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Mechanical Behavior of Materials 2nd ed - W. Hosford (Cambridge, 2010)
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Preface page xiii 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 13 Force and Moment Balances 14 Boundary Conditions 16 Note 17 Problems 17 2 Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Introduction 20 Isotropic Elasticity 20 Variation of Young’s Modulus 22 Isotropic Thermal Expansion 24 Elastic Anisotropy 25 Orientation Dependence of Elastic Response 27 Orientation Dependence in Cubic Crystals 28 Orientation Dependence in Noncubic Crystals 30 Orientation Dependence in Materials Other Than Single Crystals 31 Anisotropic Thermal Expansion 31 References 32 Notes 32 Problems 33 v vi Contents 3 Mechanical Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Introduction 36 Tensile Specimens 36 Stress–Strain Curves 37 Ductility 40 True Stress and Strain 41 The Bridgman Correction 43 Temperature Rise 43 Sheet Anisotropy 44 Measurement of Force and Strain 45 Axial Alignment 46 Special Problems 47 Compression Test 47 Plane–Strain Compression 50 Plane–Strain Tension 51 Biaxial Tension (Hydraulic Bulge Test) 51 Torsion Test 53 Bend Tests 54 Hardness Tests 56 Mutual Indentation Hardness 59 References 60 Notes 60 Problems 61 4 Strain Hardening of Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Introduction 65 Mathematical Approximations 65 Power Law Approximation 67 Necking 68 Work Per Volume 70 Localization of Strain at Defects 70 Notes 71 Problems 72 5 Plasticity Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Introduction 74 Yield Criteria 74 Tresca (maximum shear stress criterion) 75 Von Mises Criterion 76 Flow Rules 78 Principle of Normality 79 Effective Stress and Effective Strain 80 Other Isotropic Yield Criteria 82 Anisotropic Plasticity 84 Effect of Strain Hardening on the Yield Locus 86 References 87 Contents vii Notes 87 Problems 88 6 Strain Rate and Temperature Dependence of Flow Stress . . . . . . . . . . 92 Introduction 92 Strain Rate Dependence of Flow Stress 92 Superplasticity 95 Combined Strain and Strain Rate Effects 99 Strain Rate Sensitivity of bcc Metals 100 Temperature Dependence 103 Combined Temperature and Strain Rate Effects 103 Hot Working 108 References 109 Notes 109 Problems 110 7 Slip and Crystallographic Textures . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Introduction 113 Slip Systems 113 Schmid’s Law 113 Strains Produced by Slip 116 Strain Hardening of fcc Single Crystals 117 Tensile Deformation of fcc Crystals 118 Slip in bcc Crystals 120 Slip in hcp Crystals 121 Lattice Rotation in Tension 121 Lattice Rotation in Compression 123 Texture Formation in Polycrystals 124 Approximate Calculations of R Values 125 Deformation of Polycrystals 126 Texture Strengthening 127 Effects of Texture on Microstructure 128 References 132 Notes 132 Problems 133 8 Dislocation Geometry and Energy . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Introduction 137 Theoretical Strength of Crystals 137 The Nature of Dislocations 139 Burgers Vectors 141 Energy of a Screw Dislocation 142 Reactions between Parallel Dislocations and Frank’s Rule 144 Stress Fields around Dislocations 144 Forces on Dislocations 146 Partial Dislocations in fcc Crystals 147 Stacking Faults 149 viii Contents References 152 Notes 152 Problems 153 9 Dislocation Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 Introduction 155 Frank-Read Sources 155 Dislocation Pile-Ups 158 Cross-Slip 158 Dislocation Intersections 159 Climb 163 References 163 Note 163 Problems 164 10 Mechanical Twinning and Martenitic Shear . . . . . . . . . . . . . . . . . . . 166 Introduction 166 Formal Notation 167 Twinning Shear 167 Twinning in fcc Metals 169 Twinning in bcc Metals 169 Twinning in hcp Metals 171 Shapes of Twins 173 Mechanism of Twinning 175 Martensite Transformation 178 Shape Memory and Superelasticity 178 References 181 Note 181 Problems 181 11 Hardening Mechanisms in Metals . . . . . . . . . . . . . . . . . . . . . . . . . . 184 Introduction 184 Crystal Structure 184 Grain Size 184 Strain Hardening 186 Solid Solution Strengthening 187 Dispersion Strengthening 188 Yield Points and Strain Aging 191 Combined Effects 192 References 195 Notes 195 Problems 196 12 Discontinuous and Inhomogeneous Deformation . . . . . . . . . . . . . . . 199 Stick-Slip Phenomena 199 Dynamic Strain Aging 200 Other Causes of Serrated Stress–Strain Curves 205 Contents ix Strain Localization 205 Reference 206 Notes 206 Problems 206 13 Ductility and Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 Introduction 208 Ductile Fracture 210 Brittle Fracture 216 Impact Energy 218 References 221 Notes 221 Problems 223 14 Fracture Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 Introduction 225 Theoretical Fracture Strength 225 Stress Concentration 227 Griffith Theory 227 Orowan Theory 229 Fracture Modes 229 Irwin’s Fracture Analysis 229 Plastic Zone Size 231 Thin Sheets 233 Temperature and Loading Rate 234 Metallurgical Variables 235 Fracture Mechanics in Design 235 Compact Tensile Specimens 236 Strain–Energy Release 237 The J Integral 238 References 240 Notes 240 Problems 241 Appendix. Size and Shape of the Plastic Zone at the Crack Tip 243 15 Viscoelasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 Introduction 244 Rheological Models 244 Series Combination of Spring and Dashpot 245 Parallel Combination of Spring and Dashpot 246 Combined Series Parallel Model 246 More Complex Models 248 Damping 248 Natural Decay 249 Elastic Modulus – Relaxed versus Unrelaxed 250 Thermoelastic Effect 251 Snoek Effect in bcc Metals 253 x Contents Other Damping Mechanisms 254 References 255 Notes 255 Problems 256 16 Creep and Stress Rupture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 Introduction 259 Creep Mechanisms 259 Temperature Dependence of Creep 263 Deformation Mechanism Maps 264 Cavitation 265 Rupture versus Creep 266 Extrapolation Schemes 266 Alloys for High-Temperature Use 269 References 271 Notes 271 Problems 272 17 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 Introduction 275 Surface Observations 275 Nomenclature 276 S-N Curves 278 Effect of Mean Stress 279 The Palmgren-Miner Rule 281 Stress Concentration 282 Surfaces 284 Design Estimates 285 Metallurgical Variables 286 Strains to Failure 286 Crack Propagation 289 Cyclic Stress–Strain Behavior 292 Temperature and Cycling Rate Effects 292 Fatigue of Polymers 295 Fatigue Testing 297 Design Considerations 297 Summary 298 References 298 Notes 298 Problems 299 18 Residual Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 Introduction 302 Small-Scale Stresses 302 Bauschinger Effect 305 Nonuniform Cooling 306 Nonuniform Material 307 Contents xi Stresses from Welding 307 Stresses from Mechanical Working 308 Consequences of Residual Stresses 310 Measurement of Residual Stresses 311 Relief of Residual Stresses 313 References 314 Notes 314 Problems 315 19 Ceramics and Glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 Introduction 318 Elastic Properties 318 Slip Systems 319 Hardness 319 Weibull Analysis 321 Testing 322 Porosity 323 High-Temperature Behavior 324 Fracture Toughness 324 Toughening of Ceramics 326 Fatigue 329 Silicate Glasses 329 Strength of Glasses 332 Thermally Induced Stresses 333 Delayed Fracture 334 Glassy Metals 334 References 336 Notes 336 Problems 337 20 Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 Introduction 339 Elastic Behavior 339 Rubber Elasticity 344 Damping 345 Yielding 347 Effect of Strain Rate 348 Effect of Pressure 350 Crazing 354 Yielding of Fibers in Compression 356 Fracture 356 Deformation Mechanism Maps 357 Shape-Memory Effect 357 References 360 Notes 360 Problems 361 xii Contents 21 Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 Introduction 363 Fiber-Reinforced Composites 363 Elastic Properties of Fiber-Reinforced Composites 363 Strength of Fiber-Reinforced Composites 367 Volume Fraction of Fibers 368 Orientation Dependence of Strength 369 Fiber Length 369 Failure with Discontinuous Fibers 372 Failure under Compression 373 Typical Properties 374 Particulate Composites 375 Brick Wall Model 376 Lamellar Composites 378 Morphology of Foams 379 Mechanical Properties of Foams 379 Metal Foams 379 Flexible Foams – Open Cell 381 Flexible Foams – Closed Cell 381 References 381 Notes 382 Problems 382 22 Mechanical Working . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385 Introduction 385 Bulk-Forming Energy Balance 385 Deformation Zone Geometry 389 Friction in Bulk Forming 392 Formability 393 Deep Drawing 394 Stamping 396 References 401 Notes 401 Problems 402 APPENDIX I: Miller Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 APPENDIX II: Stereographic Representation of Orientations . . . . . . . . . . . . 412 Index 415 |
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