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Mechanical Behavior of Materials
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Mechanical Behavior of Materials WILLIAM F. HOSFORD University of Michigan This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. - --- - --- Cambridge University Press has no responsibility for the persistence or accuracy of s for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Published in the United States of America by Cambridge University Press, New York www.cambridge.org Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page xv Note to the Reader . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. xix 1 Stress and Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1 Introduction 1 Stress 2 Sign Convention 3 Transformation of Axes 4 Principal Stresses 6 Mohr’s Stress Circles 6 Strains 9 Small Strains 11 Transformation of Axes 12 Mohr’s Strain Circles 14 Force and Moment Balances 15 Boundary Conditions 16 Note 17 Problems 18 2 Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Introduction 21 Isotropic Elasticity 21 Variation of Young’s Modulus 24 Isotropic Thermal Expansion 26 Anisotropic Elasticity 27 Orientation Dependence of Elastic Response 29 Orientation Dependence in Cubic Crystals 31 Orientation Dependence in Noncubic Crystals 32 Orientation Dependence in Materials Other Than Single Crystals 34 Anisotropic Thermal Expansion 34 Notes 35 References 36 Problems 36 3 Tensile Testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Introduction 39 Tensile Specimens 39 Stress–Strain Curves 40 Ductility 43 True Stress and Strain 44 The Bridgman Correction 45 Temperature Rise 47 Sheet Anisotropy 47 Measurement of Force and Strain 48 Axial Alignment 49 Special Problems 49 Notes 50 References 51 Problems 51 4 Other Tests of Plastic Behavior. . . . . . . . . . . . . . . . . . . . . . . . . . 53 Introduction 53 Compression Test 53 Plane-Strain Compression 56 Plane-Strain Tension 57 Biaxial Tension (Hydraulic Bulge Test) 57 Torsion Test 59 Bend Tests 61 Hardness Tests 62 Mutual Indentation Hardness 66 Note 67 References 67 Problems 67 5 Strain-Hardening of Metals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Introduction 70 Mathematical Approximations 70 Power-Law Approximation 72 Necking 73 Work per Volume 75 Localization of Strain at Defects 75 Notes 6 Plasticity Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Introduction 80 Yield Criteria 80 Tresca Maximum Shear Stress Criterion 81 Von Mises Criterion 82 Flow Rules 84 Principle of Normality 85 Effective Stress and Effective Strain 86 Other Isotropic Yield Criteria 89 Anisotropic Plasticity 90 Effect of Strain-Hardening on the Yield Locus 93 Notes 93 References 94 Problems 94 7 Strain-Rate and Temperature Dependence of Flow Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Introduction 99 Strain-Rate Dependence of Flow Stress 99 Superplasticity 102 Combined Strain and Strain-Rate Effects 106 Strain-Rate Sensitivity of bcc Metals 107 Temperature Dependence 110 Combined Temperature and Strain-Rate Effects 111 Hot Working 115 Notes 116 References 116 Problems 116 8 Slip. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 Introduction 120 Slip Systems 120 Schmid’s Law 121 Strains Produced by Slip 123 Strain-Hardening of fcc Single Crystals 125 Tensile Deformation of fcc Crystals 126 Slip in bcc Crystals 128 Slip in hcp Crystals 128 Lattice Rotation in Tension 129 Lattice Rotation in Compression 131 Texture Formation in Polycrystals 132 Approximate Calculation of R-Values 133 Notes 134 References 135 Problems 135 9 Dislocation Geometry and Energy . . . . . . . . . . . . . . . . . . . . . 139 Introduction 139 Theoretical Strength of Crystals 139 The Nature of Dislocations 141 Burgers Vectors 142 Energy of a Screw Dislocation 144 Reactions between Parallel Dislocations and Frank’s Rule 146 Stress Fields around Dislocations 147 Forces on Dislocations 149 Partial Dislocations in fcc Crystals 150 Stacking Faults 151 Notes 154 References 154 Problems 156 10 Dislocation Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 Introduction 158 Frank–Read Sources 158 Dislocation Pile-Ups 161 Cross-Slip 161 Dislocation Intersections 163 Climb 166 Notes 166 References 167 Problems 167 11 Mechanical Twinning and Martensitic Shear . . . . . . . . . .. 170 Introduction 171 Formal Notation 171 Twinning Shear 172 Twinning in fcc Metals 173 Twinning in bcc Metals 173 Twinning in hcp Metals 175 Shapes of Twins 178 Mechanism of Twinning 179 Martensite Transformation 182 Shape Memory and Superelasticity 183 ... 22 Mechanical Working . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392 Introduction 392 Bulk-Forming Energy Balance 392 Deformation Zone Geometry 396 Friction in Bulk Forming 399 Formability 400 Deep Drawing 401 Stamping 403 Notes 407 References 409 Problems 409 Appendix A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 Appendix B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421  mechanical behavior of material.png |
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