Modeling and Simulation for Material Selection and Mechanical Design

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Modeling and Simulation for Material Selection and Mechanical Design edited by

George E. Totten G.E. Totten & Associates, LLC Seattle, Washington, i7.S.A

Lin Xie Solidworks Corporation Concord, Massachusetts, U.S.A

Kiyoshi Funatani IMST Institute Nagoya, Japan

MARCEL

MARCEL DEKKER, INC. DEKKER

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NEWYORK BASEL

Although great care has been taken to provide accurate and current information, neither the author(s) nor the publisher, nor anyone else associated with this publication, shall be liable for any loss, damage, or liability directly or indirectly caused or alleged to be caused by this book. The material contained herein is not intended to provide speciﬁc advice or recommendations for any speciﬁc situation. Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used only for identiﬁcation and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress. ISBN: 0-8247-4746-1 This book is printed on acid-free paper. Headquarters Marcel Dekker, Inc., 270 Madison Avenue, New York, NY 10016, U.S.A. tel: 212-696-9000; fax: 212-685-4540 Distribution and Customer Service Marcel Dekker, Inc., Cimarron Road, Monticello, New York 12701, U.S.A. tel: 800-228-1160; fax: 845-796-1772 Eastern Hemisphere Distribution Marcel Dekker AG, Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerland tel: 41-61-260-6300; fax: 41-61-260-6333 World Wide Web http://www.dekker.com The publisher oﬀers discounts on this book when ordered in bulk quantities. For more information, write to Special Sales/Professional Marketing at the headquarters address above. Copyright # 2004 by Marcel Dekker, Inc. All Rights Reserved. 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 and retrieval system, without permission in writing from the publisher. Current printing (last digit): 10 9 8 7 6 5 4 3 2 1 PRINTED IN THE UNITED STATES OF AMERICA

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ENGINEERING

A Series of Textbooks and Reference Books Founding Editor

L. L. Faulkner Columbus Division, Battelle Memorial Institute and Department of Mechanical Engineering The Ohio State University Columbus, Ohio

1. 2. 3. 4. 5.

Spring Designer's Handbook, Harold Carlson Computer-Aided Graphics and Design, Daniel L. Ryan Lubrication Fundamentals, J. George Wills Solar Engineering for Domestic Buildings,William .A. Himmelman Applied Engineering Mechanics: Statics and Dynamics, G. Boothroyd and C. Poli 6. Centrifugal Pump Clinic, lgor J. Karassik 7. Computer-AidedKinetics for Machine Design, Daniel L. Ryan 8. Plastics Products Design Handbook, Patf A: Materials and Components; Patf 6 : Processes and Design for Processes, edited by Edward Miller 9. Turbomachinery:Basic Theory and Applications, Earl Logan, Jr. 10. Vibrations of Shells and Plates, Werner Soedel 1I.Flat and Corrugated Diaphragm Design Handbook, Mario Di Giovanni 12. Practical Stress Analysis in Engineering Design, Alexander Blake 13. An lntroduction to the Design and Behavior of Bolted Joints, John H. Bickford 14. Optimal Engineering Design: Principles and Applications,James N. Siddall 15. Spring Manufacturing Handbook, Harold Carlson 16. Industrial Noise Control: Fundamentals and Applications, edited by Lewis H. Bell 17. Gears and Their Vibration:A Basic Approach to Understanding Gear Noise, J. Derek Smith 18. Chains for Power Transmission and Material Handling: Design and Applications Handbook,American Chain Association 19. Corrosion and Corrosion Protection Handbook, edited by Philip A. Schweitzer 20. Gear Drive Systems: Design and Application, Peter Lynwander 21. Controlling In-Plant Airborne Contaminants: Systems Design and Calculations, John D. Constance 22. CAD/CAM Systems Planning and Implementation, Charles S. Knox 23. Probabilistic Engineering Design: Principles and Applications, James N. Siddall 24. Traction Drives: Selection and Application, Frederick W. Heilich 111 and Eugene E. Shube 25. Finite Element Methods: An Introduction, Ronald L. Huston and Chris E. Passerello Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

, Brayton Lincoln, and 27. Lubrication in Practice: Second Edition, edited by W. S. Robertson 28. Principles of Automated Drafting, Daniel L. Ryan 29. Practical Seal Design, edited by Leonard J. Martini 30. Engineering Documentation for CAD/CAM Applications, Charles S. Knox 31 . Design Dimensioning with Computer Graphics Applications, Jerome C. Lange 32. Mechanism Analysis: Simplified Graphical and Analytical Techniques, Lyndon 0. Barton 33. CAD/CAM Systems: Justification, Implementation, Productivity Measurement, Edward J. Preston, George W. Crawford, and Mark E. Coticchia 34. Steam Plant Calculations Manual, V. Ganapathy 35. Design Assurance for Engineers and Managers, John A. Burgess 36. Heat Transfer Fluids and Systems for Process and Energy Applications, Jasbir Singh 37. Potential Flows: Computer Graphic Solutions, Robert H. Kirchhoff 38. Computer-AidedGraphics and Design: Second Edition, Daniel L. Ryan 39. Electronically Controlled Proportional Valves: Selection and Application, Michael J. Tonyan, edited by Tobi Goldoftas 40. Pressure Gauge Handbook, AMETEK, U.S. Gauge Division, edited by Philip W. Harland 41. Fabric Filtration for Combustion Sources: Fundamentals and Basic Technology, R. P. Donovan 42. Design of MechanicalJoints, Alexander Blake 43. CAD/CAM Dictionary, Edward J. Preston, George W. Crawford, and Mark E. Coticchia 44. Machinery Adhesives for Locking, Retaining, and Sealing, Girard S. Haviland 45. Couplings and Joints: Design, Selection, and Application, Jon R. Mancuso 46. Shaft Alignment Handbook, John Piotrowski 47. BASIC Programs for Steam Plant Engineers: Boilers, Combustion, Fluid Flow, and Heat Transfer,V. Ganapathy 48. Solving Mechanical Design Problems with Computer Graphics, Jerome C. Lange 49. Plastics Gearing: Selection and Application, Clifford E. Adams 50. Clutches and Brakes: Design and Selection,William C. Orthwein 51. Transducersin Mechanical and Electronic Design, Harry L. Trietley 52. Metallurgical Applications of Shock-Wave and High-Strain-Rate Phenomena, edited by Lawrence E. Murr, Karl P. Staudhammer, and Marc A. Meyers 53. Magnesium Products Design, Robert S.Busk 54. How to Integrate CAD/CAM Systems: Management and Technology, William D. Engelke 55. Cam Design and Manufacture: Second Edition; with cam design software for the IBM PC and compatibles, disk included, Preben W. Jensen 56. Solid-state AC Motor Controls: Selection and Application,Sylvester Campbell 57. Fundamentals ofRobotics, David D. Ardayfio 58. Belt Selection and Application for Engineers,edited by Wallace D. Erickson 59. Developing Three-DimensionalCAD Software with the ISM PC, C. Stan Wei 60. Organizing Data for ClM Applications, Charles S. Knox, with contributions by Thomas C. Boos, Ross S. Culverhouse, and Paul F. Muchnicki

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61. Computer-Aided Simulation in Railway Dynamics, by Rao V. Dukkipati and 62. fiber-Reinforced Composites: Materials, Manufacturing, and Design, P. K. Mallick 63. Photoelectric Sensors and Controls: Selection and Application, Scott M. Juds 64. finite Element Analysis with Personal Computers, Edward R. Champion, Jr., and J. Michael Ensminger 65. Ultrasonics: Fundamentals, Technology, Applications: Second Edition, Revised and Expanded, Dale Ensminger 66. Applied finite Element Modeling: Practical Problem Solving for Engineers, Jeffrey M. Steele 67. Measurement and Instrumentation in Engineering: Principles and Basic Laboratory Experiments, Francis S. Tse and Ivan E. Morse 68. Centrifugal Pump Clinic: Second Edition, Revised and Expanded, lgor J. Karassik 69. Practical Stress Analysis in Engineering Design: Second Edition, Revised and Expanded, Alexander Blake 70. An Introduction to the Design and Behavior of Bolted Joints: Second Edition, Revised and Expanded, John H. Bickford 71. High Vacuum Technology:A Practical Guide, Marsbed H. Hablanian 72. Pressure Sensors: Selection and Application, Duane Tandeske 73. Zinc Handbook: Properties, Processing, and Use in Design, Frank Porter 74. Thermal fatigue of Metals, Andrzej Weronski and Tadeusz Hejwowski 75. Classical and Modern Mechanisms for Engineers and Inventors, Preben W. Jensen 76. Handbook of Electronic Package Design, edited by Michael Pecht 77. Shock-Wave and High-Strain-Rate Phenomena in Materials, edited by Marc A. Meyers, Lawrence E. Murr, and Karl P. Staudhammer 78. Industrial Refrigeration: Principles, Design and Applications, P. C. Koelet 79. Applied Combustion, Eugene L. Keating 80. Engine Oils and Automotive Lubrication, edited by Wilfried J. Bartz 8 1. Mechanism Analysis: Simplified and Graphical Techniques, Second Edition, Revised and Expanded, Lyndon 0. Barton 82. fundamental Fluid Mechanics for the Practicing Engineer, James W. Murdock 83. Fiber-Reinforced Composites: Materials, Manufacturing, and Design, Second Edition, Revised and Expanded, P. K. Mallick 84. Numerical Methods for Engineering Applications, Edward R. Champion, Jr. 85. Turbomachinery: Basic Theory and Applications, Second Edition, Revised and Expanded, Earl Logan, Jr. 86. Vibrations of Shells and Plates: Second Edition, Revised and Expanded, Werner Soedel 87. Steam Plant Calculations Manual: Second Edition, Revised and Expanded, V. Ganapathy 88. Industrial Noise Control: Fundamentals and Applications, Second Edition, Revised and Expanded, Lewis H. Bell and Douglas H. Bell 89. finite Elements: Their Design and Performance, Richard H. MacNeal 90. Mechanical Properties of Polymers and Composites: Second Edition, Revised and Expanded, Lawrence E. Nielsen and Robert F. Landel 91. Mechanical Wear Prediction and Prevention, Raymond G. Bayer

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92. Mechanical Power Transmission Components, edited by David W. South and Jon R. Mancuso 94. Engineering Documentation Control Practices and Procedures, Ray E. Monahan 95. Refractory Linings Thermomechanical Design and Applications, Charles A. Schacht 96. Geometric Dimensioning and Tolerancing: Applications and Techniques for Use in Design, Manufacturing, and Inspection, James D. Meadows 97. An lntroduction to the Design and Behavior of Bolted Joints: Third Edition, Revised and Expanded, John H. Bickford 98. Shaft Alignment Handbook: Second Edition, Revised and Expanded, John Piotrowski 99. Computer-Aided Design of Polymer-Matrix Composite Structures, edited by Suong Van Hoa 100. Friction Science and Technology, Peter J. Blau 10 1. lntroduction to Plastics and Composites: Mechanical Properties and Engineering Applications, Edward Miller 102. Practical Fracture Mechanics in Design, Alexander Blake 103. Pump Characteristics and Applications, Michael W. Volk 104. Optical Principles and Technology for Engineers, James E. Stewart 105. Optimizing the Shape of Mechanical Elements and Structures, A. A. Seireg and Jorge Rodriguez 106. Kinematics and Dynamics of Machinery, Vladimir Stejskal and Michael ValaSek 107. Shaft Seals for Dynamic Applications, Les Horve 108. Reliability-Based Mechanical Design, edited by Thomas A. Cruse 109. Mechanical Fastening, Joining, and Assembly, James A. Speck 110. Turbomachinery Fluid Dynamics and Heat Transfer,edited by Chunill Hah 111. High-Vacuum Technology: A Practical Guide, Second Edition, Revised and Expanded, Marsbed H. Hablanian 112. Geometric Dimensioning and Tolerancing: Workbook and Answerbook, James D. Meadows 113. Handbook of Materials Selection for Engineering Applications, edited by G. T. Murray 114. Handbook of Thermoplastic Piping System Design, Thomas Sixsmith and Reinhard Hanselka 115. Practical Guide to Finite Elements: A Solid Mechanics Approach, Steven M. Lepi 116. Applied Computational Fluid Dynamics, edited by Vijay K. Garg 117. Fluid Sealing Technology, Heinz K. Muller and Bernard S. Nau 118. Friction and Lubrication in Mechanical Design, A. A. Seireg 119. lnfluence Functions and Matrices, Yuri A. Melnikov 120. Mechanical Analysis of Electronic Packaging Systems, Stephen A. McKeown 121. Couplings and Joints: Design, Selection, and Application, Second Edition, Revised and Expanded, Jon R. Mancuso 122. Thermodynamics: Processes and Applications, Earl Logan, Jr. 123. Gear Noise and Vibration, J. Derek Smith 124. Practical Fluid Mechanics for Engineering Applications, John J. Bloomer 125. Handbook of Hydraulic Fluid Technology,edited by George E. Totten 126. Heat Exchanger Design Handbook, T. Kuppan

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127.

for Product Sound Quality, Richard H. Lyon in Franklin E. Fisher and Joy R.

Fisher 129. Nickel Alloys, edited by Ulrich Heubner 130. Rotating Machinery Vibration: Problem Analysis and Troubleshooting, Maurice L. Adams, Jr. 131. Formulas for Dynamic Analysis, Ronald L. Huston and C. Q. Liu 132. Handbook of Machinery Dynamics, Lynn L. Faulkner and Earl Logan, Jr. 133. Rapid Prototyping Technology: Selection and Application, Kenneth G. Cooper 134. Reciprocating Machinery Dynamics: Design and Analysis, Abdulla S. Rangwala 135. Maintenance Excellence: Optimizing Equipment Life-Cycle Decisions, edited by John D. Campbell and Andrew K. S. Jardine 136. Practical Guide to Industrial Boiler Systems, Ralph L. Vandagriff 137. Lubrication Fundamentals: Second Edition, Revised and Expanded, D. M. Pirro and A. A. Wessol 138. Mechanical Life Cycle Handbook: Good Environmental Design and Manufacturing, edited by Mahendra S. Hundal 139. Micromachining of Engineering Materials, edited by Joseph McGeough 140. Control Strategies for Dynamic Systems: Design and Implementation, John H. Lumkes, Jr. 141. Practical Guide to Pressure Vessel Manufacturing, Sunil Pullarcot 142. Nondestructive Evaluation: Theory, Techniques, and Applications, edited by Peter J. Shull 143. Diesel Engine Engineering: Thermodynamics, Dynamics, Design, and Control, Andrei Makartchouk 144. Handbook of Machine Tool Analysis, loan D. Marinescu, Constantin Ispas, and Dan Boboc 145. Implementing Concurrent Engineering in Small Companies, Susan Carlson Skalak 146. Practical Guide to the Packaging of Electronics: Thermal and Mechanical Design and Analysis, Ali Jamnia 147. Bearing Design in Machinery: Engineering Tribology and Lubrication, Avraham Harnoy 148. Mechanical Reliability Improvement: Probability and Statistics for Experimental Testing, R. E. Little 149. Industrial Boilers and Heat Recovery Steam Generators: Design, Applications, and Calculations, V. Ganapathy 150. The CAD Guidebook: A Basic Manual for Understanding and Improving Computer-Aided Design, Stephen J. Schoonmaker 151. Industrial Noise Control and Acoustics, Randall F. Barron 152. Mechanical Properties of Engineered Materials, Wole Soboyejo 153. Reliability Verification, Testing, and Analysis in Engineering Design, Gary S. Wasserman 154. Fundamental Mechanics of Fluids: Third Edition, I. G. Currie 155. Intermediate Heat Transfer, Kau-Fui Vincent Wong 156. HVAC Water Chillers and Cooling Towers: Fundamentals, Application, and Operation, Herbert W. Stanford Ill 157. Gear Noise and Vibration: Second Edition, Revised and Expanded, J. Derek Smith

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158. Handbook of Turbomachinery: Second Edition, Revised and Expanded, Earl Logan, Jr., and Ramendra Roy 159. Piping and Pipeline Engineering: Design, Construction, Maintenance, lntegrity, and Repair, George A. Antaki 160. Turbomachinery: Design and Theory, Rama S. R. Gorla and Aijaz Ahmed Khan 161. Target Costing: Market-Driven Product Design, M. Bradford Clifton, Henry M. B. Bird, Robert E. Albano, and Wesley P. Townsend 162. Fluidized Bed Combustion, Simeon N. Oka 163. Theory of Dimensioning: An lntroduction to Parameterizing Geometric Models, Vijay Srinivasan 164. Handbook of Mechanical Alloy Design, George E. Totten, Lin Xie, and Kiyoshi Funatani 165. Structural Analysis of Polymeric Composite Materials, Mark E. Tuttle 166. Modeling and Simulation for Material Selection and Mechanical Design, George E. Totten, Lin Xie, and Kiyoshi Funatani

Additional Volumes in Preparation Handbook of Pneumatic Conveying Engineering, David Mills, Mark G. Jones, and Vijay K. Agarwal Mechanical Wear Fundamentals and Testing: Second Edition, Revised and Expanded, Raymond G. Bayer Engineering Design for Wear: Second Edition, Revised and Expanded, Raymond G. Bayer Clutches and Brakes: Design and Selection, Second Edition, William C. Orthwein Progressing Cavity Pumps, Downhole Pumps, and Mudmotors, Lev Nelik

Mechanical Engineering Sofmare

Spring Design with an IBM PC, Al Dietrich Mechanical Design Failure Analysis: With Failure Analysis System Software for the IBM PC, David G. Ullman

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In Memoriam

During the preparation of this book, one of our most valued authors and mentors passed away on April 29, 2003. Professor George C. Weatherly (1941–2003) graduated from Cambridge University in 1966. He began his career as a research scientist in the Department of Metallurgy at Harwell. In 1968 he moved to Canada where he worked for the University of Toronto for 22 years as a professor in the Department of Metallurgy and Material Science. In 1990 he became a professor of Materials Science and Engineering at McMaster University. He was Director of Brockhouse Institute for Material Research from 1996–2001 and a Chair of the Department of Materials Science and Engineering. Dr. Weatherly has published over 200 papers in diﬀerent areas of Materials Science. He was Fellow for the Canadian Institute for Mining and Metallurgy and Fellow of ASM International. George was a devoted scientist in the ﬁeld of electron microscopy and an educator with a distinguished career at McMaster University and the University of Toronto. He will be cherished by his friends, colleagues, and students for the richness of his life, his quiet humor, his humanity and care for others, and above all for his unfailing honesty. His contributions were many and are written clearly in the lives of those with whom he taught and worked. This book is dedicated to his memory.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Preface

In every industry survey, development and use modeling, and simulation technology are cited among the top ﬁve critical needs for manufacturing industries to remain viable and competitive in the future. This is particularly true for materials and component design. To address this need, various research programs are currently underway in government, academic, and industry laboratories around the world. This book addresses a number of selected, important areas of computer model development. Eﬀective material and component design procedures are vitally important with increasing pressures to improve quality at lower production costs for all traditional industrial markets. Advanced design procedures typically involve computer modeling and simulation if the necessary algorithms are suﬃciently advanced or by using advanced empirical procedures. The objective is to be able to make design decisions based on numerical simulations as an alternative to time-consuming and expensive laboratory or production experimental process development. In fact, advanced engineering processes are becoming increasingly dependent on advanced computer modeling and design procedures. This book addresses various aspects of the utilization of modeling and simulation technology. Some of the topics discussed include hot-rolling of steel, quenching and tempering during heat treatment, modeling of residual stresses and distortion during forging, casting, heat treatment, mechanical property prediction, modeling of tribological processes as it relates to the design of surface engineered materials, and fastener design. These chapters summarize and demonstrate key numerical relationships used in computer

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

model development and their application at various stages in the material production process. In particular, the material covered in this text includes:

Modeling and simulation of microstructural evolution and mechanical properties of steels during the hot-rolling process, calculation of metallurgical phenomena occurring in steel during hot-rolling, and prediction of mechanical properties from microstructure. Heat treatment processes such as quenching and tempering is an active area for process model development. Models used to simulate the kinetics of multicomponent grain boundary segregations that occur in quenched and tempered engineering steels are discussed. These models permit the evaluation of the eﬀect of alloying elements and various tempering parameters on hydrogen embrittlement, stress-corrosion cracking, and other phenomenon. Of all the various problems associated with component design and production, none are more important that residual stress and distortion. Chapter 3 discusses the metallo-thermo-mechanical theory, numerical modeling and simulation technology, coupling of temperature, inelastic behavior and phase transformation and solidiﬁcation involved with elastic-plastic, viscoplastic and creep deformation as they relate to quenching, forging, and casting processes. Modeling and simulation of mechanical properties, in particular, material behavior during plastic deformation, low-cycle fatigue, creep, and impact strength. This discussion includes the importance of the determination and implementation of adequate material data, consideration of inelastic material behavior, and the formulation of physically founded material models. Chapter 5 discusses the role played by physico-chemical interactions in modifying and controlling friction and wear of critically loaded tribo-couple surfaces during high-speed cutting operations. A comprehensive overview of one of the most important processes in manufacturing is presented in Chapter 6. Threaded fastener selection and design is addressed with many equations and ﬁgures included to aid in the design process.

Chapters 1 through 4 describe advanced computer modeling and simulation processes to predict microstructures, material process behavior, and mechanical properties. Chapters 5 and 6 describe more empirical process design procedures for tribological and fastener design.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

This book will be an invaluable resource for the designer, mechanical and materials engineer, and metallurgist. Thorough overviews of these technologies seldom encountered in other handbooks for materials design are provided. The book is an excellent textbook for advanced undergraduate or graduate engineering courses on the role of modeling and simulation in materials and component design. We are indebted to the vital assistance of various international experts. Special thanks to our spouses for their inﬁnite patience with the various time-consuming tasks involved in putting this text together. We extend special thanks to the staﬀ at Marcel Dekker, Inc. including Richard Johnson, Rita Lazazzaro, and Russell Dekker for their invaluable assistance. Without their assistance, this text would not have been possible. George E. Totten Lin Xie Kiyoshi Funatani

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Contents

Preface Contributors 1

A Mathematical Model for Predicting Microstructural Evolution and Mechanical Properties of Hot-Rolled Steels Masayoshi Suehiro

2

Design Simulation of Kinetics of Multicomponent Grain Boundary Segregations in the Engineering Steels Under Quenching and Tempering Anatoli Kovalev and Dmitry L. Wainstein

3

Designing for Control of Residual Stress and Distortion Dong-Ying Ju

4

Modeling and Simulation of Mechanical Behavior Essam El-Magd

5

Tribology and the Design of Surface-Engineered Materials for Cutting Tool Applications German Fox-Rabinovich, George C. Weatherly, and Anatoli Kovalev

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

6

Designing Fastening Systems Christoph Friedrich

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Contributors

Essam El-Magd, Dr.-Ing.habil.

Aachen University, Aachen, Germany

German Fox-Rabinovich, Ph.D., D.Sc. Ontario, Canada

RIBE Verbindungstechnik GmbH, Schwa-

Christoph Friedrich, Dr.-Ing. bach, Germany Dong-Ying Ju, Ph.D. Japan Anatoli Kovalev, D.Sc.

Saitama Institute of Technology, Okabe, Saitama,

Physical Metallurgy Institute, Moscow, Russia

Masayoshi Suehiro, Dr.Eng. Chiba, Japan Dmitry L. Wainstein, D.Sc.

Nippon Steel Corporation, Futtsu-City,

Physical Metallurgy Institute, Moscow, Russia

George C. Weatherly, Ph.D.y Canada

y

McMaster University, Hamilton,

McMaster University, Hamilton, Ontario,

Deceased

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

1 A Mathematical Model for Predicting Microstructural Evolution and Mechanical Properties of Hot-Rolled Steels Masayoshi Suehiro Nippon Steel Corporation, Futtsu-City, Chiba, Japan

I.

INTRODUCTION

A model for calculating the mechanical properties of hot-rolled steel sheets from their processing condition makes it possible not only to design chemical compositions and processing conditions of steels through off-line simulation but also to guarantee the mechanical properties of hot-rolled steels through on-line simulation. From this point of view, some attempts have been made to develop a mathematical model for calculating the evolution of austenitic microstructure of steels during hot-rolling process and their transformations during cooling subsequent to hot-rolling [1–3]. The mathematical models basically consist of four models for calculating metallurgical phenomena occurring in hot-strip mill and a model for predicting mechanical properties from the microstructure of steel calculated by the metallurgical models. In this chapter, the basic idea and several applications of the mathematical model will be presented.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 1 Schematic illustration of a hot-strip mill.

II.

THE OVERALL MODEL

Since mechanical properties of hot-rolled steels are determined by their microstructure, a model for calculating the mechanical properties of hot-rolled steels is composed of two kinds of models: one for calculating microstructure of steels from their processing conditions, and the other for calculating their mechanical properties from their microstructure. There are several kinds of hot-rolled steel products: sheet and coil, plate, beam, wire, rod, bar, etc. Although the processing conditions are dependent upon each process, each product is produced through the processes such as heating, hot-working, and cooling. Figure 1 shows the schematic illustration of a hot-strip mill. Hot-rolled steel sheets are produced through slab reheating, rough hot-rolling, finish hot-rolling, cooling, and coiling. Table 1 shows the typical thickness and temperature changes in this process and the metallurgical phenomena occurring through this process. In the slab-reheating process, transformation from ferrite and pearlite to austenite and grain growth take place. The

Table 1 The Changes in Thickness and Temperature of Steels and Metallurgical Phenomena in a Hot-Strip Mill Thickness (mm)

Temperature (8C)

Slab reheating

250

1200

Rough rolling Finish rolling Cooling Coiling

!40

1200–1000

!3

1000–850

3 3

— 600–700

Process

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Metallurgical phenomena Transformation, grain growth, dissolution, and precipitation of precipitates Recovery, recrystallization, grain growth, precipitation Recovery, recrystallization, grain growth, precipitation Transformation, precipitation Precipitation

Figure 2 The structure of the model for calculating microstructural evolution and mechanical properties of hot-rolled steels.

recovery and recrystallization, and grain growth of austenitic microstructure occur during and after rough and finish hot-rolling and the transformation from austenite to ferrite, pearlite, bainite, and martensite takes place during cooling and coiling. In the case where steels include alloying elements that form carbides or nitrides, precipitation of such carbides and nitrides takes place and affects recovery, recrystallization, and grain growth in each process. Accordingly, in order to calculate the microstructural evolution of hot-rolled steels, the model used to calculate recovery, recrystallization, grain growth during and after hot deformation, transformation kinetics during cooling and precipitation kinetics in each process is shown in Fig. 2.

III.

BASIC KINETIC EQUATION

In recrystallization and transformation, a new phase forms and grows. These new phases continue to grow until they meet each other and stop growing. This situation is called hard impingement and can be expressed by using the Avrami type equation (4a,4b,4c) X ¼ 1 expðktn Þ

ð1Þ

or the Johnson–Mehl equation (5). In these equations, the concept of extended volume fraction is adopted. By using this concept, the hard impingement can be taken into consideration indirectly. The extended volume

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

fraction is the sum of the volume fraction of all new phases without direct consideration of the hard impingement between new particles and is related to the actual volume fraction by X ¼ 1 expðXe Þ

ð2Þ

where X is the actual volume fraction and Xe is the extended volume fraction. The general form of the equation was developed by Cahn [6]. A brief explanation is presented here. The nucleation sites of new phases would be grain boundaries, grain edges, and=or grain corners. In the case of grain boundary nucleation, the volume fraction of a new phase after some time can be expressed as follows. Cahn considered the situation illustrated in Fig. 3 and calculated the volume of the semicircle. In his calculation, firstly, the area at the distance of y from the nucleation site B is calculated. The summation of this area for all nuclei gives the total extended area. From this value, the actual area can be calculated. The extended volume can be obtained by integrating the area for all distances. Finally, the actual volume fraction can be derived.

Figure 3 Schematic illustration of the situation of new phase at time t which nucleates at time t at grain boundary B.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

The area of the section at a plane A for a semicircle nucleated at a plane B is considered. The radius r at time t can be expressed as r ¼ ½G2 ðt tÞ2 y2 1=2 r¼0

for y < Gðt tÞ for y Gðt tÞ

ð3Þ

where G is the growth rate of new phase and t is the time when the new phase nucleates at plane B. In this calculation, the growth rate is assumed to be constant. From this radius, the extended area fraction dYe for the new phases nucleated at time between t and t þ dt can be obtained as dYe ¼ pIs dt½G2 ðt tÞ2 y2 for y < Gðt tÞ for y > Gðt tÞ dYe ¼ 0

ð4Þ

where Is is the nucleation rate at unit area. By integrating for the time t from 0 to t, the extended area fraction at the plane A at time t can be obtained as Zt Ye ¼

ty=G Z

½G2 ðt tÞ2 y2 dt

dYe ¼ pIs 0

ð5Þ

0

By exchanging y=Gt for x, this equation leads to 3 2 3 1x 2 x ð1 xÞ Ye ¼ pIs G t for x < 1 3 Ye ¼ 0

for x > 1

ð6Þ

The actual area fraction of new phases at plane A, Y can be calculated using Ye from Y ¼ 1 expðYe Þ

ð7Þ

The integration of Y for y from 0 to infinity gives the volume of new phases nucleated at unit area of plane B,V0, as Z1 Z1 3 2 3 1x 2 V0 ¼ 2 Y dy ¼ 2Gt x ð1 xÞ 1 exp pIs G t dx 3 0

0

ð8Þ Multiplying V0 by the area of nucleation site, the extended volume fraction is obtained as Xe ¼ SV0 ¼ bs1=3 fs ðas Þ

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ð9Þ

where Is Ns ¼ 8S3 G 8S4 G Z1 3 3 1x 2 1 exp pas dx x ð1 xÞ fs ðas Þ ¼ as 3 as ¼ ðIs G2 Þ1=3 t;

bs ¼

ð10Þ

0

and Ns the nucleation rate for unit volume. The actual volume fraction X is expressed as X ¼ 1 expðbs1=3 fs ðas ÞÞ

ð11Þ

From this equation, two extreme cases can be considered. One is the case where as is very small and the other is extremely large. For these two cases, the equation becomes X ¼ 1 expðp=3Ns G3 t4 Þ as 51

ð12Þ

X ¼ 1 ð2SGtÞ as 41

ð13Þ

Equation (12) is the same as the one obtained for the case of random nucleation sites by Johnson–Mehl. This equation implies that the increase in the volume of new phases is caused by nucleation and growth. On the other hand, Eq. (13) does not include nucleation rate and it implies that the nucleation sites are covered by new phases and the increase in the volume is dependent only on the growth of new phases. This situation is referred to as site saturation [6]. Cahn did this type of formulation for the cases of grain edge and grain corner nucleations. Table 2 shows all the extreme cases. For all cases, the increase of the volume of new phases for the case of small as conforms to the case of nucleation and growth and site saturation for the case of large as The value of as increases when the nucleation rate is small when compared to the growth rate. The early stage of reaction corresponds to small as and

Table 2 The Kinetic Equations Depending on the Modes and the Nucleation Sites of Reaction in Accordance with Cahn’s Treatment Nucleation site

Nucleation and growth

Site saturation

Grain boundary Grain edge Grain corner

X ¼ 1 expðp=3N_ G 3 t4 Þ

X ¼ 1 expð2SGtÞ X ¼ 1 expðpLG2 t2 Þ X ¼ 1 expðð4p=3ÞCG 3 t3 Þ

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

the latter stage corresponds to large as. From Table 2, we can recognize that the exponent of time depends on the mode of reaction and the type of nucleation site for the case of site saturation. A comparison of this information with the experimental results gives useful information on the mode of reaction and the nucleation site. The equations in Table 2 can be used for calculating actual reactions such as transformation and recrystallization by introducing fitting parameters obtained from experiments [7].

IV.

UTILIZATION OF THERMODYNAMICS FOR THE CALCULATION OF TRANSFORMATION AND PRECIPITATION KINETICS

As transformation and precipitation kinetics are closely related to phase equilibrium, thermodynamics can be utilized for their calculation. In this section, the method for utilizing thermodynamics for the calculation will be explained. For the consideration of kinetics, the Gibbs free-energy–composition diagram is much more useful and should be the basis. Figure 4 shows the Gibbs free-energy–composition diagram for austenite and ferrite in steels. Chemical composition at the phase interface between ferrite and austenite is obtained from the common tangent for free-energy curves of ferrite and austenite. The common tangent can be calculated under the condition that chemical potentials of all chemical elements in ferrite are equal to those in austenite. This condition is expressed as mai ¼ mgi

ð14Þ

where m is the chemical potential, the suffix i represents all elements in the system and a and g indicate ferrite and austenite, respectively. In Fig. 4, the driving force for transformation from austenite to ferrite, DGm, is indicated as well. It can be calculated by X g ð15Þ xai mi mai DGm ¼ where x is the fractions of elements. These values are necessary for the calculation of moving rate of the interface during transformation and precipitation. The Zener–Hillert equation [8,9], which represents the growth rate of ferrite into austenite, is expressed as G¼

1 Cga Cg D 2r Cg Ca

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ð16Þ

where D is the diffusion coefficient of C in austenite, r the tip-radius of growing phase, Cga, Ca, and Cg is the carbon content in austenite, ferrite at a=g interface and in ferrite apart from interface, respectively. The carbon content at the interface can be calculated from the common tangent between two phases as shown in Fig. 4. There is the other type of expression of moving rate of interface which is expressed as v¼

M DGm Vm

ð17Þ

where M is the mobility of interface, and Vm is the molar volume. The driving force in this equation can be calculated for multicomponent system by Eq. (15). This calculation makes it possible to consider the effect of alloying elements other than the pinning effect and the solute-drag effect. Details of the thermodynamic calculation have been published [10–12]. Recently, some commercial software for the thermodynamic calculation have been used for this type of calculation [13].

Figure 4 Gibbs free energy vs. chemical composition diagram.

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V.

BASIC MODELS

A.

The Concept of the Model

As mentioned above, the overall model for predicting mechanical properties of hot-rolled steels consists of several basic models: the initial state model for austenite grain size before hot-rolling, the hot-deformation model for austenitic microstructural evolution during and after hot-rolling, the transformation model for transformation during cooling subsequent to hot-rolling, and the relation between mechanical properties and microstructure of steels. In the case where steels include alloying elements which form precipitates, the model for precipitation is necessary. Precipitates affect all the models mentioned here. In this section, these basic models will be explained [14,15]. B.

Initial State Model

In this model, austenite grain sizes after slab reheating, namely before hot deformation, are calculated from the slab-reheating condition. In steels consisting of ferrite and pearlite at room temperature, austenite is formed between pearlite and ferrite and it grows into ferrite according to decomposition of pearlite. After all the microstructures become austenite, the grain growth of austenite takes place. We should formulate these metallurgical phenomena to predict austenite grain size after slab reheating. In hot-strip mill, however, the effect of initial austenite grain size on the final austenite grain size after multi-pass hot deformation is small. This can be due to the high total reduction in thickness by several hot-rolling steps in which the recrystallization and grain growth are repeated and the size of austenite grain becomes fine. This means that the high accuracy is not required for the prediction of the initial austenite grain size in a hot-strip mill. From this point of view, the next equation (14) can be applied n

o pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ dg ¼ exp 1:61 ln K þ K2 þ 1 þ 5 K ¼ ðT 1413Þ=100 ð18Þ where dg is the austenite grain size after reheating of slab and T is the temperature in K. On the other hand, the initial austenite grain size affects the final austenite grain size in the case of plate rolling because the total thickness reduction is relatively small compared to hot-strip rolling. In this case, the high accuracy of the prediction may be required and the model that is applicable for this case has been reported [16]. Three steps are considered in this model: (1) the growth of austenite between cementite and ferrite according to the dissolution of cementite, (2) the growth of austenite into

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ferrite at a þ g two-phase region, and (3) the growth of austenite in the g single-phase region. The pinning effect by fine precipitates on grain growth and that of Ostwald ripening of precipitates on the grain growth of austenite are taken into consideration. This model is briefly explained in the following paragraphs. The growth of austenite due to the dissolution of cementites can be expressed as dðdg Þ Dgc Cyg Cga ¼ dg Cga Ca dt

ð19Þ

where t is the time, Dgc the diffusion constant of C in austenite, and Cg, Cga are the C content in austenite at g=y phase interface and g=a phase interface, respectively. In the a þ g two-phase region, the austenite grain size depends on the volume fraction of austenite, Xg, which changes according to temperature. This situation is expressed as 3Xg 1=3 dg ¼ ð20Þ 4pn0 where n0 is the number of austenite grains at a unit volume when cementites are dissolved. Grain growth occurs in the austenite single-phase region. For grain growth, it is necessary to consider three cases; without precipitates, with precipitates, and with precipitates growing due to the Ostwald ripening. There are equations which are formulated to theoretically correspond to these three cases. They are summarized by Nishizawa [17]. The equation for the normal grain growth is expressed as d2g d2g0 ¼ k2 t

ð21Þ

where k2 is the factor related to the diffusion coefficient inside the interface, the interfacial energy, and the mobility of the interface. With the pinning effect by precipitates, the growth rate becomes dðdg Þ 2sV 3sVf ¼M DGpin ; DGpin ¼ ð22Þ dt R 2r where f is the volume fraction of precipitates and r is the average size of precipitates. When precipitates grow according to the Ostwald ripening, the average size of precipitates used in the Eq. (22) is obtained from r3 r30 ¼ k3 t

ð23Þ

where k3 is the factor related to temperature, interfacial energy and the diffusion coefficient of an alloying element controlling the Ostwald ripening of

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precipitates. By this calculation method, it is possible to predict the growth of austenite grain during heating when precipitates such as AlN, NbC, TiC, and TiN exist in austenite [16].

C.

Hot-Deformation Model

The hot-deformation model is required to predict the austenitic microstructure before transformation through recovery, recrystallization, and grain growth in austenitic phase region during and after multi-pass hot deformation. Sellars and Whiteman [18,19] made the first attempt on this issue and then several researchers [20–27] developed models to calculate recovery, recrystallization, and grain growth. These models are basically similar to each other. In some models, dynamic recovery and dynamic recrystallization are taken into consideration. The dynamic recovery and recrystallization are likely to occur when the reduction is high for single-pass rolling or strain is accumulated due to multi-pass rolling. They should be taken into consideration in finishing rolling stands of a hot-strip mill because, the inter-pass time might be less than 1 sec and the accumulation of strain might take place. Here, the hot-deformation model will be explained based on the model developed by Senuma et al. [20]. In this model, dynamic recovery and recrystallization, static recovery and recrystallization, and grain growth after recrystallization are calculated as shown in Fig. 5. The critical strain, ec, at which dynamic recrystallization occurs is generally dependent upon strain rate, temperature, and the size of austenite grains. The effect of strain rate on ec is remarkable at low strain rate region [28]. One of the controversial issues had been whether the dynamic recrystallization took place or not when the strain rate is high such as that in a hot-strip mill. Senuma et al. [20] showed that it takes place and the effect of strain rate on ec is small at a high strain rate. The fraction dynamically recrystallized, Xdyn, and can be expressed based on the Avrami type equation as ! e ec 2 ð24Þ Xdyn ¼ 1 exp 0:693 e0:5 where e0.5 is the strain at which the fraction dynamically recrystallized reaches 50%. On the other hand, the fraction statically recrystallized can be expressed as ! t t0 2 Xdyn ¼ 1 exp 0:693 ð25Þ t0:5

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 5 Schematic illustration of microstructural change due to hot deformation.

where t0.5 is the time when the fraction statically recrystallized reaches 50% and t0 is the starting time of static recrystallization. The growth of grains recrystallized dynamically after hot deformation is much faster than normal grain growth in which grains grow according to square of time. This rapid growth was treated with different equations [19–24]. The reason why this rapid growth takes place might be caused by the increase of the driving force for grain growth due to high dislocation density [20], the change in the grain boundary mobility [24] or the annihilation of the small size grains at the initial stage [19]. In the case of multi-pass deformation, the strain might not be reduced completely at the following deformation due to the insufficient time interval and the effect of accumulated strain on the recovery and recrystallization should be taken into consideration. This effect is remarkable for a hot-strip mill because of the short inter-pass time and for steels containing alloying elements which retard the recovery and recrystallization. This effect can be formulated by using the change in the residual strain [22,25] or the dislocation density [20,21,24]. In the modeling process, the accumulated strain is

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calculated from the average dislocation density which is obtained by calculating the changes in the dislocation density in the region dynamically recovered, rn, and in the region recrystallized dynamically, rs, according to time independently. This method makes it possible to calculate the changes in grain size and dislocation density. Table 3 shows the summary of equations used in the model developed by Senuma et al. The numbers of phenomena in Table 3 correspond to those in Fig. 5. Figure 6 shows an example of calculation of the changes in grain size and dislocation density [14]. Figure 7 shows the calculation result of the effect of the initial austenite grain size on the final microstructure in the finishing stands of a hot-strip mill, which shows that the initial austenite grain size does not affect very much the final grain size. This model can be applied to the prediction of the resistance to hot deformation as well and it can contribute to the improvement of the accuracy in thickness. In this method, the average values concerning the grain size and the accumulated dislocation density are used taking the fraction recrystallized into consideration. This averaging can be applied to the hot-strip mill because the total thickness reduction is large enough to recrystallize their microstructure. In the case of plate rolling, the use of the average values is unsuitable because the reduction at each pass is small and the total thickness reduction is not enough to recrystallize the microstructure of steels. The model applicable to this case has been developed by dividing the microstructure into several groups [26]. This type of modeling was carried out for Nb-bearing steels [19,21,25], Ti- and V-bearing steels [21], Ti- and Nb-bearing steels [22], Ti-, Nb-, and Vbearing steels [27] as well as C–Mn steels. In these steels, the recovery and recrystallization are retarded by alloying elements. This retardation might be caused by the pinning effect due to fine precipitates or by the solute-drag effect. This effect can be considered by modifying the values of fitting parameters from experimental data. D.

Transformation Model

1. Basic Idea of the Modeling In the cooling process subsequent to hot-rolling, steels transform from austenite phase to ferrite, pearlite, bainite, and=or martensite phases. Transformation model predicts the microstructural change during cooling and the final microstructure of steels after cooling. The modeling of transformation kinetics can be performed by obtaining the parameters k and n in Avrami equation [29–31], formulating new equations corresponding to transformation kinetics obtained experimentally [32], and adopting the nucleation and growth theory [33–36].

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Table 3 Equations Used for Calculating Microstructural Change During Hot Deformation Phenomena 1.

2. 3.

4.

Critical strain for dynamic recrystallization Grain size of dynamically recrystallized grain Fraction dynamically recrystallized Dislocation density in dynamically recrystallized grain Dislocation density Grain growth of dynamically recrystallized grain Grain size of statically recrystallized grain Fraction statically recrystallized

5. 6.

Change in dislocation density due to recovery Grain growth

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Calculation model ec ¼ 4:76 104 expð8000=TÞ ðaÞ ddyn ¼ 22600½_e expðQ=RTÞ0:27 ¼ Z0:27 ; Q ¼ 63800 cal=mol ðbÞ Xdyn ¼ 1 exp½0:693ððe ec Þ=e0:5 Þ2 ðcÞ e0:5 ¼ 1:144 103 d00:28 e_ 0:05 expð6420=TÞ ðdÞ rso ¼ 87300½_e expðQ=RTÞ0:248 ¼ 87300Z0:248 ðeÞ rs ¼ rso exp½90 expð8000=TÞt0:7 ðfÞ re ¼ ðc=bÞð1 ebe Þ þ r0 ebe ðgÞ dy ¼ ddyn þ ðdpd ddyn Þy ðhÞ dpd ¼ 5380 expð6840=TÞ ðiÞ y ¼ 1 exp½295_e0:1 expð8000=TÞt ðjÞ dst ¼ 5=ðSveÞ0:6 ðkÞ Sv ¼ ð24=pd0 Þð0:491ee þ 0:155ee þ 0:1433e3e Þ ðlÞ Xst ¼ 1 exp½0:693ððt t0 Þ=t0:5 Þ2 ðmÞ t0:5 ¼ 0:286 107 Sv0:5 e_ 0:2 e2 expð30000=TÞ ðnÞ rr ¼ re exp½90 expð8000=TÞt0:7 ðoÞ d 2 ¼ dst2 ¼ 1:44 1012 expðQ=RTÞt

ðpÞ

Figure 6 passes.

Changes in grain size and dislocation density during hot rolling of six

When using the Avrami equation, the fitting parameters, k and n, can be obtained from the Avrami plot based on the isothermal transformation kinetics as shown in Fig. 8. The effect of chemical composition of steels and the austenitic grain size before transformation on transformation kinetics can be taken into consideration by obtaining the dependence on the values of k and n from experiments. The first attempt of this type of modeling was carried out by Kirkaldy [29]. In his study, the prediction of mechanical properties was also tried. In order to increase the generality of the transformation model, it should be necessary to take the nucleation

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Figure 7 Effect of initial grain size on the change in grain size during hot-rolling in a hot-strip mill.

and growth theory into consideration. Utilizing the Johnson–Mehl type equation [5] or Cahn’s equation [6]. Cahn’s equation can be recognized as being the most general one because the approximation of the equations leads to the Avrami and Johnson–Mehl type equations. The modeling based on the nucleation and growth theory [33] will be explained in the following paragraphs. Assuming that the nucleation site is the surface of grain boundaries and the rates of nucleation and growth are independent of time, the transformation rate can be expressed for two cases [6]. One is the case where both the nucleation and the growth of new phase occur and the other is the case where only the growth of new phase occurs after nucleation sites are covered by new phase. The first case is described by X ¼ 1 exp p=3ISG3 t4 ð26Þ

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Figure 8 Avrami’s plot. T1, T2, and T3 show different temperatures.

and the second case is described by X ¼ 1 ð2SGtÞ

ð27Þ

Transformation rates can be obtained by differentiating the equations as 3=4

p1=4 dX 1 1=4 3=4 ¼4 ðISÞ G ln ð1 XÞ dt 3 1X

ð28Þ

dX ¼ 2SGð1 XÞ dt

ð29Þ

For obtaining Eq. (28), the term of time is replaced by the fraction transformed on the assumption of the additivity of transformation with regard to the changing temperature. Equation (29) essentially holds the additivity of transformation. By using this type of equations, it is possible to obtain fitting parameters from continuous cooling transformation

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kinetics. It should be noticed that it is difficult to obtain accurate TTT diagrams of low-carbon steels which are the primary products in a hot-strip mill. This is due to their very rapid transformation kinetics and it causes difficulty in determining the fitting parameters from TTT data. From this point of view, this type of equation is very useful. In a case where it is possible to obtain the accurate TTT data, we can use the equations in Table 2 for determining the parameters. Transformations from austenite to ferrite, pearlite, and bainite can be calculated by using these equations. The start of each transformation is assumed as follows. The start of ferrite transformation is when the temperature of steel drops to Ae3. Carbon content in austenite increases during ferrite transformation and pearlite transformation starts when the carbon content in austenite achieves the amount shown on the Acm line. Bainite transformation starts when the temperature of steel drops to Bs temperature. Ae3 and Acm can be calculated from thermodynamics. Although Bs can be calculated on the same assumptions relating to T0 temperature [37], the equation obtained from experimental data is used in this model because the calculated Bs temperature still does not fit with experimental data. 2. Ferrite Transformation The nucleation site of transformation from austenite to ferrite is mainly the surface of austenite grains and its nucleation would be completed at the beginning of the transformation. Accordingly, the transformation from austenite to ferrite in the early stage is calculated by Eq. (28) and that in the latter stage is calculated by Eq. (29) in this model. The change in transformation kinetics, i.e., from the nucleation and growth to the site saturation, is assumed when the transformation rates calculated by both equations coincide with each other. Although the dissipation of incubation time for nucleation is generally used for the condition of the start of phase transformation, it is quite unclear theoretically. In this model, g=(a þ g) temperature, A3, is used for the starting condition of the calculation of phase transformation. There are two methods for calculating g=(a þ g) temperature; one is the condition called para-equilibrium [38] and the other is ortho-equilibrium. In the ortho-equilibrium, all elements are partitioned between ferrite and austenite; on the other hand, in the paraequilibrium condition, only carbon is partitioned. The idea of the para-equilibrium comes from that the diffusion of carbon which occupies interstitial sites in steel which is much more rapid than other substitutional alloying elements such as Mn, Si, and so on. There is an idea of NP–LE (No Partition–Local Equilibrium) [39], where interstitial atoms are partitioned between ferrite and austenite, the substitutional elements are locally

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

in the state of equilibrium between ferrite and austenite and the partition between ferrite and austenite does not occur after transformation. The ortho-equilibrium should be used when the transformation occurs at a relatively high temperature and the cooling rate is very slow. The paraequilibrium and the LE–NP should be used when the transformation occurs at a relatively low temperature as in rapid cooling. For the phase transformation in the continuous hot-rolling mill where the cooling rate is rapid, the para-equilibrium or the NP–LE should be used. The A3 temperature calculated based on the para-equilibrium and will be used in this model. For this calculation, C, Si, and Mn concentrations which are commonly included in steels are taken into consideration. According to the classical nucleation theory, the nucleation rate, I, can be described by equation [40] DG I ¼ Nb Z exp ð30Þ kT where N is the number of nucleation sites, b is the rate of solute atoms arriving at the surface of new phase, Z (the Zeldovich factor) characterizes the annihilation of nucleation, T the temperature, k is the Boltzmann constant and DG is the driving force for forming the nucleus with a critical size. Z and b can be described by the following equations, respectively Z ¼ aT1=2

ð31Þ

b ¼ bD

ð32Þ

where D is the diffusion coefficient of solute atoms, a the variable related to interfacial energy and b is the variable related to the nearest atomic distance. DG is described by the equation DG ¼

cs3 DG2V

ð33Þ

where s is the interfacial energy, DGV is the free-energy difference between ferrite and austenite and c is the configurational coefficient. DGV is calculated by the thermodynamic parameters. Although there are many reports concerning interfacial energy, its value is still unclear. The values of Z and b are also unclear. In this model, we introduced two parameters for the nucleation rate as k2 I ¼ k1 T1=2 D exp ð34Þ RTDG2V

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and they are evaluated from experimental data to fit the calculation result to that obtained by experiment. As mentioned above, DGV can be calculated with thermodynamic parameters from chemical compositions of steels. In the equation, R is the gas constant and D is the diffusion coefficient of C in austenite. The diffusion coefficient of C can be calculated by the equation reported by Kaufman et. al. [41] which is expressed as QD D cm2 =sec ¼ 0:5 exp 30Cg exp ð35Þ RT QD ðcal=molÞ ¼ 38300 1:9 105 C2g þ 5:5 10

ð36Þ

where Cg is the carbon content (mole fraction) in austenite. For growth rate, the Zener–Hillert equation [8,9], Eq. (16) is used. This equation is formulated for the lengthening growth of needle-shaped ferrite based on the idea that the growth of ferrite is controlled by the diffusion of carbon in austenite. It has been reported that this equation well describes the growth of ferrite and bainite phases into austenite [41]. The tip radius of growing ferrite affects the carbon content in austenite and ferrite at phase interface and the carbon content is calculated by the method reported by Kaufman et al. [41] in this model. The carbon content in austenite increases during the transformation to ferrite due to the small solubility of carbon in ferrite and the increase in carbon content in austenite affects the growth rate of ferrite. The carbon content in austenite, Cg, can be calculated by the equation Cg ¼

C0 XF Ca 1 XF

ð37Þ

where C0 is the initial carbon content, XF is the fraction transformed to ferrite, and Ca is the carbon content in ferrite. By putting this value for Cg into Eq. (16), the change of the growth rate of ferrite by the progress of ferrite transformation can be considered. Parabolic growth equation, G ¼ at1=2, can be used instead for Eq. (16). This relation between growth rate and time can be obtained from experiment and the theory for isothermal transformation kinetics. This is due to the change in carbon content ahead of interface into austenite during transformation. This situation is considered by using Eqs. (16) and (37) [33]. Growth equations explained above can consider only the partition of carbon between ferrite and austenite during transformation. The partition of substitutional elements like Mn and Si cannot be considered. Recently, Enomoto and Atkinson [42–44] and A˚gren [45] have analyzed the partition of substitutional elements and its effect on transformation in detail. The calculation method by A˚gren [46] is based on the local equilibrium theory and

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has shown that chemical composition in ferrite and austenite changes from ‘‘para’’ to ‘‘ortho’’ during transformation. 3. Pearlite Transformation In the case of low-carbon steel, transformation to pearlite occurs subsequent to that of ferrite and can be assumed to start when the carbon content in austenite calculated by Eq. (37) reaches the extrapolated Acm line, as shown in Fig. 9. This starting condition of pearlite transformation was assumed to correspond to the site saturation case because the determination of kinetics by experiments for low-carbon steel is almost impossible. The equation formulated by Hillert [47] is used for the growth rate which is expressed as GP ¼

kP D Cga Cgb Sl

ð38Þ

where Sl is the lamella spacing, Cgb the carbon content in austenite at the interface between cementite and austenite, and kP is the constant. The lamella spacing has a linear relation with the inverse of the undercooling temperature below Ae1, DT, and Eq. (38) can be expressed as ð39Þ GP ¼ kP DTD Cga Cgb

Figure 9 Starting condition of each transformation in the equilibrium diagram.

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The effect of a chemical composition on the growth rate of pearlite is considered by using Cga, Cgb and DT calculated by the thermodynamic parameters. As the transformation from austenite to pearlite is a eutectoid reaction, the change of the chemical composition in untransformed austenite during the progress of transformation does not occur. Equation (38) shows that pearlite transformation is controlled by the volume diffusion of carbon. On the other hand, it has been recently reported that the mechanism of pearlite transformation is somewhere between the volume diffusion of carbon in austenite and the interfacial diffusion of substitutional elements [48]. 4. Bainite Transformation Transformation to bainite is assumed to start when steels are cooled to the bainite-start temperature, Bs. In this report, Bs formulated from the observation of microstructures of steels (0.05–0.15 mass% C–0.5–1.5 mass% Mn–0–1.0 mass% Si steels) which are transformed isothermally is used, which is expressed as Bs ¼ 717:5 425½mass%C 42:5½mass%Mnð CÞ

ð40Þ

Bainite transformation in low-carbon steels occurs subsequent to ferrite or pearlite transformation. No flexion point between ferrite and bainite transformations is observed in the transformation curve. This result indicates that bainite transformation subsequent to ferrite transformation can be treated by the site saturation. The nucleation site in this case would be the interface between austenite and ferrite. The progress of bainite is calculated by Eq. (29), and the transformation rate is calculated by the Zener–Hillert equation (Eq. (16)). 5.

Summary of Equations and Parameters Used for the Transformation Model Table 4 shows the summary of equations and fitting parameters. Although the fitting parameters were obtained from the experimental data of one steel, this set of equations can simulate transformations of steels with different chemical compositions due to the application of thermodynamics to the calculation of the growth rate and the free-energy difference between ferrite and austenite. Figures 10 and 11 show the calculation results of the effects of chemical composition and austenite grain sizes on transformation kinetics [33]. The calculation of the fraction of each phase after transformation can be determined. By introducing the thermodynamic parameter of other alloying elements, the applicability would be easily extended [49]. Recently, the calculation of transformation for a 10 element system was reported [50]. This

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Table 4 Equations and Parameters Used for the Transformation Model

Transformation Ferrite

Pearlite

Basic equation of transformation rate Nucleation and Growth

1=4 dx ¼ 4:046 kt 6=dg4 IG 3 dt 3=4 1 ln ð1 xÞ 1x Site saturation dx 6 ¼ k2 Gð1 xÞ dt dg

Bainite

Factor corresponding to nucleation rate and growth rate I ¼ T 1=2 D exp G ¼

1 Cga Cg D 2r Cg Ca

k3 RT DGv2

G ¼ DTDðCga Cgb Þ

G ¼

1 Cga Cg D 2r Cg Ca

Coefficient

k1 ¼ 17; 476

21100 k2 ¼ 8:933 1012 exp T k3 ¼ ðcal3 =mol3 Þ ¼ 1:305 107 K2 ¼ 6:72 106

k2 ¼ 6:816 104 exp

3431:5 T

Note: dg: austenite grain size, D: diffusion coefficient of carbon in austenite, Cg: carbon content in austenite, Ca: carbon content in ferrite, Cga: carbon content in austenite at g=a boundary, Cgb: carbon content in austenite at g/cerm boundary, DT: undercooling below Ae1, G : Zener–Hillert equation (the value was calculated with the method by Kaufman et al.), and r: radius of curvature of advancing phase.

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Figure 10

The effect of chemical compositions on transformation kinetics.

extension of the model is possible only when alloying elements affect transformation kinetics through the change in phase stability. From the viewpoint of the effect of the chemical composition on transformation kinetics, other effects such as the solute drag, the pinning etc. should be taken into consideration. Kinsman and Aaronson [51] reported that transformation in C–Mo steels is retarded due to the solute drag-like effect. There is a report that Nb retards transformation due to solute-drag effect [52]. The solute-drag effect in Fe–C–X systems was investigated as well [53–56]. The solute-drag effect and others are not considered in the model. Instead of the application of these theories, the fitting parameters for the rates of nucleation and growth are introduced [57]. The introduction of these theories into the mathematical models is the remaining problem. 6. The Calculation of Ferrite Grain Sizes After Transformation The prediction of ferrite grain size is necessary for the calculation of mechanical properties. The calculation can be carried out using the austenite grain size before transformation and cooling rate [22]. This type of formulae is useful for the calculation because the prediction can be carried out

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Figure 11 The effect of austenite grain size on transformation kinetics of 0.15%C– 0.5%Si–1%Mn steels.

without knowing the accurate transformation kinetics. It, however, could not be applied for the case where cooling rate is not constant. The next equation can be applied for the case where the cooling rate changes during cooling. On the assumption that the shape of ferrite grains is spherical, the average ferrite grain size after cooling, da, has a relation with a fraction transformed to ferrite and the number of ferrite grains and the relation is expressed as 4p da 3 ð41Þ XF ¼ N 3 2 where N is the number of ferrite grains in the unit volume and XF is the volume fraction of ferrite. The equation can be transformed into 6XF 1=3 da ¼ ð42Þ pN Since XF can be obtained from the transformation model explained above, the calculation of ferrite grain size can be carried out if we know

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

the number of ferrite grains. The formulation of the equation for calculating the number of grains is based on the idea that the number of ferrite grains is determined in the early stage of ferrite transformation. Figure 12 shows the relationship between the number of ferrite grains and the temperature at 5% transformation, T0.05, which was calculated by the above-mentioned transformation model. This experiment was carried out for (0.1–0.15) mass% C–0.5 mass% Si–(0.5–1.5) mass % Mn steels. The temperature T0.05 is used as a representative temperature indicating the early stage of ferrite transformation. This figure shows that the number of ferrite grains is dependent upon the temperature at the early stage of ferrite transformation and the austenite grain size before transformation. Based on this result, the number of ferrite grains N(mm3) was formulated as 21430 11 1:75 exp N ¼ 3:47 10 dg ð43Þ T0:05 where dg is the austenite grain size before transformation. Using Eqs. (42) and (43), we can obtain the equation expressing the ferrite grain size da as 1=3 21430 exp ð44Þ da ¼ 5:51 1010 d1:75 XF g T0:05

Figure 12 The relationship between the number of ferrite grains and the temperature, T0.05.

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where da and dg are in units of mm. Figure 13 compares the ferrite grain sizes calculated versus those observed. A good agreement between those calculated and observed is found in this figure. Umemoto et al. [58] have derived theoretical equations for ferrite grain size in an isothermally transformed steel as da ¼ 0:564ðI=GÞ1=6 d2=3 g

ð45Þ

for the austenite grain edge nucleation of ferrite, and as da ¼ 0:695ðI=GÞ2=9 d1=3 g

ð46Þ

for the grain surface nucleation. In the present study, ferrite grain size is expressed by Eq. (45), in which the relationship between da and dg is da ¼ kd1:75=3 g

Figure 13

Comparison between calculated and observed ferrite grain sizes.

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ð47Þ

where k is the coefficient depending on the transformation temperature and ferrite fraction. This result indicates that the nucleation of ferrite transformation in low-carbon steels takes place mainly at the surface of austenite grains. 7. The Effect of Residual Strain on Transformation Kinetics The austenitic microstructure with which we start the calculation using the transformation model is a fully recrystallized austenite. In the hot-rolling mill, the austenite before transformation could contain many imperfections such as dislocations, deformation bands, and so on, and they may affect the nucleation rate and the growth rate. This effect would cause deterioration in predicting the accuracy of the microstructure after cooling. At this time, it is difficult to account for the effect of imperfections on transformation perfectly on theory. In this section, we thus will consider it using the dislocation density calculated by the hot-deformation model will be considered [20].

Figure 14 Comparison between calculated and observed ferrite grain sizes with and without consideration of the effect of the dislocation density.

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Figure 14 shows the difference between the calculated and the observed ferrite grain sizes as a function of residual dislocation densities. The dislocation density was estimated from the hot-deformation model [20]. In this figure, open circles show the case when the above-mentioned model is used, i.e., the effect of the residual strain is not considered, while solid circles show the case when the effect of residual strain is considered by the method which will be explained below. In the case where the effect of residual strain is not considered, the difference between the ferrite grain sizes measured and those calculated is small for low dislocation density and large for high dislocation density. Using the observed ferrite grain sizes, T0.05 and Eq. (44), we can estimate the austenite grain size upon which the correct ferrite grain size for a whole range of dislocation density can be given, and this austenite grain size can be called the effective austenite grain size. Figure 15 shows the difference between the austenite grain size, dg, calculated from the hot-deformation model, and the effective austenite grain

Figure 15

Effect of the dislocation density on the effective austenite grain size.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

size estimated as a function of the dislocation density. From this figure, the following relationship can be obtained: dgeff ¼ dg =ð1 þ 1011 r1:154 Þ

ð48Þ

where r is the dislocation density before transformation in cm2. The ferrite grain sizes calculated from the transformation model using dgeff instead of dg agree well with those observed as shown in Fig. 14. Figure 16 compares the ferrite fractions calculated with those observed when either dg or dgeff is used. The use of dgeff provides better agreement than the use of dg. These results prove that the effect of stored strain on transformation kinetics can be predicted quantitatively.

Figure 16 Comparison between the ferrite fractions calculated and observed while taking=not taking into account the effect of dislocation density.

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Umemoto et al. [59] studied the effects of the residual strain on the rate of growth and nucleation separately in pearlite transformation and showed that only the change in nucleation rate is caused by the stored strain. In the transformation model explained above, the effect of austenite grain size on transformation kinetics is considered by using dg. The change in the area of nucleation sites and the change in the rate of nucleation and growth would be taken into consideration by using Eq. (48), although it is not clear which is the dominant factor. For quantitative evaluation of each of these effects, conducting an experiment similar to the work done by Umemoto et al. is necessary, although it is difficult to conduct such an experiment with regard to low carbon steels because of their rapid transformation. E.

Precipitation Model

Precipitation of carbides and=or nitrides in austenite phase could affect recovery, recrystallization, and grain growth after hot deformation, and transformation during cooling. Precipitation in ferrite phase could affect mechanical properties. Accordingly, it is necessary to take precipitation into consideration in the model. It is not necessary to consider the hard impingement for the modeling of precipitation. For this reason, nucleation and growth can be calculated independently and the amount, number, and size distribution of precipitates can be directly calculated. Although formulations based on Avrami’s equation have been reported [60–62], modeling based on the nucleation and growth theory has been attempted from the above point of view [63–67]. Okamoto and Suehiro [67] reported a model which can be applied from the beginning to the end (the Ostwald ripening) of precipitation. The feature of this model is in the calculation method of growth rate of precipitates. This calculation method will be explained briefly as follows. The velocity of the interface between matrix and precipitates can be expressed from the flux balance of each chemical element as v¼0

JNb JC JN ¼ ¼ CNb b CNb 0 CC b CC 0 CN b CN

ð49Þ

where Jj is the flux of each element, 0Cj and bCj the content of element j in precipitates and matrix at the interface between matrix and precipitates, respectively. For the calculation of the content of element j in matrix at the interface, the local equilibrium condition is normally applied. In this model, the content of element j is calculated considering the radius of

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precipitate using the next equation. This relationship is called the Gibbs–Thompson effect mNbCN þ 2sVNbCN =R ¼ mM j j

ð50Þ

where the second term of the left side of this equation is the increase in the Gibbs free energy, Esurf, due to the interfacial energy, s. The Ostwald ripening of precipitates appearing at the latter stage of precipitation in which the small size of precipitates would dissolve and the large size of precipitates would grow can be calculated by considering this term. Figure 17 shows the isothermal section of equilibrium diagram of three element system. From this figure, the effect of the radius of precipitates can be understood. Figure 18 compares the calculation result of the average diameter and the mole fraction of precipitates with the experiments. Figure 19 shows the calculation result of the average diameter and the number of precipitates which shows that the average diameter increases with a half power of time at the beginning of precipitation (region II) and with one-third power of time at the latter stage (region IV). Region IV would correspond to the Ostwald ripening.

F.

Relationship Between Strength and Microstructure of Steel

The mechanical properties to be predicted are dependent upon the type of products. Sheets and coils require YS (yield strength), TS (tensile strength), and El (elongation). Plates require toughness other than YS, TS and El. Wire and rods require TS and the reduction of section area. The prediction of these mechanical properties was carried out by formulating regression equations for strengths with respect to chemical compositions and grain sizes of ferrite [68]. Other formulations for strength were based on the volume fractions of ferrite and pearlite phases, ferrite grain sizes, and lamella spacing of pearlite for steels consisting of ferrite and pearlite in phases [69]. For toughness, some regression formulae based on the ferrite grain size and=or chemical compositions were reported [70–72]. Various reports on this type of formulations are available [32–74]. Irvine and Pickering [73] showed that the tensile strength of ferritepearlite steel or bainite steel was determined from the transformation temperature of steels [73]. In their experiment, only the content of alloying elements was a variable of the transformation temperature, but the result indicated that the change of transformation temperature due to processing variables such as cooling rate had a similar influence on the strength of steels

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Figure 17 Isothermal section of equilibrium diagram of Fe–Nb–C system; (a) the beginning and (b) the latter stage of precipitation.

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Figure 18 Comparison of the calculated results with the observed ones. Steel A: 0.006%C–0.14%Nb–0.0022%N, steel B: 0.018%C–0.052%Nb–0.0041%N.

consisting of ferrite, pearlite, and=or bainite. A recent study confirmed this result with regard to the accelerated cooled steels of a substantially ferritic transformation structure [75]. Therefore, the determination of a more general relationship between strength and transformation temperature applicable to the individual microconstituent in a mixed microstructure is required. Since the strength

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Figure 19 model.

Change in the size and the number of precipitates calculated by the

of steel is generally proportional to its hardness, by assuming the law of mixture for hardness, the tensile strength, TS, can be expressed as TS ¼ a½XF ðHF þ bda1=2 Þ þ XP HP þ XB HB

ð51Þ

where X is the fraction of each transformed phase (F: ferrite, P: pearlite, and B: bainite), H the hardness of each microconstituent, da the ferrite grain size in mm, and a and b are the constants. If the relationship between strength and transformation temperature for each constituent of steel is established, the tensile strength can be calculated from Eq. (51). Figure 20 shows the relation between the hardness of each microconstituent and its average transformation temperature, TM, calculated from Z Z ð52Þ TM ¼ T dX= dX

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where the transformation temperature, T, is obtained for an infinitely small transformation product, dX, from the transformation model. A linear relationship is found between the hardness and average transformation temperature for both ferrite and bainite. Such a relationship is not found for pearlite, although it is presumed. This is probably because of the narrow temperature range of transformation in the steels used. Silica has a strong effect on solid-solution hardening while C and Mn have a very small effect. Further, the hardness does not depend on the cooling rate. From these results, the hardness of each microconstituent is expressed as HF ¼ 361 0:357TF þ 50½mass%Si HP ¼ 175

ð53Þ

Figure 20 The relationship between the measured microhardness of each microconstituent and its calculated mean transformation temperature.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

and HB ¼ 508 0:588TB þ 50½mass%Si

ð54Þ

where H is the hardness and T is the average transformation temperature (8C). Other Methods of attempting to predict YS, TS, n-value, etc. have been reported. Tomota et al. [76] attempted the prediction of YS, TS, and n-value, etc. based on the prediction of flow stress curves. Shikanai et al. [77] and Iung et al. [78] utilized the analysis by the finite element method in order to consider the effect of morphology of microstructure. For steels containing chemical elements forming precipitates such as Nb, Ti, V, etc., the precipitation hardening should be taken into consideration. It would be possible by using the precipitation model. It might be possible to predict the precipitation hardening from the alloying elements in solid solution at austenite region before cooling [79,80].

VI.

PREDICTION OF STRENGTH OF HOT-ROLLED STEEL SHEETS

Using the model mentioned above, we can predict the strength of hot-rolled steel sheets from its composition and processing conditions such as hot-rolling condition, cooling condition, and so on. Figure 21 shows the flow chart of the calculation. Figure 22 compares the calculated and observed transformed fraction of each phase in 0.2 mass% C-0.2 mass% Si-0.5 mass% Mn steels hot rolled in a two-stand laboratory mill from 40 to 2.4 mm by six passes after being soaked at 11008C for 30 min. The microstructure is ferrite–pearlite in the sample (a) cooled at around 108C=sec and ferrite–bainite in (b) cooled at around 608C=sec. The values calculated by the present model are in good agreement with those measured. Tensile strengths were calculated using Eqs. (51), (53), and (54) with the constant a of 3.04 and the constant b of 2.55. An agreement between the calculated and the observed tensile strengths is good for various steels (C: 0.1– 0.2 mass%, Si: 0.006-0.5 mass%, Mn: 0.5-1.5 mass%) as shown in Fig. 23. The present integrated model has been applied to the prediction of the microstructures and strengths of steel hot rolled in a production mill. 0.15 mass% C-0.1 mass% Si-0.6 mass% Mn steel was hot rolled. In the hot-rolling, the finish rolling temperature and the coiling temperature varied lengthwise as shown in Fig. 24. Figure 25 shows the calculated and observed ferrite grain size and ferrite fraction of the steel sheet. Figure 26 compares the strengths calculated with those measured. These figures show that the values

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Figure 21 Flowchart of the calculation of microstructural change and mechanical properties of hot-rolled steels.

calculated by this model have a good agreement with those measured. These results indicate that this type of simulation could be a very efficient tool for designing chemical compositions and processing conditions in order to obtain required mechanical properties. Many empirical equations have been developed to predict the strength of hot rolled steel products. These equations combine the parameters of chemical compositions such as C, Mn, and Si, fraction of each microconstituent and cooling rate. In the present model, Eqs. (51), (53) and (54) for calculation of the strength of hot-rolled steel products have no explicit parametric terms of C, Mn and cooling rate. Therefore, it seems as if the content of C and Mn and the cooling rate do not influence the strength of these products. As mentioned above, the microstructure and the hardness of each microconstituent predicted based on the hot-deformation and transformation models are strongly affected by the C- and Mn-content and the cooling condition. The results shown in Fig. 20 indicate that the solid-solution hardening by C and Mn reported in the literature includes the variation of the microstructure with the change in the transformation temperature. Since

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Figure 22 Comparison of the calculated microstructure with that observed for steels cooled at about (a) 108C=sec and (b) 608C=sec.

the cooling rate does not appear explicitly, the present model is suitable for the prediction of strength of steels processed by thermomechanical treatment.

VII.

A.

APPLICATION OF THE MODEL TO THE PREDICTION OF TEMPERATURE OF HIGH CARBON STEELS DURING COOLING AFTER HOT DEFORMATION Modification of the Model to the Application to High Carbon Steels

Steels containing more than 0.3mass%C carbon (high -carbon steels) show a remarkable evolution of latent heat of transformation during cooling. This

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Figure 23 Comparison between the calculated and observed tensile strengths of various steels.

evolution makes on-line control of temperature difficult and thus affects mechanical properties of final products. Thus, accurate calculations of temperature of steel during cooling prior to production in a mill are desirable to enable the control and the investigation of suitable processing conditions. In order to calculate the temperature accurately, the prediction of transformation is particularly important.

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Figure 24 Finish rolling and coiling temperatures for experiments in production mill.

Figure 25 Variation of ferrite fraction and ferrite grain size from top to tail of the coil of 0.16mass%C–0.015 mass%Si–0.73mass%Mn steel hot rolled in a production mill.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 26 Variation of tensile strength from top to tail of the coil of 0.16mass% C–0.015mass%Si–0.73mass%Mn steel hot rolled in a production mill.

As mentioned above, a mathematical model for predicting transformation of low-carbon steels during cooling while taking ferrite transformation into consideration has been developed because the principal transformation product in low-carbon steels is ferrite. In high-carbon steels, however, the main transformation product is pearlite, so that the development of a model for calculating pearlite transformation accurately is necessary. In this section, the model for high-carbon steels and its application [81] will be explained.

B.

Transformation Model

1. Start of Pearlite Transformation The calculation procedure for ferrite and bainite transformations is the same as that explained in Sec. 5. The treatment for pearlite transformation is modified. The calculation of ferrite transformation which starts when the temperature drops to the equilibrium temperature Ae3 is calculated using thermodynamic parameters. Transformation from austenite to ferrite is controlled by the volume diffusion of carbon into austenite so that carbon in austenite increases with the progress of ferrite transformation. This point is explained in the Sec. 5.

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Pearlite transformation is generally assumed to start when the carbon content in austenite meets the extrapolated Acm line in the phase equilibrium diagram. The observed ferrite fraction of carbon steels transformed isothermally from austenite, however, indicates that the pearlite transformation starts earlier than the above expectation at the temperature range below 960 K shown in Fig. 27. This deviation might be due to the distribution of carbon between ferrite and austenite at the g=a phase boundary because the carbon content in austenite at=near the phase boundary can exceed the value on the extrapolated Acm line below Ae1 temperature. In this model, the start of pearlite transformation is dealt with based on this result. 2. Kinetics of Pearlite Transformation For low-carbon steels, there has been no experimental data which clarifies the mode of pearlite transformation kinetics. In 0.5mass%C steels, however, the experimental results of pearlite transformation kinetics show that pearlite transformation conforms to nucleation and growth case [81]. Accordingly, Eq. (28) is used and the fitting parameter [81] was obtained from the experimental results of 0.5mass%C steels as shown in Table 5.

Figure 27 Deviation of maximum ferrite fraction measured in isothermal transformation experiments from the value calculated thermodynamically.

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Table 5 Equations and Parameters for Pearlite Transformation of High-Carbon Steels Basic equation of transformation rate Nucleation and growth

p1=4 dX ¼4 ðk1 ISÞ1=4 dt 3 3=4 1 G3=4 ln ð1 XÞ 1X

C.

Factor corresponding to nucleation rate and growth rates Coefficient k3 I ¼ T 1=2 D exp k1 ¼ 2.01 1013 RTDGV2 k3¼2.27 109 (J3=mol3) S¼6=dg GP ¼ DTD Cga Cgb

Method for Calculating Temperature of Steels During Cooling

The transformation model developed was coupled with the model for calculating the temperature of steels during cooling by a two-dimensional finite element method in order to take into consideration the evolution of latent heat [15]. The heat conduction equation used here is as follows: mCaP

@T @2T @2T ¼l 2 þl 2 þQ @t @x @y

ð55Þ

where m is the density of steel, l the heat conductivity, and CPa is the specific heat of ferrite on the assumption of nonexistence of magnetic transformation as shown in Fig. 28. Q is the rate of latent heat evolution accompanying transformation and can be formulated by Eq. (56), in which the latent heat is divided into that of lattice transformation, ql, and that of magnetic transformation, qm: @X @ þ ðqm XÞ ð56Þ Q ¼ m ql @t @t where X is the fraction transformed and calculated by the above-mentioned transformation model. The value of ql used is 16.7 J=g and qm is expressed as Z910 qm ¼

CP CaP dT

T

where CP is the specific heat of steel. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

ð57Þ

Figure 28

D.

Specific heat and latent heat of magnetic transformation of steel.

Calculation Results

1.

Accuracy of the Model for Predicting Temperature of Steels During Cooling Figure 29 shows examples of simulation in which the temperature and the progress of transformation of 0.5mass%C steels on the run-out table of a hot-strip mill were calculated simultaneously for three different cooling conditions. In this calculation, the initial state and the hot-deformation models were also used and the average austenite grain size before transformation was calculated as being about 15 mm. A good agreement between calculated and measured temperatures was obtained. This implies that transformation kinetics on the run-out table are accurately predicted by the model. 2. Improvement of Productivity To improve the productivity in a hot-strip mill, it is necessary to increase the traveling speed of the hot-strip and intensify the cooling rate. Figure 30(a) shows the calculated results of temperature and transformation behavior of 0.5mass%C steel of 2 mm thickness cooled at a heat transfer coefficient,

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Figure 29 Simulation of temperature and progress of transformation of 0.5 mass%C steel under different cooling conditions on run-out table of a hot-strip mill.

a, of 1670 kJ=m2 h K for water cooling. In this calculation, the finish rolling temperature is 1123 K, the coiling temperature is 873 K and transformation is completed before coiling. The traveling time through the run-out table can be shortened from 11.5 to about 5 sec by increasing the heat transfer coefficient up to 5020 kJ=m2 h K, as shown in Fig. 30(b). The figure, however, shows the undesirable situation where the temperature of steel drops to about 800 K which is below the bainite-start temperature (about 823 K for 0.5mass%C steel) and bainite which deteriorates the quality of steel might appear. This situation can be avoided by changing the cooling condition. Figure 30(c) shows the suitable cooling condition in which the water cooling is stopped just before the transformation start and restarted at about 20% transformation.

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Figure 30 Temperature change of 0.5mass%C steel on the run-out table under three different cooling conditions.

The results show that the calculation by the model can be used for determining a suitable cooling pattern on the run-out table for attaining high productivity without conducting an experiment in a production mill.

3.

Effect of the Finish Rolling Temperature on Mechanical Properties In a hot-strip mill, the finish rolling temperature varies widthwise. This variation affects the transformation behavior during cooling due to the changes in austenite grain size and dislocation density in austenite, and it also changes the temperature range of water cooling on the run-out table as well. Figure 31 shows the calculated cooling curves of 0.5mass%C steel coil of 4 mm thickness and 1 m width at two different positions; the center along the width and the position of 12.5 mm apart from the edge of strip. The temperature difference between these two positions is about 408C. By changing the water-cooling condition, the temperature difference can be reduced as shown in Fig. 32. This change contributes to the reduction of the fluctuation of mechanical properties as shown in Fig. 33, in which the index of vertical

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Figure 31 Temperature changes of steel at two different positions in the direction of width on the run-out table.

Figure 32 Temperature change of steel at two different positions in the direction of width on the run-out table. Cooling condition was modified from that in Fig. 31.

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Figure 33 Changes in the index of hardness, (Ae1TP)1=2, in which TP is the mean pearlite transformation temperature, along the width under two different conditions.

axis, (Ae1TP) 1=2 where TP is the mean transformation temperature of pearlite, representing hardness of pearlite because the pearlite hardness depends on the lamella spacing of pearlite which depends upon the under-cooling from Ae1 temperature. Conditions A and B in Fig. 33 correspond to those in Figs. 31 and 32. This result indicates that the fluctuations of properties due to the variation of temperature along the width can be compensated by controlling the water-cooling intensity. 4.

Effect of Fluctuations of Coiling Temperature on Mechanical Properties Coiling temperature is fluctuated widthwise by the fluctuations of water cooling intensity even though the finish rolling temperature is constant, and this coiling temperature fluctuation affects the mechanical properties due to the change in the transformation temperature. Figure 34 shows an example of the calculated results for 0.5mass%C steel sheets with thickness

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Figure 34 Effect of thickness of steel on the relationship between the fluctuations of coiling temperature, DCT, and those of the index of pearlite hardness, (Ae1TP)1=2.

of 4 and 6 mm under the condition that the finish rolling temperature is 1122 K and the coiling temperature fluctuates between 843 K and 933 K. This result indicates that fluctuations of the index of hardness, D(Ae1TP)1=2, depend on those of coiling temperature, DCT, and their relationship is influenced by the thickness of steel sheets. The fluctuations of transformation temperature are mostly dependent on the cooling rate just before and=or at the beginning of transformation. Since the water-cooling intensity for the steel of 4 mm thickness is the same as that for steel of 6 mm thick in this calculation, the water-cooling time for steel of 6 mm thickness is longer than that for 4 mm steel because of the mass effect. Hence, the change in cooling rate, which causes a certain value of DCT, becomes smaller as steel strip thickens. This is the reason why the thickness of steel sheets causes fluctuations in hardness. Figure 35 shows the effect of traveling speed on the fluctuations of transformation temperature. The calculation shown was carried out for three different traveling speeds (300, 400, and 500 mpm) with the finish rolling temperature of 1123 K and the coiling temperature of between

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Figure 35 Effect of traveling speed of steel through the run-out table on the relationship between the fluctuations of coiling temperature, DCT, and those of the index of pearlite hardness, (Ae1TP)1=2.

853 K and 913 K. The fluctuations of the index of hardness do not vary in the order of traveling speed; the fluctuations for 400 mpm are the largest among three traveling speeds. This variation is also related to the cooling rate before and during transformation. The faster the traveling speed, the longer the water-cooling time, in the case where the intensity for water cooling is constant regardless of the traveling speed. This is due to the change in the water-cooling temperature range depending on the finish rolling temperature, the coiling temperature, the traveling speed, and the thickness. In this calculation, the water-cooling time for 300 mpm is too short to affect the transformation behavior greatly. This is the reason why the fluctuations in transformation temperature for 400 mpm are greatest in Fig. 35. These results depend on the chemical composition of steel and the capacity of the hot-strip mill, such as the water-cooling intensity and the length of the run-out table. Accordingly, the pre-calculation by this type

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of mathematical model is very useful for designing cooling facilities and determining cooling conditions for obtaining a more uniform quality product. VIII.

CONCLUSION

In this chapter, mathematical models for predicting microstructural evolution during hot deformation and subsequent cooling, and mechanical properties from the resultant microstructure of steels were explained. These models include some empirical parameters although they are based on theory. This is because mechanisms of some phenomena are still unclear; for instance, solute-drag effect on recrystallization and transformation. The model calculating mechanical properties from microstructure is much more phenomenological. To extend the applicability, the empirical parameters should be replaced by those obtained from theories. Although the models include some empirical parameters, they are very useful for investigating production conditions such as chemical compositions, processing conditions and so on. The accuracy of predicted mechanical properties is satisfactory. It is noted that these models should be widely used for off-line simulation of designing steel compositions and processing condition and on-line simulation for guaranteeing mechanical properties of steels. REFERENCES 1. Proceedings of International Conference on Physical Metallurgy of Thermomechanical Processing of Steels and Other Metals; ISIJ: Tokyo, 1988. 2. Yue, S., Ed. Proceedings of International Symposium. on Mathematical Modelling of Hot Rolling of Steel; CIM: Quebec, 1990. 3. ISIJ Int., 1992, 32. 4a. Avrami, M.J. Chem. Phys. 1939, 7, 1103. 4b. Avrami, M.J. Chem. Phys. 1940, 8, 212. 4c. Avrami, M.J. Chem. Phys. 1941, 9, 177. 5. Johnson, W.A.; Mehl, R.F. Trans. AIME 1939, 135, 416. 6. Cahn, J.W. Acta Metall. 1956, 4, 449. 7. Umemoto, M. Proceedings of International Symposium on Mathematical Modelling of Hot Rolling of Steel; Yue, S., Ed.; CIM: Quebec, 1990; 404. 8. Zener, C. Trans. AIME 1946, 167, 550. 9. Hillert, M. Jernkontrets Ann. 1957, 141, 757. 10. Kaufman, L.; Vernstein, H. Computer Calculation of Phase Diagrams; Academic Press: New York, 1970. 11. Hillert, M. In Hardenability Concepts with Applications to Steel; Doane, D.V.; Kirkaldy, J.S., Eds.; The Metallurgical Society of AIME: 1978 ; 5.

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12. Hillert, M.; Staffansson, L.I. Acta Chem. Scand. 1970, 24, 3618. 13. Sundman, B.; Jansson, B.; Andersson, J.-O. CALPHAD 1985, 9, 153. 14. Suehiro, M.; Sato, K.; Tsukano, Y.; Yada, H.; Senuma, T.; Matsumura, Y Trans. Iron Steel Inst. Jpn. 1987, 27, 439. 15. Suehiro, M.; Sato, K.; Yada, H.; Senuma, T.; Shigefuji, H.; Yamashita, Y. Proceedings of International Conference on Physical Metallurgy of Thermomechanical Processing of Steels and Other Metals; ISIJ: 1988; 791. 16. Yoshie, A.; Fujioka, M.; Morikawa, H.; Onoe, Y. Proceedings of International Conference on Physical Metallurgy of Thermomechanical Processing of Steels and Other Metals; ISIJ: 1988; 799. 17. Nishizawa, T. Tetsu-to-Hagne 1984, 70, 1984. 18. Sellars, C.M.; Whiteman, J.A. Met. Sci. 1979, 14, 187. 19. Sellars, C.M. International Conference on Working and Forming Processes; Sellars, C.M., Davies, G.J., Eds.; Met. Soc.: London, 1980, 3. 20. Senuma, T.; Yada, H.; Matsumura, Y.; Futamura, T. Tetsu-to-Hagane 1984, 70, 2112. 21. Yoshie, A.; Morikawa, H.; Onoe, Y.; Itoh, K. Trans. Iron Steel Inst. Jpn. 1987, 27, 425. 22. Roberts,W.; Sandberg, A.; Siwecki, T.; Werlefors, T.; Werlefors, T. Proceedings of International Conference on Technology and Applications of HSLA Steels; ASM: 1984, 67. 23. Wiliams, J.G.; Killmore, C.R.; Harris, G.R. Proceedings of International Conference on Physical Metallurgy of Thermomechanical Processing of Steels and Other Metals; ISIJ: Tokyo, 1988, 224. 24. Komatsubara, N.; Okaguchi, H.; Kunishige, K.; Hashimoto, T.; Tamura, I. CAMP-ISIJ 1989, 2, 715. 25. Saito, Y.; Enami, T.; Tanaka, T. Trans. Iron Steel Inst. Jpn. 1985, 25, 1146. 26. Anan, G.; Nakajima, S.; Miyahara, M.; Nanba, S.; Umemoto, M.; Hiramatsu, A.; Moriya, A.; Watanabe, T. ISIJ Int. 1992, 32, 261. 27. Siwecki, T. Proceedings of International Conference on Physical Metallurgy of Thermomechanical Processing of Steels and Other Metals; ISIJ: Tokyo, 1988, 232. 28. Sakai, T.; Jonas, J.J. Acta Metall. 1983, 32, 100. 29. Kirkaldy, J.S. Metall. Trans. 1973, 4, 2327. 30. Umemoto, M.; Komatsubara, N.; Tamura, I. Tetsu-to-Hagane 1980, 66, 400. 31. Hawbolt, E.B.; Chau, B.; Brimacombe, J.K. Metall. Trans. A 1983, 14, 1803. 32. Choquet, P.; Fabregue, P.; Giusti, J.; Chamont, B. Proceedings of International Symposium on Mathematical Modelling of Hot Rolling of Steel; Yue, S., Eds.; CIM: Quebec, 1990; 34. 33. Suehiro, M.; Senuma, T.; Yada, H.; Matsumura, Y.; Ariyoshi, T. Tetsu-toHagane 1987, 73, 1026. 34. Saito, Y. Tetsu-to-Hagane 1988, 74, 609. 35. Reed, R.C.; Bhadeshia, H.K.D.H. Mater. Sci. Tech. 1992, 8, 421. 36. Jones, S.J.; Bhadeshia, H.K.D.H. Metal. Mater. Trans. A 1997, 28, 2005. 37. Bhadeshia, H.K.D.H Acta Metall. 1981, 29, 1117.

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38. Hultgren, A. Trans. ASM 1947, 39, 915. 39. Hillert, M. Internal Report; Swedish Institute for Metal Research: Stockholm, Sweden, 1953. 40. Aaronson, H.I.; Lee, J.K. In Lectures on the Theory of Phase Transformations; Aaronson, H.I., Ed.; TMS-AIME: 1975; 28. 41. Kaufman, L.; Radcliffe, S.V.; Cohen, M. In Decomposition of Austenite by Diffusional Processes; Zackay, V.F.; Aaronson, H.I., Eds.; Interscience Publishers: New York 1962. 42. Enomoto, M. ISIJ Int. 1992, 32, 297. 43. Enomoto, M.; Atkinson, C. Acta Metall. Mater. 1993, 41, 3237. 44. Enomoto, M. Tetsu-to-Hagane 1994, 80, 653. 45. A˚gren, J. ISIJ Int. 1992, 32, 291. 46. Anderson, J.-O.; Ho¨glund, L.; Jo¨nsson, B.; A˚gren, J. In Fundamentals and Applications of Ternary Diffusion; Purdy, G.R., Ed.; Pergamon Press: New York, 1990, 153. 47. Hillert, M. In Decomposition of Austenite by Diffusional Processes; Zackay, V.F.; Aaronsson, H.I., Eds.; Interscience Publishers: New York, 1962; 313. 48. Jo¨nsson, B. TRITA-MAC-0478, Internal Report, Division of Physical Metallurgy, The Royal Institute of Technology, S-10044 Stockholm, Sweden, 1992. 49. Suehiro, M.; Yada, H.; Senuma, T.; Sato, K. Proceedings of International Symposium on Mathematical Modelling of Hot Rolling of Steel; Yue, S., Ed.; CIM: Montreal, 1990; 128. 50. Nanba, S.; Katsumata, M.; Inoue T. Nakajima, S.; Anan, G.; Hiramatsu, A.; Moriya, A.; Watanabe, T.; Umemoto, M. CAMP-ISIJ 1990, 3, 871. 51. Kinsman, K.R.; Aaronson, H.I. Transformation and Hardenability in Steels; Climax Molybdenum Co.:Ann Arbor, MI, 1967; 39. 52. Suehiro, M.; Liu, Z.-K.; Agren, J. Acta Mater. 1996, 44, 4241. 53. Purdy, G.R.; Brechet, Y.J.M. Acta Metal. Mater. 1995, 43, 3763. 54. Enomoto, M. Acta Mater. 1999, 47, 3533. 55. Enomoto, M.; Kagayama, M.; Maruyama, N.; Tarui, T. Proceedings of the International Conference On Solid–Solid Phase Transformation ’99 (JIMIC-3); Koiwa, M., Otsuka, K., Miyazaki, T., Eds.; JIM: 1999; 1453. 56. Suehiro, M. Proceedings of the International Conference on Solid–Solid Phase Transformation ’99 (JIMIC-3); Koiwa, M., Otsuka, K., Miyazaki, T., Eds.; JIM: 1999; 1465. 57. Fujioka, M.; Yoshie, A.; Morikawa, H.; Suehiro, M. CAMP-ISIJ 1989, 2, 692. 58. Umemoto, M.; Ohtsuka, H.; Tamura, I. Acta Met. 1986, 34, 1377. 59. Umemoto, M.; Ohtsuka, H.; Tamura, I. Tetsu-to-Hagane 1984, 70, 238. 60. Saito, Y.; Shiga, C.; Enami, T. Proceedings of International Conference on Physical Metallurgy of Thermomechanical Processing of Steels and Other Metals; ISIJ: Tokyo, 1988; 753. 61. Park, S.H.; Jonas, J.J. Proceedings of International Symposium on Mathematical Modelling of Hot Rolling of Steel; Yue, S., Ed.; CIM: Montreal, 1990, 446. 62. Okaguchi, S.; Hashimoto, T. ISIJ Int. 1992, 32, 283.

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63. Dutta, B.; Sellars, C.M. Mater. Sci. Technol. 1987, 3, 197. 64. Liu, W.J.; Jonas, J.J. Metal. Trans. A 1989, 20, 689. 65. Akamatsu, S.; Matsumura, Y.; Senuma, T.; Yada, H.; Ishikawa, S. Tetsu-to Hagane 1989, 75, 993. 66. Akamatsu, S.; Senuma, T.; Hasebe, M. Tetsu-to Hagane 1992, 78, 102. 67. Okamoto, R.; Suehiro, M. Tetsu-to-Hagane 1998, 84, 650. 68. Gladman, T.; Holmes, B.; Pickering, F.B. JISI 1970, 208, 172. 69. Gladman, T.; McIvor, I.D.; Pickering, F.B. JISI 1972, 210, 916. 70. Petch, N.J. Phil. Mag. 1958, 3, 1089. 71. Duckworth, W.E.; Baird, J.D. JISI 1969, 207, 854. 72. Pickering, F.B. Towards Improved Toughness and Ductility; Climax Molybdenum Co.:Greenwich, CT, 1971; 9. 73. Irvine, K.J.; Pickering, F.B. JISI 1957, 187, 292. 74. Yoshie, A.; Fujioka, M.; Watanabe, Y.; Nishioka, K.; Morikawa, H. ISIJ Int. 1992, 32, 395. 75. Morikawa, H.; Hasegawa, T. In Accelerated Cooling of Steel; Southwick, P.D., Ed.; TMS-AIME: Warrendale, 1986; 83. 76. Tomota, Y.; Umemoto, M.; Komatsubara, N.; Hiramatsu, A.; Nakajima, N.; Moriya, A.; Watanabe, T.; Nanba, S.; Anan, G.; Kunishige, K.; Higo, Y.; Miyahara, M. ISIJ Int. 1992, 32, 343. 77. Shikanai, N.; Kagawa, H.; Kurihara, M.; ISIJ Int. 1992, 32, 335. 78. Iung, T.; Roch, F.; Schmitt, J.H. International Conference on Thermomechanical Processing of Steels and Other Materials; Chandra, T., Sakai, T., Eds.; TMS: 1997, 2085. 79. Sato, K.; Suehiro, M. Tetsu-to-Hagane 1991, 77, 675. 80. Sato, K.; Suehiro, M.; Tetsu-to-Hagane. 1991, 77, 1328. 81. Suehiro, M.; Senuma, T.; Yada, H.; Sato, K. ISIJ Int. 1992, 32, 433.

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2 Design Simulation of Kinetics of Multicomponent Grain Boundary Segregations in the Engineering Steels Under Quenching and Tempering Anatoli Kovalev and Dmitry L. Wainstein Physical Metallurgy Institute, Moscow, Russia

I.

INTRODUCTION

The basic factors controlling grain boundary segregations (GBS) in engineering steels are discussed. In contrast to single-phase alloys, in engineering steels, the multicomponent segregation is developed simultaneously with undercooled austenite transformations and martensite decomposition. Based on these reasons, the influence of steel phase composition and kinetics on concurrent segregations is discussed. It is established that grain boundary enrichment by harmful impurities (S and P) is possible after carbon and nitrogen segregation dissolution. Two models of GBS are described. The dynamic model of segregation during quenching is based on the solution of independent diffusion and adsorption–desorption equations for various impurities in steel. The model of multicomponent segregation under tempering considers the influence of alloying and tempering parameters on concentration and thermodynamic activity of carbon in the a-solid solution.

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II.

GRAIN BOUNDARY SEGREGATION AND PROPERTIES OF ENGINEERING STEELS

Chemical composition and structure of the grain boundary influences various properties of engineering steels. The following are some of these properties: inclination to temper and heat brittleness, resistance to hydrogen embrittlement, corrosion, delayed fracture, and creep. The intergranular fracture is the main reason for decrease of many steel exploitation properties. Application of modern physical experimental or calculation methods has successfully helped in solving the old metallurgical problem of intergranular fracture. The affinity of various kinds of intergranular brittleness is associated with two main unfavorable factors that decrease intergranular bonds. The impurity segregation to grain boundaries (GBS) and localization of internal microstresses are necessary and sufficient conditions that could initiate embrittlement [1]. Despite the common features, certain kinds of steel brittleness are distinguishable from each other and are stipulated by complex interaction of these factors. The concentration of internal stresses on grain boundaries could be an effect of martensite transformation, hydrogen accumulation, or carbide precipitation; and grain boundary segregations could appear during the equilibrium or non-equilibrium processes of element redistribution in steel. The concentration of microstresses on grain boundaries cause the initiation of cracking and acts as the primary reason for brittleness. The enrichment of grain boundaries by harmful impurities is a major and common condition for development of various intercrystalline brittleness phenomena and it specifies crack propagation entirely along grain boundaries at low stresses. The concept of intercrystalline internal adsorption [2] that was confirmed by theoretical [3], and experimental work [4], the thermodynamic analysis of chemical element interaction during equilibrium grain boundary segregation [5], and investigations of quenched and tempered steel [6,7]. This made it possible to interpret the tempering embrittlement phenomenon. Elemental impurities enrich grain boundaries in thin layers up to several atoms and change the type and value of interatomic bonds that lead to intercrystalline fracture. Embrittlement power is commonly attributed to the elements of the 3rd to 5th periods of groups IV to VI in the periodic system [1]. Sulfur, phosphorus, arsenic, selenium, tellurium, antimony, bismuth, and oxygen are the most harmful impurities that segregate in grain boundaries. The concentration in grain boundaries could reach several atomic percentages exceeding the volume one Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

by several hundreds. Intercrystalline brittleness, as caused by GBS, due to harmful impurities is observed, as a rule, in BCC metals and alloys. The austenite alloys are significantly more resistant to this kind of fracture. The motonic increase of plasticity that is expected after martensite decomposition due to tempering of engineering steels is disturbed by two anomalies resulting in a relative decrease of impact strength. These anomalies are accompanied by intergranular fracture. Steels may be susceptible to embrittlement when they are heated for prolonged period in the temperature range 350–5508C, or when slowly cooled through it. Depending on the heattreatment cycle, the phenomenon is called either temper embrittlement (3508 embrittlement) or reversible temper embrittlement (5508 embrittlement). Common indications of embrittlement are a loss of toughness, segregation of harmful impurities to grain boundaries and the fracture path usually along prior austenite grain boundaries, and the impact transition temperature (FATT—the fracture appearance transition temperature) which is displaced towards higher values. The irreversible temper embrittlement of low-alloyed steels (<5% of alloying elements) is developed during tempering of quenched steel in the temperature range 300–4008C. The reversible temper embrittlement of medium-alloyed steels is developed during tempering in the temperature range 500–6008C. This kind of brittleness is observed after tempering and slow cooling of annealed, normalized, or quenched steel. It is now established that GBS of small impurities play a decisive role in development of these phenomena.

A.

Brittle Fracture of Steel After Quenching and Medium Tempering

The quenched medium-alloyed engineering steel is subjected to tempering in the temperature range 250–4008C to achieve high strength and plasticity. But after tempering at 300–4008C, one can see an abnormal drop in impact strength. At higher tempering temperatures, the impact strength increases again (see Fig. 1) [8]. The intergranular fracture of steel tempered at 300–4008C is due to the action of two unfavorable factors: enrichment of grain boundaries by P during austenitization and formation of lamellar Fe3C particles along the primary austenite grains and martensite packs (Fig. 2a, b). The P segregations decrease the cohesion within boundaries significantly, and carbides block the dislocation movement. This is the reason for peak stresses under plastic

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Figure 1 Impact strength at room temperature of samples with V-shape cut for several melts of industrial steel 4340 after quenching (8508C, 1 hr) in oil and 1 hr tempering at various temperatures. (From Ref. 8.)

Figure 2 (a) Lamellar parts of cementite Fe3C on primary austenite grains and (b) martensite packs boundaries. Steel 0.35C–1.5Mn–0.1P. Tempering at 3508C, 1 hr (TEM, replicas).

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Figure 3 (a) Brittle fracture through primary austenite grains and (b) martensite pack boundaries in steel 0.35C–1.5Mn–0.1P. Tempering at 3508C, 1 hr (SEM).

deformation and, consequently, formation of grain boundary cracks. The brittle crack develops, in this case, within boundaries of primary austenite grains and martensite packs (Fig. 3a, b). The significant enrichment of grain boundaries by phosphorus is confirmed by Auger spectroscopy. The decisive role of austenitization when compared with tempering in achieving equilibrium GBS is shown by low diffusion mobility of harmful impurities’ atoms (P, As, S, and Sb) for medium tempered steel. Calculations show that only nitrogen has significant diffusion mobility in this temperature range which is sufficient for diffusion at a distance of 10 mm for 1 hr at 3508C [1]. The temperature of steel for quenching is sufficiently high for intensive diffusion of P in austenite with the formation of equilibrium GBS [9], and quenching fixes this enrichment. The level of P segregation depends on the austenitization temperature and increases when the temperature decreases below 10508C. This is related to the decrease of P solubility in austenite. It is confirmed by a significant decrease of the quenched steel delay fracture resistance with respect to temperature in the austenite region (Fig. 4). Phosphorous content in steel influences its embrittlement at 3508C tempering. Its concentration in GBS is several hundred times higher than in the volume, and this harmful element segregates in austenite even at low concentrations, about 0.01% mass, leading to a significant decrease in the impact strength (Fig. 5). Change of the relative energy of grain boundaries results in segregation enrichment by impurities during austenitization. The interferometry is one such direct technique for grain boundary energy determination. For this

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Figure 4 Delayed fracture diagram of quenched steel 0.35C; 1.5Mn; 0.1P after austenitization at 1423K, 3 hr and 30 min interim cooling to temperatures: 1, 1123K; 2, 1223K; 3, 1273K and cooling in water. (From Ref. 10.)

purpose, the opening angle of GB slot (y) is determined on metallographic grinds after vacuum etching at various temperatures. The grinds are austenitized in vacuum at high temperature, then subjected to interim cooling to the desired temperature and then quenched at a high cooling rate. The relative energy of GB is calculated by the equation gb y ¼ 2 cos 2 gs

ð1Þ

where symbols b and s correspond to boundary and bulk, respectively. Figure 6 shows the change of relative surface energy with respect to the interim cooling temperature during austenitization and P content in the 0.35% C, 1.5% Mn. For the steel with low phosphorus content, the GB energy regularly decreases slowly as the temperature increases within the austenite region. Significant segregation enrichment of grain boundaries by phosphorus in the steel with 0.1% P does not show this dependence and decreases the surface energy of GB with decreasing of the temperature. The decrease of P solubility in austenite with decreasing temperature assists its adsorption on the GB and decreases significantly its surface tension energy. At the same time, one can observe another process: P enriches

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Figure 5 Temper embrittlement of steel Fe–0.3C–3.5N–1.7Cr: 1, high purity steel; 2, 0.01 mass% P; 3, 0.03 mass% P; 4, 0.06 mass% P. (From Ref. 8.)

non-metallic inclusions. The dependence of P content on Mn sulfides in steel 0.35% C, 1.5% Mn, 0.1% P from austenitization temperature is shown in Fig. 7. When annealing temperature decreases, P redistributes between the bulk and grain boundaries enriching them and the non-metallic inclusions. Steel grain size reduction can decrease significantly its tendency to temper embrittlement. Increase of the specific surface of the GB at dispersion of the steel structure decreases the concentration of the impurity in the grain boundary that leads to growth of steel brittle fracture resistance (Fig. 8) [3]. Phosphorous segregations decrease the surface energy of intergranular cohesion. Using the approach proposed in Ref. [11], one can estimate the role of phosphorus in change of surface energy of intergranular cohesion for development of this kind of embrittlement.

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Figure 6 Change of relative surface energy of grain boundaries in dependence of temperature of austenitization. Fe–0.35C–1.5Mn steel: 1, 0.03% P; 2, 0.1% P.

Figure 7 Phosphorus concentration in manganese sulfides in 0.35C–1.5Mn–0.1P steel vs. austenitization temperature.

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Figure 8 FATT (T50) of steel vs. grain size d1=2 and specific grain boundary surface P S. Phosphorus content: 1, 0.03%; 2, 0.1%. (DT50 ¼ T50(0.1% P)T50(0.03% P)).

Influence of grain size on ductile–brittle transition temperature FATT is determined from the well known Petch–Hall equation sf ¼ so þ Ky d1=2

ð2Þ

where Ky ﬃ aðGgÞ1=2 ; a is a constant (1–3); g is the surface energy of intergranular cohesion for generation of cracks on grain boundaries; G is the shear modulus. It is described by the equation dT50 1 ¼ b dðd1=2 Þ

ð3Þ

where b is determined as a tangent of inclination angle of straight lines in Fig. 8. Taking into account that

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dT50 dT ðK0y Þ; ¼ dðd1=2 Þ dsf

ð4Þ

it is possible to use the change of the inclination angle of lines 1 and 2 in Fig. 8 to determine the influence of P on GBS by the coefficient b and the effective intergranular cohesion surface energy g that is proportional to b2. The values of b for steel samples containing 0.03% and 0.1% P at the temper embrittlement state are equal to 0.54 and 0.22 sec, respectively. Taking into account dependencies (2) and (3), one can conclude that effective intergranular cohesion surface energy in steel with higher P concentration decreases in g0:03 =g0:1 ¼ b20:03 =b20=1 ¼ 6:04 times. B.

Ductile Intergranular Fracture of Overheated Steel

The ductile fracture of steel as well as brittle fracture could be characterized by the lowest energy capacity. Such a fracture occurs when the inclusions are located along grain boundaries occupying a very large volume near the boundary. The intergranular microvoid fracture is observed in this case due to overheating of the steel. The samples are exposed to high temperature heating to dissolve inclusions. As a rule, the large and lamellar oxysulfides that did not embrittle steel are dissolved. After their dissolution, segregation of O, S, P, and precipitation, disperse particles during steel cooling occurs. In low-alloyed steels, precipitates could be sulfides of chromium and manganese (MnS, CrS), and aluminum nitride, AlN. These particles build a dense network on grain boundaries. The fracture occurs at higher or room temperatures by intergranular microvoid coalescence at low stress intensity. The micrometer scale cavities nucleate on the intergranular fine dispersion of sulfide or nitride particles (Fig. 9). The segregation of harmful impurities is observed on grain boundaries in this case. C.

Reversible Temper Embrittlement

The reversible temper embrittlement (RTE) is observed in engineering steel alloyed by carbide-forming elements after quenching and high tempering (500–6008C). This phenomenon is developed in steels of industrial purity. It consists of a large decrease in the steel impact strength after slow cooling, but after rapid cooling at 6508C, the steel has a standard impact strength. The RTE phenomenon was identified for the first time in 1883 [12], when blacksmiths observed that some steels had to be water quenched after tempering, to avoid embrittlement. This decrease of impact strength is not accompanied by a change of physical or other mechanical properties of

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Figure 9 Ductile fracture of steel through grain boundaries (SEM).

steel. The duration of the exposure time within a definite range of tempering temperatures (brittleness zone) plays a decisive role in the development of RTE. The brittle fracture goes through the primary austenite grains (Fig. 10). The duration of the exposure time of the normalized or annealed steel within the dangerous temperature range also leads to this kind of embrittlement. Steels sensitive to RTE are subjected to rapid cooling from 6508C during different heat treatments. The GBS of phosphorus is the main reason for this kind of brittleness. The RTE of alloyed steels is mainly sensitive to two factors: the chemical composition of the grain boundaries, and the mechanical and microstructural parameters of the alloy. The direct correspondence of embrittlement kinetic features and GBS of P at steel tempering has been established. Figure 11 shows the iso-FATT curves for temper embrittlement of Ni–Cr steel [13].

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Figure 10 SEM image of intergranular fracture of Fe–0.35C–1.5Mn–0.1P steel after quenching with temperature of 9508C, 1 hr and tempering at 5508C, 2 hr.

At a constant temperature of embrittlement tempering, the FATT increases with time. The embrittlement is reversible. It can be rejected by short heating above the nose of the C-curve in the ferrite range. Renewed aging and slow cooling of a de-embrittled steel in the critical temperature region gives reembrittlement. These processes are accompanied by a redistribution of impurities on the grain boundaries.

III.

FACTORS DETERMINING MULTICOMPONENT INTERFACE ADSORPTION IN ENGINEERING STEELS, AND THE METHODS OF ITS CALCULATION

The intercrystalline internal adsorption, or grain boundary segregation phenomenon, means the increased concentration of small impurities on

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Figure 11 Diagram of time–temperature FATT, 8C: (1) 60; (2) 55; (3) 50; (4) 45; (5) 40; (6) 35; (7) 30; (8) 25; (9) 20; (10) 15; (11) 10; (12) 5; (13) 0; (14) þ5; (15) þ10; (16) þ15; (17) þ20; (18) þ25; (19) þ30.

the grain boundary (compared to bulk) is caused by decreasing boundary energy. The energy of impurity segregation corresponds to energy gain in the ‘‘bulk-boundary’’ system that accompanies the transition of one impurity atom from bulk to boundary. Thermodynamic description of this phenomenon is based on the Gibbs theory of the equilibrium segregation on free surface. The decrease of redundant energy of GB is the thermodynamic stimulus to change its chemical composition compared to bulk. The impurities that decrease the energy of interfaces are surface-active. These elements could form equilibrium segregations under favorable conditions. The impurities that increase surface tension escape from surface. Gibbs’ adsorption isotherm for grain boundary segregation in a solid binary system, where the matrix obeys Raoult’s law and Henry’s law of diluted solutions, may be expressed Gb ¼

Xc dgb kT dXc

ð5Þ

where Gb is the surplus concentration on the GB, mol=m2; Xc is bulk mole part of impurity; dgb=dXc is the tendency to adsorb. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

McLean [14] has developed a statistical model of intercrystalline internal adsorption. The main points of this theory are the following: A definite number of adsorption centers (one monolayer) are present on the GB. They have equal adsorption potential. 2. The impurity atoms are adsorbed independently on each of the centers. 3. The adsorption decreases at temperature growth. 1.

This model adequately describes the GBS process for two-component system: Xb Xc DG ¼ exp ð6Þ RT X0b Xb 1 Xc where Xb and Xc are the impurity concentrations on boundary and in bulk, respectively; X0b is the ultimate equilibrium concentration of the impurity on boundary; DG is the segregation energy. Hondros and Seah [15] have established the interrelation of GB enrichment and solubility limit X0c Xb Xc DG ¼ exp ð7Þ RT X0b Xb X0c The enrichment factor, determined as the GB content=bulk concentration ratio, is of the order of magnitude 104 and 101 for impurity and alloying elements, respectively (see Fig. 12). A.

Binding Energy of Impurities with Grain Boundaries

One can determine the adsorption energy as an alteration of the system free energy during transition of the dissolved atom from the grain bulk to boundary E ¼ ðEb Eb0 Þ ðEc Ec0 Þ

ð8Þ

where Eb and Ec are the free energy of the system with impurity atoms on the grain boundary or in the bulk, respectively; Eb0 and Ec0 are the free energies of boundary and bulk in the pure solvent. The value of energy E is tied with the elastic (dimensional) and chemical interaction of impurity with boundary. The influence of dimensional discordance of atoms is accounted by the Eshelby equation [16] 16 E ¼ pGr3 ðs 1Þ2 ð9Þ 3 where G is the shear modulus of the solvent; r is the solvent atom radius; s is the ratio of impurity and solvent atoms radii.

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Figure 12 Calculated and experimental enrichment coefficients for surface segregations. (From Ref. 15.)

The decrease of elastic distortion energy during the transition of the impurity atom from ideal bulk lattice to distorted boundary lattice is the driving force adsorption. According to Ref. [17], one can describe the chemical part of adsorption Ech ¼ DZðe12 e11 Þ

ð10Þ

where DZ is the difference of the atom coordination numbers in bulk and on boundary; eij is the energy of interaction between the nearest neighbors (1 for the solvent, 2 for impurity).

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The Fowler–Guggenheim theory [18] accounts for the interaction of atoms adsorbed on GB: E1 ZoXb =X0b Xb Xc ¼ exp ð11Þ KT X0b Xb X0c where Z is the coordination number for impurity atoms; o is the interaction energy of nearest atoms. The portion of segregation energy ZoXb=X 0b corresponds to interaction of the same and different atoms on boundary, and depends on the degree of neighbor centers filled. At o > 0, the atoms repulse mutually, and they attract at o < 0. The attraction increases the adsorption energy substantially. Interaction of atoms on interface influences segregation enrichment and promotes formation of 2D phases with ordered atomic structure. B.

Impurities’ Concurrence During Adsorption

None of the existing adsorption theories adequately describe the micromechanism of impurities’ concurrence on the adsorption centers. This is related to the peculiarities of adsorption from gaseous phase to the free surface to describe the grain boundary segregation mechanism [19–21]. According to this point of view, all segregating elements (for example N, C, S, and P) occupy equal positions on GB, described by the ‘‘site competition’’ term. The peculiarity of GBS formation consists of diffusion of alloying elements and impurities from bulk to interface. The migration mechanisms for substitial and interstitial impurities are different. The reason for this is that the adsorption centers on interface are different for these two kinds of impurities. Therefore, the interstitial impurities (C, N) are located in interstices, but S, P, Sb, Bi, etc. occupy substitution position on the GB. Adsorption of any surface-active impurity on GB decreases its free energy and lowers the thermodynamic stimulus for adsorption of other impurity in a similar way. This causes a site competition between atoms on the GB [22]. The concurrence of impurities A and B segregating at the same temperature and occupying the same positions in crystalline lattice (lattice points or interstices) with different binding energies to GB was investigated in Ref. [23]. The equilibrium concentration of competing impurities A and B could be calculated using equations: XA b ¼

A XA C expðEseg =kTÞ B A B 1 þ XA C expðEseg =kTÞ þ XC expðEseg =kTÞ

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ð12Þ

XBb ¼

XBC expðEBseg =kTÞ 1þ

XA C

B B expðEA seg =kTÞ þ XC expðEseg =kTÞ

ð13Þ

where Eseg is the segregation energy; XbI is the GB concentration of element I A B > Eseg , the (atomic fraction). As one can see from these equations, at Eseg concentration of element A decreases with increasing temperature. In this case, the adsorption level of the element B reaches its maximum at critical temperature: Tcr ¼

EA seg A B A k lnðEA seg =ðEseg Eseg ÞXb Þ

ð14Þ

The grain boundaries are enriched in this case by element B at low temperatures, and by element A at high temperatures.

C.

Thermodynamic Calculations of the Segregation Energy

The segregation energy calculations are based on various models of solid solution electronic structure or quasi-liquid model of grain boundary. Thermodynamic properties of the solid solution determine firstly the surface activity of small impurities in the formation of equilibrium GBS. The components of the alloy influence the energy of interaction with grain boundaries significantly. The parameters of such interaction are determined by thermodynamic calculations, phase equilibrium diagram analysis, computer modeling of GBS. The heat of solution of different atoms in solid solution is the thermodynamic measure of their interaction. The model establishing interrelationship segregation energy and heat of solutions is proposed in Ref. [24] 2=3

Eseg ¼ F Hsol PðgA gB ÞVA

ð15Þ

where F and P are empirical coefficients; Hsol is the heat of solution of A in B [25–30]; gA, gB is the surface enthalpy of elements A and B [31,32]; VA is the molar volume of A. Using the liquid grain boundary model approximation, the segregation energy of impurities (Eseg) could be determined from an analysis of the solidus and liquidus curves on phase equilibrium diagrams: Eseg ¼ KT LnðK0 Þ ¼ KT LnðCL CS Þ

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ð16Þ

where K0 is the coefficient of equilibrium distribution of the element between solid and liquid phases [33]; T is the melting temperature of the pure solvent; CL and CS are concentrations of impurity in the liquid and solid solutions, respectively. An experimental method for determination of binding energy of impurity atoms to grain boundary is used. The analysis of large number of phase equilibrium diagrams has led to the establishment of the basic property of two-component solid solutions consisting of periodic variation of the segregation formation energy of an element as a function of its location in the periodic table (atomic number). As seen in Fig. 13, the impurities could have positive or negative surface activity, or be neutral. The elements So, Mo, Ni, and Co are neutral in two-component alloys with Fe. At the same time, it is well known that molybdenum is the surface-active element in steels and it reduces the tendency of steel to the reversible temper embrittlement. This change of surface activity is observed only in multicomponent alloys, and it is due to the mutual influence of elements on its thermodynamic activity. The binding energy of an impurity to the GB depends significantly on boundary structure. The wide spectrum of Eseg exists for the given substance analogous to the spectrum of the GB energy. This circumstance explains the wide dispersion of the segregation energy for various impurities that are listed in literature sources. Based on this reasoning, it is useful, for segregation modeling, to apply the unified approach for determination of the generalized characteristic of definite impurity segregation in definite solvent. The thermodynamic calculations of segregation energy are the most suitable way for its estimation. Auger electron spectroscopy (AES) for investigation of segregation kinetics on the free surface of polycrystalline foils is a reliable experimental technique for the averaged Eseg determination. The part of elastic and chemical interaction in GBS process could be estimated experimentally based on concentration dependencies of segregation energy. These dependencies were determined for alloys whose compositions are listed in Table 1. The segregation energy was determined based on AES of equilibrium free surface segregations of phosphorus. The polycrystalline foil samples were tempered at 823K for 4 hr in a work chamber of electron spectrometer ESCALAB MK2 after quenching from austenitization temperature of 1323K. The segregation energy of P was determined using Eq. (6) based on surface and bulk impurity concentration. Figure 14 shows the dependence of the P segregation energy and its bulk content in alloy. For the diluted solid solutions, Eseg is independent of concentration or temperature. It is caused only by elastic distortions that are formed by impurity atoms in

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Figure 13 Change of calculated Eseg of impurities in Fe-base alloys in accordance to its number in periodic system. Calculations were based on Hsol in the following publications: (a) Refs. 25 and 26; (b) Refs. 27 and 28; (c) Ref. 33.

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Table 1 Composition (at.%) of the Fe–P and Fe–P–Mo Alloys Chemical composition, at.% C 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01

S

P

Mo

0.002 0.003 0.002 0.003 0.002 0.002 0.005 0.014

0.017 0.10 0.15 0.093 0.033 0.14 0.09 0.074

0 0 0 3.1 3.1 3.1 0.3 0.02

bulk and on the interface. As seen in Fig. 14, the elastic interaction energy of the P atoms with grain boundaries in iron is equal to 0.53 eV=at and decreases significantly at molybdenum alloying to 0.24 eV=at in the alloy Fe–3.1at.% Mo. Decrease of segregation energy of the impurity at its

Figure 14 Change of Eseg of phosphorus with its volume concentration in Fe (1) and Fe–3.1 at.% Mo–P alloys (2). Auger electron spectroscopy of free surface segregations at 823K.

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volume concentration growth is caused by chemical pair interaction of the atoms in alloy. Using the example of the Fe–P system, we could determine chemical interaction of elements by applying the approach proposed in Ref. [34]. Analyzing the solidus and liquidus equilibrium (volume and GB) on the equilibrium phase diagram at three temperatures permits the construction of a system of three equations that describe this equilibrium 100 Xs ð17Þ ¼ X2s W0 X2l W00 þ kqa Ta kT qa ln 100 Xl where k is the Boltzmann constant; Ta is the melting temperature of Fe; qa is melting entropy per atom divided by Boltzmann constant; W0 and W00 are the mixing energies in solid and liquid states; Xs and Xl are the impurity concentration in solid and liquid phases at the temperature T. Solving these equations for the phase diagram of Fe–P binary system [35], the sign and value of mixing energy in liquid phase equal 0.425 eV=at were determined. The positive value (in accordance with physical sense) means that binding force of P–P and Fe–Fe atoms is higher than for Fe–P atoms: 1 W ¼ WFeP ðWFeFe þ WPP Þ 2

ð18Þ

emphasizing the tendency for solid solution tendency for stratification or intercrystalline internal adsorption.

D.

Effect of Solute Interaction in Multicomponent System on the Grain Boundary Segregation

Guttman has expanded the concept for synergistic co-segregation of alloying elements and harmful impurities at the grain boundaries. His theory is very important for analysis of steels and alloys that contain many impurities and alloying elements. In accordance with the theory, the interaction between alloying elements and the impurity atoms could be estimated from enthalpy of formation of the intermetallic compounds (NiSb, Mn2Sb, Cr3P, etc.). The alloying elements could influence on the solubility of impurities in the solid solution. Only the dissolved fraction of the impurity takes part in the segregation [36]. When preferential chemical interaction exists between M (metal) and I (impurity) atoms with respect to solvent, the energy of

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segregation becomes functions of the intergranular concentrations of I and M: DGI ¼ DG0I þ

bbMI b baMI a Y X M Cb Ca M

ð19Þ

bbMI b baMI a Y a XI ab I a

ð20Þ

DGM ¼ DG0M þ

where Cb and ab are the fractions of sites available in the interface for I and M atoms, respectively ðab þ C b ¼ 1Þ; Yb is the partial coverage in the interface; Xa is the concentration in the solid solution a; bMI is the interaction coefficient of M and I atoms in a-solid solution (a) or on the grain boundary (b). For a preferentially attractive M–I interaction, the bMIare positive and the segregation of each element enhances that of the other. If the interaction is repulsive, the bMI are negative and the segregations of both elements will be reduced. For a high attractive M–I interaction in the a-solid solution, the impurity can be partially precipitated in the matrix into a carbide, or intermetallic compound. The interface is then in equilibrium with an a-solution where the amount of dissolved I, XIa, may become considerably smaller than its nominal content. In the ternary solid solutions, the segregation of impurity (I) could be lowered or neglected at several critical concentrations of the alloying element (M) whose value (CM a) depends on surface activity of each compoI,M ) and interaction features of the dissolved atoms (bMI): nent (ESeg CM a ¼

EISeg bMI ðexpðEM Seg =RTÞ 1Þ

ð21Þ

The critical concentration of alloying element is accessible for segregation of I;M > 0 and repulsion of different atoms impurity and alloying element ESeg M < 0 and with bMI > 0; or without segregation of alloying element ESeg attraction of different atoms bMI < 0. In this case, the dependence of EI,M Seg on the dissolved element concentration is not taken into account. Indeed, for systems with limited solubility, the alteration of value and sign of segregation energy is possible at a definite content of alloying element. The phase equilibrium diagram analysis allows the determination of mutual influence of components on their surface activity. The equilibrium distribution of solute elements between solid and liquid phases in iron-base ternary system (distribution interaction coefficient K0) is known to be an important factor in relation to microsegregation during the solidification of steels. As it was shown above, these analogies are useful for the prediction of GBS and for impurity segregation energy

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Figure 15 Change of the equilibrium distribution coefficient of some elements with carbon concentration in Fe–C-based ternary systems. (From Ref. 37.)

determination in the given solvent. The K0 of some elements, especially in multicomponent systems, is considered to be different from those in binary systems because of the possible existence of solute interactions, but the mechanisms are so complicated that detailed information has not yet been obtained. Therefore, it would be very useful if the effect of an addition of an alloying element on the distribution could be determined by the use of a simple parameter. Equilibrium distribution coefficient K01 of various elements in Fe–C base ternary system is calculated from equilibrium distribution coefficient in iron-base binary systems [40–43]. In Fig. 15, the calculated results are compared with the measured values by various investigators. The changes of the K01 of P and S with various alloying elements are shown in Fig. 16(a, b) in Fe–P and Fe–S base ternary system, respectively. These data could be applied for calculation of phosphorus segregation energy change under the alloying element influence in Fe–Me–0.1at.% P alloys (Fig. 17) or for calculation of the segregation energy change of alloying elements with concentration of carbon in Fe–0.1Me–C alloys (Fig. 18). For the growth of carbon volume content, the segregation energy of C and P decreases which means lowering of the segregation stimulus for these elements.

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Figure 16 (a) Change of the equilibrium distribution coefficient of phosphorus with the concentration of alloying elements; and (b) change of the equilibrium distribution coefficient of sulfur with the concentration of alloying elements. Solid line: a-phase. Chain line: g-phase. (From Ref. 38.)

E.

Kinetics of Segregation

The existing models of multicomponent adsorption do not analyze in detail the kinetics of the process. But in reality, GBS forms only during a limited time of the heat treatment process. The difference of segregation level from the equilibrium one depends on temperature and time. At low temperatures and limited time of heat treatment, segregation is controlled by diffusion. As the temperature increases, segregations with lower equilibrium concentra-

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Figure 16

(Continued)

tion are developed, but rich segregations dissolve. Distinguishing diffusion mobility and mutual influence of elements on their diffusion coefficients determines much of their segregation ability. Amplification or suppression of adsorption could be due to a kinetic factor. This peculiarity determines the fundamental factor of distinguishing adsorption from gas phase to free surface when comparing it to intercrystalline internal adsorption: GBS is controlled by diffusion during heat treatment of steels and alloys. Many GBS features in multicomponent systems cannot be predicted adequately using the equilibrium segregation thermodynamic accounting basis. Particularly, the thermodynamic concept of the cooperative (synergis-

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Figure 17 Change of Eseg of phosphorus with the concentration of alloying elements in Fe–Me–0.1% P alloys.

tic) adsorption of elements is disturbed when they do not segregate at the same temperature. The concurrence of impurities at GBS could be tied not only due to their attractive or repulsive interaction, but also with higher diffusion mobility of some impurities. In many cases, the determination interatomic interaction on grain boundary that is proposed in Guttmann’s theory has a significantly lower effect for segregation prediction than accounting of mutual influence of elements on their thermodynamic activity in the grain bulk. Mutual influence of the alloy components on their surface activity is caused by their interaction in solid solution in the bulk. The interaction on grain boundaries could be analyzed only for those elements that segregate in near temperature ranges. Many postulates of the thermodynamic theory of equilibrium grain boundary segregation could not be applied simply for heat treatment of multicomponent alloys. This is especially important for steels, which have complex phase transformations during treatment that accompany change of the solid solution composition. Auger electron spectroscopy permits the investigation of multicomponent adsorption kinetics. The composition of grain boundaries on the intercrystalline fracture surface made under high vacuum is analyzed for this purpose. In these cases, the experimental modeling of GBS is widely used. The chemical composition of free surface of thin poly-crystalline foils that are heated in situ is investigated using Auger electron spectrometers. The P grain boundary adsorption isotherms for samples of three Fe–Cr–Mn

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Figure 18 Change of Eseg of alloying elements (Me) with the concentration of carbon in Fe–0.1% Me–C alloys.

steels after quenching from 1273K and tempering at 923K for 25 min, 1 and 2 hr with air cooling are presented in Fig. 19. Dissolution of Ti and V carbonitrides after steel quenching promotes enrichment of the solid solution by these elements. They have high values of Gibbs energy for phosphide formation, decrease the thermodynamic activity of phosphorus in solid solution and reduce its GBS. Most models of kinetics are classically analyzed in terms of the law derived by McLean [14] for binary alloys " # pﬃﬃﬃﬃﬃﬃﬃ Xb ðtÞ Xb ð0Þ 4Di t 2 Di t ¼ 1 exp erfc Xb Xb ð0Þ ðXb =Xai Þ ðXb =Xai Þ2 d2

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ð22Þ

Figure 19 Kinetics of P GBS in steel 0.3C–1.6Mn–0.8Cr–008P (1) with adds of 0.047Ti (2) or (0.07Ti and 0.026V) (3), quenched from 1273K and tempered at 923K.

where Xb(t) is the interfacial coverage of element, at time t; Xb(0) — is its initial value and Xb its equilibrium value as defined by Eq. (7); Xia — is its volume concentration; Di is the bulk diffusivity of i and d is the interface thickness. Assuming Xb=Xia ¼ const, using Laplace transformation for (22), one can obtain the approximate expression rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Xb ðtÞ Xb ð0Þ 2Xai FDti ¼ ð23Þ Xb d p Xb Xb ð0Þ where F ¼ 4 for grain boundaries and F ¼ 1 for free surface. The kinetics of segregation dissolution could be described by these equations (22) and (23). But, in this case, the variables Xb(0) and Xb exchange places. The influence of Mo, Cr, and Ni additions on kinetics of P segregation has been studied in six Fe–Me–P alloys, whose base compositions are listed in Table 1. These materials were austenitized for 1 hr at 1323K and quenched in water. The tempering of foils at 773K was carried out in a work chamber of an electron spectrometer ESCALAB MK2 (VG). The kinetics of P segregation studied for Fe–Me–P alloys (Figs. 20–22) show that equilibrium is reached within several hours. Based on the starting position of adsorption isotherms, the phosphorus diffusion coefficients in these alloys were calculated using Eq. (22). The data are presented in Table 2. Molybdenum reduces significantly P surface activity and decelerates its diffusion. Nickel is not a surface-active element in carbonless alloys, Fe– P–Ni. It increases sharply P thermodynamic activity and equilibrium GB concentration, and accelerates its diffusion. Chromium segregates poorly

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Figure 20 Kinetics of P segregation on free surface in Fe–P–Mo alloys with different relative concentration of Mo=P at 773K.

in these alloys. It also, as Ni, increases diffusion mobility of P and its grain boundary adsorption. The adsorption isotherms of various elements have non-monotonous shape in multicomponent alloys. The isodose thermokinetic diagrams present the averaged information on segregation of all components. Such

Figure 21 Kinetics of P and Cr segregation on free surface in Fe–0.04P–2.3 Cr alloy at 773K.

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Figure 22 Kinetics of P segregation on free surface in Fe–P–Ni alloys with different relative concentration of Ni=P at 773K.

diagrams for steel with 0.2–0.3% C alloyed by Cr, Mo, Ni, Mn, V, and Nb are presented in Figs. 23–27. Chemical composition of steel is listed in Table 3. The T–t diagrams are obtained based on adsorption isotherms on free surface of foils that were heat treated in Auger spectrometer ESCALAB MK2 at vacuum about 1010 Torr. The isodose curves characterizing time of definite segregation level access depending on temperature are shown in these diagrams. At elevation of an isothermal exposition temperature, the mobility of impurities increases, and time for reaching of definite segregation level decreases. The lower branch of isodose curve means decrease of segregation formation Table 2 Composition (at.%) of the Fe–Me–P Alloys and Kinetics Characteristics of P Free Surface Segregation, Deduced from the Segregation Kinetics Chemical Composition, at.% P

Mo

Ni

Cr

Surface activity Xb=Xia

Bulk diffusivity of P DP 1018 (m2=sec)

0.07 0.03 0.04 0.16 0.21 0.15

0 0 0 1.0 2.1 3.1

0.9 3.1 0 0 0 0

0 0 2.3 0 0 0

285 2530 1450 380 250 80

5.34 1048 160 27 2.28 0.3

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Figure 23 The isodose C-curves of multicomponent interface segregation in 0.3C– Cr–Mo steel (see Table 3). Auger electron spectroscopy of free surface segregations.

time at increasing temperature. With temperature increase, the solubility of impurity in solid solution increases, and its GB concentration reduces. It follows that the probability to form the segregation with high impurity content reduces, and time for such segregation increases extensively. The upper branch of isodose curves corresponds to dissolution of rich segregations and access to new equilibrium with lower impurity concentration. The

Figure 24 The isodose C-curves of multicomponent interface segregation in 0.2C– Cr–Mn–Ni–Si steel (see Table 3) under its tempering. Auger electron spectroscopy of free surface segregations.

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Figure 25 The isodose C-curves of multicomponent interface segregation in 0.3C– Cr–Mn–Nb steel (see Table 3) under its tempering. Auger electron spectroscopy of free surface segregations.

adsorption patterns for engineering steels have common as well as individual features. As a rule, carbon segregates at temperatures lower than 523K, nitrogen—in 523–623K range, phosphorus—in 523–823K range, sulfur segregates at temperatures higher than 723K. The substitual and interstitial element concurrence promotes blocking of adsorption centers by mobile impurities and impedes P segregation at

Figure 26 The isodose C-curves of multicomponent interface segregation in 0.3C– Cr–Mn–V steel (see Table 3) under its tempering. Auger electron spectroscopy of free surface segregations.

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Figure 27 The isodose C-curves of multicomponent interface segregation in 0.3C– Cr–Mn–Si–Ti steel (see Table 3) under its tempering. Auger electron spectroscopy of free surface segregations.

temperatures lower than 523–673K. The preferential enrichment of GB by P and S becomes possible after dissolution of C and N segregations. The alloying elements change significantly the segregation stability regions for various elements. Fig. 28(a,b) shows the P adsorption isotherms in the investigated steels at 723K. Molybdenum sharply slows down the P segregation formation. The differences in diffusion mobility of elements and temperature intervals of segregation stability are the reasons for nonequilibrium enrichment of grain boundaries. The rich segregations are formed at the initial stage of isothermal exposition, and they are dissolved after longer exposition. Comparing the behavior of 0.3C–Cr–Mn–Nb (1) and 0.22C–Cr–Mn–Si–Ni (3) steels at 673K tempering, one can see that small (lower than 20 min) expositions 0.3C–Cr–Mn–Nb, and longer ones (about 1 hr 20 min) are dangerous for 0.22C–Cr–Mn–Si–Ni steel. Analyzing Table 3

Chemical Composition of Steels Concentration of elements, wt.%

No. 1 2 3 4 5

Steel

C

Si

Mn

Cr

V

Al

Ti

Nb

Ni

Mo

S

P

0.3C–Cr–Mn–V 0.3C–Cr–Mn–Nb 0.3C–Cr–Mo 0.3C–Cr–Mn–Si–Ti 0.2C–Cr–Mn–Ni–Si

0.32 0.29 0.33 0.28 0.22

0.25 0.33 0.23 0.61 0.43

0.88 1.04 0.56 1.15 0.92

0.92 1.07 0.96 0.75 0.89

0.088 0 0.003 0 0

0.014 0.007 0.014 0.029 0.030

0.024 0.036 0.025 0.016 0.015

0 0.025 0 0 0

0 0 0 0.32 0.91

0 0 0.25 0 0

0.016 0.014 0.005 0.013 0.015

0.027 0.027 0.004 0.022 0.025

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Figure 28 Influence of alloying on the kinetics isotherms of P free surface segregation at 723K. The following steels were investigated (see Table 3): 1, 3C–Cr– Mn–Nb; 2, 3C–Cr–Mn–Si–Ti; 3, 2C–Cr–Mn–Ni–Si; 4, 3C–Cr–Mo; 5, 3C–Cr– Mn–V.

the thermokinetic diagrams for ternary Fe–Me–P alloys based on Eqs. (23) and (6), the mutual influence of elements on their binding energy to GB was determined [36] Mo B EPseg ¼ 20:6 þ 183CPa 4:8CAl 3:4CNi a 7:2Ca a 7141Ca S Mo N þ 4:9CCr a 444Ca 183Eseg 87Eseg

ð24Þ

P Sn ESseg ¼ 6:9 151CSa 1:5CAl a þ 14:5Ca 39Eseg

ð25Þ

Al Mo Ti Mo EN þ 4:2CCr seg ¼ 16 2:6Ca þ 3Ca a 2625Ca þ 175Eseg

ð26Þ

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Al Mo N P EC þ 676CBa þ 1:2CCr seg ¼ 7:9 1:4Ca þ 5Ca a 130Eseg þ 116Eseg

ð27Þ N P EMo seg ¼ 0:7 þ 32Eseg 28Eseg

ð28Þ

C P ETi seg ¼ 17 þ 3Ca Eseg

ð29Þ

Al EAl seg ¼ 1:4Ca

ð30Þ

Ni B Cu ESn seg ¼ 21; Eseg ¼ 14; Eseg ¼ 54; Eseg ¼ 20 kJ/mol

where EIsegis segregation energy of the I element, Caj is bulk concentration of j impurity.

F.

Stability of the Segregation

The equilibrium GBS dissolves as temperature increases. Analysis of the kinetic development of the equilibrium segregation level of P shown in Fig. 29 gives the T–t plot of segregation directly. Obviously that segregation level close to the maximum exists only within a specific temperature range. This range is characterized by a maximum temperature stability Tmax, over which the intensive dissolution of the segregates is observed. This temperature can be calculated by computer analysis of Eq. (7) at dCbmax=dT ¼ 0. The temperature Tmax depends on Eseg and temperature dependencies of solubility limits, which can be determined from analysis of phase equilibrium diagrams [43]. Using these dependencies as a generalizing criterion, it is possible to simplify the analysis of data on element segregation kinetics in iron alloys. The interrelationship of maximum temperature of stability (Tmax) of rich equilibrium segregations and segregation energies of different elements is presented in Fig. 30. The common features of kinetics show the following groups: enriching grain boundaries at low- and medium-tempering temperatures—B, C, N, and Cu; 2. co-segregating with P at high tempering—P, Sn, Ti, and Mo; 3. segregating at high temperatures—S and Al. 1.

Phosphorus in Fe alloys has abnormally weak dependence of Tmax on Eseg in reversible temper embrittlement temperature range. In other

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Figure 29 The calculated segregation level of P as a function of temperature according to Eq. (7). Tmax is the maximal temperature of stability of rich segregation level. (From Ref. 42.)

words, this means that the temperature of P segregation stability in the RTE development interval weakly depends on segregation energy or alloy composition. This circumstance is associated with the specific shape of the temperature dependence of P solubility in Fe. The established regularity allows to explain the difficulties with rational alloying of engineering steels for RTE suppression. G.

Nature of Reversibility of Temper Embrittlement

The reversibility of temper embrittlement is usually associated with precipitation or dissolution of carbide phase at various modes of quenched steel heat treatment below Ac1 [44–46]. The complex character of multicomponent GB adsorption—namely interrelation of two opposite processes: concurrence between impurities, and their cooperative segregation—is not taken into account using this approach.

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Figure 30 The interconnection of Tmax-segregation stability temperature and Eseg-energy of impurities segregation in Fe-base alloys.

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Figure 31 Thermo-kinetics diagrams of multicomponent segregation on free surface in steel 0.35C–1.58Mn–0.1P–0.6Al.

Figure 31 presents the thermokinetic diagram of element segregation in 0.35C–1.5Mn–0.1P–0.6Al steel. The chemical composition of free surface segregations was determined by AES for a set of isothermal conditions in the spectrometer ESCALAB MK2 (VG). The temperature–time interval of preferential segregation of chemical elements is the result of different diffusion mobility and binding energy of elements with GB. The temperature interval of P preferential segregation is caused by concurrence of this impurity with mobile interstitial elements C and N. This process determines temperature and exposition necessary for RTE development. Direct investigation of grain boundary composition by AES confirms the conclusion about the prevailing role of concurrent segregation in RTE. The composition of several grain boundaries on brittle intercrystalline fracture of 0.35C–Mn–Al steel after heat treatment: quenching from 1223K, tempering at 923K for 1 hr with rapid (a) and slow (b) cooling is presented in Fig. 32 [47]. These data are in good correspondence with those in Fig. 31. Accelerated cooling of steel, does not provide enough time for the development of segregations with high P content, and GB are enriched by C. During slow cooling, phosphorus has enough time to enrich the grain boundaries. In this case, the carbon concentration on GB is sufficiently lower than at rapid cooling of steel. Carbon segregations are unstable at temperatures higher than 500–673K, and they are dissolved. At slow cooling, P segregates to grain boundaries, decreasing the GB redundant energy. This circumstance lessens the thermodynamic stimulus for carbon segregation as the temperature decreases. Carbon and phosphorus in steels are responsible for RTE development. They have high surface activity and diffusion mobility that

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Figure 32 Chemical composition of GB in steel 0.35C–1.58Mn–0.1P–0.6Al (AES); (a) tempering at 923K, water cooling; (b) tempering at 923K, cooling with furnace. (From Ref. 47.)

predetermines their segregation on GB at heat treatment. Difference of diffusion mobility as well as difference of maximum temperature of segregation stability is the reason for preferential segregation of an impurity. This is the reason for the characteristic temperature region of RTE development. Reversibility (i.e. disappearance) of temper embrittlement is associated with full dissolution of rich GBS of phosphorus at high temperatures and

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enrichment of GB by carbon at rapid cooling [48]. Undoubtedly, carbide transformation, internal stresses, substructure transformations are very important for RTE. One should take into account such circumstances where kinetics of C and P segregation are dependent significantly on steel alloying.

IV.

DYNAMIC SIMULATION OF GRAIN BOUNDARY SEGREGATION

A.

Interface Adsorption During Tempering of Steel

1. Decomposition of Martensite The common laws of multicomponent GBS and analysis of experimental diagrams on elements segregation kinetics in iron alloys are used to develop the computer models of these processes. The exact solution of McLean’s diffusion Eq. (21) accounting for temperature dependant of diffusion and element solubility is a complex problem. In low-alloyed steels, the concentration of surface-active impurities (S, P, and N) is rather small, and based on this reason, it is possible to analyze the diffusion of each element separately. The model takes into account mutual influence of bulk and surface concentration of elements with respect to segregation energies. Carbon in solid solution has maximum influence on phosphorus GBS kinetics. Concentration of C in martensite changes significantly during quenched steel tempering and mainly depends on alloying element content. Based on this reason, one should take into account the solid solution composition altering segregation processes modeling during tempering. Investigations of martensite tetragonality at alloyed steel tempering [6,7] are the basis for calculations of mutual influence of alloying elements on martensite decomposition kinetics and carbon content in solid solution. The carbon content change in solid solution during tempering of engineering steels is well described by equation DXC Q n a ¼ 1 exp KD t exp o XC RT a ð0Þ

ð31Þ

where C C DXC a ¼ Xa ð0Þ Xa ðtÞ

XaC(0)

XaC(t)

ð32Þ

and are the carbon content in quenched steel and after a time t; Do is the carbon diffusion coefficient; Q is the activation energy associated with the interstitial diffusion of carbon atoms; K is the constant associated

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Table 4

Coefficient A in Eq. (28) for Low-Alloying Engineering Steels Alloying element

Coefficient A

Ni

Si

Mn

Cr

Mo

433.56

1,432.54

726.35

2,898.91

971.51

with the nucleation; n is the constant independent of both temperature and XaC(0); R is the gas constant and T is the temperature. Influence of C and alloying elements on parameters Q, K, and n in Eq. (31) is determined for various steels. The activation energy Q in lowalloyed steel depends on the concentration of carbon and alloying elements in solid solution: Me Qðcal=molÞ ¼ 8571:5XC a þ A Xa þ 18; 000

ð33Þ

where XaC and XaMe are concentrations of C and alloying elements, mass%; A is a constant depending on alloying element. The values of coefficients in Eq. (31) are presented in Tables 4 and 5. The diffusion activation energy of

Table 5 Influence of Carbon and Alloying Elements on Parameters Q, K, and n in Eq. (31) Steel, wt.% 0.4C–0.24Ni 0.39C–3.0Ni 0.37C–5.6Ni 0.4C–0.32Mn 0.4C–1.32Mn 0.4C–2.43Mn 0.4C–0.2Cr 0.4C–2.1Cr 0.4C–3.6Cr 0.4C–6.7Cr 0.4C–0.37Si 0.38C–1.75Si 0.4C–2.75Si 0.4C 1.4C 1.2C–2.0Mo

Q, cal=mol

Ln K

n

21,532 22,643 23,599 21,196 20,298 19,406 20,848 15,348 10,992 2,005 21,929 23,764 25,368 21,429 30,000 26,343

15.364 17.481 18,575 15.737 14.241 13.713 15.366 10.076 5.481 1.698 16.351 15.234 10.050 16.72 40.881 29.768

0.26 0.22 0.24 0.24 0.22 0.24 0.21 0.24 0.42 2.32 0.19 0.22 0.15 0.24 0.07 0.08

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 33 Change of carbon concentration in solid solution with temperature and time of tempering. Steel 0.43C–2.43 Mn (mass%). Isodose curves for: 1, 1 at.% C; 2, 0.5 at.% C; 3, 0.1 at.% C; 4, 0.05 at.% C; 5, 0.03 at.% C.

carbon decreases on the growth of carbide-forming element (Mn, Cr, and Mo) concentration. The contrary effect is observed for Ni and Si. Obviously, it is associated with the different influence of these elements on thermodynamic activity of carbon in ferrite. These dependencies are basic for calculations of segregation kinetics of C since carbon is the element that influences on P segregation highly. The kinetics of carbon content in solid solution change during tempering of quenched steel 0.43C–2.43Mn (mass%) are shown in Fig. 33. These data are obtained by computer modeling using Eqs. (31–33) and those from Tables 4 and 5. This model provides the possibility of calculating the influence of alloying on cementite formation temperature interval, growth rate of its particles, and many other parameters of martensite decomposition at tempering [49]. Fig. 34 presents the calculation results of effective growth rate of Fe3C nucleus at tempering of engineering alloyed steels. The calculations were carried out using expression [49]: Vmax R ¼ ð27D=256pÞN

ð34Þ

where R is the cementite particle radius; N is the right part of Eq. (30). Manganese decreases martensite stability significantly promoting its decomposition at low temperatures. Silicon, at a concentration greater than 1%, activates martensite decomposition at 700–800K and inhibits it at lower

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 34 Change of effective growth rate of Fe3C nucleus with alloying of 0.4% C steel: 1, unalloyed steel with 0.4C(mass%); 2, alloyed with 0.35Si; 3, alloyed with 2.1Cr; 4, alloyed with 1.75Si; 5, alloyed with 2.43Mn.

content. Chromium does not change the temperature of intensive cementite growth. 2.

Calculation of Thermokinetic Diagrams of Impurities’ Segregation During Tempering of Steel Modeling of multicomponent adsorption kinetics is carried out using a sequence of computer calculations. At the initial stage, thermodynamic characteristics of surface activity in Fe-base binary and ternary alloys are determined. Analysis of phase equilibrium diagrams permits the determination of i the impurity segregation energy Eseg and temperature dependence of ultimate solubility X8c. These two parameters are very important for determination of equilibrium GB concentration of impurity Xbi using Eq. (17). Examples of such calculations for binary and ternary alloys have been presented. Mutual influence of alloy components on their surface activity could be refined experimentally. The equations for binding impurity segregation energy with solid solution composition could be obtained by regression analysis of multicomponent adsorption diagrams. These experiments allow the determination of the effective diffusion coefficient of elements. The diagram of the equilibrium impurity concentration calculation on grain boundary in engineering steel is presented in Fig. 35. Carbon concentration in martensite changes drastically during tempering, as it depends on chemical composition of steel, temperature, and duration

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 35 Calculation scheme of equilibrium impurity GBS. Xai (0) is the initial concentration of ith element in the steel; XaC(T,t) is the running carbon concentration in martensite during its tempering; Xbi (T) is the maximal equilibrium GBS of ith i element; Eseg Fe–i is the segregation energy of ith element in two-component Fe–I i alloy; Eseg Fe–i–j is the segregation energy of ith element in multicomponent alloy; Di(T) is the diffusion coefficient of ith element in austenite, martensite, and ferrite.

of treatment. This factor influences on thermodynamic activity of all steel components and on their energy of GB segregation. The second important stage of GBS modeling includes calculation of C volume concentration in martensite XaC(T), depending on steel chemical composition Xai (0) and parameters of tempering. New segregation energy values of each element at changing of treatment temperature or time and new equilibrium GBS level have been calculated in this way (see Fig. 35). The final stage of modeling includes a set of independent calculations of various element diffusion to GB zone, and their desorption. The limited capacity of boundary and its effective width (about 0.5 nm) are shown. It is assumed that interstitial and substitial impurities occupy different positions on GB. Time t of reaching the definite concentration of impurity in segregation Xb(t) at given temper temperature T is calculated by (22), and it is controlled by diffusion Di(T). Adsorption in multicomponent system is accompanied by concurrence: arrival of some surface-active impurity decreases GB energy and, in this way, the thermodynamic stimulus for segregation of other impurities. Dissolution of segregations is observed at increasing temperature. Impurity desorption to grain bulk is analogous to adsorption, however it is tied not with concentration Xi(0) but with Xb(t), and it is also controlled by diffusion Di(t). Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

The model is restricted to initially homogeneous bulk concentrations Xib ð0Þ ¼ Xia

ð35Þ

The kinetics of segregation to surfaces or grain boundaries from the bulk are determined by volume diffusion of impurities with bulk concentrations Xia(t) which can be treated as a one-dimensional problem. Since both bulk concentrations are very small, Arrhenius type diffusion coefficients: Di ¼

Di0

Qi exp RT

ð36Þ

can be used which are independent of Xia(t). In the case of site competition, the GB impurities concentration is qi ¼

1

Xi P

Ei exp KT J Xj

ð37Þ

The equations describing the time evolution of segregation for homogeneous initial condition [60] are sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Z t Z t X0i 1 qi ðt0 ÞDi ðt0 Þ ﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Di ðt0 Þ dt0 pﬃﬃﬃ Xi ðtÞ ¼ Xi ð0Þ þ 2 pﬃﬃﬃ ð38Þ R t0 pd 0 pd 0 00 Þ dt00 D ðt i t In the case of constant temperature (i.e. Di ¼ const), Eq. (38) can be simplified: pﬃﬃﬃﬃ pﬃﬃ 2 D 0 Xi ðtÞ ¼ Xi ð0Þ þ pﬃﬃﬃ ½Xi qi ðtÞ t pd

ð39Þ

Diffusion coefficient for impurities in Fe and Fe-base alloys in ferrite interval is present in Table 6. The calculated diagrams of multicomponent adsorption in steels 0.3C– Cr–Mo, 0.3C–Cr–Mn–V, 0.3C–Cr–Mn–Si–Ti (see Table 3) are presented in Figs. 36–38. Comparing these diagrams with the experimental ones (Figs. 24, 26, and 27), a good correlation of segregation kinetic features for various elements is observed, that confirms the basic principles of the proposed model of GBS in steels. According to this model, the main role of carbide precipitation in GBS consists of changing solid solution

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Table 6 Solute C C P P P P P P P P P P P P P S Sn Cr Co C C C C C C C C C

Coefficients of Diffusion for Impurities in a-Fe and Steels System

Temperature, K

0.3C–10Ni Martensite a-Fe a-Fe a-Fe a-Fe a-Fe a-Fe Fe–2.1Mn Fe–Ni–P a-Fe 0.1P–0.15Cr 0.1P–0.13Si 0.1P–0.17Mn 0.1P–0.14Mo 0.1P–0.14Ni Fe–3Si a-Fe Fe–Cr Fe–6.8Co Fe–0.79Si Fe–0.79Si Fe–0.79Si Fe–0.6Ni Fe–0.6Ni Fe–0.6Ni Fe–0.56Mo Fe–0.56Mo Fe–0.56Mo

723–873 623 723 748 773 798

a a a a a 973 973–1303 1048 903–1073 803 873 973 803 873 973 873 923 973

D, m2Sec1

Q, D0 (m2Sec1) kcal=mol Reference 5.26 105

5.3 2.8 7.7 2.0 4.8

1014 1019 1019 1018 1018

0.108 exp(288=RT) 0.336 exp(296=RT) 18 exp(329=RT) 0.235 exp(292=RT) 3.23 106 exp(434=RT) 43.9 exp(336=RT)

3.6 1012 1.4 1011 1.9 1010 4 104 16 104 6.9 104 7.2 104 21 104 55 104

15.2

9.55 106 1.43 104 0.51 104

50.6 54.2 55

1.7 102 5.4 2.33 104 4.69 105

61.2 55.5 57.1 44.7

[50] [51] [52] [52] [52] [52] [53] [53] [54] [55] [55] [55] [55] [55] [55] [56] [57] [58] [59] [60] [60] [60] [60] [60] [60] [60] [60] [60]

composition, as it is exactly this factor that controls mutual influence of elements on their surface activity. Only such elements that segregate in near temperature ranges mutually influence GBS. The computer calculations of segregation kinetic diagrams predict these effects with small changes of steel chemical composition. Figures 39 and 40 present the modeling data on influence of sulfur content in 0.3C–Cr–Mn–Si–Ti steel on phosphorus segregation kinetics. Sulfur and Phosphorus are strong surface-active elements, and they can compete at grain boundaries. Desulfurization of steel significantly slows down GBS of S. Indeed, P adsorption increases with a decrease of S content. According to calculations (see Fig. 40), the time of 6% P GBS formation exceeds 4000 sec at a sulfur content more than 0.02 at.%. This time it is significantly longer than the usual duration of quenched steel

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 36 The isodose C-curves of multicomponent interface segregation in 0.2C– Cr–Mn–Ni–Si steel (see Table 3) under its tempering. Computer simulation.

tempering. Deeper cleaning of steel by S activates GB adsorption of P, drops down time of segregation formation, and increases the maximum temperature of segregation stability (see Figs. 39 and 40). Such calculations are very useful for the design of optimal alloying and purification degree on harmful impurities, since they permit the determination of the influence of alloying on ultimate concentration of harmful impurities.

Figure 37 The isodose C-curves of multicomponent interface segregation in 0.3C– Cr–Mn–V steel (see Table 3) under its tempering. Computer simulation.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 38 The isodose C-curves of multicomponent interface segregation in 0.3C– Cr–Mn–Si–Ti steel (see Table 3) under its tempering. Computer simulation.

B.

Interface Adsorption During Quenching of Engineering Steels

Mathematical models of GBS [61] and phase transformations permit the analysis of heat treatment with respect to the accompanying phenomena in a greater detail than that of a simple summary of the experimental knowledge.

Figure 39 Dependence of Tmax of P GBS as a function of sulfur containing in 0.3C–Cr–Mn–Si–Ti steel under its tempering. Computer simulation.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 40 Dependence of time of 6 at.% GBS of phosphorus and sulfur as a function of sulfur concentration in 0.3C–Cr–Mn–Si–Ti steel during its tempering at 700K. Computer simulation.

The results of mathematical modeling provide backgrounds for reasonable planning of full-scale experiments when seeking for the optimum technological procedures and steel composition and they enable the extrapolation of the consequences of variations in the technological conditions even outside the boundary of the empirical experience we have available. Interaction of GB segregation enrichment and phase transformations during heat treatment of steels in the austenitic region is hard to imagine. Nb and V carbonitride precipitation in microalloyed austenite, precipitation of free ferrite, change chemical composition of austenite, and influence on GBS kinetics to a large extent. The experiments show that nonequilibrium grain boundary phenomena occur for a rather short time up to 100 sec. The minimum time of 5% volume fraction of Nb and V carbonitride precipitation is about 1000 sec [62,63]. Precipitation of free ferrite needs from several seconds to several minutes depending on steel chemical composition. Therefore, the non-equilibrium GBS in steels with a wide region of undercooled austenite stability independently from phase transformations. This computer model has some limitations but redistribution of harmful impurities between grain bulk and boundaries permits the analysis of steel quenching. The modeling of non-equilibrium GB phenomena allows during investigation of such short-time changes of chemical composition that could not be measured experimentally and that has an extreme importance for modern heat-treatment processes with high heating and cooling velocities in controlled media.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 41 The presentation of C-curve on simulating TTT diagrams. (Scheme.) Parameters U and S correspond to Table 7.

1. Phase Transformations of Undercooling Austenite At present, many computer models of evolution of structure and phase composition of steels during quenching have been developed. Most of them are based on physical models of phase transformations [64–66]. But physical models cannot describe adequately all kinetic features of undercooled austenite transformations. The computer models based on regression analysis of experimental data can best predict steel phase composition changes during steel cooling. It was introduced directly by Davenport and Bain [67] and the time– temperature-transformation (TTT) diagram was the predominant tool to describe the isothermal decomposition kinetics of supercooled austenite. In most TTT diagrams, general S- or C-curves are used to represent the kinetics of a number of isothermal transformation products: ferrite, pearlite, upper bainite, lower bainite, and martensite. Conversely, many experimental results demonstrate that each type of transformation product has a separate C-curve. To build a mathematical model, all TTT diagrams published in Refs. [68–71] were analyzed. The rationalization of the kinetics of isothermal decomposition of austenite permitted the establishment of a metastable product (phase) diagram of a number of steels of different compositions with 6% of total content of all alloying elements.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Most isothermal transformations take place by nucleation at the austenite grain boundaries, so the original austenite grain size will affect the isothermal decomposition kinetics of austenite. From the total number of factors characterizing austenite matrix, the present day experimental knowledge allows only an approximate examination of the statistically recrystallized proportion and estimation of the size of deformed austenite grains. The grain growth kinetics satisfy the law [73] Q dðtÞ ¼ d0 þ kt exp RT

ð40Þ

where d(t) is averaged grain size at moment t; d0 is initial grain size; Q is activation energy; k is a constant. The algorithm of calculating the size of austenite grains is described in Ref. [73]. The procedure for calculation of the structural proportions of anisothermal decomposition of austenite at engineering steel cooling is given in Tables 7 and 8 and shown in Fig. 41. The cooling curve is approximated partially by a constant function and at the individual time intervals Dt and the rate of decomposition is calculated as isothermal transformation corresponding to the mean temperature of that interval. The required kinetic data are available from the TTT diagrams [68–71] that can be digitized (see Table 8) by procedures shown in Fig. 41, using equation 1=2 S S0 1 U U0 1=2 U U0 ¼e exp SN S0 UN U0 2 UN U0

ð41Þ

where S ¼ Int-time interval, s; U ¼ 1000=(T þ 273). Since it is necessary to distinguish between the parts of the C-curves representing the formation of ferrite, pearlite, and bainite, only those diagrams having readily distinguishable component curves were used in the analysis. The calculation method includes the effect of the size of austenite grains on the kinetics of phase transformations. The main precondition is knowledge of this effect on the course of C-curves showing the start and end of transformations in the graph of isothermal decomposition of austenite for the relevant steel.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Table 7

The Algorithm of Calculation of the Structural Proportions

1. Temperature of start of transformations yAc3, yAc1, yBa, yMs 2. t 0; y(0) y0; V1(0) 1; Vi(0) 0, i ¼ 2, 3, 4, 5; i ¼ 1-austenite, 2-ferrite, 3-pearlite, 4-bainite, 5-martensite 2.1 Mean temperature at the interval of ht, t þ Dti y ¼ (y(t) þ y(t þ Dt))=2; if y < ¼ yMs pass to 3; if y < ¼ min (yjs) then n j; 2.2 for i ¼ 2, . . . , n carried out as follows: – calculation of the transformable proportion of austenite Vmi(t) for i ¼ 2: Vm2(t)¼0; for y ¼ > yA3, 0 yA3 y Vm2 ðtÞ ¼ Vm2 yA3 yA1 ; for yA1 < y < yA3 ;

0 Vm2 ðtÞ ¼ Vm2 ; for y <¼ yA1 ; Sð % CÞXð %CÞ ; for i > 2 and V ¼ 1 0 Vm2 ¼ mi Sð%CÞPð%CÞ – calculation of the start and end of transformation tsi, tfi and exponent ki for y ki ¼ 6.127=ln (tsi=tfi); for ferrite k2 ¼ 1; – the fictive volume fraction of the transformed proportion Xi ¼ Vi(t)=[Vi(t) þ Vi(t) Vmi(t)]; – the fictive time of isothermal transformation required for reaching the proportion Xi

ki t lnð1X Þ t0i ¼ si b i 1=ki ; S

– the fictive volume proportion of the structural component at time t þ Dt

k ti þDt i ; Xi ðti þ DtÞ ¼ 1 exp b2 tsi – the volume proportion of the structural component at time t þ Dt Vi ðt þ DtÞ ¼ Xi ðt0i þ DtÞ½Vi ðtÞ þ Vi ðtÞVmi ðtÞ; 2.3 the new value of residual content of austenite P V1 ðt þ DtÞ ¼ 1 ni¼2 Vi ðt þ DtÞ; if V1 ðt þ DtÞ <¼ 0 the transformation is finished; 2.4 t t þ Dt; pass over 2.1 3. The martensite transformation for yMf < ¼ y < ¼ yMs V5(y) ¼ (1V2V3V4)[1exp(0.011(yMsy))] P 4. The residual content of austenite at y < ¼ yMf: Vi ¼ 1 5i¼2 Vi ; I ¼ 1, 2, 3, 4, 5—austenite, ferrite, pearlite, bainite, martensite; S(%C), P(%C), X(%C)containing carbon in points S and P of Fe–C phase diagram and in the steel, consequently.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Table 8 The Constants Blk for Calculations of the YL Parameters of C-Curves k 1

2

3

4

5

6

7

8

Ferrite-start

T8C Time

Pearlite-start

T8C Time

Pearlite-finish T8C Time Bainite-start

T8C Time

Bainite-finish T8C Time MS

YL TOFS TNFS IntOFS IntNFS TOPS TNPS IntOPS IntNPS TOPF TNPF IntOPF IntNPF TOBS TNBS IntOBS IntNBS TOBF TNBF IntOBF IntNBF TMS

Const

10

11

12

13

14

15

16

Const C

Mn

Si

Ni

Cr

Mo

GS

48 1.92 2.58 0 6 0.03 0.03 107 107 5.44 1.40 76 76 7.73 1.98 0

30 57 2.80 0.20 0 32 10.12 1.31 0 4 14.08 1.31 12 30 1.46 1.29 12 30 0.75 1.17 0

66 25 3.55 1.10 15 20 3.55 0.20 15 5 0.76 1.56 –5 35 1.64 1.64 5 28 5.44 5.84 0

22 15 1.50 0.04 5 5 3.30 0.20 5 5 1.99 0.65 –5 5 0.40 0.20 7 7 0.40 0.02 0

70 15 3.00 2.55 5 27 3.00 2.55 5 36 3.00 0.98 –5 36 3.49 2.04 5 40 0.90 2.47 0

5 25 3.50 3.50 22 23 4.20 2.50 22 25 4.35 4.35 –40 2 3.00 6.60 51 96 6.88 4.00 0

0 3.90 0.0096 0.021 0 3.20 0.096 0.041 0 1.31 0.0096 0.021 0 0.37 0.0626 0.0248 0 0.37 0.0813 0.0340 0

Dlk

Blk Transformation

9

C

727 572 10.13 1.04 727 572 10.13 1.04 727 577 10.55 0.15 570 485 3.52 0.96 570 488 6.90 0.15 539 423

Mn

Si

Ni

Cr

Mo

GS

13 33 2.5 0.6 13 33 2.5 0.6 13 2 6.86 2.0 12 12 2.14 1.30 12 48 5.23 3.00 30.4

9 44 2.84 0.19 9 44 2.84 0.19 9 35 3 0.19 16 2 1.07 0.30 16 25 2.8 2.8 0

17 9 0.46 0.07 17 9 0.46 0.07 17 7 1.81 0.07 12 7 0.05 0.02 7 7 0.7 0.7 17.7

22 25 4.8 4.8 22 25 4.8 4.8 22 53 4.8 2.65 20 40 2.3 2.2 22 47 6.2 3 12.1

3.5 50 5.9 5.9 3.5 50 5.9 5.9 3.5 58 12.3 10.6 22 32 3.1 2.2 22 61 9.5 5.9 7.5

0 1.01 0.095 0.038 0 1.01 0.095 0.038 0 0.52 0.095 0.038 0 0.50 0.070 0.024 0 0.52 0.070 0.024 0

229 48 1.92 2.58

Ck

YL ¼

P8

k¼1 ½Blk

C1

C2

C3

C4

C5

C6

C7

C8

1

%C

%Mn

%Si

%Ni

%Cr

%Mo

2

þ Dlk þ 8ð0:8 C2 ÞCk ; GS—grain size (ASTM).

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

The program involves the calculation of temperatures of transformations of bainite and twinned, athermal and lamellar martensite [74] BS ¼ 720 585:63ðCÞ þ 126:6ðCÞ2 66:34ðNiÞ þ 6:06ðNiÞ2 31:66ðCrÞ þ 2:17ðCrÞ3 91:68ðMnÞ þ 7:82ðMnÞ2 42:37ðMoÞ þ 9:16ðCoÞ 0:125ðCoÞ2 36:02ðCuÞ

ð42Þ

2 MTM S ¼ 420208:33ðCÞ72:65ðNÞ43:36ðNÞ 16:08ðNiÞ

þ0:78ðNiÞ2 0:025ðNiÞ3 2:47ðCrÞ33:428ðMnÞþ1:296ðMnÞ2 þ30:0ðMoÞþ12:86ðCoÞ0:2665ðCoÞ2 7:18ðCuÞ

ð43Þ

¼ 540 356:25ðCÞ 260:64ðN 24:65ðNiÞ þ 1:36ðNiÞ2 MLM S 17:82ðCrÞ þ 1:42ðCrÞ2 47:59ðMnÞ þ 2:25ðMnÞ2 MA S

þ 17:5ðMoÞ þ 21:87ðCoÞ 16:52ðCuÞ ¼ 820 603:76ðCÞ þ 247:13ðCÞ2 55:72ðNiÞ þ 3:97ðNiÞ2

ð44Þ

31:1ðCrÞ þ 2:348ðCrÞ2 66:24ðMnÞ 24:29ðMoÞ 0:196ðCoÞ þ 0:165ðCoÞ2 31:88ðCuÞ

ð45Þ

The size of ferritic grain is expressed as follows [75] 0:5 da ¼ 11:7 þ 0:14dg þ 37:7VC

ð46Þ

where dg is the size of austenitic grain, (mm); VC is the cooling speed, (8C min1). The interlamellar distance of pearlite can be estimated as follows [75]: " # X S¼ 18:0DVP ðyi Þ=ð996 yi Þ =VP ð47Þ i

where DVP(yi) is the volume proportion of pearlite transformed at yi temperature. The thickness of the ferritic and carbide lamellae of pearlite is approximately lf ¼ 0.885S; lc ¼ 0.115S The size of martensitic and bainitic particles is identical with the original size of the austenite grains. The course of the anisothermal decomposition of austenite in several steels has been calculated by the

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

just-described method and by applying the digitized TTT diagrams of Table 7. 2.

Determination of the Kinetics of Carbonitride Precipitation in Austenite Microalloying of steels with Ti, V, Nb, and Zr affects decomposition of supercooled austenite, its recrystallization and grain boundary segregations of harmful impurities. These changes of material properties are associated with carbonitride precipitation and changes of austenite chemical composition. Based on these reasons, the modeling of the kinetics of carbonitride precipitation is important. The nucleation time t of carbonitrides per unit volume N at any temperature T, can be expressed as [76] ! ! Q B Q B exp exp t ¼ C exp t ¼ C exp RT RT T3 ðLnKS Þ2 T3 ðLnKS Þ2 ð48Þ where C ¼ 6 1013 for homogeneous nucleation; activation energy of Nb diffusion Q ¼ 270 kJ=mol; B ¼ 16pg3 V2m N0 =3R3

ð49Þ

Vm ¼ 1.28 105 m3=mol; g ¼ 0.5 J m2; N0 are numbers of nucleus by radius R per molar volume Vm; KS is supersaturation [77] LgðKS Þ ¼

A þB T

ð50Þ

where thermodynamics parameters A and B for various carbides and nitrides are calculated in Ref. [78] and presented in Table 9. Thus, the calculation of carbonitride nucleation time necessary to reproduce the C-curves

Table 9

Thermodynamics Parameters in Eq. 50 (From Ref. 77) Chemical compound

Parameter

AlN

VC

VN

TiC

TiN

NbC

NbN

ZrC

ZrN

A B

7,130 1.463

9,500 6.72

7,985 3.09

8,872 4.04

15,573 3.82

7,714 3.27

10,440 3.87

8,464 4.96

13,968 3.08

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corresponds to start or finish of this transformation in austenite under heat treatment of steel. 3.

Calculation of Thermokinetic Diagrams of Impurity Segregation During Quenching of Steel Computation of grain boundary multicomponent adsorption kinetics could be simplified for steels with high undercooled austenite stability. The GBS develops in this case in austenite in short time and has no dependence on phase and structure transformations at steel quenching. Enrichment of grain boundaries by various impurities as well as their desorption is treated as a result of multicomponent diffusion of impurities from near-boundary volume to the boundary. Impurity binding energy with GB includes mutual influence of elements in grain bulk and on the boundary in accordance with Guttmann’s theory [Eqs. (18) and (19)]. Auger electron spectroscopy is the technique for experimental investigation of GBS kinetics. These experiments are basic for analysis of correlation of impurity segregation energy with the content of other elements in the bulk and on boundaries (see Section 2.5, Eqs. (23)–(29). Adsorption and desorption of impurities on GB (qi) at steel quenching is modeled well using the equation 2q0i ﬃ qi ¼ qi ð0Þ þ pﬃﬃﬃﬃﬃ pd

ﬃ sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Z t

Di

1

Zt

ðt0 Þ dt0 pﬃﬃﬃﬃﬃﬃ

0

pd

0

Cia ðt0 ÞDi ðt0 Þ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ dt0 Rt 00 00 t0 Di ðt Þ dt

ð51Þ

where d is the grain boundary thickness; Di(t0 ) is the diffusion coefficient of impurity which depends on the temperature and phase composition (austenite, martensite, and ferrite); in the case of adsorption Cia ¼

CiGB expðGi =kTÞ P 1 j CjGB

ð52Þ

i is the element i concentration on grain boundary; Cai is the conwhere CGB centration of ith element in the adjacent bulk layer; Gi is segregation energy. Desorption is determined by GB concentrations of impurities, and in this case, the parameter Cai in Eq. (51) is equivalent to GB concentration XbI in Eqs. (12) and (13). The change of temperature at cooling or isothermal exposition is described by equation

TðtÞ ¼ ½Tð0Þ Tð/Þ expðrtÞ þ Tð/Þ

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ð53Þ

Table 10

Cooling Rates for Some Metallurgical Technologies

Name of the treatment Quenching Controlled cooling Air cooling of hot-rolled metal Cooling with furnace Controlled cooling of large-size forging

Cooling rates r (K sec1) 100–10 10 10–0.1 0.01 0.001

Table 10 presents cooling rates r for heat-treatment processes. The block diagram of multicomponent intercrystalline adsorption model is shown in Fig. 42. Adsorption of P, C, and S is determined by parameters K1, K2, K3, and their desorption by parameters K2, K4, K6. The parameters Ci are equivalent to GB concentration of element i. This model allows the computation of the condition when there is change of GB composition in steels and alloys at preselected arbitrary mode of cooling including isothermal exposition. Given below are the examples of investigation of phosphorus and sulfur grain boundary adsorption in Cr–Ni–Mo steel (see Table 11). The components of steel mutually influence their diffusion mobility and GBS activation energy. Based on this reason, one should take into account the stochastic fluctuations of diffusion flows of various impurities on GBS kinetics. For this purpose, the random fluctuation of diffusion coefficients up to 30% of its mean value was used in the model. Figures 43 and 44 present the GBS kinetics calculation results at cooling of various purity steels cooling that were carried out using the stochastic model. As one can see, the self-regulation of adsorption is observed which is developing despite significant short-time oscillations of impurity concentration on grain boundaries. The significant non-equilibrium enrichment of GB by impurities is observed at initial stage of the heat treatment. This effect is determined by cooling velocity as well as impurities content. Increasing cooling velocity from 0.001 to 1000K s1 decreases the non-equilibrium GBS of P and S. Formation of non-equilibrium rich GBS of harmful impurities at small cooling times could be established only by using computer modeling methods. The experimental verification of such phenomena needs special techniques which allow to open grain boundaries: hydrogenation of quenched samples or delayed fracture tests. Since these techniques are conducted in air and could not be applied in the vacuum chamber of electron spectrometer; for most of engineering steels, the regularities of non-equilibrium GBS formation at quenching could only be estimated by a computer experiment.

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Figure 42 carbon).

Table 11

Calculation scheme of three-component GBS (phosphorus, sulfur, and

Chemical Composition of Cr–Ni–Mo Steels Chemical composition, mass%

Smelting number 82 83

C

S

P

Ni

Cr

Mo

Time of austenite stability at 600 hr

0.38 0.38

0.027 0.01

0.054 0.006

3.95 4.02

3.0 3.0

0.51 0.50

2.0 2.0

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Figure 43 The change of GBS during quenching of Cr–Ni–Mo steel containing 0.027S and 0.054P (mass%). Computer simulation of fast (a) and slow (b) cooling.

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Figure 44 The change of GBS during quenching of Cr–Ni–Mo steel containing 0.01S and 0.006P (mass%). Computer simulation of fast (a) and slow (b) cooling.

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Figure 45 Chemical composition of GB in Cr–Ni–Mo steel containing 0.027S and 0.054P (mass%) after austenitization at 1373K (30 min), interim cooling up to 873K and quenching in water (a) and in furnace (b). Auger electron spectroscopy of intergranular fracture.

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Figure 46 Chemical composition of GB in Cr–Ni–Mo steel containing 0.01S and 0.006P (mass%) after austenitization at 1373K (30 min), interim cooling up to 873K and quenching in water (a) and in furnace (b). Auger electron spectroscopy of intergranular fracture.

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The validation of calculation reliability was done for steel composition 82 and 83 (see Table 10) by Auger spectroscopy. The samples after austenitization at 1373K (30 min) were in the interim cooled to 873K with further cooling in water or with furnace cooling. The undercooled austenite in this steel has high stability and does not transform in ferrite region for 2 hr. After cooling the samples had martensite–baintite structure. To investigate the chemical composition of grain boundaries by Auger spectroscopy, special samples were crushed in the electron spectrometer ESCALAB MK2 at vacuum at about 108 Pa at temperature 83K. The fields with intercrystalline fracture type were investigated on the fracture surface. The variation of phosphorus and sulfur content in GBS in Cr–Ni–Mo steel of several melts after heat treatment is shown in Figs. 45 and 46. At accelerated cooling the GB are significantly enriched by carbon. The P concentration in GB increases only at slow cooling of samples, and P segregation is strongly suppressed in pure steel. A good correspondence of calculated and experimental results is observed for all cases to be analyzed. The results of numerical modeling give information about the equilibrium and non-equilibrium character of a GB adsorption processes, which are frequently unavailable from experiments. Moreover, these simulation methods explain the phenomenon of reverse temper embrittlement as the result of non-equilibrium concurrent GBS of carbon and phosphorus. These results explain many questions in the multicomponent GB adsorption kinetics in engineering steels that were dynamically developed in the last 10 years. Further investigations in this direction are required especially for competitive internal adsorption in engineering steels treated by using newest schemes of heat treatment. REFERENCES 1. Briant, C.L.; Banerji, S.K. Intergranular failure in steel. Int. Met. Rev. 1978, 4, 164–196. 2. Arharov, V.I.; Ivanovskaya, S.I.; Kolesnikova, K.M.; Farafonova, T.A. The nature of phosphorous influence on temper embrittlement. Fiz. Met. Metallioved. 1956, 2, 57–65. 3. Hondros, E.D.; Seah, M.P. Segregation to interfaces. Int. Met. Rev. 1977, 22, 12,261–12,303. 4. Seah, M.P. Grain boundary segregation. J. Phys. F. 1980, 10 (6), 1043–1064. 5. Guttmann, M. Equilibrium segregation in ternary solution: a model for temper embrittlement. Surf. Sci. 1975, 53, 213–227. 6. Kaminskii, E.Z.; Stelletskaya, T.I. Kinetic of martensite dissolution in carbon steel. Problems of Fisical Metallurgy; Metallurgy: Moscow, 1949, 192–210. 7. Bokshtein, S.Z. Structure and Mechanical Properties of Alloyed Steel; Metallurgy: Moscow 1954.

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8. Briant, C.L.; Banerji, C.K. Intergranular failure of ferrum alloys in inagressive environment. In Treatise on Materials Science and Technology, Vol. 25; Embrittlement of Engineering Alloys; Briant, C.L., Banerji, S.K., Eds.; Academic Press: 1983; 29–59. 9. Erhart, H.; Paju, M. Phosphorus segregation in austenite. Scripta Met. 1983, 17, 171–174. 10. Kovalev, A.I. Influence of grain boundaries phosphorus segregation and steel microstructure on fracture after quenching and middle tempering. Fiz. Met. Metalloved. 1980, 49, 818–826. 11. Glikman, E.; Cherpakov, Ju.; Bruver, R. Dependence of fracture toughness and surface energy of grain boundaries on grain size of Si-steel under reversible temper embrittlement. Fiz. Met. Metalloved. 1978, 42, 864–870. 12. Howe, H.M. Proc. Inst. Mech. Eng. 1919, Jan–May, 405. 13. Carr, F.L.; Goldman, M.; Jaffe, L.D.; Buffin, D.C. Trans. AIME. 1953, 197, 998. 14. McLean, D. Grain Boundaries in Metals; Oxford University Press: London 1957. 15. Hondros, E.D.; Seah, M.P. The theory of grain boundary segregation in terms of surface adsorption analogues. Met. Trans. A 1977, 8, 1363. 16. Abraham, F.F.; Brundle, C.R. Surface segregation in binary solid solutions: a theoretical and experimental perspective. J. Vac. Sci. Technol. 1981, 18 (2), 506–519. 17. Abraham, F.F. Bond and strain energy effects in surface segregation. Scripta Met. 1979, 13 (5), 307–311. 18. Fowler, R.H.; Guggenheim, E.A. Statistical Thermodynamics; University Press: Cambridge 1939. 19. Grabke, H.J. Adsorption, segregation and reactions of non-metal atoms on iron surfaces. Mat. Sci. Eng. 1980, 42, 91–99. 20. Grabke, H.J. Surface and grain boundary segregation on and in iron. Steel Res. 1986, 57, 4178–4185. 21. Grabke, H.J. Surface and Grain Boundary segregation on and in Iron and Steels. ISIJ Int. 1989, 29, 7,529–7,538. 22. Kovalev, A.I.; Mishina, V.P.; Stsherbedinsky, G.V.; Wainstein, D.L. EELFS method for investigation of equilibrium segregation on surfaces in steel and alloys. Vacuum. 1990, 41 (7–9), 1794–1795. 23. Bruver, R.E. Investigation of impurities influence on intergranular low temperature failure of metallic solid solution. Ph.D. Dissertation, Tomsk, 1970. 24. Chelikowsky, J.R. Predictions for surface segregation in intermetallic alloys. Surf. Sci. 1984, 139, L197–L203. 25. Miedema, A.R.; Boer, F.R. et al. Enthalpy of formation of transition metal alloys. Calphad 1977, 1, 4341–4359. 26. Miedema, A.R. On the heat of formation of plutonium alloys. In Plutonium and Other Actinides; Blank, H.; Linder, R., Eds.; North-Holland Publ.: Amsterdam, 1976; 3–20. 27. Bennett, L.H.; Watson, R.A. A database for enthalpies of formation of binary transition metal alloys. Calphad 1980, 5 (1), 19–23.

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28. Watson, R.E. Optimized prediction for heats of formation of transition metal alloys. Calphad 1981, 5 (1), 25–60. 29. Birnie, D.; Machlin, E.S.; Kaufman, C.; Taylor, K. Comparison of pair potential and thermochemical models of the heat of formation of BCC and FCC alloys. Calphad 1982, 6 (2), 93–126. 30. Machlin, E.S. Correlation terms to pair potential model values of the energy of formation for transition element–polyvalent element phases. Calphad 1980, 5 (1), 1–17. 31. Zadumkin, S.N. Modern theory of surface energy of pure metals. In. Surface Phenomena in Liquid metals and Solid Phases; Kabardino-Balkarskoe Publ. Press: Nalchik 1965; 12–28. 32. Zadumkin, S.N. Surface energy on the interface of metals. In Surface Phenomena in Liquid metals and Solid Phases; Kabardino-Balkarskoe Publ. Press: Nalchik, 1965; 79–88. 33. Morita, Z.; Tanaka, T. Effect of solute-interaction on the equilibrium distribution of solute between solid and liquid phases in iron base. Trans. ISIJ 1984, 24, 206–211. 34. Kamenetskaya, D.S. Influence of molecular interaction on phase diagrams. Problems of Physical Metallurgy and Metal Science; Metallurgia: Moscow 1949; 113–131. 35. Toshihiro, T. Equilibrium distribution coefficient of P in Fe-base alloys. J. Iron Steel Inst. Jpn. 1984, 70 (4), 220. 36. Guttmann, M.; Dumolin, Ph.; Wayman, M. The thermodynamics of interactive co-segregation of phosphorous and alloying elements in iron and temper-brittle steels. Met. Trans. A 1982, 13, 1693–1711. 37. Morito, Z.-I.; Tanaka, T. Effect of solute-interaction on the equilibrium distribution of solute between solid and liquid phases in iron base ternary system. Trans. ISIJ. 1984, 24, 206–211. 38. Morito, Z.-I.; Tanaka, T. Equilibrium distribution coefficient of phosphorus in iron alloys. Trans. ISIJ 1986, 26, 114–120. 39. Okamoto, T.; Morito, Z.; Kagawa, A.; Tanaka, T. Partition of carbon between solid and liquid in Fe–C binary system. Trans. ISIJ 1983, 23, 266–271. 40. Yamada, K.; Kato, E. Effect of dilute concentrations of Si, Al, Ti, V, Cr, Co, Ni, Nb and Mo on the activity coefficient of P in liquid iron. Trans. ISIJ 1983, 23, 51–55. 41. Michina, V.P. Atomic interaction at grain boundary segregation in Fe alloys. Author’s Abstract of Doctor’s Thesis, Moscow, 1988. 42. Seah, M.P. Grain boundary segregation and the Tt dependence of temper brittleness. Acta Met. 1977, 25, 345–357. 43. Bannih, O.A.; Budberg, P.B.; Alisova, C.P. Equilibrium diagrams of two- and poly-component systems on base of Fe. Handbook; Metallurgia: Moscow 1986. 44. Arharov, V.I.; Konstantinova, T.S. The nature of reversible temper embrittleness of 0.35C–Cr–Mn–Si and 12C–Cr–Ni steels. Fiz. Met. Metalloved. 1974, 38 (1), 169–175.

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45. Otani, H.; Feng, H.C.; McMahon, C.J. New information on the mechanism of temper embrittlement of alloy steels. Met. Trans. 1974, 5 (2), 516–518. 46. Lei, T.C.; Tang, C.H.; Su, M. Temper brittleness of 0.3C–Cr–Mn7–Si–2Ni steel with various initial microstructures. Metal Sci. 1983, 17, 75–79. 47. Kovalev, A.I.; Michina, V.P. Role of grain boundary segregation in RTE of steels. Physical basis of construct of physical and mechanical properties of steels and alloys. In Proceedings of CNIICHERMET; Bardin, I.P., Ed., Metallurgia: Moscow, 1990, 43–46. 48. Kovalev, A.I.; Mishina, V.P.; Stsherbedinsky, G.V. Features of intergranular adsorption of carbon and phosphorus in Fe-alloys. Fiz. Met. Metalloved 1986, 62 (1), 126–132. 49. Zuyao, X.; Siwei, C. Mechanism of embrittlement in tempered martensite. Mat. Sci. Technol. 1985, 1, 1025–1028. 50. Zemskii, S.V.; Litvinenko, D.A. Diffusion of C in two-phase system. Fiz. Met. Metalloved 1971, 32 (3), 591–596. 51. Golikov, V.M.; Matosyan, M.A.; Estrin, E.I. Influence of pressure on carbon diffusion. Protect. Coat. Met. 1971, 4, 74–78. 52. Guttmann, M.; Dumolin, Ph.; Wayman, M. The thermodynamics of interactive co-segregation of phosphorus and alloying elements in iron and temper-brittle steels. Met. Trans. A 1982, 13, 1693–1711. 53. Grabke, H.J.; Hennesen, K.; Moller, R.; Wei, W. Effect Mn on the grain boundary segregation, bulk and grain boundary diffusitivity of P in ferrite. Scr. Met. 1987, 21 (10), 1329–1334. 54. Yongbin, I.M.; Daniluk, St. A surface segregation study in P and S-doped type 304 stainless steel. Met. Trans. A. 1987, 18 (1), 19–26. 55. Mastsuyama, T.; Hosokawa, H.; Suto, H. Tracer diffusion of P in iron alloys. Trans. JIM 1983, 24 (8), 589–594. 56. Gruzin, P.L.; Mural, V.V. S -diffusion in 3%Si–Fe alloy. Fiz. Met. Metalloved 1971, 32 (1), 208–212. 57. Treheus, D.; Marchive, D.; Delagrange, J. Determination of the coefficient of diffusion of Sn of infinite dilution in a-Fe. Compt. Rend. Acad. Sci. C 1972, 274 (13), 1260–1262. 58. Huntz, A.M.; Guiraldeng, P.; Aucouturier, M.; Lacombe, P. Relation between the diffusion of radioactive Fe and Cr in Fe–Cr alloys with 0–15% Cr and their a=g transformation. Mem. Sci. Rev. Met. 1969, 66, 85–104. 59. Hirano, K.; Cohen, M. Diffusion of Co in Fe–Co alloys. Trans. JIM 1972, 13 (2), 96–102. 60. Gruzin, P.L.; Babikova, Yu.F.; Borisov, E.B.; Zimskii, S.V., et al. Investigation of diffusion of C in steel and alloys by C14 isotope. Problems of Metals Science and Physical Metallurgy; Metallurgy: Moscow 1958; 327–365. 61. Militzer, M.; Wieting, J. Theory of segregation kinetics in ternary systems. Acta Met. 1986, 34 (7), 1229–1236. 62. Dutto, B.; Sellars, C.M. Effect of composition and process variables on Nb(CN) precipitation in niobium microalloyed austenite. Mat. Sci. Technol. 1987, 3 (3), 197–206.

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63. Rios, P.R. Expression for solubility product of niobium carbonitride in austenite. Mat. Sci. Technol. 1988, 4 (4), 324–327. 64. Adrion, H. Thermodynamic model for precipitation of carbonitrides in high strength low alloy steels containing up to three microalloying elements with or without additions of aluminum. Mat. Sci. Technol. 1992, 8 (5), 406–420. 65. Reed, R.C.; Bhadeshia, H.K.D.H. Kinetics of reconstructive austenite to ferrite transformation in low alloy steels. Mat. Sci. Technol. 1992, 8, 421–436. 66. Rees, G.I.; Bhadeshia, H.K.D.H. Bainite transformation kinetics Part 1. Mat. Sci. Technol. 1992, 8, 985–993. 67. Davenport, E.S.; Bain, E.C. Trans. AIME. 1930, 90, 117–144. 68. Isothermal Transformation Diagrams, 1943, 1st Ed., 1963, 2nd Ed.; United States Steel Corporation: Pittsburgh, PA. 69. Atlas of Isothermal Transformation Diagrams of BS En Steels, 1949, 1st Ed., 1956, 2nd Ed.; The Iron and Steel Institute, British Iron and Steel Research Association: London. 70. Popov, A.A.; Popova, L.E. Isothermal and Thermokinetics Diagrams of Decomposition of Supercooled Austenite; Metallurgia: Moscow 1965. 71. Atlas of Isothermal Transformation and Cooling Transformation Diagrams; ASM:Metals Park, OH: 1977. 72. BISRA Atlas of Isothermal Transformation Diagrams of BS En Steels, Special Report no. 56, 2nd Ed.; The Iron and Steel Institute: London, 1956. 73. Priestner, R.; Hodson, P.D. Ferrite grain coarsening during transformation of thermomechanically processed C–Mn–Nb austenite. Mat. Sci. Technol. 1992, 8 (10), 849–854. 74. Sellars, C.M. The physical metallurgy of hot working. In Hot Working and Forming Processes, Proceedings of International Conference, University of Sheffield, July 17–20, 1979; The Metalls Soc: London, 1980, 3–15. 75. Zhao, J. Continuous cooling transformations in steel. Mat. Sci. Technol. 1992, 8 (11), 997–1003. 76. Licka, S.; Wozniak, J. Mathematical model for analyzing the technological conditions of hot rolling of steel. Hutnicke Aktuality 1981, 22 (9), 1–49. 77. Dutta, B.; Sellars, C.M. Effect of composition and process variables on Nb(C,N) precipitation in niobium microalloyed austenite. Mat. Sci. Technol. 1987, 3, 197–206. 78. Adrion, H. Thermodynamic model for precipitation of carbonitrides in high strength low alloy steels containing up to three microalloying elements with or without additions of aluminum. Mat. Sci. Technol. 1992, 8, 406–420.

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3 Designing for Control of Residual Stress and Distortion Dong-Ying Ju Saitama Institute of Technology, Okabe, Saitama, Japan

I.

INTRODUCTION

Residual stresses in materials are often produced from metallurgical processes, such as casting, forging, welding and quenching processes, and so on. Usually, the production of residual stresses during metallurgical process depends on changes of thermal sources and volume due to microstructure. Generally, residual stresses of two types can be considered, i.e., macro-residual stresses and micro-residual stresses [1,2]. The macro-type depends on the plastic deformation of solid materials due to rapid non-uniform cooling. And, the strain and deformation due to phase transformation and change of microstructure are the sources of the micro-type residual stresses. We also know that the distortion due to thermal and elastic–plastic deformation and strain as well as change of phase transformation and texture in manufactured materials are important no matter the type of residual stress. Therefore, one of the many important problems is how to control and utilize residual stresses and distortion due to variations of macro- and microstructure in materials for increasing and ensuring strength and quality of products after metallurgical process. To improve the mechanical properties of materials, it is important to know how to raise compressive residual stress and reduce tension residual stress in materials as it is known that the compressive residual stress can increase fatigue strength of materials. Therefore, measurement method and analysis of residual stresses are always developed

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as a conspicuous technology. Many measurement methods of residual stress such as x-ray diffraction, neutron diffraction, rapid drilling method, and so on have been developed in industrial technology [3–8]. However, each measurement technique always has some limitations and problems when used for measuring, for example, the x-ray method only measures residual stresses on surface of materials; on the other hand, in the method of neutron diffraction, a major problem is how to measure the standard lattice spacing d0 of strain-free materials, which consider distortion and strain due to microstructure or texture. In order to address thermal–mechanical behavior in the entire material process, a so-called metallo-thermo-mechanical theory is proposed by Inoue et al. [9–18]. Based on this theory, computer simulation of metallurgical processes can be used as a new technology. This is a critical component of the worldwide effort to develop virtual metallurgical capabilities in order to acquire a better understanding of processing operations and optimize processes with a view to improving quality and reducing production costs. By using this technique, residual stress and distortion in metallurgical process also can be predicted; hence some useful theory and simulation methods can be proposed and introduced in the simulations of various metallurgical processes [19–23]. From these research results, we can obtain useful knowledge to seek more perfect designing for metallurgical process. In this chapter, the metallo-thermo-mechanical theory, numerical modeling and simulation technology considered with coupling of temperature and phase transformation or solidification as well as inelastic behavior involved with elastic–plastic, viscoplastic and creep deformation will be introduced. The theory and simulation technology also are used in metallurgical process, such as heat treatment, continuous casting, and thermal spray coating as well as forging for the control of residual stress and distortion in these processing. This chapter not only presents various simulation methods and results of the residual stress, distortion and thermal– mechanical behavior as well as microstructure according to the peculiarity of each metallurgical process, but also the thermo-mechanical modeling that was verified by comparison with the experimental data, such as the measured temperature, residual stresses and distortion in various metallurgical processes. In the final part of the chapter, some conclusions and remarks which are used in the designing of metallurgical process for control of residual stress and distortion are presented. From these conclusions, we summarize many, yet expected problems and subjects in future metallurgical process and material industry for reference of research.

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II.

METALLO-THERMO-MECHANICAL MODELING FOR CONTROL OF RESIDUAL STRESS AND DISTORTION

There are many physical and chemical phenomena that occur in metallurgical processes. These phenomena do not always act alone on materials; the metallic structures incorporating phase transformation, temperature and stress=strain are also strongly coupled in the process. The metallo-thermomechanics theory are considered with the coupling effect on temperature, stress=strain and phase transformation fields as schematically illustrated in Fig. 1. The coupling effects are indicated as follows: 1. Thermal Stress. The thermal expansion caused by such a temperature gradient is restricted by the shape of a solid body, thus generating thermal stress. 2. Heat Generation due to Deformation. When stress=strain that appears in the case of large inelastic deformation is applied to materials, the energy is partially discharged as heat. 3. Temperature-dependent Phase Transformation. Temperature is the major factor, which determines phase transformation start time. However, in the case of diffusion-type transformations of ferrite, pearlite, and bauxite, the temperature history also affects the phase transformation. 4. Latent Heat due to Phase Transformation. Latent heat generated in the course of phase transformation affects the temperature field.

Figure 1 Metallo-thermo-mechanical coupling during processes involving phase transformation.

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5. Stress (or Strain)-Induced Transformation. The phase transformation behavior is also affected by stress=strain existing in the solid. For example, pearlite transformation time is shortened under tensile stress, and vice versa. Martensite transformation is generated even though a material is processed at a temperature higher than the martensite transformation temperature under the applied stress or strain. 6. Transformation Stress and Transformation Plasticity. Volume dilatation in the work is caused by the phase transformations. When this volumetric dilatation is inhomogeneous depending on the complicated shape of the body, stress and strain are induced, it is defined as transformation stress and strain. The level of such induced stress is comparable to the thermal stress. The effect of transformation plasticity is sometimes important. The details of introducing the governing equations in the framework of thermo-mechanical behavior for describing temperature and stress=strain fields incorporating metallic structures in the heat treatment process are already reported elsewhere, and are applied in welding, casting and so on [24–31]. Based on the theory, a simulation program called ‘‘HEARTS’’ [32,33] for heat treatment process was developed to predict the temperature field, phase transformation, residual stress, and distortion during heat treatment process. The fundamental equations which can be applied in the metallurgical process are summarized in the following.

A.

Mixture Rule

When a material point undergoing a metallurgical treatment process is assumed to be composed of multi-phase structure, an assumption is made that a material parameter w is described by the mixture law [34] w¼

N X I¼1

wI xI

and

N P

xI ¼ 1

ð1Þ

I¼1

where xI denotes the volume fraction for the Ith phase. B.

Heat Conduction Equation

The local energy balance or the first law of thermodynamics is usually given in terms of the internal energy e ¼ gþTZ þ (sijeij)=r, as Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

re_ ¼ sij e_ ij

@hi @xi

ð2Þ

with stress power sij e_ ij . Here, r and hi are the density and heat flux, respectively. Z is the entropy of the thermodynamic state. Introducing the expression for specific heat c ¼ T(Z=T), Eq. (2). is reduced to a heat conduction equation X @ @T _ k rI lI x_ I ¼ 0 ð3Þ sij e_ pij þ rcT @xi @xi where k and lI denote the coefficients of heat conduction and the latent heat produced by the progressive Ith constituent. The boundary conditions of heat transfer on the inner surface are assumed to be k

@T ni ¼ hðTÞðT Tw Þ @xi

ð4Þ

where h(T) is a function dependent on temperature. Tw denotes the heat transfer coefficient and the temperature of coolant on heat transfer boundary with unit normal ni, respectively. C.

Diffusion Equation of Carbon Content

Carbon content during carburizing process is arrived at by the diffusion equation @ @C _ C¼ D ð5Þ @xi @xi where C is the content in the position xi-direction, D is the diffusion constant determined by the boundary condition being specified by the reaction across the surface layer D

@C ni ¼ hc ðC Cs Þ @xi

ð6Þ

where hc and Cs are the surface reaction rate coefficient and the known content of the external environment, respectively. D.

Constitutive Equation

In order to simulate distortion due to variations of temperature, phase transformation, and inelastic deformation in metallurgical processes, many

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constitutive models which are capable of representing the relation of stress and strain including macro- and microstructures are proposed and established [35–52]. A few constitutive equations to be used in simulation of metallurgical processes are introduced in this chapter. Total strain rate e_ ij is assumed to be divided into elastic, plastic, thermal strain rates and those by structural dilatation due to phase transformation and creep such that tp c e_ ij ¼ e_ eij þ e_ pij þ e_ Tij þ e_ m ij þ e_ ij þ e_ ij

ð7Þ

Elastic and thermal strains are normally expressed as eeij ¼

1þn n sij skk dij E E

ð8Þ

and eTij ¼ aðT T0 Þdij

ð9Þ

with Young’s modulus E, Poisson’s ratio n and thermal expansion coefficient a, respectively. T0 is the initial temperature of material. Strain rates due to structural dilatation and transformation plasticity depending on the Ith constituent are em ij ¼

N X

ð10Þ

bI xI dij

I¼1

and e_ tp ij ¼

N X

BI hðxI Þx_ I sij

and

hðxI Þ ¼ 2ð1 xI Þ

ð11Þ

I¼1

where bI stands for the dilatation due to structural change. BI denotes the material parameters depending on phase transformation. The plastic strain rate is reduced to the form when employing temperature-dependent material parameters ! N @F @F @F _ X @F _ @F p ^ Tþ xI s_ kl þ ¼G ð12Þ e_ ij ¼ l @sij @skl @T @xI @sij I¼1 with a temperature dependent yield function F ¼ Fðsij ; ep ; k; T; xI Þ

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

ð13Þ

with hardening parameter k, where 1 @F @F @F smn ¼ p þ ^ @k @s @e G mn mn

ð14Þ

The creep strain rate is assumed to follow a simple Norton creep law as 3 ðnmÞ=mecðm1Þ=m sij s e_ cij ¼ A1=m 2 c

ð15Þ

and e are deviatoric stress, equivalent stress, and equivalent Here, sij, s strain, respectively. Either isotropic or kinetic hardening type of yield function F is available to be used in the section. Symbol Ac, n and m are material parameters based on Norton creep law. Either isotropic or kinetic hardening type of yield function F is to be used in this section. In casting and welding processes, we often should consider inelastic deformation incorporating the solidifying behavior of materials. In the solidifying process of materials, there has been substantial development of the so-called ‘‘unified’’ theories of viscoplasticity in which all aspects of inelastic behavior are intended to be represented by the same variable. Consider three types of constitutive models which have some possibility of describing the experimental behavior obtained above. Generally, the total strain rate e_ ij is expressed as the sum of the elastic strain e_ eij and the viscovp e plastic strain rate e_ vp ij , i.e., e_ ij ¼ e_ ij þ e_ ij , where the elastic strain rate is given by Hook’s law. The models for inelastic model are Perzyna’s model [42,43] based on the excess stress theory, and superposition model [52] which are introduced below. The excess stress theory assumes that the viscoplastic strain is produced as e_ vp ij ¼ LhcðFÞi

@F @sij

ð16Þ

where L denotes a viscosity constant of the material. c(F) is a function of the static yield function ðsij ; evp ij ; k; TÞ in stress space involving inelastic , the hardening parameter k and temperature T. As a proposal strain evp ij of the viscoplastic constitutive theory, Perzyna has proposed four kinds of functions for c(F), among which a special case c(F) ¼ F is employed to give the viscoplastic strain rate e_ vp ij , * +n 1=2 3l 3 sij vp e_ ij ¼ skl skl sy ð17Þ 2 2 ð3J2 Þ1=2 where J2 is the second invariant of deviatoric stress sij, and sy denotes the yield stress. In order to deal with a viscous fluid, we choose l ¼ 1=3 m with

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

the viscosity m. When the value of parameter n tends to unity, eqn. (17) which is reduced to a uniaxial stress–strain relation under monotonic tension is then expressed as s ð18Þ e_ vp ¼ lðjsj sy Þ jsj from which the parameter l, or viscosity m is to be identified. n When the Norton’s equation (e_ c¼As ) is adopted to describe creep behavior of material associated eqn. (18), the model can deal with more complex inelastic behavior as a superposition model. E.

Kinetics of Phase Transformation in Metallurgical Processes

In the case of quenching, two kinds of phase transformation are anticipated: one is governed by the diffusionless or martensite mechanism. From a thermodynamic consideration, the formula for this type of reaction from austenite is assumed to be governed by modified Magee’s [53] rule as xM ¼ 1 exp½fðT TM Þ jðsij Þ

ð19Þ

with 1=2

jðsij Þ ¼ A1 sm þ A2 J2

ð20Þ

where TM is the martensite-start temperature under vanishing stress. The parameters A1 and A2 can be identified if we have the data of the martensitic transformation depending on the applied stress. The other type of phase transformation is controlled by diffusion mechanism, and the volume fraction of developing phase such as pearlite may be expressed by modifying the Johnson–Mehl [54] relation as xp ¼ 1 expðVe Þ

ð21Þ

where Ve is defined by Zt Ve ¼

fðT; sij Þðt tÞ3 dt

ð22Þ

0

Here, we separate the function f(T, sij) into two independent functions of temperature and stress as fðT; sij Þ ¼ f1 ðTÞf2 ðsij Þ

ð23Þ

Since the time–temperature-transformation TTT diagram under the applied mean stress sm in logarithmic scale deviates from the one without

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

stress which is represented by the function f(T), the kinetic equation of diffusion type is often applied to the variations of pearlite or ferrite structure in quenching processes. An identification of the function f(T) can be made possible by the use of some experimental data of the structure change. In casting processes, it is important to determine a moving boundary due to solidification as two phase structure with solidus and fluidus [55,56]. However, when we consider solidification of an alloy material, the mixture law also can be applied in the casting simulation. To identify the volume fraction of the solid phase xs during solidification appearing in eqns. (1) and (3), a phase diagram for the alloying system is employed, and the volume fraction of the solid phase xs is assumed to be determined by the Scheil equation [57,58]: xs ¼ 1 f1ð1k0 Þ

and

xl ¼ 1 xs

ð24Þ

Here, f is a dimensional function that is dependent on temperature: f¼

ðT Ts Þ=ms ðT Ts Þ=ms þ ðTl TÞ=ml

ð25Þ

where ml and ms are the gradients of the liquidus and solidus temperature Tl and Ts with respect to the alloying element on the phase diagram, respectively, and k0 is a distribution coefficient representing the segregation effect. When the segregation effect is assumed to be neglected as in the present article, Eq. (24) can be reduced to the simple form xs ¼

ðTl TÞ=ml ðT Ts Þ=ms þ ðTl TÞ=ml

ð26Þ

which is called the lever rule. F.

Algorithm of Finite Element Analysis

The formulated finite element equation system, considering the coupling between increment of nodal displacement fDug and temperature fTg as well as volume fraction of structure xI, can be expressed as ½PfT_ g þ ½HfTg ¼ fQðxI Þ; sij Þg

ð27Þ

½Kðui ÞfDui g ¼ fDFðT; xI Þg

ð28Þ

and

Here, [P], [H] and [K] represent the matrices of heat capacity, heat conduction and stiffness, respectively, and the vectors fQg and fDFg are heat flux, and increments of thermal load. These equations are strongly

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

nonlinear, which are derived by the use of the expression of stress increment vector as ! N N X X 3dec fdsg ¼ ½D fdeg fsg fag dT fbg dxI 2 s I¼1 I¼1 ! N X 1 @ s2 @ s2 dT þ dx fsg þ ð29Þ @xI I S0 @T I¼1 where ec and fsg are equivalent creep strain and deviatoric stress vector. S0 and [D] denote a parameter depending on material hardening and an elastic–plastic matrix based on Mises’ type yield function. Here, the func can be tions depending on temperature and phase transformation a and b written as N X @ @aI xI dTf1g ð½De 1 fsgÞ þ f ag ¼ aI xI f1g þ ð30Þ @T @T I¼1 and g ¼ fb

@ ð½De 1 fsgÞ þ bI f1g @xI

ð31Þ

aI and bI are the coefficients of thermal expansion and dilatation due to Ith phase transformation, respectively. [De] denotes the elastic matrix of materials. In order to treat the unsteady coupled nonlinear FEM equations dependent on time, a time integration scheme ‘‘step-by-step time integration’’ method and a modified ‘‘Newton–Raphson’’ method are introduced in numerical calculation, while an incremental method is used for deformation and stress analysis. Because the heat transfer coefficient is dependent on the variation of the temperature on the boundary of heat transfer, we also use the time step of non-uniform cooling to calculate temperature, phases transformation and deformation fields [59,60]. In the simulation of continuous casting, the finite element method based on the Eulerian coordinate is applied to analyze the velocity, displacement rate vector fug, strain rate e_ ij and stress rate s_ ij . Displacement ui, strain eij, and stress sij can be evaluated by integrating the rate e_ ij , and s_ ij along flow line of velocities which have been verified by Ju and Inoue [61]. A finite volume computational method [62] to simulate large deformation in forging is adopted in this chapter. The advantages of the finite element and the finite volume approaches are combined: it employs a fixed finite volume mesh for tracking material deformation and an automatically refined facet surface (material surface) to accurately trace the free surface of

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

the deforming material. This is particularly suitable for large three-dimensional material deformation such as forging since remeshing techniques are not required. By means of this finite volume method, an approach based on the metallo-thermo-mechanics to simulate metallic structure, temperature, and stress=strain in the forging process associated with strain-induced phase transformation has been developed. The material is considered as elastic–plastic and takes into account the phase transformation effects on the yield stress. The temperature increase due to plastic deformation, heat conduction in the workpiece and dies, heat transfer between workpiece= die and ambient and thermal stress has been analyzed simultaneously. Strain-induced phase transformation, latent heat, transformation stress, and strain are included. This approach has been implemented in the commercial computer program MSC.SuperForge [62].

III.

DESIGNING OF HEAT TREATMENT PROCESS FOR CONTROL OF RESIDUAL STRESS AND DISTORTION

The purpose of the quenching and carburizing quenching of steel parts is to get desired metallurgical structures, hardness and strength of steel parts increased by the cooling rate and change of microstructure in quenching. So, we need to decide the compromise between maximizing hardness and minimizing distortion must often be made. Therefore, it is very important and difficult to select the proper quenching conditions, i.e., quenchant temperature, the method, and the cooling intensity of the quenchant media, etc. [63–65]. In order to obtain the optimum conditions, computer simulation is very useful for the determination of the quenching conditions, because the application of metallo-thermo-mechanical theory is capable of describing the interaction among temperature field, stress=deformation field and microstructure changes in quenching so that the simulation technology has been developed. By using this method based on continuum thermodynamics and the finite element method, several numerical simulations were carried out for the quenching process [66–71]. The simulation of quenching process is so complicated that most of the current research focused on the validity of numerical modeling for designing steel parts. On the other hand, to obtain improved mechanical properties and fatigue strength of machine components, such as gears, and shafts carburizing–quenching process is often used for surface hardening in the industry. However, carburizing– quenching is usually accompanied with carbon concentration and leads to distortion, residual stresses, and hardness of steel parts. The effect of carbon content is especially significant on phase transformation behavior.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

The first part of this section will present the thermal–mechanical behavior included with residual stress and distortion by using quenching conditions on cylinder and ring of carbon steel, which are simulated by an FEM program ‘‘HEARTS’’ [32]. Several techniques [63,71] were used for the estimation of the heat transfer coefficients during water and polymer quenching. The effect of the heat transfer coefficients on the quench distortion and the simulation result will be discussed. The simulation accuracy will be verified by the comparison between the experimental data of the distortion and the simulated results. The second part of the section will present the simulation results of the residual stress field and distortion of a steel gear in carburizing–quenching process. The computer simulation is based on the metallo-thermomechanical theory involving the diffusion of carbon and considering the effects of coupled temperature, phase transformation, and stress=strain fields on carbon component. In carburizing–quenching process, the fields of metallic structures and stress=strain as well as temperature affect each other [67]. A series of theoretical models, taking into consideration the effect of carbon diffusion and distribution is introduced. The accuracy of simulation is also verified by comparison with the experimental data. The predicted results validated the improvement of the hardness and strength of the gear component in carburizing–quenching process. Based on the comparison with the deformation experimental work, the thermomechanical predictions are found to be in good agreement with the experimental results. A.

Residual and Distortion in Carburizing Quenching of Cylinder

1. Experimental Method of Carburizing Quenching Cylinder specimens of 20 mm diameter and 60 mm length were used to verify the accuracy of the simulation. The carbon content of carburizing environment was 1.3% and the aim is to reach 0.9% carbon content on the surface of the cylinder. To detect the temperature changes during the process, four metallic sheathed thermocouples were attached to the specimen which are shown in Fig. 2. The entire carburizing–quenching process is shown in Fig. 3. The specimen was heated and carburized in a furnace and then quenched in the oil bath. In the cooling process, the temperatures were detected by the thermocouples attached to the specimen, and the signals were fed into a personal computer after the A=D conversion. The changes of the thickness and the diameter of the specimen were measured with a digital indicator and a micrometer caliper.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 2 The specimen and sheathed thermocouples.

Figure 3 The carburizing–quenching process.

2. Models of Simulation The simulation model in carburizing–quenching process is a steel cylinder of 20 mm diameter, 60 mm length and 0.45% carbon. It is assumed that the model is located in a uniform coolant. Then, the finite element model belongs to an axisymmetrical problem. As an initial step of the heat treatment process, calculations for the heating and carburizing process were used to simulate thermal stress field, thermal distortion as well as carbon distribution in the model. The quenching process of the model was started from the initial temperature 8508C and the model was cooled to 308C with oil. The heat transfer coefficients h during quenching were calculated as a function of temperature by the methods mentioned below and were used for the simulation as the surface boundary condition in Eq. (4). 3. Identification of Heat Transfer Coefficients It is important to determine the heat transfer coefficients in the quenching process of metal parts for numerical simulation. However, it is rather difficult to evaluate heat transfer coefficients during quenching of actual steel

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

parts which depend on not only the quenchant but also the shape, size, surface condition, and thermal properties of parts, etc. It is, therefore, very difficult to evaluate the heat transfer coefficients in quenching of steel parts. Some approximate methods are estimating the coefficients from the cooling curve data of standard probes which are used for evaluation of the cooling power of liquid quenchants. We have already reported the availability of the lumped-heat-capacity method for the estimation of the heat transfer coefficient from the cooling curve data of the JIS silver probe (pure silver solid cylinder of 10 mm diameter by 30 mm length, Japanese industrial standard K 2242 [72]) which has a high thermal conductivity. A computer program ‘‘LUMPPROB’’ based on the lumped-heat-capacity method was developed [73]. On the other hand, it was confirmed that the inverse method is more suitable for estimating the heat transfer coefficients from quenching data of the ISO probe (Inconel 600 alloy solid cylinder of 12.5 mm diameter by 60 mm length, International standard ISO 9950 [74]), because of its low thermal conductivity. We developed a computer program ‘‘InvProbe-2D’’ [75], which uses both a lumped-heat-capacity method and a two-dimensional inverse method with the least residual method. In this section, we used these programs for the estimation of the heat transfer coefficients during quenching. Furthermore, more precise heat transfer coefficients were estimated by a trial-and-error method, in which the calculation of cooling curves and modification of the surface boundary condition were repeated until the simulated cooling curves gave good agreement with the measured cooling curves of the steel specimen. 4. Carbon Diffusion and Distribution Fig. 4(a) shows the changes of carbon content with time in different positions during the carburizing process. The carbon content in the surface of the steel cylinder increases from 0.45% to 0.9% in 250 min. Fig. 4(b) and (c) compares the difference of carbon content of the steel cylinder before and after the carburizing process. The carbon content decreases being reserved in heating furnace for 35 min after carburization, which shows the effect of diffusion on carbon content distribution. 5. Heat Transfer Coefficients and Cooling Curves The heat transfer coefficients used for the simulation are shown in Fig. 5. The coefficients are estimated by using the inverse method program ‘‘InvProbe-2D’’ and the cooling curve data of the ISO Inconel 600 alloy probe. The cooling curves that were calculated with these heat transfer

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 4 The distribution of carbon after carburizing and heating.

Figure 5 The heat transfer coefficient.

coefficients are shown in Fig. 6. The cooling curve of the center point in the steel specimen shows good agreement with the measured one. And those near the boundary have a little difference from the measured one due to the influence of boundary of the steel cylinder specimen. 6. Prediction of Martensite Distribution and Equivalent Stress Martensite distribution and equivalent stress with consideration of the transformation plasticity in carburizing–quenching process are predicted and shown in Fig. 7. From the result of Fig. 7(a), we know that martensite is mainly generated near the surface due to the increase of the carbon

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 6 Calculated and measured cooling curves in different position.

Figure 7 Distribution of (a) martensite and (b) equivalent stress.

content. On the other hand, depending on measured hardness as shown in Fig. 8, distribution of martensite after carburized–quenching also is verified. 7. Distortion During Quenching Figure 9 shows the distortion of the calculated and the measured diameter of the steel cylinder after carburizing–quenching. Except for the influence of surface boundary condition, the calculated distortion of the center part of the cylinder is in good agreement with the measured value as shown in Fig. 9. However, because identification of the heat transfer coefficient on the corner of the cylinder is difficult, prediction of the distortion on the corner remains to be solved.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 8 Measured hardness in center and surface.

Figure 9 The calculated and experimental diameter expansion of the steel cylinder after carburizing–quenching.

8. Effect of Transformation Plasticity To check the effect of the transformation plasticity on the simulation result, simulation results which were calculated with or without the transformation plasticity are compared. In Figs. 10 and 11, it is shown that residual stresses considering the transformation plasticity are much less than without considering transformation plasticity. These results show the importance of considering transformation plasticity in the simulation of carburizing– quenching process.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 10

The calculated and experimental residual stress on the surface.

Figure 11 Comparison of residual stresses with and without consideration of transformation plasticity.

B.

Residual Stress and Distortion in Carburizing–Quenching of Gear

Based on the series of governing equations above, a finite element program called ‘‘HEARTS’’ was developed to predict the temperature field, carbon diffusion, phase transformation and distortion during carburizing–quenching process. The simulation model in carburizing–quenching process is a JISSCM420 steel gear with edge circle diameter of 36 mm, teeth number 16 and module 2 mm as seen in Fig. 12. Figure 13 shows the variation of TTT-curves of the material when carbon content is changed to 0.8% by using

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 12

Illustration of gear specimen.

Figure 13

Variation of TTT curves depending on carbon component.

the carburizing–quenching process as seen in Fig. 14. The identified heat transfer coefficient is shown in Fig. 15. It is assumed that the model (Fig. 16) is located in a uniform heating and cooling process as in Fig. 14. Then, the finite element model belongs to an axisymmetrical problem. As an initial step of the heat treatment process, calculations for the heating and carburizing process were used to simulate thermal stress field, thermal distortion as well as carbon distribution in the model. The quenching process of the model was started from the initial temperature 8508C and the model

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 14

Process conditions of carburizing–quenching.

Figure 15

Heat transfer coefficient depending on temperature.

was cooled to 308C with oil. The heat transfer coefficients h during the quenching were calculated as a function of temperature by the methods mentioned below and used for simulation as the surface boundary condition. 1. Carbon Diffusion and Distribution Fig. 17 shows the changes of carbon content in different positions with time during the carburizing process. The carbon content in the surface of the steel gear increases from 0.45% to 0.9% in 250 min. Fig. 18(a) and (b)

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 16

FEM model of gear.

Figure 17

Variation of carbon contents in different position.

compares the difference of carbon content of the steel gear before and after the carburizing process. The carbon content decreases since it is present in heating furnace for 35 min after carburization, which shows the effect of diffusion on the carbon content distribution. 2. Prediction of Martensite Distribution Martensite distributions in carburizing–quenching process are predicted and are shown in Fig. 19. Fig. 19 shows that martensite is mainly

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 18

Distribution of carbon after carburizing and heating.

Figure 19

Simulation of martensite distribution.

formed near content.

the

surface

due

to

an

increase

of

the

carbon

3. Residual Stresses In order to predict the residual stresses in the gear, the simulation results were calculated taking into account the strain due to phase transformation. From Fig. 20, we come to know that the residual stresses are greater at the corner of the gear surface. These results show the importance of considering the transformation plasticity in the simulation of carburizing–quenching process.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 20

Equivalent stress.

4. Distortion after Quenching Figure 21 shows the distortion of the calculated and the measured diameter of the steel gear after carburizing–quenching. And except for the influence of surface boundary condition, the calculated distortions of the center part of the gear are in good agreement with the measured value as shown in Fig. 22. However, because identification of the heat transfer coefficient on the corner of the gear is difficult, prediction of the distortion on the corner remains to be solved.

Figure 21

Deformation of gear.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 22

IV.

Deformation on surface of gear teeth.

DESIGNING OF CONTINUOUS CASTING FOR CONTROL OF RESIDUAL STRESS AND DISTORTION

In order to optimize material metallurgical processes, such as casting and welding during solidification, it is important to determine the residual stress after these processes for evaluating the mechanical properties and strength of materials and to optimize the operative conditions in manufacturing [76–78]. However, the formation of residual stress not only depends on the thermo-mechanical behavior and processing effect due to the variation of in micro-=macro-structures during the manufacturing of materials, but also on the interaction of heat conduction, change of phase transformation due to solidification, and stress=strain. Especially, to describe variation of the mechanical behavior from viscous fluid to solid and the mixture domain in the material due to solidification, a unified constitutive model incorporating with solids and fluids of metal is proposed [64]. In order to solve the above-mentioned problems, this chapter presents some developments of the thermo-mechanical theory and numerical analysis method incorporating solidification of material to simulate the residual

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

stress formation during casting. A unified inelastic constitutive relationship capable of describing both elastic–viscoplastic solids and viscous fluids to apply simulation of the casting process was proposed and verified by experimental and numerical results. On the other hand, a proposal based on the finite element method to couple temperature, stress fields as well as deformation during solidification was presented. Depending on the simulations of the continuous or semi-continuous casting, the mechanism of the residual stress formation during these casting processes can be represented. The thermo-mechanical modeling was also verified by a comparison with the experimental data, such as the measured residual stress and variation temperature in casting. Vertical semi-continuous direct chill casting process is one of most efficient methods to produce ingots of aluminum alloys and other metals. It is beneficial for optimizing the operating conditions to simulate thermo-mechanical field in the solidifying ingot. So many reports have been published concerning such analyses of the temperature distribution incorporating solidification by finite element method, but a few papers treat the induced stress=strain field. Simulations of thermal stress in continuous casting slab were made by using elastic–plastic constitutive models [79,80], and viscoplastic stresses [81–84] were simulated based on the solidification analysis by Williams et al. [31]. However, in their studies, the influence of casting speed was neglected, so that the numerical simulation along with the variation of casting conditions could not be realized. In order to solve this problem, Ju and Inoue [62] proposed a numerical simulation method by the Eulerian coordinate, and application to the continuous casting process of steel slab was performed. A.

Residual Stress Formation During Semi-continuous Casting

The aim of this section is to apply the coupled method of temperature and stresses incorporating solidification developed for semi-continuous direct chill casting of aluminum alloys. When the bottom block plate is located at the upper position and the length of the growing ingot is small, the temperature, liquid–solid interface, and stresses in the ingot vary with time, both in the sense of space and of material. However, when the ingot becomes long enough, the physical field in the upper part is regarded to be time-independent or steady in the spatial coordinate fixed to the system. In the first part of this section, a steady heat conduction equation with heat generation due to solidification is formulated in a spatial coordinate system when considering the material flow. A numerical calculation for the temperature in the solidifying ingot as well as the simulation of the location of liquid–solid interface is carried out by a finite element technique.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Most metallic materials at low temperature may be treated as an elastic–plastic solid. However, if they are heated beyond the melting point, the materials can be regarded as a viscous fluid, and they behave in a timedependent inelastic manner at high temperature close to the melting temperature. Therefore, a unified constitutive model needs to be established to describe the elasto-plastic and viscoplastic behavior of the solidified part of the ingot as well as the viscous property of the liquid state. Taking into account the effects of such phenomena, a modification of Perzyna’s constitutive model similar to the one in other sections is presented in the second part of this section, and some experimental results of the viscosity appearing in the model are presented for a Al–Zn type alloy. By using the model, elastic–viscoplastic stresses are calculated for the ingot to establish the residual stress distribution, and are verified by the measured data from a hole-drilling strain-gauge technique. Finally, results of a numerical simulation are presented on the influence of operating conditions on temperature and stresses, such as ingot size, casting speed, and initial temperature, to provide fundamental data for optimizing the operating condition.

1. Finite Element Model and Casting Conditions The theory and the procedure developed above are now applied to the simulation of the vertical semi-continuous direct chill casting process shown schematically in Fig. 23. The material treated is a Al–Zn type alloy with 5.6% zinc and 2.5% magnesium. A quadrilateral finite element mesh pattern of 600 elements with 1941 nodes illustrated in Fig. 24 is employed for both analyses of temperature and stress fields. The boundary condition for heat conduction is assumed in such a way that the temperature of the meniscus of molten metal is prescribed to be w0, and that heat is insulated along the central line and the bottom of ingot as well as the surface contacted with the refractory. The cylinder facing the mold is regarded as the boundary Sq on which heat flux is given. The other part of the surface Sh is given by a heat transfer boundary due to the cooling of water. Figure 25 depicts the measured heat flux q absorbed by the mold, and heat transfer coefficient h depending on flow rate of water TW is shown in Fig. 26. Other data used for temperature calculation incorporated with solidification are shown in Table 1. Characteristic results of calculated temperature and residual stresses for an ingot of 1 m in length with the diameter of 240 mm are compared with experimental data to verify the method. Simulations in other cases of different operating conditions such as casting velocity, size of the ingot, and cooling rate are also made.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 23

Schematic view of semi-continuous vertical direct chill casting.

2. Results of Simulation Figure 27 indicates a bird’s eye view of the isothermal representation of calculated temperature distribution. The lines denoted by Tl and Ts in the figures are the liquidus and solidus temperature, respectively. The data is replotted to give the temperature change at the center and on the surface, while the circles represent the measured temperature by thermocouples as shown in Fig. 28. The fact that the calculated temperature on the surface coincides well with the measured data may indicate the validity of the simulation method. Change of the volume fraction xs at four characteristic points along the distance from meniscus is represented in Fig. 29, which may give information on the progressing mode of solidification and thickness of solidified shell.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 24 Finite element mesh pattern for semi-continuous vertical direct chill casting.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 25

Variation of heat flux from top of the mold.

Simulated results of temperature and mode of solidification presented in the above analysis of stresses was carried out on the entire area of the ingot, including the molten metal, using the finite element method based on the elastic–viscoplastic constitution model. The displacement mode is depicted in Fig. 30. The contour of radial, tangential, and axial stress distributions sr, sy, sz are shown in Fig. 31. The contours of stress distribution are represented in Fig. 32. Examples of the calculated stress distribution by elastic–viscoplastic constitutive model and the one by time-independent elastic–plastic model are shown in Fig. 33. When compared with each other, the viscoplastic stress analysis gives smaller results, at least on the surface, than elastic–plastic stresses. The stresses are found to be generated at the location where the solidification starts (see Figs. 31 and 32), and the radial distribution becomes steady owing to the flatter temperature distribution. In order to examine this effect, the stress distributions at several locations are given in Fig. 34, in which the distribution at the end of the ingot (Fig. 34d) can be regarded as residual stresses. Circles in the figure indicate the experimentally measured residual stresses by a hole-drilling strain gauge method [7]. The fact that the experimental data coincide well with the analytical results suggests the validity of the simulation procedure based on viscoplasticity. As is seen in Fig. 34 where the shear stresses are insignificant in the area

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 26 Distribution of heat transfer coefficient depending on discharge of cooling water.

of molten state, the normal stresses sr, and sz (see Figs. 31 and 33) are regarded to be hydrostatic stresses, which means that the constitutive equation employed here reveals to modify deformation of the liquid. 3. Simulations for Other Operating Conditions This procedure may be applied to other cases of operating conditions. Hereafter, the focus is on the effect of temperature and stress distributions on the casting speed, size of the ingot and cooling condition. Figures 35 and 36 represent examples of temperature profiles for different casting speed and the radius of ingots with various cooling rate. The effect of discharge of cooling water on thickness of the mussy zone at the center is summarized in Fig. 37. The effects of casting speed and ingot radius on the stress s are represented in Figs. 38 and 39, respectively, and the relation between stresses and casting speed is summarized in Fig. 40. The simulated stresses varying with the discharge of cooling water are also plotted in Fig. 41. The calculated results shown above seem to simulate the characteristic of temperature and stresses depending on the operating

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Table 1

Material Properties of Aluminum 7075

Physical item Heat conductivity Density Specific heat Latent heat due to solidification Casting speed Liquidus temperature Solidus temperature Gradient of liquidus line Gradient of solidus line Young’s modulus Poisson’s ratio Viscosity

Initial yield stress Hardening coefficient Thermal expansion coefficient Dilatation due to solidification

Value kl ¼ 0.0425; ks ¼ 0.0125 þ 0.0583T r ¼ 2.8 103 cl ¼ 0.015 þ 0.00173T cs ¼ 0.083 þ 0.00267T ls ¼ 93.16

Unit cal=(mm 8C) g=mm3 cal=(g 8C)

V ¼ 80.0 Tl ¼ 638

cal=g mm=min 8C

Ts ¼ 600 ml ¼ 3.69

8C 8C=%

ms ¼ 9.09

8C=%

El ¼ 500.0 Es ¼ 75000.0 – 76.3T n ¼ 0.33 m ¼ 3700.0 0.007178T2 21.1698T 10160.7 sv0 ¼ 2.0 v0 150.0 – 0.428T H0 ¼ 350.0 – 0.13333T H0 ¼ 330.0–1.683(T150) H0 ¼ 0.132 al ¼ 33 106 as ¼ 21.8 106 þ 0.2T 107 b ¼ 7.5%

Temperature range

MPa MPa s

T 3468C T 3468C

MPa

T 3468C T < 3468C T 1508C 150 < Ta < 3468C T 3468C

MPa

l=8C

conditions. If the data of such a simulation at different operating conditions are accumulated as shown in Figs. 35–39, the possibility of optimizing the design of the system would be realized.

B.

Residual Stress Formation During Strip Continuous Casting by Twin-Roll Method

The continuous strip casting technology by twin-roll method is a promising technology that not only saves energy, but also reduces production costs in the manufacturing of material. However, there are many difficulties in

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Figure 27

View of the calculated temperature profile.

Figure 28

Temperature variation at the center and surface of the ingot.

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Figure 29

Volume fraction of solid along the distance from meniscus.

controlling the quality of the strip because of the existence of the deformation of the strip itself, due to thermal expansion or thermal stress. There are two key points: firstly, if the solidification is completed before the liquid reaches the minimum clearance point between the rolls, then the strip will occur at a fixed gap. Hence, one of the key points is controlling of

Figure 30

View of deformation.

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Figure 31

View of stress distributions.

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Figure 32

Iso-stress contours.

solidification. Another key point is that the viscoplastic deformation incorporating material flow must be considered in this thermo-mechanical process. 1. Continuous Casting System by Twin-Roll Method The twin-roll continuous casting system is schematically illustrated in Fig. 42(a). In this process, molten metal is between the two rolls rotating in opposite directions with same angular velocity. The level of the molten metal is always kept constant by overflowing the excess molten metal from the nozzle. As soon as the molten material is poured into the rolls, solidification takes place on the roll surface, which is cooled by circulating water inside the roll. Therefore, the problem then is to find this steady solidification profile and the distribution of temperature and fluid velocities in both the liquid phase and the solid phase. On the other hand, due to the symmetry to the central line, half of the model shown in Fig. 42(b) is treated for the analysis.

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Figure 33 Calculated stresses by (a) elastic–viscoplastic model and (b) elastic– plastic models.

2. Analytical Models and Parameters The procedure developed above is now applied to the simulation of the thin slab casting process under the same operating conditions. The results are summarized as follows. Figure 43 represents the finite element descritization of the whole region of the strip and roll. The surface of roll as well as the contacted boundary with the roll and strip is assumed to belong to

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Figure 34

Stress distribution in several sections of ingot.

heat transfer boundary and the surface of the strip to the heat radiation boundary. In order to verify the numerical analysis method proposed in Section 2, continuous casting of SUS304 steel is taken into consideration in this section. In continuous casting process of SUS304, the thickness of the slab is 1 mm, and two casting speeds are used Vc ¼ 400 and 600 mm=sec. 3. Calculated Results Simulated results of steady temperature field both in the strip and roll is shown in Fig. 44(a) and (b) for the casting speeds of 400 and 600 mm=sec.

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Figure 35

Isothermal lines by effect of casting speed.

sec. Temperature distribution along the central line and surface is plotted in Fig. 45. The fraction of solid phase in solidified region of the strip with liquidus and solidus temperatures Tl ¼ 14608C and Ts ¼ 13998C is depicted in Fig. 46. In the early stage of rapid cooling by the roll, the solidified shell is seen to grow gradually toward the central part. The change in casting speed is known to affect the distribution of temperature and shell thickness. As the casting speed becomes faster, the position of the liquidus line moves downstream. Figs. 45 and 46, shows that the temperature distribution on surface of slab at the roll outlet presents violent fluctuation

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Figure 36

Isothermal lines by effect of ingot radius.

due to latent heat generation by the solidification domain. When the casting speed Vc is raised, the temperature fluctuation towards a small range is present on the surface of the slab. The distribution of the horizontal stress sx from meniscus to the kissing point at the roll outlet is represented in Fig. 47. From these figures, the high-level stress field by rapid cooling is found to occur near the surface of the shell, and the equivalent stress distribution on the surface of the slab at roll outlet also presents violent fluctuation due to the temperature fluctuation. The equivalent stress analysis results based on several constitutive equations are plotted in Fig. 48. In the section of slab at the roll outlet, calculated equivalent stress by three types of constitutive equations is

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Figure 37 Relation between thickness of mussy zone at the center depending on discharge of cooling water.

approximated to the same distribution. However, when the casting speed is lower, the effect of creep strain is evident. V.

DESIGNING OF THERMAL SPRAY COATING FOR CONTROL OF RESIDUAL STRESS

Plasma-spray coating is an important method by which a new functional layer can be produced on material surface [85,86]. In the spray coating process, solidified particles form thin lamellae whose microstructure depends on the particle cooling rate during solidification. Indeed, lamination of several kinds of materials deposited by laser thermal spray coating leads to an increase of the strength of the structural components, such as plates, and cylinders, especially in the case when exposed to severe temperature gradient. However, the residual stresses at an interface between multilayer after coating play an important role that affects thermo-mechanical properties of the materials, since it is associated with the growing liquid boundary due to the supply of the molten material and also from the moving liquid–solid interface depending on the progress of phase transformation. It is also necessary to consider the effect of coupling between

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Figure 38

Stress distribution by effect of casting speed.

temperature and stress=strain fields and the phase transformation, or solidification in this case. Some open problems still remain in the development of a mathematical model capable of treating the growing boundary of molten state and a moving interface between liquid and solid phases as well as the evaluation of residual stresses. There are three complicated aspects to be considered: The first one is that the spray coating process is nonlinear problem with respect to time and location, and the second is that the solidifying process plays an important role in the simulation of temperature and stresses field. The third is how to deal with the difference in mechanical and physical properties of the material in each layer. To solve the first and second problems, a scheme for numerical analysis by the finite element method has already been proposed by the authors [86]. This chapter shows the simulation of temperature and stress=strain induced in the layers of the plate with progressive domains based on the metallo-thermo-mechanics, and a finite element scheme is proposed to evaluate the change of both fields. Heat input due to successively pouring

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Figure 39 Stress distribution depending on effect of ingot diameter and cooling water rate.

molten metal is introduced in the heat conduction equation coupled with mechanical work and latent heat generation by solidification. Simultaneously, a method of stress analysis using an elastic–viscoplastic constitutive relationship capable of describing the mechanical behavior of both solid and liquid is proposed. Examples of the numerical calculation of temperature with solidification mode and residual stresses in the multi-layer plate in the course of the spray coating are presented, and the validity of the calculated results is discussed in comparison with the x-ray experimental results. A.

Experimental Procedure of Spray Coating

Generally, from the viewpoint of continuum thermomechanics, the spray coating process of material has many complicated phenomena which are affected by the interaction between temperature, stresses, and solidification incorporating rapid cooling, and the state in the solidifying material termed

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Figure 40

Relation between stresses at the center of ingot and casting speed.

as ‘‘mushy zone’’ which is a mixture of solid and liquid phases. Figure 49 illustrates an example of spray coating system, which is developed to fabricate laminated plate. In most cases of the spray coating process, after the spray layer is solidified completely, the other kind of material is poured onto the substrate so that the inner boundary grows and the interface of molten state moves toward spray layer direction. In the spray coating process, solidifying material in the growing domain undergoes a variation of mechanical quantities, such as mass, momentum and energy as well as the change of material properties due to phase transformation from liquid to solid state. The complicated interaction between temperature and inelastic deformation, in this case, is to be taken into consideration. B.

Numerical Model and X-Ray Residual Stress Measurement

1. Modeling of Numerical Simulation To verify the validity of the theory and the procedure stated above, simulation of the fields of temperature and solidification mode and the stress

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Figure 41 water.

Relation between stresses at the center of ingot and discharge of cooling

distribution are performed over the course of the spray coating process of laminated plates with two layers. The, assumption is made that both ends of laminated plate are constrained during the spray coating, and that the laminated plates are large enough, so that a growing model of two-dimensional finite element is proposed to interpret the experimental phenomena of the spray coating process and to compute the interfacial thermo-mechanical behavior between the impinging particles and the surface of substrate just beneath them. A model of the spraying layer represented by a flat disk of 30 mm diameter and 0.5 mm thickness of initially uniform temperature which is put into contact with the substrate elements is shown in Fig. 50. When the numerical analysis is started, the growth elements incorporated with the impinging particle from the spraying direction were put into the substrate. In this analysis, the growth model is represented by an axisymmetrical problem. Thermal flux entering and leaving each element as well as the latent heat liberated within the elements themselves during the solidification process is evaluated and the resulting element temperature is computed after each successive time increment. To simulate the spray coating processes, it is assumed that the different materials are successively poured into the substrate, i.e., the different

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Figure 42

View of (a) twin-roll casting system and the (b) model for simulation.

material is supplied after the material in the outer layer is completely solidified. On the outer surface along spraying direction, the heat radiation boundary conditions was set on the initial step of the coating, and heat transfer condition was set on the cylinder surface of the axisymmetrical model, respectively. C.

Properties and Coating Condition of Specimen Materials

Laminated layers are deposited on a stainless steel (SUS304) substrate of 5 mm thickness. In this work, the layer thickness and layer materials produced were: 0.50 mm for stainless steel. The specified thickness was obtained when spraying was performed 10 times. Table 2 shows the components of these wires which are generally used for carbon dioxide arc welding. Table 3 shows the conditions of the spray coating process. The thermo-physical properties of the wire materials used for temperature and stress calculation incorporated with solidification are shown in Tables 4 and 5, respectively [69]. It is assumed that the properties of substrate are the same as those of the wire. The heat transfer coefficient

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Figure 43

Mesh of finite element model.

for air on the surface of the model is chosen to be h ¼ 2.78 103 (cal=(mm2 sec deg)). The thermal radiation coefficient G ¼ 7.028 107 (cal=(mm sec K)) is used for the model. Depending on the inelastic constitutive model of Section 2, the inelastic strain rate can be given by a viscoplastic relationship. Here, the viscosity which described the viscoplastic model of wire material (stainless steel) is shown in Fig. 50.

D.

X-Ray Residual Stress Measurement

To measure the residual stresses in the spray coating process, CrKa characteristic x-rays were used. Diffraction planes and angles were (2 1 1) and 2y0 ¼ 1568 for the stainless steel SUS304. Surface roughness of the coated layer was about 6.5 mm. These values might be too large for x-ray stress measurement to provide reliable results. However, the parallel beam method could give stress values with sufficient accuracy on such rough surface. Before x-ray stress measurement, electropolishing conducted to remove an

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Figure 44

Distribution of temperature in strip and roll.

oxide-film from the layers. Stresses were measured parallel and perpendicular to the spray traveling direction. The x-ray measuring conditions are shown in Table 6. The full width at the half-maximum method was used to determine peak positions. We measured the residual stresses in a phase with 2 1 1 diffraction and g phase with 2 2 0 diffraction. The stresses were obtained by the sin2 c method. The c-diffractometer method was used for the measurement of residual stresses. E.

Verification and Discussion of Simulation Results

An example was used for simulating thermo-mechanical behavior and residual stress during the spray coating. Figure 51 shows the variation of temperature distribution on the central element of spraying surface and outside surface of the layer. From these results, we arrive at the temperature difference between the central element and the outside surface of the spraying layer due to the solidifying process. The distribution of temperature on the total domain dependent on time is shown in Figs. 52 and 53. The volume fraction of solid and the variation of the solidified thickness are depicted in Figs. 54 and 55, respectively. These figures, show that the temperature on the central element tends to decrease slowly by the latent heat generation

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Figure 45

Temperature variations at center and surface of strip.

Figure 46

Distribution of solid fraction.

due to solidification and also by the heat supply by the successively poured material followed by the rapid temperature decrease at the end of solidification. Difference in heat conductivity due to the temperature difference reveals the influence on the cooling rate and mode of solidification. As for the results of stress analysis, residual stress is represented in the following figures, in which increasing stress reduces fluctuation or jump depending on the solidification and growing domain. Distribution of residual stresses sr on the radial direction is shown by the lines in Fig. 56. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 47

Distribution of stress sx.

The data are compared with the experimental results represented by the same condition of the process. Relatively reasonable agreement between both values is seen even in the region with fluctuation of stresses on the interface boundary between the spraying layer and the substrate. The distributions of residual stress sy and sz are shown in Figs. 57 and 58. Here, the jump behavior of stresses on the interface is presented by these simulated results. Thus, it is important to reveal the damage of the spraying layer based on the theory and numerical method.

VI.

DESIGNING OF FORGING PROCESS FOR CONTROL OF INTERFACIAL STRESS

A.

Basic Description

A typical industrial metal component may be manufactured by forging and heat treatment. In the design of forging processes, information such

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Figure 48

Dependence of constitutive relationship on stress distribution.

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Figure 49

Schematic diagram of laser spraying.

as material flow in the dies, level of die fill, defects, strain, stress, temperature distribution in the work pieces and the dies, and forging force is necessary. In the subsequent heat treatment operations, information on combination of microstructure, residual stresses, and dimensional accuracy in the final product is also very important. Such information may be obtained by numerical simulation [87–90]. The currently available commercial (and also academic) codes of forging are usually based on the finite element method. For a forging process where the metal is plastically deformed under high pressure into machine parts with high-strength performance, the finite element method sometimes exhibits weaknesses which must be carefully monitored

Finite element meshes usually become over-distorted; hence, autoremeshing is then necessary to complete the simulation. But the auto-remeshing technology for three-dimensional problems is not so robust and is also very time consuming.

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Figure 50

Coefficient of viscosity based on viscoplastic model.

Even for two-dimensional elastic–plastic problems, the remeshing may lead to an erroneous result [70]. Each remeshing step will involve a loss in volume, which is not acceptable for a considerable forging simulation.

On the other hand, the finite element method is suitable for stimulating the heat treatment process after forging because it is principally a relatively small deformation process [88]. But when deformation-induced phase transformation during the process of metal forming (large deformation like forging) is taken into account, the finite element method will meet the same problems of remeshing and loss of volume. In this section, a method to simulate forging and subsequent heat treatment processes is described. The advantages of the finite element and the finite volume approach are combined: it employs a finite volume mesh for tracking material deformation and an automatically refined facet surface (material surface) to accurately trace the free surface of the deforming material. This is particularly suitable for large three-dimensional material deformation such as forging because remeshing techniques are not required. Table 2

Substrate Wire

Composition of the Substrate and Wire (wt%) C

Mn

Si

Cr

Ni

0.06 0.04

– 1.90

– 0.46

18 20.1

0.4 8

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Table 3

Conditions of Spray Coating

Laser output Wire feed Inner gas pressure Out gas pressure Spraying distance Nozzle Assist gas

3.0 (KW) 5.1 (m=min) 5.0 (kg=cm2) 5.0 (kg=cm2) 100 (mm) Double nozzle Argon

This finite volume method provides an approach based on the ‘‘metallo-thermo-mechanics’’ to simulate metallic structure, temperature and stress=strain coupled in the heat treatment process such as quenching. The material surface utilizes the advantages of the finite element method to ensure a level of accuracy for the small deformation process in the frame of the finite volume method. This approach also provides latitude for implementation of phase transformation analysis coupled with forging process in the future.

B.

Validation Example

In this section, we consider forging followed by subsequent quenching of an S45C carbon steel rod used in a ship engine. The outline of the basic numerical model is shown in Fig. 59. In the first process, the rod is forged from a round billet of 524 mm diameter and 500 mm length between two closed dies. A threedimensional model is necessary for the simulation. In the second process, the rod goes through the water spray quenching. The problem is an axial symmetric model. (1) In the forging process, the initial temperature of the billet is 12508C. Since the material is above the recrystallization temperature, the influence of strain upon flow stress is insignificant, while the influence of

Table 4

Thermal Properties of Wire

Heat conductivity (cal=(mm s deg) Density (g=mm3) Specific heat (cal=(g deg)) Latent heat (cal=g) Temperature of solidus and liquidus (deg)

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k ¼ 1.83 103þ1.02 106T rs ¼ 7.9 106; rl ¼ 7.4 106 c ¼ 65.2 þ 9.77 106T ls ¼ 65.0 Ts ¼ 1432; Tl ¼ 1449

Table 5

Mechanical Properties of Wire

Young’s modulus (MPa) Yield stress (MPa)

Poisson’s ratio Thermal expansion (L=deg) Dilatation due to solidification (%)

Es ¼ 2.5 1051.73 102T; El ¼ 2264 sy0 ¼ 280.35–1.4T þ 5.75 103T21.1 103T3 þ 9.8 109T4 4.14 1012T5þ6.7 1016T6 n ¼ 0.35 as ¼ 12.76 108; al ¼ 12.67 1012 b ¼ 0.25

strain rate becomes increasingly important. The flow stress for hot forging is defined as follows: sy ¼ C_eM

ð32Þ

where C and M depend on equivalent strain and temperature listed in the literature [90]. The heat transfer between workpiece and die plays an important role in hot forging. Several methods are available to determine the contact heat transfer based on data reported in the literature. Here, 5000 W=(m2 K) are used according to Ref. [88]. Other material properties of heat conduction in the workpiece and dies and the heat transfer between the workpiece=die and ambient are also taken from Ref. [88] as seen in Table 7. The punch velocity is described in Fig. 60, shows the different stages of forging, holding, and ejecting. Figure 61(a) and (b) shows a quarter model of the rod in its initial position and at the end of the ejection stage.

Table 6 X-ray Measuring Conditions Characteristic X-ray Tube voltage Tube current X-ray optics Divergence slit Receiving slit Sampling time Filter Diffraction plane Irradiated area

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CrKa 35 kV 9 mA Parallel beam 0.58 0.58 Unifixed V a Phase 211 Phase 220 2 8 mm2

Figure 51

Temperature variation on center and surface of layer.

The simulated shape of the rod is in good agreement with the experiment. The burr can be clearly seen here and is also confirmed by experiment. The residual stress and equivalent plastic strain obtained at the end of the ejecting stage is depicted in Fig. 62. The sample points are taken from the center to the surface in the middle of the rod along the punch moving direction. The residual stress will be taken into account in the subsequent quenching process as the initial condition. The temperature in the center of the rod increases during forging because of heat generation due to mechanical work. But the temperature

Figure 52

Temperature distribution at t ¼ 0.35 sec.

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Figure 53

Temperature distribution at t ¼ 0.75 sec.

near the surface drops because of die chilling. In the ejection stage, the temperature near the surface may rise again slightly since the heat transfer from the workpiece to ambient is much lower than that of the die, so that the surface can be heated again at the center. Figure 63 represents the temperature variation with time at the center and the surface in the middle of the rod during forging. (2) In the quenching process, the temperature range is from 9008C to room temperature (208C). The material at 9008C is in the austenite phase.

Figure 54

Volume fraction of solid phase at t ¼ 0.35 sec.

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Figure 55

Volume fraction of solid phase at t ¼ 0.75 sec.

Fig. 64, shows that when the rod is continuously cooled down, the austenite can transform into pearlite through diffusion transformation. If the cooling rate is high enough, austenite may transform into martensite when the temperature is decreased below the martensite transformation temperature. The properties of the material are highly dependent upon the content of each phase and are found in Ref. [34]. To obtain a relatively effective cooling medium for water spray quenching, 9100 W=(m2 K) are used as the heat transfer coefficient, and

Figure 56

Distribution of residual stress sr.

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Figure 57

Distribution of residual stress sy.

208C is used as a constant ambient temperature. Figures 63 and 64 show the temperature changes with respect to time taken at the center to the surface in the middle of the rod during quenching and illustrates the volume fraction of metallic structures formed. Figures 65 and 66

Figure 58

Distribution of residual stress sz.

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Figure 59

Table 7

Outline of basic numerical model.

Material Properties of Heat Conduction Heat conductivity

Die Workpiece

31 W=m K 35 W=m K

Specific heat 470 J=kg K 800 J=kg K

Heat transfer with ambient 20 W=m2 K 52 W=m2 K

illustrate equivalent stress and axial residual stress distribution from the center to the surface in the middle of the rod after quenching, respectively. In Fig. 66, two cases are shown for axial residual stress distribution: one case is quenching without taking into account the residual stress from the forging process; and the other is quenching, taking account of

Figure 60

Punch velocity of forging, holding, and ejecting.

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Figure 61

The rod in its (a) initial position and at the (b) end of ejecting stage.

Figure 62

Residual stress at the end of ejecting stage.

Figure 63

Cooling curve.

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Figure 64

Volume fraction of metallic structures.

the residual stress from the forging process. Experimental results measured by the Sacks method are also shown in the same figure. In both cases, the axial residual stress is in tension near the center and in compression near the surface. Because of the effect of the residual stress from the forging process, less tension near the center and more compression near the surface were obtained as seen in Fig. 66. The axial residual stress coming from the forging process does not make a big difference with the quenching calculation,

Figure 65

Effective stress after quenching.

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Figure 66

Axial residual stress after quenching.

because the axial residual stress coming from the forging process is quite small.

VII.

CONCLUSION AND REMARKS

A general discussion on the framework of thermo-mechanical theory incorporating phase transformation and solidification is described in this chapter, and a series of practical analytical schemes based on the finite element method are introduced. These schemes are applied to simulate thermomechanical fields in quenching, casting, coating, and forging processes. A coupling method to simulate phase transformation and solidification and temperature as well as stress distribution in these metallurgical processes is formulated, and the implementation by finite element calculation is presented in this chapter as examples of the application of the theory and procedure developed in the handbook. Elastic–plastic constitutive equations and a modification of Perzyna’s viscoplastic constitutive relationship were used, which reflects actual phase transformation and solidification during these metallurgical processes. The results of simulation are also verified by comparison with experimental data, and application of the technique to other operating conditions to obtain the fundamental data of optimum design of the system. From the discussion of theory, simulation method and results presented in the chapter, the conclusions and remarks obtained are summarized as follows:

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1. Comparing with calculated results and experimental data for temperature, distortion and residual stress in these metallurgical processes, the metallo-thermo-mechanical theory and simulation method proposed in Section II are verified. 2. Effects of cooling curves, distortion, and residual stresses on the occurrence of the phase transformation in quenching are proved by simulations of quenching and carburizing-quenching processes. 3. It is important to identify the heat transfer coefficients of quenchants with respect to the quenching process are obtained from simulation results. 4. The unified inelastic constitutive equation may describe the stress and deformation in the whole region of the solidifying process including liquid and solid state. 5. In the simulation of continuous casting, the development of stresses from solidifying domain is presented. On the other hand, the effects of distortion on solidification also shown to be an important factor. 6. In the simulation of coating process, the jump behavior of stresses on the interface between substrate and spraying layer is shown. Thus, it is important to reveal the damage of the spraying layer based on the metallo-thermo-mechanical theory and numerical method. 7. The advantage of finite volume technique over the finite element method in the simulation of forging was shown. From this point of view, the finite volume method is expected to be a powerful tool in the simulation of metal forming processes. REFERENCES 1. Noyan, C.; Cohen, J.B. Residual Stress, Springer Verlag, New York, 1987. 2. Mura, T. Residual stresses due to thermal treatments. Res. Rep. Faculty Eng. Meiji Univ. 1995, 10, 14–27. 3. Hanabusa, T. Japanese Standard for X-ray Stress Measurement, Proceedings of 6th International Conference on Residual Stresses, Oxford, England, July 10–12, 2000; 181–188. 4. Standard Method of X-ray Stress Measurement, JSMS, 1997 5. Bacon, G.E. Neutron Diffraction; 3rd Ed. Oxford University Press, Oxford, England, 1975. 6. Pyzalla, A. Determination of the residual stress state in components using neutron diffraction. J. Neutron Res. 2000, 8, 187–213. 7. Redner, S.; Perry, C.C. Factors affecting the accuracy of residual stress measurements using the blind hole drilling method. Proceedings of 7th International Conference on Experimental Stress Analysis, New York, August; 1982; 604–616.

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38. Inoue, T.; Nagaki, S. A constitutive modeling of thermo-viscoelastic-plastic materials. J. Therm. Stresses 1978, 1, 53–61. 39. Kujawski, D.; Mroz, Z. A viscoplastic material model and its application to cyclic loading. Acta Mech. 1980, 36, 213–230. 40. Matsui, H.; Ju, D.Y.; Inoue, T. Inelastic behavior and unified constitutive equations of SUS304 at high temperature. J. Soc. Mater. Sci. (JSMS) 1992, 41, 1153–1159. 41. Ju, D.Y.; Inoue, T.; Matsui, H. Visco-plastic Behaviour of SUS304 Stainless Steel at Ultra-high Temperature, Advances in Engineering Plasticity and its Application; Lee, D., Ed.; 1993; 521–528 42. Perzyna, P. The constitutive equations for rate sensitive plastic materials. Arch. Mech. Stos. 1968, 20, 499–512. 43. Perzyna, P. Thermodynamic Theory of Viscoplasticity, in Advance of Applied Mechanics; Academic Press: New York, 1971; vol. 11, 313–354. 44. Sorimachi, K.; Brimacombe, J.K. Improvements in mathematical modeling of stresses in continuous casting of steel. Iron Steelmaking 1977, 4, 240–245. 45. Chan, K.S.; Bodner, S.R.; Walker, K.P.; Lindholm, U.S. A survey of unified constitutive theories. Proceedings of 2nd Symposium on Nonlinear Constitutive Relations for High Temperature Applications, Cleveland; 1984; 108–112. 46. Bodner, S.R.; Partom, Y. Constitutive equations for elastic-viscoplastic strain hardening materials. J. Appl. Mech., Trans. ASME. 1975, 42, 385–389. 47. Bodner, S.R.; Merzer, A. Viscoplastic constitutive equations for copper with strain rate history and temperature effects. J. Appl. Mech., Trans. ASME. 1978, 100, 388–394. 48. Chaboche, J.L.; Rousseler, G. On the plastic and viscoplastic constitutive equation (part 1). Trans. ASME, PVT. 1983, 105, 153–158. 49. Chabache, J.L.; Rousselie, G. On the plastic and viscoplastic constitutive equations (part 2). Trans. ASME, PVT. 1983, 105, 158–164. 50. Ackermann, P.; kurtz, W.; Heinemann, W. In situ tensile testing of solidifying aluminium and Al–Mg shells. Mater. Sci. Eng. 1985, 75, 79–86. 51. Suzuki, T.; Tacke, K.H.; Schwerdtfeger, K. Influence of solidification structure on creep at high temperatures. Metall. Trans. 1988, 19, 2857–2859. 52. Inoue, T. et al., Benchmark Project on the application of inelastic constitutive relations in plasticity-creep interaction condition to structural analysis and the prediction of fatigue-creep life, part-I. Proceedings of Subcommittee Inelastic Analysis of High Temperature Materials, JSMS. 1991; Vol.1, 1–5. 53. Magee, C.L. Nucleation of Martensite; ASM: New York, 1968. 54. Johnson, W.A.; Mehl, R.F. Reaction kinetics in processes of nucleation and growth. Trans. AIME 1939, 135, 416–458. 55. Boley, A; Weiner, J.H. Theory of Thermal Stresses; Wiley: New York, 1960. 56. Rubenstein, L.I. The Stefan Problem; American Mathematical Society: Tennessee, 1971. 57. Flemings, M.C. Behavior of metal alloys in the semisolid state. Metal. Trans. A 1991, 22A, 957–980. 58. Battle, T.P.; Pehlks, R.D. Mathematical of microsegregation in binary metallic alloys. Metal. Trans. 1990, 21B, 357–375.

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59. Zienkiewicz, O.C. The Finite Element Method; McGraw-Hill: New York, 1977. 60. Peirce, D.; Shih, D.F.; Needlemen, A. A tangent modulus for rate dependent solid. Int. J. Computer Struct. 1984, 18, 875–887. 61. Williams, J.R.; Lewis, R.W.; Morgan, K. An elastic–viscoplastic thermal stress model with applications to the continuous casting of metals. Int. J. Num. Meth. Eng. 1979, 14, 1–9. 62. Ju, D.Y.; Inoue, T. Metallo-mechanical simulation of centrifugal casting process of multi-layer roll. J. Mater. Sci. Res. Int., 1996, 2 (1), 18–25. 63. Ju, D.Y.; Ichitani, K.; Nakamura, E.; Mukai, R. Simulation and experimental verification of residual stresses and distortion in quenching process with stirring, heat treatment and surface engineering. AIM 1998, 2, 283–291. 64. Narazaki, M.; Ju, D.Y. Simulation of distortion during quenching of steel effect of heat transfer in quenching. Proceedings of 18th ASM Heat Treating Society Conference Including the Liu Dai Memorial Symposium; ASM International: Ohio, 1998; 629–638. 65. Narazaki, M.; Ju, D.Y. Influence of transformation plasticity on quenching distortion of carbon steel. Proceedings of the 3rd International Conference on Quenching and Control of Distortion, Prague, March; 24–26 ASM International: Ohio, 1999; 405–415. 66. Ju, D.Y. Analysis of residual stresses during quenching process of large steel shaft. J. Saitama Institute Technol. 1994, (3), 17–21. 67. Ju, D.Y. Computer prediction of thermo-mechanical behavior and residual stresses during induction hardening of notched cylinder. J. Mater. Sci. Forum, Trans Tech Publications 2000, 347–349, 352–357. 68. Ju, D.Y.; Narazaki, M. Simulation and experimental verification of residual stresses and distortion during quenching of steel. Proceedings of 20th ASM Heat Treating Society Conference Including the Prof. J.B. Cohen Memorial Symposium; ASM International: Ohio, 2000; 441–447. 69. Ju, D.Y.; Narasaki, M.; Kamisugi, H. Computer predictions and experimental verification of residual stresses and distortion in carburizing–quenching of steel. J. Shanghai Jiaotong University 2000, E-5(1), 165–172. 70. Ju, D.Y. Computer prediction of residual stresses and distortion in carburizing–quenching of gear. Proceedings of 6th International Conference on Residual Stresses; IOM Communications: London, England, 2000; Vol. 1, 550–556. 71. Ju, D.Y.; Liu, C.C. Numerical modeling and simulation of carburized and nitrided quenching. Proceedings of International Conference on Advances in Materials and Processing Technologies, Ed. J. M. Torralba, Universidad Calos III De Madrid, Spain, Madrid, Sept 18–21; 2001, Vol. 3, 1025–1032. 72. Japanese Industrial Standard, Heat Treating Oils, JIS K 2242–1980. Japanese Standards Association: Tokyo, Japan, Analysis of Quenching Processes Using Lumped-Heat-Capacity Method, 1980. 73. Narazaki, M.; Kogawara, M.; Shirayori, A.; Fuchizawa, S. Analysis of Quenching Process Using Lumped-Heat-Capacity Method. Proceedings of the 6th International Seminar of IFHT, Kyongju, Korea; ASM International: Ohio, 1997; 428–435.

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74. Industrial Quenching Oil—Determination of Cooling Characteristics—Nickel– Alloy Probe Test Method, International Standard, ISO 9950 1995 (E). 75. Narazaki, M.; Hiratsuka, H.; Shirayori, A.; Fuchizawa, S. Examination of Methods for Obtaining Heat Transfer Coefficients by Quenching Small Probes. Proceedings of the Asian Conference on Heat Treatment of Materials, Beijing, 1998; 269–274. 76. Ju, D.Y.; Inoue, T. A. Thermomechanical model incorporating moving liquid= solid interface and its application to solidification process. Proceedings of the 6th International Conference on Mechanical Behaviour of Materials, JSMS, July 28, Kyoto, 1991; Vol. 5, 119–120. 77. Ju, D.Y.; Oshika, Y.; Inoue, T. Simulation of solidification and temperature in the centrifugal casting process (in Japanese). J. Soc. Mater. Sci. (JSMS) 1991, 40, 12–18. 78. Ju, D.Y.; Takemura, S.; Inoue, T. Analysis of coupled mode of solidification and stresses the centrifugal casting process. J. Soc. Mater. Sci. (JSMS) 1992, 41 (464), 751–757. 79. Sham, T.L.; Chow, H.W. A finite element method for an incremental viscoplasticity theory based on overstress. Int. J. Comp. Mech. 1989, 34, 143–156. 80. Grill, A.; Brimacombe, J.K.; Weinberg, F. Mathematical analysis of stresses in continuous casting of steel. Iron Steelmaking 1976, 1, 38–47. 81. Miyazawa, K.; Szekely, J. A mathematical model of the splat coolong process using the twin-roll technology. Metall. Trans. 1981, 12A, 1047–1057. 82. Ju, D.Y.; Inoue, T.; Yoshihara, N. Simulation of vertical semi-continuous direct chill casting process of cylindrical ingot of aluminum alloy (in Japanese).Trans. Jpn. Soc. Mech. Eng. (JSME) 1989, 55 (513), 1236– 1243. 83. Ju, D.Y.; Inoue, T. Simulation of solidification and Evaluation of residual stresses during centrifugal casting. Proceedings of the 3rd International Conference on Residual Stresses, Elsevier Science: Holland, 1991; Vol. 1, 220–225. 84. Ju, D.Y.; Inoue, T. Simulation of solidification and viscoplastic deformation in the twin roll continuous casting process (in Japanese), Trans. Jpn. Soc. Mech. Eng. (JSME) 1991, 57, 1147–1154. 85. Gassot, H.; Junquera, T.; Ji, V.; Jeandin, M.; Guipont, V.; Coddet, C.; Verdy, C.; Grandsire, L. A Comparative Study of Mechanical Properties and Residual Stress Distributions of Copper Coatings Obtained by Different Thermal Spray Processes, Surface Modification Technologies; IOM Communications, London, England, 2000; 16–23. 86. Ju, Y.; Nishida, M.; Hanabusa, T. Simulation of the thermo-mechanical behavior and residual stresses in the spray coating process. J. Mater. Process. Technol., 1999, 92–93, 243–250. 87. Kirara, S. Evaluation for the influence of press speed on the working load and die temperature. The Proceedings of the 44th Japanese Joint Conference for the Technology of Plasticity (in Japanese); J. JSTP 1993; 6–9.

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88. Kato, T.; Akai, M.; Tozawa, Y. Thermal analysis of cold upsetting. J. JSTP (in Japanese) 1987, 28 (319), 791–798. 89. Kennedy, K.F.; Lahoti, G.D. Review of flow shess date. Battle columbus laboratories, 1981. 90. Nakanishi, K.; Nonoyama, F.; Sawamura, M.; Danno, A. Evaluation of interface heat transfer coefficient for thermal analysis in forging. J. JSTP (in Japanese) 1996, 37 (421), 207–212. 91. Isogawa, S.; Mori, I.; Tozawa, Y. Determination of basic data for numerical simulation—analysis of multi-stage warm forging sequence for austenitic stainless steel I. J. JSTP (in Japanese) 1997, 38 (436), 84–89. 92. Ding, P.; Ju, D.Y.; Inoue, T.; de Vries, E. Numerical Simulation of forging and subsequent heat treatment of a rod by a finite volume method. Third International Conference on Physical and Numerical Simulation of Materials and Hot Working (ICPNS’99), 1999; 270–280.

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4 Modeling and Simulation of Mechanical Behavior Essam El-Magd Aachen University, Aachen, Germany

With the rapid increase of the capacity and speed of computers, work stations, and even personal computers, numerical methods can now be applied to solve easily many complex engineering problems, for example, in the fields of metal forming, strength of materials, and reliability studies of parts, components or systems. Some of the conventional methods of stress analysis, such as photo-elasticity, have nearly disappeared. Also, the interest in analytical methods like the elementary theory of plasticity and the slip line theory is decreasing to some extent with the increasing accuracy of the numerical methods. At first, great effort had to be done in developing the numerical methods themselves to insure stability, convergence, and accuracy of the computation process. In the mean time, many powerful codes that carry over the major part of this responsibility are commercially available. Especially for engineers, the main field of activities changed in another direction, namely to the development of adequate constitutive equations that describe well the behavior of the material in the macroscopic, microscopic, and even in the atomistic scale. From the practical point of view, it is not urgently required to increase numerical accuracy by some 0.1%, while the material data for plastic deformation processes deviate by more than 2% from reality or when the data for creep or fatigue life scatter by a factor between 12 and 2. There are still several important improvements to be done in the numerical codes, for example, in order to achieve an accurate consideration of large deformations. However, the determination and implementation of adequate material data seem to be one of the most important tasks. Due

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to lack of material data, the computations were carried out in the past mostly assuming an elastic material behavior using the common values of the modulus of elasticity and the Poisson ratio, even if it was well known that the material behavior is inelastic under the conditions considered. Complex procedures were developed in order to estimate the inelastic behavior using the elastic computational results. This is changing monotonically towards the consideration of the inelastic material behavior with current codes. The formulation of the material law is decisive for the experimental effort and costs needed to determine its parameters. Empirical relations may be helpful when only few variables of the process are considered and when these variables vary within limited ranges. Otherwise, physically founded material models may be more suitable, as they a priori define the tendency of the relations to be determined. However, the experimental determination of each parameter of these models according to its exact physical meaning may require such a great effort that this procedure remains restricted to academic research activities. For the practical application, a compromise is gaining increasing interest, according to which the functions are taken from physical and microstructure-mechanical models, but their parameters are determined by curve fitting of the experimental data. In the following, some examples are represented for modeling and simulation of the material behavior during plastic deformation, low cycle fatigue, creep, and impact strength.

I.

PLASTIC BEHAVIOR

Flow curves represent the relationship between the true stress and the true stain during plastic deformation at constant strain rate and temperature. They are usually determined in tensile, compression, or torsion tests. When a cylindrical rod of an initial length L0 and initial cross-sectional area A0 is loaded by a force F, its dimensions change to L and A. If the force is further increased by an increment dF, the length increases by dL and the area decreases by dA. The corresponding increments of the engineering stress and strain are defined by dS ¼ dF=A0 and de ¼ dL=L0, while the increments of the true stress and strain increments are defined by ds ¼ dF=A and de ¼ dL=L. At an arbitrary time point during the test, the stresses and strains are given by s ¼ F=A0 ;

e ¼ ðL L0 Þ=L0

s ¼ F=A;

e ¼ lnðL=L0 Þ

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ð1Þ

If the deformation is uniformly distributed along the bar and volume constancy can be assumed, the true and the conventional stresses and strains are related by s ¼ Sð1 þ eÞ and e ¼ lnð1 þ eÞ. In addition to the physical relevance, the use of true stresses and strains allows for: P (a) a simple addition of the strains of different deformation steps e ¼ ei , (b) a simple formulation of the plastic volume constancy by exx þ eyy þ ezz ¼ 0, and (c) equal absolute values in tension and compression if specimen length is increased or decreased by the same factor. Under service conditions, engineering materials are usually subjected to a multiaxial stress state. On the other hand, material data are determined in laboratory tests under almost uniaxial loading. For comparison, an equivalent uniaxial stress is to be define for the multiaxial case. In the case of isotropic incompressible materials, the equivalent stress is given according to von Mises by

seq

sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ðsxx syy Þ2 þ ðsyy szz Þ2 þ ðszz sxx Þ2 ¼ þ 3 t2xy þ t2yz þ t2zx 2 ð2Þ

No plastic deformation takes place, as long as this equivalent stress is lower than the flow stress sY of the material. When the loads are so increased that the equivalent stress reaches the flow stress, the material starts to yield. For the strain state, which is represented by the plastic strain tensor epij , an equivalent strain increment is defined by depeq

rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ i 1h i 2h p 2 ðdexx Þ þ ðdepyy Þ2 þ ðdepzz Þ2 þ ðdgpxy Þ2 þ ðdgpyz Þ2 þ ðdgpzx Þ2 ¼ 3 3 ð3Þ

where gij ¼ 2eij with i 6¼ j. The plastic strains epij , which are the irreversible response of the material to the applied stresses, depend not only on the current values of the stresses, but also on the total loading history. For isotropic incompressible materials, the plastic strain increments are proportional to the deviatoric stresses, i.e., the normal stresses reduced by their mean value ðsxx þ syy þ szz Þ=3 and the shear stresses unchanged, or in short form Sij ¼ sij ð1=3Þdij skk . If the material follows the Mises yield criterion, the plastic strain increments are given by depij ¼

3 depeq Sij 2 seq

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ð4Þ

A.

Flow Curves

In order to characterize the strain hardening behavior of metallic materials during plastic deformation, one has to determine experimentally the relation sY ¼ sY ðeeq ; e_ eq ; TÞ that defines the dependence of the flow stress sY on the plastic parts of the equivalent strain eeq , the equivalent strain rate e_ eq and on the temperature T. Flow curves are defined as the relation sY ¼ sY ðeeq Þ determined for e_ eq ¼ const: at a constant temperature. They are often determined in compression test, taking into consideration the influence of friction. They are also to be determined in tension test up to the ultimate force assuming uniform deformation. 1. Empirical Relations The flow curves are almost described by power laws. The oldest of these relations, introduced in 1909 by Ludwik [1], is given by sY ¼ K0 þ Ken

ð5Þ

This relation allows a good description of the flow curves of materials having a finite elastic limit. For a plastic strain ðe ¼ 0Þ, the flow stress equals K0 . It leads, however, to an infinite value for the slope of the curve @ sY =@ e at the yield point. A simplified form of this equation sY ¼ Ken

ð6Þ

was suggested by Hollomon [2]. Because of its simplicity, it is till now the most common relation applied for the description of the flow curve. However, no yield point is considered by this relation as sY ¼ 0 for e ¼ 0. Especially for materials with a high yield point or materials previously deformed, the flow stress cannot be described well by this relation in the region of small strains. A more adequate description is achieved by the Swift relation [3] sY ¼ KðB þ eÞn

ð7Þ

For e ¼ 0, a yield point is considered with a value of sY ¼ KBn . An alternative description sY ¼ a þ b½1 expðceÞ

ð8Þ

was introduced by Voce [4] and is well applicable for the range of small strains. Figure 1 shows the optimum fit achieved by the four equations (5–8) for the flow curves of an austenitic steel at different temperatures in the range of relatively small strain up to 0.2. The figure shows that the Swift relation and the Voce-relation describe well the flow curves in the relative

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Figure 1 Description of the flow curves of the austenitic steel X6CrNi18-11 at e_ ¼ 8 104 sec1 by empirical relations.

small strain range considered. Also, a good description is achieved by the Ludwik relation when the parameter K0 is considered as an arbitrary constant and is chosen to be much smaller than the actual yield point. 2. Microstructure Mechanical Relations In one-parametrical models, the flow stress depends only on the total dislocation density r which is considered as the single internal variable of the material according to pﬃﬃﬃ s ¼ aGb r ð9Þ where G is the shear modulus, and b is the Burger vector. If the rates of creation and annihilation of dislocation are known, an evolution equation can be determined for the flow stress. Mecking and Kocks [5] introduced the following evolution equation for the total dislocation density: dr pﬃﬃﬃ ¼ k1 r k2 r ð10Þ de and determined the slope of the flow curve by ds k2 k1 ¼ s ð11Þ de 2 k2 aGb

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If the parameters k1 and k2 are considered to be constants, the flow curves follow by: s ¼ s0 þ ðs1 s0 Þ½1 expðe=e Þ

ð12Þ

This equation is identical with the empirical Voce relation. In the range of relatively small strains, it fits the experimental data very well. However, it fails to describe the flow curves in the range of high strains because the experimental results for the flow stress do not asymptotically approach a definite value [6]. The following modification can be suggested, to yield an evolution equation that describes well the strain hardening in the range of high pﬃﬃﬃ strains. The parameter k1 ¼ 1=ðl rÞ, where l is the dislocation free path. This parameter can be considered as a function of strain and may be expressed as k1 ¼ kð1 þ ceÞ. The evolution equation of the flow stress becomes ds k kc K2 s ð13Þ ¼ þ e 2 de 2aGb 2aGb

Figure 2 Flow curve of the austenitic steel X8CrNiMoNb16-16, described by Eqs. (13) and (14).

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The solution of this differential equation is s ¼ C1 þ C2 e þ C3 ½1 expðC4 eÞ

ð14Þ

where C1 is the yield stress, C2 ¼ kc=ðk2 aGbÞ, C3 ¼ kð1 þ 2c=k2 Þ=ðk2 aGbÞ; and C4 ¼ k2 =2. This equation is identical with the empirical relation introduced in Ref. [7]. It is found to give the optimum fit for the experimental results of several materials (Fig. 2). However the determination of its parameter needs some more effort. It should be mentioned that also the empirical Swift relation given by Eq. (5) fits well the experimental data in this strain range. B.

Influence of Strain Rate and Temperature

Figure 3a shows an example for the influence of increasing temperature on the flow stress for given values of strain and strain rate [8]. Considering the slope ds=dT, three different temperature ranges can be defined: (A) range of low temperatures, between absolute zero and about 0.2 of the absolute melting point, where the influence of the temperature on the flow stress is great. The material behavior is governed by thermally activated glide, (B) range of intermediate temperatures between 0.2 and 0.5 of the absolute melting temperature. Only a slight influence of strain rate and temperature on the flow stress is usually observed in this range, and (C) range of temperatures higher than 0.5Tm in which the flow stress depends highly on the temperatures because of the dominance of diffusion-controlled deformation processes. The influence of the strain rate variation [9] is represented in Fig. 3b. Three different strain rate ranges can also be recognized according to the

Figure 3 (a) Temperature influence on the yield stress of NiCr22Co12Mo9 at e_ ¼ 3 104 sec1 [8]. (b) Influence of stain rate on shear yield stress of mild steel [9].

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variation of @s=@ ln e_ : (I) range of low strain rates with only a slight influence of the strain rate due to athermal glide processes, (II) range of intermediate and high strain rates with relatively high strain rate sensitivity due to thermal activated glide mechanisms, and (III) range of very high strain rates where internal damping processes dominate and a very high strain rate sensitivity is observed. The boundary between the ranges (I) and (II) depends on the temperature. Overviews concerning the mechanical behavior under high strain rates are represented, e.g. in Refs. [10,11]. To estimate the mechanical behavior over wide ranges of strain rate and temperature, constitutive equations must be established taking the time dependent material behavior into consideration. A visco-plastic behavior is often assumed by using, for example, the Perzyna equation [13] e_ ij ¼

S_ ij 1 2v @f s_ kk dij þ 2ghFðFÞi þ 2m 2E @sij

ð15Þ

where m is the shear modulus, f is square root of the second invariant of the stress deviator Sij and F ¼ (f=k) pﬃﬃﬃ 1 is the relative difference between f and the shear flow stress k ¼ sF = 3. The function FðF Þ is often estimated using simple rheological models assuming FðF Þ ¼ F and leading to linear relation of the type s ¼ sF ðeÞ þ Z_e which is acceptable for metals only at strain rates >103 sec1. 1. Empirical Relations Different empirical relations could be implemented in Eq. (15). With FðF Þ ¼ expðF =aÞ 1 or FðF Þ ¼ F 1=m , the corresponding relations between stress and stress rate in the uniaxial case are identical with the empirical relations introduced 1909 by Ludwik [14] s ¼ sF ðe; TÞ½1 þ a lnð1 þ e_ =aÞ

ð16Þ

s ¼ sF ðe; TÞ½1 þ ð_e=a Þm

ð17Þ

The influence of temperature on the flow stress is also described by different relations of the type s ¼ sðe; e_ Þf ðT=Tm Þ where Tm is the absolute melting point of the material, such as s ¼ s0 ðe; e_ Þ exp½bT=Tm

ð18Þ

or according to Ref. [15] s ¼ s0 ðe; e_ Þ½1 ðT=Tm Þv

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ð19Þ

On applying such empirical relations, the flow stress is usually represented by s ¼ ft ðeÞf2 ð_eÞf3 ðTÞ as a product of three separate functions of strain, strain rate and temperature. This is a rough approximation especially in the case of moderate strain rates of e_ < 103 sec1 . However, the basic problem is that nearly all the parameters of these empirical equations can only be regarded as constants only within relatively small ranges of e, e_ , and T. The determination of the functional behavior of the parameters requires a great number of experiments. Therefore, constitutive equations based on structure-mechanical models are gaining increasing interest as they can improve the description of the mechanical behavior in wider ranges of strain rates and temperature and may, if carefully used, allow for the extrapolation of the determined relations.

2. Structure-Mechanical Models The macroscopic plastic strain rate of a metal that results from the accumulation of sub-microscopic slip events caused by the dislocation motion is given by e_ ¼ brm v=MT

ð20Þ

In this equation, the Burger vector b and the Taylor factor MT are constants for a given material whereas the mobile dislocation density rm is mainly a function of strain. The relation between the dislocation velocity v and the stress was experimentally determined for several materials [16]. It can be represented in the range of low stresses by a power law approaches v ¼ v0 ðs=s0 ÞN . At very high stresses, the dislocation velocity qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

asymptotically the shear wave velocity cT and s ¼ avn =

1 ðv=cT Þ2 .

3. Athermal Deformation Processes In the range of intermediate temperatures and low strain rates (combined ranges B and I), and at relatively low temperatures, i.e., less than 0.3 of the absolute melting point Tm, the influence of strain rate and temperature depends on the e_ -range of the deformation process. Below a specific value of the strain rate, that depends on temperature, only a slight influence of strain rate and temperature on the flow stress is observed. In this region I, athermal deformation processes are dominant, in which the dislocation motion is influenced by internal long range stress fields induced by such barriers as grain boundaries, precipitations, and second phases. The flow stress varies with temperature in the

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

same way as the modulus of elasticity. The influence of strain rate can be described by s¼C

EðTÞ m e_ EðT0 Þ

ð21Þ

where E is the modulus of elasticity and m is of the order of magnitude of 0.01. 4. Thermally Activated Deformation In the ranges of low temperatures (A) and intermediate to high strain rates (II), the dislocation motion is increasingly influenced by the short range stress fields induced by barriers like forest dislocations and solute atom groups in fcc-materials or by the periodic lattice potential (Peierls-stress) in bcc materials. If the applied stress is high enough, these barriers can immediately be overcome. At lower stresses, a waiting time Dtw is required until the thermal fluctuations can help to overcome the barrier. A part of the dislocation line becomes free to run, in the average, a distance s until it reaches the next barrier within an additional time interval Dtm . The mean dislocation velocity is given by v ¼ s =ðDtw þ Dtm Þ. The waiting time Dtw equals the reciprocal value of the frequency n of the overcoming attempts. If the strain rate is lower than ca. 103 sec1, it can be assumed that Dtw 4 Dtm . The relation between strain rate and stress is then given by e_ ¼ e_ 0 ðeÞ exp½DG=kT where e_ 0 ¼ brm n 0 s =MT . The activated free enthalpy DG depends on the difference s ¼ s sa between the applied Rstress and the athermal stress according to kT lnð_e0 =_eÞ ¼ DG ¼ DG0 V ds where V ¼ bl s =MT is the reduced activation volume. For given stress and strain, the value of T lnð_e =_eÞ is constant for all temperatures and also for all strain rate values between e_ 0 exp½DG0 = ðkTÞ and e_ 0 . This means that the increase of stress at constant strain with decreasing temperature or with increasing strain rates is the same, as long as the values of DG ¼ kT lnð_e =_eÞ are equal in both cases. Depending upon the formulation of the function V ðs Þ; different relations for e_ ¼ e_ 0 ðsÞ were proposed in Refs. [17–21]. The most common are the relation introduced by Vo¨hringer [19,20] and by Kocks et al. [21] q DG0 s sa p 1 e_ ¼ e_ 0 ðeÞ exp kT s0 s a

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ð22Þ

and that by Zerilli and Armstrong [22,23] e_ 0 DG0 k ln s sa ¼ exp b0 þ T DG0 V0 e_

ð23Þ

5. Transition to Linear Viscous Behavior At strain rates higher than some 103 sec1, the stress is high enough to the extent that Dtw vanishes. Only the motion time Dtm is to be considered. The dislocation run with high velocity throughout the lattice and damping effects dominate. The dislocation velocity v ¼ s =Dtm can then be given by v ¼ bðt th Þ=B according to Ref. [24]. The flow stress follows the relation s ¼ sh ðe; TÞ þ Z_e

ð24Þ

with Z ¼ MT B=ðb2 Nm Þ. This relation is validated experimentally in Ref. [9] as well as by Sakino and Shiori [25], as shown in Fig. 4a. A continuous transition takes place, when the strain rate is increased from the thermal activation range (II) to the damping range (III). This can be described in two different ways: regarding the dislocation velocity to be equal to v ¼ s =ðDtw þ Dtm Þ, the strain rate can be represented by q 1 DG0 s sa p x _e ¼ e_ 0 exp 1 ð25Þ þ kT s0 sa s sh where x is a function of strain. Alternatively, the continuous transition can be described by an additive approximation. The stress is regarded to be the sum of the athermal, the thermal activated and the drag stress components. According to this approximation, s sa þ sth þ Z_e where sth is the thermal activated component of stress determined from Eq. (22) or (23).

6. Diffusion-Controlled Deformation In the range of high temperatures (C), the deformation is governed by strain hardening and diffusion-controlled recovery processes

s n Q1 exp e_ ¼ e_ 0 ð26Þ RT G At very high temperatures and low stresses sO 1 pdDB Dv 1 þ e_ d;e ¼ 14 kT d2 dDv

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ð27Þ

Figure 4 Dependence of flow stress on the strain rate. (a) In the range of damping controlled deformation, described by Eq. (24) [25]. (b) In the transition range between thermally activated and damping controlled deformation ranges, described by Eq. (25) [26].

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C.

Material Laws for Wide Ranges of Temperatures and Strain Rates

Material laws that describe the flow behavior over very wide ranges of temperatures and strain rates are needed for the simulation of several deformation processes, such as high-speed metal cutting. In this case, different physical mechanisms have to be coupled by a transition function. Fig. 5 shows the dependence on the stress with the strain rate at different temperatures for a constant strain. Three main mechanisms can be distinguished: (a) diffusion-controlled creep processes with e_ cr / sNðTÞ in the region (1) of low strain rates and high temperatures, (b) dislocation glide plasticity with mðTÞ s / e_ pl in the region (2) of intermediate temperatures and strain rates, and (c) viscous damping mechanism with s ¼ sG þ Zð_e e_ G Þ in the region of very high strain rates e_ > 1000 sec1 in the region (3). 1. Visco-plastic Material Law For a continuous description over the different ranges, the strain rates have to be combined [27] to obtain ð28Þ e_ ¼ ð1 MÞ e_ kr þ e_ pl þ M_edamping with the transition function M ¼ 1 exp½ð_e=_eG Þm . The complete strain rate range can be described by NðTÞ 1=mðTÞ ! s s e_ ¼ ð1 MÞ e_ þ s0 ðT; eÞ sH ðT; eÞ s sG ðT; eÞ þ e_ G ðT; eÞ þM ð29Þ Z with e_ ¼ 1 sec1. The parameters and functions s0(T, e), sH(T, e), m(T), N(T), and Z have to be determined by curve fitting in the individual regions (1)–(3), whereas the parameters sG and e_ G are determined requiring that the derivative @s=@ e_ follows a continuous function in the transition region: sG ¼ sH ð_eG =_e Þm and e_ G ¼ ðmsH =ZÞ1=ð1mÞ . The values of the parameter used are given in Ref. [28]. An exception of the rule of the reduction of flow stress with increasing temperature is the influence of dynamic strain hardening observed in ferritic steel at temperatures between 2008C and 4008C, where the flow stress increases towards a local maximum. It is caused by the interaction between moving dislocations and diffusing interstitial atoms. The additional stress can be described by Ds ¼ að_eÞ exp½fðT bð_eÞÞ=cð_eÞg2 , With this additional term, the dependence of flow stress of steel Ck45 (AISI 1045) on temperature and strain rate is determined [28] and represented in Fig. 6.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 5 True stress vs. true strain rate at different temperatures [27]. Markers: experimental results, curves: calculations according to Eq. (29).

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Figure 6 Influence of temperature and strain rate on the flow stress of unalloyed steel with 0.45% C. (From Ref. 27.)

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

2. Adiabatic Softening Flow curves determined in the range of high strain rates are almost adiabatic, since the deformation time is too short to allow heat transfer. The major part of the deformation energy is transformed to heat while the rest is consumed by the material to cover the increase to internal energy due to dislocation multiplication and metallurgical changes. On strain increase by de, the temperature increases according to dT ¼ k

0:9 s de rc

ð30aÞ

where the factor 0.9 is the fraction of the deformation work transformed to heat, s is the current value of the flow stress which is already influenced by the previous temperature rise and k is the fraction of energy remaining in the deformation zone. At low strain rate, there is enough time for heat transfers out of the deformation zone and the temperature increase is negligible. In this case, k ¼ 0. On the other hand, the deformation process is almost adiabatic at high strain rate and k ¼ 1. A continuous transition from the isothermal deformation under quasi-static loading to the adiabatic behavior under dynamic loading can be achieved considering k as a function of strain rate in the form.

Figure 7 Quasi-static and adiabatic flow curves of unalloyed fine grained steel.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

1 4 e_ kð_eÞ ¼ þ arctan 1 3 3p e_ ad

ð30bÞ

The transition strain rate e_ ad depends on the thermal properties of the material. If the temperature of the surroundings is the room temperature, e_ ad is around 10þ1 sec1. As the flow stress usually decreases with increasing temperature, the flow curve shows a maximum (Fig. 7). A thermally induced mechanical instability can take place leading to a concentration of deformation, a localization of heat and even to the formation of shear bands. An overview of different criteria for the thermally induced mechanical instability is presented in Ref. [29]. The adiabatic flow curve can be determined numerically for an arbitrary function sðe; e_ ; TÞ for the shear stress which has been determined in isothermal deformation tests. In order to obtain a closed-form analytical solution demonstrating the adiabatic flow behavior, the simple stress–temperature relation s ¼ siso ðe; e_ ÞCðDTÞ can be used [30,31]. In this case, the change of temperature can simply be determined by separation of variables and integration. For example, T T0 _ s ¼ siso ðe; eÞ 1 m ; Tm

s ¼ siso

0:9km exp rcTm

Z siso de

1 Z T T0 0:9kb s ¼ siso ðe; e_ Þ exp b siso de ; s ¼ siso 1 þ Tm rcTm

ð31Þ

ð32Þ

andc are the mean values Tm is the absolute melting point of the material, r of density and specific heat in the temperature range considered. Around room temperature, the product rc lies between 2 and 4 MPa=K for most of the materials. For a rough approximation, it can be assumed that (rcTm =0.9) 3Tm in MPa using Tm in K. Many experimental investigations e.g. Ref. [32] were carried out in order to determine the temperature dependence of the flow stress. Up to a homologous temperature of 0.6, the stress–temperature relation can be described better by Eq. (35) than by Eq. (34), showing values of b between 1 and 4. Therefore, only Eq. (35) will be considered in the following discussion. If the isothermal stress can be simply described by siso Ken Fð_eÞ

ð33Þ

the flow stress, determined in an adiabatic test with constant e_ , is then given by

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sad ¼ Ken Fð_eÞ 1 þ

ka Ke1þn Fð_eÞ ð1 þ nÞTm

1 ð34Þ

where a ¼ 0:9b=ð rcÞ. The parameter a can be considered as approximately constant represented by its mean value over the deformation process which is of the order of magnitude of 1 K=MPa. The flow curve shows a maximum smax at the critical strain ec , where nð1 þ nÞTm 1=ð1þnÞ KFð_eÞ nð1 þ nÞTm n=ð1þnÞ ; smax ¼ ð35Þ ec ¼ 1 þ n k aKFð_eÞ k aKFð_eÞ and the parameters K and a can be estimated by K¼

1 þ n smax ; Fð_eÞ enc

ka ¼

nTm smax ec

ð36Þ

the remaining unknown parameter n can be determined by fitting the curve the adiabatic flow curve [12]. Similar to the process of neck formation in a tensile specimen, the existence of a stress maximum leads to mechanical instability. Especially after reaching the stress maximum, a great part of the specimen is unloaded elastically causing further deformation localization. In dynamic torsion tests, the deformation localization leads to a heat concentration and hence a higher local temperature rise and a high shear strain concentration. Coffey and Armstrong [33] introduced a global temperature localization factor which is the ratio of the plastic zone volume to the total specimen volume. The influence of inhomogeneity on the strain distribution has been demonstrated by using a simple model [34] which represents the torsion specimen by two slices, a reference one and another slice with slight deviations in strength or dimensions. Furthermore, the deformation localization could be traced during the torsion test by observing the deformation of grid lines on the specimen surface by means of high-speed photography [35,36]. The influence of adiabatic softening can be illustrated in the case of compression test at high strain rates. Due to friction between the cylindrical specimen and the loading tools, a compression specimen becomes a barrel form during the test. In an etched cross-section of a quasi-statically tested specimen, two conical zones of restricted deformations can often be recognized after quasi-static upsetting. The deformed geometry is symmetrical about the midplane (Fig. 8). An FE-simulation is carried out for a compression test with e_ ¼ 0.001 sec1 considering stain hardening according to Eq. (8) and friction at the upper and lower surfaces by a coefficient m ¼ 0.1. The computational results indicate that the maximum values of equivalent stress as well

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Figure 8 Etched longitudinal section of a cylindrical compression specimen of steel 9SMnPb36 loaded quasi-statically (_e ¼ 0:001 sec1 ).

as that of the equivalent strain lie in the center of the cylindrical compression specimen (Fig. 9). In the case of dynamic compression with a strain rate of e_ ¼ 5000 sec1 , only one compression cone exists (Fig. 10). This is due to the influence of the mass inertia forces, which cannot be neglected at such high strain rates. The loads proceed in the form of mechanical waves propagating through the material. The stress at the upper surface which is impacted by a hammer is much lower than the stress at lower part of the specimen due to wave superposition after reflection from the lower surface which contacts the fixed tool. In the FE simulation, the mass inertia forces have to be considered. The deformation process is adiabatic. The local temperature increase is computed according to Eqs. (30a) and (30b) and its influence on the local flow stress is considered according to Eq. (32). The computation verifies the non-symmetry of the stress and strain distributions (Fig. 11). In the regions of high strain values, the critical strain is exceeded and the stress decreases with increasing strain. Therefore, low stress values are determined in these regions. 3. Extrapolation to Very High Strain Rates A large deformation concentration is expected in piercing and cutting process. The shear process can be dealt with as localized plastic deformation process. In the deformation zone, very high strains and high strain rates arise. The experimental tests are carried out using the so-called hat specimens, which is loaded by a compression force at its the upper surface

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Figure 9 Quasi-static compression test on cylindrical specimens with e_ ¼ 0:001 sec1 . (a) Etched section of a SMnPb-steel. (b) Distribution of Mises’ stress. (c) Distribution of the equivalent plastic.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 10 Etched longitudinal section of a cylindrical compression specimen of Armco iron loaded dynamically (_e ¼ 5000 sec1).

(Fig. 12a). The combination of experiment and finite-element simulation allows examining the possibility of extrapolation of materials laws to the range of very high strains and strain rates [28]. In addition, valuable information can be obtained for the optimization of the width B in shear

Figure 11 Distribution of Mises’ stress and equivalent plastic strain in a compression specimen after dynamic test with e_ ¼ 5000 sec1 , friction coefficient m ¼ 0.1.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 12

Hat-shaped specimen [37] and network of the shear zone [28].

processes of different materials. The specimens are tested dynamically using a split Hopkinson bar arrangement with a mean test velocity of 34 m=sec. The force as well as the displacements are recorded as functions of time. The process is simulated using a commercial explicit code taking mass inertia forces into consideration. Coulomb friction is considered with a coefficient of m ¼ 0.1. As loading conditions, the experimentally determined

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Figure 13 Distribution of the equivalent stress and the equivalent stress in the shear zone of a hat-shaped specimen [28]. (a) Equivalent strain. (b) Equivalent stress in MPa according to von Mises. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

displacement–time function of the upper surface is applied to upper the nodes. In order to reduce the total number of elements, the lower die is idealized using the so-called infinite elements. The material law is determined in compression tests at different temperatures with strain rates up to 7500 sec1. As discussed above, one can assume a linear viscous behavior according to s ¼ sh ðeÞ þ Z_e, when e_ > 2000 sec1 and the damping mechanism dominates. The simulation should examine the accuracy of the reproduction of the force–displacement curves determined experimentally for this geometry. The distributions of the von Mises equivalent stress and equivalent strain, represented in Fig. 13, show a great non-uniformity. High strain concentrations exist at the two diagonally opposite corners of the deformation zone. In these regions, the strain rate is so high that the influence of adiabatic softening is more than compensated and high stress values are determined there. Examples for the force–displacement curves determined experimentally and computed by the FEM are shown in Fig. 14 for different values of the shear zone width B. The deviation of the computed curves from the experimental ones is relatively small. Therefore, it can be assumed that the material law determined in the range of high strain rates e_ > 2000 sec1

Figure 14 Force–displacement curves of the hat specimen. Markers: experimental results, curves: FE simulation. (From Ref. 28.)

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

can be extrapolated to much higher strain rates assuming the dominance of the viscous damping mechanism according to Eq. (24). This result is consistent with the experimental results of Sakino and Shiori (Fig. 4a). Such material laws allow the simulation of different metal forming as well as metal cutting processes. They can be validated by high-speed metal cutting tests [38]. Structural damage during high rate tensile deformation can be accounted for by introducing a damage function [39]. II.

CYCLIC DEFORMATION BEHAVIOR

A.

Phenomenological Approach

If a specimen is extended with a constant strain rate e_ 0 , the stress increases first according to Hooke’s law of elasticity till the elastic limit is reached. Then, a plastic deformation begins accompanied with a non-linear hardening. After reaching an arbitrary total strain e1tot ¼ e1el þ e1pl , the strain rate changes to (_e0 ). At first, the material is unloaded elastically and is then compressed until a total strain of (e1tot ), as represented in Fig. 15. It can be clearly observed that the plastic compression begins at an = elastic limit Re , whose absolute value much smaller than the initial value

Figure 15 Stress–strain diagram of an experiment with a change of the loading direction.

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Re . In general, it can be stated that a previous tensile deformation reduces the compression elastic limit. Also, a compression deformation reduces the subsequent elastic limit under tension. This phenomenon,known as Bauschinger effect, is characteristic for the behavior of the material under cyclic loading in the low cycle fatigue range. With further cyclic loading, the stress range increases usually due to strain hardening (Fig. 16). If the material is highly pre-deformed or hardened, a cyclic softening takes place and the stress range decreases with increasing number of cycles. The rate of change of the stress range Ds decreases with the number of cycles and approaches a stationary value and the hysteresis loop remains unchanged. The strain hardening phenomena under cyclic loading can be classified in two terms: (a) Isotropic deformation resistance sF , that includes the yield point

as well as the isotropic change of the flow stress. It increases (or decreases) monotonically with the number of Rcycles, depending upon the specific plastic P deformation work s de, or on the accumulated plastic strain jdej. Its variation with strain can be considered as a result of the increase of the density of immobile

Figure 16 Stress–strain diagram of an austenitic steel under cyclic loading with a constant range of the total strain of De ¼ 0:0066 at 6508C.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

dislocation with an additional influence of the changing microscopic residual stress state. (b) Kinematic hardening or internal back stress si that depends on the direction of the deformation and the loading history and accounts for the Bauschinger effect. It may result from the reversible interactions of mobile dislocations with obstacles, such as in the cases of pile ups or bowing between particles. Figure 17 shows the influence of these stress parts in the biaxial case on the form of the Mises-ellipse. The isotropic hardening leads to an equal increase of the ellipse in all directions, while the kinematic hardening shifts the ellipse in the loading direction. Usually, both of these hardening types are to be expected during plastic deformation. During uniaxial cyclic deformation, the influence of the strain rate can be considered in two ways: ðs si Þ2 ¼ s2F Fð_epl Þ ð s si Þ 2 ¼

2 sF þ Cð_epl Þ

ð37aÞ ð37bÞ

If the direction of the strain rate, and hence its sign, is suddenly changed, the sign of the isotropic material resistance sF changes at once. In contrast, the value of internal back stress si changes gradually with increasing deformation approaching asymptotically a stationary value sis with the same sign as the strain rate. In the first cycle, the stress equals sF0 þ si0 , at the beginning of the plastic deformation where si0 is approximately equal to 0 for annealed materials. With increasing strain, both of sF and si increase approaching the stationary

Figure 17 Mises’ ellipse after: (a) isotropic hardening, (b) kinematic hardening, and (c) mixed mode hardening.

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values sF1 and sis . On reaching the maximum strain of Detot =2, the maximum stress is given by smax1 ¼ sF1 þ si1 . If the loading direction is changed from tension to compression, the isotropic material resistance changes from (þsF1 ) to (sF1 ) at once. The material is first unloaded and the stress drops by the amount of sF1 . With further reduction of length, plastic compression start when the stress is reduced by 2sF1 . During this short time, the internal back stress si remains unchanged at the value si1 . After the beginning of plastic compression, it starts to decrease gradually approaching a new stationary value ðsis Þ that corresponds to the new strain rate of (_e ). Each time when the strain rate changes from (þ_e) to (_e) in an arbitrary cycle, the stress drops during the elastic deformation by DsF ¼ 2sF and then gradually by Dsi during the plastic deformation of the half cycle. On the next reverse (_e) to (þ_e), a stress decreases first by DsF and then gradually by Dsi . The stress ranges is Ds ¼ DsF þ Dsi . The maximum and the minimum stress smax ¼ sF þ Dsi =2 and smin ¼ sF Dsi =2. The range DsF is defined as the difference between the maximum stress and the elastic limit in the subsequent compression phase. Especially in cyclic deformation, it is rather difficult to exactly determine the elastic limit, i.e., the transition point between the elastic and plastic deformation ranges because this transition is almost gradual. However, this point can be easily estimated if the hysteresis loop (Fig. 18a) is differentiated and ds=detot is represented as a function of s (Fig. 18b). Starting at minimum stress (point 1), the slope of the curve remains approximately constant and equals the modulus of elasticity till point 2 is reached. Then the slope decreases to a

Figure 18 (a) Hysteresis loop, and (b) the derivative with respect to the total strain as a function of the stress.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

relatively low value at point 3 of the maximum stress. The stress–strain curve rotates to point 4 of maximum strain. The slope decreases to 1, changes to þ1 and decreases again to the value of the modulus of elasticity. This value should remain unchanged till point 5, where plastic compression begins and the slope decreases again till reaching point 6. Between point 6 (minimum stress) and point 1 (minimum strain), the value of slope changes to þ1 then to þ1 and decreases to the value of the modus of elasticity. The relation between ds=detot and s can be linearized in the plastic ranges between the points 2 and 3 as well as between points 5 and 6. The intersection of these linear relations with the elastic relation ds=detot ¼ E defines the value of range DsF of the isotropic material resistance. The range of the internal back stress is the defined by Dsi ¼ Ds þ DsF : Repeating the procedure represented in Fig. 18 for the different cycles, one obtains Fig. 19a. For each half cycle, the value of DsF and the linear relation between ds=de and s can be determined. The isotropic component sF as well varies monotonically and continuously with increasing number of cycles. However, it can be assumed that its value is constant within arbitrary half cycles and changes only at the beginning of the next one, if the total number of cycles is great enough. In this case dsi ds ¼ de de within each half cycle. The linear relation dsi si si0 ¼E 1 detot sis si0

ð38Þ

ð39Þ

can be written for the internal back stress as well. The stationary value sis varies with the number of cycles. The isotropic material resistance sF as well as the stationary value sis of the internal back stress si are represented in Fig. 19b as functions of the accumulated strain. These relations may be described by sF ¼ sF0 þ ðsF1 sF0 Þ½1 expðCF eacc Þ ð40Þ sis ¼ sis0 þ ðsis1 sis0 Þ½1 expðCi eacc Þ

ð41Þ

yielding the evolution equations dsF ¼ CF ðsFs sF Þ deacc

ð42Þ

dsis ¼ Ci ðsis1 sis Þ deacc

ð43Þ

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Figure 19 (a) Description of the derivative ds=detot by a linear function of stress in the transition range between the ranges of elastic and plastic deformation. (b) sF and sis as function of the accumulated plastic strain.

Within each half cycle, si approaches the stationary value sis as shown in Fig. 20a. The transition range from the elastic to the plastic deformation ranges is fairly good described by Eq. (39). On the other hand, relatively large deviations are observed at low values of dsi =detot , which corresponds to high stress and plastic strain values. A more accurate description is

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Figure 20 Relation between stress derivative and internal back stress si . (a) Derivative with respect to the total stress. (b) Derivative with respect to plastic strain.

achieved by considering two internal variables for the internal back stress instead of only one as considered here [40]. With depl ¼ detot dsi =E, the derivative of the internal back stress with respect to the plastic strain can be obtained from Eq. (39) as dsi sis si0 ¼E 1 depl si si0

ð44Þ

A comparison of this relation with the experimental results is represented in Fig. 20b.

B.

Constitutive Equation of Cyclic Behavior

In contrast to these experimental facts, serious simplifications are usually made to reduce the number of the material parameters involved in computation. The hyperbolic function of Eq. (8) is simply linearized yielding dsi ¼ C gsi depl

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ð45Þ

where C and g are material constants. The stationary value sis is considered constant assuming that the material follows the Masing-rule and Eq. (5) is reduced to sis ¼ C=g

ð46Þ

Lemaitre and Chaboche [41,42] introduced a non-linear isotropic= kinematic hardening model, which provides predictions that are near to the experimental evidence. This model is applicable for isotropic incompressible materials. The yield surface is defined by the function F ¼ fðsij Xij Þ s0 ¼ 0

ð47Þ

where s0 is the yield stress that is equivalent to the isotropic material resistance sF and Xij is the tensor of the internal back stress denoted sis in the uniaxial case. The function f ðsij Xij Þ equals the equivalent Mises stress when the back stress X is taken into consideration: rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 3 0 ðs X0ij Þðs0ij X0ij Þ f¼ 2 ij

ð48Þ

where s0ij is the deviatoric stress tensor and is the Xij0 deviatoric part of the back stress tensor. The associated plastic flow is given by e_ pl ij ¼

@F pl 3 ðs0ij X0ij Þ pl e_ e_ ¼ @sij 2 f

ð49Þ

where e_ pl represents the rate of plastic flow and e_ pl is the equivalent plastic strain rate rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ e_ pl ¼ 2 e_ pl e_ pl ð50Þ 3 ij ij The size of the elastic range, s0 , is a function of the equivalent plastic strain epl and the temperature. For a constant temperature, it is written similar to Eq. (40) as

ð51Þ s0 ¼ s0 þ Q1 1 expðbepl Þ where sj0 is the yield surface size at zero plastic strain, and Q1 and b are additional material parameters that must be determined from cyclic experiment.

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The evolution of the kinematic component of the model, when temperature and field variable are neglected, is defined as 0 sij X0ij 2 pl pl _ X_ ij ¼ C_epl X ¼ C gX e ij ij e_ 3 ij s0

ð52Þ

where C and g are material parameters. C.

Application to Life Assessment

The assessment of the fatigue life under cyclic elasto-plastic deformation requires an accurate determination of the strain ranges of the individual loading cycles in the region of maximum local deformation. For this reason, FE simulation is often needed especially when the analytical solutions are not available or when they include unacceptable simplifications. For example, the fatigue life of notched machine parts is often predicted using approximation formulas [43–45] that have been driven using the Neuber rule [46]. However, the accuracy of these methods remains lower than that of the inelastic FE analysis, when adequate materials lows are implemented. Figure 21a illustrates the distribution of the axial stress sxx in a notched 3-point bending specimen. The mesh is built of three-dimensional continuum solid elements. Around the notch, a refined mesh is chosen so that the critical zone at notch root would cover several elements. The material considered is the AlZnMgCu alloy AA7075. The material parameters determined in uniaxial cyclic experiments are: sj0 ¼ 310 MPa, Q ¼ 75 MPa, b ¼ 36.6, C ¼ 14,844 MPa and g ¼ 86.3. As a loading condition, a line load with a total compressive force F is applied at the midlength of the upper surface. The force follows a sinusoidal time function with Fmin =Fmax ¼ 0:1. The specimen is supported at two parallel lines on the lower surface with a span width of 80 mm. The computational results of the local strain components at notch root are represented in Fig. 21b as functions of time. For an arbitrary loading cycle, the time functions eij ðtÞ are used to determine an equivalent strain range De for the cycle according to different approaches [47–52]. With an additional damage accumulation rule, a representative periodically repeated strain range can be computed which should lead to the same fatigue life. Experimentally, fatigue life is determined as the number of cycles, at which a technically detectable crack is initiated. Often, a direct current potential drop system [53,54] is used to determine the potential drop across the notch as time function. This is then converted to a relation between crack length and number of cycles to initiate cracks.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 21 (a) Distribution of the bending stress sxx in a 100 20 10 mm3 specimen with a notch radius or 6 mm. (b) FE computation results for the variation of local strain components at notch root.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 22 Representative strain range as function of the number of cycle to failure. (From Ref. 54.)

The equivalent strains, determined according to Ref. [48] for different notch radii vs. the number cycles to fracture are plotted in Fig. 22. The experimental results obtained for alternating tension–compression loading on smooth bars are also represented in Fig. 22 and are described by the usual function Detot ¼ Depl þ Deel with Depl according to the Manson– Coffin equation and Deel following a similar one: d Detot ¼ aNb i þ cNi

ð53Þ

The results of the notched bending specimens, obtained by the combination of FE analysis, strength hypothesis, and experimental life determination, lie in a scatter band around the uniaxial data. D.

LCF of Metal Matrix Composite Materials

The fatigue life of metal matrix fiber composites is found to be strongly reduced in the range of low cycle fatigue due to the formation of kink bands, at which fatigue cracks initiate. A cross-section of one of these materials is represented in Fig. 23a. This composite consists of a pure copper matrix and continuous fibers of

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Figure 23

Continued

the austenitic steel X5CrNi18-12. It is used mainly in the electrical industry as a contact material. The mean fiber diameter dm ¼ 200 mm and the volume fraction equals 40%. Under alternating elasto-plastic strains, the slim fibers buckle plastically within the softer matrix during the compression phase of the load cycle and then expand to the straight form in the tension phase. However, if the material is unloaded and the elastic part of the deformation diminishes, the fibers do not remain completely straight. This promotes lateral deflection in the next compression cycle and the fiber buckling increases from one cycle to the other. The fiber takes an S-shape in the first few cycles. With increasing number of cycles, bending localiza-

"

Figure 23 Copper reinforced by austenitic steel fibers. (a) Etched cross-section. (b) Initiation of fatigue cracks. (c) Crack growth.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

tion takes place at two points of each fiber, and a kink band is observed, which is inclined to the load direction [59–59]. Within the kink band, the matrix suffers high cyclic shear deformation, which may cause crack initiation. If the fibers are brittle, fiber fracture occurs at the kink band boundaries. Figure 23b shows the initiation fatigue cracks in a specimen subjected to alternating low cycle fatigue loading. The specimens were tested strain controlled with an alternating total strain value by a strain rate e_ ¼ 0:0017 sec1 [60]. A two-dimensional idealization is chosen in order to get a clear idea about the deformation process even when the results are only of a qualitative character. The material is supposed to consist of plain layers of cupper and austenitic steel. To simulate buckling, an imperfection must be introduced to allow for mechanical instability. This is done by bringing in an inclination with a small angle b (for example 28) which may represent a deviation between the load and the fiber directions resulting from a non-accuracy of the specimen geometry or a non-alignment of the testing machine axis. The computed distribution of the equivalent stress is shown in Fig. 24a for a small elastic tensile strain of 0.001. The volume fraction of the harder material component equals 40%. Due to the difference in the modulus of elasticity of the material components, higher stresses arise in the elements of the stiffer materials and they appear brighter in the plot. The gradient of the stress in the lateral (horizontal) direction is related to bending caused by stretching of the inclined network. Fig. 24b shows the stress distribution after reaching the maximum strain of 0.024 in the first cycle. The displacements are exaggerated in the plot. Both the material components are plastically deformed. The harder material appears in the mean brighter than the softer one. Fourteen cycles later, the mesh and the stress distribution look completely different, as shown in Fig. 24c and d for the time instants of reaching the maximum compressive strain of the 14th cycle and the maximum tensile strain of the next cycle. The originally softer materials show higher isotropic hardening due to the greater amount of accumulated strain. An inclined kink band can be easily recognized with high stresses in the matrix. The successive fiber buckling with increasing number of cycles can be more obviously observed under pulsating compressive stresses. A characteristic phenomenon is the initiation of an inclined shear band accompanied by a reduction in the specimen deformation resistance, deformation localization in the matrix, and hence a reduction in the fatigue life. Figure 25 shows a comparison between the 2D-FEM results for the deformed mesh with the fiber configuration in longitudinal section of

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Figure 24 The von Mises equivalent stress distribution in the deformed mesh. The darker the element, the lower the stress. Displacements are exaggerated. (a) Under partial elastic loading. (b) At the maximum elasto-plastic tensile strain of the first cycle. (c) At maximum compression strain of the 14th cycle. (d) At the maximum tensile strain of the 14th cycle.

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Figure 25 FEM-plots and etched longitudinal sections of cylindrical specimens subjected to pulsating compressive loads up to: (a) 135 cycles, (b) 157 cycles, and (c) 284 cycles.

specimens that have been subjected to the same number of cycles in pulsating compression LCF-tests. In both the experiment and simulation, the specimens are subjected to a compressive stress pulsating periodically between 450 MPa and –45 MPa. The influence of friction at the top and the bottom of the specimen is not taken into consideration in the simulation. The fibers are continuous with a volume fraction of 20%. The fibers do not appear as continuous dark lines in the optical photographs because they do not necessarily lie completely in the plane of the prepared section. The similarity of both configurations allows a better understanding of the failure mechanism as far as the history of deflections, local deformations, residual stresses, multiaxiality, and similar values can be followed up through out the test simulation.

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III.

CREEP BEHAVIOR

In contrast to plasticity, a long-time high-temperature creep exposure causes a continuous change in the constitution of the materials. Beside hardening by the increasing dislocation density, several microstructural events take place such as initiation of subgrains, precipitation, ripening, and coagulation of particles, oxidation, high-temperature corrosion or even phase transformation. The creep strain is accompanied by a slowly increasing damage process that covers a great fraction of the creep life. Constitutive equations based on a combination of overstress concept [62,62] and threshold stress concept [5,63] allow an adequate description of the materials behavior if successive damage is taken into consideration. The current value of the strain rate depends on the current values effective stress, which is the difference between the applied stress s and the internal back stress si , the particle deformation resistance sp , the material creep resistance sF and the degree of damage D. For long-time creep under low stresses, the creep rate can be represented by s si n sgnðs si Þ e_ ¼ C sF ð1 DÞ

ð54Þ

where in case of high-temperature creep Q C ¼ e_ 0 exp RT

ð55Þ

This relation is applicable for true stress and true strain rate. If the creep tests are carried out with a constant force, the applied engineering stress value is to be multiplied by the factor ð1 þ eÞ in order to account for the increase of true stress due to reduction of area. The engineering strain rate is to be divided by the same factor. In many cases of the modeling of high-temperature material behavior, it is highly recommended to use the same set of equation to describe timedependent creep and the time-independent plastic behavior. As discussed above, the low cycle fatigue can be described by s si ¼ 1 sF ð1 DÞ

ð56Þ

With decreasing strain rate, a transition takes place towards a timedependent creep behavior described by Eq. (54), which can be rewritten in the form.

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Figure 26 Transition between the ranges of time-dependent (creep) and timeindependent (plasticity) ranges. (From Ref. 40.)

s si ¼ sF ð1 DÞ

1=n e_ C

A continuous transition function may be given by m =n !1=m s si e_ ¼ þ1 sF ð1 DÞ e_ 0

ð57Þ

ð58Þ

as represented in Fig. 26. In contrast to low cycle fatigue behavior, with its relative short life, the parameter sF is considered in the case of long-time creep exposure as a constant reference stress and can be set equal to 1 MPa. In this case, only the overstress concept is considered. The kinematic hardening may include several components [64]: sd þ sS þ sp . The first term sd accounts for the variation of the dislocation density. An additional material resistance sS that accounts for subgrain formation can be taken into consideration, considering the material as a composite consisting of hard subgrain boundaries and soft subgrain interior [65]. The particle stress sp accounts for the interaction between mobile dislocaCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

tions and precipitates. It depends on the mean distance between the particles which may change in the course of creep exposure (Figs. 27). For engineering construction and life assessment, it is required to reduce the number of parameters to the amount that is essential for the description of the mechanical behavior and that can be determined with a tolerable experimental effort. Therefore, most engineering materials may be described well using si ¼ sd þ sS with a unique function of strain. The particle is then treated separately and eq. (54) is rewritten as s si s p n e_ ¼ C sgnðs si Þ ð59Þ sF ð1 DÞ

A.

Damage Function

Different formulations can be applied for the damage function D. Kachanov and Rabotnov [67,68] introduced the relation dD a ¼ ; dt ð1 DÞp

t 1=ðrþ1Þ D¼1 1 tf

ð60aÞ

where tf is the fracture time (Fig. 28). Other applicable functions are dD ¼ bDm ; dt dD ¼ c þ gD; dt

D ¼ ðt=tf ÞM D¼

expðgtÞ expðgt0 Þ expðgtf Þ expðgt0 Þ

ð60bÞ ð60cÞ

As the damage increases very rapidly with time in the late tertiary stage, a more accurate description can be achieved by formulating damage as a function of strain instead of the time function used above. In this case, a modified Kachanov and Rabotnov relation: D ¼ 1 ½1 ðe=ef Þ1=ðmþ1Þ or further function such as D ¼ ðe ef Þ1 ð1nÞ D ¼ ½expðbe=ef Þ 1 ½expðbÞ 1 can be applied.

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ð61aÞ

ð61bÞ ð61cÞ

Figure 27 Main factors affecting internal back stress. (a) Dislocations. (b) Subgrain boundary. (c) Particles. (From Ref. 66.)

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 27

B.

Continued

Internal Back Stress

If the applied stress is reduced from s0 to sR at a time point t0 , the strain decreases directly by ðs0 sR Þ=E to the strain value e0 , and starts to increase or to decrease depending on the value of the reduced stress sR . After a transition time, the steady state is reached again and the strain increases with normal strain rate expected for the stress sR . The relation between the subsequent creep strain e e0 and the time t t0 after the partial unloading is shown in Fig. 29. There is a certain value of the reduced stress sR at which the creep rate is reduced to 0 immediately after load reduction. This value of sR is equal to the current value of the internal back stress si according to Eq. (54). For materials with negligible particle resistance, it is equal to the internal back stress. If the particle stress sP and the additional substructure resistance sS can be neglected, the internal back stress si is only influenced by the evolution of the dislocation density and can be set equal to sd . In this case, the evolution of the internal back stress in the course of creep exposure under constant or varying stresses and temperatures can be formulated [70]. Even if the assumptions mentioned do not exactly hold, such a formulation can help in determining the creep behavior as a phenomenological description.

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Figure 28 Creep damage. (a) Crack and voids initiated in the tertiary range. (b) Description of damage as a function of creep strain.

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Figure 29 Ref. 69.)

Creep strain after partial unloading as a function of time. (From

Similar to Eq. (9), the internal stress component related to dislocation pﬃﬃﬃ density is defined as sd ¼ aGb r. With the evolution Eq. (10) of the dislocation density [5], the variation of the internal back stress is described by the relation dsi C1 ¼ ðsis si Þ de e1

ð62Þ

which is validated experimentally, e.g. in Ref. [69]. In this equation,sis is the quasi-stationary value of the internal back stress and e1 is the corresponding creep strain. Under constant stress and temperature, the internal back stress increases in the primary stage according to si e ¼ 1 exp C1 ð63Þ sis e1 with e1 as the strain at the end of the primary creep stage. This relationship is shown in Fig. 30 for different materials stresses and temperatures. The quasi-stationary value sis depends on the applied stress (Fig. 29). With increasing creep stress, sis increases approaching a saturation value siss . The experimental data for the secondary creep rate are usually well described by the Norton–Bailey relation e_ s ¼ AsN [71]. On the other hand, e_ s should follow the relation e_ s ¼ C ðs sis Þn . It can be shown that Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 30 Development of the internal back stress in the primary creep stage. (From Ref. 70.)

s=siss < N=ðN nÞ;

s=siss N=ðN nÞ;

" # sis s n N n s N=n1 ¼ 1 siss siss N N siss

ð64aÞ

sis ¼1 siss

ð64bÞ

as shown in Fig. 31. In these equations, N is the usual Norton–Bailey stress exponent N ¼ @ ln e_ =@ ln s. The parameter n depends on temperature. It can be set equal to 4 in the temperature range of the practical service conditions of high-temperature engineering materials. The saturation value siss depends on the temperature and can be described by the exponential function: siss ðTÞ ¼ k0 expðb=TÞ

ð65Þ

where k0 and b are material constants. As a rough approximation, siss can be considered as proportional to the creep strength Rm=1000 for a fracture time of 1000 hr and set equal to about 1:4Rm=1000 . Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 31 Relation between the quasi-stationary internal back stress and the applied stress.

After a sudden increase of the applied stress, the internal back stress starts to increase gradually approaching the quasi-stationary value (Fig 32a). If the applied stress is then reduced to the original value, a gradual reduction of the internal back stress towards the corresponding quasi-stationary value is observed (Fig. 32b). As the strain rate depends on the difference between the applied load and the internal back stress, a load enlargement leads to a very high strain rate that reduces gradually to normal value. In the same way, a load drop causes a severe strain rate reduction, even to negative strain rate values when s declined to a value lower than si . Figure 33a shows the creep rate curve of the austenitic 18=11 Cr–Nisteel under cyclic creep loading. The stress is changed periodically between 150 and 125 MPa. The period is equal to 96 hr. The influence of fatigue can be neglected and the material behavior can be described as a pure cyclic creep. Under cyclic stress, the influence of the creep strain transients is found to reduce the creep life. Compared with life values calculated by the linear damage accumulation rule

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Figure 32 Variation of the internal back stress after a sudden change of the applied stress. (a) Load increase. (b) Load reduction. (From Ref. 70.)

Figure 33 Description of strain transients under pulsating stress by the overstress model. (From Ref. 70.)

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Xt ¼L tf

ð66Þ

the value of L decreases to about 0.6 in case of cyclic stress at constant temperature and about 0.8 in the case of pulsating temperature under constant stress [72].

C.

Influence of Particles

1. Behavior of Dispersion-Strengthened Materials Dispersion-strengthened materials are usually produced by powder metallurgical techniques, especially mechanical alloying. They include very fine oxide or carbide particles embedded within the grains. The particles obstacle the dislocation motion and increase the resistance to deformation. The strength depends mainly on the size and the volume fraction of the dispersoids as well as on the consolidation process and the matrix material [73,74]. Contrary to precipitation hardening, the dispersoids are thermally stable and do not ripen or coagulate during long-time high-temperature exposure [75,76]. Therefore, such materials are predestined for applications under high-temperature creep conditions. Their behavior is studied under tensile and compressive loads, e.g. in Refs. [77–79]. Fig. 34a shows the creep rate curves of the Aluminum alloy AlSi20 which was produced from its powder without any additions by cold pressing and hot extrusion. This material includes an oxygen content of less than 0.5 mass%. The corresponding curves in Fig. 34b are determined for a dispersion-strengthened version AlSi20C1O2 produced by mechanical alloying. Carbon powder is added to the matrix powder and the mixture undergoes intensive milling before cold pressing and hot extrusion. The material includes a volume fraction of 4% of Al2O3 and 4% of Al4C3 as dispersoids with a mean particle size of 150 nm. The creep rate can be described by e_ ¼ f ðs sp Þ where sp is the additional resistance to deformation caused by the particles (Fig. 35a). The following simple relation can be used for the estimation of the minimum creep rate hs s iN p expðQ=RTÞ ð67Þ e_ s ¼ C E where E is the modulus of elasticity at the creep temperature, N is the Norton–Bailey stress exponent of the matrix material, Q is the activation energy for self-diffusion of the base element of the matrix. Fig. 35b shows that the creep strength is increased by a constant value which depends only on the volume fraction of the particles and their morphology.

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Figure 34 Creep rate curves of Aluminum Alloy AlSi20 [78]: (a) without, and (b) with dispersoids.

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Figure 35 Influence of dispersoids on creep stress [78], for arbitrary values of: (a) minimum creep rate, and (b) creep life.

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The particle resistance may be estimated by sp sO where sO is the Orowan stress given by MG 2b Ld ln sO ¼ 0:84 ð68Þ 4pð1 nÞ L d 2b In this equation, M is the Tailor factor, G is the shear modulus depending on temperature, L is the mean distance between particles, and b is the Burger vector. A precise description of the experimental data in the range of low creep stresses and high fracture times allows a model introduced by Reppich et al. [80]. According to this model, the additional particle resistance sp depends not only on the particle morphology but also on the applied stress. In the range of high creep stresses, sp approaches an upper limit sp , which can be set equal to the Orowan stress sO . With decreasing creep stress, the dislocation can overcome the particle resistance by partial climb, and the particle resistance is assumed to be directly proportional to the applied stress. Fig. 36 shows the relation between the relative particle resistance sp =sp as a function of the normalized creep stress s=sp . A continuous

Figure 36 Increase of additional particle resistance with increasing creep stress. (From Ref. 79.)

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transition from the range of low stresses to the range of higher once may be described by a function of the type " " #m !#1=m sp s ¼ 1 exp ð69Þ sp sp The upper limit of the particle resistance can be set equal to the Orowan stress: sp sO . 2. Precipitation Hardening The high-temperature creep behavior of precipitation hardenable industrial alloys is influenced by the kinetics of the precipitation and the ripening processes. Creep specimens are found to exhibit a longer creep life after solution treatment compared to those ones additionally aged before testing [81]. This phenomenon is attributed to the precipitation of fine particles during the early stages of creep [82], which strengthen the material and reduce the creep rate (Fig. 37). With increasing the creep time, the particle coarsening leads to an increase of the interparticle spacing and to an acceleration of creep strain rate.

Figure 37

Precipitates and dislocations in Alloy 800HT. (From Ref. 66.)

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The increase of the size of an existing precipitate can be considered according to the Oswald-ripening mechanism. However, the precipitation process under creep loads is rather complex and is expected to be dependent not only on the temperature but also on the change in the degree of supersaturation of the matrix as well as on the defect structure and dislocation density. Therefore, the rate of precipitation is assumed to depend on creep conditions. The particles strengthen the material by exerting an internal, or threshold, stress sp on the moving dislocations. According to the theory of Brown and Ham, reported by Martin [83], it is assumed that the high-temperature yield stress of particle-hardened material is controlled by local climb of dislocations over the particles sp ¼

S L

ð70Þ

where S is a material constant and L is the planar interparticle spacing. From geometrical considerations, it can be shown that the planar interparticle p spacing ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃL varies with Vp and d according to the relationship L ¼ p=ð6Vp Þd. The particle stress can be rewritten as rﬃﬃﬃ pﬃﬃﬃﬃﬃﬃ Vp 6 sp ¼ ð71Þ S d p An analytical model [84] that considers the influence of a continuous precipitation process accompanied by particle coarsening on the creep behavior of metallic materials will be discussed briefly in the following lines. The volume of particles per unit volume V p that precipitate out of the supersaturated matrix can be written as p ð72Þ Vp ¼ Np d3 6 where Np is the number of nuclei or the number of carbide particles per unit volume and d is the average particle diameter. The number of growing nuclei per unit volume, Np, that form during precipitation out of a supersaturated solid solution is known to depend on the degree of supersaturation, the temperature, and the defect structure, especially the dislocation density. At a given temperature, the value of Np can be written as Np ¼ Np0 þ fðtÞgðtÞ

ð73Þ

where Np0 is the initial number of nuclei and can be neglected in case of solution annealed materials, f(t) is a function of the temperature and the defect structure, g(t) is a function of the remaining supersaturation, which

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decreases during the precipitation process. During the primary creep stage, the dislocation density depends on the creep strain and f(t) can be written as fðtÞ ¼ f½a1 f1 ðTÞ þ a2 ðsn2 eQ2 =RT ÞM2 tgM

ð74Þ

where a1 , a2 , n2 , M2 , and M are constants, s, t, and T are stress, time, and temperature in Kelvin, respectively, Q2 is the creep activation energy and is close to the activation energy of self-diffusion. The first part of f(t) including f1(T) represents the nucleation under static conditions when no stress is acting on the material while the second part represents the effect of the applied creep stress. As precipitation progresses, the supersaturation of the matrix decreases. The function g(t) can be represented as a hyperbolic function of time gðtÞ ¼ ½1 þ ðBtÞn

m

ð75Þ

where n and m are parameters that control the rate of precipitation, B is a function of stress and temperature. The increase in particle diameter d with time due to Oswald ripening can be represented by the function [85]

1=m d ¼ dm0 þ Ct ðCtÞ1=m

ð76Þ

where d0 is the original particle diameter and may be neglected, m is a constant whose value depends on the particle growth mechanisms and C is a function of temperature given by C ¼ C0 expðQ1 =RT Þ, where Q1 is the activation energy of the coarsening process, e.g. for carbon in iron. Based on the experimental results, the first part of the function f(t) in Eq. (74) is expected to be small compared with the second part so that it may be neglected for creep loading. With this approximation, the volume fraction Vp can be written as Vp ¼

ðp=6Þ½a2 ðsn2 eQ2 =RT ÞM2 M C3=m tMþ3=m ½1 þ ðBtÞn m

ð77Þ

With increasing time, Vp approaches asymptotically a final value Vp1 that depends only on the initial supersaturation, but not on a function of time or stress, M þ ð3=mÞ must be equal to mn and the volume fraction Vp can be written as m ðBtÞn ð78Þ Vp ¼ Vp1 1 þ ðBtÞn

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As M must be positive, mn > 3=m. Taking m ¼ 3, mn > 1. Based on the above assumptions, the parameter B can be expressed as a function of stress and temperature as follows: Qa na B ¼ B0 s exp ð79Þ RT where Qa ¼ ð3Q1 =m þ M2 MQ2 Þ=ðmnÞ is an apparent activation energy without a specific physical interpretation and na ¼ n2 M2 M=ðmnÞ. Substituting Eqs. (76) and [78] in eq. (71), sp can be written as rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ m=2 S 6 ðBtÞn Vp1 sp ¼ 1=m t1=m ð80Þ p 1 þ ðBtÞn C The condition for maximum strengthening due to precipitation, e_ ¼ e_ min , is achieved when sp reaches a maximum value,sp max , after time t , thus nmm 2 1=n 1 ð81Þ t ¼ 2 B

Figure 38 Time to minimum creep rate of Alloy 800HT for different creep stresses and temperatures. (From Ref. 84.)

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 39 (a) Experimental data (markers) and (b) model results (curves) for the creep rate of Alloy 800HT as a function of time or creep strain. (From Ref. 66.)

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Figure 40 Creep rate curves of AA2024 in two heat treatment conditions. (a) Highly coarsened precipitates. (b) Solution annealed. (From Ref. 86.)

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

sp max

S ¼ 1=m C

rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ m=2 6 2 Vp1 1 þ t1=m p mmn 2

ð82Þ

Considering the stress dependence of the parameter B, the following relationships are determined: t ¼ A0 sna eQa =RT

ð83Þ

This relation is found to fit well experimental results for precipitation hardening austenitic steel (Fig. 38) and Aluminum AA2024. The variation of sp with creep time is given by the relationship sp sp max

m=2 1=m t ¼ n t ðnmm=2Þ 1 þ ðt=t Þ nmm 2

ð84Þ

Figure 39 shows a comparison between experimental results and model results for Alloy 800HT. Similar results, obtained for the Aluminum Alloy AA2024, are presented in Fig. 40. In order to determine the matrix behavior, the material is over-aged for a long span of time until the precipitates coagulate. The particle diameter and the distance between them are so increased that the particle stress can be neglected. This matrix behavior is described by Eq. (54). For the solution annealed condition, the influence of the particle stress is considered using Eqs. (59) and [84]. For practical applications, some of the parameters can be set equal to certain values. Assuming that ripening takes place on the basis of volume diffusion, the parameter m is to be set equal to 3. Furthermore, the variation of the volume fraction of the precipitates with time, according to Eq. (78), can be well described with m ¼ 2 as far as the parameter n can be determined by best fit of the experimental results (Fig. 41). With these values, the particle stress can be given by

t 1=3 sp 3n ¼ ð85Þ n t sp max 3n 1 þ ðt=t Þ

D.

Simulation of Creep Microcrack Growth

Under high-temperature creep exposure, failure takes place due to the initiation and growth of inter-crystalline cavities, in the form of voids or intercrystalline microcracks. In the case of high temperatures, low stresses and small grain size of the material, the inter-crystalline void initiation, growth and coalescence is the dominant damage mechanism. Several well-founded

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 41

Variation of the particle stress with time according to Eq. 85.

models were introduced to estimate the rate of void growth. At lower stresses, the voids grow by diffusion of atoms out of the void surface into the grain boundary. At higher stresses, the void growth takes place by a creep deformation of the surrounding material [87–94]. On the other hand, higher creep stresses can be allowed by lowering temperature or by increasing grain size. In this case, wedge type inter-crystalline microcracks are observed. A successive damage is caused by the growth of the existing cracks as well as by the continuous initiation of new ones. Most of these microcracks are extended over only few grain boundary facets (Fig. 42). In contrast to the long technical cracks, whose growth rate can be calculated by the methods of the non-linear fracture mechanics, there are only a few investigations about the initiation and growth of wedge type inter-crystalline creep microcracks. The micrograph of Fig. 42 shows a representative example for the form of the wedge type inter-crystalline creep microcracks. Few typical shapes and a preferred orientation can be identified. The microcracks start usually at grain triple points and extend along such grain boundaries, that are nearly perpendicular to the direction of the applied stress. All the different crack shapes can be explained by the fact that the initiation and growth of the cracks result from the grain boundary sliding.

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Figure 42 (a) Microcracks in a longitudinal section of a creep specimen of steel X6CrNi18-11 after creep fracture (s ¼80 MPa, T ¼ 7008C). (b) The role of grain boundary sliding in crack initiation.

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Figure 42

Continued

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

The estimation of the rate of growth of such microcracks can be achieved mainly by two methods: (a) the determination of the statistical distribution of the microcrack length and its variation with the creep time, and (b) finite-element simulation of the creep behavior regarding the material as a composite consisting of grains separated by thin grain boundary layer with different properties. 1. Statistical Model The fundamental concept of the statistical model is that a small fraction of short cracks and a high fraction of long cracks are expected when the growth rate is high, and vice versa [95–98]. In order to achieve reliable results using statistics, a great number of cracks have to be classified. Over a period of several years, about 50,000 cracks were classified in the steel X6 CrNi18-11 and more than 60,000 cracks in the steel X8CrNiMoNb16-16 for different temperatures and stresses. Based on the results of metallographic investigations, the following assumptions are introduced: (a) A crack grows quickly along the grain boundary from one triple point to the next, where it rests for a longer time before it grows again to the next triple point, (b) The crack length is always an integral multiple n of grain boundary facets and (c) every crack is initiated in the length class n ¼ 1 and grows step by step to next higher length classes. Let Z be the total number of cracks per unit area and Yn the number of cracks having a length n. In a time unit, Vn,n þ 1 cracks grow out of the length class n into the next higher length class (n þ 1). In the same time, Vn 1,n cracks grow from the lower length class (n 1) into the considered class n. The mean rate of growth is given by dn=dt ¼ Vn;nþ1 =Yn and the rate of change of dYn =dt ¼ Vn;nþ1 Vn1;n . As all cracks initiate with the length n ¼ 1, the rate V0;1 represents the rate of crack initiation and must be equal to rate dZ=dt of the increase of the total crack number. Therefore, following relation can be deduced: n dZ X dYi ð86Þ Vn;nþ1 ¼ dt dt i¼1 Denoting the fraction of cracks with the length of n by Xn, so that dYn ¼ Xn dZ þ ZdXn , the mean rate of growth ðdn=dtÞn of the cracks of the length class n can be written as ! P n dn 1 ni¼1 Xi 1 dZ 1 X dXi ¼ ¼ FðnÞGðtÞ Hðn; tÞ dt n Z dt Xn i¼1 dt Xn ð87Þ

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Figure 43

Statistical distribution of the inter-crystalline creep microcracks.

The first term denoted F(n) is determined by the statistical distribution of the microcrack length. This distribution can be described by Xn ¼ ð1 qÞqn1

ð88Þ

as represented in Fig. 43 for two different austenitic steels. Deviations are mainly observed in the range of long microcracks and low population. These deviations can be avoided by adding a second term including a Leibnitz series, but it will be neglected here. The function F ðnÞ is then given by F¼

q 1q

ð89Þ

The parameter q depends on stress, temperature, and the constitution of the material, but not on crack length. Therefore, approximately no influence of the crack length on the growth rate arises from this term. The function G, which is the relative rate of crack initiation, depends on the material and the creep conditions. In order to determine this func-

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tion, several creep tests are to be carried out until different stages of damage in tertiary creep stage are reached. Using the results of metallographic investigations and digital image analyzing systems, the function Z(t) is found to be described adequately by the Kachanov–Rabotnov-relation given in eq. (60a), as well as by the empirical relation. ðZ=Zf Þ ¼ exp½gðtf tÞ=tf

ð90Þ

where the index f indicates the value at fracture (Fig. 44). According to this relation g G¼ ð91Þ tf with g depending on material constitution, stress, and temperature. The quantity G remains constant during the creep test, as long as Eq. (90) is valid. The function H is determined by the rate of change of the statistical distribution (Fig. 45) and can be written as HðtÞ ¼ nq_ =ð1 qÞ, where q(t) is described by a power law according to q ¼ qf ðt=tf Þm . Hence, H can be written as nm q ð92Þ H¼ t 1þq

Figure 44 Number of cracks Z per unit area, related to its value at fracture as a function of the life fraction.

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Figure 45 Decrease of the fraction of short microcracks (n ¼ 1) with increasing creep exposure time.

The rate of growth reads

dn g qf ðt=tf Þm m ¼ 1þ n dt tf 1 qf ðt=tf Þm gt=tf

Just before fracture (t tf ), the creep crack growth is dn g qf m ¼ 1þ n dt tf 1 qf g

ð93Þ

ð94Þ

The model indicates that the ratio between the growth rates of long and short cracks is smaller than that expected by applying the fracture mechanics concept. 2. FEM Simulation The grain boundary can be considered as a thin amorphous layer surrounding the grains. Its thickness equals few atomic distances. At low temperatures, the grain boundary is harder than the crystalline grains. With increasing temperature, the grain boundary becomes more softer than the

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Figure 46

Idealization of the grain=grain boundary combination.

Figure 47

(a) Regular and (b) randomly modified idealization.

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grains. At higher temperatures, the grain boundary behaves as a viscous layer with much higher strain rate sensitivity than the grains. In the FEM analysis, two different material elements are used for the idealization of grains and grain boundaries with different material parameters (98), as shown in Fig. 46. The creep behavior of the grain interior and the grain boundary layers is described by the Norton–Bailey creep law e_ ¼ Cðs=s ÞN

ð95Þ

with s just equal to the stress unit. The parameters C and N are set approximately equal to the values determined for the entire in the secondary creep stage, neglecting the influence of the grain boundaries in this stage due to their small volume fraction. The grain boundary zone can be considered as a linear viscous Newton solid. Its stress exponent is set equal to unity as first approximation. A suitable thickness and the parameter C of the grain boundary layers are determined iteratively. Their values are varied till the fracture time computed for different creep stresses coincides with the experimentally determined values. In order to avoid all grain boundaries having the same orientation fracture simultaneously, the size of each individual element in the network is stochastically changed by adding random values to the grain node coordinates (Fig. 47). The network determined in this manner has to be considered as a quarter of the idealized body and to be symmetrically mirrored, so that no additional anisotropy is induced. The whole network can also be rotated by an angle between 0 and 608 to exclude preferred orientations for crack initiation. Two different crack initiation criteria are tried out: a strain criterion and a stress one. According to the strain criterion, a crack initiates as soon as the equivalent creep strain reaches a critical value. In this case, the grain boundary element is not totally eliminated but its thickness is reduced by a factor of 1=1000. Such a weakened element behaves during further deformation like a crack. The second criterion which is based on the maximum principle stress or the maximum shear stress instead of the equivalent strain is found to be non-applicable because the experimentally determined stress-life function could not be achieved with this criterion. With increasing extension of the whole mesh under constant load forces, the crack opening criterion is fulfilled first at a single grain boundary facet. The next crack opens at a different grain far from the first crack, but at a place where the orientation of the grain boundary facet is favorable. After the initiation of several individual cracks having a length of one grain

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Figure 48 Comparison between experimental data and computational results for the increase of the number of cracks with increasing creep strain.

boundary facet, the total creep extension of the mesh is high enough to induce crack growth along the neighboring facets which are steeply inclined to the load direction. In this way, cracks of length class n ¼ 2 initiate at different locations. With further growth, the individual cracks start to coalescence resulting in a great additional extension of the mesh. Fracture is considered to take place as soon as the total creep extension of the mesh reaches a predefined value, and the computation is stopped. Figure 48 presents the ratio of the number of cracks Z to that of cracks at fracture Zf as a function of relative strain e=ef determined by the finiteelement simulation and by the creep experiment. The comparison shows that most of the data from the finite-element simulation lie in the same scatter band as those of the experimental investigation. Figure 49 shows that the fraction X1 of short cracks having a length of one grain boundary facet slightly increases with increasing nominal stresses as determined in experiments and by the finite-element simulation. With these results, the main reason for crack initiation and growth seems to be the relatively high local strains, and not the local stress, in the neighborhood of the grain boundaries. Metallographic investigation confirms the existence of such deformations in the neighborhood of the

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Figure 49 Influence of creep stress on the fraction of short microcracks at fracture.

grain boundaries. The same procedure can be applied to estimate creep damage and fracture time of the technical geometries. An example is represented for the simulation of the creep behavior of a notched specimen [99]. Figure 50 shows the deformed mesh as well as a metallographic section.

IV.

BEHAVIOR UNDER IMPACT LOADING

During plastic deformation at high strain rates, such as in the case of forging or automobile crash conditions, the mechanical behavior of metallic materials is influenced by mass inertia forces, an increased strain rate sensitivity, and the adiabatic character of the deformation process. An accurate simulation of the material behavior needs an adequate consideration of the mechanical wave propagation, steeping and reflection phenomena [100]. Under impact loading, stress waves propagate through out the material and the strain distribution is time dependent and highly non-uniform. Figure 51 shows a long rod with a free front surface at x ¼ 0. The far end of the rod is fixed. The cross-sectional area is constant over the whole length and is denoted as A. If a force F is applied quasi-statically on the free

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Figure 50

Creep microcrack initiation and growth in a notched specimen.

front surface, one can assume that the stress F=A induced is uniformly distributed over the whole rod. On the other hand, if the rod is impacted, e.g. by a hammer at the front surface, the mass inertia forces cannot be neglected. The rod front is pushed forward by a velocity v. An arbitrary cross-section at a distance x from the free end dose not start immediately to move with the same velocity, before all masses between the front surface and the cross-section considered have been accelerated to the velocity v. This

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Figure 51

Material element in an impacted bar.

needs a certain time interval Dt. The longer the distance x, the longer the time interval. This explains why displacements, strains, and stresses propagate throughout the material in the form of mechanical waves with the characteristic wave properties, such as reflection at surfaces. At an arbitrary time point, the cross-section at the distance x is displaced by u. At a neighboring cross-section x þ dx, the displacement is u þ ð@u=@xÞdx. The strain in the material element dx is given by e ¼ @u=@x. The forces acting on the element are As and A½s þ ð@s=@xÞ dx. The mass inertia force is rA dxð@ 2 u=@x2 Þ. Therefore, Að@s=@xÞ dx ¼ rA dxð@ 2 u=@x2 Þ

ð96Þ

In the case of elastic behavior, @s @s @2u ¼E ¼E 2 @x @x @x

ð97Þ

and the following differential equation is obtained for the local displacement: @2u E @2u ¼ @t2 r @x2 Any function fðx ctÞ or fðx þ ctÞ fulfills this condition, when sﬃﬃﬃﬃ E c¼ r

ð98Þ

ð99Þ

A certain value of the displacement u ¼ fðx0 ct0 Þ that is observed at the distance x0 at the time point t0 arises at the distance x0 þ Dx after Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

the time interval Dt, yielding fðx ctÞ ¼ f½x þ Dx cðt þ DtÞ and hence, Dx ¼ cDt. Therefore, c is the propagation velocity of the longitudinal wave. If the load is applied in the lateral direction or if the load is a torsion moment, a transversal wave is induced that propagates with a velocity of pﬃﬃﬃﬃﬃﬃﬃﬃﬃ cT ¼ G=r, where G is the shear modulus. When plastic deformation takes place, the modulus of elasticity E and the shear modulus G are to be replaced by the tangent modules sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ @s=@e @t=@g c¼ ; cT ¼ ð100Þ r r While these equations are essential for analytical modeling, they have not to be necessarily externally considered in the numerical simulation when adequate computation codes are used. These codes must account for the mass of the material, for example, by considering point masses lumped at the nodes of the finite elements. Beside the FEM, the finite difference method and the method of characteristics are often applied. A.

Non-uniformity of Strain Distribution

If a tensile specimen is chosen too long or the impact energy input is relatively low, the local strain at the impacted specimen end is found experimentally to be much lower than that measured at the far end of the specimen. Such phenomena can be explained by an FE-simulation using a code for transient dynamic problems. The loading time function and the idealization of the impact tensile test arrangement are shown in Fig. 52. The material is considered as strain hardening and strain rate sensitive. Immediately after loading the specimen, an elastic and a plastic wave propagate along the axial direction of the specimen. The elastic wave is much faster than the plastic one. An elastic deformation propagates along the specimen to the far specimen head, where the elastic wave reflects. It runs back towards the near specimen head, where it reflects again. This

Figure 52

Input load time function and idealization of impact tension test.

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Figure 53 Variation of the distribution of the plastic strain in a tensile specimen at different time point after dynamic loading.

process is repeated many times during the propagation of the plastic wave, representing an elastic vibration superimposed plastic deformation process. The plastic wave propagates first throughout the specimen and is then reflected from the far specimen head. Due to superposition of the advancing and the reflected wave, high stresses and strains are induced at the far end of the specimen. If the impact energy is completely consumed by the plastic deformation, a permanent non-uniform strain distribution remains in the specimen (Fig. 53). With increasing impact energy, the plastic wave can run several times along the specimen, reflecting at both ends, before the impact energy W is completely consumed by the plastic deformation of the material. In this case, the strain distribution is approximately uniform over the whole gauge length (Fig. 54). B.

Fiber Composites Under Dynamic Compression

Under quasi-static compressive loading of a composite material, the slim fibers buckle within the softer matrix leading to a global plastic bending of the work piece. In order to simulate this behavior, an imperfection is

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Figure 54 Computational and experimental results for the local strain distribution along an impact–tension specimen of steel X6CrNi18-11, tested by different values W of impact energy.

introduced in form of a small inclination of 28 of the specimen axis, which showed that the specimens must buckle in the form observed experimentally (Fig. 55). Under dynamic loading, the specimens are found to get the usual barrel form of compression specimens. However, etched sections show that the fibers have undergone a buckling process. When the mass inertia forces are taken into consideration by regarding the material mass to be lumped at the nodes, the material behavior can first be understood [101,102]. A specimen buckling needs a lateral motion of the upper and lower contact surfaces in opposite directions. This motion is now obstacled by the inertia forces in the radial direction. The fibers buckle without causing a global bending of the specimen (Fig. 56). C.

Dynamic Notch Sensitivity

With increasing deformation rate, the strain rate sensitivity increases. This acts stabilizing on a tensile deformation process. As soon as neck formation starts, the local strain rate in the neck zone increases rapidly. The local flow

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Figure 55 Fiber buckling under quasi-static loading of copper reinforced by 45% volume fraction of austenitic steel fibers with 0.2 mm diameter. (From Ref. 101.) Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 56 Fiber buckling in a composite material under dynamic loading. (From Ref. 101.)

stress increases as well, so that higher tensile forces are needed for the continuation of extension. Other specimen regions undergo additional deformation, so that the uniform elongation increases with increasing strain rate sensitivity and extension rate. On the other hand, the adiabatic character

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Figure 57

Idealization of perforated plates.

of the deformation process reduces the flow stress and promotes instability. Mass inertia in the lateral direction arises in connection with radial acceleration due to the reduction of area. This causes the initiation of either lateral tensile or lateral compressive stresses depending on the time function of specimen elongation. In addition to these ductility considerations, an increased notch sensitivity is observed under dynamic loading. One of the reasons is that the local fracture strain decreases with increasing strain rate. This will be discussed later on in this chapter. The other reason lies in the interaction between

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Figure 58 Stress distribution around voids at different time points after impact loading: (a) t¼10 ms, smax¼598 MPa, (b) t¼18 ms, smax¼647 MPa, and (c) t¼24 ms, smax¼661 MPa.

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mechanical waves and notches. Figure 57 shows the idealized part of a perforated plate used in a study of the wave notch interaction [102,103]. The holes are chosen as circular or elliptical with different axes ratio and orientation. Also, the distance between the holes is variable. The variation of the stress distribution with increasing time, numerically computed, shows the propagation of the mechanical wave through the material (Fig. 58). Stress peaks are observed at the notch roots, before the maximum loading stress reaches this points. High stress values remain at the peaks, even when the maximum lading stress has passed through. Compared with the notch effect under quasi-static loading, the dynamic notch effect is characterized by higher stress and strain concentrations, greater strain gradients, lower stress relief by neighboring voids and lower influence of the orientation in the case of elliptical voids. V.

DUCTILE FRACTURE

The ductile fracture results usually from nucleation, growth, and coalescence of microvoids, that initiate mostly around inclusions. In accordance to its appearance of the fracture surface, ductile fracture can be classified into two cases [105]. In the case of softer materials, void nucleation at inclusions followed by marked void growth with internal necking and shear fracture of the intervoid matrix. The fracture surface shows a structured configuration of dimples often orientated perpendicular to the loading direction (Fig. 59). In case of high strength materials, shear fracture takes place without distinctive void growth. The matrix fails due to instabilities like shear bands forming between voids resulting in fracture with nearly no necking, promoted by low strain hardening material, high stress multiaxiality, and regions of high porosity [106]. A.

Failure Criteria

Beside macromechanical empirical failure criteria [107,108], several mesoscopic mechanical models are introduced. The failure criterion is defined by the local failure strain ef ðsm = sÞ as a function of the ratio of the local . mean stress sm to the equivalent stress s For the nucleation of microvoids, different models have been deduced considering an energy criterion [109–111], critical stress [112–114], or critical strain [115–119]. Rice and Tracy [120] deduced a closed-form solution for the rateof-change of the mean radius of a void, in an ideal plastic material, as a function of the current value of the radius and of the ratio between the mean stress and the effective stress

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Figure 59 SEM micrograph of fracture surface of highly over aged Aluminum AA7075 after tensile impact loading at room temperature. (From Ref. 104.) Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

¼ const:; s

1 dR ¼ 0:28 expð3sm =2 sÞ R de

ð101Þ

Hancock and Mackenzie [121] showed that the failure strain is assumed to be inversely proportional to the relative cavity growth rate (d ln R=de). The strain at fracture can be deduced from the Rice and Tracy criterion and be expressed as sÞ ef ¼ en þ a exp½3sm =ð2

ð102Þ

where en is the effective strain before void nucleation. The Rice and Tracey model has been used, e.g., in Ref. [122] and was verified by Thomason [123–125] in numerical simulations. Experimental results of Marini et al. [126] showed that the factor 0.28 of Eq. (101) should be replaced by higher values according to the volume fraction of inclusions. In Ref. [121], the local plastic strain which leads to coalescence of cavities was found to be highly influenced by the volume fraction of inclusions fN. Using special treatments for ferritic steels, different residual sulfur-concentrations were realized by Holland et al. [127] which were found to affect the fracture strain (Fig. 60a). These results were described by the modified relation s ef ¼ en þ a exp½bsm =

ð103Þ

where instead of the factor 3=2, a parameter b is introduced with values ranging between 5 and 23. The degree of purity had a drastic influence on en , which was affirmed by the investigation of further materials and treatments (Fig. 60b). Based on the models of McClintock [128] and of Rice and Tracey, Gurson [112] deduced a yield function for materials with randomly distributed voids of a volume fraction f. In this model, the flow rule according to Mises is extended by two additional terms including the porosity f. In more detailed investigations carried out by Tvergaard and Needleman [129–131], the Gurson model is modified yielding a plastic potential in the form h i 3 q2 skk 1 þ ðq1 f Þ2 ¼ 0 f ¼ 2 Sij Sij þ 2q1 f cosh 2sY 2sY

ð104Þ

In this equation, Sij is the stress deviator given by Sij ¼ sij dij skk =3 where dij is the second order unit tensor. sY is the yield stress of the matrix and skk is the sum of the normal stress components. f is a function of the volume fraction f of the voids according to f fc ;

f ¼f

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ð105aÞ

Figure 60 Influence of sulfur content in steel on: (a) the local effective strain at fracture as a function of ratio of mean stress to flow stress, and (b) the fracture strain for high multiaxiality as a function of the true strain in the neck zone of unnotched specimens, (Z ¼ reduction of area at fracture). (From Ref. 107.) Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

f > fc ;

1 f fc f ¼ fc þ fc q1 fF fc

ð105bÞ

where fc is the volume fraction at the beginning of void coalescence and fF is the volume fraction at fracture. The rate-of-change f_ of the void volume fraction, is considered as the sum of three different contributions: (1) the growth rate of existing voids, which is proportional to (1f ) and to the local strain rate, (2) the nucleation rate of new voids depending on the effective strain rate e_ in the matrix, and (3) the nucleation rate of new voids which is proportional to the rate of change of the mean stress sm ¼ dij skk =3. When the third contribution is neglected, the following relation is used for the evolution of fv : pl f_ ¼ f_growth þ f_nucleation ¼ ð1 f Þdij e_ pl ij þ Ae_

ð106aÞ

A non-zero value of A is only used if epl exceeds its current maximum in the time increment considered. In this case fN 1 epl eN ð106bÞ A ¼ pﬃﬃﬃﬃﬃﬃ exp sN 2 2psN where fN is volume fraction of particles that may nucleate voids, eN is the mean value strain for nucleation, and sN is the corresponding standard deviation. B.

Influence of Strain Hardening and Strain Rate Sensitivity

In an early study on the growth of cavities by plastic deformation of the surrounding material, McClintock [128] deduced a closed-form analytical solution for the rate-of-growth of cylindrical cavities of elliptical cross-section with the semi-axes a and b in a strain-hardening material which is "pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ # pﬃﬃﬃ 3ð1 nÞ sa þ sb 1 dR 3 n ¼ sinh s ¼ Ce ; ð107Þ 2 s R de 2ð1 nÞ Where R¼(aþb)=2 is the mean cross-sectional radius and sa and sb are the normal stresses in the direction of the ellipse axes. Because of its simplicity, the Hancock–Mackenzie relation is also applied to the range of high strain rates after introducing correction factors considering the influences of strain rate. Carroll and Holt [132] introduced a visco-plastic modification of the Hancock–Mackenzie model. Johnson and Cook [133] considered the strain rate sensitivity as well as the influence of the temperature on the local fracture strain ef ¼ ½D1 þ D2 expðD3 sm = sÞ½1 þ D4 lnð_e=_e0 ½1 þ D5 T=Tm

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

ð108Þ

with e_ 0 ¼ 1 sec1 and Tm the absolute melting point. As sm = s; e_ and T change during deformation, it is assumed that fracture takes place when a damage parameter D ¼ S½De=ef ðsm ; e_ ; TÞ reaches the value of 1. A failure criterion for void growth considering non-linear visco-plastic behavior of a strain-hardening and rate-sensitive material can be obtained using an analytical solution [134]. The void growth is to be determined by ¼ Ken ðe_ =_e Þm , with equivalent stress means of flow stress described by s _ , equivalent strain rate e, reference strain rate e_ ¼ 1 sec1 , equivalent plass tic strain e and the material constants K, n and m. A spherical void of radius R is considered to exist at the center of a metallic sphere (Fig. 61). At the outer radius L of this hollow sphere, a radial stress component srL is acting which is set equal to the mean stress sm ¼ ðs1 þ s2 þ s3 Þ=3, which leads to a visco-plastic deformation of the material and hence to an increase in void volume. For an arbitrary void radius r, the tangential strain rate is given by e_ t ¼ r_ =r. Under consideration of the plastic volume constancy,

Figure 61

Spherical void growing in a hollow sphere matrix.

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e_ ¼ 2_r=r. Regarding the continuity condition r2 r_ ¼ R2 R_ , the equivalent strain rate can be rewritten as e_ ¼ ðR=rÞ3e_ R ¼ ðL=rÞ3e_ L , and the correspond¼s L ðeR =eL Þn ðe_ R =e_ L Þm ðR=rÞ3ðmþnÞ follows from ing equivalent stress s _ _ ¼s L for e ¼ eL . In order to determine the distribution of the radial stress, s the condition of equilibrium @sr =@r ¼ 2ðsr st Þ=r is taken into considera where st is the tion. According to the von Mises yield criterion, st sr ¼ s tangential and sr is the radial stress component. With the boundary condition sr ¼ 0 for r ¼ R, a closed-form analytical solution is deduced for the rate of radius increase reading 1 dR 1 3ðm þ nÞ ðsr ÞL 1=ðmþnÞ ¼ ð109Þ L R deL 2 2ð1 fmþn Þ s with f ¼ ðR=LÞ3 , which is approximately equal to the volume fraction of L and voids. At the outer radius of the sphere (r ¼ L), the values of sr L , s e_ L can be regarded as equal to sm , s and e_ , which are determined for the construction element geometry considering the material as continuum. if f 51, the failure criterion is given by 3ðm þ nÞ sm 1=ðmþnÞ n m ¼ Ke ðe_ =_e Þ ; ef ¼ en þ a ð110Þ s 2 s In the cases of high temperatures or very high strain rate, this relation can be applied using n¼0 and m ¼ 1 as a special case ef en ðe_ ; TÞ þ C.

a ðsm = sÞ

ð111Þ

Growth of Microcracks

In order to increase the strength of engineering materials, several strengthening mechanism are adopted. Beside precipitation hardening, the strength of the matrix is increased by alloying elements. During plastic deformation, microcavities initiate in two different ways. (a) At low temperatures and high strain rates delamination takes place at the interface between matrix and particles leading to microcrack formation (Fig. 62a). (b) At higher temperatures or lower strain rates, particles fracture causing a microcavity that elongates with further plastic deformation (Fig. 62b). In order to consider damage by both cavitation mechanisms, a new model is introduced in Refs. [104,135]. In analogy to the Avrami theory of the kinetics of phase change [136], the following assumptions are made for the initiation and growth of microcavities. Precipitations and inhomogeneities embedded in a matrix can be interpreted as active nuclei for void

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Figure 62 SEM Micrograph of microcavitations in Aluminum AA7075 T7351 after impact tensile loading ð_e 3500 sec1 Þ. (a) Penny-shaped microcracks at room temperature perpendicular to loading direction. (b) Microvoid at 150 8C parallel to loading direction. (From Ref. 104.)

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

and crack initiation. The total number of particles representing possible nuclei for damage decreases with increasing global strain due to cavitation initiation at some of them. Around each cavitation, a region of reduced stresses and strains exists (hatched areas in Fig. 63) in which no further cavitations can initiate. This region is spherical with radius r in case of penny-shaped cracks and ellipsoid in case of microvoids which can be approximated by a cylinder with a constant radius a, which is equivalent to the mean particle diameter and a length of l. It can be assumed that the number of new cracks initiated per unit strain is proportional to the number of remaining particles lying outside the relieved regions. The size distribution of cracks in impacted specimens was determined by Curran et al. [137]. It was found that the linear crack growth rate dr=de is not a function of the current value of the radius r but only proportional to the relative nucleation rate of new small cavitations. In the case of penny-shaped microcracks, the spherical region of relieved stresses and strain grows spherically with a constant radial rate dr=de. In the case of microvoids, the cavitation radius remains constant, but its length changes with a constant rate (onedimensional growth). The degree of damage is proportional to the relieved volume fraction, so that the fraction of damaged area DðeÞ reads e k DðeÞ ¼ C 1 exp ð112Þ e

Figure 63 Particles (spots) acting as nuclei for cavity initiation. (a) Penny-shaped microcracks with spherical regions of reduced stresses (hatched areas) growing spherical. (b) Microvoids with cylindrical regions of reduced stresses growing one dimensional. (From Ref. 104.)

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 64 Experimental (marker) and computational (curves) results at different mean strain rates de=dt for tensile specimens of Aluminum Alloy AA7075 T7351. (From Ref. 138.)

with the material constant C and e , which is proportional to that strain, at which first damage occurs. The exponent k was found to be equal to 4 in the case of microcracks and 2 in the case of microvoids. As an application, this damage model was used to describe the flow curves of Aluminum AA7075 [138] measured in impact tensile tests at room temperature (microcracks) and 1508C (microvoids) (Fig. 64).

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D.

Starting Point of Ductile Fracture

In order to determine the failure criterion, which is defined by the local failure strain ef ðsm = sÞ as a function of the ratio between local mean stress sm , tensile tests on differently notched specimens and local equivalent stress s may be carried out. The time functions of specimen elongation measured experimentally can be applied as a boundary condition to FE computations in order to determine the local values of stresses and strains along the narrowest cross-section, which is assumed to be critical for fracture initiation (Fig. 65). As a result, the time-dependent distributions can be determined, as it is shown for two examples in Fig. 66 [135]. The analysis shows that in case of unnotched or smoothly notched bars, both the maximum equivalent plastic strain and degree of multiaxiality lie at the specimen axis (radius ¼ 0), whereas in case of a sharply notched specimen, the maximum equivalent plastic strain is reached in the notch root, where the degree of multiaxiality shows a minimum. Therefore, it can be stated that, in case of unnotched bars, the starting point of fracture lies at the specimen axis. On the other

Figure 65 FE Simulation of dynamic tensile test on a notched bar of Aluminum AA7075 (explicit code). (From Ref. 139.)

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Figure 66 FE simulation results for the distribution of plastic strain and multiaxiality in the notch cross-section of impact tension tests on specimens of Aluminum Alloy AA7075, highly over-aged. (From Ref. 104.)

hand, the starting point of fracture in case of notched specimens is found to depend on the notch radius. In bars with sharp notches, cracks are first initiated at the notch root. However, with increasing notch radius, the locus of the crack initiation is shifted to the specimen axis. Therefore, no general statement can be made for notched specimens and at first the starting point of fracture is considered to be unknown. Each point in the minimum cross-section is regarded to be a potential starting point for cracks. Therefore, the stresses and strains have to be checked along a radius in the minimum cross-section. Using the experimentally determined specimen extension at fracture as termination time point for the FE-simulation, the corresponding values of the local equivalent plastic strain eðrÞ and degree of multiaxiality sm ðrÞ= sðrÞ are computed for the different notch geometries at the different Gauss-integration points along the radius r of the specimen in the narrowest cross-section D0, as it is shown in Fig. 67 for Aluminum AA7075 highly over Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 67 Local equivalent plastic strain at fracture as a function of the degree of multiaxiality ðsm =sv Þ along the specimen radius at the narrowest cross-section of differently notched specimen of aluminum AA7075 highly over aged under (a) quasistatic, and (b) dynamic loading. (From Ref. 138.)

aged [138]. The results are represented by a continuous curve for each geometry (symbols). Each point of a curve represents a location r along the radius in the smallest cross-section. Only one point of each curve fulfills the failure criterion for ductile fracture, so that the envelope of all curves represents the failure criterion. For quasi-static loading (Fig. 67a), the envelope is described by the Hancock=Mackenzie relation and for dynamic loading (Fig. 67b) by Eq. (111). The comparison between the failure criterions determined for quasistatic and dynamic loading is represented in Fig. 68b in addition to that

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Figure 68 Failure criteria for Aluminum Alloy AA7075 in the (a) T7351, and (b) highly over aged condition under quasi-static and dynamic loading (elongation rate v ¼ 18 m=sec) at room temperature. (From Ref. 138.)

determined for the T7351 heat treatment condition (Fig. 68a). Under quasistatic loading, the local effective plastic strain for a given degree of multiaxiality is higher than in the case of dynamic loading. E.

Transition to Brittle Fracture

With strain rate and multiaxiality increasing, the local stress peaks become so high that they can reach the microscopic cleavage fracture strength sf of the material. Brittle fracture is expected, when the local value of the maximum principal stress s1 exceeds sf over a characteristic distance xc which depends on the microstructure of the material [140]. The transient temperature Tt from ductile to brittle fracture is shifted to higher values due to the increase of the maximum normal stress and can reach the current local temperature during the deformation process causing transition to brittle fracture (Fig. 69). The influence of the multiaxiality M ¼ sm = s on the maximum normal stress can be demonstrated by the simple case of proportional stresses with two equal principal stresses: sII ¼ sIII ¼ asI . With the mean stress ¼ ð1 aÞsI ; the maximum norsm ¼ ð1 þ 2aÞsI =3 and the effective stress s mal stress follows by eliminating a: 2 sm ðT; e; e_ Þ þ sII ¼ sIII ¼ asI ; sI ¼ s ð113Þ 3 s

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Figure 69 The transition temperature shift due to an increase in multiaxiality M ¼ sm = s, prestrain e and rate of elongation.

"

Figure 70 Influence of deformation rate and strength on the transition temperature shift [141]. (a) J-integral-temperature curves for steel 15NiCuMoNb5. (b) Transition temperature shift as a function of yield strength. (c) Measured and calculated values for the transition temperature as a function of the machine ram velocity v. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

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If this is the case, the brittle fracture condition is simply assumed to be sf sI ¼ 0. The microscopic cleavage strength sf can be considered as proportional to the modulus of elasticity EðTÞ. The transition temperature Tt from brittle to ductile fracture can be determined by the intersection of ðTÞ for given values of multiaxiality M, prestrain the functions sf ðTÞ and s e, and strain rate e_ . A variation of these parameters results in a shift of the transition temperature which is determined by DT ¼

ð@sI =@MÞDM þ ð@sI =@eÞDe þ ð@sI =@ e_ ÞD_e ðdsf =dTÞ ð@sI =@TÞ

ð114Þ

where dsf =dT dE=dT. However, this equation seems to overestimate the transition temperature shift. An alternative procedure for the determination of the effect of the loading rate on the transition temperature, which describes the experimental results more accurately, was introduced by Falk and Dahl [141]. This procedure needs the knowledge of a single value Tt1 for the transition temperature at a known loading rate as well as the relation between flow stress, strain rate, and temperature determined, e.g. in tension tests. According to their analysis, the transition temperature for another strain rate is determined by the intersection of the function mðTÞ and Tt1 þ DT=ð@m=@TÞT¼0 where m ¼ @ ln s=@ ln e_ is the strain rate sensitivity. According to this method, the transition temperature shift can be expressed by DT ¼

1 @m @m @m D ln e_ @T T¼0 @T @ ln e_

ð115Þ

Figure 70 shows experimental results determined and their description by Eq. (115).

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113. Needleman, A.; Rice, J.R. Limits to ductility set by plastic flow localization. In Mechanics of Sheet Metal Forming; Koisten, D.P.; Wang, N.M., Eds.; Plenum Press: New York, 1978; 237. 114. Fowler, J.P.; Worswick, M.J.; Pilkey, A.K.; Nahme, H. Damage leading to ductile fracture under high strain-rate conditions. Met. Trans. A 2000, 31, 831–844. 115. Argon, A.S.; Im, J.; Safoglu, R. Cavity formation from inclusions in ductile fracture. Met. Trans. A 1975, 6, 825–837. 116. Beremin, F.M. Cavity formation from inclusions in ductile fracture of A508 steel. Met. Trans. A 1981, 12, 723–731. 117. Ashby, M.F. Work hardening of dispersion crystals. Phil. Mag. 1966, 14 (2), 1157–1178. 118. Tanaka, K.; Mori, R.; Nakamura, T. Cavity formation at the interface of spherical inclusion in a plastically deformed matrix. Phil. Mag. 1970, 21, 267–279. 119. Chu, C.C.; Needleman, A. Void nucleation effects in biaxially stretched sheets. J. Eng. Mater. Tech. 1980, 102, 249–256. 120. Rice, J.R.; Tracy, D.M. On the ductile enlargement of voids in triaxial stress fields. J. Mech. Phys. Solids 1969, 17, 201–217. 121. Hancock, J.W.; Mackenzie, A.Z. On the mechanisms of ductile failure in highstrength steels subjected to multi-axial stress-state. J. Mech. Phys. Solids 1976, 24, 147–169. 122. Rousselier, G.; Phan-Ngoc, K.; Mottet, G. Elastic–plastic behaviour law including ductile fracture damage. SMIRT Paris 1981, 1, 119–128. 123. Thomason, P.F. Ductile fracture and the stability of incompressible plasticity in the presence of microvoids. Act. Met. 1981, 29, 763–777. 124. Thomason, P.F. An assessment of plastic-stability models of ductile fracture. Act Met 1982, 30, 279–284. 125. Thomason, P.F. A three-dimensional model for ductile fracture by the growth and coalescence of microvoids. Acta Met 1985, 33, 1087–1095. 126. Marini, B.; Mudry, F.; Pineau, A. Ductile rupture of A508 steel under nonradial loading. Eng. Fract. Mech. 1985, 22 (3), 375–386. 127. Holland, D.; Halim, A.; Dahl, W. Influence of stress triaxiality upon ductile crack propagation. Steel Res. 1990, 61, 504–506. 128. McClintock, F.A. A Criterion for ductile fracture by the growth of holes. J. Appl. Mech. 1968, 35, 363–371. 129. Tvergard, V. On localization in ductile materials containing spherical voids. Int. J. Fract. 1982, 18 (4), 237–252. 130. Needleman, A.; Tvergaard, V. An analysis of ductile rupture in notched bars. J. Mech. Phys. Solids 1984, 32, 461–490. 131. Needleman, A.; Tvergaard, V. Effect of material rate sensitivity on failure modes in the Charpy V-notch test. J. Mech. Phys. Solids 1986, 34, 213–241. 132. Carroll, M.M.; Holt, A.C. Static and dynamic pore-collapse relations for ductile porous materials. J. Appl. Phys. 1972, 43 (4), 1626–1636. 133. Johnson, G.R.; Cook, W.H. Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng. Fract. Mech. 1985, 21, 31–48.

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134. El-Magd, E. Influence of strain rate on ductility of metallic materials. Steel Res. 1997, 68 (2), 67–71. 135. Brodmann, M. Scha¨digungsmodell fu¨r schlagartige Beanspruchung metallischer Werkstoffe, Ph.D. Dissertation, RWTH-Aachen, 2001. 136. Avrami, M. Kinetics of phase change I. J. Chem. Phys. 1939, 7, 1103–1112. 137. Curran, D.R.; Seaman, L.; Shockey, D.A. Linking dynamic fracture to microstructural processes. In Shock Waves and High Strain Rate Phenomena in Metals; Meyers, M.A.; Murr, L.E., Eds.; Plenum Press: New York, 1981; 129–165. 138. El-Magd, E.; Brodmann, M. Influence of precipitates on ductile fracture of aluminium alloy AA7075 at high strain rates. Mat. Sci. Eng. A 2001, 307, 143–150. 139. El-Magd, E.; Brodmann, M. Ductility of Aluminium Alloy AA7075 at high strain rates. EURODYMAT Krakow, Nov. 2000. 140. Ritchie, R.O.; Knott, J.F.; Rice, R. On the relationship between critical tensile stress and fracture toughness in mild steel. J. Mech. Phys. Solids 1973, 21, 395–410. 141. Falk, J.; Dahl, W. Influence of loading rate on the transition behaviour of structural steels. J. Phys. IV 1991, 1, C3=613–C3–621.

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5 Tribology and the Design of Surface-Engineered Materials for Cutting Tool Applications German Fox-Rabinovich and George C. Weatherly McMaster University, Hamilton, Ontario, Canada

Anatoli Kovalev Physical Metallurgy Institute, Moscow, Russia

I.

INTRODUCTION

The materials for cutting tools have traditionally been chosen for their excellent hardness and wear resistance under the extreme service conditions (high stresses and temperatures) associated with a high-speed machining operation. The interaction between the tool and workpiece was once thought to lie wholly in the domain of the mechanical or physical response of the system to these conditions, and little attention was paid to the role of chemical interactions between the tool and the machined part. Recent research has challenged this viewpoint, and it is now realized that extensive physical as well as chemical interactions can occur, both between the tool and the workpiece, as well as with the surrounding atmosphere. These considerations have become of even greater importance with the current drive to higher machining rates, often under conditions where a lubricant is not or cannot be used, that marks modern manufacturing trends. The theme of this chapter is the role played by physico-chemical interactions in modifying and controlling the friction and wear of the tribo-couple (i.e., the critically loaded surfaces of the cutting tool and the workpiece) during high-speed cutting operations. The chapter is divided into three sections. In the first section, the characteristic features of

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friction and the role of ‘‘self-organizing systems’’ in helping to control the wear processes are described. A ‘‘self-organizing system’’ is one that responds to the external mechanical, thermal, and chemical forces with a positive feedback loop that leads to an improvement in the wear characteristics of the couple. Two types of stable secondary structures formed at the surface of the tool have been identified in ‘‘self-organizing systems’’. They are usually oxide films, either highly plastic or refractory and less plastic that form under machining conditions by reaction of the tool material with oxygen. The second section develops these ideas of self-organization for some common tool materials, and shows how they can be understood and exploited for alloys such as high-speed tool steels (HSS), cemented carbides, and cermets. A deep level of understanding of the complex interactions that lead to the formation of stable secondary structures has come from the use of techniques such as Auger spectroscopy and electron energy loss spectroscopy, which have been extensively used to study the wear craters formed during machining. These studies, when coupled to more conventional wear and friction experiments, clearly demonstrate the positive role of secondary structures in reducing the wear rate in the initial (runin) phase of wear. In addition, the formation of secondary structures is shown to prolong the steady-state wear regime, with positive benefits on the overall life of the cutting tool. In the third section, a number of recent trends to enhance the performance of cutting tools are discussed. These include the use of monolithic or multi-layered coatings, substrate modification, surface-engineered tools, and multi-layered self-lubricating coatings. Throughout the discussion, the role of secondary structures is highlighted, and the concept of a ‘‘smart’’ coating that can respond to the cutting environment (with a positive feedback) is proposed. Finally we propose that any future development of improved cutting tools will depend on a better understanding of the nature of the secondary structures. Examples are given as to how these improvements might be exploited for high-speed machining operations.

II.

TRIBOLOGICAL ASPECTS OF METAL CUTTING

A.

Cutting Tool Wear Mechanisms

Metal cutting is associated with mechanical and thermal processes that involve intensive plastic deformation of the workpiece ahead of the tool tip, and severe frictional conditions at the interfaces of the tool, chip, and the workpiece. Most of the work of plastic deformation and friction is

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converted into heat. In cutting, about 80% of this heat leaves with the chip, but the other 20% remains, increasing the temperature of the tool. The pressure at the nominal contact area during cutting is approximately 103 MN=m2, i.e., high pressure dominates, and extreme local temperatures (up to 13008C) can be encountered, especially during the high-speed cutting of steels [1]. The surface of the tool continuously comes into contact with virgin chip=workpiece material which has been unaffected by the environment, e.g. by oxidation. The freshly produced chips may interact chemically with the tool material. The contact friction behavior at the tool–workpiece interface has been shown to be adhesion related. The current understanding of this aspect of cutting is focused on the friction of a clean (in a physicochemical sense) and oxidized surface of a tool and a workpiece through their adhesive interaction [2]. At high cutting speeds (typical of modern operations), the mechanical and physical conditions at the tool–metal interface are far removed from the ‘‘classical friction’’ situation. These severe service conditions can lead to a very intensive, surface damaging wear of cutting tools. Several mechanisms of tool wear have been identified, namely adhesive wear, crater wear on the top rake face of the cutting tool due to chemical instability, including diffusion and dissolution, and abrasive wear. Some authors have also discussed electrochemical and de-lamination wear of HSS tools. Adhesive wear is caused by the formation of welded asperity junctions between the chip and the tool face. The subsequent fracture of the junctions by shear leads to microscopic fragments of the tool material being torn out and adhering to the chip or the workpiece. This kind of wear may occur at the flank face in low-speed cutting when the contact temperatures are low [3]. Abrasive wear is caused by hard particles of carbides or oxides in the work material or by highly strainhardened fragments detached from the unstable built-up edge of the tool. Wear due to chemical instability is very important in high-speed metal cutting because of the high temperatures prevailing at the contacting surfaces; this includes both diffusion wear and solution wear. Diffusion wear is characterized by material loss due to the diffusion of atoms of the tool material into the workpiece. Solution wear describes the wear mechanism that takes place when the wear rate is controlled by the dissolution rate rather than by convective transport. An oxidation reaction with the environment can produce a scaling of the cutting edges [1]. As shown in Fig. 1, for a given workpiece material, adhesive wear is found mainly at low cutting temperatures, corresponding to low cutting speeds. Wear due to chemical instability, including effects such as diffusion and oxidation, appears at high cutting speeds. Abrasive wear occurs under all cutting conditions. This type of wear is important for low-speed machining of cast iron and steels, but is less important for cutting conditions where wear due

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Figure 1 Schematic diagram of tool wear mechanisms appearing at different cutting temperatures corresponding to the parameters of cutting. (From Ref. 15.)

to chemical instability prevails. However, this mechanism of wear is very important for high-speed machining when oxidation of the workpiece surface leads to the formation of oxide particles which can be detached from the surface of the tool. B.

Tribological Compatibility and the Development of Materials for Surface-Engineered Cutting Tools

The increasing demands of modern manufacturing technologies for highspeed machining have spawned the development of new advanced materials for use as cutting tools, possessing a high level of productivity and wear resistance. The development of new cutting tool materials can be considered to be a typical problem of engineering optimization. In this process, an integrated engineering and physical approach is taken to the problem of developing novel wear resistant materials. The key concept, and one that forms the basis for the arguments to be developed in this review, is focused on the issue of tribological compatibility of two surfaces. Tribological compatibility is related to the capacity of the two surfaces to adapt to each other during friction, providing wear stability without damage to the two components for the longest (or given) period of time.

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In our case, the problem of compatibility is reduced to the development of materials for the ‘‘cutting tool–workpiece tribopair’’. The goal is to achieve stable tool service and a predictable rate of tool wear with a given set of cutting parameters. In this interpretation, compatibility implies an integrated optimization, both from an engineering (minimal wear rate) and physical (self-organizing) point of view. An understanding of compatibility follows from the concepts of what we might call ‘‘state-of-art’’ tribology. Modern tribology, an interdisciplinary science based on mechanics, physics, chemistry, materials science, metallurgy, etc., is a very complex subject. Models that generalize knowledge in this area of science and might be acceptable for engineering applications are critically needed. Since friction is a process of transformation and dissipation of mechanical energy into other kinds of energy, an energy-based approach is the most effective one from our point of view. In this review chapter, the feasibility of using an irreversible thermodynamic approach to the problem of the design of cutting tool materials is explored. The concepts of tribology can be used in the development of a simple algorithm for the development of novel materials. The solution can be implemented using the following steps: an assessment of the friction surface, including the analysis of selforganizing phenomena at the surface of the tribopair (2) the development of an optimal engineering solution (in our case—the development of an advanced material), ensuring the compatibility of the surfaces under severe friction, and (3) testing of the system to verify its compatibility. (1)

C.

Self-Organizing of Tribosystems

Friction is a dissipative process, with part of the mechanical energy (the work done by the external loading system) being expended by the accumulation of energy into surfaces and the generation of heat. The energy dissipation during friction leads to the accumulation of high plastic strains in the surface layers and the formation of an ultrafine-grained oriented structure [4]. This raises the free energy of the contact zone, by creating a high density of structural imperfections in the surface layers (the activation phenomenon). The activation process transforms the surface layers into an unstable or metastable state. From the point of view of thermodynamics, a transition to an equilibrium state is natural. Therefore, the activation process may be followed by passivation, i.e., a reduction in the free energy of the material as a result of interaction with the environment

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and the generation of protective secondary structures (formed by friction). A tribosystem can be considered to be an open thermodynamic system that exchanges energy, matter, and entropy with its environment. For these systems, the second law of thermodynamics is still operative, but a more complex and general behavior is found compared to the more classical case discussed in standard textbooks. According to the principles developed by I. Pigogine, the second law does not eliminate the possibility of highly organized dissipative structures being formed in an open tribosystem. In these systems, when the excursion from equilibrium exceeds some critical value (typical for cutting), the process of material ordering can proceed by the spontaneous formation of a self-organizing dissipative structure [5,6]. During friction and wear, structural adaptations of the materials of the tribo-couple evolve in response to the external conditions imposed by the cutting system, leading in many cases to drastic structural changes in the surface layers of the materials. These changes include many of the characteristic properties of the friction surfaces and the near-surface layers (e.g., geometrical parameters, microstructure, physico-chemical, and mechanical properties). The structural adaptation is completed in the initial stage of life of the tribosystem, i.e. during the running-in stage. Although evolving in a step-by-step fashion and becoming increasingly complicated during the stage, the secondary structures eventually stabilize for a given tribopair and conditions of friction. When the characteristics of the surface layers become optimal, the running-in phase is completed, and the parameters of friction (i.e. the coefficient of friction and the wear rate) stabilize [7]. During the self-organizing period, of the process of screening takes place [8]. The phenomenon of screening reflects the coordination of the rates of destructive and recovery processes in the friction zone. This is typical of a pseudo-stationary state where the processes of activation and passivation of the surface layers are in a dynamic balance. External reactions usually result in the destruction of the screening phase, but these reactions and the associated process of matter exchange with the environment may provide for its reactivation. With the correct correlation of these processes, the state of the system is stable, corresponding to a minimum in the rate of entropy production. Then, according to the principle of screening, any kind of interaction of the surfaces or destruction of the base metal should be eliminated. The contact area will be controlled by interactions of the secondary structures, and stable friction (wear) conditions prevail as long as the dissipative structures associated with friction are self-adjustable.

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1. Secondary Structures The self-organizing phenomenon (SO) is characterized by the formation of thin (from several nm up to a micron thick) films of the secondary structures (SSs) at the friction surface. These are generated from the base material by structural modification and=or by interaction with the environment. It has been estimated that 90–98% of the work of friction can be accumulated in the secondary structures, with no more than 2–10% in the primary structures. Thus, secondary structures represent an energy sink for the preferential dissipation of the work of friction [4,5,9,10]. The synergistic processes of adaptation to the extreme deformation, thermal and diffusive conditions associated with cutting can be concentrated in the thin layer of SSs. The self-organizing of the tribosystem is often accompanied by a kinetic phase transition. In this case, all the interactions are localized in a thin surface layer, the depth of which can be lowered by an order of magnitude than that typically associated with damage phenomena. The rate of diffusion and chemical reactions may also increase substantially, while the surface layers may become ductile. In addition, the solubility of many elements might be increased and non-stoichiometric compounds might form. There are two kinds of secondary structures: superductile and superstrong [10]. Secondary structures of the first type (SS-I) are observed after structural activation that is marked by an increase in the density of atomic defects at the surface. The structures are supersaturated solid solutions formed by reaction with elements from the environment (most often, oxygen). The reaction between oxygen and the substrate during the selforganizing phase can be very different from the classical case encountered in regular oxidation experiments. SS-I are similar to Beilby layers, having a fragmented and textured structure, aligned in the shear direction, and they are often free of dislocations [10]. In these secondary structures, the material may be superplastic (due to a very fine grained or amorphous-like structure) with an elongation up to 2000%. The amorphous-like structure of SS-I may also lead to a decrease in the heat conductivity of the surface, an important consideration in controlling friction of cutting tools [15]. Fragmentation of SS-I is often detected under severe friction conditions. From an energetic point of view, SS fragmentation is another mechanism whereby the structure of the surface layers can be modified. Secondary structures of the second type (SS-II or tribo-ceramics containing a higher percent of elements such as oxygen) are formed by thermally activated processes. The SS-II are usually non-stoichiometric compounds and, as a rule, they contain a deficit of the reactant. However, under heavy loading conditions (in particular, during high-speed cutting), non-stoichiometric compounds with an excess of the reactant have been

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observed [4]. Secondary structures of this type (SS-II) exhibit a very high hardness. It is thought that one of the benefits they bestow is to accommodate the stress associated with cutting by elastic rather than plastic deformation. The adaptation of the tribosystem in this case relies upon the high hardness of the thin surface film formed during cutting. On the other hand, destruction of the surface of the tool might be linked to the poor fracture toughness of certain SS-II structures. 2. Principles of Friction Control For the purposes of this paper, the entire diversity of processes that take place during friction can be divided into two groups: quasi-equilibrium, steady-state processes (encountered during normal friction and wear) and a non-equilibrium, unsteady state, associated with surface damage processes (Fig. 2). Surface damage is usually observed in the initial (running-in) and

Figure 2 Diagram of wear and friction process: (I) region of non-steady process (running-in stage); (II) region of quasi-equilibrium (steady-state) process (normal wear stage); (III) surface damage region (catastrophic or avalanche-like) wear stage. (1) Regular wear curve; (2) widening of the region of stable (normal) wear; (3) minimizing wear intensity of non-steady process (in the running-in stage); (4) combination of two main methods of wear control.

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final (avalanche-like) stages of wear. During the period of service under normal friction and wear conditions, no macroscopic damage of the contact surfaces can be observed. Normal friction corresponds here to the completion of the self-organizing processes discussed above and the transition to a stable stage of wear. Friction control in this context implies the existence of a stable tribosystem, which resists any instability leading to damage below the surface layers [4]. The transition from a thermodynamically non-equilibrium condition to a more stable, quasi-equilibrium condition is connected to the accelerated formation of a beneficial surface structure formed as a result of self-organizing. From the point of view of self-organizing, both natural and synthetic processes can be considered during friction. Therefore, it is necessary to try and control (or modify) the synthetic processes to encourage the evolution of those natural processes that lead to a minimum wear rate. The problem of compatibility includes developments that ensure the stabilization of the friction and wear parameters, in particular, by the selection of appropriate materials. 3. The Features of the Self-Organizing Process During Cutting To understand the features of the self-organizing phenomenon during cutting one should understand the processes occurring at the contact surface of the ‘‘cutting tool=workpiece’’ tribosystem over a range of cutting speeds [11,12]). Studies of cutting of a structural medium-carbon steel ( 1040) have shown that the tool life can vary dramatically (Fig. 3). At low speeds of cutting, up to 50 m=min, lying in the domain of cutting with HSS tools, intensive build-up formation takes place. The machined material transfer at the tool surface is frequently observed during the metalworking of common structural steels. At the same time, oxygen (from the air) penetrates into the cutting zone. Chip fragments containing Fe will react with oxygen and carbon at the tool surface and form a boundary layer of both iron carbides and oxides. This leads to a built-up edge. The formation of a built-up layer can be considered to be the result of self-organization of the ‘‘the toolmachined part’’ tribosystem at low cutting speeds. The built-up layer is a dissipative structure or composite ‘‘third body’’, which consists of heavily deformed and refined machining material as well as oxides, nitrides and other compounds generated during cutting. The built-up layer is similar in many ways to a composite material. The ‘‘ceramic-like’’ built-up layer offers significant protection to the tool surface. However, the stability of a built-up layer as a dissipative structure is very low, especially when cemented carbide tools are used. For example, the adhesive interaction of tungsten carbide grains with a machined part can lead to microcrack formation. These cracks

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Figure 3 Tungsten carbide tool life vs. cutting speed. Turning test data acquired with 1040 steel. Parameters of cutting: speed (m=min): 10–125; depth (mm): 1.0; feed (mm=rev): 0.2.

are generated at the interface of the phases due to the cyclical stress action at the points of adhesion with the workpiece, and leads to separation of carbide grains from the tool surface. The principal mechanism of wear (and hence, the dissipation of energy) of cemented carbide tool surface layers is the formation of microcracks and ‘‘drop-out’’ of the carbide grains. The failure of the built-up layer results in significant tool surface damage. The formation of a built-up layer demonstrates that the self-organizing of a system may sometimes lead to a minimization of the wear, but under other conditions, when a dissipative structure is unstable it may also lead to increased wear (for cemented carbide tools). At cutting speeds higher than 50 m=min (used without a coolant), the process of seizure intensifies. On the surface of the tool face close to the cutting edge, a zone of plastic contact with a high friction coefficient will be formed [3]. It results in the formation of a thin layer of heavily worked material at the tool=chip interface. The wear rate of the carbide tool is reduced with an increase in the cutting speed up to 50–80 m=min. At the optimum cutting speeds for carbide tools (50–80 m=min), the contact processes at the tool surface become nearly constant, the formation of the built-up layer decreases, and a flow zone forms [3]. The formation of the flow zone with an increase in the cutting speed is an outcome of self-organizing of the tribosystem, leading to a stabilization of friction. In this regime, the tungsten carbide grains undergo considerable fragmentation. This reduces the wear rate, due to a decrease in the volume of the spalled fragments. With a further increase in cutting speeds (more than 100–150 m=min), the wear rate again increases, due to an intensification of diffusion processes

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and the separation of carbide grains from the tool. These high cutting speeds lie in the domain of application of cermets and ceramic cutting tools. One of the principal features associated with cutting is a rapid increase in the dislocation density near the surface, with the deformation being localized in a thin layer. Under extreme cutting conditions, this layer can undergo dynamic recrystallization, leading to a very fine-grained structure. This structure appears to be very stable during wear, as it has the ability to both effectively accumulate and dissipate the energy [11–14]. The increase in dislocation density in this local volume is accompanied by activation of the surface layers of the tool leading to further interactions with the environment. This can result in the formation of passivated surface structures (i.e., solid solutions of oxygen in the metal or tribo-oxides), which might control any damaging adhesive interactions at the ‘‘cutting tool – workpiece’’ interface. Fragmentation of the carbides (or metal matrix) followed by subsequent formation of an energy-absorbing oxygen-containing surface film (at optimal cutting speeds) can also be considered to be an example of a ‘‘cutting tool=workpiece’’ self-organizing phenomenon. We conclude that a number of complicated self-organizing phenomena are encountered in a ‘‘cutting tool–workpiece’’ tribosystem. The selforganizing occurs at two different levels: (1) the macrolevel (the chip–workpiece interface), and (2) the microlevel (the workpiece–tool interface). At the first level, self-organization is associated with the formation of dissipative structures such as a built-up or flow zone (under different cutting conditions). At the second level, the self-organization is exhibited in the formation of dissipative structures such as thin films of secondary structures that may control the process of tool wear. Two advantages can be realized if the correct tool–workpiece combination can be found. Firstly, stable cutting can be achieved and the wear rate of the tool can be reduced. This leads to an improved workpiece quality [e.g., a better surface finish, improved dimensional accuracy [15]]. Secondly, the generation of specific stable secondary structures could significantly reduce both friction and surface damage. This can also lead to an increased machining productivity and improvements in the cutting tool life. The processes at both levels are interdependent. The present study is focused on phenomena that occur at the workpiece=tool interface, because these processes are critical to the tool life and improved manufacturing productivity.

III.

MAJOR CUTTING TOOL MATERIALS

It is possible to classify cutting tool materials according to their different characteristics and domains of application.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

A.

Universal Cutting Tool Materials

The principal focus of this paper is on the so-called ‘‘universal’’ cutting tool materials and their modifications (HSS and HSS-based materials and cemented tungsten carbides). These materials are used (more or less successfully) is a broad range of applications, not only for the machining of steels, but also for many other materials. A major trend in the metallurgical design of these cutting tool materials is the application of standard (or slightly modified) universal tool materials using different methods of surface engineering. There are several ways to improve the wear resistance of regular tool materials. The first one is by refining the structural components of traditional tool materials using the methods of powder metallurgy (powder HSS and fine-grained cemented carbides). The application of powder metallurgy HSS tools results in less surface damage under conditions of adhesive wear [17]. This is most important for the relatively brittle high cobalt HSS and super-HSS tool materials. Other methods are also available, for example, the refining of carbide particle sizes (and martensite grains in the case of high-speed steels) as a result of a surface laser treatment. In comparison to tool steels, cemented carbides [18] are harder and more wear resistant but they also exhibit a lower fracture resistance. On the other hand, they have lower thermal conductivities than HSS. In recent years, WC–Co alloys with submicron carbide grain sizes have been developed for applications requiring more edge strength and minimal surface damage. Typical applications include a wide variety of solid carbide drilling and milling tools. Mixed tungsten–titanium–tantalum carbides are used for steel machining to resist chemical (diffusion) wear. Tungsten carbide diffuses rapidly into the chip surface (Table 1) but a solid solution of Table 1 Dissolution Rate of Refractory Compounds vs. Temperature Relative to TiC [18] Dissolution rate at,8C Material

100

WC TiC TaC TiB2 TiN HfN Al2O3

10

1.1 1.0 2.3 9.9 1.0 2.5 1.1

500 10

1

10 108 1012 1024

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5.4 1.0 1.2 8.5 1.8 3.8 8.9

1,100

10

4

103 105 1011

3.2 1.0 8.0 2.8 2.2 2.5 4.1

102 101 101 102 105

Table 2 Relative Resistance of Different Chemical Compounds Against Abrasive Wear and to Dissolution in Iron at 7008C [16]

Material SiC WC Si3N4 Al2O3 HfN HfC ZrC TiC TaC TiCo0.75O0.25 HfB2 NbC TiO2 TiO Mo2C TiN

Relative wear resistance against abrasive wear

Material

Relative wear resistance against dissolution in iron

0.004 0.008 0.030 0.075 0.28 0.34 0.79 1.0 1.0 1.3 1.6 2.2 2.2 2.8 110 170

Al2O3 TiO2 TiO HfN TiN HfC TiCo0.75O0.25 ZrC TiC TaC NbC TiB2 Si3N4 WC Mo2C SiC

0.0000 0.0000 0.0000 0.0009 0.018 0.035 0.32 0.36 1.0 1.1 1.9 5.3 250 5,200 12,000 24,000

tungsten carbide and titanium carbide resists this type of chemical wear. Titanium carbide is more brittle and less abrasive resistant than tungsten carbide (Table 2). For this reason, tungsten carbide alloys have a better wear resistance for machining of cast iron when abrasive wear is significant. The amount of titanium carbide added to the tungsten carbide=cobalt alloys is limited to about 30%. It is obvious that during the high-speed cutting of steels, a surface phase transformation, resulting in the formation of oxygen-containing, stable secondary structures of the Ti–O type (see Table 2), might occur. The mechanism for Ti–O formation is described in some detail below for tribological materials. There is a dearth of information in the literature about the self-organization of these alloys during cutting, but it is clear that the formation of protective stable secondary structures can result in a significant tool life increase at elevated cutting speeds. B.

Specific Cutting Tool Materials

Specific cutting tool materials (e.g., ceramics, diamonds, or cubic boron nitride) have a unique serviceability but a limited domain of application.

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They are mainly used for the machining of non-ferrous alloys or hardto-machine steels and alloys. Such materials as diamond and cubic boron nitride have a high wear resistance due to their ability to dissipate the energy generated during friction into thin surface layers of atomic dimensions. The most important cutting tool materials of this type are ceramics [19] such as alumina or silicon nitride (Si3N4). The main advantages these materials offer for high-speed machining are their excellent hot hardness, chemical inertness, oxidation resistance, and ability to play a role as a thermal barrier due to their extremely low thermal conductivity at high temperatures [4]. The main drawback to ceramics is their low fracture toughness and the interactions found with ceramics such as SiAlON with certain grades of steel. Surface-engineered ceramics and functionally graded materials are the most advanced materials of this class for future application. The excellent stability of ceramics suggests the composition of the surface layer of a functionally graded tool material should be one that generates alumina at the surface on interaction with the environment. This will give a critical change in the cutting conditions due to minimal interaction with the workpiece, increased service stability, and heat flow redistribution from the surface of the tool to the chip and the surrounding environment. C.

Tribological or Adaptive Cutting Tool Materials

The characteristic feature of these materials is the formation of stable secondary protective structures during cutting. These structures lead to a concentration of the interaction between the tool and the workpiece into a thin surface layer that prevents further damage to the surface. Cermets are typical representatives of this class of material. Cermets usually contain titanium carbide or titanium carbo-nitrides (and recently more complex titanium–molybdenum–carbon–nitrogen and titanium–tungsten–carbon–nitrogen compounds) as the hard refractory phase, comprising approximately 30–85% by volume of the tool [15]. The metallic binder phase can consist of a variety of elements such as nickel, cobalt, iron, chromium, molybdenum, and tungsten. The crater and the flank wear resistance of titanium carbide and titanium carbo-nitride cermet tool materials are superior to those of conventional cemented carbide (WC) tools. Nitrogen additions to the hard phase lead to a higher wear resistance [15]. Titanium carbo-nitrides are the primary materials used for cutting tool applications. Titanium nitride and cubic boron nitride are excellent cermets when they are combined with a hard binder metal. Cermets are more wear resistant and allow for higher cutting speeds than tungsten carbides. The main drawback to traditional cermets is a lack of toughness and thermal shock resistance, but additions

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of molybdenum carbide and tantalum=niobium carbides have broadened their application range [20]. Cermets possess many of the characteristics of a tool material that is capable of filling the gap between conventional cemented carbides and ceramics. 1.

Frictional and Wear Behavior and Self-Organization of Adaptive Cutting Tool Materials As noted above, one of the characteristic features of cermets is associated with the formation of a thin layer of a protective secondary structure possessing some lubricity at the tool surface. The formation of a stable secondary structure results in an excellent surface finish and close tolerance on longer production runs [15], due to self-organization on cutting [21]. These attractive properties can be illustrated by comparing the shape of wear curves of cemented carbide and cermet tools. Cermets have a better adaptability as shown by the lower wear value during the running-in phase and more stable cutting conditions at the normal wear stage, due to the formation of these secondary structures (Fig. 4) [15]. The stability of the secondary structures is controlled by the thermodynamic stability of the compounds formed at the tool–workpiece interface. The thermodynamic stability of the compounds can be assessed by the enthalpy of formation of various cutting tool materials [15].

Figure 4 Wear comparison between cemented carbide and cermet cutting tools with 4135 alloy steel. (From Ref. 15.)

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Two types of cermets are used for cutting tools: –

–

those with a ductile metal matrix where the refractory phase content is more than 50%. The typical application of these materials is as turning inserts for high-speed cutting; those with a hard steel matrix where the matrix content is less than 30%. The typical application of these materials is as end mills for moderate cutting speeds.

One of the problems of traditional tool materials, especially at low and moderate cutting speeds when adhesion wear predominates, is connected with the low dissipative properties of the materials. The wear resistance is strongly correlated to the relaxation properties of the material, especially at the unstable stage of wear. If the tool material has a structure that is unable to effectively transform and dissipate the energy generated by friction (a concern with the majority of traditional tool materials), damaging surface relaxation processes (e.g., adhesion to the machined part or crack formation on the tool surface) dominate during cutting. Under these conditions, the thin surface films of SSs may become unstable and lose their ability to protect the metal surface against excessive wear. The SS that form on the metal substrate must possess favorable relaxation properties to avoid this situation [22]. Powder HSS, modified by the addition of titanium compounds, can adapt to the conditions of cutting and have better relaxation properties (compared to tungsten carbides), giving tribological compatibility under low-speed cutting conditions. The metallurgical design of these materials is based on the application of the principles of screening by self-organization, as discussed earlier. The screening effect prevents the direct interaction of the cutting tool and workpiece with the consequent destruction of the tool metal. The localization of the tool=workpiece interactions in the thin surface layers of the secondary structures prolongs the tool life. Presently, tool materials based on HSS made by sintering and hot extrusion of powders also contain between 10% and 50% of high-melting compounds (e.g., Sandvik Coronites, deformed composite powder materials—DCPM [23–25]). A characteristic feature of these tool materials is the reaction of refractory compounds (carbides, carbonitrides or nitrides of titanium) during cutting, leading to the formation of oxygen-containing surface layers (secondary structures). The wear resistance of these materials has been studied with regard to changes in the composition and structure at the surface of the tool during operation. The materials studied include M2 and T15 types of HSS as well as DCPM with an addition of 20% TiC. The wear resistance was assessed by the turning of a 1040 carbon steel using a tool that had indexable tetragonal inserts (with side length 12 mm).

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The cutting parameters used in the tests were at a speed of 55–70 m=min, a depth of cut of 0.5 mm and a feed rate of 0.28 mm=rev. The frictional properties of the tribopair under analysis were determined with the aid of an adhesiometer whose design is described elsewhere [20]. One rotary sample of the material to be studied was sandwiched between two polished samples made of a 1040 steel (of hardness HRC 30 or HB 180, see Fig. 5). To simulate typical machining conditions, the surface of the samples was heated by means of an electrocontact method to temperatures ranging from 1508C to 5008C. A standard load of 2400 N, was applied, leading to extensive plastic strain at the contact. The adhesion component of the friction coefficient responsible for wear at low and medium cutting speeds (typical for HSS tools) [3] was used as a measure of the friction (t). This parameter t was defined as the ratio of the resistance to shear of the adhesion bonds (formed between the sample made of the tool material

Figure 5 Schematic diagram of friction test apparatus. (1) Specimen made of machined 1040 steel; (2) specimen made of DCPM; (3) driving rope; (4) driving disk; (5) electrical contact wires; (6) isolation system.

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and the workpiece under test) to the short-time tensile yield strength of the softer contact body at the test temperature. The value of t is simply a measure of the resistance of the joint to shear. The friction condition at the surface of a cutting tool will be similar to that for which the value of t was measured. The results of the wear resistance tests are given in Fig. 6. As can be seen, the wear resistance of HSS tools is 2.0–3.5 times lower than that of DCPM tools. This reduction was associated with a significantly lower friction parameter of DCPM compared to HSS (Fig. 7), and a broadening of the range of normal friction (Fig. 6). Within the normal friction range, the rate of wear for DCPM is much lower than that for HSS (Fig. 6, curves 1–3). While the hardness and heat resistance values of the HSS T15 and DCPM are similar, the wear resistance of the latter is significantly higher (Table 3). In our opinion the lower wear intensity of the DCPM-tool material is related to the presence of titanium carbides in the structure and their subsequent transformation to oxygen-rich compounds during cutting. When studied by secondary ion mass spectroscopy (SIMS), the analysis of typical wear craters revealed the formation of oxygen-containing phases. The data in Fig. 8 demonstrate that the transformation of titanium carbide into an oxygen-containing phase starts in the initial stage of wear (during the running-in process, Fig. 8a). With further operation, there is increased surface oxide formation at the bottom of the wear crater. This process is accompanied by stabilization of the wear processes (Fig. 6 and 8b,c) and an expansion of the normal friction range. Evidently, this is determined by the phenomenon of self-organization that is connected with the emergence of secondary structures (titanium–oxygen compounds), which play the role of stable solid lubricants [25].

Figure 6 The dependence of the flank wear value of cutting tools on the cutting time: (1) HSS M2; (2) HSS T15; (3) DCPM. Turning test data acquired with 1040 steel. Parameters of cutting: speed (m=min): 55; depth (mm): 0.5; feed (mm=rev): 0.28.

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Figure 7 Impact of the test temperature on the frictional and wear characteristics as determined from wear contact tests for the DCPM with a 20% TiC addition.

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Table 3

Properties of HSS and HSS-Based DCPM materials [23] Heat Treatment

Material

Hardening Temperature of temperature tempering, 8C 8C

M2

1,220

T15

1,240

HSSbased DCPM

1,210

Triple treatment at 560 8C Triple treatment at 560 8C Triple treatment at 560 8C

Physico-mechanical Properties Hardness after heat treatment, HRC

Bending strength, MPa

Impact toughness, kJ=m2

Thermal stability, 8C

63–65

3,200

400

610

67–68

2,400

220

645

69–70

2,000

80

655

The microstructure of an as-polished lap section made across the cutting tool face in the wear zone is shown in Fig. 9(a). The corresponding distributions of Ti, O, and C along the direction I–I, as obtained by Auger

Figure 8 Mass spectra of a wear crater in a cutting tool made of HSS-based DCPM with a 20% TiC addition, determined as a function of the cutting time: (a) 4 min; (b) 20 min; (c) 24 min.

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Figure 9 Microphotograph of tool friction surface with films of secondary structures: (a) general view of the surface using secondary electrons; (b) distribution of oxygen close to the ‘‘built-up-crater’’ contact surface (SI, intensity of signals, arbitrary units).

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electron spectroscopy, are given in Fig. 9(b). In the left part of the micrograph (a), a build-up of 1040 C steel can be seen. The right part of the micrograph shows the distribution of dispersed hardening phases in the HSS-based DCPM. Angular (dark) particles of titanium carbide (less than 8 mm in cross-section) as well as dispersed tungsten and molybdenum carbides (less than 0.2–1.5 mm in diameter) are uniformly distributed in the HSS matrix. In the surface layers of the tool material, we can observe a zone of intense plastic deformation less than 5 mm in depth. There, dispersed particles of a titanium-containing phase have been drawn out parallel to the wear surface, forming a discontinuous film. The titanium carbides in the wear zone have been transformed into oxides (Fig. 8 and [23]). Titanium oxides are known to be much more plastic than titanium carbides, accounting for the plastic deformation of the particles in the surface layers of the HSS-DCPM on cutting. These results are confirmed by Auger-spectroscopy. Fig. 9(b) represents the distribution of the intensity of the characteristic Auger KLL lines for O, C, and the LMM (418 eV) line of Ti along the I–I direction in Fig. 9(a). The analysis volume includes the built-up layer (of 1040 steel), the built-up layer=wear crater boundary, and the DCPM volumes beneath the wear crater. At the interface, the titanium compounds show an increased concentration of oxygen and a decreased carbon content. The observed change in chemical composition is related to the instability of titanium carbide. Due to the high cutting temperatures (in excess of 4508C) and pronounced affinity for oxygen, titanium adsorbs the latter from the environment and forms thin films of oxygen-containing compounds, in agreement with the SIMS data presented in Fig. 8. The total plastic deformation of these particles at the wear surface is greater than 600%. The crystal structure of these compounds is believed to differ from the titanium oxides that would be obtained under equilibrium conditions (see below). An understanding of the self-organizing phenomenon is critically important for the development of advanced tool materials. A major interest in these studies (from the point of view of materials science) is the nature of the secondary structures forming under severe cutting conditions. According to the principles of current tribology, one of the main methods to control friction is the creation of stable secondary structures at the tool surface. The more stable are the secondary structures, the greater will be the tool life. The development of protective secondary structures can be manipulated by alloying or by surface treatment technologies. The type of secondary structures formed during cutting depends strongly on the conditions of cutting and the type of the material under analysis. A detailed study of the physico-chemical parameters of the SSs formed during cutting using a tool made of DCPM was done using AES, ELS, and

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EELFS methods. To interpret the atomic structure of the tool wear surface, data obtained in this work by the EELFAS method were compared to TiC and TiO2 standards. Fig. 10 presents the Fourier transform of data obtained on analyzing the extended electron energy loss fine structure (EXELFS) for titanium carbide (TiC) with a cubic (B1) structure. The positions of the main peaks (Fig. 10a) are consistent with the interatomic distances for a (1 0 0) plane in the cubic lattice of titanium carbide (see Fig. 10b).

Figure 10 (a) Fourier transform of EELFS close to the line of back-scattered electrons for TiC specimen, Ep¼1500 eV; (b) cubic lattice of titanium carbide (¼Ti; ¼ C).

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Fig. 11(a) shows data for TiO2 with the rutile (C4) structure. We can identify the type of bonds by using partial functions F(R) obtained from the analysis of the fine structure of spectra close to the characteristic Auger lines of oxygen and titanium. By comparing these data with those given in Fig. 9(a), we can see that TiO2 has a more complex crystalline structure than TiC. This explains the greater number of F(R)-function peaks. The positions of the main peaks are again in good agreement with the

Figure 11 (a) Fourier transform of EELFS close to the line of back-scattered electrons for TiO2 specimen with rutile structure, Ep¼1500 eV; (b) cubic lattice of titanium oxide (¼Ti; ¼O).

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interatomic distances for a (1 0 0) plane in the TiO2 lattice. The complete analysis of all the peak positions by the Fourier transform method shows that the interatomic distances O–O and Ti–O in the secondary structures are different from those discussed in the literature (see Fig. 11b). This may be related to a deviation from stoichiometry, or the interatomic distances, measured from an analyzed volume that is only several angstroms thick near the surface, are different from the equilibrium values. The evolution of the atomic structure in the surface films on the wear crater of the cutting tool is well illustrated by the data given in Fig. 12. The oxygen-containing films in the wear crater are significantly enriched with titanium and oxygen after only 5 min of cutting (see Fig. 12a–d). As this takes place, a periodicity in the arrangement of atoms of various types is observed both in the nearest coordination sphere and at greater interatomic distances, up to approximately 7 A˚ (see Fig. 12b). As noted above, the interatomic distances in these oxygen-containing films differ from those observed in equilibrium titanium oxides, including rutile (compare with Fig. 11). The very thinnest films may be 2D (twodimensional) phases whose atomic structure is close to the supersaturated a-solid solutions of oxygen in titanium. After 15 min of cutting, the degree of long-range order is reduced, while the intensities of peaks from higher order coordination spheres are less pronounced (see Fig. 12c). After 30 min of cutting (Fig. 12d), the translational symmetry at large interatomic distances disappears, and peaks at R > 4 A˚ are lost. The adaptability of the surface layer to external thermo-mechanical effects is the physical basis of such evolution. The surface is gradually converted to an amorphous state during the wear process (after cutting times of about 15 min). When a steady-state condition is reached, i.e., after the development of the SS is completed, the surface generates amorphous-like films having an effective protective function. The lattice instability of the solid solution of oxygen in titanium finally leads to complete amorphization of the water surface. A similar effect was observed earlier from EELFS data for TiN-coatings on worn cutting tools [26]. Typical EELS spectra of TiC, TiN, TiO2 obtained with a 30.0 eV primary electron beam are shown in Fig. 13. The elastic peak has a 30 meV FWHM (full width at half maximum). The high-resolution structures of the spectra are represented at 1000 magnification after normalizing. The experimental curves are approximated by Gaussian peaks in each spectrum in the range of 1–9 eV energy loss. In the series of titanium compounds TiC–TiN–TiO, the number of 4s electrons in the atomic sphere of the metal decreases from the carbide to the oxide. These electrons are transferred to the 2p orbital of the non-metal atom, and the band energy is lowered due to the increasing Ti–X attraction

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Figure 12 Fourier transform of EELFS close to the line of back-scattered electrons for a cutting tool made of DCPM after cutting times of: (a) initial stage; (b) 5 min; (c) 15 min; (d) 30 min.

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in this series. Accordingly, it is more likely that on being excited, electrons would pass from the 2p orbital to the 3d orbital. The peak observed at 6.8 eV corresponds to the X 2p ! Ti 3d transition (Fig. 13). The intensity of lines at about 6.8 eV is increased in the series TiC–TiN–TiO2. The Ti 3d orbital is hybridized with X 2p orbitals, but the energy of this pd orbital interaction is shifted downward along the energy scale as one moves from TiC to TiO, according to Eb(Ti–C)¼4.5 eV; Eb(Ti–N)¼4.8 eV, and Eb(Ti– O)¼6.89 eV [27]. The observed lineshift at 6.7 eV on the electron energy loss spectra for titanium compounds is in qualitative agreement with these data (see Fig. 13a–c). A partial distribution analysis of the valence electrons enables one to better understand the particular features of chemical bonds in titanium compounds and on the wear surface of cutting tools. The lines at 1.6 eV in the electron energy loss spectra reflect intraband transition t1g ! t2g in the p-band, while those at 3.1 eV correspond to transitions 2t2g ! 3eg in the s band of Ti-atoms. The reduced intensity of lines at 3.1 eV in the series TiO2 ! TiN!TiC is due to the decreased contribution of the ds-electrons of Ti to covalent-ion bonds. This arises when the 4s-electrons of Ti are transferred into the 2p orbital of a non-metal atom in a titanium compound:

Figure 13 Representative EELS spectra of energy loss region 0–10 eV below the elastic peak of (a) TiC, (b) TiN, (c) TiO2. The spectra were obtained using a 30.0 eV primary electron beam.

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this orbital is more completely filled in the case of oxygen than in either nitrogen or carbon. For this reason, when the 3d Ti- and 2p X orbitals are hybridized, the contribution of the ds-electrons of Ti is less pronounced in the oxide and more expressed in the nitride and carbide. Consequently, the oxide has considerably less strength and hardness than the carbide or nitride [27]. The interaction of Ti–Ti atoms is realized at the expense of dp-electrons. The metallic nature of this compound is related to the high density of dp-electrons. As seen in Fig. 13, the intensity of t1g ! t2g transitions in the p-band is relatively insignificant in TiC, but it is much higher in TiO2. This implies that the density of conduction electrons is low in TiO2 but it is higher for TiC and TiN. This is consistent with the electrical conductivity data of these compounds, which is extremely low for the dielectric TiO2, but 16,400 (Ohm m)1 for TiC and TiN, respectively [27]. The replacement of carbon with oxygen in titanium compounds was shown to change their properties significantly. Thus, the oxidation of TiC at 823 K for 30 min influences the electronic structure of the material, the electron spectrum acquiring some features specific to TiO2 (see Figs. 14a

Figure 14 Representative ELS spectra: (a) after oxidation of TiC by heating up to 823 K for 30 min in air; (b) wear surface of DCPM cutting tool after 5 min of operation; (c) wear surface of DCPM cutting tool after 30 min of operation. The spectra were obtained using a 30.0 eV primary electron beam.

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and 13c). After oxidation of TiC, the intensity of the lines at 6.7 and 1.6 eV is substantially enhanced. On oxidation, the titanium carbide loses its metallic properties and acquires those of a dielectric. In this case, we observe a reduced concentration of conduction electrons and a localization of the electron density both in the metal and non-metal atoms. This is shown by the increased intensity of the peak at 1.6 eV corresponding to p-states in the 3dd-band of titanium (see Fig. 13a). It was noted earlier that an intense oxidation of TiC could be observed during the operation of a DCPM tool [20,22]. In this case, the nature of the phase transformation differs significantly from that found on heating a TiC standard up to 823 K for 30 min. Figure 14(b) and (c) presents electron energy loss spectra from the wear crater after 5 and 30 min of DCPM-tool operation. As the wear time increases, the spectra display a somewhat increased intensity of peaks at 6.8 and 3.1 eV. Peaks corresponding to plasmon losses (p1 and p2) appear, while the peak at 1.6 eV is significantly attenuated. The thin SS films in the wear crater of the cutter are associated with the formation of supersaturated solid solution of oxygen in titanium due to the oxidation of titanium carbide. In this case, we observe an increase in the electron density in the 2p orbital of the non-metal (peak 6.8 eV) as well as an enhanced filling of the ds-electron band of titanium atoms (peak 3.1 eV). These effects are similar to those encountered in the model oxidation of TiC (Fig. 14). There are, however, substantial differences. As the cutting time increases, the effects brought about by the crystalline structure of phases become significantly weakened in the electron spectrum. The splitting of the 3d orbital into p and s-states degenerates, the intensity of t1g ! t2g transitions is reduced as well as the density of p-electrons which are related to the long-range Ti–Ti bonds in the lattice (along the diagonals in the (1 0 0) planes). These distinctive features of the electron structure are related to amorphization and to the increasing role of short-range interatomic bonds. Of considerable interest is the appearance of plasmon loss peaks p1 and p2 in the spectra of Figs. 14(b,c) due to the growing concentration of conduction electrons. The delocalization of p-electrons close to the titanium atoms enhances the metallic nature of bonds in the amorphous films developed on the friction surface. These specific traits of electronic and atomic structural change might help to explain the unique mechanical properties in the secondary structures of the first type. The high wear resistance and good frictional properties of DCPM tools are associated with complex structural and phase transformations on the surface, among them TiC oxidation and the development of thin protective amorphous films. The SSs are saturated or supersaturated (amorphous) solid solutions of oxygen in titanium, whose electron structure is characterized by a high density of conduction electrons giving metallic characteristics.

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These results show that the SSs formed during cutting not only increase the DCPM-tool life but also change friction characteristics as well. The amorphous-like secondary structures of the first type behave like a solid lubricant with enhanced tribological properties [4]. Additional alloying of the DCPM might be beneficial. For example, the partial substitution of titanium carbide by aluminum oxide, which is stable under cutting leads to a decrease in the friction coefficient (Fig. 15)

Figure 15 Impact of the test temperature on the wear and friction characteristics as determined from wear contact tests for the DCPM with 15% TiC þ5% Al2O3; 20% TiCþ2% BN and 20% TiCN additions.

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and in an increase in the wear resistance of the tool (Fig. 16). The decrease of the friction coefficient when Al2O3 is added is important not only as it increases the wear resistance but also because it lowers the cutting temperature at the tool surface [28,29]. Alloying often cannot be implemented by the traditional metallurgical methods since this may induce an undesirable change in the properties of the cutting material. We took a different approach by making small additions of low-density compounds, which are relatively unstable at the operational temperatures. This allowed us to use this compound in relatively small quantities (up to 2 w%) with minimal possible impact on the bulk properties. The solid lubricant (hexagonal BN) was chosen as the additional alloying compound [28]. The high probability of oxygen-containing secondary phases formed from BN during cutting was also taken into account. The possibility that TiC and BN might oxidize and generate thin surface oxide films for exploitation in cutting tools can be assessed by a thermodynamic approach [27]. Secondary ion mass spectroscopy investigations have shown that on cutting DCPM with a boron nitride addition, oxygen-containing compounds develop at the wear-crater surface, associated with a set of parallel disassociation reactions of BC, BN, TiC leading to the formation of BO, TiO and TiB,N. Figure 17a–c presents spectra of the positive and negative

Figure 16 Wear curves of friction contact materials: (1) DCPM with 20% TiC; (2) DCPM with 20% TiC and 2% BN; (3) DCPM with 15% TiC and 5% Al2O3; (4) DCPM with 20% TiCN. Turning test data acquired with 1040 steel. Parameters of cutting: speed (m=min): 90; depth (mm): 0.5; feed (mm=rev): 028.

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Figure 17 Mass spectra of secondary ions of BN-doped DCPM specimen after 4 min cutting determined at different depths beneath the surface of a wear crater: (a) 0.5 mm; (b) 0.15 mm; (c) at the surface.

ions obtained upon analyzing the chemical and phase composition of a BNdoped carbide steel, investigated at various depths beneath the crater surface. In the volume closest to the tool surface (0.15 mm), there is an increase in intensity of peaks O, BOþ, TiOþ and a decrease in the intensity of peaks BN, BCþ and TiC2þ compared to data gathered at a greater depth (0.6 mm). Weak peaks corresponding to TiBN and TiBO also appear (see Fig. 17a–c). As a rule, the observed ions in the SIMS method cannot be related directly to the compounds encountered in the analyzed regions, but they provide a useful ‘‘fingerprint’’ that allows one to identify the compound. Figure 18 presents the SIMS data from different depths beneath the wear crater surface for a specimen of the same material. Comparing these data with those shown in Fig. 17c, one can see that an appreciable weakening of the intensity of the peak BCþ, the disappearance of peak TiC2þ, as well as pronounced enhancement of peaks BOþ, TiBNþ and TiBOþ, are characteristic of the formation of thin surface films. These are compounds of titanium and boron with oxygen and nitrogen, formed as a result of the carbide and nitride reaction with the atmosphere. The degree to which particular crystalline structures can develop secondary structures depends on the composition of the tool material. A comparative analysis of the nearest atomic neighbors using EELFS

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Figure 18 Change in absolute and relative values of the peak intensity of the secondary ion mass spectra for the BN-doped DCPM tool at different depths beneath the surface of the wear crater developed after 4 min cutting.

spectroscopy was done to demonstrate this phenomenon for the phases that form on the wear crater surfaces of M2 high-speed steel, DCPM and BNdoped DCPM tools. Figure 19a–c show Fourier transforms obtained from data collected from the surface of wear craters in HSS and DCPM alloyed with either TiC or TiC with BN. The F(R) functions feature pronounced peaks in the range 1–2, 4–5 and 7–8 A˚ for all cases. Using partial F(R) functions obtained by analysis of the fine structures close to the Auger lines of C, B, and Ti, it was possible to interpret the nearest-neighbor interatomic bonds. It was found that Fe–O bonds are typical of the HSS sample, while B–O and Ti–B bonds are observed at the wear crater of the BN-doped DCPM sample. The results of these investigations have shown that the composition of the tool material not only determines the composition of the phases developed at the friction surface in the cutting zone, but it also exerts an influence on the perfection of the crystalline structure of the new phases. The thinnest films of iron oxide formed on the HSS-tool friction surface are crystalline,

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Figure 19 Fourier transforms of extended fine structure within the range of 250 eV close to the line of elastic scattering of electrons with primary energy E¼1500 eV from the wear crater surface in a cutting tool made of (a) M2 HSS; (b) DCPM; (c) BN-doped DCPM.

as shown by the pronounced F(R) function maxima at R 4.3 A˚ and R 7.4 A˚ (see Fig. 19a). These are secondary structures of the second type, i.e., oxides whose composition is close to being stoichiometric, [4,10]. As seen in Fig. 19(b and c), tools made of a TiC-containing composition of DCPM and of a [TiC, BN]-doped DCPM posses very different secondary structures in the cutting zone, which are quite distinct from the surface films formed at the HSS-tool surface (Fig. 19a). The surface of the DCPM tool reveals the development of secondary structures of the first type, i.e., supersaturated solid solutions having an amorphous-like structure [4]. This is shown by the attenuation of the peak intensity of the Fourier transforms in the vicinity of the coordination spheres at R 4–5 A˚ and R 7–8 A˚. BN-additions to DCPM enhance the amorphization effect for oxygen-containing phases. This is clearly shown by the attenuation of the peak intensity in the vicinity of 4–5 A˚ (see Fig. 19c in comparison with Fig. 19b). Thus, both mass spectroscopy and the EELFS data indicate that secondary, oxygen-rich, amorphous structures develop on the surface of the BN-doped powder sample. Judicious alloying of a carbide steel through BN-doping is beneficial for the development of complex compounds of TiBxOy that appear on the tool surface along with simpler compounds of

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the TiO family. The amorphization of secondary structures probably depends on the DCPM composition and on increases in the level of BNalloying. One can see that the wear resistance of this material is increased by 80% compared to the carbide steel having a base composition with 20% TiC (Fig. 16). This suggests that alloying enhances the stability of the secondary structures developed during friction. This is promoted by the presence of BO-type compounds that act as liquid lubricants [at elevated cutting temperatures [28]] and promote the stability and the self-organization of the complex compounds. This is of paramount importance for tool wear resistance. The thickness of the stable secondary structures layer does not exceed 0.1–0.15 mm (Fig. 18). Finally, it is possible that such alloying of DCPM provides both a reduction in the friction coefficient and a broadening of the normal wear stage. In our opinion, the same goal can also be achieved in HSS-based DCPM by the substitution of TiC with TiCN. Figures 15 and 16 demonstrate that this substitution is extremely effective, decreasing the friction coefficient to abnormally low values (in the range of 0.03–0.05) at a service temperature of 500–550 8C, and significantly increasing the tool life (Fig. 16). In this case, the self-organization mechanism differs somewhat from the process found for materials alloyed with BN. With TiCN the diffusional transfer of nitrogen into the chip arises from dissociation of TiCN during cutting [26]. The increased nitrogen concentration on the contact surface of the chip is a direct consequence of the mass transfer of nitrogen, formed by dissociation of nitrides and carbo-nitrides. Such mass transfer takes place under the extreme temperature and stress conditions encountered in the friction zone. Therefore, the selection of titanium carbo-nitride for cermets and titanium nitride as the hard phase in Sandvik Coronites seems to be completely reasonable from the standpoint of tribological compatibility. The behavior of titanium nitride should be comparable to a carbo-nitride [24,30] and this has been confirmed experimentally by the analysis of the self-organizing phenomenon of PVD TiN coatings (see below). Another important factor is the thermal stability of DCPM compared to cemented carbides. The importance of the thermal stability of this type of material is evident at elevated cutting speeds. One way to improve this property is to increase the volume fracture of the hard phase in the DCPM; e.g., Sandvik Coronite has 50% of the hard phase (TiN) [30] and its wear resistance is higher than either HSS or cemented carbides (Fig. 20). So the benefits of an adaptive material are obvious from the standpoint of both wear resistance and tribological compatibility. However, the application of these materials is currently limited, although the problems encountered might be partially solved by improved surfaceengineering techniques. For example, state-of-the-art coating technologies

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Figure 20 Comparative tool life of the cutting tool materials. End mill test data. Machined material—1040 steel. Parameters of cutting: speed (m=min): 21; depth (mm): 3.0; width (mm): 5; feed (mm=flute): 0.028; cutting with coolant.

together with the use of adaptive materials could be developed for functionally graded tool materials, i.e., materials whose structure and properties might be tailored from the core to the surface. That might result in a significant increase in tool life.

D.

Functional Graded Materials for Cutting Tools

There are two pressing problems that should be addressed in the development of materials for cutting tools. The first one is the choice of economically alloyed tool materials, due to the severe shortage of core metals such as tungsten. This problem becomes more and more pressing. The second problem is to find the optimum combination of different, and even contradictory, properties in the same cutting material. New innovative materials are needed. The material of interest will have to combine such diverse properties as high strength and toughness at elevated temperatures with excellent wear resistance. A recent development is the production of a functionally graded material, whose properties (wear resistance and strength) vary from the core to the surface. This class of functionally graded materials (FGM) combines a high wear resistance at the surface

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with high strength and toughness of the core. The intermediate layer has graded properties that lie between those of the core and the surface. Promising developments in this field have been reported by the Laboratory of Materials Processing and Powder Metallurgy of the Helsinki University of Technology. They developed a novel functionally graded material having a surface ceramic layer, a graded WC-cermet composition with high crack resistance and a cemented carbide core with excellent toughness. A high crack resistance parameter value (K1C¼25 MPa m1=2) at a hardness of 1500 HV (typical for tool steels with half the hardness) was found (http:==www.hut.fi=Units=LMP=). There are two methods used for FGM processing. The first one, noted above, is a surface-engineering method. This method has unique possibilities and versatility. But other methods, principally those based on powder metallurgy, are also widely used. Combinations of these two methods have recently been put into practice. Thus, tools manufactured by ordinary sintering processes, having high-toughness cemented carbide substrates with high wear resistant ceramic coatings and functionally graded interlayers show excellent wear resistance [31]. Functionally graded materials can have superior wear resistance, resistance to fracture, and good thermal shock resistance in the comparison to conventional cermets, with a beneficial compressive residual stress distribution [32]. Ceramics have also been recently developed with functionally graded structures. In order to combine high hardness and high toughness, graded ceramics of Al2O3 þ TiC (surface)=Al2O3þTi (inner core) and sialon (inner core) have been successfully developed [33]. Functionally graded ceramic tools can exhibit better cutting performance than regular ceramic tools [34]. Functionally graded materials have also been successfully used for milling applications [35]. Functionally graded powder materials are normally used for high-speed cutting, but they can also be successfully employed in the domain of HSS tools application particularly with functionally graded cement carbide and hard PVD coatings [36]

III.

TRENDS IN THE DEVELOPMENT OF SURFACE-ENGINEERED TOOL MATERIALS

Surface engineering has recently become one of the most effective ways of improving the wear resistance of tool materials. The principal beneficial effects associated with surface engineering for this application are shown in Table 4.

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Table 4 Improved Performance of Surface-Engineered Cutting Tools [1] Favorable effect

Improved performance of cutting tools

Reduced friction

Lower heat generation, Lower cutting forces

Reduced adhesion to the workpiece surface Improved diffusion barrier and chemical stability properties Increased hardness

Less material transfer from the tool surface Reduced diffusion

A.

Reduced cutting tool flank wear and abrasive wear

Practical advantages Increased productivity, improved workpiece quality (better surface finish, improved dimensional accuracy), increased cutting tool life

Increased productivity, increased cutting tool life Increased cutting tool life

Monolithic and Multi-layered PVD Titanium Nitride Coatings

The most widely used approach for the surface engineering of tools is based on titanium nitride coatings deposited by physical vapor deposition methods (PVD). These coatings display a favorable combination of properties, such as good adhesion to the substrate, high hot hardness, excellent chemical stability, and improved oxidation stability (up to 550–6008C), resulting in an increased resistance to solution wear. The ability to improve the contact conditions at the cutting edge (i.e., a reduction of the tool–chip interactions) has been reported, leading to lower friction and decreased temperatures at the surface of the tool [1]. However, monolithic TiN coatings have a critical weakness. Following the discussion in the previous sections, it is clear that coatings whose properties can be tailored from the substrate to the top surface are required. Unfortunately it is almost impossible to combine such divergent properties as good adhesion to a HSS substrate coupled with minimal workpiece interactions in a monolithic TiN coating. In addition, high hardness and the possibility of energy dissipation without coating failure are often mutually exclusive properties [37]. One of the solutions to this problem is to adopt a classical metallurgical design approach. For example, multi-layered coatings or coatings with a metalbased sublayer could be applied [1]. However technical problems have been encountered in the deposition of these coatings. An alternative approach is

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to vary the parameters of deposition, using a regular PVD unit, to optimize the coating properties and coating design. A study designed to optimize the deposition parameters for TiN coatings [38] determined that the nitrogen pressure is the most critical process parameter responsible for changes in the coating structure and properties of the films. For the deposition conditions described in Ref. [38], an increase in the nitrogen pressure up to 0.4–0.6 Pa leads to stoichiometric TiN (53 at.% N2). Further increases in the nitrogen pressure lead to a decrease in the nitrogen concentration of the film (to 43 at.% N2, Fig. 21a). This is probably caused by a decreased intensity of the plasma-chemical reaction as a result of a reduction in the flux and energy of the impinging ions. The phase composition changes from a-Ti þ Ti2N at very low nitrogen pressures to TiN at higher nitrogen pressures (0.4–0.6 Pa). The structural parameters of the film also depend on the nitrogen concentration in the coating. The lattice parameter and subgrain size (or equivalently the dislocation density) are related to the nitrogen concentration in the coating (Fig. 21b–d) and have maximum values at a composition corresponding to stoichiometric TiN. An increase in the nitrogen pressure leads to a pronounced axial texture (Fig. 21e), with (1 1 1) planes in the TiN being parallel to the substrate surface. The (1 1 1) axial texture increases to 95% as the gas pressure is raised to 0.6 Pa and remains practically unchanged with subsequent pressure increases. The residual compressive stress in the coating shows similar trends (Fig. 21f), with the stress increasing from 200 to 1300 MPa as the gas pressure is raised to 0.6 Pa. The rate of increase in the compressive stress slows with a further increase in the nitrogen pressure up to 2.6 Pa, reaching a maximum value of 1600 MPa. It is important to realize that the trends shown by these structural-dependent parameters depend primarily on the deposition conditions. An increase in the nitrogen pressure over 1.3 Pa decreases the ion energy, and the effective temperature at the TiN crystallization front decreases. At a nitrogen pressure in excess of 1.3 Pa, the coatings form under conditions similar to those encountered in the balanced magnetron sputtering process (for the PVD method). These conditions can be indirectly characterized by the deposition rate, which should not exceed 5–6 mm hr1. A decrease in the deposition rate enhances both the axial texture and the magnitude of the residual stresses. The most probable cause of the high compressive residual stress found in thin condensed films deposited at nitrogen pressures greater than 1.3 Pa is a high density of point defects [39]. An increase in the nitrogen pressure also decreases the crystallite dimensions (Fig. 21f). The microhardness of the coatings depends on their phase composition. The maximum microhardness (H0.5¼45 GPa) is achieved when the two-phase a-TiþTiN composition changes into the three-phase composition

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Figure 21 The dependence of the structural characteristics of TiN PVD coatings on the nitrogen pressure.

a-Ti, Ti2N, and TiN. The Palmquist toughness of the coatings (Fig. 22a) is a structure-sensitive characteristic. The maximum toughness and plasticity (determined from the hysteresis in indentation testing) correspond to a single phase coating having a stoichiometric TiN composition. Any deviation

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Figure 22 pressure.

The dependence of the properties of TiN PVD coatings on the nitrogen

from stoichiometry causes a decrease in the Palmquist toughness, particularly when a second phase is formed in the coating (e.g., Ti2N). This result seems unexpected at first, but we should remember that the coating should be regarded as a quasi-brittle material, whose toughness is determined primarily by its crack propagation resistance. The optimum nitrogen concentration corresponds to the largest lattice parameter [40], although the

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microhardness of the coating with this structure is not relatively high. In addition to the intrinsic mechanical properties of the coating, the level of the residual compressive stress is important for crack initiation and propagation. The value of the residual stress is about 800 MPa in stoichiometric TiN coatings (Fig. 21f). The fracture resistance also appears to depend on the columnar grain size, which again can be controlled if balanced deposition conditions can be achieved. The adhesion of the coating to the substrate and the shear load resistance (i.e. the cohesion of the coating) both decrease as the nitrogen pressure is increased. The nitrogen atoms (ions) in the plasma scatter the Ti ions, so that the net effect of Ti ion bombardment of the coating is reduced as the nitrogen gas pressure rises. As noted earlier, both the axial texture and the residual stress gradient at the coating– substrate interface increase as the pressure rises, and consequently the adhesion of the coating falls (Fig. 22b). The coating wear resistance during dry sliding friction under high loads (Fig. 22c) reaches its maximum value in the three-phase field area a-TiþTiNþTi2N. Cutters made of a high-speed steel with TiN coating are used under adhesive wear conditions [3]. The tool life of TiN coated parts then depends on the friction coefficient under cutting conditions that are close to galling or seizure during wear testing (Fig. 22, e). The overall conclusion of this study is that the optimum combination of properties of the coating for adhesion wear is obtained at low deposition rates (for the PVD method) of 5 mm hr1 and a stoichiometric composition of TiN. This can be achieved by optimizing the deposition parameters. In this case, the hardness and toughness increase, while the shear resistance decreases. A coating with the optimum structure will crack by shear failure at or near to the surface of the coating rather than forming deep cracks leading to a catastrophic failure of the whole tool. However, at the same time, the shear stress resistance of the coating should be strong enough to allow for easy flow of the chip (the value of cohesion should be about 0.2). Since a monolithic TiN coating usually has a low adhesion to the substrate, adhesive sublayers are necessary to achieve high efficiency from this type of coating. A number of principles guiding the selection of the processing of TiN multi-layer coatings for adhesive wear conditions can be proposed from this study. The coating should have at least three sublayers: (1)

An adhesion sublayer, deposited with substoichiometric nitrogen. These deposition conditions provide the maximum kinetic energy of the ions and a low nitrogen concentration in the layer (up to 35%). At the same time the (1 1 1) axial texture should not exceed 50%, while the residual stress at the coating–substrate interface should be low (not

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more than 200 MPa). When this combination is achieved, the adhesion of the sublayer is high. (2) A transition layer deposited with a gradual increase in the nitrogen pressure to provide: (a) development of an axial (1 1 1) texture (from 48% up to 100%) from the substrate to the top layer; (b) a residual compressive stress increase from 200 MPa in the adhesion layer up to 1700 MPa; and (c) a gradual transition from a three-phase structure a-TiþTiNþTi2N to single phase TiN. (3) A working (contact) layer, deposited under high nitrogen pressures and balanced conditions (the deposition rate for the CAPDP method is 5– 6.5 mm hr1). In addition the deposition conditions at this stage should be chosen to yield stoichiometric TiN, having a nearly perfect axial texture, a high residual compressive stress (more than 2000 MPa), and a fine columnar grain size containing minimal ‘‘droplet’’ phases. A multi-layer coating is required to meet these diverse requirements. This coating offers many advantages (in comparison to monolithic coatings) in satisfying the broad range of mechanical properties needed in these applications. It has high adhesion to the substrate but low adhesion to the workpiece (i.e. a minimal friction coefficient), a high microhardness (H 0.5¼35 GPa) and a high toughness (more than 50 J m2, see Table 5). This favorable blend of structural and mechanical properties has many advantages for wear resistance during cutting operations (Table 5).

Table 5 Comparative Characteristics of TiN Coatings Deposited by the PVD Method on the Coating Deposition Process [38] Parameters

PVD method Regular arc deposition

Filtered arc deposition

Coating design Monolithic coating Multi-layer coating Multi-layer coating

Coefficient Palmquist of adhesion Microhardness toughness to the Wear resistance (N m2) (GPa) substrate on cutting 25.0

26.0

0.5

1.0

30–35

50–60

0.8

1.5–2.0

35–37

150–200

0.8

2.0–2.5

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The same multi-layer coating could be used for filtered PVD coatings with the additional advantages offered by this technology [41]. These systems not only eliminate the ‘‘droplet’’ phase from the coating, but they can also be used to control the deposition conditions so that an excellent microstructure and properties are obtained in the film. An extremely fine-grained structure (the grain size is 10 nm in comparison to a grain size of several microns in regular coatings) can be achieved [42], with excellent mechanical properties. The nano-grained structure of the film is due to: the higher ionization rates achievable in filtered arc-evaporated plasmas, which are thought to enhance the nucleation rate and depress the growth rate of coarse crystals; and (2) a lower overall deposition rate for the filtered arc PVD process that results in a drop in the temperature at the growth front of the film. (1)

Although lower deposition rates are found with this process and can lead to a loss of productivity, these disadvantages can be offset by improvements in the quality of the film. The hardness and Palmquist toughness of a TiN coating deposited by this method can be increased up to 35–37 GPa (instead of 25 GPa) and 150–200 J m2 (instead of 26 J m2), respectively. The adhesion of this coating is also very high (kadh¼0.8, see Table 5). In addition, the wear resistance of filtered coatings is usually much better than regular coatings (Table 5). The principles outlined above for a multi-layered TiN coating can also be successfully applied to filtered coatings.

1.

Frictional Wear Behavior and Self-Organization of TiN PVD Coatings Hard TiN coatings act as surface lubricants by inhibiting the adhesion of the tool surface to the workpiece [1]. The friction parameter of this coating is also low at the operating temperature (Fig. 23). The wear behavior changes when TiN coatings are applied to cutting tools (Fig. 24a) [43]: the initial rate of wear (during the running-in stage) is significantly lower and the range of normal wear is expanded. As a result, both reduced friction and wear control can be achieved (see Fig. 2). To explain the enhanced wear characteristics imparted by TiN PVD coatings, a study of the self-organization behavior of the tool was performed [26]. Protective secondary structures (SS-I) of the Ti–O type form at the surface of hard PVD TiN coatings during cutting. The transition from the running-in stage to the normal wear stage is marked by the development of a supersaturated solid solution of oxygen in titanium (Fig. 25a–c). At the same time, as the friction drops,

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Figure 23 The dependence of the frictional parameters of TiN PVD coatings on temperature.

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Figure 24 Tool face wear vs. time. Turning test data (a, cutting speed¼70 m=min; b, cutting speed¼90 m=min; machined material, 1040 steel; depth (mm), 1.0 mm; feed, 0.28 mm=rev): (1) M2 HSS; (2) M2 þ ion nitriding; (3) M2 þ PVD TiN coatings; (4) M2 þ ion nitriding þ PVD TiN coatings; (5) T15 HSS þ ion nitriding þ PVD TiN coatings.

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Figure 25 SIMS spectra of TiN and ‘‘quasi-oxide’’ Ti–O films as a function of the service time of M2 HSS tool with coatings: (a) cutting time¼15 sec; (b) cutting time ¼ 90 sec; (c) cutting time ¼ 120 sec.

the wear rate of the tool is reduced and the process enters the steady-state stage. Titanium oxide has a high resistance to friction [44] and cutting (Table 2) and readily fulfills a protective role for the underlying TiN coating. The nature of the thin surface layer formed at the surface of the coatings was studied by using EELFS analysis. An analysis of the fine structure obtained from the surface of the wear crater at different stages of operation in coated HSS cutting tools was used to follow the changes in the structure of the surface layers (see Fig. 26a–c). When the cutting period was 30 sec, i.e. at the running-in stage, the surface features in the EELFS spectrum agreed with crystalline titanium nitride. The characteristic signature of TiN is a peak at R2¼2.0 A˚ as well as a peak at more remote interatomic distances (at about 4–5 A˚, see Fig. 26a). When the cutting lasts for 180 sec, titanium oxide develops in the coating, the degree of remote order in the crystal lattice is reduced and the coating structure appears to amorphize. This is shown by the appearance of a peak at R2¼2.20 A˚ (RTiþRO¼ 1.45þ0.73¼2.18 A˚) and by the attenuation of peaks at more remote interatomic distances (see Fig. 26b). When catastrophic wear occurs (Fig. 26c), at a cutting time of 2100 sec, the coating is destroyed while the steel surface is exposed. This is shown by the change in the form of the Fourier

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Figure 26 Fourier transform from EELFS analysis of a wear crater, TiCrN coating on nitrided T15 steel: (a) cutting time ¼ 30 sec; (b) cutting time ¼ 180 sec; (c) cutting time ¼ 2100 sec.

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transform. The first peak is now located at a distance R1¼1.7 A˚, while the second peak is at a distance R2¼2.65 A˚. These peaks correspond approximately to the length of C–Fe and Fe–Fe bonds (RCþRFe¼0.51þ1.26¼ 1.77 A˚; RFeþRFe¼1.26þ1.26¼2.52 A˚). The spectrum shown in Fig. 26c is typical of the BCC-lattice of T15 high-speed steel.

B.

Tribological Properties and the Metallurgical Design of Surface-Engineered Tools

The study of the wear resistance of coated tools demonstrates that the protective role of the coating is most efficient when the effects of the work of cutting can be localized in the near-surface region of the coating [43]. Current coating technologies achieve this goal by modifying the energy distribution (from the tool surface into the chip), and by promoting the selforganization of the tool. This is done in two ways: (1) by surface engineered and self-lubricated coatings for low and moderate speed machining, and (2) by the use of hard or superhard coatings, that can act as thermal barriers and form very stable ‘‘tribo-ceramics’’ at the surface during high-speed cutting.

1. Surface-Engineered or Duplex Coatings The principal application of these coatings [45] is for cutting at low speeds, when HSS and DCPM tools are used. It is desirable to deposit the hard coating, not directly onto the steel substrate but rather onto an engineered sublayer, so that a gradual change in properties at the coating–substrate interface, i.e., a functionally graded material, is realized. This sublayer can be obtained by different technologies, e.g. ion nitriding. Usually such coatings will then include both a nitrided sublayer and a hard PVD coating. The nitrided sublayer has two roles. It prevents intensive plastic deformation of the substrate (HSS or DCPM) and cracking of the PVD coating that might be caused by deformation of the underlying substrate, while at the same time, it provides an additional thermal barrier [43]. The advantages of HSS cutting tools with surface-engineered coatings are shown schematically in Fig. 27. However the structure of the nitrided sublayer must be optimized in duplex coatings to achieve the best tool life. The duration and temperature of the process are the most important parameters in ion nitriding [38]. The ion current density should not be high, preferably about 3 A m2. The experimental data given below were obtained when the surface temperature during nitriding was about 500–5308C. At this temperature, rapid

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Figure 27 Schematic diagrams of composite cutting tools: (a) HSS þ TiN PVD coating; (b) HSS þ surface-engineered coatings.

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nitrogen diffusion occurs. The dependence of the structure and properties of an M2 tool steel on the nitriding time is shown in Fig. 28. Ion bombardment leads to the formation of a defective structure in the surface layers, which enhances nitrogen diffusion. During the fist 10–20 min of nitriding, a saturated solid solution of N is formed. After 30 min of nitriding a supersaturated solid solution of N is obtained at the surface (Fig. 28a). The most pronounced changes in the lattice parameter and line broadening of the (2 1 1) reflection occur after 0.5–2.0 hr of nitriding (Fig. 28b). A further increase in the nitriding time from 2 to 4 hr has little effect on either the lattice parameter or the line broadening. Nitrides are observed after about 2–4 hr. (The formation of a nitride using X-ray

Figure 28 The time dependence of the structural characteristics and properties of the ion nitrided sublayer of a surface-engineered coating: (1) M2 HSS; (2) D2 tool steel; (3.1) nitrided layer of a cutting tool; (3.2) un-nitrided layer of the die steel.

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diffraction can be detected when the concentration of the nitride is approximately 5%.) The first nitride to be detected by x-ray diffraction in this study is the e-phase (W,Fe) 2–3N, while after 4 hr of nitriding, both the e and g0 (W,Fe) 4N phases are detected. After 4 hr of nitriding, the nitrides can be clearly detected by optical metallography as a network of thin, needle- or lath-shaped particles. It is known that the presence of tungsten, molybdenum and chromium in the solid solution of the steel can lead to the formation of a high density of fine nitrides with a marked increase in the hardness. When the nitriding time is increased to 2 hr or more, mixed (Cr, W, Mo) nitrides will also nucletlate. These nitrides are very finely dispersed and hence are difficult to detect by X-ray diffraction, but they contribute significantly to the increased hardness (Fig. 28d). The coefficient of plasticity of a nitrided M2 steel changes according to the data shown in Fig. 28e. This coefficient (determined from an indentation test) is highest (52%) when the hardness is low, and conversely decreases (to 48%) when the hardness is high. (The Palmquist toughness for nitrided steels cannot be used to give a meaningful measure of the fracture resistance as the depth of the nitrided layer changes as nitriding proceeds.) The plasticity of the nitrided layer is sensitive to the microstructure. When there are no nitrides in the layer, the plasticity coefficient is proportional to the nitrogen saturation. The N content in this zone can be characterized by the lattice parameter of the a-phase (Fig. 28a). As the nitrogen concentration (and lattice parameter) in the surface layer rises, there is a corresponding decrease in the plasticity, and vice versa. A low plasticity is correlated with an increased lattice deformation of the solid solution, associated with the dissolution of N into the iron lattice, as shown by the line broadening of the (2 1 1) reflection of the nitrided martensite (Fig. 28b). In addition, some influence on the plastic properties is exerted by residual stresses, which are formed in the surface layer during nitriding (Fig. 28c). The residual stresses are high when the nitrogen content in the nitrided layer increases and extensive precipitation occurs on cooling. The volume of the surface layer increases on nitriding and as a result compressive residual stresses are formed. This effect is typical for M2 grade steels. High compressive stresses in the nitrided layer of a M2 steel lead to increased hardness and plasticity, and inhibit cutting edge-flaking during the tool life. It is important that the level and sign of stresses formed in the nitrided layer are similar to those in the adhesion sublayer of multilayer coatings. then, the stress gradient between the nitrided substrate and the coating is low and the adhesion is improved. The service properties of the nitrided layer also have a high structural sensitivity. The longest tool life of nitrided HSS steels is obtained with an a-solid solution structure and is at least double that of un-nitrided tools. The tool life increases with

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the nitrogen content in the layer, which, as noted earlier, can be monitored by the change in the lattice parameter of the nitrided martensite (Fig. 28f). After nitrides have precipitated, the tool life decreases as a result of flaking at the cutting edge, caused by a decrease in the plasticity of the surface layer. The formation of a residual compressive stress also plays some role in flaking, as these stresses are highest with a N solid solution. In addition to the structure of the surface-engineered coating, the nature of the coating–substrate interface is also of great importance. The adhesion of the coating is one of the principal factors (together with the thermal stability) determining the tool life. The interface must be free from brittle compounds (such as oxides, nitrides, etc.) formed in the hardening process or during interaction with the environment. Several studies suggest that the surface of the tool should be polished to remove surface nitrides formed after the ion treatment [50]. Surface cleaning is also effective when ion etching is used, but the etching must be performed very carefully. The cutting edges of a sharp tool should not be rounded, the surface roughness should not increase and the tool dimensions should be kept to a close tolerance. All this is the subject of technological optimization, but with care, excellent results can be achieved [45]. a. Friction and Wear Behavior and the Features of Self-Organizing of Surface-Engineered Coatings. A surface-engineered coating can act as a ‘‘protective screen’’ at the surface of a cutting tool (Fig. 27). During steady-state wear, a gradual, but controlled wear of the coating takes place. All these advantages became even more obvious when surface-engineered coatings are applied. Tests done at increased cutting speeds (90 m=min)(for for HSS tools) enhance all the thermal processes associated with cutting. Under these conditions, the heat-insulating effect of a hard TiN coating is diminished, the protective function of the coating is reduced, plastic deformation of the steel substrate can occur, and the stability of cutting is disrupted. All these trends can be seen in the data presented in Figs. 24b and 29. Hardening an M2 steel by a surface-engineered coating can be employed to counteract these effects. The wear value is considerably lower and the zone of stable cutting process is significantly broader (Fig. 29, curve 4). The best results are achieved when a substrate material (T15 HSS) having a high heat resistance is used. The dissipation of energy is channeled into processes other than surface damage, i.e. compatibility of the tool and workpiece is realized to a great degree. The coating plays the role of a protective screen for the contact surfaces. It should be emphasized that the successful fulfillment of this function, however, is possible only when the external thermo-mechanical effects are localized in the coating layer. Studies of coating wear have shown that the intensive self-organizing process observed during cutting only occurs when a surface-engineered coating was used.

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Figure 29 Tool flank wear vs. time. Turning test data (cutting speed ¼ 90 m=min; machined material, 1040 steel; depth of cutting ¼ 0.5 mm; feed rate ¼ 0.28 mm=rev.): (3) M2þPVD TiN coatings; (4) M2þion nitriding þ PVD TiN coatings; (57) T15 HSS þ ion nitriding þ PVD TiN coatings.

The practical results of duplex surface-engineered coatings, i.e. a functionally graded tool material, are quite impressive. This material combines a high surface wear resistance (hard coating) and high core toughness (HSS). The tool life is increased by a factor of five to ten times [46], while at the same time, the metalworking productivity can be increased by a factor of two to four. The cutting speeds of high-speed steel tools with duplex coatings (when cutting ordinary construction grades of steel) can be as high as 130–150 m min1. These cutting speeds are found with carbide tools only under certain limited cutting conditions. 2. Multi-layered, Self-Lubricating Coatings For transient or surface damaging friction conditions (e.g., during the running-in or avalanche-like stages of wear), the efficiency of hard

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coatings becomes questionable due to their brittleness. During the machining of several types of alloys (e.g. stainless steels or nickel-based alloys), unstable conditions can dominate and surface damaging mechanisms become prevalent. In this case, the ability of a thin surface layer to protect the surface, well as dissipate most of the energy generated during cutting, thereby minimizing the cracking of the tool, becomes critically important. This is a practical application of the universal principle of dissipative heterogeneity [47]. For the most demanding cutting applications a third type of coating— the self-lubricated hard coating—has been developed. A typical example of this type of development is the multi-layer coating, TiAlN–MoS2, with two energy-dissipating mechanisms built into the microstructure [48]. The first is associated with the formation of an oxygen-containing secondary structure (SS-I) that readily forms at the surface of the hard coating (TiAlN) and plays the role of a solid lubricant. The second is associated with the thin MoS2 lubricating layer. A second example of a similar technology is the use of nano-composite nc-TiN–BN coatings [49]. These coatings give good results at moderate cutting speeds. Following the earlier discussion, it seems likely that a high-alloyed Ti–B–O secondary structure of the first type (SS I, see above) and B2O3 both form. The boron oxide plays the role of a liquid lubricant at the temperatures of cutting [50]. The most important phase of the self-organizing process is associated with the running-in stage of wear. During this stage of self-organization, the wear process gradually stabilizes and finally transforms to a stable (or normal) stage [7]. It is very important to prevent surface damage and promote intensive self-organization at the surface during the running-in stage of wear using the phenomenon of screening [4,7]. The less surface damage at the beginning of the normal stage of wear, the longer will be the tool life (Fig. 2). Hard coatings are brittle and susceptible to extensive surface damage during this running-in stage. Frequently, much of the hard coating is already destroyed at this phase, prior to the start of the stable (normal) stage of wear, where the wear rate can be lowered by an order of magnitude due to the self-organizing of the system (Fig. 2). The initial surface damage often leads to a dramatic decline in the wear resistance of the coating. For this reason, a top layer with high anti-frictional properties is a critical component, and can be used to protect the surface of the hard coating. This is one of the most important goals for wear resistant coatings, especially at low and moderate cutting speeds, and for handling hard-to-machine materials where adhesive wear dominates. This can be achieved by applying self-lubricated, multi-layer coatings. These structures have many complex microstructural features that contribute to energy dissipation [e.g. the TiAlN–MoS2 (or Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 30 Tool life of end mills with advanced coatings. Machined material, 1040 steel. Parameters of cutting: speed (m=min): 21; depth (mm): 3.0; width (mm): 5; feed (mm=flute): 0.028; cutting with coolant.

MoST) coatings [51,52], discussed earlier]. One of the most effective commercial coatings of this type is the multi-layered TiAlN=WC-C hard lubricant coating developed by Balzers [53]. The main advantage of this coating is a very low initial wear rate, during the running-in stage of wear (Fig. 2) that leads to a significant increase in the tool life (Fig. 30). Recently, several oxides such as WO3, V2O5, and TiO2 [54] were found to exhibit good tribological properties at elevated temperatures. All these oxides contain crystallographic shear planes with low shear strengths at high temperature [44]. They are promising materials as solid lubricants for elevated temperature applications, and can be deposited by PVD methods. The service performance of multi-layered coatings with an anti-friction top layer is characterized by the wear curves shown in Fig. 31. The top (antifrictional) layer leads to a decrease in flank wear as soon as the running-in stage is completed, and the tool life is significantly increased (Figs. 2 and 31). Unfortunately, not every mode of the running-in phase leads to the optimum self-organization [4,47], because damaging modes are also possible, especially during cutting. Thus, the goal of friction control is to prevent serious surface damage at the running-in stage and transform the tribosystem from its initial state into a self-organizing mode. If this can be achieved,

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Figure 31 Tool flank wear vs. time. Turning test data (with and without coolant). Cutting speed ¼ 90 m=min; machined material, steel 1040; depth of cutting ¼ 0.5 mm, feed rate ¼ 0.25 mm=rev.: (1) M2 þ ion nitriding þ PVD TiN coatings (with coolant); (2) M2 þ ion nitriding þ PVD TiN coatings (without coolant); (3) M2 þ ion nitriding þ PVD TiN coatings þ Z-DOL anti-frictional layer (with coolant); (4) M2 þ ion nitriding þ PVD TiN coatings þ Ti þ N layer, modified by ion mixing (without coolant); (5) M2 þ ‘‘smart’’ coating with programmable change of properties, combining coatings 3 and 4 (with coolant).

the effective volume of interaction between the tool and the workpiece can drop by orders of magnitude. For severe conditions of cutting, the effective thickness of the interaction volume at the self-organizing stage is in the range of 0.1–1.0 mm [4,55,56]. The high anti-frictional nature of the surface layer is necessary to achieve these goals [57]. An alternative type of anti-frictional surface layer has been successfully applied for hard coatings—the Z-DOL layer [58,59]. Z-DOL [a 0.5% solution of perfluorine polyester acid (Rf-CH2OH) in freon 113]

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Table 6 Physico-chemical Propeties of Z-DOL [58,59] Property Molecular mass Average number of units in the molecule Molecular dimensions of SAM Density Thickness of epilamon layer Load-carrying capacity Maximum service temperature

Value 2,194 12 5 nm 1,560 kg=m3 5–2,500 nm 3 GPa 723 K

can be deposited by dipping the part into a boiling solution. The physicochemical properties of Z-DOL are shown in Table 6. The thin film consists of a close-packed molecular mono-layer, that provides an even coating to a rough tool surface. This coating has a high adsorption ability and due to its low thickness it also has high adhesion to the substrate and penetrates into pores. The surface energy of oils contained in the typical coolant regularly used for machining is higher than the surface energy of the Z-DOL film. As a result of the molecular interaction of the oil and Z-DOL film, the latter film is not sheared from the surface of the cutting tool during the first stages of cutting. The principal function of the top anti-frictional layer (Fig. 32) is to increase the adaptability of cutting tools with hard nitride coatings. The two surfaces are separated by a layer of oil that prevents seizure and wear during the initial stages of the tool service. Studies of surface-engineered coatings (a PVD TiCrN hard coating and a top layer of Z-DOL) deposited on a HSS substrate in contact with a 1040 steel show that the friction characteristics are improved at the service temperature (5008C, Fig. 23). The tool life data (Fig. 31a) reflect a very low pattern of surface damage at the running-in stage of wear, leading to a marked improvement in the overall tool performance.

3. ‘‘Smart’’, Multi-layered Wear Resistant Coatings Similar problems of friction control at service conditions leading to surface damage arise when the wear process changes from the normal to the ‘‘avalanche-like’’ stage. As noted above, cutting tools made of HSS usually operate under conditions of adhesive wear, where seizure might occur, accompanied by a rapid increase in the wear intensity [56]. Prolongation of the normal friction and wear stage, however, is quite feasible, even if seizure is a problem. This can be achieved by applying an

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Figure 32 Schematic diagram of multi-layered ‘‘smart’’ PVD coatings for cutting tools with a programmable change of properties:(1) anti-frictional layer (Z-DOL); (2) hard TiN PVD coating; (3) additional sublayer formed by (TiþN) ion mixing; (4) nitrided sublayer; (5) HSS substrate.(I) Running-in stage of wear; (II) normal wear (steady-state) stage; (III) catastrophic or avalanche-like stage of wear.

additional sublayer to the multi-layered coating at the surface of the tool substrate. This layer should combine anti-frictional properties with an ability to generate protective secondary structures at the coating/substrate interface. One way to create these layers is by ion modification (ion alloying) of the surface of the tool. ‘‘Triplex’’, multi-layered coatings have been studied [60]. The coating in this study was deposited using three separate units. A high-speed M2 steel was first nitrided using the glow discharge method. This was followed by ion implantation, prior to the application of a hard (Ti, Cr) N coating deposited by the PVD method. The (Ti, Cr) N coating was chosen for its high wear resistance [61]. Before applying the PVD coating, the samples were implemented at room temperature with 60 keV ions to a total flux of 4 1017ions=cm2. Sixteen different ions were chosen for study. Prior to ion implantation, the surface of the samples was etched by argon ions and surface contamination was controlled during implantation by the use of a cold trap that maintained a background pressure of about 2 106 Torr. The sixteen elements selected for this work can be grouped as

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follows: (1) elements forming stable protective surface films under frictional

conditions [4], e.g. O, N, and Cl; non-metals (e.g., B, C, Si) forming compounds with good tribological properties when they interact with base materials and elements in the environment; and (3) metals including: (a) low-melting point elements (in particular In, Mg, Sn, Ga) used as lubricants or anti-friction materials; (b) metals with a hexagonal lattice and anti-frictional properties [62,63] (c) metals (Al, Cr) that form stable oxide films during cutting, with good anti-frictional properties, and a low coefficient of thermal conductivity; and (d) metals (Ag, Cu) known to have a low coefficient of friction, and low mutual solubility when in contact with steel, nickel and titanium alloys (Fig. 33) [63]. (2)

In addition, the study was extended to study surfaces subjected to treatments with: – four types of anti-friction alloys used to improve conditions of sliding friction, viz. Zn þ Al(9%) þ Cu(2%), Cu þ Pb(12%) þ Sn(8%), Pb þ Sn (1%) þ Cu (3%) and Al þ Sn(20%) þ Cu(1%) þ Si(0.5%) [28]; – Zr þ N, W þ C, W þ N, Ti þ N, Al þ O, to create layers with a high wear and oxidation resistance. The wear of these coatings was studied while turning 1045 carbon steels at a cutting speed of 70 m=min, a cutting depth of 0.5 mm and a feed rate of 0.28 mm=rev. with and without a coolant. The flank wear of tetragonal, indexable HSS inserts with multi-layered coatings was studied; when the flank wear exceeds 0.3 mm, the cutting tool loses its serviceability [3]. The effectiveness of ion modification was determined by comparing the cutting time to reach a specified depth of wear of tools with multi-layered coatings (i.e., those having both surface-engineered coatings and ion modification) with identical surface-engineered coatings prepared without the additional step of ion modification. Adhesion was determined using the scratch method. Friction coefficients were determined with the aid of a specially designed adhesiometer shown in Fig. 5 . The results of these tests, summarized in Table 7, demonstrate to a large extent that the influence of the implanted elements on the tool life is determined by the cutting conditions. The operational temperature during

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Figure 33 The mutual solubility of metals based on binary phase diagram data [69]. The data are characterized in ranges running from IV—low mutual solubility to I—high mutual solubility.

high-speed cutting is at least 6008C. If a coolant is used, the temperature is significantly reduced (by not less than 1008) [63]. Thus, the effects of implantation vary, depending on whether the cutting is aided by coolants or not. Ion implantation significantly affects the tool life [64], but the change in tool life is caused by a complex combination of interacting factors. The factors that are important in this context are: – the formation of liquid phases or low-melting point eutectics which act as lubricants; – the development of amorphous, oxygen-containing films with low coefficients of friction and thermal conductivity; and

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Table 7 Tool Life of Cutters with a Modified Surface Layer (Ion Implemnetation and Ion Mixing)

N of group (subgroup)

Material

Element composition

Coefficient of PVD-coating adhesion to modified surface base

Durability coefficient on cutting Without coolant

With coolant

Surface modified by ion implantation 1

Elements with high affinity for oxidation

2

Non-metals

3 a

Metals Low-melting

b

With hexagonal lattice Forming stable oxides

c

d

With low coefficient of friction

O

0.25

0.9

1.25

N I Cl B C Si

0.41 0.7–0.8

2.0 3.2 1.8 1.2 1.7 0.7

1.83 0.7

0.6 0.6

In Mg Sn Ga Co

0.6 0.25 0.6

0.65 0.83 0.6 2.1 0.08 0.7

0.5

2.4 3.0 0.8 2.0 1.8

Al

0.4

0.15

1.3

Cr Cu

0.6 0.55

0.2 1.0

1.2 2.5

Ag

0.4

3.1

2.7

Zn þ Al (9%) þ Cu (2%)

0.44

1.98

—

Cu þ Pb (11%) þ Sn (9%)

0.4

0.95

—

0.13

Surface modified by anti-friction materials 4

Zn–Al–Cu 9–1,5 GOST 21437–75 (Russia) Bronze 8–12

(Continued)

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Table 7

(Continued)

N of group (subgroup)

Material

Babbitt BK2 GOST 1320–74 (Russia) Al–Sn–Cu AO20–1 GOST 14113–69 (Russia)

Element composition

Coefficient of PVD-coating adhesion to modified surface base

Pb þ Sn (1.5%)

0.35

0.6

—

Al þ Sn (20%) þ Cu (1%) þ Si (0.5%)

0.3

0.4

—

3.0 4.0 0.53 0.4 1.33

— 2.5 — — —

Surface modified by ion mixing of wear resistant elements 5 AlþO 0.4 TiþN 0.6 ZrþN — WþN 0.4 WþC 0.4

Durability coefficient on cutting Without coolant

With coolant

a reduction in the adhesion of the tool surface to the processed material and, at the same time, an increased adhesion of the hard PVD-coating to the modified base material. The data from Table 7 show that a class of anti-frictional alloys, widely used to improve the conditions of sliding friction [28,62], can double the tool life. However, this method of increasing the tool life, i.e. one that primarily depends on a reduction in the strength of the adhesion bonds between the tool and workpiece, is not the most efficient, as the adhesion of the coating to the modified surface was found to be rather low. This precludes their usage, as de-cohesion of a coating cannot be tolerated in practical applications. Implanting elements such as indium, silver and nitrogen enhances the tool life by a factor of 2–3 (see Table 7) for a range of cutting conditions (with and without cooling). These results are consistent with the observation that indium and silver show little interaction with iron, and find use as solidstate lubricants (Fig. 33). Nitrogen implantation probably leads to the formation of an amorphous film with improved tribological characteristics [65]. Ion modification of the tool surface with the other elements studied led to unstable or negative effects, i.e. a reduction in tool life and=or poor adhesion between the hard coating and the substrate.

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The most beneficial element in this study was indium. The life of the tool was found to be a maximum, with or without the use of a coolant (see Table 7). At the same time, the adhesion between the coating and indium-modified surface of the tool was sufficient to ensure a reliable tool performance. Indium is a surface-active metal and usually displays a low tribological compatibility with traditionally machined alloys based on steel, nickel, and titanium [63]. Because of this, the wear peculiarities of In-containing coatings have been comprehensively investigated [64]. Scanning electron microscopy and x-ray microanalysis were used to study surface-engineered cutting tools, composed of an ion-doped HSS surface, nitrided by a glow discharge technique, with a hard PVD coating over the In-modified layer (Fig. 34a). Figure 34 shows the microstructure of a 58 angle lap specimen (including the surface-engineered coating), taken in the SEM with the back-scattered electron signal which is sensitive to the mean atomic number. Separate layers of the multi-layered coating (dark for TiN and gray for the In-rich sublayer) can be seen in the back-scattered electron image. The thickness of this zone is about 6.0 mm, so that the true depth of the modified (gray) layer is about 0.3 mm. It is probably a Fe-layer containing implanted Ar (as a result of etching by Arþ after nitriding) and In. The presence of W in the tool steel increases the intensity of the x-ray In Ka radiation and the background emission. This matrix effect influences the apparent emission volume of In Ka radiation and degrades the accuracy of measurement of the In distribution. In addition, surface heating (up to

Figure 34 Microstructure of the multi-layered HSS-base (Ti, Cr)N coating with an In-modified surface (ion implantation). 600 magnification. (a) Microstructure of the angle lap section of the multi-layered coating (SEM image); (b) distribution of elements along the II direction (x-ray microanalysis).

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5008C) during (Ti, Cr) N deposition will modify the as-implanted In profile, which is expected to be about 0.3 mm in depth [66]. Following the x-ray microanalysis, the intensity ratios of the characteristic lines Lb=La for an In standard (99.99% purity) and the nitrided specimen were found to be 0.63 and 0.97, respectively. Changes in the intensity of the characteristic x-ray fluorescence are frequently observed when pure elements and their chemical compounds are compared [67]. In this study, clusters of In–N are thought to develop in the zone of In implantation. SIMS data (Fig. 35) demonstrated that the ratio of the In concentration in a free state or present as clusters was approximately 10:1. To explain how the implanted indium influences the tool life, the following factors were investigated: (1) the dependence of the friction coefficient on temperature; (2) the distinctive features of indium oxidation in the wear zone (as

investigated by SIMS); and (3) the development of oxides on heating specimens with an In-

modified surface.

Figure 35 Secondary ion mass spectra from the wear zone of the cutting tool (cutting time is 30 min).

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Figure 36 Impact of test temperature on the frictional properties of surface modified HSS cutting tools.

The temperature dependence of the friction coefficient demonstrated that In improves the frictional properties of HSS (Fig. 36), by acting as a lubricant and reducing the shear strength (t) of the adhesion bonds developed in the tribo-couples. This factor, however, is probably insufficient to

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Figure 37 Change in the shape of the In 3d5=2 line from the photoelectron spectrum taken from the HSS surface after ion implantation and oxidation at 823K for: (a) 0 min; (b) 5 min; (c) 15 min; and (d) 20 min. Pressure of oxygen in the chamber ¼ 2.5 106 Pa.

account for the twofold increase in the tool life of cutters having an In-modified surface. Mass-spectrometric analysis of the wear zone (Fig. 35) suggests that the role of In is more complicated. Apart from metallic indium, the wear zone reveals the presence of indium oxide, coming from both In and In–N dissociation and reaction during the wear process. X-ray photoelectron spectroscopy (XPS) was used to study the changes in the shape of the In 3d5=2 lines in the electron spectra after oxidation. Fig. 37a–d presents the spectra obtained before and after heating the specimens to 823K, with exposure times of 0, 0.5, 15, and 20 min,

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respectively. The position of the In 3d5=2 peak in the starting sample corresponds to a binding energy of 444.8 eV. Deconvolution of the spectra from the oxidized sample gave an additional peak, initially located at about 445.7 eV and, after a 25-min exposure, at 445.8 eV. These higher binding energies correspond to the formation of the oxide, In2O3. The relative intensity of this line compared to In 3d5=2 (the ratio of IIn2O3=IIn) was 23% in the initial state (Fig. 37a), increasing to 41% after 25 min (Fig. 37d). Figure 38 presents the change in the relative concentration of In2O3 on the surface of HSS specimens during heating at 423K, 623K, and 823K for times up to 25 min. At 823K, oxidation of the implanted indium rises quickly and saturates after about a 25 min exposure. The edge of a cutting tool runs at a temperature of about 773K (5008C) during normal operations. These conditions suffice for oxidation of a fraction of the implanted indium. However, not all the indium is oxidized, as a part remains dissolved in solid solution in the iron matrix. As the hard overlay (TiCr) N-coating is worn away, typically at the transition from the normal to catastrophic wear stage [43], the In-modified layer becomes exposed at the friction surface. This usually coincides with the

Figure 38 Change in the relative concentration of In2O3 on the surface of a HSS specimen after In-implantation and oxidation at temperatures: (1) 423K, (2) 623K, and (3) 823K.

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point where the protective PVD-coating detaches from the contact face of the tool. Under conditions of high load and high temperature, partial oxidation of In will probably start before the complete destruction of the PVDcoating. Since normal friction is characterized by minimal depth of damage of the contact surface [4], even a relatively thin modified layer can enhance the tool life. Indium improves the frictional properties of the surface and reduces the sticking intensity over the friction surface. In addition, an oxygen-containing amorphous In–O film, formed by interaction with the environment, is likely to enhance favorable friction conditions in the contact zone of a cutting tool. Indium lies in the same group as Al in the periodic table, and probably forms oxygen-containing phases having a low coefficient of thermal conductivity. These protect the tool surface, enhance the thermal conditions of cutting, and delay the onset of catastrophic wear. Thus, the influence of In is twofold: on the one hand it acts as a metal lubricant; on the other, it forms protective oxygen-containing phases. Indium enhances both the self-organization of the system and extends the stage of normal and stable wear, in accord with the principal laws of friction control [4]. The data presented in Table 7 show that the highest wear resistance after the triple surface treatment is achieved when transition metals together with nitrogen are used to modify the surface by ion mixing. Compounds such as TiN, ZrN, WN, WC, Al2O3 do not appear to form, the implanted ions remaining in solid solution. The best wear resistance is shown by a 1 mm thick layer modified with Ti and N (Fig. 39a and c). At the same time, implantation can lead to amorphization of the surface layer (see Fig. 40). The decrease of the peaks intensity at Fourier transform at remote interatomic distances shows that this modifies the wear mechanism due to a delay in surface crack propagation [68]. The diffusion of the implanted nitrogen into the chip and the reverse flux of oxygen into the tool surface lead to a partial replacement of implanted nitrogen by oxygen during cutting (Fig. 39c). The rapid formation of a protective secondary structure takes place (Fig. 41), since the initial structure of the surface after mixing is similar to the structure of the films formed at the friction surface as a result of the self-organizing process. Ion mixing can produce thin surface layers with a fine, so-called, nanocrystalline structure [68]. As noted above, the secondary structures have a similar microstructure, an amorphous supersaturated solid solution of oxygen (coming from the environment) having been formed by reaction with the metal component of the tool material [4,55]. Ion mixing enhances this process, which naturally evolves in the tribosystem during the self-organizing stage and results in the formation of a stable secondary structure. In the final stage of wear, oxygen from the environment penetrates through the numerous pores and cracks in the PVD coating to the surface of the

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Figure 39 Distribution of chemical elements close to the ‘‘built-up=wear crater’’ interface: (a) Initial stage of the Ti þ N layer, as modified by ion mixing. (b) After a cutting time of 120 sec. Surface of (Ti, Cr)N PVD coating. (c) After a cutting time of 600 sec. Surface of the Ti þ N layer, modified by ion mixing.

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Figure 40 Fourier transform from EELFS analysis of the surface of the Ti þ N layer, as modified by ion mixing.

modified layer. Since this layer contains a very high density of point defects [68,69], the reaction with oxygen is rapid (Fig. 39). As the PVD coating wears, this oxygen-rich layer can act to screen the ion modified (Ti þ N) surface and protect it against subsurface damage. Thus, when the hard coating is completely worn away, protective secondary structures (SSs) have already

Figure 41 SIMS spectra of the surface of the Ti þ N layer, modified by ion mixing: (a) initial stage of the Ti þ N layer, as modified by ion mixing; (b) after a cutting time of 600 sec.

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formed on the near-surface layers. These secondary structures (SSs) delay the transformation to the avalanche-like stage of tool wear, and the tribosystem can again revert to a stable state (i.e. to a normal pattern of wear). From our point of view, this is the most beneficial effect of the modified Ti þ N layer on the wear behavior. The behavior of multi-layer coatings illustrates an important principle that can be used to design effective materials for cutting tools. The more energy dissipation channels that can be built into the microstructure for the transitional (non-steady) stage of tool wear, the longer will be the tool life. These channels can operate simultaneously in the same stage of the wear (e.g. during the running-in stage), but also subsequently, using multi-layer coatings, when the wear process transforms from one stage to another. After completion of the first stage of wear and exhaustion of the corresponding channel of energy dissipation in the top layers, the next layer of a multilayered coating can be used to control the ‘‘avalanche-like’’ wear with alternative channels of energy dissipation [37]. In this way, a multi-layered, ‘‘smart’’ coating can be developed where each layer fulfills a given function at a definite stage of wear (Fig. 32), leading to high serviceability over a wide range of operating conditions. This concept has been widely used for protective coatings, corrosion control [70], and, as shown above, this concept can be extended to wear resistant coatings. At the stable stage of wear, the coating must have adequate strength and toughness, and a stable SS. In the unstable stage(s), the coating must have sufficient energy dissipation channels to prevent surface damage. A multi-layer coating that includes an adaptive top layer, composed either of oxides with favorable friction properties (such as WO3, V2O5) or a self-lubricated layer, a working layer of a superhard or self-protecting coating, and an anti-frictional sublayer form the basis for future ‘‘smart’’ coatings. 4.

SuperHard (nano-composite=superlattice) and Self-Protecting Coatings An alternative way of improving the performance of cutting tools relies upon the deposition of multi-component compounds. Recent improvements in the lifetime of cutting tools have been achieved by the development of titanium aluminum nitride (Ti,Al) N coatings (see Fig. 30). The results of milling tests with TiAlN coatings have demonstrated that the wear behavior is improved by lowering the running-in wear and increasing the duration of the period of normal wear. This can be achieved when all the interactions between the tool and workpiece are localized in a thin surface layer, i.e. a striking demonstration of ‘‘tool–workpiece’’ compatibility. Films such as TiAlN with a Ti=Al ratio of 1.0 [71,72] display a unique combination of

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Table 8 Oxidation Stability of the Compound (PVD, CVD coating) [74] Coating TiC Ti(C,N) TiN ZrN CrN CrC TiAlN(50:50) TiC þ Al2O3

Loss of oxidation stability (max working, T 8C) 400 450 550 500=600 650 700 850 1,200

properties, viz. a high hardness at elevated temperature together with thermal and chemical stability (i.e., stability to diffusion, dissolution into the chip and oxidation stability). Considerably, more heat is dissipated via chip removal. An extremely important advantage of (Ti, Al) N coatings is their oxidation stability up to 850–9258C [73], due to the formation of stable oxide films (a mixture of rutile and alumina) [74,75], see Table 8. Stable tribo-ceramic films (SS-II) can then be formed on the surface during cutting [76] and limit the diffusion of the coating material into the workpiece. These compounds are probably a mixture of alumina and rutile, as found in the oxidation of titanium aluminides [77,78]. Another recent development is the application of compounds that ensure stable friction and wear under high-speed=high-stress cutting conditions. Two methods have been developed for this application. The first is based on the use of advanced multi-component coatings, i.e. the so-called ‘‘superhard’’ coatings, with a room temperature hardness in excess of 40 GPa, and excellent oxidation resistance up to 10008C. Under high-speed machining conditions the surface of the tool can reach 10008C, so the coating should be stable at this temperature [68]. The development of nano-composite coatings with very fine grains (about 10 nm or less) illustrates the potential of this class of material. The mechanical behavior of nano-composite materials may be controlled by the response of the grain boundary, because the number of atoms in the grain can be comparable to that in the boundary regions. Grain boundary sliding can replace dislocation climb and glide as the dominant plastic deformation mechanism. These materials can be prepared only by methods that simultaneously ensure a high rate of nucleation and a low rate of growth. Magnetron sputtering and filtered arc deposition can be used for the production of nano-crystalline films [42,68].

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In both methods, a highlyionized plasma ensures rapid crystal nucleation on the one hand and very fast cooling rates on the other. The kinetic energy of the bombarding ions is transferred into very small volumes, of atomic dimensions, and the cooling rate of the film is high [68]. These are highly non-equilibrium processes. The most familiar type of superhard coating is nc-MeN=a-nitride, where Me ¼ Ti, W, V, Zr or other transition metals and a-nitride is an amorphous Si3N4 [79]. The high hardness is associated with the formation of isolated nanocrystals of the nitride phase dispersed in an amorphous matrix, so that dislocation motion and grain boundary sliding are suppressed. The second type of superhard nano-composite coating, nc-MeN=metal [68,80], relies on a combination of soft and hard materials such as Cu, Ni, Y, Ag, and Co with TiN (or other nitrides) [81]. Superhard nano-composite films have a high hot hardness (beneficial for flank wear), a high resistance against crack formation, and increased thermal and chemical stability (beneficial for crater wear resistance), as shown by their high oxidation stability up to 11508C [82]. As noted before, the unique properties of these coatings, in particular the nc-TiN=aSi3N4 or TiAlSiN coatings [83], are associated with the small dimensions of the nanocrystals (1–10 nm). Strong segregation effects can lead to a thermodynamic stabilization of the grain boundaries, with a high energy of activation for grain coarsening [79]. Coatings such as nc-TiN=a-Si3N4; nc-TiAlSiN, and nc-TiN-ncBN [83–87] are promising materials for cutting tool application. TiAlN coatings could also be superhard [68] and show excellent wear resistance at high-speed cutting. Superlattice or multi-layer coatings with a superlattice period ranging from 5 to 10 nm have also been developed for cutting tool applications. The bi-layers in these superlattice structures can be metal layers, nitrides, carbides, or oxides of different materials or combinations of these compounds such as TiAlN=NbN; TiAlN=CrN or TiAlN=VN [88–90]. The mechanism of hardening in these coatings is associated with the restriction of dislocation motion across an interface or within the layer itself, due to the suppression of the normal dislocation source and multiplication effects encountered in bulk materials [88–90]. If we summarize all the known data of superhard coatings and ionmixed structures and compare them to the properties of dissipative structures, it is apparent that the self-organization in these systems at extremely non-equilibrium conditions of the coating deposition process can be associated with the formation of a stable, nano-structured material [91,92]. A novel material (in the form of a thin film) is created at the surface whose characteristics are very similar to the extreme properties of the dissipative, secondary structures associated with friction. The material is both

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very hard and as chemically stable as SS-II, while at the same time, its structure is similar to the amorphous state of SS-I. Thus, it is possible to create an ‘‘artificial’’ material, possessing unique, but previously unattainable properties, and a new level of tool performance under the extreme conditions of high-speed cutting. This is an exciting yet practical realization of the underlying principles of friction control. Further improvements in the use of coatings for high-speed machining will depend on a better understanding of the stable tribo-ceramics that form at the surface of superhard nano-composites. To achieve this research goal, the elements of the coating composition that have an ability to act synergistically must be investigated. All known commercial coatings (e.g. TiN, TiCrN, TiAlN) and even ‘‘state-of-the-art’’, superhard coatings probably generate only tribo-ceramics such as rutile or mixtures of rutile and alumina or rutile and chromia that possess limited stability at high-speed cutting. The generation of a stable continuous film of alumina on the surface could be a goal for the development of new coatings for high-speed cutting applications. It has been proven indirectly that a thin layer of alumina was formed on the surface of PVD TiAlN coatings, and multi-layered coatings with excellent properties have been reported [93]. Recently, some companies (e.g. Bulzers, CemeCon) have started to deposit an aluminum-rich layer (65–75 at.%) in the coating to ensure the formation of a protective alumina layer on cutting [94]. The formation of an alumina-like SS-II on the surface of the coating during cutting might enhance the tool life. For this type of coating, other alloying components in the hard coating might act synergistically to promote the formation of stable triboceramics. A promising composition of this type is based on TiAlCrN coatings [95]. It is known that certain ternary TiAlCr alloys form a very stable alumina layer during high-temperature oxidation, in contrast to TiAl alloys where the oxide that forms is non-protective [96]. Several authors have reported on the beneficial properties of these coatings for high-temperature applications [97]. TiAlCrYN and TiAlN=CrN superlattice coatings show excellent oxidation resistance [90,98,99] while the former demonstrated promising wear resistance at elevated temperature [100]. The addition of Y drastically reduces the grain size [101] and leads to superhard coatings. In ternary TiAlCr alloys, chromium forces the other elements to act synergistically, and forms a protective alumina film at the surface. The development of the next generation of coatings for high-speed machining could combine the properties of superhard coatings, as outlined above, with an ability to generate a protective alumina layer during cutting (the principle of self-protection). An alternative technology is the use of stable ceramic coatings (e.g. alumina or zirconia) [102–104]. These ceramics are the most stable and wear resistant materials for high-speed cutting applications. Unfortunately, these

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ceramics are brittle, but when they are used as thin films in coatings, this problem can be mitigated. In this chapter, we have described how current coating technologies might be exploited to develop and bring new tribological tool materials to the marketplace, based on the concept of a functionally graded microstructure. We believe that in the near future this combination of surface engineering and the further optimization of tribological materials will increase the wear resistance of cutting tools and lead to an increased productivity under the extreme conditions encountered in high-speed machining. REFERENCES 1. Holmberg, K.; Matthews, A. Coating Tribology: Principles, Techniques, and Application in Surface Engineering; Elsevier Science B.V. Amsterdam, The Netherlands, 1942; 257–309. 2. Rosenberg, O.A. Main features of friction at metal cutting. Friction Wear 1991, XII (4), 639–644. 3. Trent, E.M.; Suh, N.P. Tribophysics; Prentice-Hall: Englewood Cliffs, NJ, 1986; 125–489. 4. Kostetsky, B.I. An evolution of the materials’ structure and phase composition and the mechanisms of the self-organizing phenomenon at external friction. Friction Wear 1993, XIY (4), 773–783. 5. Mansson, B.A.; Lindgren, K. Thermodynamics, information and structure. In Nonequilibrium Theory and Extremum Principles; Sieniutycz, S.; Salamon, P., Eds.; Taylor & Francis Inc.: New York, 1990; 95–98. 6. Pigogine, I. From Being to Becoming; W.H. Freeman and Company: San Francisco, 1980; 84–87. 7. Ivanova, V.S.; Bushe, N.A.; Gershman, I.S. Structure adaptation at friction as a process of self-organization. Friction Wear 1997, 18 (1), 74–79. 8. Kostetsky, B.I.; Structural-energetic adaptation of materials at friction. Friction Wear 1985, VI (2), 201–212. 9. Kostetskaya, N.B.; Structure and energetic criteria of materials and mechanisms wear-resistance evaluation. Ph.D. dissertation, Kiev State University, Kiev, 1985. 10. Kostetskaya, N.B. Mechanisms of deformation, fracture and wear particles forming during the mechanical-chemical friction. Friction Wear 1990, XVI (1), 108–115. 11. Kabaldin, Y.G.; Kojevnikov, N.V.; Kravchuk, K.V. HSS cutting tool wear resistance study. Friction Wear 1990, XI (1), 130–135. 12. Kabaldin, Y.G. The structure-energetic approach to the fraction wear and lubricating phenomenon at cutting. Friction Wear 1989, X (5), 800–801. 13. Ivanova, V.S. Fracture synergetic and mechanical properties. Synergetic and Fatigue Fracture of Metals; Science: Moscow, 1989; 6–27. 14. Bereznikov, A.; Ventzel, E. Integrated structure adaptation of tribocouples in aspect of the I. Prigogine theorem. Friction Wear 1993, XIV (2), 194–202.

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15. Gruss, W.W. Cermets. In Metals Handbook; 9th Ed.; Burdes, B.P. American Society for Metals: Metals Park, OH, 1989; Vol. 16, 90–104. 16. Kramer, B.M.; Judd, P.K. Computation design of wear coating. J. Vacuum Sci. Technol. 1985, 3 (6), 2439–2444. 17. Pinnow, K.E.; Stasko, W.S. Powder metallurgy high-speed steels. . In Metals Handbook., Burdes, B.P., Ed.; American Society for Metals, OH, 1998, Vol. 16, 60–68. 18. Santthanam, A.T.; Tierney, P. Cemented carbides.. In Metals Handbook, Burdes, B.P., Ed.; American Society for Metals, OH, 1998, Vol. 16, 71–89. 19. Komanduri, R.; Samanta, S.K. Ceramics.. In Metals Handbook, Burdes, B.P., Ed.; American Society for Metals, OH, 1998, Vol. 16, 98–104. 20. Fujisawa, T. et al. Cermet cutting tool consisting of titanium carbonitride with high resistance to thermal shocks Jpn. Kokai Tokkyo Koho JP 2000 54,055 (Cl C22C29=04)220 Feb. 2000, Appl. 1998=220, 271 4 Aug 1998. 21. Kostetsky, B.I. Surface Strength of the Materials at Friction; Technica Kiev 1976; 76–154. 22. Shevela, V.V. Internal friction as a factor of wear resistance of the tribosystems. Friction and wear 1990, XI (6), 979–986. 23. Fox-Rabinovich, G.S.; Kovalev, A.I.; Shuster, L.Sh.; Bokiy, Yu.F.; Dosbayeva, G.K.; Wainstein, D.L.; Mishina, V.P. Characteristic features of wear in HSS-based compound powder materials with consideration for tool self-organization at cutting. 1. Characteristic features of wear in HSS-based deformed compound powder materials at cutting. Wear 1997, 206, 214–220. 24. Uchida, N.; Nakamura, H. Influence of chemical composition of matrix powders on some properties of TiN dispersed and carbide enriched HSS. Reports of 12th International Plansee Seminar, Vienna, Vol. 2, 1989; 541–555. 25. Fox-Rabinovich, G.S.; Kovalev, A.I.; Shuster, L.Sh.; Bokiy, Yu.F.; Dosbayeva, G.K.; Wainstein, D.L.; Mishina, V.P. Characteristic features of wear in HSS-based compound powder materials with consideration for tool selforganization at cutting. 2. Cutting tool friction control due to the alloying of the HSS-based deformed compund powder material. Wear 1998, 214, 279–286. 26. Fox-Rabinovich, G.S.; Kovalev, A.I.; Afanasyev, S.N. Characteristic features of wear in tools made of HSS with surface engineered coatings. II. Study of surface engineered HSS cutting tools by AES, SIMS and EELFAS methods. Wear 1996, 198, 280–286. 27. Samsonov, G.V.; Vinnitsky, I.M. Heavy Melting Compounds; Mashinostroenie: Moscow, 1976; 44–56. 28. Beliy, V.A.; Ludema, K.; Mishkin, N.K. Tribology: Studies and Applications: USA and USSR Experience. Mashinostroenie: Moscow, Allerton Press: New-York, 1993; 202–452. 29. Tretiakov, I.P.; Vereshchaka, A.S. Cutting Tools with Coatings; Mashinostroenie: Moscow, 1994; 17–297.

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30. Oskarsson, R.; Von Holst, P. Sandwick Coronite – a new compound material for end mills. Metal Powder Report , 1989, 44 (12), 44–56. 31. Zhao, C.; Vandeperre, L.; Vleugeks, J.; Van Der Biest, O. Innovative processing=synthesis ceramic, glasses, composites III. Ceramic Trans. 2000, 108, 193–201. 32. Nomura, T.; Ikegaya, A. Functionally graded cemented carbide tools. Mater. Integr. 1999, 12 (10), 13–19. 33. Moriguchi, H.; Nomura, T.; Tsuda, K.; Isobe, K.; Ikegaya, A.; Moriyama, K. Design of functionally graded cemented carbide tools. Funtai Funmatsu yakin Kyokai 1998, 45 (3), 231–236. 34. Van der Biest, O.; Vleugels, J. Perspectives on the development of ceramic composites for cutting tool application. Proceedings of International Conference on Cutting Tools and Machining Systems, Atlanta, 2001; 156–161 35. Schmauder, S.; Melander, A.; McHugh, P.E.; Rohde, J. New tool material with structure gradient for milling application. J. Phys. 1999, IV (9), 147–156. 36. Nomura, T.; Ikegaya, A. Functionally graded cemented carbide tools. Mater. Integr. 1999, 12 (10), 13–19. 37. Holleck, H.W. Advanced concepts of PVD hard coatings. Vacuum 1990, 41 (7–9), 2220–2222. 38. Fox-Rabinovich, G.S. Structure of complex coatings. Wear 1993, 160, 67–76. 39. Palatnilk, L.S. Pores in the Films; Energizdat: Moscow, Russia, 1982; 121–214. 40. Goldsmith, H.J. Interstitial Alloys; Butterworth: London, 1967; 14–23. 41. Gorokhovsky, V.I.; Bhat, D.G.; Shivpuri, R.; Kulkarni, K.; Bhattacharya, R.; Rai, A.K. Characterization of large area filtered arc deposition technology: part II. Coating properties and applications. Surface Coatings Technol. 2001, 140, 215–224. 42. Konyashin, I.; Fox-Rabinovich, G.S. Nanograined titanium nitride thin films. Advanced Mater. 1998, 10 (12), 952–955. 43. Fox-Rabinovich, G.S.; Kovalev, A.I.; Afanasyev, S.N. Characteristic features of wear in tools made of high-speed steels with surface engineered coatings. I. Wear characteristics of surface engineered high-speed steel cutting tools. Wear 1996, 201, 38–44. 44. Storz, O.; Gasthuber, H.; Woydt, M. Tribological properties of thermalsprayed Magne´li-type coatings with different stoichiometries (TinO2n 1). Surface and Coating Technol. 2001, 140, 76–81. 45. Fox-Rabinovich, G.S. The method of tool hardening. Russian Patent 2,026,419, 1995. 46. Fox-Rabinovich, G.S. Scientific principles of material choice for wearresistant cutting tools and dies from the point of view of surface’s structure optimization. D.Sc. Dissertation, All-Russian Railway Transport Research Institute, Moscow, Russia 1993. 47. Bershadskiy, L.I. On self-organizing and concept of tribosystem selforganizing. Friction Wear 1992, XIII (6), 1077–1094.

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48. Lahres M.; Doerfel O.; Neumu¨ller R. Applicability of different hard coatings in dry machining an austenitic steel. Surface Coatings Technol. 1999, 120–121, 687–691. 49. Holuba´r P.; Jı´ lek M.; Sı´ ma M. Nanocomposite nc-TiAlSiN and nc-TiNBN coatings: their applications on substrates made of cemented carbide and results of cutting tests. Surface Coatings Technol. 1999, 120–121, 184–188. 50. Nosovkiy, I.G. On the mechanism of seizure of metals at friction. Friction Wear 1993, XIY (1), 19–24. 51. Fox V.C.; Renevier N.; Teer D.G.; Hampshire J.; Rigato V. The structure of tribologically improved MoS2-metal composite coatings and their industrial applications. Surface Coatings Technol. 1999, 116–119, 492–497. 52. Fox, V.C.; Jones, A.; Renevier, N.M.; Teer, D.G. Hard lubricating coatings for cutting and forming tools and mechanical components. Surface Coatings Technol. 2000, 125, 347–353. 53. Derflinger, V.; Bra¨ndle, H .; Zimmermann, H. New hard=lubricant coating for dry machining. Surface Coatings Technol. 1999, 113, 286–292. 54. Lugscheider E.; Ba¨rwulf S.; Barimani C. Properties of tungsten and vanadium oxides deposited by MSIP-PVD process for self-lubricating applications. Surface Coatings Technol. 1999, 120–121, 458–464. 55. Kovalev, A.I.; Wainstein, D.L.; Mishina, V.P.; Fox-Rabinovich, G.S. Investigation of atomic and electronic structure of films generated on a cutting tool surface. J. Electron Spectroscopy Related Phenomena 1999, 105, 63–75. 56. Bushe, N.A. Solved and unsolved problems of tribosystems compatibility. Friction Wear. 1993, XIY (1), 26–33. 57. Karasik, I.I. Methods of Tribological Tests in Standards of Various Countries; Science and Technique: Moscow, Russia, 1993, 7–325 . 58. Napreev, I.S. Control over tribological characteristics of bearing units by the methods of epilamon formation. Ph.D. Dissertation, Bella Russian State Technology University, Minsk, Bella Russia, 1999. 59. Gulanskiy, L.G. Application of an epilamon for wear resistance of machine parts increase. Friction Wear, 1992, XIII (4), 695–701. 60. Fox-Rabinovich, G.S.; Bushe, N.A.; Kovalev, A.I.; Korshunov, S.N.; Shuster, L.S.; Dosbaeva, G.K. Impact of ion modification of HSS surfaces on the wear resistance of cutting tools with surface engineered coatings. Wear, 2001, 249, 1051–1058. 61. Panckow, A.N.; Steffenhagen, J.; Wegener, B.; Du¨bner, L.; Lierath, F. Application of a novel vacuum-arc ion-plating technology for the design of advanced wear resistant coatings. Surface Coatings Technol. 2001, 138, 71–76. 62. Bushe, N.A. Tribo-engineering materials. Practical Tribology. World Experience. International Engineering Encyclopedia; Science & Technique Centre: Moscow, Russia, 1, 1994; 21–29. 63. Rabinowicz, E. Wear Control Handbook; ASME: New York, 1980; 475–476. 64. Vladimirov, B.G.; Guseva, M.I.; NP Carbide cutting tool life improvement by ion implanting methods. . Friction Wear 1993, XIV, 544–551.

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65. Manory, R.R.; Perry, A.J.; Rafaja, D.; Nowak, R. Some effects of ion beam treatments on titanium nitride coatings of commercial quality. Surface Coatings Technol. 1999, 114, 137–142. 66. Liau, Z.L.; Mayer, J.W. Influence of ion bombardment on material composition. In Treatise on Materials Science and Technology; Hirvonen, J.K., Ed.; Ion Implantation; Academic Press: New York, 1980, Vol. 18, 49–57. 67. Komkonder, L.; Sahin, E.; Buyukksap, E. The effect of the chemical environment on the Kb=Ka X-ray intensity ratio. Nuovo Cimento 1993, 5 (10), 1215–1299. 68. Musil, J. Hard and superhard nanocomposite coatings. Surface Coatings Technol. 2000, 125, 322–330. 69. Musil, J.; Vlcek, J. A perspective of magnetron sputtering in surface engineering. Surface Coatings Technol. 1999, 112, 162–169. 70. Nicholls, J.R.; Simms, N.J. Smart overlay coating-concept and practice. Proceeding of International Conference on Metallurgical Coatings and Thin Films, San-Diego, CA, 2001; 236–244. 71. To¨nshoff, H.K.; Karpuschewski, B.; Mohlfeld, A.; Seegers, H. Influence of subsurface properties on the adhesion strength of sputtered hard coatings. Surface Coatings Technol. 1999, 116–119, 524–529. 72. Wu, S.K.; Lin, H.C.; Liu, P.L. An investigation of unbalanced-magnetron sputtered TiAIN films on SKH51 high-speed steel. Surface Coatings Technol. 2000, 124, 97–103. 73. Wang, D.-Y.; Li, Y.-W.; Ho, W.-Y. Deposition of high quality (Ti, Al)N hard coatings by vacuum arc evaporation process. Surface Coatings Technol. 1999, 114, 109–113. 74. Muntz, W.-D.M. Ti–Al nitride films: A-new alternative to TiN coatings. J. Vac. Sci. Technol. A 1986, 4 (6), 2717–2725. 75. Woo, J.H.; Lee, J.K.; Lee, S.R.; Lee, D.B. High-temperature oxidation of Ti0.3 Al0.2 N0.5 thin films deposited no steel substrate by ion plating. Oxidation Metals 2000, 53 (5=6), 529–537. 76. Bouzakis K-.D.; Vidakis N.; Michailidis N.; Leyendecker T.; Erkens G.; Fuss G. Quantification of properties modification and cutting performance of (Ti1 x Alx)N coatings at elevated temperatures. Surface Coatings Technol. 1999, 120–131, 34–43. 77. Doychak, J. Oxidation behavior of high-temperature intermetallics. In Intermetallic Compounds; Westbrook, J.H.; Fleisher, R.L., Eds.; John Wiley & Sons Ltd. New York, 1994, Vol. 2, 73–90. 78. Okafor, I.C.I.; Reddy, R.C. The oxidation behavior of high-temperature aluminides. JOM 1999, 6, 35–39. 79. Neiderhofer A.; Nesladek P.; Mannling H-.D.; Moto K.; Veprek S.; Jilek M. Structural properties, internal stress and thermal stability of nc-TiN=a-S3N4, nc-TiN=TiSix and nc-(Ti1y Aly Six)N superhard nanocomposite coatings reaching the hardness of diamond. Surface Coatings Technol. 1999, 120–121, 173–178.

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80. Musil J.; Zeman P.; Hruby´ H.; Mayrhofer P.H. ZrN=Cu nanocomposite films—novel superhard material. Surface Coatings Technol. 1999, 120–121, 179–183. 81. He, J.L.; Setsuhara, Y.; Shimizu, I.; Miyake, S. Structure refinement and hardness enhancement of titanium nitride films by addition of copper. Surface Coatings Technol. 2000, 137, 38–42. 82. Tanaka, Y. Ichimiya, N.; Onishi, Y.; Yamada, Y. Structure and properties of Al–Ti–Si–N coating prepared by cathodic arc ion plating method for highspeed cutting application. Proceedings of International Conference on Metallurgical Coatings and Thin Films, 2001, Abstracts, San Diego; 2001, 215–221. 83. Holubar P.; Jilek M.; Sima M. Nanocomposite nc-TiAlSiN and nc-TiN-BN coatings: their applications on substrates made of cemented carbide and result of cutting tests. Surface Coatings Technol. 1999, 120–121, 184–188 84. Mitterer C.; Mayrhofer P.H.; Beschliesser M.; Losbichler P.; Warbichler P.; Hofer F.; Gibson P.N.; Gissler W.; Hruby H.; Musil J.; Vlek J. Microstructure and properties of nanocomposite Ti–B–N and Ti–B–C coatings. Surface Coatings Technol. 1999, 120–121, 405–411. 85. Veprek S.; Nesla´dek P.; Neiderhofer A.; Glatz F.; Jilek M.; Sima M. Recent progress in the superhard nanocrystalline composites: towards their industrialization and understanding of the origin of the superhardness. Surface Coatings Technol. 1998, 108–109, 138–147. 86. Wong M.S.; Lee M Y.C. Deposition and characterization of Ti–B–N monolithic and multiplayer coatings. Surface Coatings Technol. 1999, 120– 121, 194–199. 87. Diserens M.; Patscheider J.; Le´vy F. Improving the properties of titanium nitride by incorporation of silicon. Surface Coatings Technol. 1999, 108–109, 158–165. 88. Zeng, X.T. TiN=NbN superlattice hard coatings deposited by unbalanced magnetron sputtering. Surface Coatings Technol. 1999, 113, 74–79. 89. Munz, W.-D.; Donohue, L.A.; Hovsepian, P.E. Properties of various largescale fabricated TiAlN- and CrN-based superlattice coatings grown by combined cathodic arc-unbalanced magnetron sputter deposition. Surface Coatings Technol. 2000, 125, 269–277. 90. Lembke, M.I.; Lewis, D.B.; Mu¨nz, W.-D. Localised oxidation defects in TiAlN=CrN superlattice structured hard coatings grown by cathodic arc=unbalanced magnetron deposition on various substrate materials. Surface Coatings Technol 2000, 125, 263–268. 91. Veprek, S. Mechanical properties of superhard nanocomposite. ICMCTF 2001, Abstracts, Proceedings of International Conference on Metallurgical Coatings and Thin Films, 2001, Abstracts, San Diego; 2001, 125–182. 92. Maennling, H-.D.; Patil, D.S.; Moto, K.; Jilek, M.; Veprek, S. Thermal stability of superhard nanocomposite coatings consisting of immiscible nitrides. Proceedings of International Conference on Metallurgical Coatings and Thin Films, 2001, Abstracts, San Diego; 2001, 263–282.

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93. Rass, I.; Leyendecker, T.; Feldehege, M.; Erkens, G. TiAlN–Al2O3 PVD multi-layer for metal cutting operation. Proceedings of Fifth European Conference on Advanced Materials Processes Application, Zeedijk, 1997; 23–27. 94. Sjolen, J.; Karlson, L. Thermal stability of arc evaporated high aluminium content TiAlN films. ICMCTF 2000, Abstracts, San-Diego, California, April 2000; 80. 95. Leyens C.; van Liere J.-W.; Peters M.; Kaysser W.A. Magnetron-sputtered Ti–Cr–Al coatings for oxidation protection of Ti alloys. Surface Coatings Technol. 1998, 108–109, 30–35. 96. Brady, M.P.; Brindley, W.J.; Smialek, J.L.; Locci, I.E. The oxidation and protection of gamma titanium aluminides. JOM 1996, 11, 46–50. 97. Tang, Z.; Wang, F.; Wu, W. The effect of several coatings on cyclic oxidation resistance of TiAl intermetallics. Surface Coatings Technol. 1999, 110, 187–199. 98. Lewis, D.B.; Donohue, L.A.; Lemke, M.; Munz, W.-D.; Kuzel, R.; Valvida, V.; Blomfield, C.J. The influence of yttrium content on the structure and properties of TiAlCrYN hard coatings. Surface Coatings Technol. 1999, 114, 187–199. 99. Leyens, C.; Peters, M.; Hovsepian, P.; Lewis, B.D.; Munz, W.-D. Novel coating system produced by combined cathode arc=unbalanced magnetron sputtering for environmental protection of titanium alloys and titanium aluminides. Proceedings of International Conference on Metallurgical Coatings and Thin Films, 2001, Abstracts, San Diego; 2001, 103–111. 100. Pfluger, E.; Schroer, A.; Voumard, P.; Donahue, L.; Munz, W.-D. Influence of incorporation of Cr and Y on the wear performance of TiAlN coatings at elevated temperatures.. Surface Coatings Technol. 1999, 115, 17–23. 101. Mennicke, C.; Shumann, E.; Ruhle, M.; Hussey, R.J.; Sproule, G.I.; Craham, M.J. The effect of yttrium on the growth process and microstructure of alumina on FeCrAl. Oxidation Metals 1998, 49 (5=6), 455–466. 102. Larsson, A.; Halvarsson, M.; Ruppi, S. Microstructural changes in CVD– Al2O3 coated cutting tools during turning operations. Surface Coatings Technol. 1999, 111, 191–198. 103. Bolt H.; Koch F.; Rodet J.L.; Karpov D.; Menzel S. Al2O3 coatings deposited by filtered vacuum arc characterization of high temperature properties. Surface Coatings Technol. 1999, 116–119, 956–962. 104. Koski K.; Ho¨lsa¨ J.; Juliet P. Deposition of aluminium oxide thin films by reactive magnetron sputtering. Surface Coating Technol.1999, 116–119, 716–720.

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6 Designing Fastening Systems Christoph Friedrich RIBE Verbindungstechnik GmbH, Schwabach, Germany

This chapter gives a compressed, but comprehensive and clearly structured view of the design of threaded fastening systems as an example for fastening of components in general. Formulae are given to transfer the aspects to own problems, but there is no space to derive them, so they are proposed and concentrated in figures. The aim is to present an effective engineering tool for optimized fastening of components, especially if made of materials this book deals with. To realize this, some basic concepts are discussed to aid the reader. This chapter will provide the designer and engineer with a new approach to threaded fastening systems.

I.

NATURE OF FASTENING SYSTEMS IN GENERAL

Nearly every component has to be fastened to another, no matter of which material it is made. Engineering of fastening systems plays a fundamental role for all engineered products all over the world. But more importantly, the optimization of components due to more power, more reliability, lower volume and weight as well as lower cost, because this leads to new requirements for the fastening system: it has to work with new materials (often with low strength and significant thermal expansion behavior), higher temperatures, it must transmit all loadings within a small material volume, it has to work without failure for a long period and must guarantee a good appearance for the operating time. In many cases, the fastening system has to be extremely low priced, because there is almost no money left to fasten the ‘very carefully designed and expensive components’ in an adequate way. Besides this, the fastening system has to function well even

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

if misuse occurs, so that an accident by overloading-failure is avoided whenever possible. To meet these different requirements, a lot of interdisciplinary physical, chemical, and engineering knowledge is necessary as well as an effective method to bring these disciplines together. Therefore, the aim of this chapter is to provide a guideline for optimized fastening systems, shown with bolted joints as an example. But, the same aspects are also valid for other fastening techniques. This chapter is written for the use in an engineer’s daily life. So, the process of designing and a comprehensive point of view are very important, to deal with some particular technical details, which are already investigated very extensively and documented. Another point is that a fast design process has become more and more important in the competitive industry—to realize this an early integration of fastening engineering in the design process is necessary—this chapter shows the reasons for these aspects. Figure 1 presents a fastening system based on the view of general systems theory, which was founded by the Society for General Systems Research in the year 1954 in London [6]. Each product is a component system, and if it has fastened components, at least two components are included (nos. 1 and 2 in Fig. 1). Each component is characterized by its geometry, its material, and its production process, which leads to inhomogeneities in material properties or limited tolerances as well as limited surface finish. Of importance is that the whole product (component–system) has to be optimized for maximum functionality due to the end-user. Also, the loading during the product life cycle—mechanical, thermal or reactive—is related to the entire product. Any connection between two or more components is a fastening system, which can be also characterized as a subsystem of the product. Figure 1 shows two very often used fastening techniques of engineering (bolted joint and welding). The basic difference between both the fastening processes is that bolted joints need an additional fastening element (3), whereas welding needs working materials [e.g. filler rod or protective gas, (3)] and much more energy. Of course, a bolted joint can be disassembled and reassembled easily in contrast to weldings—this is one important reason for the worldwide practice of using screws and bolts (and if we think about increasing recycling requirements, the importance of fastening systems with the possibility for easy disassembly will grow in the future). In practice, often specific boundary conditions of the manufacturers are decisive, and based on this, the type of fastening system is selected. These

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Figure 1 Fastening system as a subsystem of product and typical characteristics.

boundary conditions are named in Fig. 1, e.g. existing assembly equipment or existing qualified and experienced personnel. Finally, the fastening technique must be suitable for the product. Relevant aspects are summarized in Fig. 1. For example, compatibility of the fastening technique with the components (e.g. sufficient materials strength to transmit the preload force of a bolt or use of weldable materials). The following sections focus on threaded fastening systems as an example for heavy-duty fastening of components with high relevance

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and reliability. The experience with threaded fastening systems over many decades and detailed calculation methods are useful base for every design engineer. For other fastening techniques like shaft keys, adhesive bonding, clamping devices, pins, or retaining rings, see Refs. [3,4,5,8,55,65,68].

II.

CHARACTERISTICS OF THREADED FASTENINGS

For understanding the design process of a threaded fastening system, we have to look closely at the different screw design sections A–D and component design sections E, F like that shown in Fig. 2. These are: engaged screw thread, free screw thread, screw shank and screw head resp. clamped part and nut thread component. If a screw (3) is tightened to a certain preload Fp, a closed flow of preload is generated. If the bolted joint is operating over its period of life cycle, a superposition of residual preload and additional operating load is acting. This flow causes tensile stress in sections B and C. Compressive stress is generated in the clamped part (2 resp. F) and a combination of compressive stress as well as shear stress occurs in the nut thread component (1 resp. E) and in sections A and D. This inhomogeneity of stresses is the reason why the behavior of bolted joints is very complex and has to be designed carefully. The schematic diagram to the right of Fig. 2 shows another stress inhomogeneity caused by different cross-sections of the screw shank and stress concentration effects of the notched thread geometry. The result is that at the position of the first bearing screw thread flank a significant stress concentration in the range of 5–8 due to the existing average stress level. This is very important, especially for dynamic behavior of bolted joints. Since this also causes the beginning of local material plastification of the screw in the first bearing thread flank, even if the screw is tightened only to 1=5 to 1=8 of its yield limit. Therefore, the material for screws has to be ductile (as a lower limit from experience the fracture toughness of a screw has to be larger than 5%). Table 1 gives an overview over the six basic design criteria of a threaded fastening system, which have to be valid in any case. These criteria are dependent on the entire fastening system, and not merely on the screw itself. For example, the stability of a preloaded bolted joint over the period of use, depends on all stressed components within the flow of preload (no. 1 in Table 1, comp. also Fig. 2). According to no. 2 in Table 1, the dynamic loading capacity of a bolted joint is especially influenced by the

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Figure 2 joint.

Flow of preload, design sections, and stress concentrations of a bolted

local stress peaks and these local stress peaks can be determined by the design engineer. A screw shank is always under high level tensile stress so a fastening design must avoid screw material conditions which are sensible for stress corrosion cracking (no. 3 in Table 1, e.g. screws made of high-strength aluminum alloy with wrong heat treatment without safe surface protection from electrolytes during operation). Self-loosening effects are highly dependent on the vibrational (transversal) loading of the fastening system and on the contact conditions between components and screw; so this is also a significant system behavior (no. 4, in Table 1). Numbers 5 and 6 in Table 1 are self-explanatory. A.

Screw—Basic Details

Today, many details for design of screws are known. For standardized nomenclature of screw geometries, see ISO 1891 [26], for concepts of thread

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Table 1 No. 1

2

3

4

5

6

Basic Design Criteria for Threaded Fastening Systems Criteria

Remarks

Sufficient preload for the period of use

Includes worst case of tightening, worst case of friction in thread and head support contact zones as well as worst case of relaxation effects (see also Fig. 18). Includes static and dynamic loading Sufficient loading capacity capacity, includes screw thread, screw shank, to resist all operating loads screw head; material properties must be stable for the period of use over the period of use (e.g. no hydrogenembrittlement), see also Fig. 50. Sufficient corrosion resistance Includes all kinds of corrosion, also stress for the period of use corrosion cracking under tensile stress; for combination of different materials in a bolted joint galvanic corrosion is very important, see also Table 5. No self loosening Includes both, extreme decrease of preload and loosening of the screw; only a few solutions give a safe prevention from self-loosening, see also Figs. 41 and 76. Easy assembly=disassembly Includes screw drive design (Fig. 35), and high stability of assembly accessibility of fastening system, assembly process device, tightening method (Fig. 18); these factors are responsible for a guaranteed high preload and, therefore, are responsible for the function of the fastening system; assembly cost is, in any case, a very important cost factor, see also Fig. 41. Low cost target for the Includes not only low price for screw, but fastening system also for total life cycle of product=fastening system (e.g. also cost for storage and logistics, assembly cost, failure cost, cost of maintenance and repairing, quality cost; as a rough approximation purchasing cost of screw is under 20% of total cost for fastening system), see also Ref. [65] and Fig. 56.

system see Ref. [36], for general tolerances, see Ref. [35], for technical drawings see Refs. [38,49]. Figure 3 gives an overview of the basic details of an optimized screw which have been established for determining the mechanical behavior.

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For a given thread size, thread type, and screw material, the shank type, underhead fillet, and drive type have to be designed in such a manner so that the ‘‘screw design principle’’ is achieved. This means that if loading or overloading the screw, a quasistatic screw failure always has to take place in screw section B or C referred to Fig. 2. Fatigue failure has to be located in section B or between A and B (first load bearing thread flank of screw). The most used thread type is metric thread of the coarse series [defined in ISO 68 [40], ISO 724 [42], ISO 965 [47]]. This thread geometry has a flank angle of 608 and is defined by its diameter and its pitch—therefore, all ISO screw threads use the designation: ‘‘diameter’’ ‘‘pitch-value’’. The selection of shank type influences the elastic resilience of the screw and therefore affects the entire fastening system. The higher the screw resilience without changing of the clamped part, the lower is the additional stressing of the screw under external operating force. This advantage is utilized for a screw with wasted shank. The opposite is true for an increased

Figure 3 Ref. 17.)

Basic details of screws established for high-duty bolted joints. (From

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

shank which is used to obtain an additional centering function of the screw. A full shank is typical for screws with cut thread whereas threaded shank and reduced shank are typical for screws with rolled thread. To design a screw with high resilience, good yielding, and plastification behavior as well as low cost, a threaded shank should always be the first choice. Wasted shank and increased shank are relatively expensive because normally a turning operation is needed. The screw surface is responsible for appearance as well as for both corrosive and frictional behavior—therefore, the screw surface is very important for the designed operational behavior. Support diameter under screw head and thread engagement determines the surface contact pressure at the two contact zones of a screw. The thread engagement also influences the thread stripping load—this stripping load can destroy the nut thread or screw thread depending on the material strengths and diameter tolerances. It always has to be higher than the failure load of screw section B or C, so thread engagement has to be designed with sufficient length. The four most important geometries for high duty bolted joints are taken: hexagon, bihexagon, triple square and hexalobular. The plain support type is used most often, but the others, countersunk and ball section, provide a better self-loosening resistance and a centering function of the screw. Options like washers, thread ends, and cone points or adhesives against self-loosening are not covered in Fig. 3 (but see Fig. 41). All the described aspects are also valid, if a headless stud with nut is used instead of a screw, then a second thread engagement between stud and nut has to be considered (Fig. 46). The basic screw details are treated more precisely in sections below. In this chapter, the reader would get information on general interactions of screw details and design criteria. 1. Standard Thread Geometry for Existing Nut Thread When using a screw, the selection of thread type is a fundamental aspect for all mechanics of the bolted joint. Normally, a worldwide compatibility is important—this is the reason for the extensive use of metric thread system. Figure 4 proposes the metric thread system as an example of high loading capacity thread. The basic dimensions are characterized like those shown on left side of Fig. 4 by a 608-thread angle and a fundamental triangle with height H (see also Ref. [42]). The external screw thread flank tips are cut with a width of an eighth of the pitch P. The internal nut thread flank tips are cut to a quarter of the pitch P. For the basic dimensions, the major

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Figure 4 Metric thread system for fastening.

diameter (d, D), the pitch diameter (d2, D2) and the minor diameter (d1, D1) are the same for external and internal thread. The pitch diameter is defined from an imaginary cylinder whose external surface cuts a screw thread where the width of the ridge and the groove of the thread are equal [36]. To provide a solution that can be put into practice, the basic thread profile has to be added by tolerances and radii at thread roots, which is shown in right side of Fig. 4. Then any diameter must be distinguished in minimum and maximum value and corresponding external=internal diameters are different (external: small letters, internal: capital letters, e.g. D > d). In ISO 965 [47], the detailed tolerance positions and tolerance fields are standardized. The right side of Fig. 4 also provides the tolerance positions from ISO 965: e, f, g, h for the bolt thread and G, H for the internal nut thread, whereas the combination of g, H is most used. Combinations with even more clearance are used for bolts with thick coatings, e.g. for enhanced corrosion protection. The tolerance field is between 4 and 7, normally 6 is used—that means a combination of 6g for external screw thread and 6H for internal nut thread. The notation of symbols in Fig. 4 is done strictly according to ISO 965. Table 2 provides numeric values for some selected thread sizes M5–M30. In the left column, after each thread size, the pitch value is added. For coarse series, the pitch value is written in parenthesis. From the table, it is

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Table 2 Numeric Values of Metric Thread Diameters with Tolerance and Nominal Stress Area Screw thread (External)

No. 1 2 3 4 5 6 7 8 9 10 11

Nominal Size

Tolerance (ISO 965)

dmin (mm)

dmax (mm)

d2min (mm)

d2max (mm)

d3min (mm)

d3max (mm)

As (mm2)

M5 ( 0.80) M6 ( 1.00) M8 ( 1.25) M10 ( 1.50) M12 ( 1.75) M12 1.50 M12 ( 1.75) M12 ( 1.75) M16 ( 2.00) M30 ( 3.50) M30 2.00

6g 6g 6g 6g 6g 6g 6e 4h 6g 6g 6g

4.826 5.794 7.760 9.732 11.701 11.732 11.664 11.830 15.682 29.522 29.682

4.976 5.974 7.972 9.968 11.966 11.968 11.929 12.000 15.962 29.947 29.962

4.361 5.212 7.042 8.862 10.679 10.854 10.642 10.768 14.503 27.462 28.493

4.456 5.324 7.160 8.994 10.829 10.994 10.792 10.863 14.663 27.674 28.663

3.869 4.596 6.272 7.938 9.602 9.930 9.565 9.691 13.271 25.306 27.261

3.995 4.747 6.438 8.128 9.819 10.128 9.782 9.853 13.508 25.653 27.508

14.2 20.1 36.6 58.0 84.3 88.1 84.3 84.3 156.7 560.6 580.4

D1min (mm) 4.134 4.917 6.647 8.376 10.106 10.376 10.376 13.835 26.211 27.835

D1max (mm) 4.334 5.153 6.912 8.676 10.441 10.676 10.751 14.210 26.771 28.210

— — — — — — — — — —

Nut thread (internal)

12 13 14 15 16 17 18 19 20 21

M5 ( 0.80) M6 ( 1.00) M8 ( 1.25) M10 ( 1.50) M12 ( 1.75) M12 1.50 M12 1.50 M16 ( 2.00) M30 ( 3.50) M30 2.00

Tolerance (ISO 965) 6H 6H 6H 6H 6H 6H 7H 6H 6H 6H

Dmina (mm) 5.000 6.000 8.000 10.000 12.000 12.000 12.000 16.000 30.000 30.000

a

almost no root radius Rnmax. values for guidance with root radius Rnmax=P=16.

b

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Dmaxb (mm) 5.1 5.12 8.15 10.2 12.2 12.2 12.25 16.4 30.7 30.7

D2min (mm) 4.480 5.350 7.188 9.026 10.863 11.026 11.026 14.701 27.727 28.701

D2max (mm) 4.605 5.500 7.348 9.206 11.063 11.216 11.262 14.931 28.007 28.925

obvious that the permissible difference between minimum and maximum diameter using a tolerance grade of 6 is about 1–3% of the minimum value (relatively high deviations for small thread size). For a tolerance grade of 7, this deviation is about 2–6% (lines 17, 18 of Table 2); for a tolerance grade of 4, this deviation is about 0.5–2% (lines 5, 8). For M12 and M30 also, the influence of pitch value is considered (line numbers (5, 6); (10, 11); (16, 17); (20, 21); coarse and fine series). For bolt thread, it is typical that the diameters dmin and dmax do not vary much, but the flank diameters d2min and d2max and especially the root diameters d3min and d3max are different between coarse and fine thread series. This leads to a larger cross-section of a threaded screw shank with fine pitch than with coarse pitch (compare also nominal stress areas As in right column of Table 2). A fine pitch also leads to a small helix angle (lead angle or pitch angle), which produces a higher preload for given thread size and has a higher self-loosening resistance, which is more sensible for thread flank deformations and defects as a result of transportation and handling (see also Fig. 55). The influence of tolerance position can be estimated from lines (5, 7) of Table 2 (comparison between 6g and 6e for same pitch value). Between these two lines, the corresponding diameters are about 40 mm smaller for e-position than for g-position. More information about thread dimensions can be found in Refs. [3,51,56,62] or other handbooks dealing with threaded fastenings. Figure 5 compares ISO metric thread system with ANSI unified thread system. Both systems have the same basic thread profile. The effect on the left side of Fig. 5 is due to coarse series and the right side deals with fine series. The designation of metric thread system starts with ‘M’ and follows the nominal screw diameter and the pitch (for standard coarse series the pitch is usually not written). The unified thread system begins with ‘UNC’ resp. ‘UNF’, followed by the nominal screw diameter and the number of threads per inch. The two scales show the thread sizes that have similar dimension. If comparing the pitch values between metric and unified for corresponding diameters, metric system always has smaller values for same series. 2. Thread Rolling Screws for Medium-Strength Materials Producing a bolted joint involves different steps like those shown in Fig. 6a. For this reason, the price per screw piece is less important, relative to the total cost of a threaded fastening system is done. From this point of view, if a screw can produce its nut thread by itself during assembly, it is a significant advantage for the situation of total cost, because the nut thread component can be produced with lower expense (Fig. 6, part b). For casting

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Figure 5 Comparison of metric thread system with unified thread system.

components, often the manufacturing of a pilot hole can be integrated in the casting process; therefore the drilling or stamping operation is avoided. As a consequence, the production lines can work more quickly and with higher productivity. Another point, which will be more and more important in the future, is the extensive use of cooling lubricant or cutting oil in production lines. Here, thread rolling screws also offer the possibility to eliminate such environmentally unfriendly fluids. Thread rolling screws produce their nut thread by material rolling without chipping. In this case, the screw is both the thread rolling tool for the nut thread and also the fastening element to generate the preload. To obtain this in an effective way, the rolling screws at least have a forming point with lobularity and reduced diameter (Fig. 7). In most cases lobularity involves a screw geometry with three forming zones, therefore, the name ‘trilobular screws’ (see cross-section in Fig. 7). The difference between circumferential circle and minimum cross-section contour is about 4% of the screw diameter. For more information about thread rolling screws, see Refs. [57,63]. If the rolling screw is designed in the right way, a replacement by a screw with standard thread is possible after disassembling the rolling screw. To obtain this, the thread diameters of the rolling screw must be oversized

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Figure 6 Comparison of procedures for producing a bolted joint using screws for (a) existing nut thread and (b) rolling screws.

compared with the thread standard to eliminate elastic resilience of the nut thread flanks. The screw material must provide a high strength, so normally hardened steel alloys may utilize an additional surface treatment (case hardening, induction hardening). The permissible strength of the nut thread material is limited—as a rough approximation, to the strength of the nut thread material can reach half of the screw strength at forming point. Therefore, maximum nut thread material strength is about 600–700 MPa (87–101 ksi). Of course, the nut thread material must provide sufficient

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Figure 7 Basics of rolling screws—geometry and materials.

ductility and formability. The flanks can be formed by the screw—here a rough approximation is > 5% fracture toughness in tensile test, so many steel alloys are covered. Aluminum alloys are recommended materials for thread rolling screws, whereas brittle materials such as gray cast iron or materials with hexagonal crystal structure lead to a low process stability during assembly. Magnesium alloys (also hexagonal structure) thread rolling screws can be used, if a careful adaptation of all influences is considered (see also Fig. 64). The pilot hole can be drilled, stamped, or cast. The pilot diameter is in the range of the screw flank diameter d2. The tolerance of the pilot diameter (normally tolerance field and grade H11 is used) influences the forming torque necessary to bring the screw to head contact. This forming torque can be decreased by a low friction film on the screw surface (app. half of the forming torque with suitable low friction film than without). Table 3 illustrates the diameter of the pilot hole as well as a range of forming torque and tightening torque dependent on the screw strength for high-duty bolted joints with thread rolling screws. The tightening torque must be distinguished by using the rolling screw in blind hole or bringing the forming point out of thread engagement during tightening. This determines the residual forming torque which cannot be utilized for preload generation. In a blind hole, the tightening torque must be higher for producing the same preload compared to a situation with through hole and outstanding forming point of the screw (see also Fig. 67). The rolled nut thread has two significant technical characteristics. (1) There is almost no clearance between the screw thread and the nut thread, so the prevailing torque is rather high and the behavior against self loosening is improved after retightening (clearance-like theoretical profile in the left side of Fig. 4). (2) The nut thread material is strain hardened after

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Table 3 Selected Characteristic Values for Assembly of Thread Rolling Screws [63]

Thread size

Pilot diameter of hole (mm)

1

M5 ( 0.80)

4.50–4.65

1.5–3.5

2

M6 ( 1.00)

5.45–5.60

2.5–6.0

3

M8 ( 1.25)

7.40–7.60

7–15

4

M10 ( 1.50)

9.30–9.50

15–30

5

M12 ( 1.75) 11.10–11.35

25–52

6

M12 1.50

11.20–11.40

27–55

7

M16 ( 2.00) 15.10–15.40

55–115

No.

Forming Property class of torque screw (N m) 8.8 10.9 12.9 8.8 10.9 12.9 8.8 10.9 12.9 8.8 10.9 12.9 8.8 10.9 12.9 8.8 10.9 12.9 8.8 10.9 12.9

Tightening Tightening torque torque blind hole through hole (N m) (N m) 6.4 9.3 10.9 11.6 16.3 18.9 27.3 38.9 45.2 53.6 78.8 91.4 91.4 134.4 157.5 96.6 141.8 165.9 231 336 399

5.5 8.0 9.4 9.9 14.0 12.9 23.4 33.3 38.7 45.9 67.5 78.3 78.3 115.2 135.0 82.8 121.5 142.2 198 288 342

Remarks: Length of thread engagement must be sufficient to avoid stripping of nut thread (app. 2–2.5 diameter of screw); forming torque depends on various parameters, such as pilot diameter, surface conditions, lubrication; optimized assembly of rolling screws must be determined with tests experimentally; for screws with hardened surface, the tightening torque of core strength is relevant; thread rolling in thin sheet metals with extruded rim hole is possible, if the pilot diameter is reduced by app. 4% of the value from this table.

rolling of the thread flanks; so that the local strength of the nut thread material is increased which can enhance the loading capacity of the nut thread.

3. Thread Types for Low-strength Materials Materials with low tensile strength with respect to a low yield point are not able to transmit high preload forces using high contact pressure. If components made of those materials with an external or internal thread, a large

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Figure 8 Details of thread flank geometry—thread types suitable for low-strength materials.

flank engagement is required. This can be realized either by deep thread engagement and=or large radial overlapping. Figure 8 illustrates the influence of thread angle a with respect to flank angle b. Part (a) demonstrates the situation for metric thread geometry with a ¼ 608. An axial preload Fp leads to corresponding radial Force Fr, dependent on the flank angle b. For same axial preload Fp, the radial part Fr can be reduced, either by asymmetric flank geometry (part b of Fig. 8) or small thread angle (part c of Fig. 8). A small thread angle leads to thin screw thread flanks. This is no problem if the tensile strength of screw is much higher than that of the nut thread material. In case of forming the nut thread during assembly for the same overlapping distance x, a small thread angle (part c in Fig. 8) reaches only 60% of area A compared to (a) and (b) of Fig. 8. This area A determines the material volume of nut thread which has to be deformed during thread rolling for a radial flank engagement (distance x). Usually these aspects are reasonable for thread flanks with small thread angle for nut thread materials with low tensile strength, such as aluminum, magnesium, or even plastics as a rolling screw. Figure 9 shows as an example a thread rolling screw for magnesium components with reduced thread angle, so that the deformed volume of nut thread for a given flank engagement is minimized. Figure 10 shows an

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Figure 9 Special thread geometry for thread rolling in magnesium components, a 5 mm screw made of aluminum RIBE63, total thread engagement from screw point to free thread 8 mm.

Figure 10

Asymmetric thread profile.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

example for an asymmetric thread profile, which leads to reduced radial force Fr under preload. Figure 11 shows another example for a thread geometry with low thread angle. This screw can be used for fastening of components with thread rolling in both plastic materials and light metals. The forming torque for screw of dimension M5 is 4 N m in aluminum. For further performance of such thread geometry, see Fig. 75. 4. Elastic Screw Elongation Under Tensile Loading Any mechanical loading of an elastic material leads to a corresponding deformation. For a screw, which is a component with different cylindric sections, the most important loading is the preload in axial direction. The screw elongation under tensile loading is defined by the term ‘axial elastic resilience of screw ds’. This means the ratio of length-changing Dl over the applied axial force F.

‘

Figure 11 A screw with thread geometry for thread rolling in both plastic materials and light metals.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 12 emphasizes the situation schematically. The upper screw is unloaded, so it has its original length and diameter values are d, d3, dsh, lsh, lft, te respectively. The fixed point of the mechanical model is defined for the nut thread component lying on the screw axis. In contrast to the upper screw, the lower screw is loaded by a symmetric axial force F under head (F can be the sum of preload Fp and axial operating load Fax). This leads to a screw-elongation Dl, which is contributed mainly by four parts of ds: the resilience of head dh, the resilience of screw shank dsh, the resilience of free thread dft and the resilience of engaged thread det. The commonly used calculation formulae are also shown in Fig. 12 after Ref. [70]. It is clear that these formulae only give an approximation, especially for dh and det (not taking into consideration the height of head as well as of drive type or tolerances between nut thread and screw thread or length of thread engagement or modulus of elasticity of nut thread component En).

Figure 12 Definition and determination of the axial elastic resilience of a screw. (From Ref. 17.)

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B.

Nut Thread Component

The nut thread component can be a standardized nut or a mechanical component with nut thread. The main difference between these for the same material and same thread geometry is a variation of the stiffness of the nut thread component under mechanical loading as Fig. 13 shows. The hexagon nut of part (a) in Fig. 13 shows shortening and widening of its contour under an axial force F. Therefore, the height of a standard nut should be 1 nominal diameter of screw. At this height, two chamfers are included (0.8 pitch P of thread). This height is necessary for overelastic tightening without nut thread failure (if the nut thread material has same strength as screw thread material, e.g. same property classes; see also Fig. 18). The height of 1 d is also defined in modern standards for nut geometry such as ISO 4161 [32]. For a combination of different materials between the screw thread and nut thread, see Fig. 33. Screw threads manufactured in high series production can have incomplete thread flanks in a length range of (2–3) pitch of thread. The screw should extend through the nut for this distance. In contrast, part (b) of Fig. 13 contains a nut thread produced in a bulk material of a component. Caused by the much higher stiffness under loading F this configuration shows almost no deformation. The relevant thread engagement te has to be measured excluding a chamfer and excluding any screw point and reduced additionally by 1 P for incomplete thread flanks. The local axial stress distribution on the nut thread component is drawn schematically for both cases (a) and (b) in the middle of Fig. 13.

Figure 13 Stiffness of a nut thread component under mechanical loading. (a) Standard nut and (b) bulk material with a nut thread.

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It is significant that a stress peak occurs in the first bearing nut thread flank (same as in first bearing screw thread flank). This means that the material of nut thread should have a sufficient ductility to compensate for this stress peak without cracking or failure. For brittle materials, this stress peak is the critical aspect. In this case, large thread engagement should be used to reduce the stress peak or consider actions as shown in Fig. 41 for improving the fatigue loading capacity. Often nut thread components are used, which do not provide sufficient thread engagement for screw failure in the case of overloading (see design principle, Fig. 2). In those situations, the (nut) thread is stripped and the design engineer has to maximize the number of full engaged thread flanks and the materials strength of nut thread component. Besides this, the tightening specification has to be determined carefully, and the documentation for production and field service must be performed accurately (see aspects of quality management, Fig. 55). For optimized fastening solutions, special types of nut thread components exist (Fig. 14). The use of a nut thread insert is suitable for high axial preload which has to be transmitted to a soft nut thread material (e.g. prevention of relaxation). The reason for the improvement compared to use without the insert is that the contact zone of the soft material is increased significantly by the outer diameter of the insert. But always remember that

Figure 14

Special types of nut thread components.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

an insert is an additional fastening element which adds to the cost, logistics, and assembly. For more information regarding inserts, see Ref. [14]. Staking nut, shear nut, and blind rivet nut are designed for thin walled nut thread components which provide no material for engaged thread flanks. The staking nut [64] has the advantage of self-centering, the shear nut [58] provides no deformation=forming of nut thread material, and the blind rivet nut [69] needs only one side access to the component (see also blind rivet, Fig. 70). An important field of application for special types of nut thread components is nonweldable materials, where weld nuts cannot be used (e.g. metallic foam structures or reinforced fiber material for lightweight design). Another possibility for thin walled components is using a clip nut (most established for fastening of plastic components) or direct thread tapping into rim holes of metal sheets with a screw having a small diameter at the forming point (pilot hole is only 85% of nominal screw diameter d; technique belongs to thread rolling screws). A clip nut has to be made of high-strength material (e.g. spring steel) because there is only one flank engaged between screw thread and nut thread. For this reason, the screw material requires high tensile strength to obtain high failure torques for the threaded fastening system.

C.

Clamped Part

A clamped part has to be provided with a through hole and on both sides of a support area to transmit the preload by using clamping force between the screw head and nut thread component. The geometric requirements are simple. In ISO 273 [28], the size of clearance holes in clamped parts are standardized. But the stress distribution in the clamped part under preload and under loading during operation is very difficult and varies over a wide range which is dependent on the geometry, material, and type of loading. Therefore, numeric calculations like FEM are important to analyze the local stressing of clamped parts. In the next step, the numeric results must be transferred to the analytical calculation of the particular threaded fastening system. The following linear model provides a fundamental approach to stressing and deforming of clamped parts (Fig. 15). If a clamped part has thin walls like a tube with Dp < da, the whole cross-section of the clamped part is stressed homogeneously (sketches (a) and (b) of Fig. 15). Between unloaded and loaded situation, the clamped part shows a shortening Dl, which can be obtained from Dl ¼ dpF. In this case, the axial elastic resilience Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 15

Axial elastic resilience dp of clamped part. (From Refs. 17, 70.)

can be calculated from dp ¼ lc=(Epp(Dp2 dh2)=4). Sketch (c) of Fig. 15 gives an example for a component with more detailed geometry. The local stress in the clamped part under axial load F is dependent on the particular location within the clamped part. To obtain the same simple linear calculation procedure as with (a) of Fig. 15, the real stress distribution is reduced to a virtual diameter Dsub with homogeneous stress distribution. Dsub represents the same shortening as with inhomogeneous stress distribution and leads to a substituting area Asub for calculation of axial elastic resilience dp ¼ lc=(EpAsub). An extreme situation is given for bulk materials (sketch (d) in Fig. 15, e.g. large component compared to the screw dimension). The resilience of the clamped part is small compared to (a) of Fig. 15 but substituting diameter Dsub is still limited. The complete set of formulae is given in Fig. 15. Normally, the resilience of clamped part dp is much smaller than that of the of screw ds. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Some general rules for designing surroundings of the screw for clamped parts are: 1. 2. 3. 4. 5. 6.

7.

D.

Use cost-optimized tolerances for through-hole diameter. Through hole must not have any burrs. Avoid geometrical mismatch between through hole and underhead fillet of screw. Make the clamping length as long as possible (small load factor F). Avoid overstressing the clamped part by excessive contact pressure compared to the yield point of clamped part Rp0.2p (see also Fig. 39). Do not use washers between screw head and clamped part, except special requirements to avoid surface damaging of clamped part or reduction of contact pressure. Use the right design of clamped part for accessibility of screw, nut, wrench or bit. Screw Assembly

Effective screw tightening involves significant static loading of the entire bolted joint prior over the operating period. Therefore, the loading and stressing of the screw under tightening conditions has to be considered in detail. An experienced and accepted approach is shown in the mathematic formula in Fig. 16. Eight steps summarize the calculation of screw tightening with a torque load for a given stressing of the screw shank by the equivalent one-dimensional stress seq. In this case, the axial stress sax is equal to seq divided by ks (step 1). The equivalent stress should be taken from 90% of yield point of screw material for torque-controlled tightening. For yield-point controlled tightening, it is the yield point itself and for angular controlled tightening, it is approximately the mean value of yield point and ultimate tensile strength of screw material. The factor ks depends on the screw and thread geometry and on the frictional coefficient mt of the thread d0 is the minimum of the diameter of the nominal stress area or the diameter of the screw body (important if using a wasted shank). For a metric screw with highest stressing in the screw thread, ks can be simplified as shown in step 1 of Fig. 16. From this axial stress sax and the relevant stress area A0, the axial preload Fp acting in the screw shank can be calculated (step 2). Then, step 3 gives the corresponding thread torque Tt which is generated by the lead angle j of the thread profile and the thread friction coefficient mt. The result of step 4 is the head frictional torque caused by friction coefficient mh. The reason for this head frictional torque is the sliding of Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 16 Loading and stressing of a screw under tightening conditions with torquings (From Refs. 17, 18.)

head during tightening under the preload Fp with an effective mean bearing diameter Deb. Deb has to be calculated separately and is dependent on the head type (see Fig. 38). Step 5 finally results in the necessary assembly torque Ttot. This torque value has to be applied to the screw drive to obtain the given stress seq and this torque leads to the calculated preload Fp. After step 5 for the calculated geometry, material, and friction of the bolted joint, three main characteristics are determined: stressing seq, preload Fp, and assembly torque Ttot. As additional information, step 6 allows the calculation of the maximum torsional stress tmax. For calculation of tmax, a polar section modulus

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Wp for full plastified cross-section is used (Wp ¼ pdo3=12). Step 7 offers the lead angle of the thread profile j. Step 8 formulates the theory of maximum distortion energy for producing a material failure (this is also called ‘‘vMises theory of failure’’). This is the background-formula for step 1 to combine equivalent stress and axial stress. General information about theories of failure can be found in Ref. [3]. In general, the friction coefficient m is defined as the ratio of normal force acting over produced tangential frictional force in a sliding motion of two bodies (Fig. 17). The frictional force is always directed against the direction of motion. For a screw, the normal force is the preload Fp. The tangential force can be formulated as mtFp in the thread contact zone and as mhFp in the head support area. These tangential forces cause frictional torques, because of the radii of thread and head contact zones due to screw axis (diameters Deb resp. d2, see also Fig. 16). Therefore, the frictional

Figure 17

Definition of friction coefficients mh and mt .

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

coefficients define the part of preload, which acts tangentially in the contact areas of a screw. Table 4 proposes classes of frictional coefficients valid for bolted joints, based on the VDI 2230 guideline [70] and experience [17]. If no exact value is available, one can select a value from this table which is valid for low surface roughness. But one must always remember that the friction coefficient depends on complex influences like materials surfaces, lubrication incl. homogeneity, hardness ratio of the two surfaces in contact, local stress peaks or stress distribution in contact zone, tolerances for contact geometry as well as tightening level and number of (re) tightenings. A selection table can only provide rough approximations. The supplier of screws can provide information related to friction behavior. In practice, all parameters for calculations of Fig. 16 have deviations. Main influences are based on minimum and maximum strength of screw material (e.g. heat treatment process) as well as minimum and maximum friction coefficients (e.g. roughness and lubricant). Geometry is usually very precise, so tolerances from diameters are not significant for screw tightening. This situation is shown schematically in Fig. 18 with two corresponding diagrams for highest material stressing in the screw shank. The upper case A refers to conditions with minimum friction mmin (both, mtmin and mhmin) and maximum screw strength Rmsmax. On the abscissa axis, the

Table 4 Values for Guidance of frictional Coefficients mt and mh in Classes A–E [17,70] mt, mh (—)

Characteristics=Typical examples

A

0.04–0.10

B

0.08–0.16

C

0.14–0.24

D

0.20–0.35

E

0.30–0.45

Hard polished surfaces, thick lubrication with wax or grease, high pressure lubricants, anti-friction coatings, e.g. polished magnesium and screw with PTFE-low friction coating and MoS2, no peak pressure at edges of support area Commonly used conditions with defined friction by optimized lubricants, such as oil, wax, grease for fasteners; suitable for ferritic steel metallic blank, phosphate, zinc and microlayer surfaces as well as nonferrous metals with relevant lubricant Usual conditions with only thin or inhomogeneous lubricant, austenitic steel screws with suitable lubricant; zinc, zinc alloy, and nonelectrolytical applied surfaces without lubricant Austenitic steel with oil, rough surfaces and Zn=Ni coating without lubricant Austenitic steel, aluminum, and nickel alloys blank without lubricant

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 18

Basics of screw tightening for applying an assembly torque.

rotation angle u is drawn; on the ordinate axis the preload Fp and the assembly torque Ttot are drawn. If the screw is tightened with Ttott, for case A a certain preload Fptmax is generated (due to mechanics of screw assembly in Fig. 16). With the same torque Ttot1 and same screw in case B only a preload of Fptmin is obtained. For this reason with a very precise torque a significant preload deviation can occur. The ratio Fptmax=Fptmin is app. in the range of 2 for torque controlled tightening—currently overelastic tightening methods with lower preload deviation are established for high-duty bolted joints. One method is yield point controlled tightening. By measuring and evaluating the gradient of torque-increasing over the increasing of rotation-angle, the screw will be tightened exactly to the beginning of

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

plastification of the screw shank (transition of the strong gradient of the tightening curve in Fig. 18 to the low gradient in the range of plastified screw). Another possibility to reach high tightening levels is using the angular controlled tightening method (also called ‘‘turn-of-the-nut-method’’): After applying a snug-torque Ts an additional, fixed defined tightening angle Du is added, so the screw is plastified to a certain grade in any case (comp. markings in Fig. 18). For yield point controlled tightening and angular controlled tightening the ratio of Fpymax=Fpymin resp. Fpanmax=Fpanmin is about 1.1–1.3. The deviation in practice is reduced drastically. For this reason, the greatest advantage of overelastic tightening methods is a significant increase of the minimum preload and a slight increase of the maximum preload. But one must always note the resulting torque value can vary extremely for overelastic tightening methods, because torque is no controlled parameter. Some hints for selection of parameters considering deviations in practice are: for calculating the highest preload (related to the highest screw stressing) always take minimum friction coefficients and maximum screw strength. This is relevant for maximum contact pressure under head). If the lowest preload has to be determined, maximum friction coefficients and lowest screw strength are relevant. To obtain maximum assembly torque for overelastic tightening method, take maximum friction coefficients and highest screw strength. This is relevant for maximum screw drive loading. If new tightening devices have to be designed for a production line with screw assembly, these devices should be able to apply a high torque value for angular controlled tightening. In practice, more than the double torque limit should be designed compared to torque controlled tightening. E.

Loading During Operation

1. Mechanical Loading If a threaded fastening system is tightened, then screw, clamped part, and nut thread component are loaded mechanically by the flow of preload without external force (Fig. 19). The preload leads to head contact pressure pch between screw head support and clamped part surface as well as to thread contact pressure pct at engaged thread flanks. Between clamped part and nut thread component, the component contact pressure pcc is generated (important for sealing). Following considerations due to force—elongation-behavior which are based on Ref. [70], details are discussed in Refs. [7,67,72].

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 19

Tightening and loading of threaded fastening system. (From Ref. 17.)

If a threaded fastening system is loaded by mechanical forces, these can act into the direction of screw axis (Fax) or transversal axis (Ft). Transversal forces produce shear loading of the bolted joint. If no transmission of transversal forces by contour interaction is possible, they have to be smaller than mccFp to avoid (micro)slipping between clamped part and nut thread component. Then, a transversal force does not load the screw. The mechanics of screw loading illustrated in Fig. 20 suggests the simplification of a threaded fastening system with a ‘‘spring-model’’.

Figure 20

Spring model of a threaded fastening system. (From Ref. 17.)

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

This idealized model reduces all elastic contributions within the system to rigid bodies and two springs with defined resilience: The screw shank is modeled as one tensile spring with ds, the clamped part is represented by a compressive spring with elastic resilience dp. Before tightening, all ‘‘springs’’ are unloaded (left side of Fig. 20). After tightening, usually the tensile spring of the screw is elongated much more than the compression spring of the clamped part (right of Fig. 20). If an external axial force Fax is induced within the clamping length lc, the inducing factor n determines which part of the clamped part is additionally loaded (towards the screw head) and which part is unloaded by Fax (towards the nut thread component). These parts of additional loading and unloading by an external axial force Fax influence the relevant elastic resiliences of ds and dp, if the fastening system is loaded. Therefore the resiliences vary between tightening and operating, if n < 1. Fig. 20 leads to the following force–elongation diagram shown in Fig 21. The diagram shows on the x-axis the elongation of screw (left of ‘‘0’’) and clamped part with clamping length lc (right of ‘‘0’’). On the y-axis, the corresponding preload Fp in the screw shank is drawn. For

Figure 21

Force–elongation-characteristics of screw and clamped part.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

the stable tightening level Fp0, a (positive) screw elongation of Fp0ds and at clamped part an (negative) elongation of Fp0dp is generated. The representative curves of screw and clamped part are linear up to the yield point of each material. Here, the stable tightening level Fp0 is completely within the linear range. If screw or clamped part show plastification, each nonlinear behavior has to be considered for force–elongation diagram (degressive dashed lines in Fig. 21). If a tensile external axial force Fax is applied to the fastening system, on the one hand, the screw is loaded additionally by nfFax and on the other hand the clamped part is unloaded by (1 nf)Fax, because the two springs are a parallel arrangement. The consequence is that Fax reduces the residual clamping load and increases the tension in the screw shank, but always only a part of Fax acts in any ‘‘spring’’. The additional operating force of screw (nfFax) besides the load factor f is dependent on the inducing factor n. For this reason, Fig. 22 gives some examples for the value of n, which are approximations. Some references propose a calculation of n [70], but an analytical solution is usually a lot of work, and a simple approximation often gives the same range in practice.

Figure 22

Examples for approximation of inducing factor n (From Ref. 70.)

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Numeric calculations like FEM are very suitable to determine nf ¼ Faxscrew shank=Fax external directly for a given geometry by selecting the nodes of the screw shank cross-section for Faxscrew shank and all nodes, which are loaded externally for Fax external. With the result of nf, the analytical calculation can be continued; therefore, FEM can be used to consider all influences from geometry and inhomogeneous stress distribution (e.g. for clamped part). The determination of the inducing factor n is an example, to show that very detailed design modifications lead to significant changing in screw loading. In general, it is valid that a small inducing factor n decreases the additional operating force of screw (interesting for increasing the fatigue loading capacity of the fastening system), and reduces also the residual clamping force under axial loading with an operating force (compare also Fig. 21). If no numeric calculation is done, the load factor f can be approximated with the analytical model of Fig. 23, see also Ref. [70,72]. This load factor can be calculated from f ¼ dp=(ds þ dp), if the axis of screw, clamped part centerline and external axial force Fax is the same. If these axes have different positions, additional bending of the screw and clamped part occurs, so that the elastic resiliences and in consequence the load factor f are changed.

Figure 23

Linear model for determination of load factor F. (From Ref. 17.)

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

For the model shown in Fig. 23, the force Fax, the distances of axes s and a, the through-hole diameter dh as well as the elastic resiliences ds and dp from Figs. 12 and 15 and the substituted area Asub must be known. From these, the substituted diameter Dsub can be calculated. This constant diameter corresponds to Asub for the same resilience dp. The model is assuming a linear stress distribution s(x) within Dsub. For the use of Fig. 23, it is necessary that the real stress distribution is similar to the linear distribution in the model. The size of the clamped part may not be much larger than Dsub, so the moment of inertia Ifull keeps valid. Then, the moment of inertia Ifull can be obtained and as a next step f can be calculated. Ifull does include the cross-section area of the screw, because the screw gives also a bending resistance during loading with Fax. After tightening, any threaded fastening system shows relaxation effects. This short time relaxation often is called ‘seating’: it leads to a preload reduction as demonstrated in Fig. 24. Important influence for this is the roughness and strain hardening of all surfaces in contact zones between screw, clamped part(s) and nut thread component as well as the direction of mechanical loading due to a normal vector on the contact area. Under contact pressure, the high surface spots are deformed axially which leads to a seating distance fz of the fastening system and in consequence to a reduction of preload down to a stable preload level Fp0. Significant short time relaxation always occurs if the fastening system is partially overloaded, such as when thread engagement is too small

Figure 24

Preload reduction by seating (short time relaxation).

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

(see Fig. 33) or if contact pressure under the head is too large (see Fig. 39), material mismatch (e.g. material strength of clamped part is too low) or geometric mismatch (e.g. nonperpendicular nut thread or screw head, oversized underhead fillets). The approximational equation for fz given in Fig. 24 can be used if there is no partial overloading. An eccentric loading of a threaded fastening system can lead to component separating. Figure 25 demonstrates this for an external force Fax acting with a distance a from the axis of symmetry 0–0 of clamped part. The configuration of Fig. 25 is the same as in Fig. 23.

Figure 25 Mechanics of component separating as a result of eccentric loading by Fax (From Ref. 17.)

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

There exists a point of tilting on one side of clamped part; on the opposite side, of the first component separating occurs. With the given values Fp0, Fax, s, a, dh, Dp and f after calculating the area Ap of clamped part in the contact zone between components and the moment of inertia Ip, the preload for first separating Fps can be estimated for a given axial force Fax. If the preload Fp0 is larger than Fps, then component separation does not occur for loading with Fax. On the other hand, if a stable preload after tightening Fp0 is given, Faxcrit determines the beginning of component separating, if Fax > Faxcrit. This leads to two cases indicated in Fig. 25. Case 1 is determined by elastic screw loading regarding the force–elongation diagram of a threaded fastening system. The additional operating load of screw Fsa is equal to nFFax. Case 2 refers to the situation of a beam lever system, built by Fp and Fax and the length values a, s, Dp. Component seperation must be avoided (case 2) because it leads to extensive additional loading of the screw Fsa and to early failure either by static overloading or by fatigue fracture. But in some cases, for optimized components with high resilience dp and with exactly defined tightening by loading, a partial component separation can be allowed without problems (e.g. bolted joints at lightweight piston rods). For more details regarding component separation under eccentric mechanical loading, see Refs. [67,70].

Figure 26

Preload behavior for overelastic tightening.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 26 explains the preload behavior for overelastic tightening of screw. The corresponding force–elongation diagram illustrates the screw plastification with a degressive curve for exceeded elastic limit under the tensile and torsional stressing during tightening. The first preload level after tightening Fp1 is reduced to the stable preload Fp0 by the reason of seating effects. Besides this, a general aspect is that after tightening a screw the torsional stress is reduced significantly—to app. 30–50% of the torsional stress under applied torque. This leads to an increased elastic limit of screw and leading to a higher preload limit during operating compared to tightening. A screw, which was tightened overelastic, can be loaded by a large operating force Fax. In practice, there is almost no difference between the tightening methods due to the loading capacity during operation (for dynamic loading, see also Fig. 52). Up to now, no time dependence of mechanical load is considered. Fig. 27 displays the effects for an alternating axial force Fax. For positive axial force Fax (tensile loading), the preload in the screw shank will be increased and the clamping force will be reduced, producing the same effect as for static loading. If a threaded fastening system is loaded axially, the preload in the screw shank is not the same as the clamping force between components. For a negative axial force Fax, just the opposite aspects are true: the preload in the screw shank will be reduced and the clamping force between

Figure 27

Preload behavior for mechanical dynamic axial loading.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

the components will be increased. In this case, by the negative axial loading Fax, a plastification of the clamped part can be generated which does not occur during tightening and leading to relaxation effects that are not acceptable during operation. But overall, also for dynamic axial loading, the screw has to bear only the part (nfFax) due to the complete axial force Fax. For a well-designed threaded fastening system, this part normally should be smaller than 10– 20% of Fax. 2. Thermal Loading Often, a threaded fastening system must be used at different temperatures, e.g. tightening at room temperature (t1) and operating at elevated temperature (t2). If screw material and material of clamped part have different thermal properties like Young’s modulus (Es, Ep) or thermal expansion coefficient (as, ap) or if the properties are temperature-dependent in the range of temperatures applied, the preload Fp varies, and this can be significant. The design engineer must check if the thermal loading of the paricular threaded fastening system does not lead to overloading by preload increasing or missing of clamping force by preload reduction. Figure 28 shows a linear approximation of the temperature-dependent preload change DFp. Again, the screw is tightened to its stable preload level Fp0 at temperature t1. The temperature change DT ¼ t2 t1 leads to thermal elongations at screw and clamped part Dl1, Dl2 and to changed elastic constants Es, Ep. Therefore, the force-elongation diagram is modified so that, a

Figure 28 Ref. 17.)

Approximation of preload changing by thermal loading. (From

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preload change DFp is generated. Influences from nut thread component are neglected because the main part of the preload is transmitted by the first thread flanks, therefore only a very short expansion length is relevant compared to the clamping length lc. This preload change DFp can be positive or negative. It is positive, if Young’s moduli are constant and the clamped part has a larger thermal expansion coefficient than the screw (typical for threaded fastening systems with light metals and steel screws). For example, it is negative for titanium screws and steel components. A positive preload change DFp can result in a screw failure (static fracture of screw by too large yielding=plastification). For example, in an extreme relaxation of preload by plastification of clamped part or screw, a negative DFp can result in a component separation and finally in a fatigue failure of screw. The preload change demonstrated in Fig. 28 is valid for the same temperature of screw and clamped part (steady state); during heating up or down a peak difference in temperature can occur, which generates even more preload change. The equation indicates what can be done to minimize DFp: reduce the thermal expansion mismatch (ap as), reduce temperature difference DT, maximize for given clamping length lc both the resiliences ds and dp (e.g. by low Young’s moduli). This means that in practice the positioning of screws away from extreme hot or cold places using the same materials for screw and clamped part (e.g. Al-screws for Al-components) and using long thin walled distance tubes (e.g. for pipe constructions). Figure 29 proposes a fundamental example for thermal loading with numeric values. A description of the situation is given with the sketch on the leftside of Fig. 29. A screw with nominal diameter d and support diameter da is tightened with a clamped part with through-hole diameter 1.1d, then heated to a temperature difference between tightening and operating of DT. This generates a preload change DFp which results in an axial stress change Dsp in the screw shank and also in a change of contact pressure under head Dpch. The diagram contains values for ferritic steel screws and aluminum screws combined with a clamped part made of aluminum or magnesium (Young’s moduli are set to constant for this calculation). The highest thermal stress increase takes place for steel screw with magnesium component. If applying DT ¼ 1008C, this combination has about 250 MPa stress increase which means 170 MPa contact pressure increase. If a standard ISO 4014 screw is used only 65 MPa contact pressure increase using a flange head with da ¼ 2d will be obtained. The result from this thermal stress increase can be the plastification of clamped part and leading to extensive relaxation; see also examples in Fig. 66.

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Figure 29 Linear approximation of thermal stress increase and thermal contact pressure increase. (From Ref. 16.)

The reason that the contact pressure pch is relevant for the highest stressing of clamped part is that a flange head should always be used if the clamped part is sensible for thermal preload change (e.g. low creeping strength at elevated temperatures like for magnesium alloys). 3. Reactive Loading Another important group of loadings to threaded fastening systems is characterized with the term ‘‘reactive loading’’. This term consists of chemical reaction (all kinds of corrosion) or aging (embrittlement of materials, e.g. by heat=radiation or radioactive effects with defect generation in grain structure of materials). Reactive loading effects always are time dependent, so the design has to take into account the life time of the threaded fastening system and the period of use. The primary aspect is corrosion, because almost all technical materials have a corrosive behavior which must be considered. Aging effects in many cases can be avoided by using suitable materials. Types of corrosion can be divided into three main groups: chemical corrosion (area corrosion), galvanic corrosion (electrochemical corrosion), and selective corrosion (e.g. stress corrosion cracking). Details are characterized in Table 5. Other types of corrosion exist like fretting, crevice corrosion, or microbiological corrosion [72], but in this chapter, only basic aspects and general hints are provided. For more details, see the literature, e.g. Ref. [1,3].

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Table 5 1.

2.

3.

General Types of Corrosion

Chemical corrosion. Chemical reaction of the material surface with electrolyte; the metal dissolves in a corrosive liquid until either it is consumed or the liquid is saturated (in practice, the ‘‘liquid’’ also can be humid air atmosphere, possibly with solvents of compounds, such as SO2 or salt at sea coasts). Galvanic corrosion. Chemical reaction of two electrically coupled metals using an electrolyte as transmitter for electrons (electrochemical cell). Then, the corrosion rate of the less corrosion-resistant metal is increased significantly. Therefore, this type of corrosion normally shows high corrosive speed, but the corrosion-rate depends on many parameters, such as potential-difference, temperature, purity, grain structure, convection=diffusion, influence of corrosion-products, ratio of cathodic and anodic areas, geometry. In practice galvanic corrosion is always a subject, if only one of two coupled metals is attacked and if the attack is reduced with increasing distance from the borderline between the two materials. Selective Corrosion. Chemical reaction located within a part of a material. This corrosion type is typical for alloys where different elements=phases with different sensibility for corrosive media exist e.g. dezincification of brass. Stress corrosion cracking is an intercrystalline reaction at grain boundaries, induced by the existing mechanical loading of special material=electrolyte=environmentcombinations. Examples for this are stainless steel and chloride-electrolyte (seawater) or some high-strength aluminum alloys and electrolyte with saltsolvent. Another type of selective corrosion is the so-called ‘‘hydrogenembrittlement’’ of high-strength steels (see also text).

When designing for corrosive behavior of different material surfaces, Table 6 with normal potential, measured against a standard H-electrode (flat electrode, 258C, 1 M-solution of ions in the electrolyte) is used for theoretical estimation of suitable metal combinations. But galvanic corrosion is determined by system behavior so that any table can only provide a tendency not quantitative information. Metals with low (negative) potential are called anodic (base metals, likely to corrode). The materials with high potential are called cathodic (noble metals, unlikely to corrode). The existing corrosion current in a galvanic cell is determined by the combination of the metals. For a minimum corrosion activity, the design engineer should combine materials with low difference in electrochemical potential. One can conclude that the ideal situation would be a screw made of the same material as the clamped part. Besides the corrosive stability, this also has almost no thermal loading under changing temperature (see Fig. 29). Exceptions are passivated metals (indicated with ). They build a thin oxide layer on their surface which has a dense structure and, therefore,

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Table 6 Guidance Values for Electrochemical Potential of Metals, Measured Against Standard H-electrode [1,3,72] Metal Chemical Pure (Active, if Passivating)

Potential (mV)

Li Mg Ala Tia Mn Zna Cra Fe Nia Sn Pb H Cua Ag Pta Au

3,050 2,370 1,660 1,630 1,630 760 740 440 240 140 130 0 340 800 1,200 1,500

a

metal is able to passivate.

insulates against further corrosion current. This thin oxide layer is stable (utilized for protective functions of Zn-coatings, Al-alloys, stainless steels). These metals can be either in ‘‘active’’ or in ‘‘passive’’ state. This is an important mechanism that demonstrates why also some base materials with quite negative electrochemical potential do not corrode. This is because they have their own integrated ‘‘protective coating’’ by passivation. In Refs. [3,50], a table of galvanic series for sea-water is given which includes not only pure metals, but also metal alloys (Table 7). This list refers to an environment other than the laboratory values from Table 6. Comparing both the tables, the main sequence is the same, but single combinations lead to a varying potential difference. Steels with high tensile strength over approximately 1200 MPa include the danger of hydrogen-induced embrittlement (see also Refs. [50,71]). This means a brittle behavior without deformation in the event of failure which is produced by a typical intercrystalline fracture along the grain boundaries with loosened grains (Fig. 30). As a preventive action, a production process with minimizing exposure to hydrogen atoms (electroplating) and tempering for H-effusion is established. But hydrogen diffusion into steel also can take place

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Table 7 Galvanic Series for Seawater from [3,50] in part, Measured Against Saturated Calomel Reference Electrode (SCE) Metal=Alloy Titanium Ni–Fe–Cr-alloys Ni–Cu-alloys Silver Platinum Stainless steels, active Stainless steels, passive Copper Brass Cast iron Low-carbon steel Low-alloy steel Aluminum alloys Zinc Magnesium Bronze Cu–Sn

Range of potential (mV) 40 to þ40 30 to þ30 150 to 30 150 to 100 þ180 to þ230 300 to 50 550 to 350 350 to 250 400 to 270 730 to 590 730 to 590 610 to 580 1000 to 750 1200 to 900 1650 to 1580 320 to 240

Measured against SCE, flow of seawater 2.4–4.0 msec; temperature 5–308C

during operation, e.g. H atoms from corrosion reactions. As a result, screws made of steel should be coated nonelectrolytically for class 12.9 or higher. The data is shown in Fig. 31 suggests fundamental corrosion mechanisms of threaded fastening systems. The characteristics are printed to each part in the figure itself. If the screw material is a base metal and the component material is noble chemical, the screw material corrodes (e.g. steel screw in copper component). If the difference of electrochemical potential is opposite the component corrodes (e.g. steel screw in magnesium component). This is shown in part (a) of Fig. 31 (left and right). Any corrosion product like oxide generates a limited appearance and can increase the speed of corrosion. For a further state of corrosion, destroying the support area leads to extreme relaxation because the residual original material cannot bear the initial preload from tightening. In general, the first step of corrosion is relevant for appearance, the second step of corrosion is relevant for preload function. Part (b) of Fig. 31 demonstrates the same situation for a coated component and coated screw with internal drive. An internal screw drive can collect electrolyte, and therefore, is set to a severe corrosive environment. This is the reason why often screws with internal drive configura-

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 30 1000 .

SEM image of fracture from screw M12-12.9; loosened grains are typical for hydrogen embrittlement, magnification

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 31

Fundamental aspects of corrosion for threaded fastening systems.

tion begin to corrode within their screw drive. Coatings separate the function of the component into (1) surface protection, and (2) mechanical performance of the bulk material under the coating. But the most important point is that coatings always have defects and can be damaged—and

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

then the protection is partly reduced. For coated screws with high corrosion resistance, a hexagon drive configuration should be avoided by the reason of the high bit contact pressure and possibly high edge-deformation of screw (see also Fig. 36). Coating systems make the chemical corrosion complex (four materials in Fig. 31b), which can react: two bulk materials, two coating materials). The noble material does not corrode (compare damaged component coating and the resulting local corrosion). Coating systems for screw protection must provide a high quality adhesion, because they have to work under extreme mechanical surface pressure (explanations of Fig. 31b). Besides electrolytical coatings, there are also very effective nonelectrolytical coating-systems for enhanced corrosion protection of steel screws known. For established suppliers of nonelectrolytical coatings, see Refs. [54,12,13,53,54]); for standardization see Ref. [23]. Part (c) of Fig. 31 focuses on electrical insulation as a mechanical way to prevent from corrosion. Remarks are given in the figure. Part (d) summarizes general aspects for corrosion of threaded fastening systems in practice.

III.

DESIGN STRATEGY FOR THREADED FASTENINGS

For realizing an optimized threaded fastening system, an effective development procedure is necessary. Figure 32 demonstrates this with a flow diagram by distinguishing three columns: calculation=design, verification, and realization. The main topics of calculation=design are: tightening= operating (determination of loadings the bolted joint has to bear), screw, clamped part, nut thread component (specifications of all parts of the bolted joint), and design analysis (engineering results based on theory and experience). If the design analysis meets the requirements and is proposing a reliable function of the bolted joint, the verification column is started. Prototypes are the very first practical realization of the theoretical design. With these parts, the laboratory tests and the field tests can be done, if the prototypes are representative for series production. The realization column contains assembly process (parameters often are determined by assembly process capability as a result of laboratory tests), purchase, series production and field service. Today, basic aspects of quality management are teamwork, documentation of results and history, failure modes and effects analysis as well as feasibility reviews. These concepts can be transferred to several topics of Fig. 32 (only drawn for design analysis and prototypes, because here they are necessary in any case, see also Ref. [19]).

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 32

A.

Development process of a threaded fastening system.

Determination of Screw Material and Surface

In general, materials for screws must provide both high strength to obtain sufficient preload and compatibility to the environment of operating. This paragraph provides a compressed overview over the main aspects important for material selection of screws. Details of certain materials can be found in Refs. [1,3]. For the selection of suitable screw surface, specialized coating companies can offer established and enhanced solutions, e.g. Refs. [13,53,54]. As an introduction to screw material selection, Table 8 gives a 10-question list for checking the qualifications.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Table 8

Check List for Screw Material Selection

No.

Question for Theoretical Checking of the Selected Screw Material

1

Is the screw material suitable for sufficient preload (material strength high enough)? Is the screw material suitable for required dynamic loading (notch-sensitivity, material fatigue behavior)? Is the screw material suitable for operating temperature? Is the thermal expansion coefficient of screw material suitable for permitted change of preload under temperature? Is the screw material resp. screw surface suitable for corrosion requirements (climate, fluids=electrolytes, material contacts)? Is the screw material suitable for tightening (adhesion, friction in mechanical contacts)? Is the screw material suitable for screw manufacturing (availability of raw material, forming, cutting, heat treatment, large batch production requirements)? Has the screw material good-natured behavior if overloading (ductility resp. significant plastification before fracture, no embrittlement)? Has the screw material sufficient long-term properties under tensile stress (stable grain-structure, no creeping, no embrittlemement)? Is the screw material economic?

2 3 4 5 6 7

8 9 10

1. Operating Environment and Material-Related Standards The operating environment determines the materials that are suitable. Table 9 gives fundamental selection criteria and a few examples for alloys (for established materials, see Tables. 10–12). Only when standard materials cannot be used should special solutions be considered. In this case, the supplier of fastening elements can give support, e.g. Refs. [2,62]. The European standard EN 10269 provides steels and nickel alloys for fasteners at elevated or low temperatures with temperature-related properties [11]. As a rough estimation, the material strength at limiting temperature of the material is approximately half of the strength at room temperature. The European designation system for steels is defined in standard EN 10027. The Vickers hardness test procedure is defined in standard ISO 6507 [39]. Electrolytical surface coatings for fastening elements are defined in ISO 4042 [31] (types of coatings, coating thickness, tolerances, hydrogen-embrittlement, designations of coating systems), nonelectrolytical coatings for fastening elements are defined in ISO 10683 [23]. Detection of hydrogen embrittlement is dealt in ISO 15330 [25]. Surface discontinuities are proposed and evaluated in ISO 6157 [37].

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Table 9 No.

Fundamental Selection of Screw Material and Screw Surface Characterization of environment

1

Dry and temperature < app. 3008C

2

Humid þ (salt) solution þ temperature < 3008C

3

High temperature up to app. 6008C

4

High temperature over app. 6008C

5

Low temperatures under app. 508C

6

Long time appearance requirements

7

Chemical reactive components like magnesium, lithium as clamped part or nut thread component Fastening of light metal components, e.g. made from aluminum or magnesium Small volume and extreme lightweight designs

8

9

Examples of experienced materials for high-strength screws and bolts Low alloyed- or carbon steel (C35, C45, 35 B2, 20Mn5, 42CrMo4), painted or other corrosion protection coating suitable for this temperature range Low alloyed- or carbon steel (C35, C45, 35B2, 20Mn5, 42CrMo4), enhanced corrosion protection coating suitable for this temperature range High alloy steel with Cr-, Ni- or Mocontent (42CrMo4, 42CrMo5-6, X5CrNi18-10, X22 Cr MoV12-1), ferritic or austenitic Heat-resistant steels with high Cr-content and alloyed elements Ti, Nb (10CrNiMoMnNbVB15-10-1, X6 NiCrTiMoVB25-15-2); Ni-base alloys (NiCrTiAl20) Austenitic steels with sufficient Cr- and Nicontent (X5CrNi18-10, X2CrNiMoN1713-3) Screws made of stainless steel (X5CrNi1810), chemical inert materials like titanium (TiAlV6-4), steel with multilayer coatings Screws made of component material, screws made of passivating=chemical inert metals, steel with multilayer coatings Screws made of aluminum (AA 6013, AA 6056, AA 7075; matching of corrosive behavior and high thermal expansion coefficient, [16]) Highest screw strength over 1400 MPa up to app. 2000 MPa (use in aviation- and aerospace-industry, special production requirements necessary and high contact pressures must be acceptable; 38NiCrMoV7-3, X2NiCoMo18-8-5) or lightweight materials for screws (TiAlV6-4, tensile strength app. 1100 MPa)

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Table 10 Important Properties of Screws Made of Carbon Steel or Alloy Steel, Defined in ISO 898 [46], for Design Purpose and Details, Refer to Standard Example Minimum Proof for suitable Minimum Minimum Minimum Maximum resp. yield material tensile elongation vickers stress vickers (not Property strength after hardness ReL, Rp0.2 hardness defined class Rm (MPa) (MPa) fracturea (%) HV 10 HV 10 in ISO 898) 3.6 4.6 4.8 5.6 5.8 6.8 8.8b

330 400 420 500 520 600 800

190 240 340 300 420 480 640

25 22 14 20 10 8 12

95 120 130 155 160 190 250

250 250 250 250 250 250 320

8.8c

830

660

12

255

335

9.8

900

720

10

290

360

10.9

1,040

940

9

320

380

12.9

1,220

1,100

8

385

435

C35, 35B2 C45, 35B2 C45, 35B2 C45, 35B2 C45, 35B2 C45, 35B2 35B2, 19MnB4 35B2, 19MnB4 35B2, 19MnB4 37Cr4, 34CrMo4 37Cr4, 42CrMo4

Measured at unnotched, cylindric sample from screw with length of cylinder ¼ 5 diameter of cylinder. b d 16 mm. c d < 16 mm. a

But one must always remember that any screw is only one part of a fastening system (Fig. 1) and the behavior of the entire system is relevant for function and reliability. For the time-dependent behavior of a threaded fastening system within the operating period, the superposition of mechanical, thermal, and reactive loading is important (for example strength of screw at high temperature). Besides corrosion for long operating periods, the material creep can be critical (permanent increase of screw elongation under preload, which leads to drastically reduced clamping force in threaded fastening systems). Creep should be considered if the operating temperature of a material is higher than 1=3 of its melting temperature. Face-centered cubic crystal systems have lower creeping resistance than other crystals. Creep can be reduced=eliminated by special creep-resistant alloys. Second, for long operating periods, the case of misuse can=will be probable, especially if the fastening system has to be disassembled or

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Table 11 Some Properties of Screws made of Stainless Steels, Defined in ISO 3506 [29], for Design Purpose and Details, Refer to Standard Steel group and grade

Minimum tensile strength Rm (MPa)

Minimum proof stress Rp0.2 (MPa)

Minimum elongation after fracturea (%)

Minimum vickers hardness HV 10

Maximum vickers hardness HV 10

A2-70

700

450

24

—

—

A2-80

800

600

16

—

—

A4-70

700

450

24

—

—

A4-80

800

600

16

—

—

700 1,100 800 600

410 820 640 410

8 8 8 8

220 350 240 180

330 440 340 285

C1-70 C1-110 C3-80 F1-60 a

Example for suitable Material (not defined in ISO 3506) X5CrNi-18-9, X5CrNi1816 X5CrNi-18-9, X5CrNi1816 X5CrNiMo17-12-2, X2CrNiMo17-13-3 X5CrNiMo17-12-2, X2CrNiMo17-13-3 X12Cr13 X12Cr13 X19CrNi16-2 X3Cr17, X6CrNb12

in ISO 3506 originally measured at manufactured screw as elongation over total length in mm.

retightened by nonprofessionals (e.g. wheel bolts of cars, Fig. 73). Also, misuse has to be tested during verification of the design (Fig. 32). 2. Established Materials for Screws If searching for established screw materials, three main groups can be found: low alloyed- or carbon-steels (mostly used, ISO 898 [46]), stainless steels (ISO 3506 [29]) and nonferrous metals for screws (ISO 8839 [44]). In ISO 898 and ISO 3506, only grades for groups of materials are specified. Besides this, in ISO 7085 [41], mechanical properties of case hardened and heat treated screws and in ISO 2702 [27] mechanical properties of heat treated tapping screws are defined. The well-known property classes of screws (3.6, 4.6, 4.8, 5.6, 5.8, 6.8, 8.8, 9.8, 10.9, 12.9) are defined in ISO 898 are only valid for screws made of carbon steel or alloy steel (definition of property classes: first number: minimum tensile strength Rmmin of material=100 in N=mm2; second number: 10 ratio of proof stress Rp0.2 over tensile strength Rmmin). ISO 898 does not apply to high temperatures above 3008C or low temperatures under 508C. Table 10 summarizes the important properties defined in ISO 898. Another material group is also well established: screws made of stainless steels. Related properties for fasteners are defined in ISO 3506 [29].

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Table 12 Nonferrous Metals for Screws from ISO 8839 [44], for Design Purpose and Details refer to Standard

Symbol

Material

CU1

CU-ETP or CU-FRHC (ISO 1337) CuZn37 (ISO 426)

CU2 CU3

CuZnPb39-3 (ISO 426)

CU4

CuSn6 (ISO 427)

CU5

AL1

CuNiSi1 (ISO 1187) CuZnMnPb-40-1 CuAlNiFe10-5-4 (ISO 428) AlMg3 (ISO 209)

AL2

AlMg5 (ISO 209)

AL3

AlMgSiMn1 (ISO 209) AlCuMgSi4 (ISO 209) AlZnMgCu0.5 AlZnMgCu5.5 (ISO 209)

CU6 CU7

AL4 AL5 AL6 a

Minimum tensile strength Rm (MPa)

Minimum proof stress Rp0.2 (MPa)

Minimum elongation after fracturea (%)

M39

240

160

14

M6 M7–M39

M6

440 370 440

340 250 340

11 19 11

M7–M39

M12 M13–M39

M39

370 470 400 590

250 340 200 540

19 22 33 12

M7–M39 M13–M39

440 640

180 270

18 15

< M10 M11–M20 < M14 M15–M36 < M6 M7–M39 < M10 M11–M39 < M39 < M39

270 250 310 280 320 310 420 380 460 510

230 180 205 200 250 260 290 260 380 440

3 4 6 6 7 10 6 10 7 7

Diameter range

test specification according ISO 898-1.

There are three groups of stainless steels: austenitic (A), martensitic (C), and ferritic (F). Each group can have different steel grades, which are distinguished by different digits following the characteristic letter. Then, a third value is added to indicate 1=10 of the tensile strength of the fastener. For example, after ISO 3506, the designation for an austenitic screw of steel group 2 with a tensile strength of 700 MPa is A2-70.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Table 11 contains some properties of screws made of stainless steels regarding ISO 3506. Austenitic steels cannot be hardened and are usually nonmagnetic. Alloys of steel grade A2 are most frequently used (kitchen equipment, apparatus industry), but they are not stable in environments with chlorides (e.g. swimming pools or chemical devices). Alloys of grade A4 are the so-called ‘‘acid proof steels’’ with molybdenum as alloy element to increase corrosion resistance, to a certain extent, also against chloride ions (used for chemical industry, food industry, ship-building industry). Steels of martensitic grades C1 and C3 can have higher strength than austenitic steels and can have relatively higher proof stress Rp0.2, but they have a limited corrosion resistance, so they are widely used in machines with high loading and controlled environment, such as pumps and turbines. Ferritic steels of grade F have a permanent ferritic grain structure at room temperature, so they cannot be hardened, but they are magnetic. They are an alternative for steels of grade A2. For all situations, where ISO 898 and ISO 3506 cannot offer suitable materials for screws or bolts, the materials of ISO 8839 should be checked. Table 12 proposes the nonferrous metals of this standard which are used for electrical contacts (screws made of copper, brass), special corrosive conditions, lightweight design or constructional elements (screws made of aluminum). AL5 and AL6 of Table 12 can be sensitive for stress corrosion cracking, depending on their grain structure. Currently, additional aluminum alloys for screws are available, which provide high strength without stress corrosion cracking (e.g. alloys 6013 and 6056, in work standards often called AL9, see also Refs. [15,16]).

B.

Determination of Screw Thread Size

The screw thread size normally is the main parameter used to determine the initial preload of a threaded fastening system. The other parameters are in many cases preselected, such as screw material (determined by environment), assembly method (determined by assembly line, field maintenance or philosophy), and frictional situation (determined by surfaces in contact). But the design engineer always has to distinguish both initial preload (generated during tightening, see also Fig. 18) and residual preload (stable preload level during operating, see also Fig. 24). The initial preload can be calculated in a detailed manner, the residual preload strongly depends on the material’s behavior and the local contact conditions. Therefore, this value often is estimated from experience or if necessary measured (preload measurement by ultrasonics or strain gauges).

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Table 13 Estimated Preload Level for Different Metric Screw Types Preload Level (kN), Metric Screw Thread Tensile strength and yield strength ratio of screw Thread size M1 M2 M3 M4 M5 M6 M8 M10 M12 M12 M14 M14 M16 M16 M18 M18 M20 M22 M24

1.5 1.5 1.5 1.5

Nominal As (mm2) 0.458 2.069 5.000 8.800 14.20 20.10 36.60 58.00 84.30 88.10 115.4 124.6 156.7 167.3 192.5 216.2 244.8 303.4 352.5

Rm (MPa) kR ()

300 0.6

400 0.6

400 0.8

500 0.6

500 0.8

600 0.8

800 0.8

900 0.8

1,000 0.9

1,100 0.9

1,200 0.9

1,400 0.9

0.06 0.28 0.68 1.20 1.94 2.75 5.01 7.93 11.5 12.1 15.8 17.0 21.4 22.9 26.3 29.6 33.5 41.5 48.2

0.08 0.38 0.91 1.61 2.59 3.67 6.68 10.6 15.4 16.1 21.0 22.7 28.6 30.5 35.1 39.4 44.7 55.3 64.3

0.11 0.50 1.22 2.14 3.45 4.89 8.90 14.1 20.5 21.4 28.1 30.3 38.1 40.7 46.8 52.6 59.5 73.8 85.7

0.10 0.47 1.14 2.01 3.24 4.58 8.34 13.2 19.2 20.1 26.3 28.4 35.7 38.1 43.9 49.3 55.8 69.2 80.4

0.14 0.63 1.52 2.68 4.32 6.11 11.1 17.6 25.6 26.8 35.1 37.9 47.6 50.9 58.5 65.7 74.4 92.2 107.2

0.17 0.75 1.82 3.21 5.18 7.33 13.4 21.2 30.8 32.1 42.1 45.5 57.2 61.0 70.2 78.9 89.3 110.7 128.6

0.22 1.01 2.43 4.28 6.91 9.78 17.8 28.2 41.0 42.9 56.1 60.6 76.2 81.4 93.6 105.2 119.1 147.6 171.5

0.25 1.13 2.74 4.82 7.77 11.00 20.0 31.7 46.1 48.2 63.1 68.2 85.7 91.5 105.3 118.3 134.0 166.0 192.9

0.31 1.42 3.42 6.02 9.7 13.7 25.0 39.7 57.7 60.3 78.9 85.2 107.2 114.4 131.7 147.9 167.4 207.5 241.1

0.34 1.56 3.76 6.62 10.68 15.12 27.5 43.6 63.4 66.3 86.8 93.7 117.9 125.9 144.8 162.7 184.2 228.3 265.2

0.38 1.70 4.10 7.22 11.7 16.5 30.0 47.6 69.2 72.3 94.7 102.3 128.6 137.3 158.0 177.5 200.9 249.0 289.3

0.44 1.98 4.79 8.43 13.6 19.2 35.0 55.5 80.7 84.4 110.5 119.3 150.1 160.2 184.3 207.0 234.4 290.5 337.6

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M24 2 M27 M30 M36 ( 4) M36 3 M36 2 M36 1.5 M39 M48 M56 M64 M80 M90 M100

384.4 459.4 560.6 816.7 864.9 914.5 940.3 975.8 1,475 2,032 2,678 4,490 5,594 6,998

52.6 62.8 76.7 111.7 118.3 125.1 128.6 133.5 201.7 278.0 366.4 614.3 765.3 957

70.1 83.8 102.3 149.0 157.8 166.8 171.5 178.0 269.0 370.6 488.5 819.1 1,020 1,277

93.5 111.7 136.3 198.6 210.3 222.4 228.7 237.3 358.6 494.2 651.4 1,092 1,361 1,702

87.6 104.7 127.8 186.2 197.2 208.5 214.4 222.5 336.2 463.3 610.7 1,024 1,275 1,596

116.9 139.7 170.4 248.3 262.9 278.0 285.9 296.6 448.3 617.7 814.2 1,365 1,701 2,128

140.2 167.6 204.5 297.9 315.5 333.6 343.0 356.0 538.0 741.2 977 1,638 2,041 2,553

187.0 223.5 272.7 397.2 420.7 444.8 457.4 474.6 717.3 988 1,303 2,184 2,721 3,404

210.3 251.4 306.8 446.9 473.3 500.4 514.5 534.0 806.9 1,112 1,466 2,457 3,061 3,830

262.9 314.2 383.5 558.6 591.6 625.5 643.2 667.4 1,009 1,390 1,832 3,071 3,826 4,787

289.2 345.7 421.8 614.5 650.8 688.1 707.5 734.2 1,110 1,529 2,015 3,379 4,209 5,266

315.5 377.1 460.1 670.3 709.9 750.6 771.8 800.9 1,210 1,668 2,198 3,686 4,592 5,744

368.1 439.9 536.8 782.1 828.2 875.7 900.4 934.4 1,412 1,946 2,565 4,300 5,357 6,702

Boundary conditions: (1) Yield point controlled tightening; (2) Friction tot ¼ 0.16; (3) As is smallest area of cross-section; (4) proper screw section design, so failure is located at threaded cross-section, (no thread stripping, no head stripping). Notes (1) For torque controlled tightening in practice, the preload can be reduced (app. 0.7); (2) for utilization of eq ¼ 90%; of Rp0.2, multiply relevant preload by 0.9; (3) yield strength ratio kR ¼ Rp0.2=Rm; (4) for angular controlled tightening, multiply relevant preload by [1 þ 0.3(1 kR)=kR ].

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Table 14

Estimated Preload Level for Different Unified Screw Types

Preload level (kN), Unified Screw Thread Tensile strength and yield strength ratio of screw Thread size

Nominal As (mm2)

1=4–20 5=16–18 3=8–16 7=16–14 1=2–13 9=16–12 5=8–11 3=4–10 7=8-9 1–8 1 1=4–7 1 1=2–6 1 3=4–5 2–4 1=2 3–4 4–4 5–4 1=4–28 5=16–24

20.5 33.8 50.0 68.6 91.5 117.0 146.0 215.0 298.0 391.0 625.2 906.4 1,226 1,613 3,852 7,148 11,484 23.5 37.4

Rm (MPa) kR ()

300 0.6

400 0.6

400 0.8

500 0.6

500 0.8

600 0.8

800 0.8

900 0.8

1,000 0.9

1,100 0.9

1,200 0.9

1,400 0.9

2.80 4.62 6.84 9.38 12.5 16.0 20.0 29.4 40.8 53.5 85.5 124.0 167.7 220.6 526.9 978 1,571 3.21 5.12

3.74 6.17 9.12 12.5 16.7 21.3 26.6 39.2 54.4 71.3 114.0 165.3 223.6 294.2 702.5 1,304 2,095 4.29 6.82

4.99 8.22 12.2 16.7 22.3 28.5 35.5 52.3 72.5 95.1 152.0 220.4 298.1 392.3 936.7 1,738 2,793 5.72 9.10

4.67 7.71 11.4 15.6 20.9 26.7 33.3 49.0 67.9 89.1 142.5 206.7 279.5 367.7 878.2 1,630 2,618 5.36 8.53

6.23 10.3 15.2 20.9 27.8 35.6 44.4 65.4 90.6 118.9 190.0 275.6 372.6 490.3 1,171 2,173 3,491 7.14 11.4

7.48 12.3 18.2 25.0 33.4 42.7 53.3 78.4 108.7 142.6 228.1 330.7 447.2 588.4 1,405 2,608 4,189 8.57 13.6

10.0 16.4 24.3 33.4 44.5 56.9 71.0 104.6 144.9 190.2 304.1 440.9 596.2 784.5 1,873 3,477 5,586 11.4 18.2

11.22 18.5 27.4 37.5 50.1 64.0 79.9 117.6 163.1 214.0 342.1 496.0 670.8 882.6 2,108 3,912 6,284 12.86 20.5

14.02 23.1 34.2 46.9 62.6 80.0 99.9 147.1 203.8 267.4 427.6 620.0 838.4 1,103 2,634 4,889 7,855 16.07 25.6

15.42 25.4 37.6 51.6 68.8 88.0 109.9 161.8 224.2 294.2 470.4 682.0 922.3 1,214 2,898 5,378 8,640 17.68 28.1

16.8 27.7 41.0 56.3 75.1 96.0 119.8 176.5 244.6 320.9 513.1 744.0 1,006 1,324 3,161 5,867 9,426 19.3 30.7

19.6 32.4 47.9 65.7 87.6 112.0 139.8 205.9 285.4 374.4 598.7 868.0 1,174 1,545 3,688 6,845 10,997 22.5 35.8

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3=8–24 7=16–20 1=2–20 9=16–18 5=8–18 3=4–16 7=8-14 1–12 1 1=4-12 1 1=2–12 1 3=4–12 2–8 3–8 4–6 5–6

56.6 76.6 103.0 131.0 165.0 241.0 328.0 428.0 692.3 1,020 1,413 1,787 4,200 7,465 11,871

7.74 10.5 14.1 17.9 22.6 33.0 44.9 58.6 94.7 139.5 193.3 244 575 1,021 1,624

10.3 14.0 18.8 23.9 30.1 44.0 59.8 78.1 126.3 186.0 257.7 326 766 1,362 2,165

13.8 18.6 25.0 31.9 40.1 58.6 79.8 104.1 168.4 248.1 343.6 435 1,021 1,815 2,887

12.9 17.5 23.5 29.9 37.6 54.9 74.8 97.6 157.8 232.6 322.1 407 958 1,702 2,707

17.2 23.3 31.3 39.8 50.2 73.3 99.7 130.1 210.4 310.1 429.5 543 1,277 2,269 3,609

20.6 27.9 37.6 47.8 60.2 87.9 119.7 156.1 252.5 372.1 515.4 652 1,532 2,723 4,331

27.5 37.3 50.1 63.7 80.3 117.2 159.5 208.2 336.7 496.1 687.2 869 2,043 3,631 5,774

31.0 41.9 56.4 71.7 90.3 131.9 179.5 234.2 378.8 558.1 773.1 978 2,298 4,085 6,496

38.7 52.4 70.5 89.6 112.9 164.8 224.4 292.8 473.5 697.7 966.4 1,222 2,873 5,106 8,120

42.6 57.6 77.5 98.6 124.1 181.3 246.8 322.0 520.9 767.4 1,063 1,345 3,160 5,616 8,932

46.5 62.9 84.5 107.5 135.4 197.8 269.2 351.3 568.2 837.2 1,160 1,467 3,447 6,127 9,744

54.2 73.4 98.6 125.4 158.0 230.8 314.1 409.9 662.9 976.8 1,353 1,711 4,022 7,148 11,368

Boundary conditions: (1) Yield point controlled tightening; (2) Friction tot ¼ 0.16; (3) Proper screw section design, so failure is located at threaded cross-section (As is smallest area of cross-section; no thread stripping, no head stripping). Notes (1) For torque controlled tightening in practice, the preload can be reduced (app. 0.7); (2) for utilization of eq ¼ 90% of Rp0.2, multiply relevant preload by 0.9; (3) yield strength ratio kR ¼ Rp0.2=Rm; (4) for angular controlled tightening, multiply relevant preload by [1 þ 0.3(1 kR)=kR].

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

The difference between initial and residual preload is caused by contact plastification (seating) or relaxation (material creeping, especially at high temperatures). 1. Minimum Initial Preload The minimum preload required is responsible for the selection of screw size. For a given screw strength and assembly method, the minimum level is generated for maximum friction coefficient. Therefore, in Table 13 for metric screw thread geometry, a friction coefficient mtot ¼ 0.16 is assumed (relevant values of mtot see Table 4). The listed preload levels are reached for yield point controlled tightening. Using the legend, preloads for other tightening methods can be calculated. To achieve a preload level for a friction coefficient mtot ¼ 0.08, multiply relevant value of table by 1.15. From the preload level of Table 13, with formulae of Fig. 16, the corresponding torque values can be obtained. But for torque controlled tightening one must remember that the smallest torque corresponds to the smallest friction coefficient and this has to be specified for assembly specification. If a screw with high friction is tightened with the specified torque of low friction, the generated preload is reduced (see aspect 1 of legend from Table 13). Table 13 refers to screws for existing nut thread. If thread rolling screws (Fig. 6) are used, the preload level is reduced by some percentage because of the higher thread friction (app. 5%). For generating nearly the same preload with thread rolling screws as with same screws for existing nut thread, the tightening torque has to be increased significantly (see also Ref. [63] or Fig. 67). Table 14 gives the same information as Table 13 for unified screw thread geometry. For designations of screw threads, see Fig. 5. How does one find the required minimum initial preload Fp0? As a rule, the initial preload should be at least five times the maximum operating load of the screw (nfFax) added by 10% for relaxation loss. This rule applies to stable threaded fastening systems without creeping effects. The initial preload must prevent any component from separating (guaranteeing sealing function, see also Fig. 49; avoiding of increasing load factor f, see also Fig. 25), microsliding (fretting, self-loosening) or significant relaxation (continued preload loss with possible failure in consequence).

2. Boundary Conditions in Practice For selection of screw size, handling during operation and field maintenance is an important consideration. As an example, a screw of dimension M6 or higher can normally be hand tightened by workers without danger of

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

overtightening. A screw up to M12 can be tightened=retightened with normal wrenches and moderate manpower. Screw dimensions between M6 and M12 can be used by nearly every person without special qualification=training and=or special equipment. The design engineer can always decide if a few large screws or more small screws are used to achieve the summarized preload. An increased number of small screws has the advantage of better stress homogeneity in the components, better sealing of flanges, reduced local separating of components with low stiffness under operating load. But a multi-screw-fastening-system needs a detailed calculation of the loading of each particular screw and a defined tightening sequence during assembly. Screws, which need exact preload, should be tightened by yield point control or angular control (see also Fig. 51). Finally, the requirements from deproliferation have to be met. The number of different parts which have to be purchased, stored, and managed, has to be minimized. This means, consolidating similar screws due to screw length, screw diameter, screw head, screw material, and screw surface. C.

Determination of Screw Geometry

If the screw thread size is known, several additional geometry details have to be determined. These are screw head, length of thread engagement, screw body, thread length, and other design options. This chapter shows the fundamental aspects for design decisions.

1. Thread Engagement If the design principle from Fig. 2 is valid, the thread engagement requires a minimum value temin, and thread stripping of screw or nut cannot happen. Figure 33 points out the result from calculations regarding the VDI 2230 guideline [70] for metric thread series (thread standard, see Fig. 4). The diagram illustrates the relative minimum thread engagement temin=d over tensile strength of nut thread component Rmn for different property classes of screw. Details are printed in the diagram. Generally speaking, the required length of thread engagement increases with increasing screw strength Rms and decreasing nut strength Rmn. This diagram has two dimensions of interpretation: for thread engagements higher than the relevant temin, no thread stripping will occur and in any case the screw shank will fail (direction of ordinate-axis). If the relevant point for temin on the selected hyperbolic curve is located in the tangential section, the screw thread will strip for engagements smaller than temin. If the relevant point for temin is Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

in the gradient section, for engagements lower than temin, the nut thread will strip (direction of abscissa). A special characteristic is important for low-strength nut thread components (e.g. made of magnesium): for example, a nut thread with a tensile strength Rmn of only 250 MPa requires theoretically as a minimum thread engagement of 2 d (d: nominal diameter of screw thread) with a screw of class 8.8; whereas only 1 d are necessary for a screw made also of moderate screw strength (Rms ¼ 400 MPa, which could be a screw made of aluminum). As a rule, the screw strength Rms should not exceed 1.0 – 2.5 the strength of nut thread component Rmn from the point of thread engagement. The diagram in Fig. 33 does not consider incomplete thread flanks at thread end of screw and does not include any safety factors, so the values for temin in practice should be multiplied with 1.3–1.5. For experimental verification of Fig. 33, see Fig. 58. 2. Screw Body and Thread Length Figure 34 describes the fundamental possibilities to design a screw shank (a)–(e). Normally, a screw shank has two different cross-sections: the

Figure 33 Calculation of thread engagement vs. strength of nut thread material. (From Ref. 16.)

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Figure 34 Clamping length lc and plastification length lp of threaded fastening system from Ref. 18.)

threaded cross-section with area As and the unthreaded cross-section with area Ab resp. A2 (area of cross-section with flank diameter d2). The length of a threaded shank with rolled thread flanks as shown in (a) is limited by the length of the rolling die for screw production. A full shank (b) has a constant outer diameter in the range of the nominal screw diameter d. Such a screw possesses good self-centering behavior through holes. An exactly defined centering function can be realized with an increased shank (c). A reduced shank (d) often is an optimum between screw-weight, -cost, and -function, because the reduced shank has a diameter in the range of thread flank diameter d2, so the screw production line can be made effective. A wasted shank (e) gives a high screw resilience with low additional screw force under loading; here the body diameter dB should be made as long as possible (a guiding diameter is necessary under head and the transition between different diameters has to be designed with large radii for avoiding of stress concentrations). As a guideline, a shank type (a) or (d) should be taken whenever possible. The clamping length is the distance between head support and start of thread engagement and the plastification length is the length of free shank under preload with smallest cross-section As or Ab. Therefore, lc is the same Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

for all screw types (a)–(e). In contrast, the plastification length varies from lp ¼ lc at type (a) to smaller values at types (b)–(e). By reason of the significant area difference between As and Ab resp. A2 at the same screw, only the smallest cross-section will plastify under tensile load; this smallest cross-section comes to failure before the other cross-section gets plastified dependent on the materials ratio of Rp0.2s over Rms. 3. Screw Head The screw head includes two important aspects: (a) type of screw drive, and (b) type of support area. The type of screw drive is responsible for capability of assembly process, the type of head support area is influencing the designed function of the fastening system. Figure 35 presents the established and widely used types of screw drive geometries. They are distinguished by external and internal types. For external and internal geometry four designations are important: hexagon, bihexagon, triple square, and hexalobular. If considering internal configurations also, cross-recess drives (e.g. [21]) and slotted screw drives are of interest. These two geometries are dominant for small screws without high

Figure 35

Basics of screw drive selection.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

preload because they cannot provide high torque values which can be transmitted reliably between bit and screw. The most common screw drive globally is the hexagon geometry. This is important for components which have to work and must be repaired in areas without technical experience. This drive type is suitable for high torque values if there is only a small clearance between bit=wrench wrench and screw and if the drive has no damage. Using an open wrench as a rough estimation, only half of the torque compared with a ring spanner can be applied with reliability. The reason is that when using an open wrench, only two flanks are used for torque transmission. Since six drive flanks and a small contact angle between bit and screw for the line contact, the hexagon drive may lead to damaging the surface of the screw, especially if the screw is coated for corrosion protection or if worn bits are used. In Fig. 35, these aspects lead to a sum of 9 assessment-points from the 20 possible. A significant improvement of drive torque loading capacity and reliability is achieved with 12 flanks (bihexagon and triple-square drive geometries). A bihexagon drive geometry is created by two hexagon drives, which have the same center point and an angular misfit of 308. A triple square drive geometry is created by three square contours, which have the same center point and an angular misfit of 308 each. A hexalobular drive geometry [established by Textron-Camcar under the designation TORX#] consists of one (small) convex and one (large) concave contour radius, which are alternately combined [22]. This leads to smooth contact pressure between screw and bit as well as small-sized outer bit diameters for compact design structures. There is no significant difference in using this design compared to bihexagon or triple square, except that the same maximum drive diameter, the hexalobular drive geometry has a lower drive section modulus against torsional failure. Triple square or bihexagon drives should be used. For the internal drive configurations, the same comments are valid. Compared to the external configurations with the same head diameter, the drive flanks are smaller and the internal configurations are stressed to a higher level for same torque transmission. The bit is much smaller which is very positive for the accessibility. In most cases for internal bihexagon, triple square or hexalobular drive, the bit determines the torque limit, not the drive of the screw. Internal drive configurations usually have lower weight of the screw head than external drives, but internal drives can lead to head stripping under preload, if their bit-engagement is too deep. On the other hand, a minimum bit engagement is necessary for reliable assembly process. These two influences determine the height of head for screws with internal drive.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Slotted screws are only relevant for applications with low requirements for screw tightening. They have a cam-out-reaction under torque loading and the blade of the screw driver can have a radial misalignment, which leads to damage of screw, screw driver and possibly of component surface. Cross-recess drives are an obvious improvement over the slotted screws in low torque applications like screws for fastening wooden constructions or plastic components. They provide a radial alignment between screw and driving bit, but the negative cam-out-reaction is significant. The life time of cross-recess bits is quite short. Of course, there exists many other drive systems for special requirements, such as Square drive, Multispline, Hexapol#, Triwings#, Clutch-

Figure 36

Contact conditions of high torque screw drives. (From Ref. 17.)

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

type#, Torx-Plus#, or Polydrive#, which often are trademarks of different companies. Figure 36 demonstrates the contact conditions of high torque screw drives from Figure 35 in a more detailed manner. In any case, the tolerance situation is important for the torque loading limit of the drive. The clearance in Fig. 36 is oversized in order to emphasize that all screw drives have single contact lines at each drive flank, if they are undeformed (only contact points in drawn cross-sections). The applied torque Ttot leads at each drive flank to a circumferential force Fc, which can be divided into a normal part Fn (torque transmission) and a tangential part Ft (contact sliding and in consequence flank wear). For an ideal drive geometry, this Fc can be calculated as shown in Fig. 36. Between Fc and Ft, one can measure the contact angle E. This value is 308 for hexagon and bihexagon drive, 458 for triple square (see also Fig. 63) and about 608 for hexalobular drive geometry. A small contact angle means high contact sliding under torque loading. This is the reason for surface damaging of the screw area engaged to the bit as well as the reason for wear of the bit flanks. Figure 36 confirms that a bihexagon drive has the same contact conditions as a hexagon geometry, but the increased number of engaged flanks lowers the Fc at each single flank. The triple square and hexalobular drive systems have an increased contact angle, so they should be taken as a designed screw drive system today, if no advantages of other drive systems are predominant. If the clearance between bit and screw drive contour is too large, the bit life time decreases significantly and the danger of screw drive damaging occurs. Often for small-volume-designs, the space for screw head and the accessibility for bit are limited. Figure 37 compares the space requirements of three screw head designs with hexalobular drive type for same thread diameter d and same support diameter da. Part (a) refers to an external configuration, which is characterized not only by high stiffness of the screw head, but also by large height requirements. The bit for driving the screw normally has a largest diameter up to 2.0d as the head support diameter da. If using a standard design with internal configuration (b) the height of screw head is reduced to 80% of (a). Also, the size of the screw drive flanks is reduced to only 60% of (a). This can cause problems if the screw has high material strength and if the screw is tightened to high preload level beyond the screw material yield limit. In this case, the cross-section of the driving bit exceeds its fatigue limit, so that the life time of the bits is decreased drastically. Another aspect of internal drive configuration is the ratio of screw head height and length of bit engagement. This ratio has to

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 37

Comparison of screw head designs for same diameters d and da.

be large enough for a given head geometry, so that no head stripping occurs under preload. An optimized design with low height of head, large screw drive flanks and deep bit engagement is proposed in part (c) of Fig. 37. Even if the height

Figure 38 Types of support area and calculation of effective bearing diameter. (From Ref. 17.)

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

of head is only 0.7d, no head stripping occurs under preload due to the reason of the conical head-shank-transition. The large length of bit engagement guarantees a high assembly process capability. The large size of screw drive flanks leads to a long bit life time for any tightening method. The internal configuration offers an easier drive accessibility by a small bit diameter compared to the external configuration of (a). Another important design aspect of screw head is the type of support area. Figure 38 displays three established types of support area between screw head and clamped part. Each type has its own calculation for the effective bearing diameter Deb [72]. This diameter Deb represents the virtual diameter, where the circumferential force produced by the contact friction can be concentrated for calculation; it influences the head frictional torque Th directly (see Fig. 16). A plain support type is used as a standard; it is easy to manufacture and requires no special geometrical matching of screw and clamped part. Large head support diameters da are suitable for low surface contact pressure (see also Figure 39) and for covering large clearance holes. Countersunkand ball-section-support types provide a centering function between screw

Figure 39 Required relative support diameter for given maximum contact pressure. (From Ref. 16.)

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

axis and position of clamped part. Therefore, the positioning tolerance of such multi-screw-fastenings has to be precise (e.g. wheels of vehicles). Countersunk- or ball-section-support types have to be tightened with different torque values to obtain the same preload depending on the effective support diameter Deb. Normally the assembly torque Ttot is increased by 15% compared to the plain support type and similar other boundary conditions. However, this approximation cannot replace a detailed calculation. By reason of the increased head frictional torque Th, countersunk and ballsection-support types provide an enhanced safety against self-loosening. If using countersunk- and ball-section-support types, the tolerances of countersunk angle, the ball diameter of the screw, and the clamped part must fit together. In any case, a full bearing area in the support contact is guaranteed [see also ISO 7721 [43]]. If using plain support type with clamped parts of high strength in the range of the screw strength or higher, the detailed geometry of the screw support area should be designed in a slightly concave manner, so that the contact diameter is defined clearly. If using thin sheet materials, significant angle tolerances between screw axis and support area or rough surfaces. The effective bearing diameter Deb in practice can differ from the theoretical calculations regarding Fig. 38. A measurement of Deb in experiment is recommended. Important for design of screw geometry is the support diameter da. Figure 39 illustrates the dependence of required minimum head support diameter for a given permitted maximum surface pressure (plain support type). The three functional curves belong to different property classes of screws (tensile strength values 1200, 800, and 400 MPa; for property classes, see also Table 10). The lowest curve represents a screw made of low-strength material like aluminum. For example, a given maximum surface pressure of 100 MPa in the contact zone between head and surface of clamped part means a very large relative head diameter of 3.2 d if using a bolt with a strength of 1200 MPa and a relative diameter of only 2 d if using a bolt of strength 400 MPa (e.g. made from aluminum). This diagram makes it clear that only screws with flange head and a low screw strength can reach the demand for low surface pressure with acceptable head diameter. This is required for materials of clamped part with limited loadability and significant creep behavior, e.g. magnesium components at elevated temperatures. The permitted contact pressure pchperm for the particular material clamped should not be exceeded to avoid any excessive plastic deformation in the head contact area, even if the bolted joint is in operation (this would result in a loss of preload). As a rough estimation, the permitted contact pressure pchperm should not exceed the minimum of (Rp0.2 þ Rm)=2, either of the screw material or of the clamped part material. This can only be done

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 40

Influence of head support details on tightening behavior.

if no creep occurs. In that case, experiments must determine the contact pressure limit pchperm, which does not lead to significant preload loss. Often it is about half of Rp0.2. If a high-strength screw with only low assembly torque to limit the low permitted head contact pressure is used, the danger of misassembly occurs (missing information for the right handling in field service, perhaps by unauthorized workers). Figure 40 finally emphasizes the result of a torque-preload measurement over tightening angle done at RIBE laboratory with two slightly different contact angles for head support (with plain, but concave bearing geometry). Part (a) belongs to a support angle of only 18 between screw head support area and spot face of clamped part. Here, the maximum preload reaches about 57 kN and the maximum tightening torque increases up to 107 N m. Part (b) contains a screw with support angle of 38, which leads to almost the same maximum preload of 55 kN, but to a very high maximum tightening torque of 168 N m (as a result of metallic adhesion between screw and clamped part caused by severe local stress peaks at support diameter region). This means that very small changes of the head support geometry or surface can lead to significant changes in tightening behavior, especially if overelastic tightening methods are applied (see also Fig. 18). Besides this, Fig. 18 confirms that in spite of the large difference in friction for both situations (a) and (b), the preload is almost the same—this result can be achieved only with overelastic tightening methods.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

D.

Design Options

1. Established Main Types Besides the rules of basic mechanics for threaded fastening systems, a large number of design options exist. The most important options are proposed below. The design engineer has to select the correct options important for him. Of course, some options are suitable for more than one design target and others are very specialized. Figure 41 indicates design options for three optimization targets (a)–(c): improved assembly, improved fatigue limit, and avoiding of self-loosening. For all optimization targets, the most important actions are listed. Figure 41 is self-explanatory, but some aspects are discussed in a more detailed manner in the following lines. Thread ends for finding the best nut thread are most important for short screws which have no significant self-alignment by the through hole of the clamped part (clamping length lc under 1 d, see also Ref. [21]). The automated handling of screws is much easier if the screw exhibits a center of gravity location with dominating shank-weight so that the screws tend to fall ‘‘head-up’’. The mathematical condition given in Fig. 41 is a rough approximation for guidance. For further details, see Ref. [21]. The fatigue limit of a bolted joint depends on all the parts of the fastening system. One action to improve the fatigue behavior is to increase the material limit of the screw (materials selection, etc. local residual stresses, etc. rpar; or to reduce the additional operating force of the screw during operating by increasing the elastic resilience of the screw. Examples are given in Fig. 41. Another aspect is the reduction of stress concentrations which appear most at first bearing thread flank (see also Fig. 2). Self-loosening can happen under high preload if microsliding in the contact zones of head support and thread contact appears (e.g. large dynamic transversal loading, see also Fig. 76). A head support with locking teeth is a very effective action to prevent self-loosening without influencing the preload level of the fastening system. Washers or similar additional elements with ribs or teeth are usually of no help against self-loosening. Thread flank clamping as an alternative is based on ‘zero-clearance’ between nut thread and screw thread flanks, but a clamping torque reduces the acting preload after tightening. Adhesives also eliminate flank clearance between nut thread and screw thread without a clamping torque (but with a thread frictional coefficient mt of about 0.20). Adhesives have a limited operating temperature of 2508C depending on the adhesive material. Three other design targets can be: improving preload, reducing weight, and avoiding unauthorized disassembly. Established design options to meet these requirements are demonstrated in Figure 42.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 41 loosening.

Design options for bolted joints due to assembly, fatigue, and self-

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 42

Design options for bolted joints due to preload, weight, and disassembly.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

For improving the preload acting in the fastening system, the main actions are increased screw diameter (1), increased screw strength (2) and selecting an optimized tightening method (3, see also Fig. 18). For components made of low-strength materials, the time dependency of preload is important (relaxation effects, see also Fig. 66). In this case often, it is more useful to reduce the preload retention during time of operation than increasing the initial assembly preload which is decreased extremely over time (4 in Fig. 42). For reducing weight in part (b) of Fig. 42, six actions are mentioned. Of course, first the weight of the fastening element can be minimized, e.g., by using an aluminum screw instead of steel screws. This is very positive especially if light metal components with low-strength and high thermal expansion coefficient have to be fastened. A secondary weight saving effect is that for low-strength nut thread components an aluminum screw offers a reduced minimum thread engagement with chance for a small component size (see also Fig. 33 for screw with a strength of 400 MPa and section 4 in Fig. 42). For components with high strength and in consequence high load bearing limit, the use of a high-strength screw is suitable. The size of this high-strength screw can be reduced compared to a screw made of material of a lower property class (2). The same effect can be realized with a better tightening level of the screw (3). Here also, the design limits of screw and components must be sufficient so that, the tightening method is fundamental for a design analysis (3 in column (a) and Fig. 50). Additional actions for reducing weight can be minimizing screw head volume and, if necessary, a hollow screw shank (interesting for large screws, which are not stressed up to their loading limit). The right column in Fig. 42 shows actions for avoiding unauthorized disassembly of a threaded fastening system. For using a special screw drive (2), the compatibility with maximum torque level during tightening and with available tightening tools in production and field service has to be checked. A shear-off-drive is designed, so that the drive is sheared-off if the ultimate tightening torque is generated. Then the screw can be disassembled by extensive mechanical work resulting in destroying the screw. Applications include locking devices. An important aspect is the missing corrosion protection in the broken shear plane of the screw. Another way to avoid an unauthorized disassembly is using a combination of thread rolling screw, adhesives, and large thread engagement. The screw can be tightened, but the screw drive is not suitable to transmit such a high torque which would be necessary for disassembly. This solution is used for components with safety relevance (which may not be opened, e.g., control units for anti-locking-brake-systems).

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From the point of screw mechanics, washers should be avoided because they always lead to more surface contacts in the fastening system with roughness and in consequence with possible preload retention (seating, relaxation). But washers are useful to prevent surface damage of component surface by rotating screw head during tightening (e.g., for fastening of painted components). Another reason for using washers can be providing a high-strength contact surface for the screw head, which transmits the preload to the lowstrength component material (reduction of contact pressure for the component). then, the washer needs a thickness of about 20% of the nominal screw diameter and a hardness, which is in the range of the screw or higher. To avoid self-loosening of the screw, any washer design must be checked very critically because only a few washer geometries can guarantee this (see Fig. 41). 2. Special Elements for Threaded Fastenings Two groups of fastening elements which have a strong growth for new developments of components are visible in Figs. 43 and 44. Staking elements are of great importance for automated generation of a screw thread or nut thread in thin sheet metal components without sufficient material for thread engagement. Figure 43 contains self-explanatory details for a staking bolt with additional characteristics for use. In contrast to welding bolts or nuts,

Figure 43

Principle of staking bolt; system RIMS. (From Ref. 64.)

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 44

Principle of screw combined with sleeve, system Rifixx. (From Ref. 61.)

staking elements produce no thermal loading of the component and, therefore, can be used for nonweldable materials or components with surface finishing. Besides this, they need no welding equipment, but can be integrated in stamping tools or deep-drawing tools of existing production lines, so they are very economic high-duty fastening elements. If the screw is combined with a sleeve, this preassembled product can be inserted to the clamped part with interference fit tolerance, so the screw is part of the component and cannot get lost. Significant advantages are achieved if used with components with integrated screws: no searching for screws, no falling of screws, no separate fastening elements (purchase, storage, logistics), better positioning of component (especially for overhead assembly), and no mixing up of different screws (e.g. screw lengths). As Fig. 44 shows, these elements can offer the additional functions of preload transmission by the sleeve itself (e.g., for low-strength components made of plastic, see also Fig. 65) or acoustic insulation (reduction of structure-borne noise in engines or machines, Fig. 45). 3. Characteristics of Studs Often, instead of screws with head, as an alternative, headless studs with nuts are used. On the one hand, studs have their advantages in easy positioning of clamped part by the stud itself (field service and repair) and in small space requirements for inserting the nut instead of a long screw. On the other hand, the screw has the advantage that only one fastening element for one fastening system is used, which means well-defined assembly

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 45

Example of Rfixx-plus-element. (From Ref. 61.)

and a high total process capability, especially for high preload levels (e.g. overelastic tightening). Figure 46 summarizes the most important aspects comparing studs and screws. 4. Characteristics of Washers Both washers and flange heads can be designed with the same support diameter for the component (Fig. 47). The design engineer has to decide which geometry must be selected for the fastening solution. In Fig. 47, the most important aspects are summarized. In practice, the main reasons for using washers are the prevention of damage of (painted) surfaces, the reduction of contact pressure at clamped parts with low material strength (e.g. plastics) or covering large through holes. For high-duty threaded fastening systems, always a washer head (flange head) of the screw should be considered by reason of the enhanced assembly process capability. Flange heads of screws can be produced economically up to (2.5–3) nominal screw diameter.

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Figure 46

Comparison of screw and stud with nut.

In Fig. 47, the outer support diameter is drawn equally for washer and flange head. But for the assembly behavior only the sliding diameter da is relevant. The maximum preload requires different tightening specifications between washer and flange head. Washers often have chamfers. The

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 47

Comparison of screw with washer and screw with flange head.

maximum washer diameter has to be placed on the clamped part. But it is possible that a washer rotates on the clamped part during tightening. This leads to changing assembly behavior of the threaded fastening system (see also Fig. 48). Figure 48 demonstrates the assembly behavior of a screw with captive washer, tightened on a clamped part made of aluminum with low surface roughness of the machined spot face, where the washer with almost the same washer diameter as the screw head diameter is supported. By reason of these boundary conditions, during tightening, it is possible that for a low preload,

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Figure 48 Assembly behavior of screw and washer with similar support diameter; measured data.

the washer rotates on the component and for higher preloads the screw rotates on the washer. But the contact zones under screw head change (different roughness, different materials, and different lubrication), which leads to a significant change of the head frictional torque (recorded in the measuring diagram of Fig. 48 over preload in screw shank). For automated assembly procedures, this can cause error signals of the tightening device, especially if the screw is tightened with yield control. 5. Characteristics of Sealings If a gas- or liquid-tight threaded fastening system is required, three contacts have to be considered: (1) head contact sealing, (2) component contact sealing, (3) thread contact sealing (Fig. 49). Often, number (2) is most important. For the design engineer, the task of selecting the right ratio between clamping length lc and screw distance x is an important one. This ratio x=lc should be smaller than 10 in order to minimize critical zones for leaking. The mean nominal contact pressure for a gasket should be larger than 2 MPa. In order to obtain the same tightening behavior with and without sealing, a gasket should be as thin as possible (e.g., spring steel sheet with some mm polymer-coating to fill the roughness of technical surfaces). For further details, see Fig. 49. For sealing technology with liquid gaskets and adhesives, see Ref. [52]. E.

Loading vs. Loading Capacity—Design Analysis

1. General Procedure A design analysis has to guarantee that no failure of the fastening system can happen. This is only possible by comparing maximum loading (of screw,

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Figure 49

Fundamental aspects of sealing with threaded fastening systems.

clamped part, and nut thread component) and loading capacity of these components in a bolted joint; and this has to be done for both tightening and operating situations. Distinguishing tightening and operating is important for considering different stress states and different temperatures (t1, t2). Figure 50 proposes a fundamental approach to this for a given data of screw, clamped part, and nut thread component. The design requirement is a sufficient preload Fpnec (often this preload is based on technical experience). Besides this, also time- and temperature-related limits are input data for design analysis. These are, on the one hand, material strength values of screw (static Rmst1, Rmst2 and dynamic saspermt2), clamped part (Rmpt1, Rmpt2), and nut thread component (Rmnt1, Rmnt2), on the other, force and Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 50 Principle of comprehensive design analysis for threaded fastening system. (From Ref. 17.)

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

pressure limits, which are also dependent on the specific geometry (Ttotpermt1, pchpermt1, pchpermt2, Fthreadpermt1, Fthreadpermt2, Fheadpermt1, Fheadpermt2, and Ftranspermt2). For example, the permitted contact pressure under head after tightening at temperature t1 (pcht1) and during operating at temperature t2 (pcht2) must not reach extensive plastification of the bearing surface, which is characterized by pchpermt1 and pchpermt2. Ttotpermt1 is the maximum torque during tightening which can be transmitted by the screw drive without problems. Fthreadpermt1 and Fthreadpermt2 are the maximum preloads before thread stripping of the bolted joint occurs (stripping can take place at both, nut thread or screw thread depending on the tolerances and material strengths, see also Fig. 33). Fheadpermt1 and Fheadpermt2 are the maximum preloads before head stripping of the screw takes place. During operation, acting transversal forces have to be lower than Ftranspermt2. The first loading of the fastening system is done during tightening. So, the minimum and maximum assembly preload Fpamin and Fpamax have to be calculated (of course, dependent on the tightening method). If the assembly preload is known, also the tightening torques Ttotamin and Ttotamax for assembly can be determined. From these tightening preloads and tightening torques, the loadings with bullets under (2) are applied during operation, e.g., axial static or dynamic force. This leads to the results of minimum and maximum operating preload Fpomin and Fpomax. One important aspect, especially for tightening methods with screw plastification, is the reduction of torsional stress after taking away the tightening torque (about 10% to 30% of the highest torsional stress under torquing conditions). This increases the axial loading limit of the screw, so also plastified screws can bear significant additional loads in a threaded fastening system. Besides this, a chemical stability is assumed in general for this design analysis. The design criteria under (3) compare all relevant loading values with the corresponding loading limits (forces, stresses, pressure, and torque). Only if all criteria are valid, the bolted joint is designed safety. But sometimes, certain criteria are not important; so the number of relevant criteria can vary (e.g., only low level tightening makes stripping, contact pressure, drive torque limit, and screw overloading uncritical, so most of the design criteria can be neglected). The design criteria are distinguished for axial= transversal force and design section compatibility (see also Fig. 2). The selection and assessment of the design criteria are an engineering task. If the threaded fastening system only works at room temperature, no temperature influence has to be considered (t1 and t2 are missing). If the fastening system operates at various temperatures, the highest and lowest temperature have to be considered, so then t3 occurs. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

2. Preload Deviation in Practice For engineering design, it is important to consider that the initial preload can vary significantly for the same screw specification, depending on the tightening method, the deviation of friction coefficient in contact zones and for overelastic tightening methods depending on the deviation of screw strength. Figure 51 gives an example for a threaded fastening system with screw M8-10.9. The diagram specifies the torque-preload-behavior for four cases A–D, calculated with formulae from Fig. 16. The cases A–D distinguish independent deviations of frictional coefficients mth and mh from 0.08 to 0.16 as

Figure 51

Torque-preload-behavior of screw M8-10.9.

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well as deviation in screw strength from 1000 to 1200 MPa (10.9). This results in four different linear functions between tightening torque and preload. On each curve, there are three markings (rhomb for an equivalent one-dimensional stress seq ¼ 0.9Rp0.2 during tightening, triangle for corresponding seq ¼ Rp0.2 and quadrangle for seq ¼ Rm). Now, if the screw is tightened with torque control in the range of 16– 20 N m (see gray field in Fig. 51), the generated preload can vary from 8 to 22 kN (8 kN for case D and minimum torque of 16 N m; 22 kN for case A and maximum torque of 20 N m). Please note this is a ratio of maximum preload over minimum preload of almost 3. In practice, this means that for this fastening system and this tightening specification, only 7 kN are guaranteed at minimum. On the other hand, for case A, the yield point of the screw is achieved at about 24 N m (position of triangle), so for this situation, the tightening torque cannot be increased significantly. As a result, in general, the disadvantage of torque controlled tightening is that the tightening torque Ttot must be specified for lowest possible torque value (case A in Fig. 51). For other combinations of deviations, this gives a poor preload Fp (e.g. case D in Fig. 51). The difference of overelastic tightening compared to torque control is outlined for yield point controlled tightening in Fig. 51. If yield control is used, for every screw the beginning of plastification is detected, so every screw, is tightened to its triangle marking. Then the preload is generated in the range from 18 to 27 kN (ratio maximum preload over minimum preload is reduced significantly from 3 for torque control to 1.5!; arrows with dashed lines). In practice, this means a slightly increase of maximum preload and an extensive increase of minimum preload (see also Fig. 18). The smaller deviation of preload must lead to higher deviation in torque values (Ttot is in the range of 24–43 N m in Fig. 51). One should never worry about changing torque values if overelastic tightening is used; the preload is safe, if the screw strength and the friction are as specified. 3. Dynamic Loading Capacity The dynamic loading capacity of threaded fastening systems depends on a lot of details regarding the entire joint-like value of external alternating loading, stiffness and resilience, eccentricity, symmetry, component separating, thread geometry, residual stresses, occurring stress peaks, manufacture of screw, and finally besides others also fatigue strength of screw material. Therefore, an exact determination is only possible by experiment resp. measurement of the original system in the particular application. Testing of the dynamic behavior of a designed structure covers the most often performed tests.

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Generally speaking, the maximum stress concentration factor of about 8 (at the first bearing thread flank of screw, see Fig. 2) reduces the screw material fatigue limit by a theoretical factor of 8 compared to results obtained with cylindrical samples without notch geometry effects (often listed in engineer’s handbooks. For a first approximation of the screw fatigue limit without additional information, take the sample value of the cylindrical screw diameter and divide by 10. This often is necessary for screws made of nonferrous metals). If no data for fatigue-limit are available, as a rough approximation, the sample fatigue limit of steels is about half of the tensile strength and the fatigue limit of aluminum is about one-third of the tensile strength regarding the same sample for axial loading, see Ref. [48]. Reference [70] gives an empirical relationship between steel screw fatigue limit and screw diameter as reported in Fig. 52. The diagram, on the one hand, distinguishes between thread rolling before and after heat treatment, and on the other, considers the preload dependence, correlated by the term Fp=(Rp0.2As)—a ratio up to 0.7 belongs to screw tightening without plastification, a ratio of 0.8 belongs to yield point controlled tightening and a ratio of 0.9 belongs to angular controlled tightening with significant plastification of screw shank. The diagram shows two general aspects: (1) overelastic tightened screws still have a significant fatigue limit, and (2) the fatigue limit of screws

Figure 52 Fatigue limit sasperm0 of steel screws depending on screw diameter d. (After Ref. 70.)

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with rolled thread after heat treatment depends significantly on the preload level (reason: strain hardening and residual stresses from thread rolling are not compensated by a new grain structure from heat treatment, so nonlinear profiles from loading stresses and residual stresses are superposed). The test principle for determining axial fatigue load saspermt2 is defined in ISO 3800 [30] or more detailed in DIN 969 [10] for threaded fastening elements. Normally, the screw shank is the location of fatigue failure, but the clamped part or nut thread component can also end in fatigue failure, e.g., thin sheet metals as clamped part and a screw head with locking teeth. If the location of fatigue failure is at screw head fillet, significant bending of screw is probable (see also Fig. 54). Minimizing fatigue problems can be realized by reducing the screw stressing (e.g., larger screw size, lower additional force for screw in fastening system), proper screw section design (see Fig. 2, e.g., sufficient radius at head-to-shank-fillet, perpendicularity of screw axis and head support, smooth transition of each discontinuity at screw shank, such as different diameters of screw, running out of thread to unthreaded shank), no overlapping of stress concentrations (e.g., chamfer at clamped part under head or at

Figure 53 Typical cross-section of screw M18 1.5-12.9 failed in fatigue, result of testing procedure according ISO 3800, stress amplitude sa ¼ 80 MPa, mean stress 555 MPa, symmetric axial force without bending moment.

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first nut thread flank, avoiding corrosive pittings at thread flanks or at head-shank-transition). The most established actions to increase the fatigue limit of the screw itself are discussed in Fig. 41. Figure 53 contains a cross-section of a screw M18 1.5 which has failed in fatigue. A plane fracture zone can be seen at outer regions of the cross-section (area of crack initiation and crack propagation) and an unplane fracture area in the center of the cross-section (residual area of rapid failure under preload). Figure 54 in contrast to Fig. 53, gives an impression of a fatigue failure with significant bending moment under external loading. This result was obtained with a transversal vibrational test (see also Fig. 76). Now, the area of crack initiation and crack propagation with ‘‘cycle lines’’ is clearly different from the residual fracture area. The size of this second part of cross-section gives information whether the acting preload at the event of failure was high or not (fatigue failures often are induced by wrong tightening or loss of preload caused by relaxation or self-loosening).

F.

Aspects of Quality Management

The overall objective for quality aspects of a threaded fastening system is to guarantee sufficient preload. This preload normally is not specified directly. Due to this reason, a large number of details must fit together, which have to be realized by different responsibilities. Figure 55 demonstrates seven main groups of authorities which have to give their contribution to quality of the fastening system. The drawn boxes make clear that every authority has its objective, its risk and takes actions due to different criteria. Besides this, it is important for clarifying failures that each authority in most cases belongs to different business units or companies, so various communication interfaces exist, which have to work without deficit or error. So, from the point of organization, a ‘‘fastening manager’’ is recommended. A few more quality aspects are:

The calculation of threaded fastening systems in any case is an approximation because numerous details have to be estimated like real screw loading in the system, local fatigue strength of screw, material inhomogeneities, real external loading spectrum or others. By these uncertainties, the compatibility of a designed fastening system with experience from former solutions is valuable, and critical calculations have to be verified by experimental testing. But proper designing due to guidelines of this chapter avoids a lot of failure situations and reduces testing expense.

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Figure 54 Fatigue failure of screw with bending moment under preload from vibrational testing with transversal displacement .

From the viewpoint of manufacturing, it is very important to realize that the (mass) production of screws is characterized by a high degree of automization and a high precisement due to geometry tolerances and material tolerances of the fastening element (e.g. see tolerances in Fig. 4). The lifetime of products tends to be higher; so the degree of longterm quality due to relevant fastening systems also has to be enhanced. The most important aspects are corrosion and relaxation as well as fatigue strength. These properties cannot be tested during component production. Optimized components with high material utilization have strong requirements to their fastening systems. So, a component optimization always has to include the fastening systems as early as possible. In most cases, high quality and expensive components cannot use low-quality and low-price fastening elements.

In practice, often problems during tightening resp. assembly exist. The reasons may be: 1. wrong size (diameters, lengths, positions),

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Figure 55 Authorities responsible for reliable function of a threaded fastening system.

2. wrong alignment (axis of screw, clamped part through hole and nut thread), 3. wrong thread (screw thread or bolt thread tolerances, crossed thread flanks, deformed flanks, wrong nut thread depth), 4. local materials mismatch (chamfers, burrs, dirt in holes, chips), 5. wrong=inprecise screw drive, 6. wrong material strength (screw, clamped part, nut thread component), and 7. wrong lubrication (screw surface, cleanliness of components). All assembly problems lead to reduced preload after tightening or overstressing of screw. Therefore, it is important that these problems are detected by the assembly process (e.g., tightening device with specific evaluation routines). Assembly problems can be the reason of failure of welldesigned fastening systems during operation. Therefore, for analysis of

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

every screw failure during operation, the assembly process has to be analyzed too. Always, three general reasons for failures during operation have to be considered: 1. wrong initial preload (tightening process, poor design), 2. wrong residual preload (relaxation by creeping of materials, gaskets), and 3. overloading mechanically, thermal or reactive (too high operating load with plastification or sliding, too high temperature with creeping or decreasing of strength, too strong environment with significant corrosion). G.

Cost Accounting of Fastening Systems

Always cost accounting of a fastening system has to be done due to life cycle of the component system (product) because only this life cycle cost can be compared to the customer value. Then, all boundary conditions of Figs. 1 and 32 have to be included and evaluated monetarily—the fastening element is only one contribution to this life cycle cost. Figure 56 proposes a fundamental approach to total cost accounting, which takes into account the main types of cost related to a fastening system. Options for cost optimizing are thread rolling (Fig. 7), standard materials (Fig. 10), coarse tolerances for geometry (Table 2). But one must always remember that the guaranteeing of reliable function has to be of higher priority than the cost for a technical system. Otherwise, the product has no customer value and therefore no market. IV.

EXAMPLES OF DESIGN

A.

Fastening with Optimized Initial Preload

Traditionally, screws are tightened with torque control (see Fig. 19). The tightening torque Ttot is specified for the conditions with lowest friction. This is shown on the left side of Fig. 57 (as a supplement to Fig. 51) for a steel screw 8.8, tensile strength of 800 MPa. The first case A considers a low friction situation with coefficients of mt ¼ mh ¼ 0.08. This screw at 20 N m tightening torque is stressed up to 0.9 Rp0.2 (rhomb marking) and produces a preload of almost 20 kN. Because of high screw stressing, the torque specification cannot be increased over 20 N m if yielding or breaking of screw has to be avoided in any case. For the same screw in large series assembly lines, the frictional situation can change to mt ¼ mh ¼ 0.16 (curve B). Then, for the same tightening Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 56

Comprehensive cost accounting of fastening system.

torque of 20 N m, a preload of roughly 9 kN is achieved because the high frictional torque in screw head contact Th consumes the main part of tightening torque. This influence of friction on the preload has to be considered carefully for designing bolted joints with torque controlled assembly method. On the right side of Fig. 57, the corresponding diagram for an enhanced aluminum screw with tensile strength of 400 MPa is drawn. It is

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Figure 57 Tightening diagram and preload level for steel screw and aluminum screw. (From Ref. 15.)

obvious that the lower screw strength leads to lower torque values on the xaxis if the screw is stressed up to Rp0.2 or Rm. But the resulting initial preload of this diagram is in the range of 12–14 kN and, therefore, exceeds the minimum preload of the steel screw. The enhanced aluminum screw with low torque and low strength yields the same performance with 1=3 of weight and other significant advantages (see Refs. [15,16]) including low required thread engagement, stable corrosive behavior, excellent thermal fit to light metal components made of aluminum or magnesium. This result is achieved with two additional actions: (1) The screw must provide an effective and reliable low friction film which reduces the frictional coefficients to the range of 0.08–0.12. Such a low friction film requires greater performance than normal lubrication for established steel screws. (2) The screw must be suitable for yield point- or angular controlled tightening. Then, the materials utilization is much better and the minimum preload is increased significantly. To obtain this, the screw requires a

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defined minimum plastification before fracture, therefore, the manufacturing process must be optimized. In principle, using yield point controlled tightening, the screw cannot be overloaded. Using angular controlled tightening, the screw cannot be overloaded, if the snug torque is low enough (e.g. 10 N m þ 908 in Fig. 57). Figure 26 explains why also a screw tightened with angular control can be loaded additionally. As a side-effect, the diagrams in Fig. 57 make it clear that torque-controlled tightening (and a steel screw for aluminum components) is an ‘‘oldfashioned’’ and not very optimized solution from the viewpoint of engineering threaded fastening systems. The diagrams confirm that a torque value mentions ‘‘nothing’’ about the preload acting in the joint. B.

Fastening with Small Thread Engagement

For every component design, the necessary minimum thread engagement needs space and therefore generates component weight. A minimization of thread engagement is required. Figure 33 contains the basic mechanics and suggests the use of relatively high-strength nut thread material or the use of relatively low-strength screw material.

Figure 58 Measured low minimum thread engagement for AluformTM screws M6 (From Ref. 15.)

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Figure 58 gives a practical verification of the calculation from Fig. 33 for a pull-out-test with RIBE-Aluform# screws [60] M6 (Rm > 400 MPa) engaged to an aluminum nut thread plate (Rm ¼ 300 MPa) with certain lengths of thread engagement te. The bar diagram shows the maximum pull-out-forces Fzmax in the event of failure. The upper level of 9 kN belongs to a tensile screw breaking in the screw shank. The lower level belongs to nut thread stripping. The transition begins exactly at the point 0.7 d which is also predicted by Fig. 33 (do not forget to consider chamfer of 1 P in Fig. 33). So, indeed Aluform# screws have a reliable behavior against stripping also for low-strength nut thread components and low thread engagements te, which would never be fulfilled with a steel screw 8.8 or higher.

C.

Fastening of High-strength Components

High-strength components provide the chance for small threaded fastening systems because contact pressure at screw head as well as thread flanks can be in the range between minimum of Rp0.2 and Rm of the materials in contact. Besides this, hard surfaces are almost unaffected by roughness chan-

Figure 59 surface.

Screw head design with small head diameter for tightening on hard

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ging with adhesive or abrasive wear meachanisms, so that the frictional situation is constant over a wide range of preload. Figure 59 demonstrates a small-diameter screw head design for tightening on hardened component surface in the range of Rm ¼ 1400 MPa (for high-strength screw materials see Table 9). Such a screw of dimension M11 1.5 and a screw tensile strength of 1150 MPa produces an initial preload of about 60 kN. This leads to a mean contact pressure of 950 MPa (compare also diagram in Fig. 39 and explanations related). In addition, for such design, the lubrication of the screw is of significant importance. These screws offer the possibility for small space flanges and in consequence for a compressed design of component. In contrast to light metal com‘ ponents, these high-strength materials possess significant mass density, but can be used for an extreme compact design. The same aspects are valid for thread engagement but at least te ¼ 0.8 d should be realized to avoid stripping of screw thread flanks (compare asymptotic behavior of Fig. 33 for high nut thread strength Rmnut). If fastening high-strength components, precise support geometries and small contact roughness is required, then peak contact pressure is avoided, which can be the origin of crack propagation and fatigue failure of the component. Threaded fastenings with components made of high-strength materials provide the possibility for meeting small space requirements (low thread engagement, small head diameter, small screwing boss diameter at clamped part). If this is combined with overelastic tightening and reliable lubrication, then also lightweight fastening is possible. D.

Fastening of Components Made of Brittle Materials

‘‘Brittle’’ means that a material has a low ductility before fracture, which leads to a sudden rupture without plastified deformation in the case of tensile testing or overloading a component. As a guide, the fracture toughness from tensile test is for brittle materials smaller than 3–5%). For such a component (e.g., made of magnesium, titanium with hexagon crystal structure or cast iron with high carbon content or ceramic materials), not only is the mean stressing important, but also all local stress peaks have to be minimized. Therefore, thread engagement of a screw in brittle materials should be increased by at least þ20% due to Fig. 33 because of the inhomogeneous stress distribution up to the event of fracture, which is not compensated by local plastification of the nut thread flanks. Brittle materials of low strength (cast iron, magnesium) tend to produce increased adhesive-abrasive wear in the screw head contact zone

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Figure 60 Adhesive–abrasive wear of head support area after angular controlled tightening of screw M14 2-11.9, specification 150 N m þ 908 þ 908 þ 908, preload app. 90 kN, surface gray cast iron GG25.

during tightening (Fig. 60). This results in increased roughness, particles and undefined contact conditions, so the head frictional torque is increased and—if the screw is tightened by torque control—the preload is reduced significantly. To avoid this, the lubrication of screws for brittle materials should be enhanced. Use of thread rolling screws in brittle materials is critical. Figure 61 presents an example from thread rolling with a high-performance thread rolling screw M8 (induction hardened forming point) in high-strength ductile gray iron GGG 50. The result is that particles of nut thread material are produced in an unacceptable amount. They lead to poor nut thread quality as well as screw thread damage and therefore to insufficient process capability for series production (see torquing diagram in Fig. 61 with temporary breakdown of torque curve). E.

Fastening of Light Metal Components

Light metals, such as aluminum and magnesium, are characterized mechanically by low strength and high thermal expansion coefficient. Especially in

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Figure 61 Thread rolling in high-strength cast iron as an example for critical application.

the field of automotive and transportation as well as for design of handheld-equipment, these materials are used more and more. For the design of threaded fastening systems with light metal components, it is important that: 1. Realization of sufficient thread engagement for low-strength nut thread material (Fig. 33, for steel screw app. te ¼ (2.5–3)d and for aluminum screws te ¼ (1–1.5)d). This guarantees reliable tightening and avoids component damage by wrong tightening=repairing. 2. Realization of sufficient head contact area for low contact pressure under screw head (use of screws with flange head, at least da ¼ 2d, Fig. 39). This helps to minimize creeping problems. An additional action is to design the screwing-boss-diameter in the range of (2–3)d. 3. Applications with aluminum components or aluminum screws should use enhanced lubrication because frictional coefficients are high for contacts of materials with cubic face-centered crystal structure (e.g., aluminum, nickel, and austenitic steel). For uncertain frictional situation, one must use yield point controlled

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tightening or angular controlled tightening (Fig. 26) and a screw with threaded screw shank (Fig. 3). 4. If operating at elevated temperatures, a special adaptation of thermal fit for minimization of thermal stress increase is necessary (often screws made of aluminum are an effective alternative compared to steel screws, Fig. 29). 5. For aluminum components, thread rolling screws are widely used (Fig. 7, Fig. 62). 6. For corrosion stability, use enhanced corrosion protection for steel screws or use aluminum screws (Fig. 63). Figure 64 contains the fastening of a magnesium component with thread rolling screw made of aluminum in two columns: the left side refers to five repetitions of screwing with same screw into the same nut thread hole. The right side refers to the situation where the same screw is screwed into a new pilot hole without nut thread for each repetition. The images of the screwing bosses confirm a high quality of the produced nut thread in magnesium for both columns of Fig. 64. The diagram is very detailed due to the formation of positive torque and prevailing torque (negative). All values are proposed for 1 to 5 screwing operation.

Figure 62 Trilobular stud M6 32 for thread rolling in aluminum component, dry lubrication, maximum thread forming torque 3 N m, tightening torque for stud 10 þ 0.5 N m, thread engagement 11 mm, casted pilot hole with diameter 5.4–5.6 mm.

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Figure 63 Appearance of aluminum component with blank aluminum screw after salt spray test: only the component (alloy Al–Mg–Cu) shows white corrosion products, no galvanic corrosion between screw and component; for details of triple square drive see Fig. 36.

The result is that for the left column the torque values are reduced due to repetitions. For the right column, the values are increased. But also for the right column of Fig. 64, the forming torque does not exceed the half of the tightening torque, which is acceptable. If using magnesium components, the reduction of forming torque for retightening into the same screwing boss is higher compared to steel or aluminum components. Finally, Fig. 65 illustrates a fastening solution for very soft materials as clamped part in a threaded fastening system with aluminum metal foam. The length of sleeve is undersized due to the length of clamped part, so that the level of compression=preload in the foam is defined. The wall thickness of the sleeve has to be adapted to the total preload of the screw. This design has no problem with contact pressure under the screw head or sliding of the screw head during tightening because the sleeve has a flange support area. Some impressive examples that the initial tightening preload is not equal to the residual preload after a long time of operation are shown in Fig. 66 which result from several thermal exposure tests with different bolted magnesium components and different screw dimensions. Magnesium is very sensitive for creep at elevated temperatures. All details due to the test conditions are given in Fig. 66. During the tests, there was no additional mechanical loading applied.

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Figure 64 Fastening of magnesium component with thread rolling screw; retightening behavior for two different situations (left and right).

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Figure 65 Fastening of aluminum metal foam with screw–sleeve-combination, see also Fig. 44.

Figure 66 Thermal decrease of preload by relaxation of threaded fastening systems with magnesium components at elevated temperatures; measured data. (From Ref. 16.)

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Every case, from 1 to 7, shows the initial preload for steel screw (light bar) and aluminum screw (dark bar) before and after thermal exposure. For case 1 (screw M10), this means 32 kN resp. 19 kN before thermal exposure and 5 kN resp. 9 kN after exposure. The other cases confirm similar behavior. The most extensive preload relaxation occurs for fastening systems with the widely used magnesium alloy AZ91 (high-strength alloy with 9 wt.% aluminum and 1 wt.% zinc; relatively stable corrosive behavior; low creeping resistance at temperatures above 1208C). Cases 3 and 5 confirm where the steel screw leads to almost no preload after thermal exposure— here aluminum screws are the only solution for reliable fastening systems. In general, for these situations, an aluminum screw always gives a higher residual preload than a steel screw.

F.

Fastening of Components with Thread Rolling Screws

What is the difference between thread rolling screws and screws for existing nut thread in practice? The fundamental principle of thread rolling screws is

Figure 67 Functional behavior of thread rolling screw compared to a screw for existing nut thread used for the same application, see also Ref. 63.

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emphasized in Fig. 7. Figure 67 demonstrates the behavior of tightening torque Ttot and preload Fp compared between metric screw for existing nut thread and thread rolling screw of same nominal diameter M8. Part (a) refers to a metric screw in machined nut thread—there is no forming torque for the first eight revolutions until the screw head is in contact with the clamped part surface. Then, the preload is generated for further screw turning. To obtain a preload of 15 kN, a tightening torque of 28 N m is necessary for case (a). A similar situation states case (b), but there exists a forming torque during the first 12 revolutions of 10 N m. This forming torque is reduced to 3 N m, if the forming point of the screw is turned outside of the nut thread. Therefore, to obtain a preload of 15 kN, the tightening torque has to be increased to 31 N m. For case (c), the forming torque in the situation of head contact is 8 N m, so the tightening torque for a preload of 15 kN has to be increased to 35 N m. As a result, thread rolling screws need a higher tightening torque, if they have to generate the same preload as a screw for existing nut thread (with related dimension). Therefore, the maximum preload in event of failure is not as high as for screws without thread rolling function, but the level of failure torque is in the same range. Overall, the preload difference is not very significant. Critical application of thread rolling screws, see Fig. 61.

G.

Fastening of Sheet-metal Components

More and more sheet metal designs are used for automated production of components with large lot sizes. These components should also be fastened automated. This can be done in two ways: (1) use of thread rolling screws for sheet metals, and (2) use of staking elements for generating a high-duty thread at thin walled components (for principle see Fig. 43). Thread rolling screws for sheet metals are based on the principle shown in Fig. 7 but in contrast to bulk materials sheets offer only a very low thread engagement. Therefore, the diameter of pilot hole is as small as possible, so the screw must provide a small thread tip diameter. Screws as shown in Fig. 68 can be used with and without an extrusion around the pilot hole (rim-hole, see also Ref. [63]). For an estimation of pilot hole diameter, see Table 3. Another tendency to fasten sheet-metal components is using modern riveting systems such as self-piercing rivets (Fig. 69) or high-strength blind rivets. Self-piercing rivets are the first choice if thermal joining technologies like welding are not suitable or not possible and if liquid-tight fastenings with

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Figure 68

Cross-section of thread rolling screws M6 for sheet metals.

Figure 69 Example of self-piercing rivet made of high-strength aluminum by RIBE; ideal solution for high reliability and easy recycling of fastened light metal components. (From Ref. 16.)

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Figure 70

Simplified principle of blind rivets (break-stem-system).

low precisement in positioning of the fastening-element are required. Another advantage is the very fast and fully automized assembly process. Figure 70 demonstrates the principle of blind rivets as a two-piecefastening-element (rivet body and stem). The clamping force of the rivet is generated by deforming the rivet body under tensile load Fax of the rivet stem, which leads finally to a breaking of the stem at the desired breaking area. Figure 70 displays an expanding of the rivet shank— another possibility is bulbing the rivet shank. Blind rivets are first choice, if only one-side-access to the clamped parts exists (chassis structures, e.g. in vehicle-, transportation-, and aerospace-industry). A blind rivet requires a minimum of surface preparation before setting (low roughness requirements). The residual stem is important for high shear strength and high fatigue strength of the joint. Figure 71 shows an example for a bulbing blind rivet (in contrast to blind rivets with expanding head) which is applied to aluminum sheet metals (sheet thicknesses 2 and 3 mm). This kind of blind rivet produces a high level clamping force. In general, riveting systems always have material deformation either of clamped part and=or of rivet, so high-strength rivets have to be engineered for each particular application (size and number of rivets, geometry tolerances, and setting parameters). For more information regarding riveting systems, see Ref. [59]. For standardization of blind rivets, see Ref. [24].

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Figure 71

H.

Blind rivet application, RIBE Ribulb#.

Fastening of Components, Which Need Extreme Reliability

A typical example for threaded fastening systems which must guarantee extreme reliability, is wheel bolts for fastening of wheels to car suspensions. These bolts are exposed to extreme operating conditions, such as a large number of retightenings, poor exactness of tightening torque, severe salt environment, elevated and low temperatures. One corrosion test procedure with strong corrosive loading is the RIBE-acid-salt-spray-test. Figure 72 shows the corrosion test result for wheel bolts with two surface coatings—the nonelectrolytical standard coating (left) failed in this test already after 96 hr exposition with starting substrate corrosion, which normally occurs after 1000 hr. The right side of Fig. 72 demonstrates an enhanced corrosion protection by a nonelectrolytical multilayer coating with silicate top layer. After the same test duration no substrate corrosion can be found. Coatings for enhanced corrosion protection must provide a very dense structure and an additional electrical insulation. The ball-section-support geometry with relatively small ball section diameter dbs results in a cone-clamping with significant head frictional torCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 72 Corrosion of wheel bolts after severe testing with salt spraying and additionally daily wetting with phosphoric acid (pH ¼ 2, RIBE-test).

que, which avoids any self-loosening (for calculation of ball-section-head support, see Fig. 38). Figure 73 demonstrates the measured tightening behavior of a screw corresponding to the right side of Fig. 72. The diagram contains the tightening torque Ttot and preload Fp over the applied tightening angle n for a new bolt as fabricated. The bolt was tightened on steel surfaces. Normally, the bolt is tightened with a specification of 150 N m þ 20 N m. From the diagram, we can see that with this specification the bolt is utilized only to 50% of the possible tightening torque. The other 50% are reserves for wrong tightening or misuse as well as tightening on light metal surfaces (e.g. aluminum wheels). The friction coefficients mtot are calculated for different tightening angles—they show only a slightly change, but an increase of friction is obvious for large tightening angles—such a change of friction coefficient is typical for angular controlled tightening. Wheel bolts only can be tightened by torque control in practice because of unprofessional workers and light metal wheels, which would be damaged by the too-high preload of angular controlled tightening. I.

Fastening with Reduced Total Cost

As considered in Fig. 56, only the total cost is relevant for monetary assessment of a fastening system. One typical example is given in Fig. 74

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Figure 73 Tightening behavior of wheel bolt with multilayer coating for enhanced corrosion protection with integrated lubrication, measured data.

Figure 74

Thread rolling screw for reducing total cost of fastening system.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

which compares the main types of cost between metric screw for existing nut thread and thread rolling screw of the same nominal diameter M6. As a conclusion, thread rolling screws should always be used if the functional properties are sufficient (preload level, large thread engagement, no disassembly=repair by unprofessionals, limited number of retightenings). An example for significant deproliferation is shown in Fig. 75. The same thread rolling screw is used for (nut thread) components made of three materials: aluminum, magnesium, and plastics. This could be realized by a reduced thread angle a similar to Fig. 11, by varying the pilot diameter in the nut thread component from 4.7 mm down to 4.0 mm and by a special dry lubrication of the screw. If only low quality of the fastening system is required, one specified tightening torque can be used for the three cases (Ttot ¼ 3.8 þ 0.4 N m). Note that the thread engagement te is relatively small in this fastening system. Other practical aspects of total cost saving for designing threaded fastening systems are given in Table 15. In no case, can all aspects be realized for the same application. Therefore, the design engineer has the responsibility to set priorities. More information due to cost-optimization of fastening systems can be found in Ref. [66].

Figure 75

Thread rolling with same screw geometry in different materials.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Table 15 No. 1

2

Aspects of Cost Saving for Design of Threaded Fastening Systems Aspect

Explanation=Remark

No oversizing of screw; use of high screw strength, if a high contact pressure under head is possible Designing an easy and reliable assembly process (preassembled screws like in Fig. 44, thread rolling screws like in Fig. 74, suitable screw drive like in Fig. 36)

Gives smaller space requirements and in consequence smaller components

3

Use of overelastic tightening methods, whenever possible

4

Use of optimized high quality fastening elements with exact specification and low deviations in functional properties

5

Use of coarse geometric tolerances for fastening system at right place (e.g. through-hole diameter, length of screw, length of external thread, height of screw head, etc.) Design of clamped part and nut thread component as simple as possible

6

7

8

Use of synergy effects by design of standard classes of fastening systems Use of comprehensive design process after Fig. 32 including calculations and guidelines from this book chapter

Assembly process is very important for the total cost of a fastening system, so the assembly process should analyzed precisely (e.g. time required for pressembly=inserting of screws and washers, cost for additional lubrication, lifetime of bits) This is increasing the minimum preload significantly (see also Fig. 51) The design has to consider the worst case of properties, so low quality of screw leads to poor performance of fastening system or oversized components (see influences in Fig. 40 or 51) Makes production of screw and components only as precise as necessary

For example, no separate machining of screw head support (spotface of clamped part) for use of screw with locking teeth under head; use of rolling screws for ductile materials Deproliferation (minimization of number of different fastening elements) Gives short development period with reduced efforts for testing, modifications and repairing (Continued)

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Table 15

Continued

No.

Aspect

Explanation=Remark

9

Intensive and permanent cooperation between supplier and user of fastening elements and fastened components

10

Use of enhanced logistics to minimize overhead cost for management, delivery and transport of fastening elements

Most functional effects of fastening systems are based on the interaction between screw and component, so all responsible people must work together from the first development stage on to open up the potential for optimization—this aspect is very important for future For example, purchase of higher lot size reduces cost of transport and gives reserves for sudden needs, using electronic ordering systems to minimize managing cost

J.

Fastening Without Self-loosening

For many fastening systems, it is important that a self-loosening failure cannot happen. Figure 76 shows the characteristics of commonly used actions against self-loosening of threaded fastening systems. The diagram contains

Figure 76

Self-loosening of threaded fastening systems.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

results from vibration measurements with the well-known Junkers configuration (see sketch in Fig. 76 or Refs. [7,72]). The Junkers test procedure is performed with a very extensive loading in order to compare different fastening solutions. For this test, the screw is tightened up to a certain initial preload (here 40 kN). Then, a predefined transversal displacement x is applied and the preload-behavior over the number of cycles is recorded. A threaded fastening system without actions against self-loosening fails after a short number of cycles. In most cases, a system with serrated washers or cone washers fails in a short period of testing. Only three kinds of prevention are relevant for high transversal loading: (1) washers with optimized locking teeth on both sides, (2) using adhesives in thread contact zone, or (3) using a flange head screw with optimized locking teeth under head. The use of a ballsection-head support can be an action against self-loosening (compare Fig. 72). The self-loosening-behavior is strongly dependent on the entire fastening system, such as stiffness, tolerances, materials, tightening level, number of contact zones, level of loading. For a detailed assessment, each system must be evaluated individually. V.

LIMITED WARRANTY

All data are given with best knowledge and references. For design purpose always refer to referenced standards. Because of various influences on the behavior of a threaded fastening system, the author does not warranty the correctness of the results in using this chapter. VI.

APPENDIX A

A.

Notation

Variable

Unit

Explanation

d d1 d2 d3 d0

mm mm mm mm mm

Major diameter of external screw thread Minor diameter of external screw thread Pitch diameter of external screw thread Root diameter of external screw thread Relevant diameter for calculation of screw assembly (loaded diameter of screw with smallest cross-section; db or diameter of nominal stress area) Continued

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Appendix A

(Continued)

Variable

Unit

Explanation

D D1 D2 Deb

mm mm mm mm

Dsub

mm

Dp P

mm mm

H R Rnmax da Di

mm mm mm mm mm

dbs

mm

db dsh dh x l f Dl lsh lft

mm mm mm mm mm mm mm mm mm

te lc lp

mm mm mm

a

mm

s

mm

sd2

mm

Major diameter of internal nut thread Minor diameter of internal nut thread Pitch diameter of internal nut thread Effective mean diameter of bearing surface between screw head and clamped part Substituting diameter, which represents the resilience of clamped part dp by a tube of constant diameter Dsub Diameter of clamped part Pitch of thread (axial displacement of one flank for one rotation of 3608 around the screw axis) Height of fundamental triangle of thread profile Root radius of external thread profile Maximum root radius of internal thread profile Maximum support diameter of screw head Minimum support diameter of clearance hole, which is in contact with the screw head Ball section diameter for screw head with ball section geometry Diameter of screw body (unthreaded shank) Screw shank diameter unthreaded Diameter of clearance hole (through hole) Distance transversal to screw axis Length in direction of screw axis Axial deformation of threaded fastening system Change of screw length under tensile force Length of unthreaded screw shank Length of shank with free thread flanks under tensile loading Length of thread engagement Clamping length Plastification length (length of smallest cross-section within clamping length of a threaded fastening system) Length transversal to screw axis, which describes the distance between bending axis of clamped part and axis of external axial force Fax Length transversal to screw axis. which describes the distance between bending axis of clamped part and axis of through hole in clamped part Largest length of a screw drive in a plane transversal to screw axis (e.g., width across corners for hexagon drive) Continued

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Appendix A

(Continued)

Variable

Unit

fz

mm

A A0 As

mm2 mm2 mm2

Ah An Asub

mm2 mm2 mm2

Ifull

mm4

Ip

mm4

Wp

mm3

a b j g e

8 8 8 8 8 8

ds dh dsh dst det dp dst1 dst2 dpt1 dpt2

mm=N mm=N mm=N mm=N mm=N mm=N mm=N mm=N mm=N mm=N

Explanation Seating distance, which leads to preload reduction caused by roughness of technical surfaces in contact Area Values Area in general Circular area corresponding to d0 Nominal stress area for tensile loading of screw thread; As ¼ [0.5(d2 þ d3)]2p=4 for metric thread system Contact area at head support between bearing surfaces Nominal circle area from thread size Substituted area relevant for resilience of clamped part Moment of Inertia and Polar Section Modulus Moment of inertia for bending of clamped part and screw shank together, used for calculating of load factor under eccentric loading Moment of inertia for bending (clamped part), used for calculating of component separating under eccentric loading Polar section modulus. used for calculating of torsional stress of screw thread from thread torque T t ; Wp ¼ pd3=12 Angle Values Thread angle Flank angle (in most cases b ¼ a=2) Lead angle (pitch angle) Rotation angle resp. tightening angle Angle of cone section at countersunk head of screw Contact angle at screw drive flank Values of Axial Resilience Linear elastic axial resilience of entire screw Linear elastic axial resilience of screw head Linear elastic axial resilience of screw shank Linear elastic axial resilience of free thread Linear elastic axial resilience of engaged thread Linear elastic resilience of clamped part Elastic resilience of screw at temperature t1 Elastic resilience of screw at temperature t2 Elastic resilience of clamped part at temperature t1 Elastic resilience of clamped part at temperature t2 Continued

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Appendix A

(Continued)

Variable

Unit

t1 t2 DT as ap

8C 8C 8C K1 K1

F Fp DFp Fp0 Fps

kN kN kN kN kN

Faxcrit

kN

Fsa

kN

Ftangenial, Ft Faxial, Fax Fpnec Fthreadpermt1

kN kN kN kN

Fthreadpermt2

kN

Fheadpermt1

kN

Fheadpermt2

kN

Ftranspermt2 Fpamin Fpamax Fpomin Fpomax Fpanmin Fpanmax Fpymin Fpymax Fptmin Fptmax

kN kN kN kN kN kN kN kN kN kN kN

Explanation Temperature-related Values Temperature of tightening Temperature of operating Change of temperature (between tightening and operating) Linear thermal expansion coefficient of screw material Linear thermal expansion coefficient of clamped part material Force Values Force in general Preload acting in screw shank Change of preload (e.g. by thermal expansion or relaxation) Stable preload after tightening and sort time relaxation Separating preload for given eccentrical loading with axial force Fax Maximum axial force for given preload Fp0, before component separating occurs Additional axial force of screw under external axial force Fax Tangential force related to the screw axis Axial force related to the screw axis Necessary preload for safe working of bolted joint Permitted axial stripping force of nut thread at temperature t1 Permitted axial stripping force of nut thread at temperature t2 Permitted axial stripping force of screw head at temperature t1 Permitted axial stripping force of screw head at temperature t2 Permitted transversal force at temperature t2 Minimum preload after tightening of bolted joint Maximum preload after tightening of bolted joint Minimum preload of bolted joint for operating Maximum preload of bolted joint for operating Minimum preload for angular controlled tightening Maximum preload for angular controlled tightening Minimum preload for yield point controlled tightening Maximum preload for yield point controlled tightening Minimum preload for torque controlled tightening Maximum preload for torque controlled tightening Continued

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Appendix A

(Continued)

Variable

Unit

Fc Ft Fn

kN kN kN

Ttot Ttott Tt Th Ttotpermt1

Nm Nm Nm Nm Nm

Ts

Nm

sax seq

MPa MPa

sa sast2

MPa MPa

saspermt2

MPa

sasperm0 tmax pch pchmaxt1 pchmaxt2 pct

MPa MPa MPa MPa MPa MPa

pcc

MPa

Rmst1, Rmst2 Rmnt1, Rmnt2

MPa MPa

Rmpt1, Rmpt2 Rp0.2s

MPa MPa

Es Ep

MPa MPa

Explanation Circumferential force at screw drive flank Tangential part of Fc, tangential force Normal part of Fc Torque Values Total torque (torque applied on screw drive for assembly) Total torque for torque controlled tightening Thread torque during tightening Head frictional torque during tightening Maximum permitted total torque, which can be transmitted by the screw drive without problems during tightening Snug torque for angular controlled tightening Stress and Pressure Values Axial stress in screw shank One-dimensional equivalent stress from maximum distortion energy theory (vMises theory) for reducing combined stresses to one uniaxial stress value (e.g. reducing the combination of tensile- and shear stress in the screw shank to one value) Axial stress amplitude in general Axial stress amplitude of screw at temperature t2 modulated by dynamic operating force of bolted joint Permitted axial stress amplitude of screw at temperature t2 modulated by dynamic operating force of bolted joint Fatigue limit at room temperature (ISO 3800: sa) Maximum shear stress in screw shank Pressure in contact area Ah Maximum pressure in contact area Ah at temperature t1 Maximum pressure in contact area Ah at temperature t2 Pressure in helical contact area of thread engagement normal to loaded thread flanks Component contact pressure between clamped part and nut thread component Tensile strength of screw at temperature t1 resp. t2 Tensile strength of nut thread component at temperature t1 resp. t2 Tensile strength of clamped part at temperature t1 resp. t2 Proof stress with 0.2% plastic strain under conditions of tensile test Young’s modulus of screw material (modulus of elasticity) Young’s modulus of clamped part material (modulus of elasticity) Continued

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Appendix A

(Continued)

Variable

Unit

Explanation

Est1, Est2

MPa

Ept1, Ept2

MPa

mt mh mtot mcc

— — — —

Young’s modulus of screw material at temperature t1 resp. t2 Young’s modulus of clamped part material at temperature t1 resp. t2 Frictional Coefficients Thread frictional coefficient Head frictional coefficient Total frictional coefficient Frictional coefficient of component contact between clamped part and nut thread component Ratio Values and Numbers Load factor; ratio between external axial force of bolted joint and additional axial force in screw shank Inducing factor; defines, in which position the external axial force is applied to the fastening system; n ¼ 0–1 Number of transversal displacements for vibration testing Stress factor for relationship between sax and seq (based on von Mises theory of failure)

— n

—

nx ks

— —

Abbreviations FMEA SOP FEM PTFE MoS2 Me SCE x-axis y-axis

Failure modes and effects analysis Start of production Finite element method Poly tetra fluoro ethylene Molybdenum disulfide Chemical symbol for ‘metal’ Standard calomel electrode (reference potential for measurement of corrosion current) Abscissa Ordinate

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

B.

Conversion of Units

Length Area Volume Mass Force Torque Pressure=stress Temperature

Metric unit

English unit

To convert metric to english multiply by

To convert english to metric multiply by

mm ma mm2 m2 mm3 m3 g Nc Nm Nm MPa Nmm2 8C

in ftb in2 ft2 in3 ft3 lb lbf lbf ft lbf in KSId KSId 8F

0.039370 3.2808 0.001550 10.764 0.000061024 35.315 0.0022046 0.22481 0.7376 8.8508 0.145037 0.145037 8F ¼ (1.8 8C)þ 32

25.400 0.3048 645.16 0.092903 16387 0.028316 453.59 4.44822 1.3558 0.1130 6.89479 6.89479 8C ¼ (8F32)=1.8

a

1 m 1000 mm. 1 ft 12 in. c 1 N 9.81 gf. d 1 ksi 1000 lbfin2. b

ACKNOWLEDGEMENTS The author thanks Mr. H. Meier and Mr. T. Riehl for performing and evaluating a large number of investigations and testings, Mr. W. Thomala for valuable discussions, Dr. G. E. Totten, Dr. K. Funatani, Dr. L. Xie, and Mr. R. Johnson for engaged management of the editorial process, RIBE GmbH Schwabach for support with photographs and experimental results and finally my family for support with plenty of time during preparing the manuscript. REFERENCES 1. Askeland, D.R. The Science and Engineering of Materials, 3rd Ed.; Chapman and Hall: London, 1996. 2. ATF Inc., 3550 W. Pratt. Ave., Lincolnwood, IL 80712, USA. www.atfinc.com 3. Avallone, E.; Baumeister, T, III. Marks’ Standard Handbook for Mechanical Engineers, 10th Ed.; McGraw-Hill: New York, 1997. www.mcgraw-hill.com

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4. Bauer, C.O., Ed. Handbuch der Verbindungstechnik (german language). Hanser: Mu¨nchen, 1991. www.hanser.de 5. Beitz, W.; Ku¨ttner, K.H. Dubbel – Taschenbuch fu¨r den Maschinenbau; 17th Ed.; Springer: Berlin, 1990. www.springer.de 6. Bertalanffy, L.V. General System Theory; Penguin Press: London, 1971. 7. Bickford, J.H. An introduction to the Design and Behaviour of Bolted Joints; Series Mechanical Engineering; Marcel Dekker, New York: 1981; Vol 13. 8. Carvill, J. Mechanical Engineer’s Data Handbook. 1st Ed.; ButterworthHeinemann: Oxford, 1994. www.butterworth-heineman.co.uk 9. Dacromet=Dacral. Metal Coating International. 275 Industrial Parkway Chardon, Ohio 44024-1083, USA. www.dacral.com 10. Deutsches Institut fu¨r Normung: DIN 969:Verbindungselemente mit Gewinde – Schwingfestigkeitsversuch bei Axialbelastung. www.din.de 11. Deutsches Institut fu¨r Normung: DIN EN 10269: Sta¨hle und Nickellegierungen fu¨r Befestigungselemente fu¨r den Einsatz bei erho¨hten und=oder tiefen Temperaturen. www.din.de 12. Dow Corning Inc., 2704 West Pioneer Parkway, Arlington, TX 76013, USA. www.dow-corning.com 13. Ewald Do¨rken AG. Industriebeschichtungssysteme, Wetterstr. 58, D 58313 Herdecke, Germany. www.doerken.de 14. Frick, W. Gewindeeinsa¨tze—Systemprodukte fu¨r sichere Schraubenverbindungen, Verlag Moderne Industrie: Landsberg, 1999. www.mi-verlag.de 15. Friedrich, C. Elements made of aluminum for better fastening of light weight components. Workshop of Industrial Fasteners Institute, Aluminum Fastening Technology Seminar, Michigan State University, Management Education Center, Troy, Michigan, USA, May 9, 2001. www.industrial-fasteners.org 16. Friedrich, C. Fastening of Light Weight Components with Elements Made of Aluminum. SAE-Paper technical series no 2000-01-1118, SAE 2000 World Congress, Detroit, March 6–9, 2000. www.sae.org 17. Friedrich, C. Software for design of bolted joints. Abenberg, Germany 2003. www.screw-designer.de 18. Friedrich, C.; Thomala, W. Berechnung der drehwinkelgesteuerten Montage von Schraubenverbindungen. J. Materialwissenschaft und Werkstofftechnik 2000, 31, 6–17, Wiley-VCH: Weinheim, Germany. www.wiley-vch.de 19. Hoyle, D. Automotive Quality Systems Handbook; Butterworth-Heinemann: Oxford, 2000. www.butterworth-heinemann.co.uk 20. Hoyle, D. Automotive Systems Quality Handbook; Butterworth-Heinemann: Oxford, 2000. www.butterworth-heinemann.com 21. ICS Handbuch Automatische Schraubmontage; Mo¨nnig: Iserlohn, 1997. www.schraubenverband.de 22. International Organization for Standardization: ISO 10664: Hexalobular internal driving feature for bolts and screws. www.iso.ch 23. International Organization for Standardization: ISO 10683: Fasteners—nonelectrolytically applied zinc flake coatings. www.iso.ch 24. International Organization for Standardization: ISO 14588: Blind rivets— terminology and definitions. www.iso.ch

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25.

26. 27. 28. 29. 30.

31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41.

42. 43. 44.

45.

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