa grade cobalt-free maraging steel Grain-refined copper maraging steels References

49 59 65 65

2.1 2.2 2.3 2.4 2.5



3 3.1 3.2 3.3 3.4



vi

Contents

4

Thermodynamic calculations for quantifying the phase fraction and element partition in maraging systems and precipitation hardening steels

67

Methodology of thermodynamic calculations and choice of alloy systems 2400 MPa grade cobalt-free maraging steel Fe–Ni–Al–Mo Fe–Ni–Mo and Fe–Ni–Co–Mo Fe–Ni–Mn References

67 68 68 70 72 73

Quantification of phase transformation kinetics in maraging steels

74

4.1 4.2 4.3 4.4 4.5 4.6



5 5.1 5.2 5.3 5.4 5.5 5.6



Evolution of precipitates Overall process Precipitation in Fe–12Ni–6Mn maraging-type alloy 18 wt% Ni C250 Phase fraction by x-ray diffraction analysis References

74 78 79 88 101 108

6

Quantification of age hardening in maraging steels

109

6.1 6.2 6.3 6.4 6.5 6.6

Precipitation hardening theories Kinetics Fe–12Ni–6Mn C250 C300 References

109 119 121 122 123 124

7

Maraging steels and overageing

125

7.1 7.2 7.3 7.4

125 127 128

7.5 7.6

Mechanism of particle coarsening Influence of volume fraction on coarsening What is the controlling mechanism? Quantification of precipitation kinetics and age hardening for Fe–12Ni–6Mn Reconsidering the precipitate fraction effect References

8

Precipitation hardening stainless steels

141

8.1 8.2

Microstructural evolution in PH13-8 after ageing Small-angle neutron scattering analysis of precipitation behaviour

141

129 136 140

156

Contents

8.3 8.4 8.5 8.6 9 9.1 9.2 9.3 9.4 9.5 9.6

vii

Improving toughness of PH13-8 through intercritical annealing Thermodynamic calculations Quantification of early stage age hardening and overageing References

159 168 171 173

Applications of artificial neural network to modelling steel properties

174

Model development Model performance Comparison of model predictions with experimental data Applications of the models Summary References

174 182 186 187 194 194

Index

195

viii

Author contact details

Professor Wei Sha Professor of Materials Science Queen’s University Belfast Belfast BT7 1NN UK E-mail: [email protected]

Dr Zhanli Guo Senior Materials Scientist Sente Software Ltd Guildford GU2 7YG UK

ix

Preface

This book is a research monograph, accumulating the experience of many years’ research by the authors. It includes more recent results, since 2000, but also covers relevant, recent work by other researchers around the world. The book includes both conventional maraging steels and precipitation hardened (PH) stainless steels. Since 2000, the authors have been funded by the UK Engineering and Physical Sciences Research Council (EPSRC), for carrying out the following projects: (1) Computer modelling of the evolution of microstructure during processing of maraging steels (2) Collaborative research in modelling the evolution of material microstructures and by Queen’s University Belfast, the Royal Society, Royal Academy of Engineering, and Invest Northern Ireland in smaller projects, most of them jointly with international collaborators. The research from these projects has resulted in many research publications. These research papers are the backbone of this book, but the underlying structure of the book is based on the physical metallurgical phenomena of the maraging process. In addition, other researchers’ work is reviewed and the major results presented and discussed. The last book devoted exclusively to maraging steels was a conference proceedings published in 1989: Maraging steels: Recent developments and applications, R.K. Wilson (ed.), 1989, TMS, Warrendale, PA. The only other major book on maraging steels was published in 1979: Source book on maraging steels, R.F. Decker (ed.), 1979, American Society for Metals, Metals Park, OH. However, research and development (R&D) into maraging steels has been ongoing until today. Therefore, a book on this subject is very much needed and we hope that this book will be welcomed by academics and industrialists alike. Computer-based modelling is a fast growing field in materials science, demonstrated by the large recent literature. We intend to fill a big gap in the

x

Preface

book literature in the application of modelling techniques in maraging steels, whilst at the same time documenting the latest research in this area. A large chunk of this latest research is from the authors themselves, but, as stated before, the book also covers important relevant research by others. Much of the microstructural modelling is about phase transformations and kinetics. The book is primarily intended for researchers who are interested in either maraging steels or modelling, or both. The maraging steels expert will be able to learn modelling and apply this increasingly important technique in their maraging steel materials research and development. The modelling expert will be able to apply their modelling expertise to the remarkable material that is maraging steel. The idea behind this book is to combine modelling and maraging steel into one place. There is no other book at present covering the combination of maraging steels and computer modelling. Computer modellers have many opportunities to read entire books that are devoted to the modelling techniques used in this book, but these are not applied to maraging steels. The chapter division is according to phenomena being modelled. Wei Sha Professor of Materials Science, Queen’s University Belfast, UK Zhanli Guo Senior Materials Scientist, Sente Software, UK

xi

Acknowledgements

We thank: ∑ ∑

∑ ∑ ∑ ∑ ∑ ∑ ∑

Our past and present collaborators including Yi He, Ke Yang, Eric Wilson, Dan Li, Kai Liu, Ke-Gang Wang, M.E. Glicksman, K. Rajan, David Cleland, David Vaumousse, Richard Grey. Professors G.D.W. Smith and A. Cerezo, Mr. T.J. Godfrey and other personnel working in the atom probe laboratory, Department of Materials at Oxford University for introducing WS to the maraging field, providing the 3D atom probe facility and software for data analysis, and useful discussions. Dr. S. Malinov at Queen’s University Belfast for his help with X-ray diffraction analysis using synchrotron radiation and useful discussions. Ms J. Patrick and Mr S. McFarland at the Electron Microscopy Unit, Queen’s University Belfast for their technical assistance. Ms Wendy Martin (nee Beck) at Allvac UK Ltd. for providing the C250 and the PH13-8 alloys. The referees of some of our research papers for their suggestions for improving the integrity and quality of the papers. Support from the Young Scientist Research Fund in Liaoning Province, China, Fund number 20031006. Support from the US National Aeronautics and Space Administration, Marshall Space Flight Center, under Grant NAG-8-1468. Support from the US National Science Foundation International Materials Institute program for the Combinatorial Sciences and Materials Informatics Collaboratory (CoSMIC-IMI) through NSF Grant DMR-0231291.

1

Introduction to maraging steels Abstract: This chapter introduces maraging steels and then gives extended background information on the topics of each subsequent chapter. Because of the specialised nature of this research monograph, the first part is relatively brief, assuming that the reader will already have good knowledge of physical metallurgy. The main part of the chapter discusses past literature and poses research questions that are intended to raise the reader’s interest in studying the detailed text of subsequent chapters. For this reason, the sections are arranged roughly in the order of the subsequent chapter subjects. The reader should gain an overview of the contents of the book through this chapter. Key words: precipitation, age hardening, reaction kinetics, phase transitions, mechanical properties.

1.1

What are maraging steels?

Maraging steels are a special class of ultrahigh strength steels that differ from other steels in that they are not hardened by carbon. Carbon, in fact, is an impurity element in these steels and is kept as low as is commercially practicable. Instead of relying on carbide precipitation, these steels are hardened by the precipitation of intermetallic compounds. The absence of carbon in the steels confers significantly better hardenability, formability, and a combination of strength and toughness. A number of grades of maraging steels have been optimised to provide specific yield strength levels. The compositions of some common grades developed by International Nickel Ltd. (Inco) are shown in Table 1.1. Typically, these steels contain high levels of nickel, cobalt and molybdenum. Maraging refers to the ageing of martensite, a hard microstructure commonly found in steels. Martensite is easily obtained in these steels owing to the high nickel content. The only transformation that occurs at ordinary cooling rates is martensite formation. The martensite without carbon is quite soft, but heavily dislocated. Hardening and strengthening of these steels are subsequently produced by heat treating (ageing) for several hours at 480–510°C, Table 1.1 Nominal compositions (wt%) and the respective strength of commercial maraging steels (Inco) Alloy designation

Ni

Mo

Co

Ti

Al

Ys (MPa)

18Ni 18Ni 18Ni 18Ni 18Ni

18 18 18 18 17

3.3 5.0 5.0 4.2 4.6

8.5 8.5 9.0 12.5 10.0

0.2 0.4 0.7 1.6 0.3

0.1 0.1 0.1 0.1 0.1

1400 1700 2000 2400 1650

(200) (250) (300) (350) (cast)

1

2

Maraging steels

caused by precipitation, as first observed by Floreen and Decker. During this stage, the metastable martensite in the steels decomposes. Fortunately, the precipitation hardening occurs much more rapidly than the reversion reactions producing austenite and ferrite. Thus, substantial hardening can be produced before reversion occurs. Austenite reversion, or the prevention of it in most cases, is important to ageing, because austenite is a stable phase at room temperature for maraging steel compositions. Since the earliest research on these steels carried out by Bieber of Inco in the late 1950s, work on the further development of alloys has been extensive. The precipitation process and identification of the precipitates have been the focus of the research and development of maraging steels. The hardening alloying elements include titanium, vanadium, aluminium, beryllium, manganese, molybdenum, tungsten, niobium, tantalum, silicon and copper. In this chapter, attention will be focused on the recent results of physical metallurgical studies. Maraging steels are characterised by a large number of alloying elements and, consequently, they are expensive materials compared with many other engineering alloys. The compositions shown in Table 1.1 may be compared with carbon steels with typically 0.04–1.7% C and 0.8% Mn. The resulting ultrahigh strength (Ys) in maraging steels (the last column of Table 1.1, compared to standard yield strength grades of 275 and 355 MPa for carbon structural steels) is accompanied by a much higher cost in producing them. The maraging alloy development is significantly influenced by the availability and price of the alloying elements. For instance, the development of a family of cobalt-free maraging steels in the late 1970s was solely due to the sharp rise in cobalt pricing. Although the manufacturing of maraging steels requires special processes, their ageing heat treatment is very simple, resulting in minimum distortion. Maraging steels have good machining properties and are widely used in many military and commercial industries, mainly for aircraft, aerospace and tooling applications, for example as a rocket motor case and in the important parts of aeroplanes (He et al., 2002a,b; 2003a,b). Over the past half a century, two major types of maraging steels have been developed (He et al., 2002c), the 18Ni maraging steels and the cobalt-free maraging steels. Between the two types, the 18Ni maraging steels are in a more advanced and mature stage of development and applications, with maximum strength levels reaching 2400 MPa accompanied by good toughness and ductility. However, these steels contain an expensive alloying element, cobalt, at levels as high as 8–13%. This keeps the steels rather expensive, preventing wider selection and application. Therefore, developing cobalt-free maraging steel with reduced quantities of expensive alloying elements in order to lower the production cost has been an important direction of maraging steels research. Over the past two decades, enormous advancement has been achieved in

Introduction to maraging steels

3

the development of cobalt-free maraging steels, to a strength level of 2000 MPa (He et al., 2002c). With the development of commercial industry, further improvement in mechanical properties is needed for maraging steels with strength above 2000 MPa, especially the fracture toughness. In addition, it has become important to develop low cost cobalt-free maraging steels with properties close to the current 18Ni-type maraging steels. This will save the strategic cobalt resource, reduce the cost of maraging steels and promote their application in wide areas.

1.2

Microstructure and mechanical properties

A great amount of research has been carried out over the years on the ageing microstructure, mechanical properties and strengthening mechanisms of 18Ni maraging steels (Tewari et al., 2000). Dense, fine and complex microstructures form in maraging steels during ageing treatment, with precipitates having complicated diffraction patterns. These, coupled with compositional variations of different steels have resulted in differing opinions in the research literature. For example, regarding the nucleation process of ageing reaction, classical nucleation theory as well as spinodal decomposition have been proposed. Different precipitation phases have been identified, including g-Ni3Mo, h-Ni3Ti (Tewari et al., 2000), Laves-Fe2Mo, s-FeMo, m-Fe7Mo6, FeTi, Fe2Ti, w (Tewari et al., 2000), dispersion austenite, either singly or simultaneously occurring. Moving on to precipitation strengthening mechanisms, there are dislocation looping mechanisms and shearing mechanisms. Many authors observed reverted austenite with different morphology under overageing or special treatment conditions, its orientation relationship with martensite varying ranging from Nishiyama–Wassermann (N–W, (111)A//(110)M, [110]A//[100]M) (Farooque et al., 1998; Sinha et al., 1995; Viswanathan et al., 1993) to Kudjumov–Sachs (K–S, (111)A//(110)M, [110]A//[111]M) (Farooque et al., 1998; Li and Yin, 1995; Viswanathan et al., 1993) types. N–W is close to K–S so that this spread may simply be a result of the technique used or difficulties in resolution between the two especially in early work rather than because of a significant difference. In terms of mechanical properties, there was embrittlement in 18Ni (350 ksi grade) maraging steels after low temperature ageing at 400–450°C. Overageing decreases strength, ductility and toughness, but there were also reports of improved strength and toughness owing to reverted austenite. To date, research on cobalt-free maraging steels has concentrated on T-250 and other grades with an 1800 MPa strength level. There is discrepancy among the results similar to that for 18Ni cobalt-containing maraging steels. For example, some believed that in T-250, austenite nucleated first in martensite, followed by nucleation of Ni3Ti from the austenite site, contrary

4

Maraging steels

to other’s work showing Ni3Ti to be the only precipitation phase. In T-300 (Fe–18.5Ni–4Mo–1.85Ti, wt%), Ni3Ti forms first followed by the precipitation of a spheroidal Fe7Mo6 phase after longer ageing times, mostly at different sites from Ni3Ti. No austenite forms after 360 hours at 510°C. So far, there have not been many reports on microstructure and mechanical properties of higher strength cobalt-free maraging steels. Chapters 2 and 3 describe systematically the microscopy and microstructure and their relation to mechanical properties and testing, respectively, in a 2000 MPa grade cobalt-free maraging steel after ageing at 440–540°C, above and below the intermediate or normal ageing temperature, 480°C. The steel composition is Fe–18.9Ni–4.1Mo–1.9Ti (wt%). Strengthening and toughening mechanisms and other controversial issues are also discussed. Following this steel, the titanium content is further increased to boost the strength. At the same time, the amounts of other alloying and impurity elements are controlled to avoid detrimental effects on toughness. The effect of heat treatment on mechanical properties will be shown and the effects of cobalt, molybdenum and titanium on steel toughness will be discussed (He and Yang, 2002).

1.3

Thermodynamic calculation

Precipitation hardening (PH) or strengthening remains one of the most effective processes in the development of ultrahigh strength alloys. It is achieved by producing a particulate dispersion of obstacles to dislocation movement, using a second-phase precipitation process. Identification of the precipitates has been the focus of research and development of PH steels. Thermodynamic calculation can supplement experimental characterisation and allows the prediction of phase type, fraction and element distribution in different phases. Thermo-Calc, a computer package developed particularly for thermodynamic calculations, is used to quantify the precipitates formed during ageing of some precipitation hardening steels of maraging type. This package is developed for the calculation of multi-component equilibrium as a function of pressure, temperature and the combined effect of alloying elements, using a databank of assessed thermodynamic data and models for the phases in the system that are as good approximation of the actual nature as possible. It employs rigorous thermodynamic expressions and numerical methods of minimising the chemical energy of the system, so that interpolation between the available experimental data can be made. Good agreement is obtained between the calculated phase compositions and experimental measurements from an atom probe. In Chapter 4, Thermo-Calc is used to quantify the phases formed during ageing of, among others, a Fe–Ni–Al–Mo alloy system. The calculated results are compared with experimental measurement data by atom probe microanalysis. Such calculations, however, are restricted by the limited

Introduction to maraging steels

5

availability of thermodynamic data relating to intermetallic phases in maraging systems.

1.4

Phase transformation kinetics and age hardening

1.4.1 Quantification of precipitation hardening and evolution of precipitates It has been nearly a century since age hardening was first discovered in aluminium alloys. The precipitation strengthening mechanism and precipitation kinetics have become the subject of research since then. It was not until the introduction of the concept of dislocation was the fundamental understanding of the mechanism of precipitation age hardening really achieved. The Orowan equation derived later stands as a landmark achievement, as it established the relationship between the applied stress and the extent of dislocation bowing. Although having been refined since, it still serves as a basis for the theory of dispersion strengthening, or strengthening of alloys by nondeformable particles. After the early efforts to formulate theories and models of precipitation hardening, advances in understanding the mechanisms of precipitation hardening focused on the ways in which dislocations interact with precipitates. Progress up to the early 1980s with the theory of age precipitation hardening concentrated on understanding the statistical nature of dislocation–precipitate interactions and the kinetic mechanisms. Research into precipitation hardening and mechanisms of hardening since then has not been very extensive. There has been progress in understanding of precipitation kinetics. Quantification of precipitation hardening is a challenging subject, as it demands a combined knowledge of precipitation strengthening mechanism and growth and coarsening kinetics. Many attempts have been made to reproduce experimental observations through computer modelling based on the theories of strengthening and kinetics. However, having not seen many attempts to develop new theories in recent years, we are aware of the fact that even many existing concepts and developed theories are sometimes neglected or misused. Although no attempt is made to review all the aspects involved in hardening mechanisms and precipitation kinetics, Chapters 5 and 6 aim to clarify and highlight some aspects which have not been fully addressed and have sometimes been misused. Some recent developments in this subject will be mentioned. Difficulties in quantification of precipitation strengthening effects in alloy systems are also discussed.

6

Maraging steels

1.4.2 Fe–12Ni–6Mn Attempts were made in Russia and Japan with the aim of developing cheaper alternatives to the classical 18Ni maraging steels, studying experimentally maraging in a series of Fe–Ni–Mn alloys. Research with a Fe–12Ni–6Mn alloy showed that age hardening is achieved owing to precipitation of q-NiMn in the lath martensite, the quenched structure before ageing, as observed through electron microscopy. Zones of size 1–10 nm are formed in the aged state at the maximum hardness. The particles are formed uniformly in the matrix and no preferred precipitation occurs at grain boundaries or sub-grain boundaries. In the overaged state, these zones become platelets and lose coherency with the matrix. Age hardening is principally caused by strain hardening owing to the formation of zones or particles with high solute concentration. In Chapters 5 and 6, based on experimental data, quantification of age hardening during the ageing period is shown. The precipitation fraction and precipitate growth as functions of time and temperature are also illustrated.

1.4.3 C250 Strengthening of 18 wt% Ni (18Ni) maraging steels results from the combined presence of Ni3Ti and Fe2Mo or Fe7Mo6 precipitates. The formation of Ni3Ti takes place rapidly owing to the fast diffusion of titanium atoms. When good toughness is required, maraging steels have to be treated to overaged condition to allow the formation of a certain amount of austenite which remains stable at room temperature. Austenite also affects other properties of maraging steels such as magnetic properties and stress corrosion cracking resistance. Research into precipitate formation and austenite reversion has received great attention owing to their importance to the properties of maraging steels. In contrast to extensive experimental studies, there has been limited work on physical modelling of the precipitation formation kinetics and austenite reversion kinetics in maraging steels. With the development of differential scanning calorimetry (DSC), it is possible to trace the phase transformation kinetics under a controlled temperature programme. Therefore, DSC has been widely used in various systems (Sha and Malinov, 2009). In Chapter 5, the results of DSC study are used to model the kinetics of precipitation formation and austenite reversion in a commercial 18Ni grade-250 (C250) alloy. The kinetics are simulated based on the classical Johnson–Mehl–Avrami phase transformation theory. The kinetic parameters derived from continuous heating experiments are used to calculate the phase transformation kinetics

Introduction to maraging steels

7

during isothermal holding. Comparison between the calculated results and experimental study is shown. The increase in the strength and hardness of maraging steels is a function of the precipitate fraction and size. Therefore, quantification of precipitation hardening requires detailed knowledge of the evolution of precipitate size and fraction during ageing. Although there have been numerous studies determining the precipitate type and size in maraging steels, little attention has been paid to studying the precipitate fraction. The main difficulties are the small precipitate size and its low volume fraction. The formation of precipitates during ageing results in a change in the concentration of the precipitate-forming elements in the martensite matrix. This concentration change usually leads to a change in the lattice constant of the martensite matrix. The more precipitates formed, the larger the change in the lattice constant. Since lattice constant can be measured by X-ray diffraction (XRD), one may be able to measure the change in the lattice constant of the martensite matrix by comparing the XRD profiles of steels prior to and after ageing treatment. Consequently, the precipitate fraction may be estimated for a known precipitate type. The change in lattice constant caused by precipitation was observed in an 18 Ni wt% C350 maraging grade using a conventional X-ray diffractometer. Following the ideas described above, in the last part of Chapter 5, a method is introduced to estimate the precipitate fraction based on X-ray diffraction analysis. The applicability of the method is discussed. The fraction of reverted austenite is also quantified whenever detected.

1.4.4 Basic age hardening theories Age hardening process in metallic alloys caused by precipitation can be quantified with the aid of phase transformation theories. Two ageing stages are of particular interest, for both theory and practice. The early stage of precipitation hardening is described by the Johnson–Mehl–Avrami equation. A detailed theoretical analysis of the early stages of ageing gives Eq. [1.1] (Wilson, 1997; 1998):

DH = (Kt)n

[1.1]

where DH is the increase in hardness, K is a temperature dependent rate constant, t is ageing time and n is the time exponent, which is slightly temperature dependent. The other ageing stage is overageing. The strength–microstructure relationship is governed by Orowan bowing. The change in hardness is related to ageing time by a different equation (Wilson, 1997): 3



Ê 1 ˆ Ê 1 ˆ ÁË DH ˜¯ = M (t – t 0 ) + ÁË DH ˜¯ 0

3

for t ≥ t 0



[1.2]

8

Maraging steels

where DH0 is the increase in hardness at commencement of coarsening time t0 and M is a temperature-dependent rate constant. The above two equations can successfully quantify the early and overageing stages of hardening in the Fe–12Ni–6Mn maraging-type alloy, as will be shown in Chapters 6 and 7, respectively.

1.5

Overageing

The kinetics and quantification of the overageing in the Fe–12Ni–6Mn alloy system is the main topic of Chapter 7. Precipitation kinetics combined with hardening effects during ageing and overageing are very challenging topics; a full understanding in two-phase alloys will make the microstructure and property control more purposeful, more certain, more efficient and less empirical. In developing a process model for age hardening, based on kinetic models for microstructural evolution and dislocation model for the dependence of the strength on microstructure, it is important to avoid using complicated calibration procedures to determine all the parameters involved in the model. Failure to do so would make it difficult to extend the model to other alloy systems. Chapters 5 and 6 feature an accurate model of the kinetics and quantification of the early stages of ageing in Fe–12Ni–6Mn which covers the period before peak hardness is reached. Early models of the hardening effect during the overageing period were able to predict hardness levels after the near-equilibrium precipitation amount is reached. In Chapter 7, an accurate quantification model that can predict the hardening effect during the entire overageing period is shown. The influence of the precipitate fraction on particle coarsening and hardening effect is taken into account, since the coarsening rate increases with volume fraction, modifying the commonly used Lifshitz–Slyozov–Wagner (LSW) relationship for a zero volume fraction of precipitate. The Ashby–Orowan relationship, recognised as a more accurate expression than the Orowan relation, is employed in the model to describe the influence of particle size on the critical shear stress during dislocation looping. During the overageing period, the particles start to coarsen, which results in a drop in hardness. Precipitation kinetics directly affect age hardening phenomena and the maturity and sophistication of kinetic models describing population dynamics during solid-state precipitation have progressed steadily over time. The first statistical mechanical formulation of the kinetics of precipitate ageing is the LSW theory, for diffusion-limited as well as interface-limited precipitate coarsening. These early mean-field formulations are valid only in the limit of a vanishing small volume fraction of precipitates, where essentially one particle interacts with the mean field of its surrounding matrix. The prediction of LSW theory, that the cube of the average length scale of particles increases

Introduction to maraging steels

9

linearly with time, has been validated by numerous experiments, even in cases where there was a finite volume fraction of the dispersed phase. The most significant limitation within LSW theory is its neglect of any interactions occurring between the particles. In LSW theory, the coarsening rate of a precipitate particle is given by the linear form:

dr = K LSW 1 – 1 dt r r* r

[1.3]



where r and r* are the radius of the particle and the critical radius of the precipitate population, respectively. KLSW is the kinetic coefficient and is independent of the volume fraction of the precipitates. In real materials, however, the volume fraction of precipitates, f, is never zero, so that, even in –1

dilute dispersions, the mean separation between precipitates f 3 is typically less than a few particle diameters, so that interactions normally occur among the individual particles. Numerous theories of phase coarsening (Baldan, 2002) have been published since the time of LSW, addressing cases of phase coarsening with a non-zero precipitate volume fraction. Most are LSW-like, that is, they consider a single particle interacting with a mean field set by the microstructure. Single particle theories alter the kinetic coefficient, KLSW, in Eq. [1.3], to account for thermodynamic interactions in alloys, such as multi-component solution effects. A few coarsening theories, such as diffusion screening theory for precipitation kinetics (Glicksman et al., 2001; Wang et al., 2004, 2005) belong to another classification, the many-body theory. By contrast, many-body interaction theory modifies the dependence of the coarsening rate of particles in a non-linear form:

dr = K LSW Ê 1 – 1ˆ Ê1 + r ˆ dt r ÁË r* r˜¯ ÁË RD ˜¯



[1.4]

where RD is the diffusion Debye screening length which depends on the volume fraction (Wang et al., 2004). Introducing many-body interactions insures that the coarsening rate of precipitates relates to their volume fraction more accurately. This key difference distinguishes the many-body theory from LSW-like theory. Moreover, diffusion-screening theory for precipitation kinetics recently yielded predictions that were in quantitative agreement with experimental kinetic results (Glicksman et al., 2001; Wang et al., 2004). Coarsening theory for multi-component alloys modifying the kinetic coefficient KLSW only with consideration of multi-component effects belongs to the LSW-like classification. The kinetics and quantification of the early stages of ageing in Fe– 12Ni–6Mn were based on experimental work on hardening of this steel. However, the LSW theory for treating the precipitation kinetics suggests

10

Maraging steels

that the effect of volume fraction on precipitation kinetics and hardness was not fully dealt with. Reconsidering the influence of the precipitate fraction on particle coarsening and hardening, a model of coarsening uses Laplacian (direct) screening. In the latter parts of Chapter 7, we combine a recent kinetic model developed by Wang et al. (2004) for precipitation and coarsening that uses Debye screening to account for the effect of the precipitate fraction on particle coarsening with a model for precipitationenhanced hardening. We require accurate extraction of diffusion data from microstructural modelling. Specifically, we use: (1) Thermo-Calc coupled to Kaufman’s binary alloy database to obtain equilibrium values of the solubility at different temperatures. These data, in turn, are used to calculate the kinetic coefficients appearing in the theoretical precipitation kinetics during overageing. (2) We use the Ashby–Orowan formulation to develop the relationship between hardness levels, particle size and spacing. (3) We combine experimental measurements of hardness in maraging steel with thermodynamic data derived from Thermo-Calc calculations and insert these results into the coarsening model to provide an in-depth study of the effect of precipitate kinetics on hardness and to extract the diffusion coefficient for this alloy. We implement the overall methodology by applying it to the ternary alloy Fe–12Ni–6Mn. Lastly, employing accurate expressions for the coarsening rate of precipitates, with due consideration given to the effect of volume fraction, we found significant improvement in the accuracy of microstructural modelling. The organisation of the chapter includes outlining briefly the theoretical foundation for our study on microstructure evolution and hardness, the analysis, calculations and the main conclusions.

1.6

Precipitation hardening stainless steels

1.6.1 Microstructural evolution PH13-8 stainless steel is a martensitic PH steel. It has high strength and hardness with good levels of resistance to both general corrosion and stress-corrosion cracking. In addition, the alloy exhibits good ductility and toughness in large sections in both the longitudinal and transverse directions and offers a high level of useful mechanical properties under severe environmental conditions superior to PH17-4 and PH15-5 stainless steels. It has been used for many applications, such as landing gear parts, nuclear reactor components and petrochemical applications requiring resistance to stress-corrosion cracking. The ferritic and martensitic phases in high alloy steels, including stainless steels such as PH13-8, containing nickel and aluminium can be hardened by ageing at temperatures above 400°C. The strengthening is due to the

Introduction to maraging steels

11

precipitation of the ordered phase NiAl which has a B2 (CsCl) superlattice structure. However, owing to instrument limitation, in the past, it was not possible to analyse directly fine precipitates on the nanometre scale. Therefore, the materials studied had to be treated under seriously overaged conditions to achieve precipitates of detectable sizes by transmission electron microscopy (TEM). In a wrought PH13-8 stainless steel, precipitates formed during ageing at temperatures lower than 500°C for 4 hours could not be resolved using TEM. In the steel overaged at 575°C, the precipitates are spherical and uniformly distributed in the matrix. A selected area diffraction pattern (SADP) analysis reveals the existence of the intermetallic compound NiAl. In Fe–19Cr–Ni–Al systems, the NiAl precipitates are homogeneously nucleated and coherent with the matrix after 400 minutes at 650°C. Precipitation information obtained in seriously overaged conditions does not represent what happens in the commercially treated materials, where the ageing treatment is usually 1 or 4 hours at temperatures below 600°C. In a PH13-8 stainless steel cast grade, the precipitate type is found to be NiAl, through SADP analysis, and spherical (H1150M treatment, i.e. 760°C for 2 hours followed by 4 hours at 621°C). It is very difficult to image the precipitates using TEM even after ageing at 510°C for 4 hours. The size only reaches 40–50 nm after the H1150M treatment. The age hardening kinetics of the cast grade differs from its wrought counterpart significantly. When not carried out on overaged materials, the precipitates are not large enough to allow TEM examination and SADP identification. How and when the precipitates start to form during ageing of the PH13-8 alloy and how they evolve in terms of size, composition and even type remains unclear. Atom probe field-ion microscopy (APFIM) has proved to be very powerful in the investigation of small precipitates when other microscopy techniques are unsatisfactory. Its unique capability of measuring composition variations at the nanometre scale, together with equal detection efficiency for all elements, make it particularly suitable for investigation of early stages of precipitation. The early atom probe analysis was essentially one-dimensional in nature. Later developments allow a three-dimensional reconstruction of the distribution of different atoms in the analysed volume. In a Fe–20Cr–2Ni–2Al (at%) alloy, the composition of the B2 intermetallic precipitate phase is close to the stoichiometric composition NiAl with only a limited amount of dissolved iron, which decreases with ageing time. Ageing treatments at 550°C for 6, 17 and 117 hours are used. In a Fe–Ni–Al–Mo system, molybdenum partitioned preferentially to the a matrix, and NiAl b¢ precipitates also contained approximately 11% iron. PH13-8 steel contains chromium. Most of the chromium-containing alloys contain a higher amount of chromium than PH13-8. Alloys Fe–30.1Cr–9.9Co, Fe–20.2Cr–8.8Al–0.55Ti and Fe–26Cr–(0, 3, 5, or 8)Ni (all in at%) all show

12

Maraging steels

spinodal decomposition of chromium during the ageing process (Danoix and Auger, 2000). Stainless steel PH17-4 (0.3C–17.5Cr–4Ni–3Cu–lSi in at%) is strengthened by e-Cu particles produced during ageing. The phase separation occurs through a spinodal mechanism while ageing at 400°C. Tempering this alloy at 580°C for 4 hours does not lead to any chromium separation in the martensite phase, which is the condition before this alloy enters service. Another maraging stainless grade 1RK91 (13Cr–9Ni–2Mo–2Cu in wt%) is a low-chromium type. No a to a¢ transformation, that is the spinodal decomposition of chromium occurs in this alloy at 475°C even after 1000 hours. The good mechanical properties are attributed to the heterogeneous precipitation of nickel-rich aluminium–titanium precipitates, possibly Ni3(Ti,Al) type, on the copper particles formed in the very early stages of ageing. Enrichment of molybdenum at the precipitate/matrix interface impedes the coarsening of particles during ageing. In a ferritic–martensitic steel (with 11 at% chromium), after ageing at 400°C for 17 000 hours, long range fluctuations with a composition difference of 2.9 at% are present. There is a lack of information about a few aspects about PH13-8 steel during ageing, such as when and how the precipitates start to form during ageing, how they evolve in terms of type, composition, shape, size and fraction, and what kind of precipitates contributes to the strengthening effects. It will also be useful to determine whether chromium decomposes spinodally in a steel with such a low chromium level. If so, how fast does this take place? What will be the influence on the evolution of other precipitates and strengthening kinetics? Does molybdenum segregate to the precipitate/matrix interface, as in the 1RK91 steel? Answers to the above questions (Chapter 8) will help in understanding the strengthening mechanisms during ageing and make possible a computer model of the age hardening kinetics based on existing precipitate hardening theories.

1.6.2 Small-angle neutron scattering analysis of precipitation behaviour Characterisation of the precipitates is difficult, primarily because of their fine size which is usually on the nanometre scale. A variety of techniques has been employed to study the type, composition, size and volume fraction of the precipitates formed in maraging steels. These include direct methods, such as transmission electron microscopy and atom probe field-ion microscopy, and indirect methods like small angle X-ray scattering (Tewari et al., 2000), small angle neutron scattering and Mössbauer spectroscopy. Staron et al. (2003) studied precipitation behaviour in a chromium-containing maraging steel using energy filtering transmission electron microscopy (EFTEM) and small angle neutron scattering (SANS). Their analyses of the experimental results led to the conclusion that the precipitates formed are solely intermetallic G-phase

Introduction to maraging steels

13

Ti6Si7Ni16, with no Ni3Ti type. This is in contradiction to studies using atom probe field-ion microscopy which show the existence of both Ni­3Ti and the Ti6Si7Ni16 G-phase. Formation of reverted austenite is also observed when the alloy is overaged. The second part of Chapter 8 explores what may be responsible for the above discrepancies. Advantages and disadvantages of SANS and APFIM are briefly discussed.

1.6.3 Improving toughness through intercritical annealing For PH13-8, the commercial treatment that provides the best strength level is the H950 treatment, that is ageing at 510°C for 4 hours. However, the toughness property, reflected by the Charpy impact strength is relatively low. When better toughness is required, the alloy has to be treated differently where toughness is improved at the cost of strength. The third part of Chapter 8 explains attempts to improve the toughness without significant reduction in the strength, to maximise the potential of this alloy. Grain refinement is the most effective way to improve material strength and toughness simultaneously. The well-known Hall–Petch relationship, which predicts an increase in yield strength and a decrease in the ductile–brittle transition temperature (DBTT) with a decrease in grain size, is applicable to a wide variety of metals. The principle of the beneficial effect of small grain size on impact toughness is valid for all metallic materials, but it is especially important for steels that have a tendency for poor toughness at low temperatures. While thermomechanical processing can achieve very fine grain sizes, purely thermal treatments are also of considerable interest since these can be applied to thick plates and weldments. There has been extensive research on the topic of grain refinement through thermal treatments (Luo et al., 2000). A common practice is thermal cycling, which was developed and first applied to Fe–12Ni–0.25Ti, Fe–8Ni–2Mn–0.25Ti and 9Ni steels. Similar treatments were carried out on Fe–8Mn, resulting in considerable grain refinement and improvement in toughness. Attempts were also made to improve the mechanical properties of maraging steels such as 350-grade and 300-grade through thermal cycling. However, the toughness properties were improved owing to the combined contribution of the retained or reverted austenite and grain refinement, usually at the expense of strength properties. In a 250-grade maraging steel, the prior austenite grain was refined to about 6 µm after thermal cycling with no formation of reverted austenite (Luo et al., 2000). Both strength and ductility properties of the alloy in both the unaged and aged condition were effectively improved. The beneficial effect on strength provided by grain refinement was amplified by ageing treatment. In 18Ni grade-250 and grade-300 maraging steels, thermal cycling could refine the prior austenite grain size. This grain refinement increased the strength of the alloy at room temperature and a significant increase

14

Maraging steels

in ultimate tensile strength was observed at elevated temperatures. Guo et al. (2000) reported that introducing an intercritical annealing step before the solution treatment of AerMet 100 (Fe–13.4Co–11.1Ni–3.1Cr–1.2Mo–0.23C in wt%), a high strength lath martensitic steel, may result in a fine effective grain size. For maraging steels, that is martensitic precipitation hardening steels (Luo et al., 2000), attempts at grain refinement were made through rapid austenitisation procedures, whereas studies on other alloys employed intercritical annealing in their thermal treatments (Guo et al., 2000). In the latter cases, even when tempering treatments were included, the purpose was to introduce thermally stable austenite but not to achieve precipitation hardening. The grain size was retained through the tempering step. It is not yet clear how the introduction of intercritical annealing will affect the precipitation kinetics and mechanical properties of precipitation hardening steels. The aim of the third part of Chapter 9 is to refine the grain size of PH13-8 stainless steel through the introduction of intercritical annealing treatment. The influence of thermal treatment on grain size, mechanical properties of the alloy before and after ageing, and precipitation kinetics is examined. The relationships between heat treatment, microstructure and mechanical properties are also discussed.

1.7

Modelling correlations using an artificial neural network

Maraging steels belong to the category of PH steels. They share many features with low carbon PH (stainless) steels. In the context of this section, the term ‘maraging steels’ covers both maraging steels and the group of low carbon PH (stainless) steels. Understanding the correlations between alloy composition, processing parameters, microstructures and the final properties of maraging steels is of great importance since they govern alloy design and production. Moreover, the fact that a single grade of maraging steel cannot easily be heat treated to produce widely different strength levels necessitates different grades of steels, each tailored to a specific strength level. This makes understanding such correlations even more desirable. Essentially, there are two ways to understand such correlations. First, one can adopt a model that describes the physical relationships between the parameters and verify this model using experiments. However, an explicit physical model that quantitatively describes all the relationships between alloy composition, processing parameters and the final properties of maraging steels does not exist. Alternatively, a model can be created by applying statistical techniques to the existing product data. Early attempts usually employed multi-linear regression (MLR) methods. However, in maraging steels, rather strong interactions can occur with specific combinations of

Introduction to maraging steels

15

elements, such as cobalt and molybdenum. These effects are not simply the sum of the influences of each single element. Applying this consideration, artificial neural network (ANN) modelling is a powerful alternative. It is essentially an advanced method of statistical analysis. Since little prior knowledge of the physical background of the processes is required, this method can dramatically benefit the industry, as industrial metallurgists often have to solve their problems without full comprehension of the scientific background involved. This modelling technique has found a variety of applications in the field of materials science (Sha and Malinov, 2009). Chapter 9 will show an ANN for the prediction of the mechanical properties of maraging steels as functions of alloy composition, processing parameters and working temperature. Martensitic transformation start temperature (Ms) as a function of alloy chemistry is also examined because it has to be closely controlled for maraging steels. This model will benefit the development of future alloys by optimising composition design and processing.

1.8

References

Baldan A (2002), ‘Progress in Ostwald ripening theories and their applications to nickelbase superalloys Part I: Ostwald ripening theories’, J Mater Sci, 37, 2171–202. Danoix F and Auger P (2000), ‘Atom probe studies of the Fe-Cr system and stainless steels aged at intermediate temperature: a review’, Mater Charact, 44, 177–201. Farooque M, Ayub H, ul Haq A and Khan A Q (1998), ‘Effect of repeated thermal cycling on the formation of retained austenite in 18% Ni 350 grade maraging steel’, Mater Trans JIM, 39, 995–9. Glicksman M E, Wang K G and Marsh S P (2001), ‘Diffusional interactions among crystallites’, J Cryst Growth, 230, 318–27. Guo Z, Sato K, Lee T K and Morris J W (2000), ‘Ultrafine grain size through thermal treatment of lath martensitic steels’, in Ultrafine Grained Materials, Mishra R S, Semiatin S L, Suryanarayana C, Thadhanis N N, Lowe T C (eds), TMS, Warrendale, 51–62. He Y and Yang K (2002), ‘Pilot study of the mechanical properties for 2400 MPa grade cobalt-free maraging steel’, J Mater Eng (China), 325–9. He Y, Yang K, Qu W, Kong F and Su G (2002a), ‘Strengthening and toughening of a 2800—MPa grade maraging steel’, Mater Lett, 56, 763–9. He Y, Su G, Qu W, Kong F, He L and Yang K (2002b), ‘Grain size and its effect on tensile property of ultra-purified 18Ni maraging steel’, Acta Metall Sin, 38, 53–7. He Y, Yang K, Kong F, Qu W and Su G (2002c), ‘Mechanical properties of ultra-highstrength 18Ni cobalt-free maraging steel’, Acta Metall Sin, 38, 278–82. He Y, Yang K, Qu W S, Kong Y and Su G Y (2003a), ‘Effects of solution treatment temperature on grain growth and mechanical properties of high strength 18% Ni cobalt free maraging steel’, Mater Sci Technol, 19, 177–124. He Y, Liu K and Yang K (2003b), ‘Effect of solution temperature on fracture toughness and microstructure of ultra-purified 18Ni(350) maraging steel’, Acta Metall Sin, 39, 381–6.

16

Maraging steels

Li X and Yin Z (1995), ‘Reverted austenite during aging in 18Ni(350) maraging steel’, Mater Lett, 24, 239–42. Luo H, Yin Z, Zhu J, Li M, Li H, Guo H, Fang H, Lai Z and Liu Y (2000), ‘Influence of grain size on mechanical properties of 18Ni maraging steel’, Mater Sci Technol (China), 8(1), 59–62. Sha W and Malinov S (2009), Titanium alloys: Modelling of microstructure, properties and applications, Woodhead Publishing, Cambridge. Sinha P P, Sivakumar D, Babu N S, Tharian K T and Natarajan A (1995), ‘Austenite reversion in 18 Ni Co-free maraging steel’, Steel Res, 66, 490–4. Staron P, Jamnig B, Leitner H, Ebner R and Clemens H (2003), ‘Small-angle neutron scattering analysis of the precipitation behaviour in a maraging steel’, J Appl Cryst, 36, 415–19. Tewari R, Mazumder S, Batra I S, Dey G K and Banerjee S (2000), ‘Precipitation in 18 wt% Ni maraging steel of grade 350’, Acta Mater, 48, 1187–200. Viswanathan U K, Dey G K and Asundi M K (1993), ‘Precipitation hardening in 350 grade maraging steel’, Metall Trans A, 24A, 2429–42. Wang K G, Glicksman M E and Rajan K (2004), ‘Modeling and simulation for phase coarsening: A comparison with experiment’, Phys Rev E, 69, 061507. Wang K G, Glicksman M E and Rajan K (2005), ‘Length scales in phase coarsening: Theory, simulation, and experiment’, Comput Mater Sci, 34, 235–53. Wilson E A (1997), ‘Quantification of age hardening in an Fe-12Ni-6Mn alloy’, Scripta Mater, 36, 1179–85. Wilson E A (1998), ‘Quantification of early stages of age hardening in Fe-12Ni-6Mn maraging type alloy’, Mater Sci Technol, 14, 277–82.

2

Microstructure of maraging steels Abstract: This chapter describes microstructures in some relatively new maraging steels. A great deal of precipitates with diameters of a few nanometres are formed in the early ageing stage. Ni3Ti precipitates grow into needle or rod shapes and become the main precipitation as the ageing time is prolonged. Under higher temperature ageing, the size of precipitates is seriously non-uniform during the early stages and a small amount of interlath reverted austenite is formed. Thereafter, precipitates coarsen sharply. Intra-lath reverted austenite appears subsequently. In later stages of ageing, the coarsened Ni3Ti precipitates dissolve into strip-like intra-lath reverted austenite which is disorderly embedded in the matrix. Key words: heat treatment, Ni3Ti, transmission electron microscopy (TEM), dark field, selected area electron diffraction.

2.1

2000 MPa grade cobalt-free maraging steel

2.1.1 Ageing at low temperature (440°C) After ageing for 3 hours, the martensite diffraction spots (Fig. 2.1a) of the 2000 MPa grade cobalt-free maraging steel (Table 2.1) are not sharp spherical ones like those observed before ageing. Streaking and distortion are visible. Although the diffraction from precipitates is weak, fine and extremely densely distributed Ni3Ti precipitates are visible in the dark field (DF) image (Fig. 2.1b), along certain crystallographic orientations of the matrix. The average diameter is about 2 nm. There is another type of spherical precipitate (Figs. 2.1c and 2.1d). Its diffraction pattern cannot be identified as Ni3Mo, Ni3Ti, Fe7Mo6 or Fe2Mo phases, the usual precipitation phases in maraging steels (a detailed discussion is given in section 2.1.2). There are some other compounds in the Ni–Mo system, reported by Arya et al. (2001), but their diffraction patterns have not been well established and not been observed in past studies of maraging steels. The average diameter of these spherical precipitates is 3–4 nm, with extremely dense distribution in the martensite matrix. After ageing for 6 hours, Ni3Ti remains distributed in the matrix as an extremely dense dispersion (Fig. 2.2a). Its diameter remains almost the same as it was after ageing for 3 hours, but the average length has grown to about 5 nm. The precipitates are aligned along their longitudinal direction in a uniform and almost ordered fashion. The spherical, crystallographically unidentified precipitates have the same morphology and similar distribution as after ageing for 3 hours, with an average diameter of 4–5 nm (Fig. 2.2b). As ageing proceeds to 12 hours, the Ni3Ti has grown into an obvious 17

18

Maraging steels

100 nm (a)

(b)

100 nm (c)

(d)

2.1 TEM images and selected area diffraction (SAD) patterns of the 2000 MPa cobalt-free maraging steel aged at 440°C for 3 hours. (a) [113]M SAD pattern; (b) DF image taken using the (0111)Ni3Ti diffraction spot indicated by an arrow in (a) showing precipitates; (c) [110]M SAD pattern; (d) DF image of spheroidal precipitates taken using the spot circled in (c).

Table 2.1 Chemical compositions of some recently developed maraging steels (wt%) Ni

Mo

Co

Al

1800 MPa (T250)

18.5

3

2000 MPa (He et al., 2002a; 2003)

18.9

4.1

1.26

–

–

–

–

–

–

1.9

0.22

0.047

0.0037

0.002

0.0007

0.02

2400 MPa low Mo

19.1

4.4

2400 MPa high Mo

18.8

2.63

–

–

0.0012

0.0012 0.0016

≤0.01

0.01

0.0029 0.001

5.39 2.59

–

–

0.0038

0.0006 0.0023

≤0.01

0.01

2800 MPa

17.9

6.69 1.1

0.0018 0.001

14.8

–

–

–

–

–

–

–

–

18Ni (300)

18

4.8

18Ni (350)

18.8

4.22 1

13Ni (400) (He et al., 2002b)

13

10.8

Ti

0.6 0.2

C

S

P

Si

Mn

O

N

–

–

–

0.01

0.0036 0.0016

9.0

–

–

–

–

–

–

–

–

10.8

–

–

–

–

–

–

–

–

15.5

–

–

–

–

–

–

–

–

Microstructure of maraging steels

Steel

19

20

Maraging steels

100 nm (a)

100 nm (b)

2.2 TEM DF images of the 2000 MPa cobalt-free maraging steel aged at 440°C for 6 hours. (a) Taken from the (1120)Ni3Ti spot; (b) spheroidal precipitates.

rod or needle shape, with approximately an average diameter of 3 nm and average length of 15 nm (Fig. 2.3a). The precipitates are uniformly dispersed and aligned. Number density seems to decrease compared with Fig. 2.2a. The spherical precipitates in Fig. 2.3b are similar to those in Fig. 2.2b (after ageing for 6 hours), in terms of morphology, distribution, amount and size. After a further increase in the ageing time, to, for example, 30 hours, use of transmission electron microscopy (TEM) observation has shown that the Ni3Ti precipitates have grown or coarsened to larger rods or needles, with an average diameter of 5 nm and length of 15 nm. The amount of the spherical, crystallographically unidentified precipitates has reduced. After ageing for 50 hours, the average diameter of Ni3Ti is about 5 nm, length about 25 nm (Fig. 2.4a). The unidentified precipitation phase, referred to as spherical or spheroidal precipitates above, has significantly reduced with slightly increased sizes (average diameter about 7 nm, Fig. 2.4b). Comparing the diffraction patterns with a same martensite zone [011] M at 3 hours (Fig. 2.1c) and 50 hours (Fig. 2.4c), the diffraction spots from Ni 3Ti in the latter case have become clearer. In contrast, the amount of the spherical unidentified precipitate, which is the one of major strengthening phase in the early stages of ageing, gradually reduces with increasing ageing time. There is no reverted austenite formed at this ageing temperature. The amount of austenite judging from X-ray diffraction fluctuates between

Microstructure of maraging steels

100 nm

100 nm (a)

21

(b)

2.3 TEM DF images of the 2000 MPa cobalt-free maraging steel aged at 440°C for 12 hours. (a) Taken from the (1120)Ni3Ti spot; (b) spheroidal precipitates

0% and 2%, which is not statistically significant as it is around the lower detection limit of the X-ray technique for this phase. An extremely high number density, of the order of 10 23 m–3, of Ni3Ti precipitates form at the beginning of low temperature ageing, in addition to the spherical unknown precipitates. With increasing ageing time, the Ni 3Ti precipitates evolve from spherical to rod or needle shape and continue to grow. The high number density of precipitates implies an extremely high nucleation rate and a large number of nucleation sites. This requires a very short diffusion distance of the alloying elements and extremely small precipitates are formed as a result. The mismatch along the close packed directions between <1120> of Ni3Ti and <111> of martensite is 2.22%, the smallest of all possible matching directions. Therefore, to minimise mismatch, fine precipitates grow along the <111>M direction. There is full or near full coherency of the precipitate nuclei with the matrix. The coherent strain energy is the dominant energy term, as against the interfacial energy. At the same time, nickel, titanium and other alloying elements have a large degree of supersaturation and a large concentration gradient in the matrix, short diffusion distance and fast diffusion. These factors, collectively, determine the rod shape of the Ni3Ti precipitates after some growth. According to the lattice mismatch between the close packed directions of Ni3Ti and martensite matrix, the length of the precipitates along the <111>M direction when the coherency is lost or

22

Maraging steels

100 nm

100 nm (a)

(b)

(c)

2.4 TEM DF images and SAD pattern of the 2000 MPa cobalt-free maraging steel aged at 440°C for 50 hours. (a) DF image of Ni3Ti precipitates taken from the (1 120)Ni3Ti spot and its associated secondary diffraction in (c), showing vividly the almost periodical distribution of the precipitates with alignment along habit planes {0111} and {1100}; (b) DF image of spheroidal precipitates taken from the diffraction spot labelled 2 in (c); (c) [110]M SAD pattern, where the downward arrows point to the spots attributed to the unknown phase.

semi-coherency is necessary is estimated to be 10.5 nm. Therefore, full coherency should be maintained up to ageing for 12 hours; after that, a semi-coherent relationship will be required. The large amount of Ni 3Ti and unknown spherical precipitates after only 3 hours is in disagreement with spinodal decomposition theory in 18Ni(350) maraging steel after 4 hours at 430°C with no precipitation. In addition, the present steel shows a difference from the T-250 cobalt-free steel, with no precipitation of austenite before the intermetallic phases. Obviously, in the early stages of the low temperature ageing, the large quantity of nanometre scale precipitates is the reason for the rapid increase of hardness and strength (Chapter 6).

Microstructure of maraging steels

23

2.1.2 Ageing at intermediate temperature (480°C) For a cobalt-free maraging steel aged for 3 hours, needle-shape precipitates are visible in the martensite matrix which itself has a high dislocation density (Fig. 2.5a). The average diameter and length of the precipitates, which are dispersed in the martensite laths, are about 5 and 15 nm, respectively (Fig. 2.5b). In addition, similar to ageing at 440°C (Section 2.1.1), there is an extremely fine dispersion of spherical precipitates in the lath martensite, with an average diameter of about 7 nm (Fig. 2.5c). The diffraction patterns from these spherical precipitates could not originate from any common types of precipitates in maraging steels, as discussed in section 2.1.1. The clear and bright diffraction spots (for example the spot labelled 2) from this type of precipitate, shown in Fig. 2.5d, enable an accurate determination to be made of two of its interplanar distances, at 2.44 and 1.394 Å. These eliminate the possibility of the formation of common types of precipitates in maraging steels, Ni3Mo, Ni3Ti, Fe2Mo, Fe2Ti as well as the surface oxidation products Fe3O4, Fe2O3, and so on. The interplanar spacing is listed in Table 2.2 and compared to make this clearer. Therefore, it may be regarded as a new, unknown type of precipitate. The spherical precipitates and the Ni 3Ti rod or needle shape precipitates are found in about the same numbers in this cobalt-free maraging steel in the early stages of ageing. After ageing for 12 hours, the peak hardness is reached (Chapter 6). The spot labelled 1 in Fig. 2.6a, belonging to the Ni3Ti family shown using open square symbols in Fig. 2.6b, is the (2240)Ni3Ti diffraction spot, in the line connecting the incident beam spot and the matrix spot (222)M. The orientation relationship between the h-Ni3Ti precipitates and the martensite matrix is:

(011)M//(0001)h−Ni3Ti



[111]M//[1120]h−Ni3Ti

The spot labelled 2 in Fig. 2.6a, belonging to the Ni3Ti family shown using circle symbols in Fig. 2.6b, is from Ni3Ti in relation to an equivalent martensitic orientation. The spot is again (2240)Ni3Ti, this time along the line connecting the transmission spot and the (2 22)M spot. The orientation relationship between this set of Ni3Ti precipitates and the martensite matrix is:

(011)M//(0001)h−Ni3Ti



[1 11]M//[1120]h−Ni3Ti

The rod-like Ni3Ti precipitates have very dense distribution in the martensite matrix and the two sets are both evenly distributed along their respective orientations (Figs. 2.6c and 2.6d). The average diameter and length are about 10 and 35 nm, respectively. In the schematic diffraction pattern shown in

24

Maraging steels

100 nm (a)

100 nm (b)

100 nm (c)

(d)

2.5 TEM images and SAD pattern of the 2000 MPa cobalt-free maraging steel aged at 480°C for 3 hours. (a) Bright field image showing precipitation and high density dislocations in the martensite matrix; (b) dark field image taken from the (0111)Ni3Ti spot labelled 1 in (d); (c) dark field image of spheroidal precipitates taken from the spot labelled 2 in (d); (d) [011]M zone SAD pattern, i.e., with the incident electron beam along this direction in the martensite lattice, including a complete and clear set of diffraction patterns from the spherical precipitate, exhibiting typical hexagonal arrangement with six-fold symmetry.

Microstructure of maraging steels

25

Table 2.2 Interplanar spacing of precipitates and oxides (in Å) and intensity (%) Ni3Mo

Ni3Ti

Fe2Mo

Fe2Ti

Fe3O4

4.84/30 2.96/60 2.36/60 2.388/30 2.53/100 2.224/20 2.21/20 2.18/100 2.199/100 2.220/50 2.112/80 2.13/50 2.05/60 2.038/100 2.09/70 2.07/50 1.969/80 1.95/100 2.02/100 1.998/100 1.951/100 1.98/60 1.947/30 1.72/20 1.828/30 1.712/40 1.611/80 1.523/50 1.51/20 1.37/60 1.341/60 1.481/90 1.280/50 1.330/20 1.33/60 1.302/60 1.327/20 1.267/20 1.276/50 1.29/100 1.247/60 1.280/40 1.191/20 1.23/60 1.196/60 1.211/20 1.186/50 1.173/20 1.18/60 1.122/40 1.094/50 1.087/50 1.09/60 1.094/80 1.085/20 1.068/50 1.050/50 1.046/20 1.04/100 1.038/20 1.027/20 0.990/40 0.819/20

Fe2O3 3.68/30 2.69/100 2.52/80 2.21/40

1.843/60 1.697/70 1.604/30 1.488/50 1.457/50 1.313/40 1.261/20 1.192/20 1.166/20 1.143/40 1.106/40 1.058/50

0.99/30

*

The first number in each entry is the interplanar spacing and the second (after the forward slash/) is the intensity. Only the strong diffractions (I/I0≥20%) are selected.

Fig. 2.6b, the small filled circles denote double diffraction spots due to the two orientations of Ni3Ti. The dark field images shown in Figs. 2.6e and 2.6f using diffraction spots labelled 3 and 4 display the same orientation, distribution and size of the rod-like Ni3Ti precipitates as in Figs. 2.6d and 2.6c, respectively. Ni3Ti has a hexagonal crystal structure and thus has 12 equivalent orientation relationships with martensite, or 12 variants. In the [011]M zone diffraction pattern, there is also a complete set of spots from the spherical precipitates, labelled 5 in Fig. 2.6a and using open triangle symbols in Fig. 2.6b. This type of precipitate is evenly distributed in the matrix, slightly coarsened compared with those in the specimen aged for 3 hours, now having an average diameter of about 9 nm (Fig. 2.6g and 2.6h). Comparing the diffractions patterns in Figs. 2.5d and 2.6a, both from the [011]M zone, Ni3Ti spots are stronger after ageing for a longer time. In TEM, the magnetic field of the steel samples deflects the electron beam, in a manner that cannot be controlled, significantly deteriorating the

26

Maraging steels

image quality. In addition, the extremely large thickness of the ‘thin’ foil specimens (even thicker when they are tilted) compared to the size of these ultra fine precipitates makes the precipitates appear to have a much higher number density.

5 1 2

(a)

(b)

100 nm (c)

100 nm (d)

2.6 TEM images and SAD pattern of the 2000 MPa cobalt-free maraging steel aged at 480°C for 12 hours. (a) [011]M SAD pattern, showing full sets of diffraction patterns from Ni3Ti and the unknown spherical precipitates; (b) schematics of (a), the large filled circles denote martensite spots, the open squares (one labelled 1) denote Ni3Ti with (0001)//(011)M and [1120]// [111]M, the open circles (one labelled 2) denote Ni3Ti with (0001)//(011)M and [1120]//[1 11]M, the small filled circles refer to double diffraction spots and the open triangles denote spheroidal precipitates; (c), (d), (e), (f) are dark field images taken from the (1120)Ni3Ti spots labelled 1, 2, 3 and 4 in (a), respectively; (g), (h) are dark field images showing the morphology of spheroidal precipitates taken from the spots labelled 5 and 6 (double diffraction spot of 5) in (a), respectively. (a) and (b) should be examined in conjunction with each other. Not all sets of precipitate patterns are included in the schematic pattern (b) so spot 6 in (a) does not appear in (b).

Microstructure of maraging steels

27

After the long ageing, 50 hours, Ni3Ti precipitates grow, but they do not coarsen or dissolve into the matrix. The average diameter and length are now about 17 and 40 nm, respectively, but their distribution remains almost the same as under peak hardness ageing condition (Fig. 2.7a). The spherical precipitates are still present. Their average diameter is larger, about 13 nm (Fig. 2.7b). For ageing up to 20 hours, there is no austenite reversion. The austenite peaks in X-ray diffraction are not statistically significant. After 50 hours ageing at this temperature, the amount of austenite becomes significant, at 9%. Reverted austenite is also clearly visible between martensite laths (Figs. 2.8a and 2.8b). There is no precipitation within the austenite phase. The orientation relationship between austenite and martensite is of N–W type, that is, (111)A//(110)M, [110]A//[100]M (Fig. 2.8c). Although the precipitation behaviour and hardening mechanisms in maraging steels have been widely studied, there are differing opinions about the nature of precipitation phases. For example, in the 18Ni series steels, there have been reports of many different types of precipitation phases including g-Ni3Mo, h-Ni3Ti (Tewari et al., 2000), Laves-Fe2Mo, s-FeMo, m-Fe7Mo6,

100 nm (e)

100 nm (f)

100 nm (g)

2.6 (Continued)

100 nm (h)

28

Maraging steels

100 nm (a)

100 nm (b)

2.7 TEM DF images and SAD patterns of the 2000 MPa cobalt-free maraging steel aged at 480°C for 50 hours. (a) Ni3Ti precipitates taken from the (1120) spot in [011]M SAD pattern; (b) spheroidal precipitates.

FeTi, Fe2Ti, w (Tewari et al., 2000), dispersion austenite. Although research has concentrated less on cobalt-free grades, there are already, sometimes conflicting, reports on dispersion austenite, Ni3Ti, Fe7Mo6, and Fe2Mo, FeMo or FexTi multi-phase large particles. Many possible precipitation phases have similar structures and interplanar distances, which are further complicated by double diffraction and overlapping of diffraction from multiple phases. In addition, variations in alloy composition, ageing temperature and time also affect the type and morphology of precipitation phases. Nanometre-sized ultra fine precipitates are difficult to analyse for many if not all available techniques. We have revealed the precipitation of highly dispersed needle or rod shape Ni3Ti at both low (Section 2.1.1) and medium (this section) temperatures in

Microstructure of maraging steels

100 nm (a)

100 nm (b)

(c)

2.8 Reverted austenite TEM images and SAD pattern in the 2000 MPa cobalt-free maraging steel aged at 480°C for 50 hours. (a) Bright field image of the inter-lath reverted austenite; (b) dark field image of the inter-lath reverted austenite; (c) [001]M and [011]A SAD, where the subscripts M and A refer to martensite and austenite, respectively.

29

30

Maraging steels

cobalt-free maraging steel, with strong resistance to coarsening. Ni3Ti has hexagonal structure, with lattice constants a = 0.5101 nm and c = 0.8307 nm. Computer simulation of diffraction patterns of precipitates combined with composition analysis eliminated the possibility of Ni3Mo in a T250 cobaltfree maraging steel. Atom probe field-ion microscopy was used to study the composition of the rod or needle shape precipitates in a T300 steel (Fe–18.5Ni–4Mo–1.85Ti, wt%). The results confirm that the precipitate is Ni3Ti rather than Ni3Mo, but with the replacement of a fraction of nickel and titanium in the precipitate by iron and aluminium, respectively. Of course, the composition differences between different maraging steels will affect the precipitation phases. Therefore, accurate identification and repeated confirmation are always necessary. TEM experiments have also revealed the extremely fine spherical precipitates in the cobalt-free maraging steel after low and medium temperature ageing. This type of precipitate, although yet unidentified in terms of crystal structure, also has strong resistance to coarsening. Based on the lattice constants of possible precipitation phases of hexagonal, cubic and orthorhombic systems, the interplanar distances and indexing from diffraction patterns from this precipitate, no match with any type of precipitate mentioned above could be made. In addition, attempts at matching other compounds Fe3Mo, Ni4Mo, Fe2Mo3, Fe0.54Mo0.73, NiTi, Ni3Fe, as well as possible surface oxidation products Fe2O3, Fe3O4, FeO have all failed. Therefore, it is likely that this spherical precipitate is a new, unknown type of phase or a complex of multiple intermetallic compounds. Further investigation is necessary. When the radius of the precipitates is smaller than 15b, b being the Burger’s vector, dislocations shear through precipitates. Otherwise, a looping mechanism operates. The critical radius (15b) in the current system would be about 3.8 nm. After ageing for 12 hours, the Ni 3Ti precipitates have an average diameter of 10 nm and a length of 35 nm, much larger than this critical size. Therefore, the hardening mechanism may be interpreted using the Ashby–Orowan relationship: Ê1 + 1/(1 – n )ˆ Ê l – dˆ Gb [2.1] ˜¯ ln ÁË 2b ˜¯ 2π (l – d ) ÁË 2 where s0.2 is the yield strength of the maraging steel in aged condition, s0 is the yield strength in solid solution condition, G is the shear modulus of the lath martensite matrix, b is the Burgers vector, n is Poisson’s ratio, l is particle spacing between precipitates and d is diameter of precipitates. The type of orientation relationship between the precipitates and the matrix in maraging steels keeps the precipitates coherent with the matrix for significant ageing periods, limiting their growth and coarsening to larger, less

s 0.2 = s 0 +

Microstructure of maraging steels

31

effective sizes. This contributes to the ultra-high strength of the material. In maraging steels, a high dislocation density is produced during the phase transformation in the Fe–Ni matrix. The very low impurity inclusion levels (Table 2.1) ensure that dislocations are not strongly pinned in the solid solution condition. Therefore, the matrix has good ductility and can resist a relatively large stress concentration. After ageing, during the dislocation looping through the nano-sized precipitates, dislocation pile-up and the associated stress concentration are not so severe, so the cracking between the precipitates and the matrix is minimised. Although the precipitate dispersion makes the dislocation movement difficult, when the dislocations start to move, their uniform movement in the matrix can be sustained over short distances. Stress concentrations are more easily formed around impurity inclusions such as Ti(C,N,S), leading to void formation, coalescence and enlarging. In addition, the use of molybdenum in this cobalt-free maraging steel minimises precipitation at prior austenite grain boundaries, thereby avoiding cracking along the grain boundaries. This also improves fracture toughness. The combination of these effects is the main reason why this cobalt-free maraging steel can sustain good ductility and toughness at strength levels above 2000 MPa. Ageing at the intermediate temperature can achieve the best combination of strength and toughness, compared to ageing at low and high temperatures (see Chapter 3). After very long-term ageing, a small amount of reverted austenite forms along the martensite lath boundaries. In the overageing condition, slight precipitate coarsening combined with the small amount of reverted austenite causes a limited reduction in strength accompanied by an increase in toughness and ductility.

2.1.3 Ageing at high temperature (540°C) Large quantities of rod-shaped Ni3Ti precipitates form after isothermal ageing for only 15 minutes, with varying sizes ranging from 2–3 nm for the smallest to the largest with a diameter and length of 9 and 60 nm, respectively. In addition, some precipitates have coalesced or joined. The distribution in the matrix is not uniform (Figs. 2.9a and 2.9b). These are in stark contrast to the same type of precipitates in the steel aged at lower temperatures (Sections 2.1.1 and 2.1.2). Fine, spherical precipitates, unidentified and extensively discussed in Sections 2.1.1 and 2.1.2, are also present. The average diameter of these is about 4 nm. Also present is reverted austenite, along the martensite lath boundaries (Fig. 2.9c). There are no precipitates inside the reverted austenite phase. The orientation relationship between reverted austenite and martensite follows the K–S type, viz. (1 11)A//(110)M, [110]A//[111]M (Fig. 2.9d). The orientation relationship between martensite and austenite is clarified by analysing diffraction patterns from the adjacent

32

Maraging steels

grains of martensite and austenite. The fraction of reverted austenite in the steel is 5% under this ageing condition. After ageing for 1 hour, the rod-shaped Ni3Ti precipitates, homogeneously distributed in the matrix, have attained a uniform size, with an average Rod

Spherical

Spheroidal

100 nm (a)

(b)

2.9 Microstructure and SAD patterns of the 2000 MPa cobalt-free maraging steel aged at 540°C for 15 minutes. (a) Dark field image showing Ni3Ti precipitates and spheroidal precipitates taken from the open circle labelled in (b); (b) [110]M SAD pattern, the open circle contains the spot of spheroidal precipitates (set of spots from this phase indicated by downward small arrows) and the spot of (2240)Ni3Ti; (c) bright field image showing the inter-lath reverted austenite circled by the arrow heads pointing to the contour of its interface with martensite; (d) [111]M and [011]A SAD pattern. The three circled diffraction spots could not be indexed.

Microstructure of maraging steels

33

200 nm (c)

(d)

2.9 (Continued)

diameter of 9 nm and length of 38 nm (Fig. 2.10a). The spherical precipitates have disappeared (Fig. 2.10c). The reverted austenite is not only along the martensite lath boundaries, but also inside the laths, appearing as islands in the photograph in Fig. 2.10b. The orientation relationship between the intra-lath reverted austenite and the lath martensite is of N–W type (Figs. 2.10c and 2.10d). There is a small deviation in the exact directions of 1 11A and 110M, causing the martensite adjacent to the austenite to be out of the diffraction condition in Fig. 10b, but this should be allowed for within an N–W relationship. The amount of reverted austenite is now 7%. With increasing ageing time, Ni3Ti precipitates continue to grow. At 3 hours, the average diameter and length of the precipitates are 12 and 50 nm,

34

Maraging steels

100 nm

400 nm

(a)

(b) 110M 110AA 111

1

2 110M 110AA 111

(c)

000

(d)

2.10 Typical microstructures of the 2000 MPa cobalt-free maraging steel aged at 540°C for 1 hour. (a) Dark field image showing Ni3Ti precipitates taken from (202 2)Ni3Ti labelled 1 in (c); (b) Dark field image showing the inter-lath and intra-lath reverted austenite taken from (111)A labelled 2 in (c). The diffraction spots of reverted austenite and precipitates always overlap, so in the dark field, the precipitates and reverted austenite are shown simultaneously; (c) [001]M and [011]A SAD pattern. There are no spots from the spherical precipitate phase; (d) key to (c).

respectively (Fig. 2.11a). The amount of austenite continues to increase (Fig. 2.11b), now reaching 8%. After ageing for 12 hours, further growth of Ni3Ti precipitates is observed, up to an average diameter and length of 18 and 70 nm, respectively (Fig. 2.12). There is an increase of the amount of austenite, both on the lath boundaries and inside the laths. At 50 hours ageing, there is continued coarsening of the precipitates, with an average diameter and length 20 and 85 nm, respectively (Fig. 2.13). Further austenite reversion took place and a great deal of the precipitate in the martensite laths gradually dissolves to form island-like austenite. Such austenite islands eventually join, forming larger ribbon-like austenite (Fig. 2.13b). The K–S relation is identified using electron diffraction (Fig. 2.13c), consistent with the austenite in early stages of ageing. X-ray diffraction shows 25% austenite in the steel.

Microstructure of maraging steels

100 nm (a)

35

300 nm (b)

2.11 Typical microstructure of the 2000 MPa cobalt-free maraging steel aged at 540°C for 3 hours. (a) Dark field image showing Ni3Ti precipitates; (b) dark field image showing the inter-lath and intra-lath reverted austenite.

Thus, there is a gradual increase in the quantity of reverted austenite upon ageing (Fig. 2.14). The reverted austenite first forms at grain or martensite lath boundaries through a shear transformation, followed by its precipitation inside the laths. Finally, the dissolution of precipitates causes diffusional transformation, resulting in austenite inside the laths through coalescence and joining processes. Austenite precipitates in the martensite matrix by diffusional transformation. As a result, Ni3Ti may dissolve in austenite. Cobalt-free maraging steel has an extremely high hardening rate under high temperature ageing, with large amounts of Ni3Ti and spherical unknown precipitates forming after just 15 minutes ageing (Fig. 2.9a). The precipitates have a strong tendency towards coarsening. After 1 hour ageing, the size of the Ni3Ti precipitates has already reached or exceeded the maximum sizes at low (Section 2.1.1) and intermediate (Section 2.1.2) temperature ageing. After 50 hours ageing, there is serious coarsening of the precipitates, reaching an average size of 20 nm in diameter and 85 nm in length. Therefore, the coarsening rate of the Ni3Ti precipitates at the high ageing temperature is much higher than the coarsening rates at low and medium temperatures. The Ni3Ti precipitates usually have extremely strong resistance to coarsening. However, this depends heavily on the ageing temperature; decreasing ageing temperature is very effective in controlling the coarsening of the precipitates. Nucleation of the m-Fe7Mo6 phase was observed in the molybdenum-rich region and at the interface between Ni3Ti and matrix at the later stages of ageing, in a T300 steel. No spherical precipitates are seen after long-term ageing at high ageing temperature in the cobalt-free maraging steel. The spherical unknown precipitates are seen persistently after ageing at low and intermediate temperatures, but they disappear after initial ageing at high temperature. This phenomenon deserves further investigation. A small amount of reverted austenite forms along the martensite lath

36

Maraging steels

300 nm (a)

100 nm (b)

2.12 Typical microstructure of the 2000 MPa cobalt-free maraging steel aged at 540°C for 12 hours. (a) Dark field image showing Ni3Ti precipitates, inter-lath and intra-lath reverted austenite; (b) bright field image.

boundaries after just 15 minutes ageing (Fig. 2.9c). At this time, the precipitate phases are relatively small. Even with some limited coarsening, they do not dissolve and transform into reverted austenite. The inter-lath reverted austenite is probably due to the local segregation of nickel on the martensite lath boundaries. This segregation causes a local decrease in the austenite start temperature, As, resulting in the formation of austenite through K–S shear. With increasing ageing time, reverted austenite starts to form inside the martensite lath, following the N–W orientation relationship with the martensite parent phase. There are no precipitates inside the reverted austenite (Figs. 2.10b and 2.11b). The reverted austenite inside the martensite lath and at lath boundaries formed in the early stages of ageing has essentially a same character. When aged at high temperature, nickel gradually segregates to the martensite lath boundaries as well as to localised areas inside the laths, for example at dislocations and stacking faults. Lattice reconfiguration in these regions leads to the formation of austenite. In the intermediate and late stages of ageing (after 3 hours) at high temperature, some precipitates coarsen significantly locally inside the martensite laths, forming nickel-rich regions, leading to the transformation to island-like isolated reverted austenite. After long-term ageing for 50 hours, a large quantity of precipitates dissolves, resulting in more nickel-enriched regions. The reverted austenite islands coarsen, merge and form ribbon morphology, with the K–S orientation relationship with the martensite. This indicates that the formation of ribbon-like reverted austenite at the later stages of ageing may be a result of the simultaneous action of two mechanisms, namely element diffusion and shear. Comparing the behaviour of reverted austenite at different ageing temperatures, lowering the temperature is more effective in controlling the austenite reversion than using the precipitation reaction.

Microstructure of maraging steels

37

100 nm (a)

200 nm (b)

(c)

2.13 Typical microstructure of the 2000 MPa cobalt-free maraging steel aged at 540°C for 50 hours. (a) Dark field image showing Ni3Ti precipitates; (b) bright field image showing precipitate dissolution and the strip intra-lath reverted austenite; (c) [111]M and [011]A SAD pattern.

38

Maraging steels 30

Reverted austenite (%)

25

20

15

10

5

0



0.25

0.5

1

2 4 8 Ageing time (h)

16

32

64

2.14 Variation of reverted austenite content with the ageing time at 540°C in the 2000 MPa cobalt-free maraging steel

Literature papers should be consulted regarding the orientation relations between austenite and ferrite or martensite, (Headley and Brooks, 2002; Mun et al., 2002). A school of opinion regards 540°C and 15 minutes as being enough for the diffusional transformation. A curved boundary between austenite and martensite would indicate that the specified orientation relation is not always necessary for the inverse transformation. In cobalt-free maraging steel, the rapid precipitation of large quantities of Ni3Ti after only 15 minutes ageing is the reason why the strength reaches design level so early (Chapter 3). At this time, the amount of reverted austenite is very low, not enough to affect the mechanical properties. The non-uniform size distribution of the precipitates probably is the reason for the relatively low toughness. As the reverted austenite has little influence on the mechanical properties, the fracture mode of the steel is still transgranular. With increasing ageing time, the precipitates grow and become more homogeneous in size. After 1 hour ageing, the size and distribution are similar to the peak hardness condition at the intermediate ageing temperature of 480°C. However, a large amount of austenite has formed both along the martensite lath boundaries and inside the laths, affecting the mechanical properties significantly. Therefore, the strength does not increase, but instead decreases drastically to around 1800 MPa. With a further increase in ageing time, a greater amount of reverted austenite is formed, together with large scale coarsening of precipitates. In addition, island and ribbon-like reverted austenite forms inside the laths. These cause a dramatic decrease in strength to 1300 MPa. In maraging steel

Microstructure of maraging steels

39

systems, the reverted austenite can have a larger degree of influence on hardness and strength over the coarsening of precipitates. With decreasing strength after high temperature ageing, the yield to tensile strength ratio also continues to decrease, that is, there is a large strain-hardening rate. This confirms the effect of austenite on mechanical properties. Under overaged condition at high temperatures, reverted austenite co-exists with coarse precipitates. Microcracks can form easily at the interface regions between reverted austenite and the brittle matrix. The crack tips can pass the coarse precipitates rapidly. Although the reverted austenite can blunt the crack tips and therefore increase the resistance to crack growth, serious embrittlement in the matrix cancels this effect.

2.1.4 Other microstructural features There is no obvious effect of solution treatment temperature for the range of 800–1200°C on the microstructure and mechanical properties in the solution state. The size and morphology of precipitates and microstructure in strained steel (Fig. 2.15) appear to be the same as those in the unstrained steel.

(a)

(b)

2.15 TEM bright field and dark field images of a thin foil specimen cut from the neck breakpoint of a 2000 MPa steel tensile sample. (a) Bright field; (b) dark field.

40

Maraging steels

The deformation process has not significantly changed microstructure and precipitate distribution, which is reasonable considering the relatively small elongation of maraging steels.

2.1.5 Summary In the early stages of ageing at 440°C, cobalt-free maraging steel has extremely fine precipitates with an average diameter 2–3 nm. Ni3Ti precipitates are identified, but there is another family of spherical precipitates whose crystallography has not been identified. Ni3Ti is the main precipitate, growing and coalescing into its normal needle or rod-shape along the <111>M direction with increasing ageing time. This type of precipitate has strong resistance to coarsening at this ageing temperature. The spherical precipitates exist in a stable manner after low temperature ageing, with strong resistance to coarsening. When aged at 440°C, there is no reverted austenite. The orientation relationship between h-Ni3Ti and martensite matrix is (011)M//(0001)h-Ni3Ti, [111]M//[1120]h-Ni3Ti. At peak hardness after ageing at the intermediate temperature of 480°C, the rod-shaped Ni 3Ti precipitates have an average diameter of 10 nm and length 35 nm and, still have strong resistance to coarsening. The crystallographically unidentified spherical precipitates which exist after ageing at 480°C, have a strong resistance to coarsening. At the later stages of ageing at 480°C, reverted austenite starts to form along the martensite lath boundaries. In the early stages of ageing at the high temperature of 540°C, precipitation of Ni3Ti is inhomogeneous. Rapid and severe coarsening follows this. At the later stages of ageing, some precipitates dissolve and form reverted austenite. The crystallographically unidentified spherical precipitates disappear after overageing at the high temperature. The composition and the formation mechanism of this type of precipitate need further detailed investigation. Overall, Ni3Ti is the major precipitation hardening phase in cobalt-free maraging steel. The morphology, amount and the formation mechanism of reverted austenite are closely related to the ageing temperature and time. During high temperature ageing at 540°C, reverted austenite first forms at grain boundaries or martensite lath boundaries, followed by formation inside the laths. Eventually, precipitate dissolution leads to diffusional transformation to austenite, which then coalesces and joins inside the martensite laths. The amount of austenite increases with prolonged ageing time.

2.2

2400 MPa grade cobalt-free maraging steel

Both low and high Mo steels (Table 2.1) have a lath martensite structure, with no noticeable residual austenite between the laths, after solution treatment at

Microstructure of maraging steels

41

810°C for 1 hour (Fig. 2.16a). These steels essentially complete the austenite to martensite transformation upon cooling to room temperature. The prior austenite has a fine grain size, approximately 15 mm. The hardness is HRC28 and HRC29 for low and high Mo steels, respectively, the marginally higher hardness of the second steel is due to its higher molybdenum content in the solid solution at this stage of the heat treatment. Cross-examination of the microstructure after solution treatment at a higher temperature of 1200°C for 1 hour shows coarse lath martensite structure, with no noticeable residual austenite along the lath boundaries (Fig. 2.16b). The prior austenite grain size after this higher temperature treatment is about 450 mm, with slight hardness reduction to HRC27, for both steels. Therefore, the solution treatment has a classical effect on maraging steels, that is the increasing prior austenite grain size does not have a significant influence on martensite

20 µm (a)

20 µm (b)

2.16 Typical optical microstructure of the experimental 2400 MPa low Mo grade cobalt-free maraging steel after solution treatment followed by air cooling. (a) 810°C for 1 hour; (b) 1200°C for 1 hour.

42

Maraging steels

transformation during cooling. The prior austenite grain size does not affect the hardness significantly, owing to the probability that unchanged martensite lath size and high dense dislocation in the martensite lath play a dominant strengthening role (He et al., 2002a; 2003). Because the significantly different prior austenite grain sizes (15 versus 450 mm) only give a rather marginal hardness difference (HRC28/29 versus HRC27), solid solution strengthening is dominant over grain boundary strengthening, the latter being described normally by the Hall–Petch relationship detailed in most physical metallurgy text books. The microstructure in the peak-ageing condition (480°C for 3 hours) after solution treatment at 810°C for 1 hour consists of martensite lath with many coarse precipitates along the lath boundaries (Fig. 2.17a) or in the lath matrix randomly (Fig. 2.17b). The mean diameter of these coarse precipitates

400 nm (a)

400 nm (b)

2.17 TEM bright field images of the typical microstructure of the martensite matrix and coarse phase for low Mo steel (a) and high Mo steel (b).

Microstructure of maraging steels

43

is about 120 nm. The TEM bright field image of Fig. 2.18 clearly shows the extremely densely distributed needle-shape precipitates and dislocations as well as dislocation tangles in the martensite matrix. The needle-shape precipitates are Ni3Ti using the (0111)Ni3Ti diffraction spot indicated by an arrow in Fig. 2.19b. The average diameter and length of the precipitates are about 4 and 15 nm, respectively (Fig. 2.19a). These extremely dense nanometre-size Ni3Ti precipitates uniformly distribute in the martensite matrix with a particular crystallographic orientation and play a dominating strengthening role by pinning the movement of dislocations. Besides the overwhelmingly populated nanometre-size Ni3Ti precipitates in the martensite matrix of both steels, a large number of coarse phases with a mean diameter of 120 nm are randomly distributed in the matrix and along the lath boundaries (Fig. 2.17). This kind of coarse phase is much larger than Ni3Ti precipitates and there is no coherency or crystallographic orientation relationship with the matrix (Fig. 2.20). Another kind of coarse phase has a hexagonal close packed (hcp) crystal structure (Fig. 2.21). The clear and bright diffraction spots from this type of coarse phase in Fig. 2.21c, as indicated by the arrows, enable an accurate determination of two of its interplanar distances, at 2.23Å and 1.99Å. These interplanar spacing values are very close to some spacing values of Fe2Ti, Fe2Mo, Fe3Mo, Fe63Mo37, Fe0.54Mo0.73, which are listed in Table 2.3. The data in Table 2.3 are taken from the Powder Diffraction File (Joint Committee on Powder Diffraction Standards, 2003), published by the International Center for Diffraction Data (ICDD), which are listed here to compare with the lattice spacing of the precipitates. This Powder Diffraction File contains data card for many minerals, each having a number. The numbers are given in

200 nm

2.18 TEM bright field image of microstructure for low Mo steel, showing high densities of dislocations and precipitates and a coarse phase in the martensite matrix.

44

Maraging steels

100 nm (a)

(b)

2.19 TEM dark field image and SAD pattern for low Mo steel. (a) Dark field image, showing high density of Ni3Ti precipitates taken from the (0111)Ni3Ti spot indicated in (b); (b) [113]M SAD pattern.

brackets under the compound names in Table 2.3. This type of coarse phase might be Fe2Mo intermetallic phase mixed with Ti element, and herein it is denoted as Fe2(Mo, Ti). Similar to the Fe2Ti coarse phase, this type of coarse phase is without coherency and does not have a crystallographic orientation relationship with the martensite matrix. The coarse phases have been confirmed by thermodynamic calculations (Chapter 4). In TEM, no signs of residual austenite or reverted austenite are visible in the peak-ageing condition. The mechanism of strengthening and toughening is the same as in the 2000 MPa grade cobalt-free maraging steel, which is discussed in Section

Microstructure of maraging steels

45

400 nm (a)

(b)

2.20 TEM dark field image and diffraction pattern of a typical Fe2Ti coarse phase for the high Mo steel. (a) Dark field image; (b) electron diffraction pattern of the Fe2Ti coarse phase with zone axis [2423].

2.1. However, a large number of Fe2Ti and Fe2(Mo,Ti) coarse phase particles with mean diameter of 120 nm embedded in martensite lath boundary or in the lath are detrimental to fracture toughness and ductility. Microvoids and microcracks might easily nucleate around the coarse phase, propagate into macrocracks and finally result in failure. Therefore, these coarse phases are the cause of the low fracture toughness. Eliminating the coarse phase or decreasing the size and amount might effectively enhance the fracture toughness and ductility.

46

Maraging steels

200 nm (a)

200 nm (b)

(c)

2.21 TEM bright field and dark field images and SAD pattern for the high Mo steel. (a) Bright field image showing Fe2(Mo,Ti) coarse phase; (b) dark field image of Fe2(Mo,Ti) coarse phase taken using the diffraction pattern in (c); (c) electron diffraction pattern of the coarse phase with zone axis [1213].

Microstructure of maraging steels

47

Table 2.3 Interplanar spacing of intermetallic phases (in Å) and intensity (%)* Fe2Ti

Fe2Mo

Fe3Mo

Fe63Mo37

Fe0.54Mo0.73

(15-0336)

(6-0622)

(9-0297)

(19-0608)

(41-1223)

2.388/30

2.36/60

2.373/90

2.4431/35

2.199/100

2.18/100

2.179/65

2.2084/100

2.181/100



2.167/100



2.077/100

2.114/70



2.05/60

2.05/40

2.061/70

2.079/81

2.038/100

2.02/100

2.031/50

2.015/70

2.0273/69

1.998/100

1.997/100



1.978/70

1.98/60

1.947/30

1.963/50

1.91/30

1.828/30

1.365/60

1.341/60

1.327/60

1.291/40

1.302/60

1.287/100

1.274/50



1.272/40



1.25/40

1.247/60

1.23/60

1.241/40

1.196/60

1.183/60

1.221/40



1.089/60

1.062/40



1.04/100

1.038/40



0.9748/50



0.9648/50



0.905/50

1.2624/52

*

The first number in each entry is the interplanar spacing and the second (after the forward slash/) is the intensity. Only the strong diffractions (I/I0≥30%) are selected. The Powder Diffraction File card number is given in brackets.

2.3

18Ni (350) cobalt-containing grade

The type, amount and size of inclusions are greatly reduced after an ultrapurifying process and TiN is the main inclusion in these ultra-purifying maraging steels (Table 2.1). Strengthening and toughening of the 18Ni (350) maraging steel are attributed to the ultra-purifying and optimisation of the alloying elements. There is no obvious effect of solution treatment temperature for the range 800–1200°C on the microstructure and mechanical properties of the ultra-purified 18Ni (350) maraging steel under solution state. The strength and the ductility of the steels before ageing are independent of prior austenite grain size owing to the constant martensite lath spacing and dislocation tangles. When aged, the Ni3(Mo,Ti) precipitates severely

48

Maraging steels

segregate, and reverted austenite forms at both the prior austenite grain boundaries and the martensite lath boundaries in steels subjected to high temperature solution treatment, which makes strength and ductility decrease with increasing solution temperature and, inversely, fracture toughness increases as solution temperature increases, that is, there is less ageing embrittlement. There are no Ti(S,C) or (Ti,Mo)C inclusions in the ultrapurified maraging steel, which is different from normal maraging steels. This has eliminated the thermal embrittlement resulting from the segregation of inclusions at grain boundaries at higher solution temperature causing a sharp decrease in strength, ductility and fracture toughness.

2.4

2800 MPa cobalt-containing grade

An increase in nickel content plays an essential role in maintaining a high dislocation density structure in martensite lath. There is more Ni3(Mo,Ti) precipitation in martensite matrix owing to the increase in cobalt and titanium content. Furthermore, there are no coarse particles such as m-(Fe,Co)7Mo6, s-Fe2Mo or Ni4Mo in the matrix and the damage to their strength and toughness is avoided because of the significant decrease of molybdenum content. Therefore, ultra-purifying melting is necessary to achieve ultra-high strength with good toughness.

2.5

References

Arya A, Banerjee S, Das G P, Dasgupta I, Saha-Dasgupta T and Mookerjee A (2001), ‘A first-principles thermodynamic approach to ordering in Ni-Mo alloys’, Acta Mater, 49, 3575–87. He Y, Su G, Qu W, Kong F, He L and Yang K (2002a), ‘Grain size and its effect on tensile property of ultra-purified 18Ni maraging steel’, Acta Metall Sin, 38, 53–7. He Y, Yang K, Qu W, Kong F and Su G (2002b), ‘Strengthening and toughening of a 2800-MPa grade maraging steel’, Mater Lett, 56, 763–9. He Y, Yang K, Qu W S, Kong Y and Su G Y (2003), ‘Effects of solution treatment temperature on grain growth and mechanical properties of high strength 18%Ni cobalt free maraging steel’, Mater Sci Technol, 19, 177–224. Headley T J and Brooks J A (2002), ‘A new bcc–fcc orientation relationship observed between ferrite and austenite in solidification structures of steels’, Metall Mater Trans A, 33A, 5–15. Joint Committee on Powder Diffraction Standards (2003), Powder Diffraction File (PDF-Data Base), Newtown Square, PA, International Centre for Diffraction Data (ICDD). Mun S H, Watanabe M, Li X, Oh K H, Williams D B and Lee H C (2002), ‘Precipitation of austenite particles at grain boundaries during aging of Fe–Mn–Ni steel’, Metall Mater Trans A, 33A, 1057–67. Tewari R, Mazumder S, Batra I S, Dey G K and Banerjee S (2000), ‘Precipitation in 18 wt% Ni maraging steel of grade 350’, Acta Mater, 48, 1187–200.

3

Mechanical properties of maraging steels Abstract: Strength increases and fracture toughness decreases with the growth of precipitates. Strengthening in the underaged condition is a combination of dislocations cut through precipitates, and the Orowan mechanisms. Under peak-aged conditions, precipitates of moderate size are uniformly distributed in the martensite matrix, leading to optimal combination of strength and fracture toughness. The ultra-high strength of maraging steels subjected to long-term ageing is attributed to the high resistance to coarsening of the precipitates. The Orowan mechanism is the dominant strengthening mechanism. Towards the end of the chapter, there is a focus upon concentration of alloying elements, for example Mo, Ti and Cu. Key words: fracture, ductility, high strength steels, ageing, precipitation.

3.1

2000 MPa grade cobalt-free maraging steel

3.1.1 Ageing at low temperature (440°C) After ageing, the strength continues to increase (Fig. 3.1a). After the relatively long ageing time of 12 hours, it reaches approximately the design strength for this steel. After 50 hours ageing, there is still slight increase in the yield and tensile strength, reaching their maximum values. Over the ageing time span, the ratio between the yield and tensile strength remains constant for longer times, increasing to its maximum value at maximum strength, and the work hardening rate decreases gradually. The elongation at failure and the reduction in area after failure have the opposite trend to the two strength parameters (Fig. 3.1b). The fracture toughness, KIC, shows similar behaviour to tensile ductility (Fig. 3.1c), which is at its highest after 3 hours ageing (underageing). With increasing ageing time and strength, fracture toughness decreases. After ageing for 12 hours, when the strength approaches the design strength, the KIC value is 62 MPa m1/2. With a further increase in ageing time, the KIC value remains almost constant despite the slight increase in strength. The highest fracture toughness exhibited during early stage ageing is still far below the fracture toughness of lower strength grade cobalt-free maraging steels when treated to the same strength level. Fractography Macroscopically, the failure surface of tensile specimens exhibits a cone feature, typical of good, ductile fracture. Microscopically, at all ageing times, the fracture is intracrystalline (transgranular) (Fig. 3.2). Smaller dimples have a freer, dispersed structure and strong shear deformation is evident 49

Maraging steels 2100

sb

Strength (MPa)

2000 s0.2

1900 1800 1700 1600

Elongation (%)

Reduction in area (%)

2

4

8 16 Ageing time (h) (a)

32

64

2

4

8 16 Ageing time (h) (b)

32

64

40 2

4

8 16 Ageing time (h) (c)

32

64

80 70 60 50 40 30 18 16 14 12 10 8 6

90 85 80 Kic (MPa m1/2)

50

75 70 65 60 55 50 45

3.1 Effect of ageing time on mechanical properties of the 2000 MPa cobalt-free maraging steel, after ageing at 440°C. (a) Yield (0.2% proof stress) and tensile strength; (b) elongation at failure and reduction in area after failure; (c) fracture toughness, KIC.

Mechanical properties of maraging steels

51

during the fracture process. In the underaged condition, the dimples are big and deep (Fig. 3.2a). With increasing ageing time, the dimples become uniform and shallow (Fig. 3.2c). This is in agreement with the observed tensile ductility behaviour, in the decrease of shear deformation ability (ductility) with increasing hardening as ageing proceeds from underageing to peak hardening. The fracture surface of KIC specimens is not exactly the same as for tensile specimens. In the early stage of ageing, although the overall surface can be classified as having dimple morphology, there is extensive tearing of the martensite laths block (Fig. 3.2d), coupled with secondary tearing and tearing steps as a result. After longer ageing, the KIC fracture surface remains similar in principle (Fig. 3.2e). In the process of crack growth, which is caused when the main cracks connect to large tearing steps in addition to the blunting of the crack tips, the growth consumes a large amount of energy, resulting in a high toughness. At peak hardening, there is significant reduction in the tearing steps and kinks, with smaller and shallower dimples (Fig. 3.2f). Therefore, the crack growth is now a low energy tearing process, corresponding to a low KIC. This 2000 MPa maraging steel exhibits slight embrittlement under low temperature ageing, the extent of which is not as severe as for 18Ni 350 grade (composition in Table 2.1). This is probably related to its relatively low strength and small amount of precipitates compared with the 350 grade, leading to relatively easy dislocation slide and the good ductility of the matrix. After ageing for 3 hours, the strength of this steel is the same as for the commercial T250 steel (composition in Table 2.1) after its standard ageing (480°C for 3 hours), but the KIC value is much lower, 73.7 MPa m1/2, compared to 98.2 MPa m1/2 for T250. This may be understood from the following arguments. The 2000MPa grade steel has fine precipitates after low temperature ageing, while T250 would have precipitates with larger sizes after its normal, higher temperature ageing. In T250, at peak hardness, the average precipitate diameter is 6 nm, length 24.5 nm, with an average interparticle spacing of 24.5 nm. In a plane strain state, microcracks nucleated at precipitate sites coalesce and grow. When aged at 440°C, the 2000 MPa steel has increased strength with prolonged ageing time, accompanied by decreased ductility. This decreased ductility reduces the fracture surface energy (the energy required to create a unit fractured surface area), resulting in lower fracture toughness. Finally, it should be noted that reverted austenite has no influence throughout the low temperature ageing process.

3.1.2 Ageing at intermediate temperature (480°C) The development of strength (Fig. 3.3a) is consistent with the development of hardness over time (Chapter 6). At peak strength, the cobalt-free maraging

52

Maraging steels 50 µm

20 µm

(a) 20 µm

(d) 50 µm

(b)

(e) 50 µm

20 µm

(c)

(f)

3.2 SEM fracture morphologies of the 2000 MPa cobalt-free maraging steel aged at 440°C. (a), (b), (c) Tensile specimens aged for 3, 12 and 50 hours, respectively; (d), (e), (f) KIC specimens aged for 3, 12 and 50 hours, respectively.

steel can still maintain its good ductility, with 9% elongation at fracture and 51% reduction in cross-section area after fracture (Fig. 3.3b). After prolonged ageing for 50 hours, there is a slight reduction in strength, accompanied by marginal increases in elongation and reduction in area. Over the entire ageing range, the ratio between yield and tensile strength is between 0.96–0.98. Although there is a significant increase in strength (Fig. 3.3a) (100–200 MPa) after overageing compared to underageing, the ductility parameters, viz. elongation and reduction in area, remain at reasonable levels (Fig. 3.3b). The KIC value gradually decreases with increasing ageing time (Fig. 3.3c). At peak hardness, that is, after 12 hours ageing, KIC reaches its minimum, at a level similar to the fracture toughness of the 18Ni (300) cobalt-containing

Mechanical properties of maraging steels

53

2200

Strength (MPa)

2100 sb 2000 s0.2 1900

Reduction in area (%)

80

Elongation (%)

1800

15

2

4

8

12 16 20 Ageing time (h) (a)

50

2

4

8

12 16 20 Ageing time (h) (b)

50

2

4

8

12 16 20 Ageing time (h) (c)

50

70 60 50 40 30 20

10 5 0

85

Kic (MPa m1/2)

80 75 70 65 60

3.3 Effect of ageing time on mechanical properties of the 2000 MPa cobalt-free maraging steel, after ageing at 480°C. (a) Yield (0.2% proof stress) and tensile strength; (b) elongation at failure and reduction in area after failure; (c) fracture toughness, KIC.

54

Maraging steels

maraging steel with similar strength level. With further increase in ageing time, that is, decrease in strength, KIC recovers gradually. Under peak hardness conditions, there is a good combination of strength and fracture toughness. Fractography After ageing at the intermediate temperature, the cobalt-free maraging steel demonstrates good stable tensile ductility, with a typical cone-shaped fracture surface seen macroscopically. This cone-shaped fracture surface seen with the naked eye cannot be shown in the fractomicrographs in Fig. 3.4 owing to their high magnification, but it was assessed based on visual examination of the fractured sample. Under all ageing conditions, a dimple structure is apparent. The fracture process occurs through the nucleation, growth and coalescence of microvoids, resulting in intracrystalline (transgranular) fracture. In underageing condition (3 hours), the dimples are relatively small and shallow (Fig. 3.4a), indicating relatively poor plastic deformability. Under peak ageing (12 hours, Fig. 3.4b) and overageing (50 hours, Fig. 3.4c) conditions, the dimples are relatively large and deep, showing good plastic deformability of the materials, consistent with the observed slight increase of tensile ductility over increasing ageing time. In essentially the same way as for tensile fractured specimens (Figs. 3.4a, 3.4b and 3.4c), KIC specimens exhibit a ductile dimple structure under all ageing conditions (Figs. 3.4d, 3.4e and 3.4f). Although the difference between different ageing times is not significant, careful examination reveals that there are almost no large dimples under peak ageing. A uniform distribution of relatively shallow dimples is exhibited in this condition (Figs. 3.4b and 3.4e). In comparison, there are relatively large deep dimples in the underaged (Figs. 3.4a and 3.4d) and overaged (Figs. 3.4c and 3.4f) conditions. Compared to ageing at low temperature (Section 3.1.1), the large deep dimples when aged at intermediate temperature are indicative of a larger amount of energy absorption through the relatively large plastic deformation during crack growth. The crack tips are easily blunted, with a large fracture surface energy. This agrees with the generally high fracture toughness after ageing at this temperature.

3.1.3 Ageing at high temperature (540°C) With increasing ageing time, the yield and the tensile strengths decrease rapidly (Fig. 3.5a), while the elongation increases continuously (Fig. 3.5b). The reduction in area is maintained at quite high levels (Fig. 3.5b). From the variations of the yield and tensile strengths as functions of ageing time, the yield to tensile ratio decreases with decreasing strength from 0.96 to

Mechanical properties of maraging steels

55

20 µm

20 µm

(a)

(d) 20 µm

20 µm

(e)

(b) 100 µm

50 µm

(c)

(f)

3.4 SEM fracture morphologies of the 2000 MPa cobalt-free maraging steel aged at 480°C. (a), (b), (c) Tensile specimens aged for 3, 12 and 50 hours, respectively; (d), (e), (f) KIC specimens aged for 3, 12 and 50 hours, respectively.

0.85. This is in sharp contrast to the independency on ageing time of the yield to tensile ratio when aged at low (Section 3.1.1) and medium (Section 3.1.2) temperatures. After high temperature ageing, the fracture toughness of the cobalt-free maraging steel does not reach the levels of other maraging steels at comparable strength grade. For example, after ageing for 15 minutes, although the strength reaches 1900 MPa, the KIC is only 63.1 MPa m1/2. After 30 minutes ageing, with a reduction in the yield and the tensile strengths by about 100 MPa, there is no accompanying significant increase in KIC (64.6 MPa m1/2). Within the first 6 hours of ageing, the Charpy V notch (CVN) values are

56

Maraging steels

around 25 J cm–2 (Fig. 3.5c), although the strength can be reduced by as much as about 300 MPa. Afterwards, with a further more rapid decrease in strength, CVN gradually picks up, but only to 30.3 J cm–2, far below the impact toughness of other maraging steels at similar strength levels. This shows that high temperature ageing is not a good way of achieving a good combination of strength and toughness. Normally, one type of maraging steel cannot be heat treated under different parameters to provide different good combinations of properties and each maraging steel only has one optimum set of properties after an optimum ageing process. Fractography After ageing at the high temperature, although the cobalt-free maraging steel has cone-shaped fracture features macroscopically, microscopically, the morphology is rather different. After a short ageing time, the tensile fracture surface consists of relatively uniformly distributed dimples (Fig. 3.6a), similar to the morphology after ageing at the intermediate temperature. With increasing ageing time, that is, with a reduction in strength and an improvement in tensile ductility, large and deep dimples are apparent, with increasing tear kinks and steps (Fig. 3.6b). After long-term ageing, although the elongation is very large, the fracture surface shows a mixed morphology (Fig. 3.6c), with a reduced number of dimples that are also small. The fracture is accompanied by small amounts of plastic deformation. Although the fracture toughness is relatively low, the fracture surface still consists of dimples (Fig. 3.6d), the same as the fraction surface of KIC specimens after ageing at the medium temperature. After ageing for 12 hours, the fracture surface has very shallow dimples, with multiple small cleavage planes (Fig. 3.6e). After ageing for a longer time, there are almost no dimples, but only cleavage planes and tearing kinks (Fig. 3.6f). The fracture mode appears to be a quasi-cleavage fracture along phase boundaries. This is closely related to the microstructural features after high temperature ageing. There are fine dimples and quasi-cleavage tearing cracking in the fracture morphology giving a mixed appearance. In terms of properties, the toughness cannot increase significantly with the decreasing strength. The toughness values are significantly lower than the fracture toughness of lower strength grade maraging steels after normal, standard ageing.

3.1.4 Summary The formation of a great amount of extremely fine precipitates leads to a rapid increase of the yield strength at the initial stages of ageing at low temperature. With the growth of the precipitates, the yield strength gradually increases, accompanied by a reduction in ductility. The KIC value reduces gradually.

Mechanical properties of maraging steels

57

2100

Strength (MPa)

2000 1900 1800 1700

sb

1600 1500 1400

s0.2

1300

Elongation (%)

Reduction in area (%)

1200

0.25 0.5

1 2 4 8 Ageing time (h) (a)

16

32 64

0.25 0.5

1 2 4 8 Ageing time (h) (b)

16

32 64

1 2 4 8 Ageing time (h) (c)

16

32 64

80 70 60 50 40 18 16 14 12 10 8 6

35

CVN, J/cm2

30

25

20

15

0.25 0.5

3.5 Effect of ageing time on mechanical properties of the 2000 MPa cobalt-free maraging steel, after ageing at 540°C. (a) Yield (0.2% proof stress) and tensile strength; (b) elongation at failure and reduction in area after failure; (c) impact toughness measured using Charpy V notch, CVN.

58

Maraging steels

20 µm

50 µm

(a)

(d) 50 µm

20 µm

(b)

(e) 50 µm

20 µm

(c)

(f)

3.6 SEM fracture morphologies of the 2000 MPa cobalt-free maraging steel aged at 540°C. (a), (b), (c) Tensile specimens aged for 15 minutes, 12 hours and 50 hours, respectively; (d) KIC specimen aged for 15 minutes; (e), (f) CVN impact toughness specimens aged for 12 hours and 50 hours, respectively.

The extremely fine precipitates at the early stages of ageing are the cause of the slightly low fracture toughness. The strengthening mechanism during the early stages of low temperature ageing involves the shearing and looping of high-density dislocations passing the precipitates. In the later stages, an Orowan looping mechanism operates. After ageing at an intermediate temperature, the precipitates have a suitable and effective size and uniform dispersion distribution. The combination of strength and toughness is optimal, compared to ageing at low and high temperatures. The combined properties reach the level for 18Ni (300) cobaltcontaining maraging steels.

Mechanical properties of maraging steels

59

After ageing at a high temperature, the yield strength rapidly drops from its peak value with increasing ageing time. The impact toughness only has a limited increase over the decrease in strength. The seriously inhomogeneous size and distribution are the cause of the low toughness. At later stages, the precipitates coarsen rapidly, leading to significant embrittlement in the matrix. This, combined with the large amount of randomly distributed reverted austenite, results in low strength and low toughness in overageing conditions.

3.2

2400 MPa grade cobalt-free maraging steel

The yield strength after solution treatment is similar for the low and high Mo steels (Table 3.1). In the solution state, both steels have good ductility. This is related to the high dislocation density structure in this heat treatment state. Deep quenching, also called pre-ageing, is a new concept which is specific to maraging treatment and is not normally met in other tempering or ageing sequences in other ferrous alloys. This treatment at, for instance, –73°C, is to ensure full martensite transformation, in case the martensite finish temperature is around or just below the room temperature. Steels pre-aged at –73°C for 0.5 hour show higher yield and tensile strength levels, with similar ductility (Table 3.2). However, the properties with and without deep quenching down to –73°C are largely similar, indicating complete transformation to martensite upon air or water cooling to room temperature after solution treatment. At an ultra-high strength like 2400 MPa, reasonable ductility is maintained. The fracture toughness (KIC) is relatively low. In the solution state, the high Mo steel (5.39% Mo, full composition in Table 2.1), with 1% extra molybdenum, has a higher tensile strength, by about 150 MPa compared to the low Mo steel (4.4% Mo, full composition also in Table 2.1). However, in aged conditions, the two steels have almost identical strength and toughness. This is mainly due to their similar titanium content (2.59% and 2.63%, respectively). Titanium is the main strengthening element and determines the strength and toughness properties in aged conditions.

Table 3.1 Tensile properties of the 2400 MPa cobalt-free maraging steels after solution treatment at 810°C for 1 hour Steel

Tensile strength (MPa)

0.2% proof Elongation (%) stress (MPa)

Reduction in area (%)

Low Mo High Mo

1090–1303 1350

954–976 993–1004

52–75 51

13–16 14–15

60 Maraging steels

Table 3.2 Mechanical properties of the 2400 MPa cobalt-free maraging steels under aged conditions Steel Ageing treatment

Tensile strength (MPa)

0.2% proof Elongation (%) stress (MPa)

Reduction in area (%)

KIC (MPa m1/2)

Low Mo High Mo

2368–2390 2390–2405 2401–2413 2338–2401 2306–2383 2394–2433

2324–2361 2354–2373 2367–2373 2300–2361 2275–2345 2334–2387

18–29 6–28 23–25 22–25 9–26 26

20.8 – – 18.4 – –

480°C, 3 h 460°C, 3 h –73°C, 0.5 h + 460°C, 3 h 480°C, 3 h 460°C, 3 h –73°C, 0.5 h + 460°C, 3 h

5–7 3–5 3–5 7 3–7 4

Mechanical properties of maraging steels

2 mm

2 mm

(a)

(d)

10 µm

10 µm

(b)

20 µm

(e)

20 µm

(c)

(f)

3.7 SEM fracture morphologies of the 2400 MPa cobalt-free maraging steels aged at 480°C for 3 hours. (a,b,c) Low Mo steel; (d,e,f) high Mo steel; (a,d) low magnification morphology of tensile specimens; (b,e) fractographs of tensile specimens; (c,f) fractographs of KIC specimens.

61

62

Maraging steels

3.2.1 Fractography At the ultra-high strength level of 2400 MPa, the steels exhibit a cup-cone feature (Figs. 3.7a and 3.7d). Although the middle fibre region is relatively small, a slow propagation process of the microvoids in the middle of the specimens is likely. The shear region around the specimen edges is rather small, indicating small plastic deformation. Small and shallow dimples confirm that the fracture process took place through the nucleation, growth and coalescence of microvoids, transgranularly (Figs. 3.7b and 3.7e). Owing to the high strength and low ductility of the matrix, the degree of microvoid coalescence is not significant, resulting in small and shallow dimples. Under plane strain conditions, the KIC specimens of the steels show very flat fracture surfaces, almost without shear edges. However, no cleavage fracture occurs (Figs. 3.7c and 3.7f). The fracture surfaces still consist of shallow and fine dimples. This indicates that, during the crack propagation process, there is very limited plastic deformation in front of the crack tip, leading to very little blunting. Thus, energy absorption during crack propagation is small, as shown by the low KIC values.

3.2.2 Effects of alloying elements on strength and toughness During the development of cobalt-containing maraging steels, the effects of the major alloying elements on strength and toughness have been largely elucidated. The development of cobalt-free steels has supplemented and further advanced this understanding. This section discusses the strengthening and toughening effects of the alloying elements and their concentrations on maraging steels. The chemical compositions of the steel grades are listed in Table 2.1. Table 3.3 compares the compositions and mechanical properties of various maraging steel grades that have been developed. Cobalt is dissolved in the matrix in maraging steels and does not participate in precipitation, but a strong interaction between cobalt and molybdenum increases the strength. Comparing the 18Ni (350) grade with the 2800 MPa grade maraging steels, for similar nickel and titanium contents, large increases in cobalt and molybdenum contents do not affect significantly the solid solution strengthening. However, since cobalt lowers the solid solubility of molybdenum, it promotes precipitation of molybdenum. Therefore, with increasing molybdenum content, aged strength increases significantly. Comparing the 18Ni (350) grade with the 2000 MPa grade maraging steels, the solutionised strength is at similar levels, again confirming that cobalt does not contribute much to strengthening. For this reason, cobalt cannot significantly harden the martensite matrix. Because cobalt promotes molybdenum precipitation, although titanium in

Steel Ni Co Mo Ti

Tensile 0.2% proof Elongation (%)* Reduction strength (MPa)* stress (MPa)* in area (%)*

KIC (MPa m1/2)

18Ni (350) (He et al., 2003) 2800 MPa (He et al., 2002) 2400 MPa low Mo 2400 MPa high Mo 2000 MPa 1800 MPa

2339 2693 2380 2370 2017 1696

76.6 31.6 20.8 18.4 74.0 46.2†

*

18.8 17.9 19.1 18.8 18.9 18.5

10.8 14.8 – – – –

4.22 6.69 4.4 5.39 4.14 3

1 1.1 2.63 2.59 1.93 1.26

(1053) (1191) (1200) (1350) (1019) (992)

2318 2617 2340 2330 1957 1647

(937) (972) (965) (999) (862) (871)

8.0 (16.7) 6.0 (16) 6.0 (15) 6.7 (15) 8.0 (16.7) 13.1 (15)

55 26 24 24 53 61

(74) (67) (64) (51) (72) (74)

The numbers before brackets are for the peak aged condition and the numbers in brackets are for the solution-treated condition (1 hour at 810°C except for the 2800 MPa grade for which deep quenching dawn to –73°C is used). † This value is a measurement result of Charpy V notch impact energy (CVN, J cm–2).

Mechanical properties of maraging steels

Table 3.3 Chemical compositions and mechanical properties of some maraging steels

63

64

Maraging steels

the 18Ni (350) steel is lower by 0.93% compared to the 2000 MPa steel, the cobalt-containing steel still has a higher strength, by over 300 MPa, whilst maintaining the same toughness. This confirms the interaction between cobalt and molybdenum. Among the cobalt-free steels in Table 3.3, comparing the 2000 MPa grade with low Mo steel, increasing the titanium content whilst keeping other alloying contents at similar levels boosts the strength considerably owing to the larger quantity of titanium-containing precipitates. Semi-quantitatively, the additional 0.7% titanium in low Mo steel has given 100 MPa extra yield strength and 180 MPa extra tensile strength in the solid solution state, but 400 MPa extra yield strength in the aged state. However, because the matrix is very hard in these conditions, the toughness is reduced significantly. Comparing the chemical composition and mechanical properties of the low and high Mo steels, because there is no cobalt, molybdenum cannot fully contribute to precipitation hardening during ageing, thus providing no significant contribution to strength and no effect on ductility. In many ultra-high strength steels, cobalt can suppress the recovery of dislocation sub-structures, making M2C carbides smaller and more densely distributed (Chen et al., 2000). Under normal ageing conditions, even and fine dispersion of precipitates can be achieved in both cobalt-containing and

30

K3359 Fe–9.4Ni–4Cu–0.04Si < 0.005C K3364 Fe–9.8Ni–4Cu–0.24Nb–0.038C K3365 Fe–9.7Ni–4Cu–2.4Mo–0.037C

Impact energy (J)

K3363 Fe–9.8Cu–5Cu–5Mo–0.24Nb–0.025C

20

377 HV DH = 70 HV

DH = Increase in hardness on ageing 418 HV DH = 80 HV

10

433 HV DH = 70 HV

329 HV DH = 30 HV

Half size “V” Notch Charpies 5 ¥ 10 ¥ 55 mm 0 –200

–100

0 100 Testing temperature (°C)

200

3.8 Ductile–brittle transition temperature of grain-refined copper maraging steels, forged at 1050°C and aged for 2.5 hours at 450°C. HV is the unit of hardness when measured with a Vickers indenter.

Mechanical properties of maraging steels

65

cobalt-free maraging steels. The size of the precipitates and the dislocation density in the matrix do not seem to be affected by the presence of cobalt. This apparent discrepancy is because the types of precipitate are different in cobalt-containing and cobalt-free maraging steels. The former relies on molybdenum-based precipitates while the latter relies on titanium-based precipitates. The co-alloying of cobalt and molybdenum in maraging steels enhances the nucleation rate along dislocation lines. However, a very high nucleation rate is also achieved in 2000 MPa grade cobalt-free maraging steel (Section 2.1), but again the precipitates are largely based on titanium. Essentially, to utilise and maximise the effect of cobalt, molybdenum needs to be employed in the system. By adjusting and controlling the alloying contents, it is possible to eliminate the detrimental effect of certain elements on toughness and achieve a good combination and balance of ultra-high strength and high toughness.

3.2.3 Summary An ultra-high strength cobalt-free 2400 MPa grade maraging steel has a nominal composition of Fe–18Ni–4Mo–2.5Ti. After appropriate ageing treatment, the maximum hardness of the cobalt-free steels reaches HRC5758. At the ultra-high strength, the cobalt-free maraging steels exhibit good ductile fracture. Titanium is the most important strengthening element in cobalt-free grades. It is possible to achieve a good balance of ultra-high strength and high toughness by rational modification of the main alloying element contents and appropriate heat treatments.

3.3

Grain-refined copper maraging steels

As-forged alloys are aged for 2.5 hours at 450°C, just past peak hardness. The toughness of these alloys in this condition is shown in Fig. 3.8. When comparing K3359 with K3364, the effect of grain refining with niobium is particularly evident. Owing to its high toughness, K3364 may provide a suitable base for increasing the strength using other alloy additions to form other intermetallics. The forged ternary alloy K3359 shows some edge cracking, but alloys K3364, K3365, and K3363 exhibit excellent hot workability with no edge cracking.

3.4

References

Chen K, Su J, Li R, Weng Y and Wang J (2000), ‘Alloy design of cobalt-free secondary hardening ultra-high strength steel’, Iron and Steel, 35(8), 40–4.

66

Maraging steels

He Y, Yang K, Qu W, Kong F and Su G (2002), ‘Strengthening and toughening of a 2800-MPa grade maraging steel’, Mater Lett, 56, 763–9. He Y, Liu K and Yang K (2003), ‘Effect of solution temperature on fracture toughness and microstructure of ultra-purified 18Ni(350) maraging steel’, Acta Metall Sin, 39, 381–6.

4

Thermodynamic calculations for quantifying the phase fraction and element partition in maraging systems and precipitation hardening steels Abstract: Thermodynamic calculations can quantify the phase fraction and element partition in maraging systems and precipitation hardening steels. Excellent agreement is obtained between calculation and experimental measurements mainly using the atom probe. For instance, calculations show that the precipitates formed in Fe–Ni–Al–Mo systems are in the NiAl phase, in accordance with atom probe microanalysis. In addition, thermodynamic calculation can help identify the existence of some phases that are not readily observed experimentally. It can be used as a guide in alloy design. Key words: phase transformations, precipitates, phase stability, atom microprobe, heat treatment.

4.1

Methodology of thermodynamic calculations and choice of alloy systems

Thermodynamics modelling is usually based on the Gibbs energy calculation. Two most commonly used calculation packages are Thermo-Calc (Andersson et al., 2002) and MTDATA (Davies et al., 2002). These packages have been successfully applied in the past for thermodynamic calculations of different materials systems (Dore et al., 2000; Ekroth et al., 2000; Eskin, 2002; Gorsse and Shiflet, 2002; Guo and Sha, 2000; Jarvis et al., 2000; Zackrisson et al., 2000). Thermodynamic calculations can supplement experimental characterisation and allow the prediction of phase type, and fraction and element distribution in different phases. Thermo-Calc is a computer package developed particularly for thermodynamic calculations of multi-component equilibrium as a function of pressure, temperature and the combined effect of alloying elements, using a databank of assessed thermodynamic data and models for the phases in the system that are as good approximation of their nature as possible. It employs rigorous thermodynamic expressions and numerical methods of minimising the chemical energy of the system, so that interpolation between the available experimental data can be made. Good agreement was obtained in the past between the calculated phase compositions and experimental measurements. In this chapter, thermodynamic calculations of the phase equilibria in different maraging alloys will be shown, including the 2400 MPa grade 67

68

Maraging steels

cobalt-free maraging steel, Fe–Ni–Al–Mo, Fe–Ni–Mo and Fe–Ni–Co–Mo, and Fe–Ni–Mn. These alloys are chosen from different maraging alloy groups and they include both well-investigated and relatively new alloys. The calculations are performed for the actual alloy composition taking into account all major alloying elements. Further thermodynamic calculation procedures are given in Chapters 7 and 8. The results of the thermodynamic calculations, their coupling with the models for simulation of the evolution of microstructure during ageing and the resulting mechanical properties and behaviour of a specific maraging alloy system are discussed in Chapter 8.

4.2

2400 MPa grade cobalt-free maraging steel

Thermodynamic calculations of equilibrium phases, phase fractions and their compositions can be carried out as functions of temperature. Calculations that exclude the austenite phase are more relevant to the practical heat treatment of maraging steels, where austenite reversion normally does not occur because of the kinetic limitations. Within the temperature range of ageing (440–540°C), the Laves phase appears as pure Fe2Mo, that is, there is no titanium in Fe2(Mo,Ti), see Fig. 4.1. Calculations with austenite included are also presented. These are of theoretical interest and are useful for ageing and solution treatment at relatively high temperatures where austenite reversion occurs. The following discussion will help in understanding the alloys. The solution treatment temperature was 810°C. When austenite is included, Ni3Ti does not form, but Fe2(Mo,Ti) forms (Fig. 4.1). Its compositions under this condition are Fe61Ni6Mo14Ti19 and Fe62Ni5Mo16Ti17 for the low and high Mo steels, respectively. This implies that before ageing, Fe2(Mo,Ti) already exists. Probably because such particles are large, they do not contribute much to strengthening before ageing. As these particles are considered detrimental to the toughness, increasing solution treatment temperature may help improve the toughness by removing the large Fe2(Mo,Ti) particles in the solutionised state. If Fe2(Mo,Ti) has already formed before ageing, the ferrite composition, where Ni3Ti and further Fe2(Mo,Ti) will form, will not be the alloy composition. In summary, thermodynamic calculations show that Ni3Ti is the major precipitate phase at the ageing temperatures used. The second type of precipitate is Fe2(Mo,Ti), which has been confirmed by transmission electron microscopy and electron diffraction analysis.

4.3

Fe–Ni–Al–Mo

Iron-based Fe–Ni–Al superalloys were developed as an alternative to nickelbased superalloys. These alloys are based on NiAl-b¢ precipitates in a ferrite

Thermodynamic calculations for quantifying the phase fraction

69

matrix. High aluminium content in the alloys extends the ferrite phase field to higher temperatures and retards the ferrite to austenite transformation at high temperatures. As a result, these alloys can be used for elevated temperature applications. Two Fe–Ni–Al–Mo alloys have compositions of Fe–10Ni–15Al–1Mo and Fe–15Ni–20Al–4Mo (the concentration in this section is in at%), aged at 775°C for 100 hours and 750°C for 50 hours, respectively. The precipitate formed is identified experimentally as B2-ordered NiAl (b¢). Thermodynamic calculation gives useful results for the identity, fraction and

70 Ni3Ti Fe2(Mo, Ti)

Mole fraction (%)

60 50 40 30 20 10 0 400

500

600 700 800 Temperature (°C) (a)

900

1000

70 Ferrite Ni3Ti Fe2 (Mo, Ti)

Mole fraction (%)

60 50 40 30 20 10 0 400

500

600 700 800 Temperature (°C) (b)

900

1000

4.1 Thermodynamic phase equilibrium of (a,b) low Mo and (c,d) high Mo steels as a function of temperature. (a,c) Calculations with austenite excluded, the balance of the phase composition is ferrite. (b,d) Calculations with austenite included, the balance of the phase composition is austenite.

70

Maraging steels 70 Ni3Ti Fe2(Mo, Ti)

Mole fraction (%)

60 50 40 30 20 10 0 400

500

600 700 800 Temperature (°C) (c)

900

1000

70 Ferrite Ni3Ti Fe2 (Mo, Ti)

Mole fraction (%)

60 50 40 30 20 10 0 400

500

600 700 800 Temperature (°C) (d)

900

1000

4.1 (Continued)

element distribution in different phases (Table 4.1). The observed FeMo phase is possibly the m-phase (Fe7Mo6), as predicted by the calculations, since the compositions are close. Experimentally, the precipitates have not reached the equilibrium composition, owing to kinetic reasons.

4.4

Fe–Ni–Mo and Fe–Ni–Co–Mo

The compositions of the maraging steels are Fe–18.7Ni–4.81Mo and Fe–18.5Ni–9Co–4.77Mo (wt%). The austenite phase is excluded from the calculation, as this phase does not form until the steels are significantly overaged. Ferrite is used in place of martensite. Included in the calculations are the m, R, Laves, P, s, b-Ni4Mo, g-Ni3Mo, d-NiMo and c phases. The m

Steel

Phase

Mo

Ni

Al

Fe

Mol%

Fe–10Ni– 15Al–1Mo Fe–15Ni– 20Al–4Mo

Matrix b¢ Matrix b¢ m

1.2 (1.2±0.1) 0 (0) 1.8 (3.7±0.7) 0 (0) 43.0 (48.5)

1.9 (2.2±0.2) 50.2 (37.9±1.6) 1.1 (0.7±0.3) 50.1 (45.5±0.4) 0.7 (0.7)

8.0 (11.8±0.4) 49.8 (50.9±1.7) 8.9 (8.0±1.0) 49.9 (43.0±0.4) 0 (1.5)

Balance 0 (11.3±1.0) Balance 0 (11.4±0.2) 56.2 (49.3)

83.2 16.8 65.0 28.4 6.6

Thermodynamic calculations for quantifying the phase fraction

Table 4.1 Calculated phase constitution and element distribution in Fe–10Ni–15Al–1Mo and Fe–15Ni–20Al–4Mo with experimental data from atom probe microanalysis in parentheses for comparison

71

72

Maraging steels

Table 4.2 Calculated phase constitution and element distribution (at%) in Fe–Ni–Mo and Fe–Ni–Co–Mo maraging steels at 510°C with experimental data from atom probe microanalysis in parentheses for comparison Steel

Phase

Ni

Fe–Ni–Mo Fe–Ni–Co–Mo

Matrix m Matrix m

18.7 12.1 18.3 16.1

(17.4±1.7) (13±2) (17.6±2.6) (15±2)

Co

Mo

Fe

– – 9.3 (9.5±2.0) 0.0 (3±1)

0.6 (1.2±0.5) 46.1 (49±3) 0.6 (1.4±0.8) 46.1 (46±3)

Balance Balance Balance Balance

Table 4.3 Driving forces (DG/RT) for formation of phases in bcc of Fe–12Ni–6Mn maraging steel Phase

500°C

350°C

fcc NiMn Ni2Mn Ni3Mn NiMn2 NiMn3 Ni3Fe

0.72 0.45 0.39 0.04 –0.13 –0.27 –0.34

1.04 0.97 0.90 0.50 0.25 0.78 0.12

phase is the equilibrium intermetallic phase, as shown in the calculation results summarised in Table 4.2 together with atom probe measured compositions in steels aged for 4 hours, for comparison. There is excellent agreement.

4.5

Fe–Ni–Mn

The Kaufman database contains more phase data relevant to the system. At 500°C, the equilibrium phases are body centred cubic (bcc) and face centred cubic (fcc). The driving forces in a bcc matrix are given in Table 4.3. At 350°C, the equilibrium phases are again bcc and fcc. When fcc is excluded from the calculation, the equilibrium consists of bcc, NiMn (3.7 mol%) and Ni2Mn (11.2 mol%). When both fcc and Ni2Mn are excluded from the calculation, the equilibrium consists of bcc, NiMn (11.5 mol%), and Ni3Fe (2.4 mol%). The driving forces in a bcc matrix at 350°C are also given in Table 4.3. These results are in general agreement with those of experimental studies. To make a direct comparison with the estimated fraction of NiMn precipitates, the equilibrium in Fe–11.9Ni–5.75Mn at 450°C is considered. The equilibrium phases are bcc and fcc. When fcc is excluded, the equilibrium consists of bcc, NiMn and Ni2Mn. When both fcc and Ni2Mn are excluded, the equilibrium consists of bcc and NiMn. The fraction of NiMn is 9.7 mol%, equivalent to 9.9 wt%. This is in reasonable agreement with the rough estimation from solubility data of a value of 12.3 wt%.

Thermodynamic calculations for quantifying the phase fraction

4.6

73

References

Andersson J-O, Helander T, Hoglund L, Shi P and Sundman B (2002), ‘Thermo-Calc & DICTRA, computational tools for materials science’, Calphad, 26, 273–312. Davies R H, Dinsdale A T, Gisby J A, Robinson J A J and Martin S M (2002), ‘MTDATA – thermodynamic and phase equilibrium software from the National Physical Laboratory’, Calphad, 26, 229–71. Dore X, Combeau H and Rappaz M (2000), ‘Modelling of microsegregation in ternary alloys: application to the solidification of Al-Mg-Si’, Acta Mater, 48, 3951–62. Ekroth M, Dumitrescu L F S, Frisk K and Jansson, B (2000), ‘Development of a thermodynamic database for cemented carbides for design and processing simulations’, Metall Mater Trans B, 31B, 615–9. Eskin D G (2002), ‘Hardening and precipitation in the Al–Cu–Mg–Si alloying system’, Mater Sci Forum, 396–402, 917–22. Gorsse S and Shiflet G J (2002), ‘A thermodynamic assessment of the Cu–Mg–Ni ternary system’, Calphad, 26, 63–83. Guo Z and Sha W (2000), ‘Modelling of beta transus temperature in titanium alloys using thermodynamic calculation and neural networks’, in: Titanium’99: Science and Technology, Proceedings of the Ninth World Conference on Titanium, Gorynin I V and Ushkov S S (eds), Central Research Institute of Structural Materials, St. Petersburg, Russia, 61–8. Jarvis D J, Brown S G R and Spittle J A (2000), ‘Modelling of non-equilibrium solidification in ternary alloys: comparison of 1D, 2D, and 3D cellular automaton-finite difference simulations’, Mater Sci Technol, 16, 1420–24. Zackrisson J, Rolander U, Jansson B and Andren H O (2000), ‘Microstructure and performance of a cermet material heat-treated in nitrogen’, Acta Mater, 48, 4281– 91.

5

Quantification of phase transformation kinetics in maraging steels Abstract: Research on the kinetics of precipitate formation and austenite reversion in maraging steels has received great attention owing to their importance to the properties of steels. In this chapter, phase transformation kinetics is discussed. Based on the calorimetric data obtained at different heating rates, the kinetics of precipitate formation and austenite reversion is modelled using the Johnson–Mehl–Avrami (JMA) theory. Good agreement between the calculated transformed fraction and the experimental data is demonstrated for both phase transformations. The derived JMA kinetic parameters are then used to simulate the phase transformation kinetics during isothermal ageing. Key words: precipitation kinetics, austenite, Johnson–Mehl–Avrami theory, differential scanning calorimetry, computer modelling.

5.1

Evolution of precipitates

5.1.1 Growth and coarsening Precipitate growth and coarsening both need solutes from elsewhere. Solutes for growth are from the surrounding matrix, whereas for coarsening of larger precipitates they are released by the dissolving smaller particles (Fig. 5.1). However, in reality, the two sources that supply solutes that precipitates need, the surrounding matrix and the dissolving particles, usually operate simultaneously, regardless of whether the ongoing process is growth or coarsening. During precipitate growth, when transition phases are formed prior to the formation of a stable precipitate, the size of the stable phase increases at the expense of the transition particles. During particle coarsening, solute concentration in the surroundings of a smaller precipitate is expected to be higher than of particles of bigger size. From the view of the precipitate that grows or coarsens, the solutes are from both its surroundings and dissolved precipitates. The driving force for coarsening always consists of two parts: the difference in solute concentration and the decrease in interfacial free energy. So, the diffusion processes involved in precipitate growth and coarsening make no essential difference. The difference is only in the distance of diffusion field (DoDF). The DoDF during precipitate growth decreases slightly with time, if nucleation sites saturate at the beginning, and fast if more nucleation sites form during ageing. Coarsening, featured by a decrease in the number of precipitates, is always accompanied by an increase in the average DoDF. Therefore, size increment during precipitate coarsening always proceeds at a rate slower than that during particle growth. 74

Quantification of phase transformation kinetics

(a)

75

(b)

5.1 Schematic comparison of the difference in diffusion routes between (a) growth and (b) coarsening.

5.1.2 Spinodal decomposition and normal nucleation There are two types of phase change in solid solutions. First, there is the normal precipitation reaction which involves a thermally activated nucleation step and, secondly, there is spinodal decomposition in which the material is inherently unstable to small fluctuations in composition and hence decomposes spontaneously. Nucleation is associated with metastability and requires the occurrence of a relatively large composition fluctuation to surmount the energy barrier in order to form a nucleus of critical size which can grow further. These intense fluctuations are relatively small in spatial extent and have composition amplitudes approaching the equilibrium composition of the precipitating phase. Spinodal decomposition refers to decomposition of an unstable solution where concentration waves of small amplitude and long wavelength are selectively amplified to develop progressively a twophase modulated structure. During spinodal decomposition the composition of the solute-enriched regions is initially far removed from the equilibrium value.

5.1.3 Particle size There is not just one critical particle size during the evolution of precipitate growth or coarsening. The change in the nature of coherency makes the situation even more complicated. The critical particle radius (rc) below which the particle will dissolve can be calculated as (Rivera-Díaz-del-Castillo and Bhadeshia, 2001):

rc = 2caG/(c0 – ca)

[5.1]

where ca is the solid solubility of the controlling elements in the matrix, c0 is concentration of the precipitating elements in the matrix before ageing and the capillarity constant G is given by:

G=

s N AWq (1 – ca ) RT (cq – ca )



[5.2]

where s is the interface energy per unit area between the precipitate and the

76

Maraging steels

matrix, NA is Avogadro’s number, Wq is the atomic volume of the precipitate, cq is the concentration of the controlling elements in the new phase, R is the gas constant and T is temperature (in Kelvin). The interfacial free energy s will be different depending on whether the interface is coherent or incoherent, resulting in a different critical particle radius rc0 or rc3. Another critical particle size rc1 is defined to distinguish the controlling mechanism of precipitate growth in a supersaturated solid solution. The possible limiting factors considered are the rate at which atoms are brought to or removed from the interface by diffusion, and the rate at which they cross the interface. The interface reaction is likely to be the rate-controlling step during the early stages of growth since the diffusion distance tends to be zero. At large particle sizes, lattice diffusion is likely to be the slower step, since the continuous removal of solute from the matrix reduces the concentration gradient (the driving force for diffusion). A list of the critical particle sizes is needed (Table 5.1). Since rc0 and rc1 are usually very small, they can be treated as zero in the calculation, that is, diffusion is assumed to be the only controlling mechanism and the particles start to grow at zero radius. As the Orowan process does not occur when particles remain coherent with the matrix, rc3 should be no larger than rc4. If the particle size at the start of coarsening is rc5, the entire picture of the particle size evolution can be illustrated in Fig. 5.2. The relations between these critical sizes are rc0 < rc1 ≤ rc2 ≤ rc5, and rc0 < rc3 < rc4. It is now useful to work out which is larger, rc2 or rc4, which will lead to a better understanding of the softening mechanism. A simple geometrical criterion for coherency is that an interface with a length Dt remains coherent when Dt·d ≤ b, where d is linear strain accompanying precipitation from the matrix and b is Burgers vector of dislocation, that is rc4 = b/2d. Assuming Kq ≈ Ea where Kq is bulk modulus of the precipitate and Ea is Young’s modulus of the matrix, and na ≈ 1/3 where na is Poisson’s ratio, then d will ≈ 1.5e where e is the strain energy constant, and then rc4 ≈ b/3e. Thus, rc2 will always be smaller than rc4, which implies that coherency strengthening is always followed by a coherency softening stage before it is finally taken over by an Orowan looping softening mechanism. Another possibility is that dislocation looping can take place whenever the precipitate is too big or strong for dislocation to cut through, regardless of Table 5.1 Definitions of critical particle sizes rc0 below which particles will dissolve when the interface is coherent rc1 above which diffusion becomes the rate-controlling step rc2 above which the effect of coherency strengthening decreases with increasing particle size rc3 below which particles will dissolve when the interface is incoherent rc4 above which dislocation passes particles by looping instead of shear-cutting rc5 above which coarsening starts to take control

Quantification of phase transformation kinetics

Precipitate size

rc5

rc1

77

Diffusion-controlled n3 coarsening: (rc5 + D · t)1/n3 Diffusion-controlled 2 growth: (rc1 + D · t)1/2 Interface-controlled growth: rc0 + G0·t

rc0 Ageing time

5.2 Schematic diagram of the evolution of precipitate size during ageing. G0 is the growth coefficient during interface-controlled growth, t is the time, D is the diffusion coefficient and n3 is the exponent in coarsening theories.

the coherency nature of the interface between the precipitate and matrix. Although some of the above theories were understood as early as 1960s, they did not receive enough attention when quantification of precipitation hardening was carried out.

5.1.4 Calculation of interparticle spacing When the precipitation fraction increases, the particle size should not be ignored when calculating the interparticle spacing L. Assuming that the precipitates are spherical, the relationship between precipitate fraction f, interparticle spacing and particle radius r is given by:

L = (1.23 2π /(3f ) – 2 2/3)r



[5.3]

When the precipitation fraction increases, the L/r ratio decreases dramatically (Fig. 5.3). L and r become comparable when f increases to about 0.1. The simple formula significantly overestimates the interparticle spacing when the precipitation fraction is large. If the volume fraction can be estimated using the Johnson–Mehl–Avrami (JMA) equation (Section 5.3.1), then particle spacing as a function of time will be determined. This procedure allows the quantification of age hardening to be carried out in a more accurate manner. In concluding this section, the size increment of particles during the early ageing period may be slower than classical parabolic growth law would allow, regardless of whether the phase separation follows spinodal decomposition or a nucleation process. Although sometimes it is difficult to determine the controlling step, and in turn the operating coarsening law, Lifshite–Slyozov– Wagner (LSW) theory (Chapter 7) may be used in practice.

78

Maraging steels

L/r ratio

20

10

0

0

0.2 0.4 Precipitation fraction

0.6

5.3 Comparison of L/r ratio as a function of precipitation fraction, between Eq. [5.3] (solid line) and the simple formula L/r = 2p/3f (dotted line).

5.2

Overall process

The overall transformation curve can be recorded using a dilatometer (Fig. 5.4). Uniform expansion continues until 510°C when a small contraction starts to occur, indicating the start of precipitation at this temperature. This is followed by a small amount of linear expansion with increasing temperature. When the temperature is raised to 602°C, a large contraction appears in the dilatometry curve, which can be taken as the start of the austenite formation (As). At 660°C, the contraction starts to slow down, until 720°C when the curve resumes linear expansion. Therefore, the austenite transformation ends at around 720°C (Af). Complete solution is ensured by heating continuously to 900°C and holding at this temperature for 30 minutes. During cooling to room temperature, there is drastic expansion at approximately 135°C, owing to the sudden start and the rapid transformation from austenite to martensite, corresponding to the martensite start temperature, Ms. The martensite finish temperature (Mf) is about 48°C. Thus, the cobalt-free maraging steel should have a single-phase structure upon cooling to room temperature that is martensite. A discrepancy in dilation at room temperature is apparent in Fig. 5.4. In literature dilatometry curves for T-300 and C-350 (He et al., 2003), the cooling curve normally does not return to zero but to below the original point. This residual strain may be induced by the martensite phase transformation, owing to thermal and metallurgical strains. The transformation-induced plasticity in the free dilatometry cycle is seen in martensite transformation in many experiments (He et al., 2003; Coret et al., 2004). However, the exact mechanism is not clear. It is possible that the lattice had been sheared and could not return to the original position.

Quantification of phase transformation kinetics

Precipitation

79

As 602°C Af 720°C

Dilation 0

510°C

Mf 48°C Ms 135°C

0

Heating rate 4°C min–1 Cooling rate 10°C min–1

100 200 300 400 500 600 700 800 900 Temperature (°C)

5.4 Dilatometry curve of the 2000 MPa grade cobalt-free maraging steel.

Cobalt raises the martensitic phase transformation temperature. In general, the martensitic transformation temperature in 18Ni maraging steels is 50–100°C higher than their cobalt-free counterparts. However, controlling correctly the amount of nickel and molybdenum in cobalt-free maraging steels can still ensure complete martensitic transformation upon cooling to room temperature after solution treatment.

5.3

Precipitation in Fe–12Ni–6Mn maraging-type alloy

5.3.1 Theoretical analysis of the early-stage ageing process Coherent zones, possibly with a bcc structure, form at the early stages of ageing. After these, for example 0.2 hour at 450°C, q-NiMn forms well before peak hardness. Deformation occurs by dislocations cutting through the coherent zones or precipitates. Based on the fact that the increase in yield stress is proportional to the increase in hardness (DH) for maraging steels and applying a coherency-strengthening mechanism, one may obtain:

DH = Ar1/2f 1/2

[5.4]

where r is the radius of the particle, f is the volume fraction of the transformed particles and A is the coefficient relating the increase in hardness to precipitate size and fraction:

80

Maraging steels

A=

MT Ê 3 ˆ (ke )3/2 Á q Ë 2πb ˜¯

1/2

[5.5] where MT is the Taylor factor, q is the conversion constant between Vickers hardness and yield strength, k is a numerical constant, between 3 and 4, taken as 3.5, e is the strain energy constant, m is the shear modulus of the matrix, taken as 81 GPa and b is the Burgers vector of dislocation. Since k, e, m and b are all material constants and can be obtained from the literature, the quantification of DH is now switched to the determination of the particle size r and precipitation fraction f. The relationship between ageing time t and radius r of the zone or precipitate (assumed to be spherical) is given by Zener’s parabolic relationship:

r = a (Dt)1/2

[5.6]

where a is a constant related to solid solubility of precipitate and matrix and composition of the alloy, and D is the diffusion coefficient. When time t is small for the early ageing stage, a can be considered as a constant and calculated following Christian’s suggestion for a spherical precipitate for a small degree of supersaturation:

a=

21/2 (c0 – ca )1/2 (cq – c0 )1/2

[5.7] where c0 is the concentration of the precipitating elements in matrix before ageing, taken as the sum of Ni and Mn, equal to the composition of the alloy, ca is the solid solubility of the controlling elements in the parent phase and cq is the concentration of the elements in the new phase, that is, the q-NiMn precipitate. The Johnson–Mehl-Avrami (JMA) equation can be used to describe the relationship between transformation fraction and time at a certain temperature:

f = 1 – exp [–(kt )m ] feq

[5.8]

where feq is the equilibrium fraction of the precipitation (temperature dependent), k is the reaction rate constant and m is the Avrami index. At the early ageing stage, that is, when kt << 1, the above equation reduces to the following:

f = feq(kt)m

[5.9]

Combining Eqs. [5.4], [5.6] and [5.9], one obtains:

DH = A(afeq)1/2D1/4km/2t(m/2+1/4) = (Kt)n

[5.10]

Quantification of phase transformation kinetics

81

where n is the time exponent in the relationship between the increase in hardness in the early stage of ageing and the ageing time, n = (2m + 1)/4 and K is the temperature dependent rate constant. Assuming that K follows the Arrhenius type of equation: Ê Qˆ K = K 0 exp Á – Ë RT ˜¯

[5.11] where K0 is a pre-exponential term, R is the gas constant, T is temperature (in Kelvin), and the activation energy Q for the precipitation process during ageing can be calculated. Using Eq. [5.11] to replace K in Eq. [5.10] and then taking the natural logarithm of both sides, one may obtain: Q ˆ Ê 1n DH = nÁ ln K 0 – + ln t˜ RT ¯ Ë

[5.12] For a constant increase in hardness DH0 at different temperatures, one will have: Q ln DH 0 [5.13] + – ln K 0 RT n Assuming that n is constant, the activation energy Q can be obtained by plotting ln t versus 1/T, where t is the time to reach DH0 at temperature T. The slope of the straight line is Q/R as can be seen from the above equation. K0 can be obtained simultaneously from the interception of the straight line with the ln t axis. When the activation energy Q and K0 are known, DH during the age hardening can be calculated using Eq. [5.10], in conjunction with Eq. [5.11]. ln t =

5.3.2 Overall ageing process There are a few assumptions in the above theory which may prohibit its application to the overall ageing process: (A1) (A2) (A3) (A4)

coherent precipitate strengthening mechanism; spherical precipitate (zone or particle); constant activation energy; kt << 1, which allows the simplification from Eq. [5.8] to Eq. [5.9]; (A5) constant a for precipitate growth. Strengthening is due to coherent precipitates before the peak hardness is reached and the particles do not change to platelets until overageing takes place. These allow assumptions A1 and A2 to be applied to describe the overall ageing period. Assumption A3, concerning the activation energy, may change during the ageing process. When DH0 takes different values, the

82

Maraging steels

calculations that will be shown later imply that the activation energy does not vary very much. Therefore, the activation energy will be considered to be a constant value in the current model. Assumptions A4 and A5 will not be acceptable when ageing proceeds beyond the early stage. The growth constant a in Eq. [5.6] is no longer constant when the precipitates continue to form and grow, because the composition of the matrix changes a lot when more precipitates form from the matrix. A more accurate way to calculate r is formulated below, considering a as a function of t through the change in c0, the composition of the matrix. Before ageing takes place, c0 is the concentration of the precipitating elements in the alloy. Both are considered as the total amount of Ni and Mn. From Eq. [5.6], the growth rate of particle is:

dr = 1 D1/2a (t )t –1/2 + D1/2 da (t ) t 1/2 dt 2 dt

[5.14]

so

r=

Ú

da (t ) 1/2 ˆ Ê D1/2 Á 1 a (t )t –1/2 + t ˜ dt dt ¯ Ë2

[5.15]



where a can still be calculated from Eq. [5.7]. However, it should be noted that the concentration in the matrix c0, taken as the sum of Ni and Mn, in Eq. [5.7] changes during the ageing process simultaneously with the fraction of the precipitation f, denoted as c¢0, therefore:

c¢0 = c0 – cq f

So, for the overall ageing process, we have: Ê Ê1 da (t ) 1/2 ˆ ˆ DH = AD1/4 feq1/2 Á Ú Á a (t )t –1/2 + t ˜ dt ˜ dt ¯ ¯ Ë Ë2

[5.16]

1/2

(1 – exp(–(kt )m ))1/2

[5.17] where A is as defined in Eq. [5.5]. In Eq. [5.17], if the transformation fraction f is known (i.e. k is known), the precipitate size r can be calculated (assuming D is known), through calculation of c¢0 and a. As a result, DH as a function of time and temperature can be clearly described.

5.3.3 Parameter determination Strengthening In Eq. [5.17], A can be calculated when parameters MT, q, k, e, m, b in Eq. [5.5] are known. The strain energy constant e for precipitation of q-NiMn

Quantification of phase transformation kinetics

83

in the a-iron matrix is:

e=

3Kq (1 + na )d 3Kq (1 + na ) + 2 Ea

[5.18]



where Kq is the bulk modulus of the q-NiMn, na is Poisson’s ratio of ferrite in pure iron, taken as 0.282, Ea is Young’s modulus of ferrite in pure iron, taken as 206 GPa and d is the linear strain accompanying precipitation from matrix:

d=

2(Wq – Wa ) 3(Wq + Wa )

[5.19]

where Wa and Wq are the atomic volumes of the ferrite (0.011 76 nm3/atom) and the q-NiMn precipitate (0.012 24 nm3/atom), respectively. Alternatively, d can be determined from (1 + d)3 = Wq/Wa, which gives a value close to that from Eq. [5.19]. The above parameters are summarised in Table 5.2. The Taylor factor MT is taken as 2.75 for body centred cubic materials and k is assigned as 3.5. Activation energy and Avrami index The activation energy Q is calculated using Eq. [5.13], based on early ageing data. When DH0 takes different values 70, 100, 150 HV, Q is determined as 141, 133 and 125 kJ mol–1, respectively. It is reasonable to treat it as a constant. In the following calculation, Q is taken as 133 kJ mol–1, the average of the above three values. Growth-related constants n and m are 0.475 and 0.45, respectively. Reaction rate constant in the Johnson–Mehl–Avrami equation Experimental research shows that the peak hardness is reached either by holding at 400°C for 16 hours, at 450°C for 1.4 hours or at 500°C for 0.24 hour. Assuming that the precipitate fraction corresponding to the peak hardness at 400°C or 450°C is known, f/feq is known, one can obtain the value of the pre-exponential term k0, if the reaction rate constant in the Johnson–Mehl–Avrami equation k is assumed to follow an Arrhenius type equation with the same activation energy as K: Table 5.2 Values of parameters involved in the calculation of precipitation strengthening in Fe–12Ni–6Mn maraging type alloy M T

q (MPa/HV) k

Wa (nm3) Wq (nm3) d

2.75

2.5

0.011 76

3.5

e

m (GPa) b (nm)

0.012 24 0.013 33 0.0084 81

0.248

84

Maraging steels



Ê Qˆ k = k0 exp Á – Ë RT ˜¯

[5.20]

Combining Eq. [5.20] and Eq. [5.8], one will obtain:

k0 =

(–ln(1 – f /feq ))1/m ÊQˆ exp Á ˜ tp Ë RT ¯

[5.21]

where tp is time to reach the peak hardness. The percentage of the precipitate formed at peak hardness will be determined later. As will also be shown later, the precipitation fraction corresponding to the peak hardness at 400°C is higher than that at 450°C, which partially contributes to the stronger age hardening effect at 400°C than at 450°C. Growth and diffusion constants Eq. [5.7] shows that a is a function of c0, cq and ca. In the calculations below, as discussed earlier, c0 will be replaced by c¢0, calculated from Eq. [5.16]. Both cq and ca are to be considered as the sum of Ni and Mn in atomic fraction. Since NiMn only contains Ni and Mn, cq always equals 1. The values of ca at different temperatures are calculated using Thermo-Calc with Kaufman binary (KP) database (Table 5.3, together with the equilibrium amount of NiMn precipitate). The value for c0 is 0.1728 in atomic fraction, which is the equivalent of 0.1765 in the weight fraction, that is the sum of 11.9 wt% Ni and 5.75 wt% Mn, the precise composition of the alloy studied. At 450°C, the diameter of precipitate is around 3 nm after 0.2 hour ageing and 6 nm after 2 hours (peak hardness). Based on these, the diffusion coefficient can be estimated. One may assume that D follows an Arrhenius type equation with the same activation energy as K:

Ê Qˆ D = D0 exp Á – Ë RT ˜¯

[5.22]

Then, the pre-exponential term D0 can be obtained by combining Eq. [5.22] and Eq. [5.15]: Table 5.3 Results calculated with Thermo-Calc using Kaufman binary database related to precipitation in Fe–12Ni–6Mn maraging type alloy Temperature (°C)

350

375

400

425

450

Ni in ferrite (at%) Mn in ferrite (at%) ca (at%) feq (vol%)

6.6 0.4 7.0 11.4

6.7 0.5 7.2 11.1

6.8 0.7 7.5 10.8

7.0 0.9 7.9 10.5

7.2 1.1 8.3 9.7

Quantification of phase transformation kinetics

85

2



Ê ˆ Á ˜ ÊQˆ r D0 = Á ˜ exp Á ˜ Ë RT ¯ 1 d ( ) a t ˆ Ê Á Á a (t )t –1/2 + t 1/2 ˜ dt˜˜ ÁË Ú Ë 2 dt ¯ ¯

[5.23]

Critical nucleus size Critical nucleus size (Rc) is the size of the precipitate above which the nucleus is stable and able to grow. It can be calculated as:

Rc =

–2s N A Wq DGn

[5.24]

where s is the interface energy per unit area between precipitate and matrix, taken as 0.2 J m–2, NA is Avogadro’s number and the Gibbs energy difference between the precipitate and ferrite DGn can be calculated using Thermo-Calc software with the KP database. Rivera-Díaz-del-Castillo and Bhadeshia (2001) calculated the critical nucleus size taking into account the Gibbs–Thomson capillarity effect, which influences the equilibrium compositions at the particle/matrix boundary:

Rc =

2ca G c 0 – ca

[5.25]

where the capillarity constant G is given by:

G=

s N AWq 1 – ca RT cq – ca

[5.26]

DGn and Rc calculated from both methods at various temperatures are listed in Table 5.4. When calculating the incubation period, the larger Rc values calculated from Eq. [5.24] are used. It should be noted that even for size smaller than the critical radius, a parabolic growth law described by Eq. [5.6] is assumed. Precipitation fraction at peak hardness The determination of precipitation fraction f at peak hardness, fp, as a percentage of the equilibrium precipitation fraction feq at different temperatures involves an optimisation procedure. Using the various transformation fraction values, the ageing hardening curves at various temperatures can be obtained. One may therefore obtain the transformation fraction value to best fit the calculated hardness curves with the experimental curves (Table 5.5).

86

Maraging steels

Table 5.4 Driving force and the critical nucleus radius of precipitation in Fe–12Ni–6Mn maraging type alloy Temperature (°C)

350

375

400

425

450

Driving force (–DGn/RT) Rc (nm) (Eq. [5.24]) Rc (nm) (Eq. [5.25])*

0.97 1.05 0.39

0.86 1.10 0.39

0.77 1.16 0.41

0.67 1.24 0.43

0.59 1.34 0.46

*

Rivera-Díaz-del-Castillo and Bhadeshia, 2001

Table 5.5 Values of parameters obtained by best fitting Temperature (°C) k0(s–1) 400 450 500

D0(m2s–1)

2.392 ¥ 105 2.532 ¥ 10–10 2.392 ¥ 105 2.532 ¥ 10–10 2.392 ¥ 105 2.532 ¥ 10–10

fp/feq

feq(vol%)

fp(vol%) rp(nm)

0.56 0.44 0.39

10.8 9.7 8.7

6.1 4.3 3.4

3.9 3.0 2.2

In general, peak hardness increases with decreasing temperature owing to greater supersaturation giving a greater volume fraction of precipitate. This agrees with the calculated results in Table 5.3, where the increase of ca with increasing temperature means a decrease in the degree of supersaturation.

5.3.4 Precipitate size and fraction as functions of time and temperature As discussed earlier, the matrix concentration c¢0 and growth constant a change over the ageing period, as functions of time and temperature (Fig. 5.5). Their values change significantly during the ageing and therefore taking them as constants cannot be justified. The precipitation fraction and precipitate size as functions of time and temperature are shown in Fig. 5.6. In these two figures, the curve for 400°C reflects the age hardening curve up to the peak hardness.

5.3.5 Time–temperature–precipitation (TTP) diagram Based on Eq. [5.8] or Eq. [5.15], the time-temperature-precipitation (TTP) curve can be obtained for lines either corresponding to 5% (start) and 95% (completion) of the equilibrium precipitation amount (for precipitate fraction), or corresponding to the critical radius (start) and an arbitrary precipitate particle size of 5 nm in diameter (Fig. 5.7). For small particles, coherency strain hardening increases with increasing particle size, whereas for larger particles, the coherency strain hardening decreases with increasing particle size, giving rise to a maximum in the strengthening (peak hardness) at a critical particle radius rp which is of the order of 0.25e–1b. For the Fe–12Ni–6Mn system, it is 7.4 nm (in radius). This value is bigger than experimental observation and calculated results shown in Table 5.5.

Quantification of phase transformation kinetics

87

0.18 350∞C 375∞C 400∞C 425∞C 450∞C

c¢0

0.16

0.14

0.12

0.1

0

5

10 Time (h) (a)

0

5

10 Time (h) (b)

15

20

0.5

0.45

a

0.4

0.35

0.3

0.25

15

20

5.5 Matrix concentration c ¢0 (a), and growth constant a (b), as functions of time and temperature.

5.3.6 Summary The growth of the precipitate and the increase in the precipitation fraction as functions of time and temperature can be treated accurately. The model can be applied to the overall ageing process (excluding overageing). TTP diagrams can be determined with respect to precipitate size and fraction. The precipitation process is far from completion when peak hardness is reached. Ageing at 400°C produces precipitates with a higher fraction and larger size than at 450°C and 500°C. This explains why ageing at 400°C produces a stronger hardening effect.

88

Maraging steels

Precipitate fraction (%)

8

6

350∞C 375∞C 400∞C 425∞C

4

2

0 0.01

0.1

1 Time (h) (a)

10

100

0.1

1 Time (h) (b)

10

100

5

Precipitate size (nm)

4

3

2

1

0 0.01

5.6 Precipitate fraction (a) and size (b) as functions of time and temperature.

5.4

18 wt% Ni C250

There are differing opinions on the interpretation of phase transformations taking place during continuous heating (Table 5.6), using the differential scanning calorimetry (DSC) curves in Fig. 5.8 as an example. The exothermic process at 310–510°C contributes only limited hardening effects. The formation of intermetallic precipitates, which is the main precipitation process, is the exothermic reaction between 535°C and 603°C. The endothermic peak at

Quantification of phase transformation kinetics

89

440

Temperature (°C)

420

Start (r = Rc)

400

End (r = 2.5 nm) Start (5% feq)

380

End (95% feq)

360

340 0.01

0.1

1

10 Time (h)

100

1000

5.7 TTP curves for precipitate size and fraction. Table 5.6 Interpretation of DSC results, using the DSC curve obtained at a 50°C min –1 heating rate as an example Zone DSC feature

Temperature Possible transformations span (∞C)

I Exothermic 310–510 II Exothermic 535–603 III Endothermic 635–730 IV Endothermic 730–800

Recovery of martensite Formation of carbide precipitates (minor hardening) Formation of coherent precipitation zones Formation of the main strengthening precipitates Austenite reversion Formation of retained austenite* by diffusion Martensite to austenite by shear Dissolving of precipitates or recrystallisation

*Retained austenite is the austenite not transformed after cooling. This term is used here to denote the part of reverted austenite formed during heating that retains the austenite structure during the following cooling to room temperature. The other part of reverted austenite will transform back to martensite.

635–730°C corresponds to the martensite to austenite transformation or the formation of austenite that can be retained at room temperature. Grain growth may also result in exothermic effects. It is accepted that the peak at 535–603°C is from the precipitation process. However, there are different opinions about the austenite reversion peak. Thermodynamic calculation can estimate the reversion completion temperature, which agrees well with the termination temperature of the endothermic peak III (Section 5.4.1). The transformation enthalpy corresponding to this peak is also in agreement with the value for ferrite a to g transformation in pure iron, 16 J g–1 (Section 5.4.1). The martensite to

90

Maraging steels

austenite reversion during continuous heating could take place through shear, or diffusion, or a combination of these two mechanisms in Fe–Ni alloys (Sagaradze et al., 2002). The transformation temperatures are not affected by heating rate in shear mode. The increase of transformation temperatures with increasing heating rate as observed here is a strong indication of diffusion mechanism for austenite reversion. Based on this evidence, the transformation at peak III is the (major) martensite to austenite reversion reaction. No Curie point is observed in the DSC curves at different heating rates. The major reactions of austenite reversion and precipitate formation will be analysed in detail in the following sections.

5.4.1 Austenite reversion The usual accuracy in determining enthalpy value is within the range of ±5%, which is slightly affected by the determination of the start and finish temperatures of the transformation. Large errors are associated with the enthalpy values at 5 and 10°C min–1, which is due to the difficulty in determining the start and end temperatures of the DSC peaks (Table 5.7). The enthalpy values at other heating rates are close to the latent heat of the ferrite a to g transformation in pure iron, a confirmation that the peaks correspond to the austenite reversion transformation. In order to demonstrate the influence of heating rate clearly, the peaks in Fig. 5.8 have been shifted downwards and the base line corrected so that all the onset and termination points are on the same horizontal line, while preserving the shape of the curve (Fig. 5.9). Determination of transformed fraction Usually, for DSC experiments, the degree of transformation at any given time is taken equal to the fraction of heat released or absorbed: t

Út H dt f (t ) = t Út H dt s

[5.27]

E



s



Table 5.7 Parameters of the DSC peak and transformation enthalpies for austenite reversion at various heating rates Heating rate Start temperature (°C min–1) (°C)

Peak temperature (°C)

End temperature Enthalpy (°C) (J g–1)

5 10 20 30 40 50

636 649 662 671 677 683

680 700 710 718 725 730

610 615 620 625 630 635

7.4 10.2 13.5 14.6 15.5 13.8

Quantification of phase transformation kinetics

91

1 50°C 40°C 30°C 20°C 10°C 05°C

Heat flow (mW mg–1)

0.8

0.6

min–1 min–1 min–1 min–1 min–1 min–1

0.4

0.2

0 300

350

400

450

500 550 600 Temperature (°C)

650

700

750

800

5.8 Recorded differential scanning calorimetry (DSC) curves for the C250 alloy at different heating rates.

where H is the heat flow measured, f(t) is the degree of transformation at any given time (t) and tS and tE are transformation start and end time, respectively. The denominator in Eq. [5.27] is the total enthalpy for a transformation calculated from the corresponding peak in the DSC curves (Fig. 5.9). The total enthalpy is the integration of heat flow H over a period of time, instead of temperature. The degree of transformation as a function of time or temperature can be calculated from the DSC signal (Fig. 5.10). The calculated transformed fraction curves trace the course of the martensite a¢ to g reversion of the C250 alloy. Equilibrium fraction and determination of activation energy The Thermo-Calc package can estimate the equilibrium austenite phase fraction as a function of temperature (Fig. 5.11). The calculated temperature for austenite reversion completion is 674°C, in good agreement with the value 680°C measured at a heating rate of 5°C min–1. The activation energy of the austenite reversion process can be estimated based on the DSC results at different heating rates using a modified Kissinger method:

ln

Tf2 = E + ln E + ln b f RK 0 f RTf



[5.28]

where Tf is the characteristic temperature for a given process, f is the heating rate, E is the activation energy, R is the gas constant and K0 and bf are constants. The activation energy E is given by the gradient of the

92

Maraging steels 0.3

Heat flow (mW mg–1)

0.25 0.2

50°C 40°C 30°C 20°C 10°C 05°C

min–1 min–1 min–1 min–1 min–1 min–1

0.15

0.1

0.05 0 600

620

640

660 680 Temperature (°C)

700

720

740

5.9 Processed DSC peaks for austenite reversion at different heating rates.

straight line obtained by linear regression on the plot of ln(Tf2/f) versus 1/(RTf). Using the peak temperature at different heating rates, the activation energy of the austenite reversion process is estimated as E = 342 kJ mol–1 (Fig. 5.12). Kissinger type methods were originally derived for homogeneous reactions, but can also be applied to heterogeneous reactions. The activation energy of austenite reversion, 342 kJ mol–1, can be considered close to the activation energy for lattice diffusion of substitutional atoms in a-iron, Ni, 245.8 kJ mol–1, Ti, 272 kJ mol–1, and Mo, 238 kJ mol–1, which implies that this transformation is a diffusion-controlled process. Calculation of transformation kinetic parameters The kinetics of an isothermal transformation is usually expressed by the modified JMA equation:

f = 1 – exp (– kt n ) feq

[5.29]

where f is the volume fraction of the product phase, feq is the equilibrium fraction at the studied temperature, k is the reaction rate constant and n is the Avrami index. Within the temperature range of the DSC peaks recorded at various heating rates (610–730∞C), the equilibrium austenite fraction increases from about 73% to 100%. In the following text, f is the transformation fraction which varies in the range of 0–feq, and f/feq is the degree of transformation, ranging from 0 to 1. The reaction rate constant k is temperature dependent and can be expressed as:

Quantification of phase transformation kinetics

93

1 50°C 40°C 30°C 20°C 10°C 05°C

Transformed fraction

0.8

0.6

min–1 min–1 min–1 min–1 min–1 min–1

0.4

0.2

0 600

620

640

660 680 Temperature (°C) (a)

700

720

740

1

Transformed fraction

0.8

0.6

0.4

0.2

0

0

100

200

300

400 500 Time (s) (b)

600

700

800

900

5.10 Calculated transformed austenite fraction as a function of (a) temperature and (b) time at different heating rates.

Ê – Eˆ k (T ) = k0 expÁ ˜ Ë RT ¯

[5.30] where k0 is the pre-exponential factor, E the activation energy, R the gas constant and T the temperature. The activation energy of the austenitisation process is estimated as 342 kJ mol–1 in the previous section. Since Eq. [5.29] is used to depict the isothermal process, the next step is to use finite isothermal steps to represent the non-isothermal process based on the additivity principle from Scheil. A computer program is needed to optimise

94

Maraging steels 100

Austenite fraction (%)

90 80 70 60 50 40 30 400

450

500 550 600 Temperature (°C)

650

700

5.11 Equilibrium volume fraction of austenite as a function of temperature. All the possible phases, a matrix, austenite and various types of precipitates are included in the calculation.

13

ln (T f2/f)

12

11

10

0 0.124

0.126

0.128 0.130 1000/(RTf) (mol kJ–1)

0.132

0.134

5.12 Determination of the activation energy for austenite reversion from the peak temperatures at different heating rates. Activation energy, in kJ mol–1, is the slope of the straight line.

the kinetic parameters n and k0, so that the best fit between the experimental (derived from DSC data) and the calculated transformed fraction versus T/t curves can be achieved. The Avrami index n can normally be assumed to be temperature independent, which is valid for most transformations in an appreciable temperature range. These two parameters are determined as n = 0.97 and k0 = 1.73 ¥ 1017. Using the derived n, k0 and E, the transformed fraction as a function of time at various heating rates can be calculated (Fig. 5.13). A good fit between the experimental and the calculated results is evident.

Quantification of phase transformation kinetics

95

0.9 0.8

Transformed fraction

0.7 0.6

50∞C min–1 (exp.) 50∞C min–1 (cal.) 40∞C min–1 (exp.) 40∞C min–1 (cal.) 30∞C min–1 (exp.) 30∞C min–1 (cal.) 20∞C min–1 (exp.) 20∞C min–1 (cal.) 10∞C min–1 (exp.) 10∞C min–1 (cal.) 05∞C min–1 (exp.) 05∞C min–1 (cal.)

0.5 0.4 0.3 0.2 0.1 0

0

100

200

300

400

500 600 Time (s)

700

800

900

1000

5.13 Comparison between the calculated austenite transformation fraction and DSC experimental values.

According to Christian’s kinetics theory, an n value close to 1 may correspond to one of the following mechanisms: thickening of long cylinders, needles and plates of finite long dimensions, or grain boundary nucleation after saturation. However, there is no straightforward explanation for the n value obtained for austenite reversion. It remains unclear which mechanism takes control.

5.4.2 Precipitate formation The enthalpy values of the precipitation process at different heating rates are close (Table 5.8), which indicates that about the same amount of precipitate forms regardless of heating rate. Following the similar procedures described in Section 5.4.1, the activation energy of the precipitation process is determined to be 205 kJ mol–1. The activation energy for precipitate formation, 205 kJ mol–1, can be considered as being close to the lattice diffusion activation energy of Ni, Ti, and Mo in a-Fe, in agreement with study of a Fe–18Ni–8Co–5Mo alloy from resistivity data. The Thermo-Calc package can estimate the equilibrium precipitate fraction as a function of temperature. The type of precipitate is assumed to be Ni3Ti

96

Maraging steels

Table 5.8 Parameters of the DSC peak and transformation enthalpies for the main precipitate formation at various heating rates Heating rate Start temperature (°C min–1)* (°C)

Peak temperature (°C)

End temperature Enthalpy (°C) (J g–1)

10 20 30 40 50

522 536 547 556 562

570 585 590 596 603

505 520 525 530 535

–1.8 –1.5 –1.1 –1.7 –1.6

*The DSC curve at 5°C min–1 does not allow an accurate assessment of the exothermic peak.

only. Therefore, the phases included in the calculation are a and Ni­3Ti. Although austenite is a stable phase within the temperature range for ageing treatments, it does not form until the alloy is seriously overaged. Therefore, when the fraction of precipitate is calculated, the austenite phase is not included in the calculation. The equilibrium precipitate fraction decreases with increasing temperature (Fig. 5.14). However, such temperature dependence is very weak. In the following calculations on precipitation kinetics, the precipitation process is assumed to be complete, reaching the equilibrium precipitate fraction, which is assumed to be temperature independent, 2.0 vol%. The processed DSC curves of the precipitation process at different heating rates are displayed in Fig. 5.15. Since the equilibrium precipitate fraction can be considered to be a constant function of temperature, a simpler approach, rather than applying the additivity rule, can be used to trace the precipitation kinetics:

f = 1 – exp (– q n ) feq

[5.31]

The difference between Eq. [5.29] and Eq. [5.31] is the introduction of a new state variable q:

q=

t

Ú0 k(T )dt



[5.32]

where k(T) has the form of Eq. [5.30]. This model has been successfully applied to describe the kinetics of phase transitions or transformations during continuous heating such as crystallisation, recrystallisation and the precipitation process. The JMA parameters for the precipitation process are derived as n = 1.46 and k0 = 1.60 ¥ 1011. The calculated degree of precipitation shows good agreement with the experimental values from DSC (Fig. 5.16). The n value, 1.46, seems to suggest that the precipitation process follows the diffusion-controlled growth of small dimensions at zero nucleation rate. Although the value of kinetic parameters may give some indication to the

Quantification of phase transformation kinetics

97

Precipitation fraction (vol %)

2.20 2.15 2.10 2.05 2.00 1.95 1.90 1.85 1.80 500

520

540 560 580 Temperature (°C)

600

620

5.14 Equilibrium volume fraction of Ni3Ti precipitate as a function of ageing temperature. The phases included in the calculation are a matrix and Ni­3Ti only. The equilibrium precipitate fraction is considered to be a constant 2.0 vol% in the kinetics calculations. 0

Heat flow (mW/mg)

–0.01

–0.02 50∞C min–1 40∞C min–1 –0.03

30∞C min–1 20∞C min–1 10∞C min–1

–0.04 500

510

520

530

540

550 560 570 Temperature (°C)

580

590

600

610

5.15 Processed DSC peaks for the main precipitation process at different heating rates.

mechanism of the phase transformations taking place, there is still a lack of fundamental understanding of this topic. For instance, the value of n for the austenite reversion in a PH17-4 precipitation hardening stainless steel was calculated as 0.5, with activation energy as 138.8 kJ mol–1. The activation energy of the precipitation process in a C250-grade was estimated as being between 101 and 181 kJ mol–1 with increasing time, whereas the n value was about 0.2–0.4 for different temperatures.

98

Maraging steels 1

0.9

Degree of precipitate fraction

0.8 0.7 0.6 0.5

50∞C min–1 (exp.) 50∞C min–1 (cal.) 40∞C min–1 (exp.) 40∞C min–1 (cal.) 30∞C min–1 (exp.) 30∞C min–1 (cal.) 20∞C min–1 (exp.) 20∞C min–1 (cal.) 10∞C min–1 (exp.) 10∞C min–1 (cal.)

0.4 0.3 0.2 0.1 0

0

50

100

150

200 Time (s)

250

300

350

400

5.16 Comparison between the calculated degree of precipitation and DSC experimental values.

5.4.3 Isothermal ageing Austenite reversion The good agreement between the experimental and calculated degree of transformation at different heating rates confirms the applicability of the JMA theory to the transformation and the accuracy of the derived JMA kinetic parameters n, k0, and E. These parameters can be used to trace the course of austenite reversion in the C250 alloy in practice for any heating path. In this section, the austenite reversion at a given ageing temperature is simulated by employing Eq. [5.29] for an isothermal process (Fig. 5.17). In the range of practical use, an ageing time no longer than 10 hours, the model demonstrates good agreement with experimental observations (Fig. 5.18). When ageing time is longer than 10 hours at 538°C, the experimentally observed reverted austenite fraction is lower than the predicted amount. The kinetic parameters used are derived from continuous heating experiments. In essence, calculation of isothermal kinetics using such parameters is an extrapolation procedure and errors may be expected. A close look at Fig. 5.13 reveals that the discrepancy between experimental and calculated transformed

Quantification of phase transformation kinetics

99

fractions becomes large when the heating rate is low. The long-term isothermal transformation kinetics may deviate from the experimental values. The alloy used in the experimental work is Fe–18.6Ni–7.65Co–4.97Mo–0.45Ti (wt%), in comparison with Fe–18.06Ni–8.29Co–5.01Mo–0.47Ti, the alloy used for DSC. This composition difference, though not large, may contribute to some extent to the deviation illustrated in Fig. 5.18. 0.6 538∞C 482∞C Austenite fraction

427∞C 0.4

0.2

0 0.01

0.1

1

10

100 1 ¥ 103 1 ¥ 104 1 ¥ 105 1 ¥ 106 1 ¥ 107 Time (h)

5.17 Calculated degree of austenite reversion as a function of time at three ageing temperatures. 0.6

Austenite fraction

0.5

0.4

0.3

0.2 Equil. (0.55)

0.1

Cal. Exp.

0 0.1

1

10 Time (h)

100

1000

5.18 Calculated fraction of retained austenite (austenite reversion) and the equilibrium fraction in comparison with experimental data during ageing of a C250 grade at 538°C.

100

Maraging steels

A detectable amount of austenite forms after 50 hours at 482°C, which is reflected in our calculation, see Fig. 5.17. It may have been noticed that at the early stage of the transformation, Fig. 5.13, the discrepancy between the experimental and the calculated curves is large. The model obtained, to improve the fitting, by allowing n to change with temperature and heating rate would be more complicated and less useful than the present model where n is taken as a constant. Precipitation Using the kinetic parameters n, k0 and E derived in Section 5.4.2, the ageing kinetics in terms of degree of precipitation process at a given temperature can be simulated (Fig. 5.19). The precipitation process in the C250 alloy is considered as one stage here, without distinguishing between the types of precipitates and their precipitation periods, although Fe 2Mo appears after ageing over 3 hours at 482°C. The contraction in a dilatometry curve caused by precipitate formation increases with the amount of titanium in the matrix, which implies precipitation of Ni3Ti or Ti-enriched particles. There is not yet an effective experimental method to characterise directly the precipitate fraction. The fact that the composition of the hardening precipitates changes with time makes estimation of the precipitate fraction even more difficult (Section 8.1). Nevertheless, the quantification method in this section provides a way of simulating the precipitation kinetics in precipitation hardening steels. 1 538∞C

Degree of precipitation

0.8

482∞C 427∞C

0.6

0.4

0.2

0 1¥10–4

1¥10–3

0.01

0.1 Time (h)

1

10

100

5.19 Calculated degree of precipitation at three different ageing temperatures. A 100% precipitation process corresponds to an actual precipitate fraction of 2.0 vol%.

Quantification of phase transformation kinetics

101

5.4.4 Summary Differential scanning calorimetry (DSC) can trace the phase transformation kinetics of maraging steel during heating. Reactions corresponding to precipitate formation (exothermic) and austenite reversion (endothermic) are revealed in the DSC curves during heating. Based on the calorimetric data, the kinetics of precipitate formation and austenite reversion can be modelled using the JMA theory. Good agreement between the calculated transformed fraction and the experimental data from DSC measurement is achieved for both precipitate formation and austenite reversion. The derived JMA kinetic parameters can then be used to calculate the isothermal ageing kinetics. Both the precipitation process and austenite reversion during ageing seem to be controlled by the lattice diffusion of substitutional atoms. Strictly, the theoretical analysis in this section has its flaws in that the interaction between precipitation and austenite formation is not considered. There is an overlap between these two transformations in the DSC curve. Since each of them appears as a complete peak on its own, it is difficult to remove the overlapping parts. However, this should not undermine the general conclusions of the section.

5.5

Phase fraction by X-ray diffraction analysis

5.5.1 Precipitate The martensite matrix of maraging steels has a body centred cubic (bcc) structure, whose unit cell contains two atoms. The volume of one unit cell, V, can be estimated from the chemical composition of the alloy, when the alloy is of a fully martensitic structure: [5.33] V = a 3 = 2 ¥ S XiVi /100 i where a is the lattice constant, Xi and Vi are the atomic percentage and the atomic volume of the i-th element, respectively. When precipitates form, the composition of the martensite matrix changes from Xi to X¢i, resulting in a change of V to V¢ and a to a¢. When a certain number of precipitate-forming elements leave the martensitic matrix to form precipitates, their positions are occupied by other atoms of different atomic volume (Table 5.9). For instance, the precipitation of molybdenum atoms, whose atomic volume is larger than V/2, will result in V¢ smaller than V, whereas the precipitation of nickel atoms will lead to a larger V¢ than V. The lattice constant a relates to the diffraction angle q through: d{hkl } =



a h + k2 + l2 2



[5.34]

102

Maraging steels

Table 5.9 Volume of the alloying elements Element

Volume (cm3 mol–1)

Volume (¥ 10–29 m3/cell)

Ni Co Fe Mo Al Ti

6.59 6.7 7.1 9.4 10 10.64

1.094 1.112 1.179 1.561 1.661 1.767

68 96 4 46 13 44

and



l = 2d{hkl} sin q{hkl}

[5.35]

where {hkl} is the index of a reflection plane, d{hkl} is the spacing of the {hkl} planes and l is the wavelength of the Cu Ka1 radiation. Therefore, a can be calculated from an X-ray diffraction (XRD) profile. The change in a, Da, caused by precipitation, is reflected in the change in 2q{hkl} in XRD profiles. Usually, the absolute 2q{hkl} value varies in different XRD scans of the same specimen, probably through some deficiency in the experimental method.  However, the intervals, in degrees, between 2q values for different planes remain the same for different measurements of a same sample. Therefore, D2q{220}-{110}, the change in the interval between 2q{220} and 2q{110} can be used as a parameter to monitor the change in XRD profiles caused by ageing and precipitation. In essence, this approach is a type of internal calibration of the absolute 2q angles, akin to the more standard internal calibration technique using standard materials with precisely known lattice parameters such as silicon powders deposited on sample surfaces. The correlation between precipitate fraction f, Da and D2q{220}-{110} can be established when the precipitate type is known. This method is only applicable when no austenite phase, a phase of no fixed composition as ageing proceeds before equilibrium, forms during ageing. A significant hardening effect has been achieved in all the aged samples (Fig. 5.20). The precipitate formed in the C250 alloy during ageing can be Ni3(Ti,Mo) or Fe2Mo. The precipitate type is therefore assumed to be Ni3Ti, Ni3Mo or Fe2Mo in the calculation. The maximum precipitate fraction allowed by the alloy composition is 0.56 mol% for Ni3Ti, 3 mol% for Ni3Mo and 3 mol% for Fe2Mo, respectively, when all the titanium or molybdenum atoms have formed precipitates. Here, mol% is the molar percentage of an intermetallic compound but not the molar percentage of atoms. For instance, 1 mol% Ni3Ti equals 4 mol% atoms, that is, about 4 vol% of Ni3Ti precipitates. The equilibrium precipitate fraction calculated using Thermo-Calc is 0.54 mol% for Ni3Ti, 0.95 mol% for Ni3Mo and 2.75 mol% for Fe2Mo, respectively, when only the matrix a phase and one type of precipitate are included

Quantification of phase transformation kinetics 700

538∞C 482∞C 427∞C

600 Vickers hardness

103

500

400

300

200 0

1

Ageing time (h)

10

100

5.20 Age hardening curves showing Vickers hardness of the C250 alloy at different ageing temperatures.

in the calculation. The correlations between precipitate fraction f, Da and D2q{220}-{110} are established first (Figs. 5.21 and 5.22). The values for Da are negative since the lattice constant after precipitation of Ni3Ti, Ni3Mo or Fe2Mo during ageing becomes smaller than that in the as-quenched condition. The absolute value, –Da, is used here because it reflects the amount of precipitation. Then, from the D2q{220}-{110} value obtained by comparing the XRD profiles of samples under different conditions, the corresponding precipitate fraction is calculated whenever possible (Table 5.10). The method is first applied to calculate the precipitate fraction in an 18 wt% Ni C350 maraging grade. Its composition is Fe–3.96Mo–18.14Ni– 0.1Al–12.5Co–1.65Ti in wt%. The lattice constant measured by X-ray diffraction changes from 0.2878 to 0.2874 nm after ageing at 460°C, which corresponds to 1.44 mol% Ni3Ti, 3.64 mol% Ni3Mo or 1.27 mol% Fe2Mo precipitates. The equilibrium fraction at this temperature is 1.97 mol% for Ni3Ti, 1.49 mol% for Ni3Mo or 3.89 mol% for Fe2Mo. The lattice change becomes bigger when austenite forms, that is the formation of reverted austenite leads to a decrease in the lattice constant of the martensite matrix, as does the precipitation of Ni3Ti, Ni3Mo or Fe2Mo. If reverted austenite forms but is undetected, the precipitate fraction will be overestimated. The extent of such overestimation is difficult to evaluate because the composition of the austenite phase formed evolves during ageing before reaching equilibrium. For the C250 alloy aged at 482°C, the calculated fraction of Ni3Mo and Fe2Mo seems to be reasonable, whereas the Ni3Ti fraction at 3 and 10 hours exceeds the maximum Ni3Ti amount allowed. This indicates that the precipitates formed are of Ni3(Ti,Mo) type in early stages and then Fe2Mo

104

Maraging steels

Precipitate fraction (mol %)

6 5 4 3 2

Ni3Ti Ni3Mo

1

Fe2Mo

0 0.000

0.002

0.004

0.006 –Da (Å)

0.008

0.010

0.012

5.21 Correlations between Da and precipitate fraction for different types of precipitates, with limits extended to beyond the maximum possible precipitate fraction for demonstration purposes. The values for Da are negative since the lattice constant after ageing becomes smaller than that in the as-quenched condition. The absolute value, –Da, is used here because it reflects the amount of precipitation.

Precipitate fraction (mol %)

6 5 4 3 2

Ni3Ti Ni3Mo

1

Fe2Mo

0 0.0

0.1

0.2 D2q(220)–{110} (°)

0.3

0.4

5.22 Correlations between D2q{220}-{110} and precipitate fraction for different types of precipitates, with limits extended to beyond the maximum possible precipitate fraction for demonstration purposes.

starts to form when ageing proceeds. The precipitate fraction increases when ageing is prolonged. For an ageing time of 50 hours, the calculated values for both Ni3Ti and Ni3Mo are far over the maximum possible amount. This suggests that Fe2Mo is the main precipitate type under this condition. Another possible reason is that reverted austenite has started to form, which results in a change in a and 2q in the same direction as the precipitation of Ni3Ti, Ni3Mo or Fe2Mo. However, no austenite is observed at this condition. When the amount of austenite is lower than 2 vol%, it is not detectable in normal X-ray diffraction analysis. For steel aged at 538°C for 1 and 3 hours,

Quantification of phase transformation kinetics

105

Table 5.10 Precipitation fraction f of precipitates Ni3Ti, Ni3Mo and Fe2Mo Heat treatment

2q{220}-{110}

Water-quenched 427°C, 1 h 427°C, 3 h 427°C, 10 h 427°C, 50 h 482°C, 1 h 482°C, 3 h 482°C, 10 h 482°C, 50 h 538°C, 1 h 538°C, 3 h 538°C, 10 h 538°C, 50 h

53.7914 53.7748 53.7626 53.7538 53.7648 53.8012 53.8067 53.8173 53.8721 53.9450 53.8975 53.9820 53.9240

D2q{220}-{110} f (mol%) (aged-quenched) Ni3Ti 0 –0.0166 –0.0288 –0.0376 –0.0266 0.0098 0.0153 0.0259 0.0807 0.1536 0.1061 0.1906 0.1326

0 * * * * 0.44 0.69 1.17 + + + ** **

Ni3Mo 0 * * * * 1 1.63 2.76 + + + ** **

Fe2Mo 0 * * * * 0.16 0.25 0.42 1.30+ 2.47+ 1.71+ ** **

*

An unknown type of precipitate forms in this ageing condition. Reverted austenite may have formed, although is not detected, in this ageing condition. ** Reverted austenite was clearly detected in this ageing condition. +

the calculated fraction exceeds the maximum amount of Ni3Ti and Ni3Mo. This may also be explained by the formation of Fe2Mo or reverted austenite, or both. For steel aged at 538°C for 10 and 50 hours, the austenite phase clearly exists (Fig. 5.23) and the amount is calculated as 7% and 12.5%, respectively, using Eq. [5.36], detailed in Section 5.5.2. For the steel aged at 427°C, the D2q{220}-{110} values are all negative, that is, the volume of the unit cell after precipitation V¢ is larger than that prior to precipitation V and the values of Da are positive. This volume change is different from what takes place at 482°C and 538°C and may indicate the formation of a different type of precipitate at 427°C from those at 482°C and 538°C. The precipitates at 427°C and 482°C are different in nature in the C250 alloy. In a C350 alloy, the precipitation process has two separate parts, one for the evolution of the w phase at 400–480°C and the other for nucleation and growth of Ni3(Ti,Mo) in a higher temperature range (Tewari et al., 2000). The composition of the w phase formed in a Fe–18Ni–9Co–3Mo (at%) alloy after ageing at 414°C for 15.8 hours is Fe–47Ni–1Co–40Mo. Precipitation of an w phase of this composition in C250 alloy would not cause V¢ to be larger than V. On the other hand, if the precipitate formed is very much Ni-enriched and consists of small quantities of large atoms like Mo and Ti, a larger V¢ than V may be obtained. Nevertheless, in general, the absolute value of D2q{220}-{110} increases with ageing time, which indicates that the precipitate fraction increases when ageing prolongs. In conclusion, the precipitate formed at 427°C is not the precipitate types usually observed through microscopy in the C250 alloy, that is, Ni3Ti, Ni3Mo

Maraging steels

{211}a

{220}g

{200}a

50 h at 538°C 10 h at 538°C 3 h at 538°C 1 h at 538°C water quenched

300

{311}g

Intensity

350

{200}g

400

{111}g

450

{110}a

500

{220}a

106

250 200 150 100 50 0 35

45

55

65

2q (°)

75

85

95

105

5.23 XRD profiles of C250 steel aged at 538°C for different lengths of time.

and Fe2Mo, or other possible types reported in literature, for example the, w phase. It must contain many small atoms like nickel or cobalt and a few large atoms. No such precipitate types have been reported before. Experimental characterisation of the precipitate type and composition using atom probe field ion microscopy may be able to provide the experimental evidence needed (Section 8.1). Calculation of the precipitate fraction using this method can be applied to mixed precipitates. This method only considers the number or percentage and type of atoms in precipitates, but not their packing order, that is the entropy of the system. For example, 1 mol% Ni3Mo plus 1 mol% Ni3Ti is considered the same as 2 mol% Ni3Mo0.5Ti0.5 (or 1:1 ratio mixture of Ni3Mo and Ni3Ti). Thermodynamically, the formation of a joint compound like Ni3(Ti,Mo) may increase the total amount formed relative to the individual cases because the increased entropy of formation would increase the stability of the compound. However, this is not thought to be the primary explanation for the apparently excessive amount of precipitate. Although no attempt was made in this section to calculate the fraction of a precipitate type of complicated composition, such a calculation can be easily done if the composition of the precipitate is known. The method is not affected by the precipitate size distribution either. Few large precipitates and many small ones should give the same result, providing that the elastic strain effect for coherent precipitates is small. One main assumption in the method is that the stress and strain caused by precipitation is negligible. When precipitates such as Ni3Mo, Ni3Ti, Fe2Mo

Quantification of phase transformation kinetics

107

or the w phase form, the volume difference between the bcc martensitic matrix and the hexagonal precipitates will result in transformation stress and strain. However, such stress and strain will be relaxed during the ageing treatment. It is therefore rational to neglect them. Quantification of precipitate size and fraction in maraging steels is difficult, compounded by the fact that the composition of precipitate changes during ageing even when there is no change of precipitate type (Section 8.1). Assuming the precipitates to be Ni3Ti, Ni3Mo or Fe2Mo with stoichiometric composition, as well as making the above assumption, is a rational simplification procedure. Although the assumptions result in uncertainties in the estimation of the precipitate fraction, the values obtained do seem to reflect the precipitation evolution taking place during ageing. As demonstrated in this section, the precipitate fraction formed in C250 and C350 grades can be estimated using this method, which should be applicable to other maraging grades such as C300, T250, T300 and T350. For other precipitation strengthening materials with large atomic volume differences between matrix and precipitation elements, for example some aluminium alloys and Ni-base superalloys, this method may also be applicable. It is to be noted that, however, the aim of this method is to estimate the precipitate fraction when there is no easy way to measure it directly.

5.5.2 Austenite Austenite may form in C250 alloy during ageing. The volume fraction of austenite, Vg, can be determined from XRD profiles in the case where there is no preferential grain orientation: Vg =



(I {200}g

I {200}g + I {220}g R{200}g + R{220}g + I {220}g ) + I {200}a R{200}a

[5.36]

where I{200}g and I{220}g are the integrated intensities of the {200} and {220} diffractions of austenite and I{200}a is the intensity of the {200} diffraction of martensite. R{200}g, R{220}g and R{200}a are the factors that depend on {hkl} and the crystal structure of phase, whose values are 81.6, 44.4 and 31.9, respectively, for a steel with 0.2 wt% carbon.

5.5.3 Summary The precipitation kinetics of a maraging grade, 18 wt% Ni C250, can be investigated by X-ray diffraction (XRD) analysis, in order to estimate the precipitate fraction. The amount of reverted austenite can also be quantified when it is observed. The method gives reasonable values of precipitate

108

Maraging steels

fraction, which increases when ageing is prolonged. The precipitate formed at 427°C in the C250 alloy is not Ni3Ti, Ni3Mo, Fe2Mo or the w phase, but an unknown type. A significant amount of reverted austenite is present in the C250 alloy after ageing at 538°C for 10 hours or for a longer time. The method for estimation of precipitate fraction using XRD analysis may be applicable to other precipitation hardening alloys.

5.6

References

Coret M, Calloch S and Combescure A (2004), ‘Experimental study of the phase transformation plasticity of 16MND5 low carbon steel induced by proportional and nonproportional biaxial loading paths’, Eur J Mech A-Solid, 23, 823–42. He Y, Liu K and Yang K (2003), ‘Effect of solution temperature on fracture toughness and microstructure of ultra-purified 18Ni(350) maraging steel’, Acta Metall Sin, 39, 381–6. Rivera-Díaz-del-Castillo P E J and Bhadeshia H K D H (2001), ‘Theory for growth of spherical precipitates with capillarity effects’, Mater Sci Technol, 17, 30–2. Sagaradze V V, Danilchenko V E, L’Heritier P and Shabashov V A (2002), ‘The structure and properties of Fe–Ni alloys with a nanocrystalline austenite formed under different conditions of g–a–g transformations’, Mater Sci Eng A, 337, 146–59. Tewari R, Mazumder S, Batra I S, Dey G K and Banerjee S (2000), ‘Precipitation in 18 wt% Ni maraging steel of grade 350’, Acta Mater, 48, 1187–200.

6

Quantification of age hardening in maraging steels Abstract: Quantification of precipitation hardening is a challenging subject, as it demands combined knowledge of precipitation strengthening mechanisms and precipitate growth and coarsening kinetics. As we have not seen many attempts to develop new theories in recent years, the authors are aware of the fact that many existing concepts and developed theories are sometimes even neglected or misused. This chapter therefore aims to describe an overview of some aspects that have not been fully addressed or have been misused. Recent developments in this subject include an accurate determination of the equilibrium precipitate fraction and interparticle spacing. In addition, difficulties in quantification of precipitation strengthening effects in commercial systems are discussed. Key words: hardness, kinetics, diffusion, computer modelling, precipitate growth.

6.1

Precipitation hardening theories

A typical one-peak precipitation-strengthening curve consists of two stages (Fig. 6.1). In stage I, the resistance of precipitates to dislocation cutting results in an increase in strength. In stage II, dislocations are forced to loop around the precipitate rather than cutting through it, which also results in an increase in strength compared with the solution-treated material. The term ‘strengthening’ is usually used to describe the strength increase in stage I – the underageing period, and ‘softening’ for stage II – the overageing period. It should be emphasised, however, that both mechanisms lead to an increase in strength compared with the no-particle condition and both are classified as strengthening mechanisms.

6.1.1 Strengthening – critical particle size – coherency strain Strengthening and particle size Although rarely claimed, people usually have such impression that precipitates grow during underageing, which results in hardening, and they coarsen during overageing, which leads to softening. This is not correct. Precipitate growth can lead to softening and strengthening can be achieved when precipitates coarsen. The interaction mode between a dislocation and a particle is determined by the particle strength. The strength of a certain type of particle is related to its size. Strengthening or softening only relates 109

110

Maraging steels

Strength increment

Stage I small particles

Stage II large particles

Strengthening curve

Ageing time

6.1 A typical one-peak age hardening curve.

to the particle size. It is not determined by how the particle reaches such a size, by growth or through coarsening. If we define the critical particle size as rc4 (Chapter 5), then: (1) when r < rc4, the particle is sheared by a dislocation, resulting in hardening or softening; (2) when r > rc4 , dislocations loop across the particle, leading to softening. From a theoretical point of view, the second statement might be arguable. Derivation of the original Orowan equation Dty = 2G·b/L assumes the precipitation fraction to be constant, where Dty is increase in shear stress and G is shear modulus of the matrix. A drop in strength results from the increase in L caused by the increase in particle size with time. Theoretically, it is possible that the number of particles increases with time if there is a fast increase in precipitation fraction with time. Irrespective of the ‘hardness’ of hard particles, there will be a transition to the particle cutting mechanism at very small particle sizes. Since the hardness of a small particle is practically imaginary, understanding such phenomenon from the viewpoint of particle size is more convenient. Strengthening versus softening A real precipitation process is never simple. Precipitate particles can impede the motion of dislocations through a variety of interaction mechanisms, which are listed in Table 6.1. In this table, gs is the energy of a matrix–precipitate interface created by slip, Dg is the difference in stacking fault energy between the precipitate and the matrix, Tl is the line tension of a dislocation, DG is

Quantification of age hardening in maraging steels

111

Table 6.1 Different mechanisms for precipitation hardening Strengthening mechanism

Expression for CRSS Dty

Chemical

Ê 3ˆ 2G Á ˜ Ë π¯

Strengthening or softening

1/2 Ê g ˆ 3/2 Êbˆ 1/2 s f

Á ˜ ËGb¯

Softening*

ÁË r ˜¯



Stacking-fault

µ (Dg)3/2b–1/2(r · f )1/2

Modulus

Ê 2r ˆ ˆ 0.9Tl Ê DGˆ 2 Ê Á 2b lnÁ 1/2 ˜ ˜ b ÁË G ˜¯ Ë Ëf b ¯ ¯

Strengthening

3



Order

Coherency

–

3 2

Decreases when r increases Ê g apb Ê 3π 2g apbf · r ˆ Á ˜ 2 ÁÁ 32Tl 2b Ë ¯ Ë 4.1Ge3/2f 1/2(r/b)1/2 0.7Ge1/4f 1/2(b/r)3/4

1/2

ˆ – f˜ ˜ ¯

1

Strengthening

(r · f )2



Softening Strengthening

Strengthening Softening*

*These statements were made based on the assumption that the precipitation fraction is nearly at equilibrium. If the number of precipitates does not change at the beginning of ageing, f µ r 3 and in turn Dty µ r1/2 for chemical hardening, i.e. strengthening rather than softening, and Dty µ r 3/4 for coherency hardening for large particles, i.e. strengthening rather than softening.

the modulus difference between the precipitate and the matrix and gapb is the antiphase boundary energy on the slip plane of an ordered precipitate. Among the mechanisms, chemical strengthening, stacking-fault strengthening and order hardening predict monotonic relationships between the critical resolved shear stress (CRSS) and particle radius r. The situation becomes complicated when coherency hardening or modulus strengthening is the controlling factor. For simplicity, we assume that the precipitation fraction has reached the equilibrium amount in the following discussion. In the case of coherency hardening, the dislocation interacts with the coherency strain field in the matrix around the coherent particle. When the particles are relatively small, one solution, relevant to very limited dislocation bending, yields coherency strengthening that increases with increasing particle size. In the case of larger particles, where considerable flexing of the dislocations occurs because of the spacing of individual particles, any movement of the dislocation will have to overcome a larger number of obstacles per unit length. The coherency strengthening decreases with increasing particle size. Such a relationship between strengthening effect and particle size gives rise to a maximum in the strengthening at a critical particle size rc2 that is of the order of:

112

Maraging steels



rc2 = b/(4e)

[6.1]

e = (3Kq(1 + na) d)/(3Kq(1 + na) + 2Ea)

[6.2]

d = 2(Ωq – Ωa)/(3(Ωq + Ωa))

[6.3]

where and

where Ωa is atomic volume of the matrix. For modulus strengthening, there are theories that predict a higher strength with larger particle size. However, there are also theories that predict a very different effect, that is, a drop in strength when the particle grows larger. There are no experimental data to support either theory to date.

6.1.2 Age hardening Theoretical derivation The age hardening effects in Fe–18Ni maraging steels over a certain temperature range could be expressed by the simple relationship:

DH = Ktn1

[6.4]

where DH is increase in hardness and n1 is a time exponent in the relationship between the increase in hardness and ageing time. This hardening effect is due to the particles precipitated during ageing. A theoretical analysis will be given below. When particles are small, they are sheared by moving dislocations. Their contribution to the strength of the alloy involves a convolution of the resistance to shear of one particle, their population and the flexibility of the dislocations with which they interact, known as the ‘Friedel effect’. Many studies have been built on this idea and they have tested the idea experimentally. For present purposes, it is adequate to accept that the contribution to the increase in yield strength, Dsy, of a volume fraction f of particles that can be sheared of radius r has the form:

Dsy = c1 f m1rm2

[6.5]

where m1 and m2 are, respectively, exponents of f and r in this particle shearing equation. For most dislocation–particle interactions, both m1 and m2 have the value 0.5. Sensitivity analysis of the complete process model shows that Dsy is insensitive to the values of m1 and m2 near 0.5. The relationship between ageing time t and radius r of the zone or precipitate (assumed spherical) is given by Zener’s parabolic relationship:

r = a(Dt)1/m3

[6.6]

Quantification of age hardening in maraging steels

113

where a is a constant related to the solid solubility of the precipitate and the matrix and the concentration of the alloy, m3 (= 2) is a reciprocal of the time exponent in the growth law. Based on different assumptions, different equations were derived that, however, only differ from Eq. [6.6] in the coefficient a term. The development of this theory and calculation of a under different circumstances are reviewed in Christian’s Theory of Transformations book (Christian, 1975). The Johnson–Mehl–Avrami (JMA) equation can be used to describe the time dependence of the dispersion’s volume fraction with time at a given temperature, that is, the relationship between transformation fraction and time at a certain temperature. At the early ageing stage, when kt << 1, it takes the following form:

f = feq{1 – exp [–(kt)

m4

]} � feq(kt)

m4

(when kt << 1)

[6.7]

where feq is the temperature dependent equilibrium volume fraction of the precipitates, k is the reaction rate constant, t is the ageing time and m4 is the Avrami index. For maraging steels, the increase in yield stress is proportional to the increase in hardness, DH. After applying the Taylor factor MT for isotropic polycrystalline materials, one has:

Dsy = qDH = MTDty

[6.8]

where Dsy is the yield strength increase and q is a conversion constant between Vickers hardness and yield strength. Combining Eqs. [6.5]–[6.8], we have:

DH = c2tn2

[6.9]

where n2 is the time exponent in the relationship between the increase in hardness and the ageing time: n2 = m1m4 + m2/m3 and c2 is a materials constant:

[6.10]

c2 = c1 feqm1a m2 D m2 /m3 k m1m4 /q [6.11] where c1 is a materials constant. It seems that Eq. [6.9] is of the same form as the experimental relationship Eq. [6.4]. However, this is not always correct. For most types of dislocation–particle interaction, both m1 and m2 have values close to 0.5 and m3 equals 2. Eq. [6.10] becomes n2 = m4/2 + 1/4. As the precipitation fraction increases with time at the early stage of ageing, m4 always takes on positive values, so under no circumstances should n2 be less than 0.25. However, experimental observations found values of n1 to be, for example, 0.22. A possible explanation is given in the following section.

114

Maraging steels

An explanation of n2 < 0.25 It is not difficult to find out that, in deriving Eq. [6.9], if the value of m3 is larger than 2, then an n2 value smaller than 0.25 becomes possible. This assumption means that the precipitate size evolution does not follow the growth law but an even slower procedure. Since the low n1 values were first reported in Fe–18Ni maraging systems, what happens during ageing of such grades is examined first. There are three stages during ageing of a Fe–18Ni (350-grade) maraging steel at 500∞C. Spinodal decomposition appears first at the early stage of ageing after solution treatment at 820°C for 1 hour, as revealed by Mössbauer spectroscopy. During the early stages of ageing, the shape of the concentration is close to a pulse wave, which is characteristic of spinodal decomposition. Then, the Ni3(Mo,Ti) intermetallic particles containing iron precipitate in the Ni–Mo–Ti rich regions of the modulated structure by in situ nucleation. With increasing ageing time, Ni3Mo and Ni3Ti particles coarsen significantly and they may be partly dissolved back into the matrix, which can last for at least one hour. After ageing at 500°C for 7 hours, the Fe2Mo particles precipitate and reverted austenite can be found. The redistribution of atoms is fast at the initial stages of ageing. After 15 minutes, intermetallic compounds start to precipitate. From experimental observation, a Fe–18Ni alloy has demonstrated a significant hardness increase after ageing for 15 minutes at 482°C following solution treatment at 815°C. Therefore, hardening at the early stage of ageing is due to the formation of zones enriched with nickel, molybdenum and titanium by spinodal decomposition, but in the later stages is due to the precipitation of Ni3Mo and Ni3Ti particles. The theory for hardening by strong diffuse particles may be suitable to describe the hardening by spinodal decomposition. This theory leads to a relation Dty µ L2/3 µ f –1/3 · r2/3. This relationship is covered by Eq. [6.5] but the values of m1 and m2 differ from those for dislocation–particle interactions. The spinodal decomposition behaviour in a Fe–28.5Cr–10.6Co (wt%) alloy during ageing is chosen to exemplify the evolution of the spinodal process. The work was carried out using field-ion microscopy and atom probe. Coarsening of the microstructure occurs from the earliest time that the two developing phases can be distinguished with the field-ion microscope. The coarsening of the network structures could be fitted to a power law with a time exponent of 0.14, which corresponds to an m3 value of 7.1, a much slower size increment rate than the growth law described by Eq. [6.6]. If the hardening effect is caused by spinodal decomposition, the values of m1, m2 and m3 will differ from the typical values given in the previous section and consequently an n2 value smaller than 0.25 is possible. However, there are different reports on the study of the same Fe-18Ni 350-grade, which cast some doubts on what happens in this alloy during

Quantification of age hardening in maraging steels

115

early ageing. Is it spinodal decomposition or normal nucleation and growth? Tewari et al. (2000) studied the evolution of precipitates in the maraging steel of grade 350 using small angle x-ray scattering (SAXS) and transmission electron microscopy (TEM). The sequence of phase evolution at temperatures below 450°C involves first a rhombohedral distortion of the supersaturated martensitic a, accompanied by the appearance of a diffuse w-like structure. In the subsequent stage, well-defined w particles form which also contain a chemical order. The growth exponent of the w precipitates has been found to be 1/5 from the SAXS results. At higher ageing temperatures, the Ni3(Ti,Mo) phase is the first precipitating phase to appear. SAXS results have revealed a growth exponent of 1/3 consistent with the coarsening model of Lifshitz–Slyozov–Wagner (LSW). Although two types of precipitates form in different temperature ranges, their growth behaviour does not follow Eq. [6.6], but a slower procedure. As a result, even though Eq. [6.4] may be able to quantify the hardening effect, the time exponent n1 will be temperature dependent. Even when the formation of precipitate follows the nucleation procedure, the growth law described by Eq. [6.6] may not be a good representation of the precipitate growth process. This is because one or more metastable or transition phases, not included in the phase diagram, may appear prior to or in addition to the equilibrium precipitate when the supersaturated solid solution decomposes. The formation of such phases, whose crystal structure and habit plane allow them to achieve exceptionally good lattice matching with the matrix, is more favourable than formation of the equilibrium phase. In many systems of technological importance, a transition phase completely coherent with the matrix may be formed. A simple example is the Guinier– Preston (GP) zones in the Al–Cu system. Such zones can subsequently act as nucleating sites for other metastable precipitates. The general process that occurs, therefore, when a supersaturated solid solution is aged, is the formation of a more stable product accompanied by the dissolution of less stable phases formed in the earlier stages. This means that even for the normal nucleation process, the size increment of particles (either transition phases, or stable precipitate formed in the end) involves the dissolution of previously formed particles. In fact, based on work using an atom probe, most of the ageing curves of aluminium alloys are controlled by coarsening kinetics. The equilibrium precipitation fraction is very small and the formation of transition phases, either by interface-controlled growth or by diffusioncontrolled growth, takes a very short period of time. In conclusion, whether the phase separation proceeds through the nucleation process or through spinodal decomposition, the particle size increment may not be suitably described by the growth law of Eq. [6.6]. Instead, the coarsening law may be a more reasonable option in the light of the physical background. An n1 value smaller than 0.25 becomes possible. However, quantification of

116

Maraging steels

age hardening does not become any easier owing to the complicated situation in particle coarsening, which will be discussed in Chapter 7.

6.1.3 Matrix concentration and precipitation fraction The initial precipitation kinetics is adequately dealt with, when the mean solute concentration c(t) in the matrix, which is changing during the ageing process, decays exponentially with time, raised to a power close to unity:

c(t) = ca + (c0 – ca) exp (–t/t1)

[6.12]

where c0 and ca are the initial solute concentration and equilibrium concentration at the ageing temperature, respectively, and t1 is a temperature-dependent exponential time constant. The volume fraction of transformed precipitate particles f(t), as a function of the ageing time, is directly proportional to solute loss, tending to a final temperature dependent equilibrium fraction value of the precipitation feq when c = ca, thus:

f(t)/feq = (c0 – c(t))/(c0 – ca) = 1 – exp (–t/t1)

[6.13]

Alternatively, if the volume fraction evolution is described by the JMA equation, the mean matrix concentration will be:

c(t) = (c0 – cq f )/(1 – f)

[6.14]

The latter procedure appears more rational since it allows the precipitation fraction calculation first and then calculation of the mean solute concentration in the matrix. As discussed by Christian, the JMA equation represents a good approximation of the real precipitation process, to an accuracy of within 5% error even when the volume fraction is high. The advantage of the latter procedure is that it allows a wide range of m4 values, the Avrami index in the JMA equation. If Eq. [6.13] is used, f (t) = feq·t/t1 when t is small, an explanation of n1 smaller than 0.25 will again present a problem. Another advantage of the JMA equation is that although the derivation is from a geometric consideration, it does take into account the overlap of diffusion field, that is, soft impingement. Changes in the mean solute concentration were observed using an atom probe. Dc = (k¢t)–1/3 represented observations very well. In fact, experimental data can be also well described by Eq. [6.14], which becomes c(t) � c0 –cq feq(kt)m4 when kt is small. The advantage of Eq. [6.14] is that it can give a close approximation when t approaches zero. The JMA equation has been widely used to describe precipitation reactions, as well as the austenite reversion process during ageing. For interstitial alloy systems containing a substitutional solute, for example, when the precipitate type is carbide, the interface compositions ca and cq can be calculated using the regular solution model. When the alloy system is complicated, such as in commercial alloys, these thermodynamic calculations

Quantification of age hardening in maraging steels

117

can be carried out using packages such as Thermo-Calc (Chapter 4) and ALSTRUC. The equilibrium amount of the precipitation feq can be obtained through such calculations as well (Fig. 6.2).

6.1.4 Difficulties Quantification of precipitation hardening remains very challenging despite a few decades of intensive research on this subject. Precipitate type determination and size and fraction measurement become possible with the aid of advanced characterisation techniques such as atom probe field-ion microscopy (APFIM). However, many difficulties, practical and theoretical, still exist. Determination of the diffusion coefficient There is not yet a direct method to measure the diffusion coefficient at low temperatures. As a result, quantification of age hardening always features an optimisation procedure, in other words, some parameters are determined through fitting calculated results with experimental observations. The diffusivity value obtained in this way is usually much faster than what is extrapolated from high temperature data. Although it has been recognised that diffusion during the very early stage of ageing can be very fast owing to the high concentration of vacancies caused by water quenching, the fast diffusion during overageing cannot be accounted for by this explanation. Without a reliable way of measuring diffusion coefficient, attempts to quantify precipitation hardening will always be semi-empirical. Another difficulty

Fraction/concentration (%)

12

8

Equilibrium fraction (mol%) Mn in matrix (at%) Ni in matrix (at%) Mn + Ni in matrix (at%)

4

0 350

400 450 Temperature (°C)

500

6.2 The equilibrium solute concentrations and volume fractions of the NiMn precipitates in the matrix as functions of ageing temperature in an Fe–12Ni–6Mn system calculated using Thermo-Calc software.

118

Maraging steels

caused by the ‘abnormal’ diffusion is that the age hardening during the underageing period cannot be quantified by a constant diffusion coefficient (at a certain temperature). An experimental manifestation of such an effect is that the measured as-quenched hardness differs noticeably from what is extrapolated from the hardness points during the underageing period. This phenomenon has been observed in many alloy systems, such as PH13-8Mo, Fe–18Ni 350-grade and PH15-5 steels. As a result, quantification of age hardening, without taking into account the varying diffusion coefficient, unsurprisingly encounters difficulty. Uncertainty in the calculation of line tension All the strengthening mechanisms involve the calculation of dislocation line tension Tl. Its value is usually taken as Gb2/2, quoted from an approximation for fixed line tension. The accuracy of this expression is an order-of-magnitude. The experimental result is usually lower than this value. Since almost all the quantification of age hardening of a real system features optimisation procedures, the error caused by such an approximation will be transferred to other parameters such as the diffusion coefficient. The calculated results based on the optimised parameters may agree very well with experimental observations, but this does not necessarily suggest a perfect model. In extreme cases, good agreement between experimental and calculated values can be generated based on a wrong model. Nevertheless, such quantification procedures may be of some practical use. An accurate estimation of the line tension requires analytical theories covering the spectrum of dislocation precipitate interaction mechanisms and computer simulations of dislocation motion through arrays of localised, but finite obstacles. Until such efforts have been made, the uncertainties in quantification of precipitate hardening will remain.

6.1.5 Summary Precipitation in metals has long been a common strengthening method. This overview section has discussed some theoretical analysis aspects in order to interpret the hardening exponent. When carrying out quantification of age hardening, good agreement between calculation and experimental observation does not always prove a correct or suitably applied theory. Some recent improvements in quantification of age hardening include the influence of precipitate fraction, despite difficulties in quantification of precipitation hardening in commercial systems.

Quantification of age hardening in maraging steels

6.2

119

Kinetics

6.2.1 2000 MPa grade cobalt-free maraging steel At all ageing temperatures, the hardness increase rate is very high, taking the 2000 MPa grade steel, extensively discussed in Chapters 2 and 3, as an example (Fig. 6.3). Within the first 30 minutes, even at the low ageing temperature of 440°C, the hardness can reach 60% of the maximum hardness. 18Ni cobalt-containing maraging steels show a similar ageing behaviour. It is difficult to separate the nucleation and growth stages from the results of such experiments. When aged at 440°C, within the ageing time of 50 hours, the hardness increases relatively slowly compared to other ageing temperatures, but continuously until it reaches the maximum hardness of HRC55. At 480°C and 500°C ageing temperatures, the hardness peaks at 9 hours and 2 hours, respectively, followed by slow reduction. When aged at 540°C, the hardness reaches its maximum value after 15 minutes, followed by a rapid decrease. At ageing temperatures up to 500°C, the hardness reaches the same maximum value after different ageing times. There is a large plateau around the maximum hardness. At a high ageing temperature (540°C), however, owing to the martensite to austenite transformation (see microstructural characterisation in Chapter 2), the maximum hardness is only HRC53.5. With a longer ageing time at this temperature, owing to the increasing

60 55

Hardness (HRC)

50 45 40 35 440∞C 480∞C 500∞C 540∞C

30 25 0.0625 0.125 0.25 0.5

1 2 4 Ageing time (h)

8

16

32

64

6.3 Age hardening curves of the 2000 MPa grade maraging steel after solution treatment at 800°C for 1 hour, showing the effect of ageing time on hardness at different ageing temperatures.

120

Maraging steels

amount of austenite formed, there is a large drop in the hardness. The ageing temperature has a significant effect on age hardening. Chapters 2 and 3 describe systematically microstructure and mechanical properties of the steel at three ageing temperatures, 440°C, 480°C and 540°C, as being representative of low, medium and high ageing temperatures. In summary, there is rapid age hardening across the ageing temperature range of 440–540°C in the cobaltfree maraging steel.

6.2.2 2400 MPa grade cobalt-free maraging steel The hardness for the two 2400 MPa grade steels, low and high Mo, in the solution condition is HRC28 and HRC29, respectively. At the relatively low ageing temperature of 440°C, there is rapid hardness increase after just 5 minutes ageing (Fig. 6.4). With increasing ageing time, the hardness continues to increase, peaking at 12 hours. The hardness remains at this level with further increase of the ageing time to 80 hours. As the ageing temperature increases to 470°C, the peak hardness is reached after ageing for 3 hours. With prolonged ageing, the low Mo steel keeps its hardness up to about 15 hours and it drops slightly at 50 hours (Fig. 6.4a). For the high Mo steel, a slight reduction trend is apparent after 4 hours (Fig. 6.4b). At 500°C, the low Mo steel reaches peak hardness after only about 30 minutes ageing.

Hardness (HRC)

60 55 50 45

440∞C 470∞C 500∞C 540∞C

Steel 1#

40

Hardness (HRC)

25 60

(a)

55 50 45

440∞C 470∞C 500∞C 540∞C

Steel 2#

40 25

4

8

16

32

64 128 256 Ageing time (min) (b)

512

1024 2048

4096

6.4 Age hardening curves of the 2400 MPa grade maraging steels after solution treatment at 810°C for 1 hour. (a) Steel 1# = low Mo; (b) Steel 2# = high Mo.

Quantification of age hardening in maraging steels

121

Following this, the hardness reduces with increasing ageing time. The high Mo steel, however, somewhat surprisingly has its peak hardness after 3 hours ageing. Further increase in the ageing temperature to 540°C resulted in a similar hardening behaviour. The low Mo steel peaks at 15 minutes, whilst the high Mo steel peaks after a much longer ageing time, 3 hours. A common feature regardless of the ageing temperature is that both steels have an extremely rapid hardening response, achieving over 80% of peak hardness within the first 30 minutes of ageing (Fig. 6.4). The 2000 MPa grade steel (Section 6.2.1) is similar. According to classical nucleation and growth theory, alloying atoms diffuse through vacancy and other defects during ageing leading to nucleation. With increasing ageing temperature, diffusivity increases, accelerating nucleation rate and shortening the growth period of the precipitation phases. The rapid hardness increase at the initial stages of precipitation of the two steels is related to the extremely high dislocation density of the lath martensite. Alloying atoms can diffuse quickly along dislocations, causing nucleation and growth of the precipitates. The ageing kinetics is controlled by the high dislocation density of the martensite matrix. At 440°C and 470°C, before reaching the peak hardness, the high Mo steel has a higher hardness (Fig. 6.4). This is probably related to its higher molybdenum content, causing stronger solid solution strengthening. However, at the higher ageing temperatures, the early stage ageing hardness of the high Mo steel is much lower than the low Mo steel (Fig. 6.4).

6.3

Fe–12Ni–6Mn

This section quantifies the age hardening effect caused by precipitation in Fe–12Ni–6Mn maraging steel. The age hardening effect at various temperatures after different periods can be calculated from Eq. [5.17], plotted with experimental data for comparison (Fig. 6.5). The calculated hardening effects agree well with the experimental data. The degree of age hardening at peak hardness depends on the ageing temperature. The precipitation fractions corresponding to peak hardness at different ageing temperatures are significantly different (Table 5.5). The precipitate size at peak hardness ranges from 4 nm to 8 nm in diameter (Table 5.5). It is not difficult to understand why the age hardening effect at 400°C is stronger than at 450°C and 500°C. The hardness increase at peak hardness at 400°C is calculated as 314 HV, which agrees well with the experimental value 323 HV. However, in the current calculation, the activation energy is treated as a constant over the ageing period, although in fact it decreases when DH0 increases, in other words when ageing continues. Using the average value of the activation energy gives an underestimation of the energy barrier at the earlier stage and an overestimation at the later stage. As a result,

122

Maraging steels

350 350∞C – Calc. 350∞C – Exp. 375∞C – Calc. 375∞C – Exp. 400∞C – Calc. 400∞C – Exp. 425∞C – Calc. 425∞C – Exp.

Hardness increase (HV)

300

250

200

150

100

50

0 0.01

0.1

1 Time (h)

10

100

6.5 Age hardening calculation and comparison for Fe–12Ni–6Mn at 350°C, 375°C, 400°C and 425°C.

the calculated hardness increase is higher than the experimental value at the earlier stage and lower at later stages. This tendency is suggested in Fig. 6.5. When ageing proceeds near the peak hardness point, the error caused by this treatment will become larger.

6.4

C250

The ageing time for C250 to reach peak hardness at 538°C, 482°C and 427°C is about 3 hours, 10 hours and >50 hours, respectively. Comparing the kinetics curves in Figs. 5.17 and 5.20, there is no austenite formed at the peak hardness position at temperatures 427°C and 482°C, but about 4.4% at 538°C. The austenite formed at 538°C may partly contribute to the lower peak hardness at this temperature. The models indicate that precipitation growth is completed (10, 1 and 0.1 hour at 427, 482 and 538°C, respectively) well ahead of the peak hardness (>50, 10 and 3 hours at 427, 482 and 538°C, respectively). This is of particular interest. It indicates that the size increment of precipitates during age hardening should mainly follow coarsening rather than growth kinetics, in agreement with work on a PH13-8 Mo alloy (Chapter 8). Precipitation process may reach equilibrium before the peak hardness is achieved during ageing, which indicates that the hardening effects may be due to precipitate coarsening.

Quantification of age hardening in maraging steels

6.5

123

C300

The quantification in this section is based on a detailed characterisation of C300 maraging steel, where the change of Vickers hardness was measured as a function of time at the ageing temperature of 510°C. The composition of the steel is Fe–18.5Ni–9Co–4.8Mo–0.6Ti (wt%). The steel is strengthened by Ni3Ti and Fe7Mo6 precipitates, the former starting to precipitate at very short ageing times and the latter appearing after ageing for 30 minutes. Therefore, in this steel, 30 minutes may be taken as beyond the end of the early stages of ageing, as the onset of the second type of precipitates changes the source of hardening. At between 160 seconds and 25 minutes, the hardness shows a good correlation with ageing time (Fig. 6.6). The constants in the equation DH = (Kt)n, a modified form of Eq. [6.4], are K = 3.1 ¥ 108 h–1 and n = 0.29. In C300, the hardness response to ageing at the early stages is controlled by the diffusion of titanium. The Ni3Ti precipitates are spheroidal at the early stages. Thermodynamic calculations for the equilibrium between bcc and Ni3Ti give equilibrium chemistry data (Table 6.2).

1000

Increase in hardness

Cr-steel 420∞C Cr-steel 420∞C deformed C-300

100 0.01

0.1

Ageing time (h)

1

10

6.6 Variation of initial increase in hardness DH, with ageing time. Table 6.2 Equilibrium phase compositions (mol%) and fraction in C300 at 510°C with only bcc and Ni3Ti entered in the calculation Phase

Fe

Ni

Co

Mo

Ti

Fraction (mol%)

bcc Ni3Ti

71.4 –

16.5 75

9.1 –

3.0 –

0.0 25

97.2 2.8

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Maraging steels

6.6

References

Christian J W (1975), The theory of transformations in metals and alloys, 2nd edition, Pergamon, Oxford. Tewari R, Mazumder S, Batra I S, Dey G K and Banerjee S (2000), ‘Precipitation in 18 wt% Ni maraging steel of grade 350’, Acta Mater, 48, 1187–200.

7

Maraging steels and overageing Abstract: The influence of precipitation fraction on precipitate coarsening and hardening kinetics is accounted for quantitatively, allowing hardening quantification to be carried out accurately. Precipitation hardening in Fe–12Ni–6Mn maraging steel during overageing is quantified in this chapter. Based on hardness measurements, precipitate size as a function of time and temperature is calculated by applying the Ashby–Orowan relationship. The commonly used Lifshitz–Slyozov–Wagner (LSW) relationship is revised by taking into account the progress of precipitate fraction during overageing. Calculated hardness results based on the revised LSW model agree very well with experimental observations. Key words: precipitate coarsening, age hardening, kinetics, Thermo-Calc, Ashby–Orowan relationship.

7.1

Mechanism of particle coarsening

When precipitation from a supersaturated solid solution is complete, further ageing leads to precipitate coarsening driven by the interfacial free energy between the precipitate and the matrix – the process known as Ostwald ripening. The coarsening kinetics depends on the rate-controlling step in the process. A different controlling step results in different coarsening rate. Most of the derived relations between particle size and coarsening time (t) follow similar expressions: [7.1] r n3 – r0n3 = c ◊ t where r is the particle radius, n3 is an exponent in coarsening theories and c is a constant. Values of c under different mechanisms are summarised in Table 7.1. In this table, Vmq is molar volume, K is a temperature dependent rate constant, wgb is the width of a grain boundary, Dgb is the diffusion coefficient in a grain boundary, cgb is the solute concentration at a grain boundary in equilibrium with an infinitely large precipitate, A, B are constants involved in coarsening of precipitate on a grain boundary, sb is the grain boundary energy and fb is the fraction of the grain boundaries covered by precipitates. What kind of diffusion controls the particle coarsening is difficult to determine in real systems, though LSW theory is the most widely used theory. Application of this theory to interpret hardness or strength data achieves satisfactory agreement with experimental results (Section 7.4). Some attempts were made to calculate the diffusion coefficient, which is within the constant c. However, the calculated diffusion values are usually much larger than the lattice diffusion coefficient extrapolated from high temperature diffusion data. For instance, based on the particle-size measurement in a Ni–11.46Si (at%) 125

126

Controlling mechanism

n3

c

Remark

Lattice diffusion

3

8 Ds c V q 2 9 RT a m

The classic LSW theory

Interface atom transfer

2

64 K s c V q 2 81 RT a m

–

Precipitation on grain boundary

4

9 w gbDgbs c V q 2 32 RT · A · B gb m

Ês ˆ s A = 2 + b + 1 Á b ˜ , B = 1 ln 1 3 2s 3 Ë2s ¯ 2 fb



Precipitation on low angle boundary 5 – (dislocation) 4 –

3

Dislocation spacing larger than interparticle spacing Dislocation spacing smaller than interparticle spacing

Maraging steels

Table 7.1 Different mechanisms for particle coarsening

Maraging steels and overageing

127

system, the estimated values of diffusion coefficient are 10 times greater than the values extrapolated from high-temperature diffusivities. Recent work on quantification of age hardening during underageing and overageing also shows diffusivities about two orders of magnitude faster than extrapolated lattice diffusion values (Chapters 5 and 6, and Sections 7.4 and 7.5). Though it is commonly observed that the early stages of precipitation in alloys at low ageing temperatures occur at a rate seven or eight orders of magnitude greater than that expected from the extrapolation of high temperature diffusion data owing to the presence of quenched-in vacancies, no such claim has been made for the overageing period. The general form of coarsening kinetics as predicted by LSW theory appears to be well supported by experimental evidence, in spite of various theoretical objections and alterations to the rate constant and particle size distribution. The physical basis of the LSW theory is the Gibbs–Thomson equation, which assumes that the interfacial tension and density are independent of particle size. There have been some arguments for the variation of interfacial tension with radius of curvature. Such effects become insignificant for particles greater than 1 mm in radius, but may be significant when particles are very small. In precipitation hardening alloys, strengthening precipitates are usually tens of nanometres in size. Thus, one should be aware that application of this theory might not always give very good accuracy.

7.2

Influence of volume fraction on coarsening

Precipitation hardening consists of a few stages, as shown in Table 7.2. Which procedure operates depends on how fast precipitation reaches the equilibrium fraction. If the precipitate fraction reaches or is close to equilibrium at peak hardness, precipitation procedures follow what is listed in the top half of Table 7.2. However, in many cases, the precipitation fraction does not reach the equilibrium amount at peak hardness. For instance, when peak hardness is reached in the Fe–12Ni–6Mn maraging system, only about 50% of the equilibrium amount of precipitation forms. This precipitation behaviour follows the stages listed in the bottom half of Table 7.2. When quantification of age hardening is carried out, the influence from volume fraction has to be taken into account, since strictly, the relationship given by LSW theory becomes invalid when the precipitation fraction deviates from zero. The effect of volume fraction f on coarsening can be taken into account by introducing a parameter k(f), a function of f. k(f) is precipitation fraction factor in particle coarsening. The revised LSW relationship becomes (Section 7.4):

r3 – r30 = MD(t – t0)/RT

[7.2]

where r0 is the particle radius at the start of coarsening, t0 is time when a

128

Maraging steels

Table 7.2 Stages of precipitation hardening (≠ for increase and Ø for decrease) Stage

r

f

Number Effect

Remarks

(a) When the equilibrium fraction is reached at peak hardness I ≠ ≠ ≠ Strengthening Underageing II ≠ = feq Ø Strengthening then softening Peak hardness III ≠ = feq Ø Softening Overageing (b) When the equilibrium fraction is reached after peak hardness I ≠ ≠ ≠ Strengthening II ≠ ≠ Ø Strengthening III ≠ ≠ Ø Strengthening then softening IV ≠ = feq Ø Softening

Early ageing Underageing Peak hardness Overageing

particle starts to coarsen, the time at the start of overageing, D is the diffusion coefficient and M is a parameter related to particle coarsening: M = 8/9 · sVq0ca (1 – ca)k(f)/(cq – ca)2 [7.3] When f is between 0 and 0.1, such as in the Fe–12Ni–6Mn system, k(f), a function of the volume fraction, can be approximated as k(f) = 1 + 5f [7.4] These procedures have been taken into account in quantification of the hardening effect during overageing of a Fe–12Ni–6Mn alloy (Section 7.4). Good agreement between experimental work and the calculated results is achieved.

7.3

What is the controlling mechanism?

Although many mechanisms were proposed theoretically to describe the particle coarsening process, no matching experimental evidence has been obtained, except for the LSW theory, which found very good agreement with experimental observations in Ni-base alloys with g¢ precipitates. When Eq. [7.1] is used to fit experimental results, the fitting accuracy does not change significantly when n3 varies from 2 to 5 or even higher. Using the accuracy of fitting alone to determine the mechanism of diffusion is not convincing considering that each data point usually has some experimental error. Determination of the controlling mechanism of precipitation kinetics remains difficult experimentally and so does theoretical prediction. Dislocation looping is the most widely used mechanism for interpreting the softening effect during overageing. In fact, apart from dislocation looping, large coherent particles and the modulus difference between particle and matrix can also lead to softening. There is mounting evidence that modulus hardening may be an important mechanism of overageing in several alloy systems. Overageing is definitely not the result of the Orowan mechanism in some overaged alloys. Evidence for Orowan looping and cross slip is a considerable enhancement of work hardening. As there is no sign of enhancement in work

Maraging steels and overageing

129

hardening for PH13-8 Mo during overageing, it is unlikely that Orowan looping is the controlling softening mechanism.

7.4

Quantification of precipitation kinetics and age hardening for Fe–12Ni–6Mn

7.4.1 Transformation fraction at longer time The precipitation process at peak hardness is far from complete (Table 5.5). The precipitates continue to form or grow over the overageing period. During ageing at higher temperatures, such as 500°C or 525°C, there is always a tendency for austenite to form spontaneously. Such reverted austenite can help to increase the fracture toughness of the maraging steel and therefore achieve a good balance between strength and toughness. Since the reverted austenite normally also appears as a dark phase under the transmission electron microscope (TEM), the image analysis can easily give an overestimated precipitation fraction that is even higher than the equilibrium fraction calculated from thermodynamics. In a Fe–12Ni–6Mn specimen aged at 500°C for 150 hours, precipitation is very close to its equilibrium state, that is, the precipitation fraction of 0.087 calculated using Thermo-Calc with a KP (Kaufman’s binary) database. The equilibrium fraction of reverted austenite at 500°C is 0.346. Image analysis gives an experimental fraction of 32%. The model described in Sections 5.3 and 6.3 works well in the low temperature range, but not for temperatures higher than 450°C. Some of the errors were caused by taking the activation energy as a constant. In addition, when the temperature increases, the amount of reverted austenite increases. A more complete model should therefore combine the ageing hardening effect and the softening effect caused by austenite reversion and particle coarsening.

7.4.2 Theoretical analysis Orowan first studied the mechanism of hardening in a matrix containing a dispersion of hard particles using the concept of dislocation bowing. He established a relationship between the applied stress and amount of bowing along the dislocation line, known as Orowan’s equation Dty = Gb/L, where Dty is the increase in the shear stress, G is shear modulus of the matrix, taken as 81 GPa, b is the Burgers vector of the dislocation and L is particle spacing. Ashby further developed this equation to introduce and take into account the effects of statistical distribution of particle spacing in Orowan’s equation and obtained the so-called Ashby–Orowan equation: Ê1.2Gbˆ r Dt y = 0.84 Á ln Ë 2π L ˜¯ b

[7.5]

130

Maraging steels

where L and r are the average interparticle spacing and the average particle radius, respectively, both of which provide key characteristics of the microstructure. This equation demonstrates the link between a two-phase microstructure and the mechanical behaviour of a precipitation-hardened material. If the precipitation volume fraction, f, of the dispersion phase changes, the average particle size, r, and the average interparticle spacing, L, must change accordingly. When particles coarsen, the particle size should not be ignored when calculating the interparticle surface-to-surface spacing L. Assuming that the precipitates are spheres, the relationship between precipitate volume fraction f, their average interparticle spacing L and average particleradius r is given by:

ˆ Ê L = Á1.23 2π – 2 2˜ r = pr 3f 3¯ Ë

[7.6]

where f is the volume fraction of the transformed particles and p is a coefficient between the particle spacing L and the particle radius r. The auxiliary function p(f) is:

p(f ) = 1.23 2π – 2 2 3f 3

[7.7]

Combining Eqs. [7.5], [7.6] and [6.8] yields a relationship between the hardness increase in a precipitation-hardened microstructure and the average precipitate radius,

Ê1.2M T Gˆ b r DH = 0.84 Á ln Ë 2πqp ˜¯ r b

[7.8]

where H is the hardness, G is the shear modulus of matrix, taken as 81 GPa, q is the conversion constant between Vickers hardness and yield strength and b is the Burgers vector of dislocation. During overageing, incoherent precipitates form with negligible strain energy and particles coarsen. Large particles tend to grow at the expense of smaller ones. If the volume fraction of precipitates is extremely small, a rigorous formula may be derived relating the average particle size and the ageing time based on Lifshitz, Slyozov and Wagner (LSW) theory, namely: r 3 – r03 = 8 D s ca Vmq (t – t 0 ) [7.9] 9 RT where D is the matrix interdiffusion coefficient, R is the universal gas constant, T is absolute temperature in Kelvin, s is interfacial energy per unit area between precipitate and matrix, ca is the equilibrium solid solubility of the growth-controlling elements in the parent phase (the matrix), expressed as a mole fraction, and V mq is the molar volume of the q-NiMn precipitate

Maraging steels and overageing

131

phase. The above LSW equation was derived under the assumptions that the concentration of the elements in the matrix phase, ca ≈ 0 and cb ≈ 1, where cb is the equilibrium concentration of the elements in the new precipitate phase, that is the q-NiMn precipitate, also expressed as a mole fraction. Eq. [7.9] lacks any contribution from the volume fraction of the precipitates, because LSW theory excludes interactions between particles and is valid only for the extreme case of a vanishing volume fraction of the second phase. In the case of a non-zero volume fraction of precipitate, the cubed average radius of the particles remains proportional to time, but the proportionality coefficient is different from that given in Eq. [7.9]. Three modifications are required regarding Eq. [7.9] to extend its validity to the general case of precipitation-hardened alloys. First, the Gibbs–Thomson correction [(1 – ca)/(cb – ca)](1/ea) must be included, where ea is non-ideality correction, particularly when considering the case of precipitates that are intermetallic compounds. When ca itself is small, the Darken’s correction, 1/ ea, approaches unity. Second, the amount of solute needed for precipitate growth, cb – ca, must also be included. Finally, the effect from volume fraction on coarsening needs to be included by introducing a parameter k(f), which as indicated is a function of the volume fraction f. k(f) is precipitation fraction factor of particle coarsening. After including all of the modifications mentioned above, the revised LSW growth law for a non-zero precipitate volume fraction becomes Eqs. [7.2] and [7.3]. The value of k(f), however, depends on the specifics of the coarsening kinetics. Theories excluding interactions between the particles belong to LSW-like theories and yield the value k(f) = 1. However, coarsening theories that include many-body interactions yield k(f) > 1. If r as a function of ageing time at different temperatures is known, the diffusion coefficient D can be determined in terms of D0 and Qd since D = D0 exp (– Qd/RT), where D0 is pre-exponential term in Arrhenius expression for the diffusion coefficient and Qd is the activation energy of diffusion through the matrix during overageing. Prediction of the particle coarsening over a wide temperature range becomes possible, so does the hardening effect.

7.4.3 Calculations Some of the parameters used in these calculations are summarised in Table 7.3 (Chapter 5). The interfacial energy of the NiMn precipitate/matrix interface is estimated as 750 mJ m–2, the common value for an incoherent interface. cb and ca are the sum of atomic fractions of Ni and Mn present in the matrix and precipitate phases, respectively. Since NiMn only contains Ni and Mn, cb always equals 1. The values of ca at different ageing temperatures are calculated using Thermo-Calc linked to Kaufman’s binary (KP) alloy database, together with the equilibrium amounts of NiMn precipitate (Fig.

132

Maraging steels

6.2). ca increases by about 30% as the temperature increases from 400°C to 500°C. It would be inappropriate to consider ca as a constant over this range of ageing temperatures. The exact alloy composition is Fe–11.9Ni–5.75Mn (wt%). The Johnson–Mehl–Avrami (JMA) reaction rate parameter, k, defined previously in Eq. [6.7] can be calculated using an Arrhenius expression, as k0 exp(–Q/RT), where k0 is a pre-exponential term and Q is the activation energy. Their values are included in Table 7.3. Hardness data for this alloy during overageing were the measured hardness at different overageing times, from 16.5 to 50.9 hours at 400°C, from 1.4 to 14.5 hours at 450°C, and from 0.244 to 5 hours at 500°C. Based on these data, the average precipitate particle radius r is calculated by reversely applying Eq. [7.8], using graphical methods. Using the obtained particle size, the revised LSW Eq. [7.2] can be reversely applied to calculate the interdiffusion coefficient D. Normally, M is considered to be a constant at a certain temperature, but Fig. 7.1 shows that its change with time during overageing can be up to 15% (at 500°C). The diffusion coefficient is calculated as 1.1 ¥ 10–19, 1.0 ¥ 10–18 and 3.1 ¥ 10–18 m2/s–1 for 400°C, 450°C and 500°C, respectively (Fig. 7.2). If there is sufficient data for different temperatures, the result can be expressed in the usual Arrhenius form, D = D0exp(–Qd/RT), as the product of a frequency factor, D0, and a Boltzmann probability term, exp(–Qd/RT). Using the derived diffusion coefficient, the particle coarsening (i.e. the average radius of the precipitates, r) and hardening effects during overageing Table 7.3 Values of parameters used for calculation of precipitation hardening kinetics and extraction of the interdiffusion coefficient G (GPa) b (nm) MT

q (MPa HV–1) V mq (m3 mol–1) k0(1/s)

81

2.5

0.248

2.75

7.368 ¥ 10–6

Q (kJ mol–1) m

2.56 ¥ 105 133.0

1.15 ¥ 10–10 1.1 ¥ 10

400∞C 450∞C 500∞C

–10

M

1.05 ¥ 10–10 1 ¥ 10–10 9.5 ¥ 10–11 9 ¥ 10–11

0

10

20 30 Time (h)

40

7.1 Variation of parameter M during overageing.

50

0.45

Maraging steels and overageing

133

–40

ln (D)

–41

–42

–43

–44 1.25

1.3

1.35 1.4 1000/T (1/K)

1.45

1.5

7.2 Diffusion coefficient at different temperatures.

can be calculated as functions of ageing time at various temperatures (Figs. 7.3 and 7.4). The particle size is calculated from Eq. [7.8] based on hardness data (Fig. 7.3). The values at peak hardness at 400°C, 450°C and 500°C are 6.3 nm, 6.3 nm and 5.5 nm, respectively, which are larger than the particle size observed experimentally (2 hours at 450°C to reach peak hardness gives particles of radius 3 nm). The particle size at peak hardness position is overestimated by the current model. This is probably because a dislocationlooping mechanism, leading to hardness drop, starts to be involved before peak hardness is reached. At peak hardness point, the hardness drop is compensated somewhat by the strengthening from smaller particles, that is, the hardness drop caused by particle coarsening should be bigger than what is observed. This consideration will lead to a smaller particle size at peak hardness, Eq. [7.8]. When particle coarsening proceeds, the contribution of strengthening becomes less significant and the calculated size matches the real precipitate size more closely. Apart from particle coarsening, austenite reversion during ageing also contributes to the hardness drop during overageing. However, although the amount of reverted austenite reaches nearly 10% when peak hardness is reached at 500°C, it does not seem to increase dramatically afterwards, in other words, its contribution does not vary much during overageing, if not negligible. The diffusion coefficient at different temperatures is compared with the diffusion coefficient in the ageing period (Chapter 5) in Table 7.4. The D values during overageing derived from the current model are about 20–30 times higher than during the ageing period. This seems to imply that the precipitate coarsening during overageing and the precipitate growth during ageing are controlled by different mechanisms. Bearing in mind that the diffusion coefficient in this alloy decreases when the solute concentration decreases,

134

Maraging steels

400∞C 450∞C 500∞C

Radius (m)

1.5 ¥ 10–8

1 ¥ 10–8

5 ¥ 10–9 0.1

1

Time (h)

10

100

7.3 Precipitate size as a function of time and temperature, calculated from Eq. [7.8], or using the derived D (lines). Table 7.4 Comparison of the diffusion coefficients for ageing and overageing

400°C (m2 s–1)

450°C (m2 s–1)

500∞C (m2 s–1)

Overageing (Section 7.4.3, VG) Overageing (Section 7.5, WGR) Ageing (Chapter 5) Ni* Mn*

1.3 ¥ 10–19 4.5 ¥ 10–20 5.9 ¥ 10–21 1.2 ¥ 10–23 1.2 ¥ 10–22

7.6 ¥ 10–19 4.7 ¥ 10–19 3.0 ¥ 10–20 2.5 ¥ 10–22 2.1 ¥ 10–21

3.6 ¥ 10–18 1.8 ¥ 10–18 1.3 ¥ 10–19 3.4 ¥ 10–21 2.6 ¥ 10–20

*

These data are for lattice diffusion of Ni (700–760°C) and Mn (600–680°C) in ferromagnetic a-Fe.

the diffusion coefficient during overageing should only be lower, rather than higher as observed here, than that during ageing, if the same diffusion mechanism applies throughout the precipitation process. Our explanation of these results points to a different mechanism operating during overageing from that during ageing. This seems possible, since particle coarsening (overageing) takes place by redistribution and gathering of solutes released from dissolving smaller particles in a near-equilibrium, a locally saturated matrix, when free solutes in the matrix are used up, whereas precipitate growth (ageing) occurs by diffusion through a supersaturated, that is, metastable matrix (Glicksman, 2000). The lattice diffusion data for nickel and manganese in ferromagnetic a-iron are also listed in Table 7.4, which are one to four orders of magnitude lower than those for ageing or overageing. The ageing temperatures used, 400°C, 450°C and 500°C, are not in the temperature range of the literature Arrhenius

Maraging steels and overageing

135

350

Hardness increase (HV30)

300

250

200

150 0.1

1

Time (h)

10

100

7.4 Comparison of hardness calculated from the Voorhees and Glicksman (VG) model (Section 7.4.3) and Wang, Glicksman and Rajan (WGR) (Section 7.5) models with experimental results of hardening. Data point symbols of unfilled diamonds, circles and triangles represent experimental results at temperatures of 400°C, 450°C and 500°C, respectively. The solid line represents WGR model results and the dashed line represents the VG calculation.

parameters D0 and Q for lattice diffusion. Either the diffusion mechanism during ageing and overageing is unlikely to be lattice diffusion, or the values of the Arrhenius parameters D0 and Q for lattice diffusion at the low temperature range differ significantly from the values at high temperatures. The LSW model assumes that the rate controlling process is lattice diffusion. However, the diffusion mechanism during the precipitation process is not yet clearly understood. It is possible that q-NiMn precipitates form on dislocations in the lath martensite, which implies one-dimensional pipe diffusion along dislocations. If, however, precipitate particles in this system form uniformly throughout the matrix and no preferred or enhanced precipitation occurs at the grain boundaries, sub-grain boundaries or at dislocations, it will indicate only a lattice diffusion mechanism mediating the precipitation and overageing processes. A combination of this model with the previous model for the precipitate ageing period (i.e. the period before the microstructure reaches its peak hardness, Chapters 5 and 6) can comprehensively describe the entire process of precipitation hardening during ageing. These models are based on well-

136

Maraging steels

recognised fundamental physical metallurgical principles and theories and therefore may be applied broadly to any precipitation-hardening alloy.

7.4.4 Summary The current model quantifies the hardening effect during overageing in an Fe–12Ni–6Mn maraging steel. The coarsening of the precipitate and the resulting drop in hardness are treated accurately by taking into account the influence of the precipitation fraction. Precipitate size as a function of time and temperature during overageing is quantified, as well as the hardening effect. The increase in precipitation fraction is clearly demonstrated, so is its influence on the course of precipitate coarsening. The diffusion coefficient obtained for the overageing period implies that the diffusion mechanisms for precipitate growth and coarsening are different. The LSW relationship can be applied to studying precipitate coarsening when the diffusion mechanism is not understood experimentally. Eqs. [7.8] and [7.2] are the governing equations linking the characteristics of precipitation-hardened microstructures to their mechanical behaviour and allowing extraction of diffusivities from microstructural modelling. One may predict the hardness theoretically and compare it with measurements. Thus, using calculations of precipitate characteristics in an evolving microstructure, one can estimate a mechanical response, such as hardness, from basic kinetic and mechanical principles.

7.5

Reconsidering the precipitate fraction effect

Values of f in the case of the Fe–12Ni–6Mn alloy considered here fall between 0 ≤ f ≤ 0.15 depending on the temperature. The diffusion screening theory of phase coarsening (Wang et al., 2004, 2005) yields a value for the function k(f) that may be expressed as: È Ê Ê ˆˆ ˘ Í2 – Á1 – 3f Á1 – 1 + 1 + 1 + 1˜ ˜ ˙ 3f Í ÁË 3f 3f Ë ¯ ˜¯ ˙ ˙ [7.10] k (f ) = 6.4125 Í 3 ˙ Í ˘ È 1 + 1 + 1 +1 ˙ Í ˙ Í1 – 3f 3f 3f ˙˚ ÍÎ ˙ ÍÎ ˚ Adjustable parameters do not appear in any of the the microstructure and hardness calculations presented here. During ageing and overageing, the volume fraction of the precipitate, f, also changes with time, a process that is estimated through the first part of Eq. [6.7]. Figure 7.5 shows that the volume fraction changes with ageing time at three temperatures, about 30% over the course of overageing at 400°C, more than 80% at 450°C, and more than

Maraging steels and overageing

137

0.11 0.10 0.09

Precipitation fraction

0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00



103

104

Time (s)

105

106

7.5 Precipitate volume fraction variations with overageing time. The solid, dashed and dotted lines represent ageing at 400°C, 450°C, and 500°C, for equilibrium volume fractions, 0.108, 0.097 and 0.087, respectively. Triangles represent the volume fractions at the start of experimental measurements of hardness at each corresponding temperature. Open circles represent the volume fractions at the end of hardness measurements at the corresponding temperatures.

double at 500°C. Although one may expect the volume fraction to approach its equilibrium value after a sufficiently long time, one finds instead that the volume fraction is still slowly changing during the measurements. Substituting the value of r into Eq. [7.2] allows calculation of the interdiffusion coefficient, D, through the matrix. The quantity M is a complicated function of the volume fraction of precipitates, as it is influenced by the precipitate volume fraction through the function k(f) in Eq. [7.10]. However, the early treatment relied on LSW theory for the description of precipitate coarsening kinetics, so that k(f) = 1 and any effect from the volume fraction of the precipitates on hardness was neglected. The treatment in Section 7.4.3 chooses the VG (Voorhees and Glicksman) model for coarsening kinetics, defined previously in Eq. [7.4]. The VG coarsening model tends to underestimate the influence of the precipitate volume fraction on hardness, particularly at lower volume fractions. Figure 7.6 compares the kinetic coarsening parameter calculated from models of VG and of WGR (Wang, Glicksman and Rajan), defined previously in Eq. [7.10], changing continually with volume fraction. It shows that in the range of volume fraction 0 < f < 0.25, the values of k(f) predicted by the WGR model are always larger than those from the VG model. Note that the value of k(f)

138

Maraging steels

approaches 1 in both models, which is the LSW limit where the volume fraction of the precipitates vanishes. The matrix interdiffusion coefficient calculated at different temperatures from the overageing experiments is included in Table 7.4, which is roughly half of that obtained in Section 7.4.3. The reason for the discrepancy is that Section 7.4.3 uses the kinetic coarsening parameter, k(f), derived from the VG model, which, as mentioned earlier, underestimates the effect of precipitate volume fraction. The diffusion coefficient allows both precipitate coarsening (Eq. [7.2]) and hardening effects (Eq. [7.8]) to be estimated during overageing at various temperatures. We calculate the microstructural hardness values and compare them with experimental results in Fig. 7.4. The calculated hardening effect during overageing is in agreement with experimental observations, considering the lack of any free parameters. The hardness increase from precipitation, as calculated in this section, appears to be in better agreement with experiment than that calculated using the model described in Section 7.4.3. We ascribe this finding to the fact that the theory in Section 7.4.3 underestimates the effect of volume fraction. The D values derived during overageing in this section are about 8–16 times those found for the ageing period. Nevertheless, as clearly demonstrated in this section, the WGR coarsening model yields theoretical predictions for microstructural evolution that are in good agreement with experimental observations. This coarsening model can therefore be applied to

Coarsening parameter, k(f )

3.0

2.5

2.0

1.5

1.0 0.00

0.05

0.10 0.15 0.20 Volume fraction, f

0.25

0.30

7.6 The coarsening kinetic parameter, k(f), plotted versus volume fraction. The solid line represents behaviour based on the coarsening model by Wang, Glicksman and Rajan, Eq. [7.10]. The dashed line shows behaviour obtained with the coarsening model of Voorhees and Glicksman, Eq. [7.4].

Maraging steels and overageing

139

the study of precipitate coarsening even when the diffusion mechanism might not be experimentally delineated. In summary, we employ Thermo-Calc linked to Kaufman’s binary alloy database to calculate the equilibrium values of the matrix solubility at different temperatures. These data are used to calculate the thermodynamic parameters that are required for estimating overageing kinetics. Using the Ashby–Orowan theory and hardness measurements for the maraging steel allows for the calculation of the average precipitate size as a function of time and temperature. Finally, by combining the calculated average precipitate size, thermodynamic data and a coarsening model based on diffusion screening theory, we extract the interdiffusion coefficient. The entire methodology is applied to and checked against experiments for the alloy Fe–12Ni–6Mn. A few additional conclusions may be drawn: (1) Microstructural evolution kinetics was successfully linked to hardness increase, which is a key mechanical property of materials determined via an advanced coarsening modelling and the Ashby–Orowan relationship. The calculation of the hardness increase is in agreement with experiment. It also shows that the current predictions are more accurate than those described in Section 7.4.3. This result also suggests that WGR coarsening kinetics may be generally applicable for the calculation of hardness and other mechanical properties and for the estimation of the interdiffusion coefficient and service life at elevated temperatures. (2) Using experimental hardness data and a suitable coarsening model, one may extract the matrix interdiffusion coefficient at different temperatures. This represents a novel procedure for extracting diffusion data from microstructural modelling, which differs from the traditional diffusion couple experiment. However, introducing a correct estimate of the influence of the precipitate volume fraction is non-trivial and remains a key factor in determining accurate diffusion data. The effect of volume fraction on precipitation kinetics was ignored in early work. (3) Comparing diffusion data during overageing derived from this section with existing lattice diffusion data reveals that the diffusion mechanisms for precipitate growth (ageing) and coarsening (overageing) are different. Therefore, the study of precipitate coarsening may help identify the diffusion mechanism when it is not fully delineated through other experiments. (4) The model of microstructure evolution and precipitation hardening described in this section is based on fundamental physical metallurgical theories. The present methodology, although applied here only to a specific maraging steel, could be extended to other precipitation hardening alloys. Section 7.4 and this section also provide a template to demonstrate how coupling advanced computational tools for microstructural modelling with

140

Maraging steels

thermodynamic databases can be used to extract the multi-component diffusion coefficient, which otherwise would be difficult and slow to assess experimentally.

7.6

References

Glicksman M E (2000), Diffusion in Solids, field theory, solid-state principles and Applications, Wiley, New York. Wang K G, Glicksman M E and Rajan K (2004), ‘Modeling and simulation for phase coarsening: A comparison with experiment’, Phys Rev E, 69, 061507. Wang K G, Glicksman M E and Rajan K (2005), ‘Length scales in phase coarsening: Theory, simulation, and experiment’, Computat Mater Sci, 34, 235–53.

8

Precipitation hardening stainless steels Abstract: The precipitation process in wrought PH13-8 steel during ageing is the main topic of this chapter. The precipitates formed are enriched in nickel and aluminium, and depleted of iron and chromium, but the composition is far from the stoichiometric NiAl phase. They may take on different shapes at different temperatures. The hardening effects observed during the early stages of ageing should be caused by the redistribution of atoms such as iron, chromium, nickel and aluminium. Particle coarsening takes place simultaneously with the development of the composition of the NiAl-enriched precipitates. Other topics include the use of small-angle neutron scattering, and the effects of intercritical annealing. Key words: atom probe, microstructure, ageing, toughness, grain refinement.

8.1

Microstructural evolution in PH13-8 after ageing

The hardness of PH13-8 (Fe–0.97Al–12.43Cr–2.15Mo–8.39Ni) reaches a peak after 30 minutes at 593°C, but still increases after ageing for 4 hours at 510°C (Fig. 8.1). The ageing behaviour of this wrought PH13-8 stainless steel is significantly different from cast PH13-8 steel. There is no contrast in the field-ion microscopy (FIM) image at peak hardness after ageing at 593°C (Fig. 8.2), where, for maraging and PH steels, austenite normally shows a contrast. Atom probe data is obtained from the instrument in the form of a sequence of the mass-to-charge ratio of each of the ions evaporated. The 550 500

HV2

450 400 510∞C 593∞C As quenched

350 300 0

10 100 Ageing time (min)

1000

8.1 Age hardening curves at 510°C and 593°C of PH13-8 steel

141

142

Maraging steels

8.2 Field-ion microscopy image of PH13-8 steel aged at 593°C for 30 minutes. The distance across the image is about 70 nm.

three-dimensional (3D) atom probe (3DAP) instrument allows a high mass resolution, through the introduction of a reflectron-based energy-compensation system. In the example mass spectrum shown in Fig. 8.3, a minor problem is the exact coincidence of 58Fe2+ and 58Ni2+, and 64Ni2+ and 96Mo3+ peaks. In this section, these are regarded as 58Ni2+ and 96Mo3+, respectively, following the abundance distribution of each isotropic species in its natural form and the amount of the elements in the alloy. A small peak at mass/charge ratio 1 is also present, corresponding to H+. This is not included in the composition calculations, as the hydrogen atoms are absorbed to the tip surface from the vacuum chamber. After homogenisation at 1121°C for 4 hours (furnace cooled), followed by solution treatment at 927°C for 1.5 hours (fan cooled), with no refrigeration treatment, no retained austenite was present in the PH13-8 stainless steel, determined by Mössbauer spectroscopy. After solution-treating PH13-8 at 900°C for 30 minutes, X-ray diffraction confirms that there is a complete martensite transformation. The martensitic transformation start and finish temperatures, Ms and Mf, are about 60°C and 20°C, respectively. In the

Precipitation hardening stainless steels

143

15

35

Number of ions

10000

1000

100

10

1 10

20 25 Mass/charge ratio

30

8.3 Mass spectrum of the steel aged at 510°C for 4 minutes.

research described in this section, the solution treatment is 1.5 hours at 927°C, so it is reasonable to neglect the influence from retained austenite. The following sections focus on the evolution of the precipitation process during ageing.

8.1.1 Ageing at 510°C 4 minutes The distribution of the elements seems to be homogeneous from observation of the atom maps of aluminium, chromium and nickel under this condition (Fig. 8.4, using aluminium and nickel as examples). Frequency distribution analysis is used to examine whether each element is distributed randomly. If all the atoms of one type of element have a random distribution, the frequency distribution will follow what is described by a binomial model. When the frequency distribution analysis result deviates significantly from the binomial model, the element distributes non-randomly. Such analysis reveals that chromium, iron and nickel are not randomly distributed in the matrix whereas the other elements are. It is difficult, however, to identify which of the following is the cause for this inhomogeneity: ∑ ∑ ∑

There is inhomogeneity in the material before ageing that is not erased after the re-austenisation treatment (1.5 hours at 927°C); The steel is homogeneous at the end of the re-austenisation treatment at 927°C, but decomposition occurs during the cooling process from this temperature; Decomposition occurs during the 4 minutes ageing at 510°C.

Although aluminium was not determined as having a non-random distribution from the frequency distribution analysis, the contingency tables

14 nm

Maraging steels

14 nm

144

15 nm

15 nm 10 nm (a)

10 nm (b)

8.4 Atom maps of (a) aluminium and (b) nickel in steel aged at 510°C for 4 minutes (the size of aluminium atoms has been made larger to enhance the display).

of nickel and aluminium show that these two elements are correlated (Table 8.1). Contingency table analysis also shows the rejection between chromium and nickel, and between iron and chromium. There is no correlation between chromium and aluminium. It is not surprising to see that iron and chromium tend to reject each other as iron is the major element in the matrix and chromium is non-randomly distributed. The rejection between chromium and nickel is normally present in Fe–Cr–Ni ternary alloys. 15 minutes The atom map of aluminium in the steel does not clearly show any nonrandom distribution (Fig. 8.5); neither do the atom maps of the other elements. Frequency distribution analysis indicates that aluminium, chromium, iron and nickel atoms are non-randomly distributed, which is also revealed by composition profiles. Contingency table analysis is used to test the correlations between different species of atoms. The correlations between nickel and aluminium, between chromium and nickel, and between iron and chromium are similar to those in the steel aged for 4 minutes. Rejection between chromium and aluminium is also present in this condition. 40 minutes Detectable particles form after ageing for 40 minutes at 510°C (Fig. 8.6). Smooth data visualisation can reveal the shape of the precipitates clearly.

Precipitation hardening stainless steels

145

Table 8.1 Contingency tables between nickel (across) and aluminium (down) in steel aged at 510°C for 4 minutes (atoms per block: 10) Observed table   0 1 2–10

0 4473 641 51

Expected table 1 2963 374 29

2–10 1009 0 101 1 6 2–10

0 4521 597 45

1 2946 389 29

2–10 974 128 9

40 nm

c probability: 1% (c2: 13.2, degrees of freedom (DoF): 4).

27 nm

26 nm

8.5 Aluminium atom map of steel aged at 510°C for 15 minutes.

The three-dimensional morphology obtained through a two-point-simple smoothing method matches well with the visual impression from atom maps through rotating the analysed volume. Nickel-enriched areas and aluminiumenriched areas are at about the same locations, indicating cosegregation (Figs. 8.6c and 8.6d). The value of the iso-surface may significantly affect the apparent size of the precipitates in the smooth data visualisation image. One value is used for each element type throughout this section to make the particle size comparable. The particles are enriched with aluminium and nickel, and depleted of iron and chromium (Table 8.2, where data in each row is from one single particle). Correspondingly, the matrix is depleted of aluminium and nickel (Table 8.3). The difference between the amount of chromium in the matrix and its nominal level is not significant, and the amount of iron in the matrix is expected to be higher than that in the overall composition. Molybdenum is randomly distributed, with a level of around 1 at% in all particles. A particle analysis method has been developed to quantify particles from

146

Maraging steels

(a)

(b)

(c)

(d)

8.6 Atom maps of (a) aluminium and (b) nickel after ageing at 510°C for 40 minutes, and iso-surface maps with iso-surface values of (c) 7.5% for aluminium, and (d) 18% for nickel, respectively. The box size is 11 ¥ 11 ¥ 110 nm. Table 8.2 Compositions of the particles measured by 3DAP (at%) Tage (∞C)

tage

Al

Cr

Ni

Fe

510 40 min 4 h

14±2 17±2 26±3 17±2

6±1 6±1 5±1 5±1

18±2 26±3 23±3 24±2

61±2 50±3 44±3 51±3

593 6 min 30 min

19±2 16±2 26±2 19±2

5±1 7±1 3±1 4±1

27±2 19±2 35±2 22±2

48±3 57±3 34±2 53±2

3D atom probe data (Vaumousse et al., 2003). The determination of soluterich regions is performed by connecting solute atoms that lie within a given distance, 0.5 nm in the present case. Then, only particles containing above a certain minimum number of solute atoms (ten in this study) are kept for further quantification. Data selected in this way can be used for subsequent

Precipitation hardening stainless steels

147

Table 8.3 Compositions of the matrix measured by 3DAP (at%) Tage (∞C)

tage

Al

Cr

Mo

Ni

Fe

510

40 min 4 h

0.9±0.2 0.3±0.1

12.7±0.6 12.9±0.5

1.4±0.2 1.4±0.2

6.2±0.4 5.7±0.3

78.6±0.8 79.4±0.6

593

6 min 30 min

0.4±0.1 0.59±0.01

14±1 1.5±0.3 8.04±0.08 1.94±0.09

6.7±0.6 6.88±0.46

77.5±0.9 82.36±0.65

determination of parameters such as size, shape, solute composition, number density and volume fraction. The particles of aluminium being referred to here do not necessarily contain 100% aluminium. However, within a particle, at least two aluminium atoms are always spaced within 0.5 nm. The distribution shows a larger number of small particles (less than 20 aluminium solute atoms) than advanced particles (Fig. 8.7). This reflects the early stage of particle formation after 40 minutes at 510°C. The average size of the precipitates is 1–2 nm in diameter. 4 hours The precipitates have an irregular plate morphology rather than a needlelike shape (Fig. 8.8). Smooth data visualisation shows the plate morphology. The size of the plate precipitates is about 8–10 nm in diameter and 2 nm in thickness. The composition profiles in Fig. 8.9 are in a direction perpendicular to the plate surface. The profiles of aluminium and nickel show a plate thickness of about 2 nm. The precipitate shape observed from atom maps may somehow deviate from the actual shape of the precipitate owing to the evaporation sequence and irregularities of atoms from the specimen and the subsequent reconstruction. The compositions of three precipitate particles calculated around their cores are given in Table 8.2 individually to demonstrate the diversity in the apparent particle composition. Again, these particles are NiAl-enriched and Fe, Cr-depleted.

8.1.2 Ageing at 593°C 6 minutes The precipitates are needle-like and along the same direction (Fig. 8.10). They are about 2 nm in diameter and 4–5 nm in length. The compositions of two particles and the matrix are listed in Tables 8.2 and 8.3, respectively. 30 minutes From the smooth data visualisation of aluminium (Fig. 8.11), the particle in the middle of the view is needle-like. However, it is not clear what shape

148

Maraging steels 16 Number of clusters

14 12 10 8 6 4 2 0 0

20

40 60 Number of aluminium atoms

80

100

8.7 Distribution of aluminium clusters particle size against the number of particles in the steel aged at 510°C for 40 minutes. Sample volume 8.27 × 10–24 m3.

the precipitate takes from the smooth data visualisation of nickel atoms. The composition of the particles and the matrix are again included in Tables 8.2 and 8.3. It is possible that reverted austenite forms after 30 minutes at 593°C. Thermodynamic calculation gives a body centred cubic (bcc) (55.3 mol%) composition of 80.0Fe–14.2Cr–2.9Ni–1.3Mo–1.5Al (at.%) and a face centred cubic (fcc) (44.7 mol%) composition of 69.9Fe–12.1Cr–14.2Ni–1.2Mo2.6Al (at%).

8.1.3 Precipitate characteristics The precipitation progress during ageing is described in the above two sections. It is now clear that the particles formed are NiAl-enriched zones. When ageing at 510°C, such zones start to form at a time between 15 and 40 minutes. At 593°C, such precipitates form in less than 6 minutes ageing. The composition of such zones is far from that of the stoichiometric NiAl phase. However, the amounts of aluminium and nickel in precipitates increase and the amounts of iron and chromium decrease when ageing is prolonged. In Fe–Ni–Al–Mo systems, after prolonged ageing at high temperatures, NiAl precipitates contain only a small amount of iron. Stoichiometric NiAl exhibits an ordered B2 structure up to its congruent melting point, and the superlattice is stable over an aluminium concentration range of 41.5–55 at% at room temperature. It is not clear whether the NiAlenriched phase observed using the atom probe has a B2 structure since the total of nickel and aluminium atoms is less than half of the particle composition. The observed superlattice spots in the selected area diffraction patterns are found in steel after much more prolonged ageing. At an early stage of precipitation, 40 minutes at 510°C, the NiAl-enriched particles are spherical. However, when ageing proceeds, the precipitates

149

20 n m

20 n m

Precipitation hardening stainless steels

17 nm

17 nm

16 nm

16 nm

(a)

20 n m

20 n m

(b)

16 nm

16 nm (c)

17 nm

(d)

17 nm

17 nm

17 nm

20 nm (e)

8.8 Distribution of (a, c, e) aluminium and (b, d) nickel after 4 hours ageing at 510°C. (a–d) are atom maps recorded from two different directions of projection, since it is difficult to visualise the shape of the precipitates from one direction. Their relationship can be discerned from the different lengths of the edges. (e) is an iso-surface map of aluminium with an iso-surface value of 7.5%.

Maraging steels

Concentration (at%)

30

Al

25 20 15 10 5 0 0

5

10

15

Concentration (at%)

40

20 Ni

35 30 25 20 15 10 5 0

0

5

10

15

20

Concentration (at%)

30 Cr

25 20 15 10 5 0

Concentration (at%)

150

0

5

10

15

20

90 80 70 60 50 Fe

40 30 0

5

10 Distance (nm)

15

20

8.9 Composition profiles of aluminium, nickel, chromium and iron of a 2 ¥ 2 ¥ 18 nm3 tube of the steel aged at 510°C for 4 hours (block size: 0.2 nm).

151

13 n m

13 n m

Precipitation hardening stainless steels

10 nm

10 nm 9 nm

9 nm (a)

(b)

9 nm

9 nm 10 nm

13 nm

(c)

10 nm

13 nm

(d)

8.10 Distribution of (a, c) aluminium and (b, d) nickel in the steel aged at 593°C for 6 minutes. (a, b) Atom maps in the analysed volume; (c, d) iso-surface after performing smooth data visualisation treatment to show the 3D morphology.

become plate like (4 hours at 510°C). When the ageing temperature is 593°C, the precipitates formed after 6 minutes have a needle shape. The general trend in the precipitate sequence is that needles are observed at small supersaturation and plate morphology is observed at large supersaturation. The precipitate size increases with increasing ageing. At 510°C, detectable precipitates can only be observed after ageing for 40 minutes. The number density of the aluminium particles containing ten or more aluminium atoms is about 2.6 ¥ 1025 m–3. After 4 hours ageing, the particle density decreases to about 2.2 ¥ 1024 m–3. This decrease in number density can only suggest particle coarsening during ageing.

17 nm

Maraging steels

17 nm

152

17 nm

17 nm

17 nm

17 nm (b)

(a)

17 nm

17 nm

17 nm

17 nm

17 nm

17 nm

(c)

(d)

8.11 Distribution of (a, c) aluminium and (b, d) nickel in the steel aged at 593°C for 30 minutes. (a, b) Atom maps in the analysed volume; (c, d) iso-surface after performing smooth data visualisation treatment to show the 3D morphology.

Longer ageing times may allow further development of the composition of the precipitates or new types of precipitate. Thermodynamic calculation shows that Laves phase (Fe,Cr)2Mo may exist in the equilibrium state of PH13-8 steel at 510°C or 593°C. This Laves phase is observed in a cast PH13-8 alloy aged at 621°C, with coexistence of M23C6 in the H1150M condition (homogenisation at 1038°C for 1.5 hours, then 2 hours at 760°C followed by 4 hours at 621°C).

Precipitation hardening stainless steels

153

8.1.4 Molybdenum segregation at precipitate/matrix interface The effect of molybdenum segregation at the precipitate/matrix interface differs from alloy to alloy. There is clear molybdenum segregation at the interface in 1RK91 maraging steel, whereas there is no molybdenum segregation in other Fe–Ni–Al–Mo systems. There is no clear indication that molybdenum segregates to the precipitate/matrix interface in the PH13-8. One important feature of the PH13-8 alloy is that the precipitates are highly resistant to coarsening, which enables the alloy to maintain its mechanical properties during service at elevated temperatures. The mean size of the particles is only about 7 nm even after ageing at 625°C for 4 hours in wrought grades, and no larger than 50 nm after H1150M treatment of a cast product. The coarsening rate is dependent on the lattice parameter mismatch between the precipitates and the matrix. The molybdenum segregation first proposed through transmission electron microscopy of Fe–Ni–Al–Mo systems is disputed, based on atom probe work on the same material. The mechanism in 1RK91 whereby molybdenum segregation at the particle/matrix interfaces impedes the precipitate coarsening may not apply in PH13-8 alloy. Some of the coarsening theories do predict a very sluggish size increment with size proportional to time1/n, where n can be 4 or 5. This gives a much slower coarsening process than the classical relationship with size proportional to time1/3. In addition, the coarsening process of precipitates can be accompanied by the formation of reverted austenite during ageing. Reverted austenite is a phase that contains a much higher nickel and aluminium content than the matrix. Its formation will undoubtedly decrease the supply of nickel and aluminium atoms to the NiAl-enriched precipitates as, effectively, some nickel and aluminium atoms that dissolved from the smaller precipitates participate in the formation of austenite.

8.1.5 Spinodal decomposition of chromium Chromium shows a non-random distribution in binomial frequency distribution analysis under all the ageing conditions. Two methods are applied to measure the spinodal amplitude of chromium, both based on the comparison of the sample and a model frequency distribution. One is Cahn’s sinusoidal or linear Pa model and the other is the Langer, Bar-on and Miller (LBM) or non-linear model. In each case, the model distribution is compared with the measured distribution using the method of maximum likelihood and a c2 estimator is used to find the degree of fit. The c probability values from the two models are in all but one case 100%, which means that both models for spinodal decomposition fit the observed data well (Table 8.4). However, the measured amplitudes, from Pa or m2–m1,

154 Maraging steels

Table 8.4 Pa and LBM analysis of the decomposition of chromium (atoms per block: 100) Tage (∞C) tage Pa c2 (DoF)

Probability m1 m2 s c2 (DoF) (%)

Probability (%)

510

4 min 15 min 40 min 4 h

2.2 1.7 2.7 2.9

20.6 28.1 29.2 35.2

(16) (20) (22) (19)

100 100 100 1.3

0.5 0.5 1.5 1.0

3.5 2.5 2.5 3.5

1.0 0.5 0.5 1.0

18.0 21.9 28.8 14.4

(17) (20) (21) (19)

100 100 100 100

593

6 min 30 min 1 h

2.5 2.2 1.8

11.1 (15) 11.6 (16) 9.1 (10)

100 100 100

1.0 1.5 0.5

3.0 1.5 3.5

0.5 0.5 0.5

10.0 (15) 12.4 (16) 7.6 (10)

100 100 100

Precipitation hardening stainless steels

155

are comparable to the errors in the average composition in one block of 100 atoms (3%). Nevertheless, this analysis shows some indication of a spinodal decomposition of chromium elements. The distributions of other elements that show non-random distribution, iron, nickel, and aluminium, show significant deviation from the two models and therefore their decompositions are not the spinodal type. Chromium redistribution in low-chromium steels is observed in an aged 11 at% chromium ferritic–martensitic steel using an atom probe. Owing to the high carbon content (0.46–0.83 at%), the actual chromium in the matrix is even lower since chromium takes part in forming M23C6 carbides. After ageing at 400°C for 17 000 hours, there are long range fluctuations, with a concentration difference of 2.9 at%. Therefore, in lowchromium steels, the decomposition of chromium can still follow a spinodal pattern. The possible relation between this spinodal decomposition process and the hardening effects is discussed in the next section.

8.1.6 Hardening mechanisms No detectable precipitates are formed in the steel aged for 4 and 15 minutes at 510°C, although the hardening effects at these ageing conditions correspond to about 20% and over 40% of the total hardness increase, respectively (Fig. 8.1). A similar phenomenon is observed in PH17-4 alloy, where the hardening effect is caused by the chromium spinodal decomposition since no precipitates are present when significant hardening is evident. However, from the 3DAP data, it is impossible to determine which element starts to redistribute first. Spinodal decomposition, in terms of redistribution, assumes that chromium is the first element to start to decompose. The hardening effects during early ageing should be caused by the redistribution of atoms such as iron, chromium, nickel and aluminium. In another precipitation hardening system Al–Mg–Cu, the initial rapid hardening during ageing is associated with a solute–dislocation interaction, that is the solute segregation to the existing dislocations, which causes dislocation locking. The zones formed through atom redistribution or the solute–dislocation interaction caused by solute segregation to dislocations contribute to the early hardening effects. The correlation between aluminium and nickel changes during the ageing process. In the steel aged for 4 and 15 minutes at 510°C where there are no precipitates observed, they reject each other. At a later stage of ageing, there is cosegregation of nickel and aluminium (Table 8.5). It is possible that aluminium or nickel atoms tends to form vacancy–atom complexes, which are then driven to vacancy sinks, i.e. dislocations, resulting in the apparent rejection between nickel and aluminium. When ageing proceeds, the vacancy sinks become fully occupied and the affinity between nickel and aluminium starts to operate, resulting in the cosegregation of nickel and aluminium. A strong indication of the formation of vacancy–Mg complex is shown in an Al–Cu–Mg alloy (Nagai et al., 2001).

156

Maraging steels

Table 8.5 Contingency tables between nickel (across) and aluminium (down) in the steel aged at 510°C for 40 minutes (atoms per block: 10) Observed table 0 1 2 3 4–10

0 34 673 2876 425 88 35

Expected table 1 17 213 2004 397 112 31

2–10 6587 0 1177 1 263 2 41 3 14 4–10

0 33 784 3499 626 139 45

1 17 520 1814 325 72 22

2–10 7164 740 129 28 7

c probability: 0.1% (c2: 743.7, degrees of freedom (DoF): 8).

Modelling the precipitation hardening kinetics has been a long-term interest. Precipitate hardening theories usually assume the composition of the precipitate to be stoichiometric and then correlate the strength change to the precipitate size and fraction. In a more complete, physical model, the composition change during ageing should be taken into account. The growth and coarsening kinetics should be revised accordingly as well.

8.1.7 Summary In wrought PH13-8 steel, detectable precipitates form after 40 minutes ageing at 510°C, or 6 minutes at 593°C. They are enriched in nickel and aluminium, but depleted of iron and chromium. The amount of nickel and aluminium increases when ageing proceeds, but the precipitate composition is far from the stoichiometric NiAl B2 phase after 4 hours at 510°C (H950), or 30 minutes at 593°C. Ageing for 40 minutes at 510°C produces spherical NiAl-enriched particles. The precipitates may take on different shapes at different ageing temperatures. Coarsening processes take place simultaneously with development of the composition of the NiAl-enriched precipitates. There is no significant molybdenum segregation at the precipitate/matrix interface. The decomposition of chromium differs from that of the other elements. It is possible that spinodal decomposition of chromium takes place in this low-chromium stainless steel. The hardening effects observed during the early stages of ageing should be caused by the redistribution of atoms, possibly through the solute–dislocation interaction caused by solute segregation to dislocations.

8.2

Small-angle neutron scattering analysis of precipitation behaviour

In the work by Staron et al. (2003), qualitative information about the composition of the precipitates was provided by the energy filtering transmission electron

Precipitation hardening stainless steels

157

microscopy (EFTEM) mapping images of various elements, in Fe–1.2Al– 13Cr–0.6Mo–8.3Ni–1Ti–1.1Si steel. They then claimed that all precipitates are of one type, showing depletion in iron and chromium, and enrichment in nickel, titanium and silicon. However, such a qualitative approach may result in misleading conclusions. On one hand, it is virtually impossible to tell that depletion or enrichment of various elements indeed takes place at each precipitate, especially when the precipitates have an extremely fine scale and large number density. On the other hand, precipitates of different types may be adjacent, one type being the nucleation site of the other type. Fine particles of G-phase, enriched in silicon, nickel and manganese, have been found in intimate contact with the copper precipitates in a PH17-4 stainless steel. The subtle position difference of such precipitates of different type may not be discernible by EFTEM. The EFTEM mapping images do not provide enough evidence to discard the existence of Ni3Ti precipitates. There is indeed another reason for Staron et al. (2003) to exclude the possible presence of Ni3Ti. The calculated nuclear scattering length density (NSLD) and the ratio A of magnetic to nuclear scattering intensity for Ni3Ti deviate from the measured values from small-angle neutron scattering (SANS). However, a closer look at their calculations reveals that some of the assumptions used can be improved. (1) The precipitate formed was assumed to have a stoichiometric composition in their calculations. In reality, the composition of a certain type of precipitate evolves during ageing and it may deviate far from the stoichiometric formula (Chapter 4 and Section 8.1). Since the calculation of NSLD and the A ratio is very sensitive to the phase composition, the calculated NSLD and A ratio values may not be accurate. If a real composition of the Ni3Ti, measured by atom probe field-ion microscopy (APFIM), Fe–2Cr–2Mo–65Ni–7Al–20Ti (at%), is used, the calculated values for the nuclear scattering length density hnuc, and the A ratio will be 5.68 ¥ 1014 m–2 and 7.44, respectively. If the ageing is carried out at lower temperatures for a shorter time, the NSLD and A ratio values calculated from the real composition may fall in the range of the measured values. In fact, when the volume fraction of precipitates formed is examined closely (Staron et al., 2003), whatever type the precipitate is, Ti6Si7Ni16, Ni3Ti or Ni3Mo, the alloy composition simply does not allow such high amounts of precipitates to form. The formation of 7.8 mol% (mol% very close to vol% in numerical values) Ti6Si­7Ni16 requires about 1.6 mol% Ti and 1.9 mol% Si, whereas the alloy only contains 1.0 mol% Ti and 1.1 mol% Si. Indeed, Staron et al. (2003) did realise that the composition could change with time but they probably underestimated the extent of its influence. (2) The composition of the matrix is assumed to be unchanged prior to and

158

Maraging steels

after ageing, which cannot be justified. If a measured martensite matrix composition is used, Fe–0.7Si–11.4Cr–1.1Mo–2.8Ni–0.5Al–0.1Ti (at%), the calculated NSLD value for the nuclear scattering length density of the martensite matrix, hnuc, m, would be 7.39 ¥ 1014 m–2, instead of 7.24 ¥ 1014 m–2. In turn, the calculated A ratio for Ni3Ti is 6.3 (hnuc = 5.68 ¥ 1014 m–2), whereas the calculated values for hnuc and the A ratio for the G-phase are 4.87 ¥ 1014 m–2 and 3.5, respectively. It is not clear what role the reverted austenite will play in the calculations. The austenite formed during ageing has a composition different from that of the parent martensite. It can be considered to be a precipitate and sometimes termed a precipitated austenite. Its existence after long-term ageing is a matter of fact, which contributes greatly to the softening of maraging steels after peak hardness. A comparison between the newly calculated values and the ones reported by Staron et al. (2003) is given in Table 8.6. One can see the uncertainties involved in the SANS analysis. Both SANS and APFIM are well-established techniques for the study of fine precipitates. Each has its own advantages and disadvantages and which technique is to be used depends on the purpose of the research. One significant advantage of SANS over TEM and APFIM is that its sampling size can be many orders of magnitude larger and therefore the inhomogeneity statistics of SANS are more representative of the microstructure sampled. The size distribution and number density of the precipitates formed during the early stages, when they are very small, can be determined by SANS. However, interpretation of the SANS results may not be straightforward if there is more than one type of precipitates in the matrix simultaneously (Grobe et al., 2000). On the other hand, APFIM has unique capability of measuring composition variations at a nanometre scale. The precipitates formed in the chromium-containing steel consist of both Ti6Si7Ni16 G-phase and Ni3Ti. Table 8.6 Calculated nuclear scattering length densities and A ratios of some intermetallic coherent precipitates compared to the values obtained from measurements

hnuc, p (1014 m–2)

A ratio

Calculated

Staron et al. New values* (2003)

Staron et al. (2003)

Ti6Si7Ni16 5.10 Ni3Ti 5.86 Ni2Ti 4.88 NiTi 2.93 NiAl 5.87 Ni4Mo 8.18 Ni3Mo 8.03 Measured

4.87 4.4 5.68 9.2 – 3.8 – 1.8 – 9.3 – 18.8 – 26.4 5.2–5.5

*Calculated based on the phase composition after 5 hours at 520°C.

New values* 3.5 6.3 3.5 1.8 7.7 26.6 40.1 4.6–6.4

Precipitation hardening stainless steels

159

In conclusion, atom probe field-ion microscopy is a powerful tool for studying the precipitation process in maraging steels. It can determine the type, size and composition of the precipitates formed. The precipitates formed in the chromium-containing maraging steel consist of Ti6Si7Ni16 G-phase and Ni3Ti phase. Interpretation of SANS results should be treated with caution, especially when little information is known about the precipitate type(s) and size.

8.3

Improving toughness of PH13-8 through intercritical annealing

8.3.1 Hardness and Charpy impact strength The ageing time to reach peak hardness position is significantly shortened to 1 hour by QL treatment, but the peak hardness value, HV 482, is lower than after other treatments (Table 8.7 and Fig. 8.12). The age behaviour after Q, Table 8.7 Grain refinement heat treatments Treatment label

Treatment procedures*

Q QL L LQ 2B (QLQL) 2K (LQLQ)

0.5 hour at 927°C, followed by water quenching (WQ) 0.5 hour at 927°C (WQ), followed by 2 hours at 760°C followed by air cooling (AC) 2 hours at 760°C, followed by air cooling 2 hours at 760°C (AC), followed by 0.5 hour at 927°C (WQ) 0.5 hour at 927°C (WQ), 2 hours at 760°C (AC), and 0.5 hour at 927°C (WQ), followed by 2 hours at 760°C (AC) 2 hours at 760°C (AC), 0.5 hour at 927°C (WQ), and 2 hours at 760°C (AC), followed by 0.5 hour at 927°C (WQ)

*All the treatments are followed by ageing at 510°C. 550

Q QL

500

LQ 2B 2K

HV2

450 400 350 300 0

1

10 Time (min)

100

8.12 Age hardening kinetics of the steel subjected to different grain refinement thermal treatments at 510°C.

1000

160

Maraging steels

LQ, 2B and 2K treatments is similar, although the achievable peak hardness values may be different. Q treatment is a standard procedure before ageing in commercial treatments and the mechanical properties after this treatment are therefore reference values for comparison. Since the hardness value is a good representation of the strength level of the alloy, the change in hardness reveals the change in strength. Different heat treatments have little influence on the hardness prior to ageing, although hardness of the steel after 2K treatment may be considered marginally higher (Table 8.8). The Q treatment provides the highest hardness value after 4 hours at 510°C, though the hardness values of the alloy after LQ and 2K treatments are close. The hardness values after 4 hours at 510°C of the alloy which has had QL and 2B treatments are lower than those which have had Q, LQ and 2K treatments. The expected hardness increase through these treatments is not achieved either before or after ageing. However, the Charpy impact strength is significantly improved indeed. Without significant hardness loss, the LQ and 2K treatments provide higher ambient Charpy impact values. The improvement in Charpy impact strength owing to QL and 2B treatments is more significant. Even when the loss in hardness is considered, these two treatments still provide a good combination of strength and toughness properties, and so do the LQ and 2K treatments.

8.3.2 Microstructure and X-ray diffraction analysis Electro-etching is used to reveal the grain boundaries in the specimens. The grain size is 28 µm, 25 mm and 15 mm for Q, LQ and 2K treatments, respectively (Fig. 8.13). 2K treatment significantly refines the grain size, whereas the refinement effect of LQ treatment is weak. With such an obvious refinement effect of 2K treatment, it is surprising to see that the hardness of this treatment is not significantly higher than that of the Q and LQ treatments prior to ageing treatment (Table 8.8). Such refinement has no significant effect on the hardness during ageing, unlike that observed for 18Ni 250-grade where the beneficial effect of grain refinement on hardness and strength is amplified by ageing (Luo et al., 2000). Table 8.8 Charpy impact toughness of the steel (5 ¥ 10 ¥ 55 mm specimens) aged at 510°C for 4 hours after different heat treatments, together with the hardness values before and after ageing Treatment –78°C (J) –40°C (J) 22°C (J) 100°C (J)

HV after ageing

HV before ageing

Q QL LQ 2B (QLQL) 2K (LQLQ)

516 472 498 477 495

331 325 331 333 337

– – – 6 –

– 11 – 15 –

5.5 20 10 24 12

32 – 29 – 39

Precipitation hardening stainless steels

161

0.1 mm

0.1 mm (a)

(b)

0.1 mm (c)

8.13 Optical microstructures of the steel after (a) Q, (b) LQ and (c) 2K treatments after electro-etching.

Although the electro-etching does not reveal the grain boundaries, the microstructure after 2B treatment is finer than that after QL treatment. The brighter phase in Fig. 8.14 is not austenite; otherwise, such an austenite fraction would have been detected by high-resolution x-ray diffraction (HRXRD) analysis using synchrotron radiation. The fact that no reflection peaks for austenite are present in the HRXRD pattern after 2B treatment followed by ageing suggests that little austenite is retained during the 2B treatment and no reverted austenite is formed during the 4 hours ageing at 510°C (Fig. 8.15). The amount of retained or reverted austenite should be no higher than 0.5%. Significant improvement in Charpy impact strength is achieved after ageing the QL and 2B treated alloy, at little expense of hardness. Considering that retained or reverted austenite normally leads to a significant hardness drop, the dual-phase structure after QL and 2B gives a better combination of strength/hardness and toughness properties.

162

Maraging steels

0.2 mm (a)

0.2 mm (b)

8.14 Optical microstructures of the steel after (a) QL and (b) 2B treatments after electro-etching: fresh martensite and parent martensite have a different etching response.

The steel has a clear lath structure after these treatments (Fig. 8.16). Figures 8.16a and 8.16e show two morphologies. It could be that the granular one shows a cross-section of laths, although this morphology is rarely seen in practice. QL and 2B treatments generate similar lath martensitic structures, whereas the martensite packs in Fig. 8.16d are finer than those in Fig. 8.16b. The grain size of the 2B-treated steel is about 10 mm.

Precipitation hardening stainless steels

163

100 90

Normalised intensity

80 70 60 50 40 30 20 10 0 35

45

55 2q (°)

65

75

8.15 XRD profile of the steel after 2B treatment followed by 4 hours at 510°C.

8.3.3 Grain refinement mechanism of intercritical annealing Improvement in toughness of the PH13-8 stainless steel is achieved through the introduction of intercritical annealing. However, a few questions remain to be answered, the topics in this and the next two sections. Intercritical annealing is accomplished by holding the alloy in a a + g twophase region and then cooling to room temperature. It forms a high volume fraction of alloy-rich g-phase, reverted austenite and well-tempered, alloylean at. However, the g-phase formed at temperatures near the temperature at which the transformation of ferrite to austenite is completed on heating, Ac3, is only slightly enriched in alloy content and largely retransforms during cooling, producing a ‘dual-phase’ structure that is a mixture of tempered (at) and fresh (a¢) martensite. While intercritical annealing produces a dual-phase microstructure, it does not significantly refine the grain size. The LQ treatment shows no clear sign of grain refinement. The reason is that the austenite precipitated along a lath boundary has a strong tendency to retransform into the particular variant of martensite that defines the surrounding packet. However, the martensite packet is chemically heterogeneous after intercritical annealing. The at is relatively lean in solute while a¢ is relatively rich. Although this treatment does not refine the grain size, the chemical redistribution sets up the microstructure for effective grain refinement in subsequent steps, as can be seen from the refinement effects of 2B and 2K treatments. To understand how intercritical annealing can lead to grain refinement, let L-treated steel be given a reversion Q treatment. On heating into the austenite field, both constituents of the L-treated steel revert to austenite.

164

Maraging steels

10 µm (a)

10 µm (b)

10 µm (c)

(d)

(e)

8.16 Scanning electron micrographs (SEM) of the steel after (a) Q, (b) QL, (c) LQ, (d) 2B, and (e) 2K treatments after chemical etching.

However, low diffusivity of the substitutional species in the g-phase prevents their homogenisation. The ‘dual-phase’ character of the alloy is preserved. On subsequent quenching, the ‘dual-phase’ alloy undergoes a two-step martensitic transformation. The low-alloy constituent transforms first. Since it is constrained by the surrounding austenite during its transformation, it is severely worked and this deforms the austenite in turn. The high alloy phase then transforms, while constrained and deformed by the martensite that has already formed. The result is that the transformation occurs under severe mechanical constraint, which encourages local volumes to transform into the martensite variants that are most compatible with the local stress

Precipitation hardening stainless steels

165

rather than those that continue the pattern in a martensite packet. The result is a very fine-grained microstructure. To clarify whether the chemical redistribution resulting from the L treatment might disappear after the Q treatment, we can calculate the diffusion distance of nickel, chromium and molybdenum after 2 hours at 760°C or half an hour at 927°C, using x = √ D · t, where D = D0 exp(–Q/Rt) and x is the diffusion distance, D is the diffusion coefficient, t is time, Q is the activation energy, R is the gas constant and T is the temperature (Table 8.9). The diffusion distance of the three elements after 2 hours at 760°C is longer than that after half an hour at 927°C, which means that the element redistribution caused by L treatment cannot be completely erased by the Q treatment.

8.3.4 Relationships between heat treatment, microstructure and mechanical properties Introduction of intercritical annealing does not always lead to grain refinement. LQ treatment does not have the grain refinement effect. One possible explanation for the non-refinement is that L-treatment may not have set up the chemical redistribution required for grain refinement to take place in subsequent steps. This explanation can be tested by studying the influence of the lower temperature or longer holding time of the L-treatment on grain refinement. However, as discussed below, the contribution to better toughness achieved from grain refinement may not be significant. Even when significant grain refinement is achieved after 2B and 2K treatments, the hardness values show little improvement. In fact, for grade 250 maraging steels, Luo et al. (2000) reported that both hardness and strength were significantly increased owing to grain refinement, whereas other authors found that the grain size had only a minor effect on mechanical properties. The applicability of the Table 8.9 Diffusion distance of nickel, chromium and molybdenum: (a) after 2 hours at 760∞C, (b) half an hour at 927∞C, using different diffusion parameters for 760∞C (diffusion in a-Fe) and 927∞C (diffusion in g-Fe), respectively Element D0 (10–4 m2/s) Q (kJ/mol) D (m2/s) (a) Ni

2.41

Temperature Diffusion distance range (°C) (mm)

242.2

1.37 ¥ 10–16 –16

800–900

0.99

(a) Cr

2.33

238.8

1.97 ¥ 10



775–1698

1.19

(a) Mo

0.663

224.2

3.06 ¥ 10–16

775–1509

1.48

(b) Ni

0.108

273.0

1.42 ¥ 10–17

930–1356

0.16

263.9

5.52 ¥ 10

–17



900–1345

0.32

1.32 ¥ 10

–16



1050–1360

0.49

(b) Cr (b) Mo

0.169 0.036

239.8

166

Maraging steels

Hall–Petch relationship to hardness and strength is difficult to evaluate owing to the existence of the two types of morphology. It is possible that a very small amount of austenite forms between martensite laths after QL and 2B treatments. The amount is too small to be detected even by high-resolution X-ray diffraction analysis using synchrotron radiation. Nevertheless, the lath structures after QL and 2B treatments do appear thinner and shorter than after Q, LQ and 2K treatments. If the toughness of the alloy after Q, LQ and 2K treatments is compared, grain refinement does not significantly improve the toughness. It is, in fact, when a ‘dual-phase’ exists, especially when L-treatment is the end treatment, that the toughness is significantly increased. Such a ‘dual-phase’ structure acts in a similar manner to a mixture of martensite and retained or reverted austenite when toughness is considered, but offers better hardness and strength. Although the possibility that a very small amount of austenite, which is not detectable by high-resolution X-ray diffraction analysis, formed during QL and 2B treatments cannot be excluded, its contribution to toughness, and hardness and strength, should be limited. Dispersion of the precipitates may also influence the strength and toughness of the alloy. There are two types of precipitate in the aged PH13-8 alloy. One type are intermetallic compounds and the other are carbides. The intermetallic compounds contribute to the main strengthening effects and their size is on the nanometre scale. Study of the dispersion of such fine particles requires advanced techniques such as atom probe field-ion microscopy (APFIM, Section 8.1). PH13-8 steel achieves its ultra-high strength through intermetallics precipitation. The amount of carbon is kept as low as possible to minimise the formation of carbides. M23C6 is present in a cast PH13-8 grade with H1150M treatment, about 70 nm in size and with a low number density. Usually, the dispersion of such precipitates would not be expected to affect the properties much. Even if their influence is not negligible, it will have similar effects on the alloy after different treatments, unless the alloy is heated up to 1038°C or above, when the particles dissolve and homogenisation is achieved. In other words, the existence of such precipitates would affect the properties of the Q-treated alloy in about the same way as it would for the QL, LQ, QLQL, and LQLQ treated conditions. The existence of such particles may help grain refinement by pinning grain boundaries. However, this is not the main grain refinement mechanism. The maximum hardness is rather low in the QL and QLQL treated specimens. A possible explanation is given below. QL and QLQL treatments result in a dual-phase structure. Although both phases are martensitic, they have a slightly different composition. Therefore, the hardness of these two phases may not differ very much, which explains why the prior-ageing hardness values for different treatments are very close. However, in the following

Precipitation hardening stainless steels

167

ageing treatments, the softer martensite may act like retained austenite, that is, the strength drop due to its existence may be exaggerated by ageing.

8.3.5 Comparison with commercial H950 treatment PH13-8 alloy after commercial H950 treatment has a yield strength 1449 MPa, HRC hardness 47 (Vickers hardness 471) and Charpy impact strength 27 J (Carpenter Technology Corporation, 2004). Many factors, such as alloy history, composition and Charpy impact specimen size, may play some roles in affecting properties. If one compares the properties of the alloy after different treatments, one will see that both QL and 2B treatments offer much higher Charpy impact strength than the commercial H950 treatment. The hardness values after these treatments are close. The alloy after 2B treatment may be used when the temperature is under –40°C. QL treatment, adding one intercritical annealing step to the commercial H950 treatment, offers a competitive combination of hardness and Charpy impact strength. While H1000 treatment offers similar Charpy impact strength, the hardness is only HV446 (HRC45), much lower than that of QL treatment (HV472). 2B, that is QLQL, which offers better combined properties than QL, might be less cost effective owing to its complex heat treatment steps. LQ and 2K treatments improve the Charpy impact strength when hardness is largely maintained. They may provide alloys with similar toughness but higher hardness than the commercial treatment. 2K treatment, that is LQLQ, might be less cost effective owing to its complex heat treatment steps. The microstructure with ‘dual-phase’ feature might also have superior corrosion-resistant properties, as dual phase steels have been proven to have superior corrosion-resistant properties. In conclusion, QL, 2B, LQ and 2K treatments all provide a better combination of properties than the commercial treatment. Which one is to be used depends on the application requirements as well as the justification for cost. Since thermal cycling treatment is a costly procedure, simple treatment procedures LQ and QL may be more applicable economically.

8.3.6 Summary An intercritical annealing step can be introduced in the treatment of PH13-8 alloy, resulting in four different treatment cycles, austenitisation (Q) and intercritical annealing (L), LQ, 2B (QLQL) and 2K (LQLQ), where Q denotes 0.5 hour at 927°C followed by water quenching, and L denotes 2 hours at 760°C, followed by air cooling. A significant grain refinement effect is achieved after 2B and 2K treatments. Although such refinement of prior austenite grain does not lead to significant increase in hardness either before or after ageing, the Charpy impact strength of the aged alloy is improved.

168

Maraging steels

No retained or reverted austenite is present in the aged alloy. Although grain refinement may improve the alloy toughness, the main contribution is due to the ‘dual-phase’ martensitic structure formed during L-treatment. Such a ‘dual-phase’ structure may provide better combined properties than the usual martensite plus a retained or reverted austenite mixture. All four treatments offer better combined properties than the commercial treatment. QL and LQ treatments may be cost competitive.

8.4

Thermodynamic calculations

Atom probe analysis shows that in a Fe–0.5Si–10.5Cr–2.2Mo–9.6Ni–0.6Al– 0.9Ti alloy, phases present after ageing at 520°C for 5 hours are the a matrix, austenite, Ni3(Ti,Al) with 7 at% Al and a Ti6Si7Ni6 phase. The Kaufman (KP) database contains the Ni3Ti phase and a large number of other relevant compound phases (but not including Ti6Si7Ni6). The computation of driving forces for precipitation of the various phases in a bcc matrix is made by keeping only the bcc matrix as the phase present; the other phases are kept ‘dormant’, that is they are not allowed to become equilibrium phases. A positive driving force indicates a tendency for the phase to be in equilibrium, although if all phases are allowed in the equilibrium calculation, this phase may not appear as an equilibrium phase, depending on the presence of other equilibrium phases. The phases with positive driving forces are Ni3Al (DG/RT = 1.84, where DG is the Gibbs energy change, R is the universal gas constant and T is the temperature), austenite (1.08), and Ni3Ti (0.52). Therefore, the experimental result of an apparently aluminium-enriched Ni3Ti is a mixture of Ni3Al and Ni3Ti. The equilibrium phases are bcc, fcc and Ni3Al, when Laves and m phases are excluded from the calculations. The latter phases appear as equilibrium phases when included, but presumably do not form for kinetic reasons. One of the advances in maraging steels is the successful development by Sandvik Steel of a maraging stainless steel, 1RK91. The thermodynamic equilibria in this steel and its companion, C455, are calculated using the Kaufman database, again because of its more complete inclusion of the relevant phases. At 475°C, a number of phases have a positive driving force in a bcc matrix (Table 8.10). Copper is most unstable in the system and readily precipitates in several forms. Experimentally, almost pure copper particles are found in the early stages of ageing. In later stages, mixed Ni3(Al,Ti) with approximately equal aluminium and titanium concentrations is present in contact with these copper particles, which apparently serve as nucleation sites. This is in agreement with the high driving forces for Ni3Al and Ni3Ti phases. One unresolved issue in the atom probe experiments is whether this mixed Ni3(Al,Ti) is titanium in Ni3Al solution or aluminium in Ni3Ti

Precipitation hardening stainless steels

169

Table 8.10 Driving forces for formation of phases in bcc of 1RK91 maraging steel at 475°C: ThermoCalc calculations Phase

Driving force (DG/RT)

hcp (99% Cu) Ni3Al Cu77Ti23 Ni3Ti Rhombohedral (98% Cu) fcc m Laves FeMo FeCr

3.62 1.86 1.26 0.83 0.32 0.27 0.18 0.14 0.02 0.001

solution. As Ni3Al has a much higher driving force, it is likely that this phase forms first and attracts titanium into it. A number of phases appear in the equilibrium of 1RK91 when all the phases are included in the calculation. However, several strange, iron-rich phases form as matrix, not simultaneously, but all of them preferably to bcc; this is the effect of copper in the development of the equilibrium. These phases are rhombohedral, hexagonal close packed (hcp), fcc, b-Mn, a-Mn and liquid. The rhombohedral and hcp phases here appear as iron rich and form the matrix, presumably to accommodate copper in the equilibrium. When all these are excluded from the calculation, the equilibrium phases are as given in Table 8.11. The equilibrium composition of the bcc phase is Fe–12Cr–2.1Mo–5.4Ni–0.7Cu–0.lTi (wt%). The presence of the copper phase agrees with the atom probe observation of copper clusters in this steel and the Ni3Al and Ni3Ti phases are supported by atom probe work. The absence of some equilibrium phases in experimental observations is probably because the steel did not reach equilibrium during the heat treatments. It is always the case that the equilibrium thermodynamic calculations may only be used as a guideline for systems far from equilibrium. The calculated phase equilibrium of C455 at 475°C when fcc is excluded is summarised in Table 8.12. The comparison of matrix and precipitate compositions between experimental and calculation results, the latter when only the relevant phases present are entered, is excellent. In both steels, experimentally, after ageing at 475°C for 2 hours, Ni3(Al,Ti) phase and copper clusters appeared in the bcc matrix. After 400 hours at this temperature, in 1RK91, the precipitation phases are Ni3(Al,Ti), copper and Fe2Mo Laves, by atom probe composition analysis. Electron diffraction work has identified a quasi-crystalline R¢ phase, as a precursor to the R and Laves phases. The composition of the Fe3Mo2 m phase in the calculation is close to that of the R¢ phase. PH13-8 steel is a low-carbon precipitation hardening stainless steel. The

170

Maraging steels Table 8.11 Equilibrium phases in 1RK91 maraging steel at 475°C Phase

Mole fraction (%)

bcc Ni3Al Cu77Ti23 Ni3Ti µ FeCr

85.9 2.8 1.6 2.9 3.2 3.7

Table 8.12 Equilibrium phases in C455 maraging steel at 475°C Phase

Mole fraction (%)

bcc (Fe–11.9%Cr–5.8%Ni–0.7%Cu–0.1%Ti) Ni3Ti Cu77Ti23 FeCr

92.2 3.3 1.6 2.9

Table 8.13 Calculated compositions of the precipitates and matrix in PH13-8 steel with experimental measurement data from atom probe microanalysis of the steel after ageing at 510°C for 4 hours in parentheses Phase Al

Cr

Ni

Fe

Mo

Mol%

NiAl 49.0 (26±3) 0 (5±1) 51.0 (23±3) 0 (44±3) 0 (0) 2.9 bcc 0.65 (0.3±0.1) 13.5 (12.9±0.5) 6.8 (5.7±0.3) 78.6 (79.4±0.6) 0.4 (1.4±0.2) 94.4 Laves 0 18.3 0 48.4 33.3 2.7

absence of carbon in the steel results in significantly better formability and a good combination of strength and toughness. The only transformation taking place during cooling is martensite formation. Hardening is subsequently achieved by ageing for several hours at 480–620°C. Owing to precipitation during the ageing process, substantial hardening can be achieved before reverted austenite forms. The composition of the alloy is Fe–2.02Al–13.36Cr–1.36Mo–7.96Ni. It is aged at 510°C for 4 hours (the commercial H950 treatment). Since no reverted austenite is formed after such treatment, austenite is excluded in the thermodynamic calculation. Comparison between calculation and atom probe measurement (Table 8.13) shows that the precipitates formed after ageing at 510°C for 4 hours are nickel and aluminium enriched, but the amounts of nickel and aluminium are far from the equilibrium composition. This is because the precipitates have not reached the equilibrium composition for kinetic reasons and the amounts of nickel and aluminium in the precipitates increase when the ageing time increases from 40 minutes to 4 hours at 510°C (Section 8.1). The precipitate type is a B2-ordered NiAl phase when the PH13-8 steel is aged for 4 hours at 621°C. The significant hardening effects after the H950 treatment are caused by the dispersion of these

Precipitation hardening stainless steels

171

nickel and aluminium enriched particles, instead of NiAl precipitates with a stoichiometric composition. Thermodynamic calculation also predicts the existence of Laves phase (Fe,Cr)2Mo. This phase is observed experimentally in a PH13-8 alloy aged at 621°C.

8.5

Quantification of early stage age hardening and overageing

The hardness of the Fe–0.5Si–10.5Cr–2.2Mo–9.6Ni–0.6Al–0.9Ti maraging steel in the early stages of ageing at 420°C is quantified, for the steel without and with cold rolling to 20% thickness (Fig. 6.6 and Table 8.14). The variation of hardness in relation to ageing time in the overaged condition is given in Fig. 8.17. The regression fitting gives the following equation: 3

Ê 1ˆ Ê 1 ˆ –7 ÁË DH ˜¯ = 1.22 ¥ 10 (t – 1.4) + ÁË140˜¯

3

for t ≥ 1.4 hours where the start of the overageing is 1.4 hours. The hardness increase at the start of overageing (HV140) is in good agreement with the experimental value of DH of 141 at the ageing time of 2 hours. Table 8.14 Hardening parameters for the early stages of ageing, using DH = (Kt)n Steel

Temperature (°C)

Cr-steel Cr-steel deformed C455

420 420 425

Time range 2–5 h 2–4 h 12 s – 2 h

K (h–1)

n 4

5.7 ¥ 10 1.5 ¥ 106 1.3 ¥ 105

0.43 0.35 0.254

3.0 ¥ 10–6 2.5 ¥ 10–6

DH–3

2.0 ¥ 10–6 1.5 ¥ 10–6 1.0 ¥ 10–6 5.0 ¥ 10–7 0

0

5

10 15 Ageing time (h)

20

25

8.17 Variation of increase in hardness DH, with ageing time, in the chromium-containing maraging steel aged at 520°C under overageing conditions.

172

Maraging steels

Similar analysis is attempted for the deformed Cr-steel aged at 520°C, for ageing periods between 2 to 4 hours and 20 hours. An appropriate fitting equation could not be reached, presumably because of the recovery process occurring simultaneously with precipitate coarsening. 1RK91 and C455 maraging steels are developed by Sandvik AB, for surgical applications. The precipitates in 1RK91 have an extraordinarily slow coarsening rate owing to molybdenum. The quantified analysis of hardness change in this steel for increasing hardness stages constantly results in very small n values in DH = (Kt)n, well under 0.25, which is the minimum for the traditional hardening theory to be valid (Section 6.1.2). Thus, it is thought that the early stages of ageing in this steel finish earlier than the shortest ageing time used. In C455, however, analysis shows the anticipated linearity (Fig. 8.18). The parameters are included in Table 8.14. The overageing kinetic analyses for C455 and 1RK91 steels give parameters in the overageing equation: 3

Ê 1 ˆ Ê 1 ˆ ÁË DH ˜¯ = M (t – t 0 ) + ÁË DH ˜¯ 0

3

as listed in Table 8.15, with the data points in Fig. 8.19. In summary, age hardening behaviour in stainless maraging steels follows the classical growth and coarsening theories and it can be quantified using just a few accurately measured hardness points.

DH

1000

100

10 0.1

1

10 Ageing time (min)

100

1000

8.18 Variation of initial increase in hardness DH, with ageing time, in C455 maraging steel aged at 425°C. Table 8.15 Hardening parameters for overageing, using (1/DH)3 = M(t – t0) + (1/DH0)3 Steel C455 1RK91

Temperature (°C) 500 580

t0 (h) 33 3.7

M (h–1)

DH0 10

7.2 ¥ 10 1.3 ¥ 108

197 140

Precipitation hardening stainless steels

173

8E-07 C455 500∞C

7E-07

1RK91 580∞C

6E-07 DH–3

5E-07 4E-07 3E-07 2E-07 1E-07 0

100

200 Ageing time (h)

300

400

8.19 Variation of increase in hardness DH, with ageing time, in C344 maraging steel aged at 500°C and 1RK91 at 580°C, under overageing conditions.

8.6

References

Carpenter Technology Corporation (2004), Technical Datasheet: Carpenter 13-8 Stainless, UNS Number S13800, Wyomissing, PA, CRS Holdings Inc. Grobe M, Gokhman A and Böhmert J (2000), ‘Dependence of the ratio between magnetic and nuclear small angle neutron scattering on the size of the heterogeneities’, Nucl Instrum Methods Phys Res B, 160, 515–20. Luo H, Yin Z, Zhu J, Li M, Li H, Guo H, Fang H, Lai Z and Liu Y (2000), ‘Influence of grain size on mechanical properties of 18Ni maraging steel’, Mater Sci Technol (China), 8(1), 59–62. Nagai Y, Murayama M, Tang Z, Nonaka T, Hono K and Hasegawa M (2001), ‘Role of vacancy–solute complex in the initial rapid age hardening in an Al–Cu–Mg alloy’, Acta Mater, 49, 913–20. Staron P, Jamnig B, Leitner H, Ebner R and Clemens H (2003), ‘Small-angle neutron scattering analysis of the precipitation behaviour in a maraging steel’, J Appl Cryst, 36, 415–9. Vaumousse D, Cerezo A and Warren P J (2003), ‘A procedure for quantification of precipitate microstructures from three-dimensional atom probe data’, Ultramicroscopy, 95, 215–21.

9

Applications of artificial neural network to modelling steel properties Abstract: Artificial neural network models are suitable for the analysis and simulation of the correlations between the properties of maraging steels and composition, processing and working conditions. The input parameters are alloy composition, processing parameters including cold deformation degree, ageing temperature and ageing time, and working temperature. The outputs are property parameters, including ultimate tensile strength, yield strength, elongation, reduction in area, hardness, notched tensile strength, Charpy impact energy, fracture toughness and martensitic transformation start temperature. These models can be used to calculate properties of maraging steels as functions of alloy composition, processing parameters and working conditions. Key words: precipitation hardening, mechanical properties, processing, composition, martensitic transformations.

9.1

Model development

Artificial neural network (ANN) modelling is a non-linear statistical analysis technique. It links input data to output data using a particular set of non-linear functions. It provides a way of using examples of a target function to find the coefficients that make a certain mapping function approximate the target function as closely as possible. A fully connected feedforward network consists of at least three layers: the input, hidden and output layers (Fig. 9.1). Each node in the input layer represents the value of one independent variable in the network. The nodes in the hidden layer are only for computation purposes. Each of the output nodes computes one dependent variable. A three-layer (one input, one hidden and one output) ANN with sigmoid transfer functions can map any function of practical interest. ANN modelling normally follows these steps: determination of input/ output parameters, data collection, analysis and pre-processing of the data, training of the neural network, testing of the trained network, and using the trained network for simulation and prediction. Model training includes the choice of architecture, training algorithms and parameters of the network.

9.1.1 Input and output parameters The selection of property-related parameters, or input parameters, is based on the physical background of the determination of the target property. Omitting the unimportant parameters benefits the development of the model 174

Applications of artificial neural network to modelling steel



Input layer

Hidden layer

175

Output layer

9.1 Structure of a neural network.

and simplifies further application. For maraging steels, there are two major thermal treatment processes: austenitising and ageing. A cold deformation procedure is sometimes used between the two treatments to increase the achievable strength level. As long as the austenitising process ensures a full transformation to austenite, the temperature and time only marginally affect the mechanical properties after ageing, in that an increase in austenitising temperature (Taus) or time (taus) usually leads to slightly better toughness and a slight drop in strength. Therefore, Taus and taus need not be used as inputs. In practice, the chosen Taus and taus should be, respectively, sufficiently high and long to ensure a fully austenitic structure and then as low and short as possible to avoid austenite grain growth. The cooling method after austenitising is usually air cooling or water quenching (occasionally oil quenching). It is chosen to ensure a full martensitic transformation and need not be taken as an input parameter either. The cold deformation and ageing treatment are important to the mechanical properties of maraging steels. Therefore, the input parameters include cold deformation degree (e), ageing temperature (Tage), and ageing time (tage). Maraging steels are frequently used and sometimes essential for many high-temperature applications, so the working temperature is another input parameter for the ANN model. Therefore, the inputs for the model consist of alloy composition, processing parameters (including e, Tage, and tage) and working temperature. The outputs of the ANN model are the mechanical properties including ultimate tensile strength (UTS), 0.2% yield strength (YS), elongation (EL), reduction in area (RA), hardness (HV), notched tensile strength (NTS), Charpy impact energy (Ak) and fracture toughness (KIc), as well as martensitic transformation start (Ms) temperature (Fig. 9.2).

176

Maraging steels

Alloy composition

C

Ms temperature

Al

Ultimate tensile strength

Co

Yield strength

…

Elongation Artificial neural network

Deformation degree

Area reduction Hardness

Maraging parameters

Temperature Time

Testing temperature

Notch tensile strength Charpy impact energy Fracture toughness

9.2 Schematic diagram of the ANN model for predicting properties of maraging steels.

9.1.2 Database construction and analysis The performance of an ANN model depends on the dataset used for its training. Construction of a reliable dataset is therefore the first critical step. The dataset is constructed by collecting the available data on properties of maraging steels and low-carbon PH steels from the literature. In total, 2959 input/output data pairs are collected. All the data are for the longitudinal direction. The difference in strength is not significant between the longitudinal and transverse directions, but toughness is directional. Three types of hardness data, HB, HRC and HV, are available. Before model training, the HB and HRC data need to be converted to HV using a conversion table especially for martensitic steels. When the amount of carbon is not given for an alloy (less than 50 cases), it is set as 0.03% by weight. The chemical composition of the alloys contains 13 elements: C, Al, Co, Cr, Cu, Mn, Mo, Nb, Ni, Si, Ti, V and W (Table 9.1). Elements B and Zr are not efficient alloying elements and their uses are rare in the development of maraging steels. Element Be, although classified as a strong hardener, has not been widely employed because of toxicity concerns. Influences from residual impurities Ca, N, O, P and S are ignored. For each of the different output properties, the number of data pairs collected, the data availability and temperature range for each property vary

Applications of artificial neural network to modelling steel

177

(Table 9.2). This defines the range of application of the ANN model. Although most of the data are for properties at room temperature, a significant amount of data at either cryogenic or high temperature are also available (Fig. 9.3). Hardness measurement must be carried out at room temperature. The model will be more influenced by steels with many data points and therefore biased. This should not be considered as a disadvantage, however, as the reliability will be higher where the number of data points is greater.

9.1.3 Neural network training Many parameters can be altered in order to get a well-trained model, among which the training algorithm is important. It has become standard for some years to train ANNs by a method called backpropagation. The term backpropagation refers to the manner in which the gradient is computed for non-linear multilayer networks. The early standard algorithm consisted of assigning a random initial set of weights to the neural network, then presenting the data inputs, one set at a time and adjusting the weights with the aim of reducing the corresponding output error. This was repeated for each set of data and then the complete cycle was repeated until an acceptably low value of the sum of squares error was achieved. Such an algorithm is usually both inefficient and unreliable, requiring many iterations to converge if it converges at all. Therefore, a number of variations of the standard algorithm have been developed, based on other optimisation techniques, with a variety of computation and storage advantages. The two most popular algorithms are the Levenberg–Marquardt algorithm and the Bayesian regularisation (TRAINBR). TRAINBR is a MatLab command for the corresponding function. PREMNMX, POSTMNMX, TRAMNMX, TANSIG, PURELIN and NEWGRNN, which appear later, are also MatLab commands. The Levenberg–Marquardt algorithm is the fastest training algorithm for networks of moderate size. It has a memory reduction feature for use when the training set is large. The time required for training can be dramatically reduced using this method. However, it is sometimes difficult to find the best model using this algorithm. Bayesian regularisation (BR) is a modification of the Levenberg–Marquardt algorithm for obtaining networks that generalise well. It reduces the difficulty in determining the optimum network parameters. A method of avoiding the overfitting problem is the early stopping technique. This is used in combination with Bayesian regularisation. The data are divided into three groups, one-half for the training set, one-quarter for the validation set, and one-quarter for the test set. The model obtained in this way has better performance than using TRAINBR itself. Training of ANN models combines the early stopping technique with the TRAINBR algorithm.

178



C

Al

Co

Cr

Cu

Mn

Mo

Nb

Ni

Si

Ti

V

W

Number* Minimum Maximum Mean Standard deviation

2959 0.001 0.085 0.020 0.029

1479 0 3.2 0.24 0.11

1402 0 20.0 5.7 4.8

1326 0 26.0 6.6 5.1

477 0 4.0 1.0 0.4

1890 0 8.0 1.3 0.4

1782 0 17.5 3.6 2.8

316 0 3.1 0.13 0.03

2505 0 25.5 7.2 11.7

2183 0 2.9 0.32 0.16

1831 0 2.5 0.57 0.46

45 0 10.0 0.34 0.02

281 0 9.6 1.6 0.5

*

The number of alloys that contain the relevant element.

Table 9.2 Database analysis of properties as output data

UTS (MPa)

YS (MPa)

NTS (MPa)

EL (%)

RA (%)

Ak (J)

KIc (MPa m1/2)

Number 922 951 220 801 671 500 107 Minimum 252 283 68 0 0.7 1 8 Maximum 3660 2531 396 43 85 213 260 Mean 1494 1452 287 13 53 50 86 Standard 441 442 71 6 18 43 60 deviation Data All All No W All No No No Cu, availability deformation deformation Nb, V and W Temperature –196 to 816 –196 to 649 –196 to 343 –196 to 816 –196 to 816 –196 to 788 –137 to 316 range (∞C)

HV

Ms (∞C)

1655 89 962 440 154

215 –197 684 245 178

All

No W

Room – temperature

Maraging steels

Table 9.1 Statistical analysis of the alloy composition as input variables (wt%)

Applications of artificial neural network to modelling steel

179

250

872

Number of data points

200

150 117 100

86 64

57

50

52

32 7

11

6

0 –200 to –100 to 0 to –100 0 100

100 to 200 to 300 to 400 to 500 to 600 to > 700 200 300 400 500 600 700 Temperature (°C)

9.3 Distribution analysis of data on mechanical properties versus testing temperature ranges. The 1655 data pairs for hardness are not included in this analysis.

Backpropagation may not always find the correct weights for the optimum solution and re-initialising and retraining the network help to obtain the best solution. Neural networks of other types may also be considered in model creation, such as radial basis function (RBF) networks. Such networks may require more neurons than standard feedforward backpropagation networks, but often they can be designed in a fraction of the time that it takes to train standard feedforward networks. The performance of RBF networks (NEWGRNN) in modelling the Ms temperature of maraging steels is not as good as the model achieved using a backpropagation algorithm, although model training takes less time. Other new generation learning systems, such as support vector machines, are described in dedicated books (Cristianini and Shawe-Taylor, 2000; Hu and Hwang, 2002). Comparatively, the standard ANN method is well developed and has been proven suitable for modelling metallurgical correlations (Sha and Malinov, 2009). Separate models are used for individual properties. This is because training time increases dramatically when the number of outputs increases. Therefore, setting up a series of ANN models where each model deals with only one output value significantly simplifies and speeds up the training of the ANN model. On the other hand, the data available for each individual output property are different. For instance, for one set of input variables whose corresponding UTS is known, the fracture toughness may not have been measured. This makes it difficult to set up one single model where both

180

Maraging steels

UTS and fracture toughness can be trained. Such models, each corresponding to one individual output property, are incorporated into one integrated model (Fig. 9.2). When one set of input parameters is fed into the integrated model, different models, each for one output, will be employed to calculate the set of output properties.

9.1.4 Pretreatment of ageing time In the hardness database, the input parameter ageing time (tage) ranges from 0.001 to 1968 hours with a heavily skewed distribution (Fig. 9.4a). The distribution is presented as a form of histograms in 10 equal ranges between the minimum and maximum values. The ANN model obtained does not perform well when untreated ageing time is used as input. When the ln(tage) value is used as an input parameter, the performance of the ANN model is different. The distribution of ln(tage) is shown in Fig. 9.4b. The performance of the model after this treatment is much better compared with the model without treatment (Table 9.3). This is because most statistical learning techniques, including ANN modelling, can improve model performance by normalising the training data. Taking a logarithm of the parameter tage in the present case is akin to a normalisation procedure. This treatment makes the distribution of this input parameter close to a normal distribution (Fig. 9.4), which is more readily dealt with by ANN modelling in achieving better performance. This treatment of tage is made for modelling other properties since ln-treatment always leads to a more balanced input distribution. Other parameters such as data preprocessing methods, transfer functions and the number of hidden nodes should also be altered to achieve the best model. A program can identify the model with the best performance after model training has been undertaken several hundred times with different training parameters. When each training parameter is altered manually, about 50–100 times of training are carried out to find the best model for this set of training parameters. This model is then stored for later comparison. Another parameter is then altered, followed by 50–100 times of training to achieve the best model corresponding to this set of training parameters. This model is then stored for later comparison. In the end, the models obtained, with the best performance for different training parameters, are compared with each other and the best model is picked for use in future prediction. For example, the optimised model for Ms modelling is a 12-6-1 structure, with functions PREMNMX, POSTMNMX and TRAMNMX for pre- and post-processing. PREMNMX is used to scale inputs and targets so that they fall in the range [–1,1]. This preprocessing procedure can make the neural network training more efficient. POSTMNMX, the inverse of PREMNMX, is used to convert data back to standard units. TRAMNMX normalises data using previously computed minimums and

Applications of artificial neural network to modelling steel

181

600 1558

Number of points

500 400 300 200 100

37 0

1

2

14

12

3

4

19

2

5 6 (a)

0

1

1

11

7

8

9

10

700 604

600

Number of points

500 400 300 249 200

214

163

100 0

27

41

1

2

154

71

3

4

5

(b)

6

7

8

73

59

9

10

9.4 Distribution of the input parameter tage (a) without and (b) with ln-treatment for modelling hardness of maraging steels. Table 9.3 Comparison between two hardness models without and with ln-treatment of ageing time using the mean error and the error deviation as defined in Eqs. [9.1] and [9.2], respectively ln-treatment Range

Input analysis

Prediction analysis



Mean error

Error deviation

Mean error

Error deviation

223.3

–

>40

–

2.7

0

32

0.976

Without With

0.001 to 60.1 1968 h –6.9 to 7.6 1

R in linear regression

182

Maraging steels

maximums by the PREMNMX function. It is used to preprocess new inputs to networks that have been trained with data normalised with PREMNMX. The transfer functions are the hyperbolic tangent sigmoid function (TANSIG) and the linear function (PURELIN). Detailed information about these functions can be found in the manual of Neural Network Toolbox for MatLab (Demuth and Beale, 1998).

9.2

Model performance

Two parameters are used to evaluate the performance of ANN modelling, ‘mean error’ and ‘error deviation’ as defined in Eqs. [9.1] and [9.2]: n



Mean error = 1 ∑ (Ai – Ti ) n i =1 Error deviation =



[9.1]

n ∑ (Ai – Ti )2 – (∑ (Ai – Ti ))2 n(n – 1)

[9.2] In these equations, Ai is the calculated result for the i-th alloy, Ti is the corresponding experimental value and n is the number of alloys in the data set. When two models have close mean errors, both of which are smaller than the target error (for example, 5°C for Ms temperature), the one with the smaller error deviation is better.

9.2.1 Ms temperature The Ms temperature of maraging steels must be closely controlled in order to ensure complete transformation of austenite to martensite. Because Ms is mainly a function of alloy chemistry, the usual requirement for the composition throughout the development of maraging steels is to guarantee an Ms above room temperature. It is highly desirable to understand the influence of alloying elements quantitatively on the Ms temperature of steels. For this purpose, empirical relationships between Ms and the chemical composition of low-carbon high-strength steels have been derived by employing multilinear regression (MLR) analysis. However, the existing expressions neither consider the interactions between individual alloying elements, nor are they fully tested for alloys with many different types of alloying elements since most of the data are for ternary or quaternary alloys. In the database for Ms modelling, most of the data are for alloys with more than four elements. The input variables are the concentration of 12 elements. The performance of different datasets is shown in Fig. 9.5. The mean error of this model on the whole dataset is –1°C, with an error deviation 32°C. On the testing dataset, the mean error and error deviation are –2°C and 46°C,

700

700

600

600

500

500

400

400

Calculated

Calculated

Applications of artificial neural network to modelling steel

300 200 100 0

300 200 100 0

–100

–100

R = 0.976

–200 –200

0

200 400 Experimental (a)

–200 –200

600

700

700

600

600

500

500

400

400

Calculated

Calculated

183

300 200 100 0

R = 0.99 0

200 400 Experimental (b)

600

300 200 100 0

–100

R = 0.962

–200 –200

0

200 400 Experimental (c)

600

–100 –200 –200

R = 0.963 0

200 400 Experimental (d)

600

9.5 Performance of the ANN model for Ms temperature, for (a) all data, (b) training, (c) validation and (d) testing data, respectively.

respectively. For comparison, the error deviation of a MLR analysis of the whole dataset is 64°C (mean error 0°C). The influence of each alloying element on Ms temperature from MLR analysis is Ms = 549 – 500C + 15.9Al – 3.8Co – 18.3Cr – 6Cu – 22Mn + 0.2Mo – 1.6Nb – 17.5Ni – 10Si – 29Ti – 54V (°C), where the element symbol represents the concentration of the element in weight percent. MLR analyses cannot predict correctly the influence of cobalt. This is because one of the important roles of cobalt in maraging steels is raising the Ms temperature, therefore increasing the permissible amount of other age-hardening alloying elements without leaving residual austenite. It would be a major drawback if such an effect cannot be predicted. ANN modelling shows its clear advantage in this aspect, as will be discussed later.

184

Maraging steels

9.2.2 Mechanical properties

600

600

500

500

400

400 Calculated

Calculated

UTS and Charpy impact energy (Ak) are used to demonstrate the ANN models of mechanical properties (Figs. 9.6 and 9.7). For UTS, the model calculation fits the experimental observation well. The mean error of this model is –4 MPa, with an error deviation of 102 MPa. For the test dataset only, the mean error is –2 MPa, with an error deviation of 128 MPa. Evidently, the trained model is capable of predicting new cases. The model for Charpy impact energy also shows good performance, although it is less accurate than the UTS model. All the models perform well overall judging by the performance of the test datasets (Table 9.4). The number of nodes in the hidden layer is six for all of the models, except for KIc (three nodes). Only the data in training and validation datasets are used in the model optimisation process. The test dataset is not involved in the model training

300 200 100 0

200 400 Experimental (a)

200 100

R = 0.968 600

0

400

400

350

350

300

300 Calculated

Calculated

0

300

250 200 150 100

0

200 400 Experimental (b)

600

250 200 150 100

50 0 0

R = 0.983

50

R = 0.947 100

200 300 Experimental (c)

400

0 0

R = 0.946 100

200 300 Experimental (d)

400

9.6 Performance of ANN model for UTS, for (a) all data, (b) training, (c) validation and (d) testing data, respectively.

250

250

200

200

150

150

Calculated

Calculated

Applications of artificial neural network to modelling steel

100 50 0

100 50 0

R = 0.931 0

50 100 150 200 250 Experimental (a)

–50 –50

250

250

200

200

150

150

Calculated

Calculated

–50 –50

100 50 0 –50 –50

R = 0.955 0

50 100 150 200 250 Experimental (b)

100 50 0

R = 0.929 0

50 100 150 200 250 Experimental (c)

185

–50 –50

R = 0.842 0

50 100 150 200 250 Experimental (d)

9.7 Performance of ANN model for Ak, for (a) all data, (b) training, (c) validation and (d) testing data, respectively.

Table 9.4 Statistical analysis of the output data for whole and test datasets of neural network models for prediction of the mechanical properties and Ms temperature of maraging steels

All data

Test data



Mean error

Error deviation

R in linear Mean regression error

Error R in linear deviation regression

UTS (MPa) YS (MPa) NTS (MPa) EL (%) RA (%) Ak (J) KIc (MPa m1/2) HV Ms (∞C)

–4 6 –3 0.1 0.2 –0.8 0.3 0 –1

102 103 186 2.8 8.8 15.8 9.2 32 32

0.968 0.963 0.935 0.887 0.903 0.931 0.988 0.978 0.976

128 137 288 3.2 10.8 21.7 12.3 36 46

–2 14 –1 –0.4 1.6 –0.3 –0.2 –3 –2

0.946 0.954 0.816 0.858 0.886 0.842 0.969 0.976 0.963

186

Maraging steels

process, but solely for the testing purpose. Therefore, the accuracy of an ANN model in prediction is clearly demonstrated by its performance on the testing dataset (Table 9.4). The performance of ANN models for EL, RA and Ak is not as good as that for UTS, YS and HV. This is because ductilityrelated parameters are more easily affected by experimental factors, such as the specimen condition and dimension, rather than strength parameters. The performance of the model for fracture toughness is surprisingly better than that of EL, RA and Ak. Owing to the smaller quantity of KIc data available, the number of hidden nodes is three. Nevertheless, caution should be exercised with this model.

9.3

Comparison of model predictions with experimental data

9.3.1 Ms temperature Following the development of maraging steels, the most important family of grades are C200, C250, C300, C350 and C450 (the strength level in ksi is indicated in the product grades). They are tailored to certain strength levels mainly by varying alloy composition. The first four grades are based on the classical Fe–18Ni system, with different amounts of cobalt, molybdenum, titanium and aluminium, whereas C450 (Fe–6Ni–15Cr–1.5Cu–1Mn–1Si) is very different in that it contains no cobalt. The Ms temperatures of these alloys calculated from the ANN model are in good agreement with experimental values, shown in Fig. 9.8. 350 Calculation

Ms temperature (°C)

300

Experiment

250 200 150 100 50 0

C200

C250

C300 Alloy type

C350

C450

9.8 Comparison of the Ms temperature calculated using the ANN model with experimental values.

Applications of artificial neural network to modelling steel

187

9.3.2 Room temperature properties Since most of the data is for mechanical properties at room temperature, the highest accuracy for the neural network is expected for the prediction of room temperature properties. PH13-8, a martensitic precipitation hardening (PH) stainless steel, offers good mechanical properties under severe environmental conditions, superior to PH17-4 and PH15-5 stainless steels. The alloy is chosen here to show the influence of a common ageing treatment on mechanical properties (Fig. 9.9). The models predict results very close to the experimental results. The accuracy of the ANN models is best for hardness. This is probably because the number of training data pairs is largest for the hardness, compared to the other mechanical properties. However, the accuracy of the network predictions is within the acceptable error range for all the other properties.

9.3.3 Properties over a wide temperature range PH13-8 steel has excellent resistance to oxidation up to approximately 600°C. One important feature of ANN is the ability to simulate materials behaviour over a wide temperature range (Fig. 9.10). The models predict reasonably well between room temperature and 300°C. The model again predicts well the properties of a 450-grade alloy (Fe–15Cr–6Ni–1Mn–1Si–0.75Mo–0.3Nb) when the temperature is up to 300°C (Fig. 9.11). Higher temperature leads to larger deviations from the experimental values. This is because there is a lack of experimental data at cryogenic or elevated temperatures in the database compared with room-temperature data. Therefore, the material behaviour at elevated temperatures cannot be well represented. Although there are not many data between room temperature and 300°C, as the material behaviour remains similar within this temperature range, it is easy to predict it with reasonable accuracy. Caution should be exercised when properties at temperatures above 300°C are calculated using the ANN models.

9.4

Applications of the models

The ANN models can be used to predict Ms and mechanical properties of maraging steels with sufficient accuracy within the data range used in model development. In maraging steels, the interactions between cobalt and molybdenum are complicated. Many alloy developments are based on these interactions. They will be examined here based on model calculations. Since the models have been designed using statistical analysis and not from physical theories, some of the model outcomes will be discussed from the metallurgical point of view, to justify and validate them.

Maraging steels 1800 Exp. UTS

UTS or YS (MPa)

1600

Exp. YS Calc. UTS

1400

Calc. YS

1200 1000 800 600 500

550 600 Ageing temperature (°C) (a)

650

70 60

EL or RA (%)

50 Exp. EL Exp. RA Calc. EL Calc. RA

40 30 20 10 0 500

550 600 Ageing temperature (°C) (b)

650

500 Exp. HV 450

Calc. HV

400 HV

188

350 300 250 500

550 600 Ageing temperature (°C) (c)

650

9.9 Comparison of room temperature properties calculated using the ANN model with experimental values for PH13-8, aged at five different temperatures for 4 hours: (a) UTS and YS, (b) EL and RA and (c) HV.

Applications of artificial neural network to modelling steel

189

2000

Uts/YS (MPa)

1600 1200 800 400

Exp. UTS Exp. YS Calc. UTS Calc. YS

0 –200

100

EL/RA (%)

80

0

200 400 Test temperature (°C) (a)

600

Exp. EL Exp. RA Calc. EL Calc. RA

60 40 20 0 –200

0 200 400 Test temperature (°C) (b)

600

9.10 Comparison of ANN model calculations with experimental values for PH13-8, aged at 538°C for 4 hours: (a) UTS and YS, and (b) EL and RA.

9.4.1 Interactions between cobalt and molybdenum on Ms temperature The alloy system is chosen based around the chemical composition of the classical Fe–18Ni maraging steels, Fe–0.01C–0.1Al–18Ni–0.4Ti–9Co–4Mo (referred to as Fe–18Ni–9Co–4Mo). The amounts of cobalt and molybdenum are variables with values as low as zero so that the influence from these elements can be shown (Fig. 9.12). Cobalt always raises the Ms temperature when no molybdenum is present. However, with molybdenum present, the influence of cobalt becomes complicated. Experimentally, with the addition of 1.5% Mo, cobalt decreases the Ms temperature when its amount is higher than 15%. This tendency can

190

Maraging steels 2000

Uts/YS (MPa)

1600 1200 800 400

Exp. UTS Exp. YS Calc. UTS Calc. YS

0 –200

0 200 400 Test temperature (°C)

600

9.11 Comparison of ANN model calculations with experimental values over a wide temperature range for a 450 grade maraging steel, aged at 482°C for 4 hours.

Without Mo 2 wt% Mo 4 wt% Mo 6 wt% Mo

400

Ms temperature (°C)

350

300

250

200

150

0

2

4

6 Co (wt%)

8

10

9.12 Influence of cobalt and molybdenum on the Ms temperature of the Fe–18Ni–Co–Mo system.

be seen in the curve corresponding to 2% Mo in Fig. 9.12, where the increase in Ms with cobalt content ceases when cobalt is higher than about 9%. From the ANN model, an amount of cobalt above 6% will cause a reduction in Ms when molybdenum is 6%. An increase in molybdenum content always suppresses Ms, and the extent of the reduction is enhanced by an increase in the percentage of cobalt in the alloy.

Applications of artificial neural network to modelling steel

191

9.4.2 Combined influence of cobalt and molybdenum on age hardening kinetics The rate of the precipitation is reflected by the increase in hardness in the early stages of the ageing process. The rate of increased hardness of systems with cobalt is greater than for the system without it (Fig. 9.13). The hardness increase at the peak position of the cobalt-containing systems is much larger than that of the cobalt-free system. This effect can be explained by a metallurgical mechanism. One important role of cobalt in maraging steels is to lower the solubility of molybdenum in martensite, thus producing more densely distributed molybdenum-containing precipitates to increase the strength. The equilibrium fraction of such precipitates increases, promoting the hardening effect. The precipitation of molybdenum is strongly modified by the presence of other elements, most noticeably cobalt. Without cobalt, the precipitation of molybdenum takes place much more slowly. In conclusion, the prediction of the neural network model is in agreement with what is expected from a metallurgical viewpoint.

9.4.3 Combined influence of cobalt and molybdenum on mechanical properties The combined influence of cobalt and molybdenum on other mechanical properties is demonstrated here, using UTS and Ak as examples. The alloy system is Fe–18Ni–xCo–xMo, aged at 482°C for 4 hours, without cold 550

Without Co 5 wt% Co 10 wt% Co

HV

500

450

400

350 10–2

10–1

100 Ageing time (h)

101

102

9.13 Influence of cobalt on the precipitation age hardening kinetics of a Fe–18Ni–Co–4Mo system at 482°C simulated using the ANN model.

192

Maraging steels

deformation, and tested at room temperature. The calculated results show that the addition of a small amount of molybdenum (lower than about 4%) decreases the UTS (Fig. 9.14). Experimentally, the combined effects of cobalt and molybdenum may not be beneficial when the alloying amount of molybdenum is less than 2%. In fact, in commercial maraging steels, the amount of molybdenum is usually higher than 2%. Without molybdenum, the alloying of cobalt increases the Ak values (Fig. 9.15) but such a system will have little ageing response. Alloying with 2% 2200 2000

UTS (MPa)

1800 1600 1400 1200

Without Mo 2 wt% Mo 4 wt% Mo 6 wt% Mo

1000 800

0

2

4

6 Co (wt%)

8

10

9.14 Influence of cobalt and molybdenum on the UTS of the Fe– 18Ni–Co–Mo system. 150

Without Mo 2 wt% Mo 4 wt% Mo 6 wt% Mo

Ak (J)

100

50

0

0

2

4

6 Co (wt%)

8

10

9.15 Influence of cobalt and molybdenum on the Charpy impact energy Ak value of the Fe–18Ni–Co–Mo system.

Applications of artificial neural network to modelling steel

193

molybdenum significantly increases the Ak value of the alloy for cobalt concentrations lower than 8%. When the amount of molybdenum is further increased, the Ak value is significantly decreased. The establishment of Fe–18Ni–9Co–4Mo–0.4Ti as the nominal composition of commercial grade C250 is of no surprise as this provides a good combination of strength and toughness. The laboratory tested UTS and Ak values for the C250 alloy (Fe–18Ni–8.5Co–5Mo–0.4Ti) aged at 480°C for 5 hours are 1870 MPa and 37 J, respectively, in reasonable agreement with the predicted values shown in Figs. 9.14 and 9.15.

9.4.4 Test on alloy 1RK91 1RK91 (Fe–12Cr–9Ni–4Mo–2Cu–1Ti–0.3Al) was developed by Sandvik and is characterised by good fatigue strength at elevated temperatures. It can reach ultrahigh strength through ageing treatment. The agreement between calculation and experimental measurement is acceptable (Fig. 9.16). The calculated room temperature UTS value is 2543 MPa (4 hour ageing at 475°C), within the range of 2450–3000 MPa, quoted by Sandvik Steel (2001) for aged products. This alloy differs from many previous maraging grades in that it contains about 2 wt% copper. Without copper, the alloy may still be age hardened, but the time to achieve considerable hardening will be extraordinarily long, as shown in Fig. 9.16. In fact, although the good mechanical properties of this alloy are attributed to precipitates rich in nickel, aluminium and titanium, copper clusters form before these and act as nucleation sites. The application 750 700

HV

650

425∞C 475∞C 540∞C 475∞C (without Cut) 475∞C (exp.)

600 550 500 450 10–4

10–2

100 Ageing time (h)

102

104

9.16 Age hardening kinetics curves of 1RK91 maraging steel simulated from a model calculation compared with experimental hardness measurements data.

194

Maraging steels

of the neural network model to this alloy demonstrates that it can be a good guide in the development of new alloys. In concluding this section, these ANN models can predict well even the complicated cobalt–molybdenum influences on Ms temperature and mechanical properties of maraging steels. The ANN models can also be a guide for new alloy design. Based on these models, optimisation of alloy composition and processing parameters can be carried out (Sha and Malinov, 2009). For a specified working temperature and the required combination of strength and toughness properties, the model can recommend the most economical composition and processing routes and therefore benefit the industry.

9.5

Summary

Using data from the literature, ANN modelling can simulate the correlation between alloy composition, processing parameters and the properties of maraging steels. The input parameters in the model are the concentrations of 13 elements, C, Al, Co, Cr, Cu, Mn, Mo, Nb, Ni, Si, Ti, V and W, the degree of cold deformation prior to ageing, ageing temperature and ageing time. The output parameters are the mechanical properties and the Ms temperature. Different training parameters are evaluated and the optimum model is used for simulation. The calculations are in good agreement with experimental data. The simulation of the influence of combined cobalt and molybdenum alloying on Ms temperature, precipitation kinetics and mechanical properties is compared with experimental data. Explanations of the simulation results based on metallurgical mechanisms are put forward. The model can be used as a guide for practical optimisation of alloy composition and processing parameters for maraging steels, and low-carbon precipitation hardening steels in order to achieve the desired combination of properties at different working temperatures.

9.6

References

Cristianini N and Shawe-Taylor J (2000), An introduction to support Vector machines and other kernel-based learning methods, Cambridge University Press, Cambridge. Demuth H and Beale M (1998), Neural Network Toolbox User’s Guide for use with MatLab, Version 3, The Math Works, Inc., Natick, MA. Hu Y H and Hwang J N (editors) (2002), Handbook of neural network signal processing, CRC Press, Boca Raton, FL. Sandvik Steel (2001), Data Sheet–Precision Wire Products, Sandviken, Wire Division. Sha W and Malinov S (2009), Titanium Alloys: Modelling of microstructure, properties and applications, Woodhead Publishing, Cambridge.

Index

AerMet 100, 14 age hardening, 112–16 C250, 122 C300, 123 different mechanisms, 111 difficulties, 117–18 calculation uncertainty in line tension, 118 diffusion coefficient determination, 117–18 equilibrium solute concentrations and volume fractions of NiMn precipitates in matrix, 117 Fe–12Ni–6Mn, 121–2 kinetics, 119–21 2000 MPa grade cobalt-free maraging steel, 119–20 2400 MPa grade cobalt-free maraging steel, 120–1 maraging steels quantification, 109–23 matrix concentration and precipitation fraction, 116–17 n2 0.25 explanation, 114–16 precipitation hardening theories, 109–18 strengthening–critical particle size–coherency strain, 109–12 strengthening and particle size, 109–10 strengthening vs softening, 110–12 theoretical derivation, 112–13 typical one-peak curve, 110 ageing, 175 ALSTRUC, 117 AMA equation, 116 Arrhenius expression, 132 Arrhenius parameters, 135

artificial neural network, 14–15 applications to modelling steel properties, 174–94 comparison of ANN model calculations with experimental values MS temperature, 186 over a wide temperature range for 450 grade maraging steel aged at 482°C, 190 for PH13-8, aged at 538°C, 189 room temperature properties for PH13-8, aged at five different temperatures, 188 model applications, 187–94 combined influence of cobalt and molybdenum on age hardening kinetics, 191 combined influence of cobalt and molybdenum on mechanical properties, 191–3 interaction between cobalt and molybdenum on Ms temperature, 189–90 test on alloy 1RK91, 193–4 model development, 174–82 ageing time pretreatment, 180, 182 alloy composition as input variables statistical analysis, 178 data distribution analysis of mechanical properties vs testing temperature ranges, 179 database construction and analysis, 176–7 input and output parameters, 174–5 input parameter distribution, 181

195

196

Index



neural network training, 177, 179–80 properties database analysis as output data, 178 with and without In-treatment of ageing time with mean error and error deviation, 181 model performance, 182–6 mechanical properties, 184, 186 MS temperature, 182–3 model predictions vs experimental data, 186–7 MS temperature, 186 properties over a wide temperature range, 187 room temperature properties, 187 neural network structure, 175 performance for Charpy impact energy, 185 performance for MS temperature, 183 performance for ultimate tensile strength, 184 schematic diagram for predicting properties of maraging steels, 176 steps, 174 test datasets performance for prediction of mechanical properties and MS temperature of maraging steels, 185 Ashby–Orowan equation, 10, 129 Ashby–Orowan relationship, 8, 30 Ashby–Orowan theory, 139 atom probe field-ion microscopy, 11, 12, 13, 30, 114, 117, 157, 159, 166 atom probe microanalysis, 4 austenite reversion, 2, 6, 116, 129, 133 austenitising, 175 Avrami index, 116



backpropagation, 177 Bayesian regularisation, 177 bcc see body centred cubic body centred cubic, 72 Boltzmann probability, 132 Burgers vector, 30, 129, 130

face centred cubic, 72 fcc see face centred cubic Fe–2.02Al–13.36Cr–1.36Mo–7.96Ni, 170 Fe–1.2Al–13Cr–0.6Mo–8.3Ni–1Ti–1.1Si, 157 Fe–28.5Cr–10.6Co, 114 Fe–2Cr–2Mo–65Ni–7Al–20Ti, 157 Fe–12Cr–2.1Mo–5.4Ni–0.7Cu–0.1Ti alloy, 169

C200, 186 C250, 122, 186, 193 C300, 186

age hardening quantification, 123 equilibrium phase compositions and fraction at 510∞C, 123 variation of initial increase in hardness with ageing time, 123 C350, 186 C450, 186 C455, 169, 172 Cahn’s sinusoidal model, 153 carbide, 116 carbon, 1 Charpy impact strength, 13, 160, 161, 167 Charpy V notch, 55–6 classical nucleation theory, 3 coarsening theory, 9 cobalt, 1, 15 cobalt-free maraging steels, 2, 3, 4 computer-based modelling, xi–xii copper, 168 copper maraging steels, grain-refined, mechanical properties, 65 critical particle size, 110, 111 critical resolved shear stress, 111 Darken’s correction, 131 Debye screening, 10 duration, 9 deep quenching, 59 differential scanning calorimetry, 6 diffusion screening theory, 9, 136 dislocation looping, 128 dispersion strengthening theory, 5 electro-etching, 160 electron diffraction analysis, 68 energy filtering transmission electron microscopy, 12, 157 error deviation, 182

Index Fe–19Cr–Ni–Al, 11 69.9Fe–12.1Cr–14.2Ni–1.2Mo–2.6Al, 148 80.0Fe–14.2Cr–2.9Ni–1.3Mo–1.5Al, 148 Fe–18Ni, 112, 114, 118 Fe–Ni–Al–Mo, 68–70 Fe–Ni–Al–Mo alloy system, 4 Fe–Ni–Co–Mo, 70, 72 Fe–18Ni–Co–Mo system influence of cobalt and molybdenum Charpy impact energy value, 192 MS temperature, 190 ultimate tensile strength, 192 influence of cobalt on precipitation age hardening kinetics, 191 Fe–18.5Ni–9Co–4.8Mo–0.6Ti, 123 Fe–Ni–Mn, 72 Fe–12Ni–6Mn, 9, 10, 117 age hardening calculation and comparison at different temperatures, 122 age hardening quantification, 121–2 best fitting parameters, 86 calculations, 131–6 coarsening kinetic parameter vs volume fraction, 138 diffusion coefficient at different temperatures, 133 diffusion coefficients for ageing and overageing, 134 hardness calculated from VG model vs WGR model, 135 parameter values used for precipitation hardening kinetics and extraction calculation, 132 precipitate size as function of time and temperature, 134 precipitate volume fraction variations with overageing time, 137 variation of parameter M during overageing, 132 driving force and critical nucleus radius, 86 matrix concentration and growth constant as functions of time and temperature, 87 overall ageing process, 81–2 parameter determination, 82–6





197

activation energy and Avrami index, 83 critical nucleus size, 85 growth and diffusion constants, 84–5 precipitation fraction at peak hardness, 85–6 reaction rate constant in Johnson–Mehl–Avrami equation, 83–4 strengthening, 82–3 parameters involved in calculation of precipitation strengthening, 83 precipitate size and fraction as functions of time and temperature, 86, 88 precipitation, 79–87 precipitation kinetics and age hardening quantification, 129–36 theoretical analysis, 129–31 transformation fraction at longer time, 129 results calculated with Thermo-Calc using Kaufman binary database, 84 theoretical analysis of early-stage ageing process, 79–81 time–temperature–precipitation diagram, 86 TTP curves for precipitate size and fraction, 89 Fe–Ni–Mo, 70, 72 Fe–0.5Si–10.5Cr–2.2Mo–9.6Ni–0.6Al– 0.9Ti alloy, 168, 171 field-ion microscopy, 114, 141 fractography 2000 MPa grade cobalt-free maraging steel ageing at high temperature (540°C), 56 ageing at intermediate temperature (480°C), 54 ageing at low temperature (440°C), 49, 51 2400 MPa grade cobalt-free maraging steel, 62 fracture toughness, 49 Friedel effect, 112 Gibbs energy calculation, 67

198

Index

Gibbs energy change, 168 Gibbs–Thomson correction, 131 Gibbs–Thomson equation, 127 grain refinement, 13 Guinier–Preston zones, 115 H950 treatment, 167, 170 H1000 treatment, 167 Hall–Petch relationship, 13, 42, 166 high-resolution X-ray diffraction analysis, 161, 166 H1150M treatment, 153, 166 HRC27, 41 HRC28, 41, 120 HRC29, 41, 120 HRC45, 167 HRC53.5, 119 HRC55, 119 HRC57-58, 65 HV 446, 167 HV 482, 159 International Centre for Diffraction Data, 43 International Nickel Ltd., 1 Johnson–Mehl–Avrami equation, 7, 113, 116 Johnson–Mehl–Avrami phase transformation theory, 6 Johnson–Mehl–Avrami reaction rate parameter, 132 K3359, 65 K3364, 65 Kaufman database, 10, 72, 129, 131, 139, 168 K-S shear, 36 Langer, Baron and Miller model, 153 Laplacian (direct) screening, 10 Laves phase, 68, 152, 171 Levenberg–Marquardt algorithm, 177 Lifshitz–Slyozov–Wagner equation, 131 Lifshitz–Slyozov–Wagner growth law, 131 Lifshitz–Slyozov–Wagner model, 8, 115, 135, 137 Lifshitz–Slyozov–Wagner theory, 125, 127, 128, 130

linear Pa model, 153 many-body theory, 9 maraging steels, 1–15, xi see also specific type age hardening quantification, 109–23 artificial neural network modelling correlations, 14–15 chemical compositions and mechanical properties, 63 commercial, nominal compositions and respective strength, 1 description, 1–3 major thermal treatment, 175 mechanical properties, 49–65 microstructure, 17–48 2800 MPa cobalt-containing grade, 48 2000 MPa grade cobalt-free maraging steel, 17–40 2400 MPa grade cobalt-free maraging steel, 40–6 18Ni (350) cobalt-containing grade, 47–8 microstructure and mechanical properties, 3–4 overageing, 8–10, 125–40 phase transformation kinetics and age hardening, 5–8 C250, 6–8 Fe-12Ni-6Mn, 6 precipitation hardening and evolution of precipitates quantification, 5 phase transformation kinetics quantification, 74–108 precipitation hardening stainless steels, 10–14 improving toughness through intercritical annealing, 13–14 microstructural evolution, 10–12 small-angle neutron scattering analysis of precipitation behaviour, 12–13 recently developed maraging steels chemical compositions, 19 thermodynamic calculation, 4–5 for phase fraction and element partition quantification, 67–72 types, 2

Index martensite, 1 MatLab command, 177 matrix interdiffusion coefficient, 138 mean error, 182 mechanical properties 2000 MPa grade cobalt-free maraging steel, 49–59 ageing at high temperature (540°C), 54–6, 58–9 ageing at intermediate temperature (480°C), 51–2, 54 ageing at low temperature (440°C), 49, 51 2400 MPa grade cobalt-free maraging steel, 59–65 effects of alloying elements on strength and toughness, 62, 64–5 fractography, 62 grain-refined copper maraging steels, 65 ductile-brittle transition temperature, 64 of maraging steels, 49–65 microcracks, 39, 45 microvoids, 45 molybdenum, 1 Mössbauer spectroscopy, 12, 114, 142 2800 MPa cobalt-containing grade, 48 2000 MPa grade cobalt-free maraging steel age hardening curves after solution treatment at 800°C for 1 hour, 119 age hardening kinetics, 119–20 ageing at high temperature (540°C) after ageing for 1 hour, 34 after ageing for 3 hours, 35 after ageing for 12 hours, 36 after ageing for 50 hours, 37 after ageing for 15 minutes, 32–3 effect of ageing time on mechanical properties, 57 fractography, 56 mechanical properties, 54–6, 58–9 microstructure, 31–6, 38–9 SEM fracture morphologies, 58 ageing at intermediate temperature (480°C) after ageing for 3 hours, 24





199

after ageing for 12 hours, 26–7 after ageing for 50 hours, 28 effect of ageing time on mechanical properties, 53 fractography, 54 mechanical properties, 51–2, 54 microstructure, 23, 25–8, 30–1 reverted austenite images after ageing for 50 hours, 29 SEM fracture morphologies, 55 ageing at low temperature (440°C) after ageing for 3 hours, 18 after ageing for 6 hours, 20 after ageing for 12 hours, 21 after ageing for 50 hours, 22 effect of ageing time on mechanical properties, 50 fractography, 49, 51 mechanical properties, 49, 51 microstructure, 17, 20–2 SEM fracture morphologies, 52 interplanar spacing of precipitates and oxides and intensity, 25 mechanical properties, 49–59 other microstructural features, 39–40 size and morphology of precipitates and microstructure in strained steel, 39 variation of reverted austenite content, 38 2400 MPa grade cobalt-free maraging steel, 68 age hardening curves after solution treatment at 810°C for 1 hour, 120 age hardening kinetics, 120–1 effects of alloying elements on strength and toughness, 62, 64–5 fractography, 62 high densities of dislocations and precipitates and coarse phase in martensite matrix, 43 interplanar spacing of intermetallic phases and intensity, 47 mechanical properties, 59–65 under aged conditions, 60 microstructure, 40–6 after solution treatment followed by air cooling, 41

200

Index



martensite matrix and coarse phase for low and high Mo steel, 42 SEM fracture morphologies, 61 tensile properties after solution treatment at 810°C, 59 transmission electron microscopy bright and dark field images and SAD pattern for high Mo steel, 46 dark field image and SAD pattern for low Mo steel, 44 dark field images and diffraction pattern of typical Fe2Ti coarse phase for high Mo steel, 45 MTDATA, 67 multilinear regression analysis, 182 n2 0.25 explanation, 114–16 NEWGRNN, 177, 179 18Ni (350) cobalt-containing grade microstructure, 47–8 18 wt% Ni C250, 88–101 activation energy determination for austenite reversion, 94 austenite reversion, 90–5 equilibrium fraction and activation energy determination, 91–2 transformation kinetic parameters calculation, 92–5 transformed fraction determination, 90–1 calculated austenite transformation fraction as function of temperature and time, 93 vs DSC experimental values, 95 calculated degree of austenite reversion as function of time, 99 calculated degree of precipitation at different ageing temperatures, 100 vs DSC experimental values, 98 calculated fraction of retained austenite and equilibrium fraction, 99 equilibrium volume fraction austenite as function of temperature, 94 Ni3Ti precipitate as function of ageing temperature, 97



interpretation of DSC results of phase transformations, 89 isothermal ageing, 98–100 austenite reversion, 98–100 precipitation, 100 parameters of DSC peak and transformation enthalpies austenite reversion, 90 main precipitate formation, 96 precipitate formation, 95–7 processed DSC peak austenite reversion, 92 main precipitation process, 97 recorded DSC curves, 91 18Ni maraging steel, 2, 3, 6 nickel, 1 niobium, 65 normal nucleation, 75 nuclear scattering length density, 157, 158 nucleation process, 114, 115, 119, 121 N-W relationship, 33 Orowan bowing, 7 Orowan equation, 5, 110, 129 Orowan looping mechanism, 58, 128–9 Ostwald ripening, 125 overageing controlling mechanism, 128–9 Fe–12Ni–6Mn precipitation kinetics and age hardening quantification, 129–36 and maraging steel, 125–40 particle coarsening mechanism, 125–7 precipitate fraction effect reconsideration, 136–40 volume fraction on coarsening, 127–8 particle coarsening, 133 controlling mechanism, 128–9 different mechanisms, 126 mechanism, 125–7 stages of precipitation hardening, 127 volume fraction influence, 127–8 PH13-8, 187 PH15-5, 10, 187 PH17-4, 10, 12, 187 PH17-4 alloy, 155, 157 PH13-8 stainless steel, 10, 11

Index PH steels see precipitation hardening steels PH15–5 steels, 118 phase coarsening, 136 phase transformation kinetics 18 wt% Ni C250, 88–101 austenite reversion, 90–5 isothermal ageing, 98–100 precipitate formation, 95–7 dilatometry curve of 2000 MPa grade cobalt-free maraging steel, 79 evolution of precipitates, 74–7 during ageing, 77 critical particle size definition, 76 difference in diffusion routes between growth and coarsening, 75 growth and coarsening, 74 interparticle spacing, 77 interparticle spacing and particle radius ratio, 78 particle size, 75–7 spinodal decomposition and normal nucleation, 75 maraging steels quantification, 74–108 overall process, 78–9 phase fraction by X-ray diffraction analysis, 101–8 age hardening curves showing Vickers hardness of C250 alloy, 103 alloying elements volume, 102 austenite, 107 correlation between Da and precipitate fraction, 104 correlation between 2Dq- and precipitate fraction, 104 precipitate, 101–7 precipitation fraction of Ni3Ti, Ni3Mo and Fe2Mo, 105 XRD profiles of 250 steel aged at 538°C, 106 precipitation in Fe–12Ni–6Mn maraging type alloy, 79–87 overall ageing process, 81–2 parameter determination, 82–6 precipitate size and fraction as functions of time and temperature, 86





201

theoretical analysis of early-stage ageing process, 79–81 time–temperature–precipitation diagram, 86 PH13–8Mo, 118, 122, 129 Poisson’s ratio, 30 POSTMNMX, 177, 180 Powder Diffraction File, 43 power law, 114 pre-ageing, 59 precipitation hardening, 4 stages, 127 precipitation hardening stainless steels, 141–72, xi calculated nuclear scattering length densities and A ratios, 158 early stage age hardening and overageing quantification, 171–3 hardening parameters early stages of ageing, 171 overageing, 172 improving toughness through intercritical annealing, 159–68 age hardening kinetics of steel, 159 calculated composition of the precipitates and matrix in PH13-8 steel, 170 Charpy impact toughness of steel, 160 comparison with commercial H950 treatment, 167 diffusion distance of nickel, chromium, and molybdenum, 165 driving forces for formation of phases in bcc of 1RK91, 169 equilibrium phases in C455, 170 equilibrium phases in 1RK91, 170 grain refinement heat treatments, 159 grain refinement mechanism of intercritical annealing, 163–5 hardness and Charpy impact strength, 159–60 microstructure and X-ray diffraction analysis, 160–2 optical microstructures after grain refinement heat treatments with electro-etching, 161, 162

202



Index

relationships between heat treatment, microstructure and mechanical properties, 165–7 SEM after grain refinement heat treatments after chemical etching, 164 XRD profile after grain refinement heat treatment followed by 4 hours at 510°C, 163 microstructural evolution after ageing, 141–56 age hardening curves at 510°C and 593°C, 141 chromium spinodal decomposition, 153, 155 hardening mechanisms, 155–6 matrix compositions measured by 3DAP, 147 molybdenum segregation at precipitate/matrix interface, 153 Pa and LBM chromium decomposition analysis, 154 particles compositions measured by 3DAP, 146 precipitate characteristics, 148, 151–2 microstructural evolution after ageing at 510°C, 143–7 4 hours, 147 4 minutes, 143–4 15 minutes, 144 40 minutes, 144–7 aluminium, nickel, chromium, and iron composition profiles, 150 aluminium and nickel distribution after 4 hours ageing, 149 aluminium atom map of steel, 145 aluminium clusters particle size distribution, 148 atom maps of aluminium and nickel after ageing for 40 minutes, 146 atom maps of aluminium and nickel in steel aged for 4 minutes, 144 contingency tables between nickel and aluminium in steel aged for 4 minutes, 145 contingency tables between nickel

and aluminium in steel aged for 40 minutes, 156 mass spectrum of steel aged for 4 minutes, 143 microstructural evolution after ageing at 593°C, 147–8 6 minutes, 147 30 minutes, 147–8 aluminium and nickel distribution after 6 minutes ageing, 151 aluminium and nickel distribution after 30 minutes ageing, 152 field-ion microscopy image aged for 30 minutes, 142 small-angle neutron scattering analysis of precipitation behaviour, 156–9 thermodynamic calculations, 168–71 variation of increase in hardness with ageing time C455 maraging steel aged at 425°C, 172 C344 maraging steel aged at 500°C and 1RK91 at 580°C, 172 chromium-containing maraging steel aged at 520°C, 171 precipitation hardening steels, 10–14 thermodynamic calculations for phase fraction and element partition quantification, 67–72 PREMNMX, 177, 180, 182 PURELIN, 177, 182 radial basis function, 179 1RK91, 153, 168, 169, 172, 193–4 age hardening kinetics curves, 193 Sandvik Steel, 168, 172, 193 selected area diffraction pattern, 11 shear modulus, 129, 130 single particle theories, 9 small angle neutron scattering, 12, 157 small angle X-ray scattering microscopy, 12, 115 soft impingement, 116 softening, 109 spinodal decomposition, 3, 75, 114, 115, 153, 155 stainless steels see specific type strengthening, 109

Index sum of squares error, 177 T-250 cobalt-free maraging steel, 30 T300 steel, 30, 35 TANSIG, 177, 182 Taylor factor, 113 theoretical derivation, 112–13 Thermo-Calc, 4, 10, 67, 117, 129, 131, 139 thermodynamic calculations 2400 MPa grade cobalt-free maraging steel, 68 calculated phase constitution and element distribution Fe–10Ni–15Al–1Mo and Fe–15Ni– 20Al–4Mo, 71 Fe–Ni–Mo and Fe–Ni–Co–Mo, 72 driving forces for formation of phases in bcc of Fe–12Ni–6Mn, 72 Fe–Ni–Al–Mo, 68–70 Fe–Ni–Mn, 72 Fe–Ni–Mo and Fe–Ni–Co–Mo, 70, 72 for phase fraction and element

203

partition quantification in maraging systems and PH steels, 67–72 thermodynamic phase equilibrium, 69–70 three-dimensional atom probe, 142 titanium, 65 TRAINBR, 177 TRAMNMX, 177, 180 transmission electron microscopy, 11, 12, 20, 68, 115, 129, 153 ultra-purifying melting, 48 Vickers hardness, 113, 123, 130 Voorhees and Glicksman model, 137, 138 Wang, Glicksman and Rajan model, 137 X-ray diffraction, 7, 106, 142, 163 XRD see X-ray diffraction Zener’s parabolic relationship, 112