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METAL FORMING, THIRD EDITION



This book is designed to help the engineer understand the principles of metal forming and analyze forming problems – both the mechanics of forming processes and how the properties of metals interact with the processes. The first third of the book is devoted to fundamentals of mechanics and materials; the middle to analyses of bulk forming processes such as drawing, extrusion, and rolling; and the last third covers sheet forming processes. In this new third edition, an entire chapter has been devoted to forming limit diagrams; another to various aspects of stamping, including the use of tailor-welded blanks; and another to other sheet forming operations, including hydroforming of tubes. Sheet testing is covered in a later chapter. Coverage of sheet metal properties has been expanded to include new materials and more on aluminum alloys. Interesting end-of-chapter notes and references have been added throughout. More than 200 end-of-chapter problems are also included.

William F. Hosford is a Professor Emeritus of Materials Science and Engineering at the University of Michigan. Professor Hosford is the author of more than 80 technical articles and a number of books, including the leading selling Mechanics of Crystals and Textured Polycrystals, Physical Metallurgy, Mechanical Behavior of Materials, and Materials Science: An Intermediate Text.

Robert M. Caddell was a professor of mechanical engineering at the University of Michigan, Ann Arbor.





METAL FORMING

   Mechanics and Metallurgy

   THIRD EDITION



   WILLIAM F. HOSFORD
   University of Michigan, Ann Arbor

   ROBERT M. CADDELL
   Late of University of Michigan, Ann Arbor





CAMBRIDGE UNIVERSITY PRESS
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Cambridge University Press
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www.cambridge.org
Information on this title: www.cambridge.org/9780521881210

© William F. Hosford 2007

This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without
the written permission of Cambridge University Press.

First published 2007

Printed in the United States of America

A catalog record for this publication is available from the British Library.

Library of Congress Cataloging in Publication Data

Hosford, William F.
Metal forming : mechanics and metallurgy / William F. Hosford, Robert M. Caddell. – 3rd ed.
   p. cm.
Includes bibliographical references and index.
ISBN: 978-0-521-88121-0 (hardback)
1. Metal-work. 2. Deformations (Mechanics) I. Caddell, Robert M. II. Title.
TS213.H66  2007
671.3–dc22      2007008558

ISBN 978-0-521-88121-0 hardback

Cambridge University Press has no responsibility for
the persistence or accuracy of URLs for external or
third-party Internet Web sites referred to in this publication
and does not guarantee that any content on such
Web sites is, or will remain, accurate or appropriate.





Contents



Preface to Third Edition page xiii
1   Stress and Strain 1
  1.1  Stress 1
  1.2  Stress transformation 2
  1.3  Principal stresses 4
  1.4  Mohr’s circle equations 5
  1.5  Strain 7
  1.6  Small strains 9
  1.7  The strain tensor 10
  1.8  Isotropic elasticity 10
  1.9  Strain energy 11
  1.10  Force and moment balances 12
  1.11  Boundary conditions 13
  NOTES OF INTEREST 14
  REFERENCES 15
  APPENDIX – EQUILIBRIUM EQUATIONS 15
  PROBLEMS 15
2   Plasticity 17
  2.1  Yield criteria 17
  2.2  Tresca criterion 18
  2.3  Von Mises criterion 20
  2.4  Plastic work 21
  2.5  Effective stress 22
  2.6  Effective strain 22
  2.7  Flow rules 23
  2.8  Normality principle 25
  2.9  Derivation of the von Mises effective strain 26
  NOTES OF INTEREST 27
  REFERENCES 28
  PROBLEMS 28
3   Strain Hardening 30
  3.1  The tension test 30
  3.2  Elastic–plastic transition 32
  3.3  Engineering vs. true stress and strain 32
  3.4  A power-law expression 34
  3.5  Other strain hardening approximations 36
  3.6  Behavior during necking 36
  3.7  Compression testing 38
  3.8  Bulge testing 38
  3.9  Plane-strain compression 39
  3.10  Torsion testing 40
  NOTE OF INTEREST 40
  REFERENCES 40
  PROBLEMS 41
4   Instability 43
  4.1  Uniaxial tension 43
  4.2  Effect of inhomogeneities 44
  4.3  Balanced biaxial tension 45
  4.4  Pressurized thin-wall sphere 47
  4.5  Significance of instability 48
  NOTE OF INTEREST 49
  REFERENCES 49
  PROBLEMS 49
5   Temperature and Strain-Rate Dependence 52
  5.1  Strain rate 52
  5.2  Superplasticity 55
  5.3  Effect of inhomogeneities 58
  5.4  Combined strain and strain-rate effects 62
  5.5  Alternative description of strain-rate dependence 63
  5.6  Temperature dependence of flow stress 65
  5.7  Deformation mechanism maps 69
  5.8  Hot working 69
  5.9  Temperature rise during deformation 71
  NOTES OF INTEREST 72
  REFERENCES 73
  PROBLEMS 73
6   Work Balance 76
  6.1  Ideal work 76
  6.2  Extrusion and drawing 77
  6.3  Deformation efficiency 78
  6.4  Maximum drawing reduction 79
  6.5  Effects of die angle and reduction 80
  6.6  Swaging 81
  REFERENCES 82
  PROBLEMS 82
7   Slab Analysis and Friction 85
  7.1  Sheet drawing 85
  7.2  Wire and rod drawing 87
  7.3  Friction in plane-strain compression 88
  7.4  Sticking friction 90
  7.5  Mixed sticking–sliding conditions 90
  7.6  Constant shear stress interface 91
  7.7  Axially symmetric compression 92
  7.8  Sand-pile analogy 93
  7.9  Flat rolling 93
  7.10  Roll flattening 95
  7.11  Roll bending 99
  7.12  Coining 101
  7.13  Dry friction 102
  7.14  Lubricants 102
  7.15  Experimental findings 103
  7.16  Ring friction test 105
  REFERENCES 106
  PROBLEMS 106
8   Upper-Bound Analysis 110
  8.1  Upper bounds 110
  8.2  Energy dissipation on plane of shear 111
  8.3  Plane-strain frictionless extrusion 112
  8.4  Plane-strain frictionless indentation 116
  8.5  Plane-strain compression 116
  8.6  Another approach to upper bounds 119
  8.7  Combined upper-bound analysis 120
  8.8  Plane-strain drawing 121
  8.9  Axisymmetric drawing 121
  REFERENCES 123
  PROBLEMS 123
9   Slip-Line Field Analysis 128
  9.1  Introduction 128
  9.2  Governing stress equations 128
  9.3  Boundary conditions 132
  9.4  Plane-strain indentation 133
  9.5  Hodographs for slip-line fields 134
  9.6  Plane-strain extrusion 135
  9.7  Energy dissipation in a slip-line field 137
  9.8  Metal distortion 137
  9.9  Indentation of thick slabs 138
  9.10  Plane-strain drawing 142
  9.11  Constant shear–stress interfaces 146
  9.12  Pipe formation 147
  NOTES OF INTEREST 148
  REFERENCES 150
  APPENDIX 150
  PROBLEMS 153
10   Deformation-Zone Geometry 163
  10.1  The Δ parameter 163
  10.2  Friction 164
  10.3  Redundant deformation 164
  10.4  Inhomogeneity 166
  10.5  Internal damage 171
  10.6  Residual stresses 175
  10.7  Comparison of plane-strain and axisymmetric deformation 178
  NOTE OF INTEREST 180
  REFERENCES 180
  PROBLEMS 180
11   Formability 182
  11.1  Ductility 182
  11.2  Metallurgy 182
  11.3  Ductile fracture 186
  11.4  Hydrostatic stress 187
  11.5  Bulk formability tests 191
  11.6  Formability in hot working 192
  NOTE OF INTEREST 193
  REFERENCES 193
  PROBLEMS 193
12   Bending 195
  12.1  Sheet bending 195
  12.2  Bending with superimposed tension 198
  12.3  Neutral axis shift 200
  12.4  Bendability 201
  12.5  Shape bending 202
  12.6  Forming limits in bending 203
  NOTE OF INTEREST 203
  REFERENCES 205
  PROBLEMS 205
13   Plastic Anisotropy 207
  13.1  Crystallographic basis 207
  13.2  Measurement of R 209
  13.3  Hill’s anisotropic plasticity theory 209
  13.4  Special cases of Hill’s yield criterion 211
  13.5  Nonquadratic yield criteria 212
  13.6  Calculation of anisotropy from crystallographic considerations 215
  NOTE OF INTEREST 216
  REFERENCES 216
  PROBLEMS 216
14   Cupping, Redrawing, and Ironing 220
  14.1  Cup drawing 220
  14.2  Anisotropic effects in drawing 223
  14.3  Effects of strain hardening in drawing 224
  14.4  Analysis of assumptions 225
  14.5  Effects of tooling on cup drawing 227
  14.6  Earing 228
  14.7  Redrawing 230
  14.8  Ironing 231
  14.9  Residual stresses 233
  NOTES OF INTEREST 234
  REFERENCES 234
  PROBLEMS 234
15   Forming Limit Diagrams 237
  15.1  Localized necking 237
  15.2  Forming limit diagrams 241
  15.3  Experimental determination of FLDs 242
  15.4  Calculation of forming limit diagrams 244
  15.5  Factors affecting forming limits 247
  15.6  Changing strain paths 251
  15.7  Stress-based forming limits 253
  NOTE OF INTEREST 253
  REFERENCES 253
  PROBLEMS 253
16   Stamping 255
  16.1  Stamping 255
  16.2  Draw beads 255
  16.3  Strain distribution 257
  16.4  Loose metal and wrinkling 258
  16.5  Flanging 259
  16.6  Springback 260
  16.7  Strain signatures 261
  16.8  Tailor-welded blanks 261
  16.9  Die design 262
  16.10  Toughness and sheet tearing 265
  16.11  General observations 267
  NOTES OF INTEREST 267
  REFERENCES 268
  PROBLEMS 268
17   Other Sheet-Forming Operations 270
  17.1  Roll forming 270
  17.2  Spinning 271
  17.3  Hydroforming of tubes 272
  17.4  Free expansion of tubes 272
  17.5  Hydroforming into square cross section 274
  17.6  Bent sections 276
  17.7  Shearing 276
  REFERENCES 277
  PROBLEMS 277
18   Formability Tests 279
  18.1  Cupping tests 279
  18.2  LDH test 281
  18.3  Post-uniform elongation 282
  18.4  OSU formability test 282
  18.5  Hole expansion 283
  18.6  Hydraulic bulge test 284
  18.7  Duncan friction test 285
  REFERENCES 286
  PROBLEMS 286
19   Sheet Metal Properties 289
  19.1  Introduction 289
  19.2  Surface appearance 290
  19.3  Strain aging 290
  19.4  Aluminum-killed steels 295
  19.5  Interstitial-free steels 295
  19.6  HSLA steels 295
  19.7  Dual-phase and complex-phase steels 296
  19.8  Transformation-induced plasticity (TRIP) steels 296
  19.9  Martensitic steels 297
  19.10  Trends 297
  19.11  Special sheet steels 298
  19.12  Surface treatment 298
  19.13  Stainless steels 299
  19.14  Aluminum alloys 300
  19.15  Copper and brass 302
  19.16  Hexagonal close-packed metals 303
  19.17  Tooling 305
  19.18  Product uniformity 305
  NOTES OF INTEREST 306
  REFERENCES 306
  PROBLEMS 306
Index 309




Preface to Third Edition



My coauthor Robert Caddell died in 1990. I have greatly missed interacting with him.

   The biggest changes from the second edition are an enlargement and reorganization of the last third of the book, which deals with sheet metal forming. Changes have been made to the chapters on bending, plastic anisotropy, and cup drawing. An entire chapter has been devoted to forming limit diagrams. There is one chapter on various aspects of stampings, including the use of tailor-welded blanks, and another on other sheet-forming operations, including hydroforming of tubes. Sheet testing is covered in a separate chapter. The chapter on sheet metal properties has been expanded to include newer materials and more depth on aluminum alloys.

   In addition, some changes have been made to the chapter on strain-rate sensitivity. A treatment of friction and lubrication has been added. A short treatment of swaging has been added. End-of-chapter notes have been added for interest and additional end-of-chapter references have been added.

   No attempt has been made in this book to introduce numerical methods such as finite element analyses. The book Metal Forming Analysis by R. H. Wagoner and J. L. Chenot (Cambridge University Press, 2001) covers the latest numerical techniques. We feel that one should have a thorough understanding of a process before attempting numerical techniques. It is vital to understand what constitutive relations are imbedded in a program before using it. For example, the use of Hill’s 1948 anisotropic yield criterion can lead to significant errors.

   Joining techniques such as laser welding and friction welding are not covered.

   I wish to acknowledge the membership in the North American Deep Drawing Group from which I have learned much about sheet metal forming. Particular thanks are given to Alejandro Graf of ALCAN, Robert Wagoner of the Ohio State University, John Duncan of the University of Auckland, Thomas Stoughton and David Meuleman of General Motors, and Edmund Herman of Creative Concepts.


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