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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 76

Problems 77

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

Notes 184

References 185

Problems 186

12 Hardening Mechanisms in Metals 188

Introduction 188

Deformation of Polycrystals 188

Texture Strengthening 190

Crystal Structure 191

Grain Size 193

Strain-Hardening 194

Solid-Solution Strengthening 195

Dispersion Strengthening 196

Yield Points and Strain-Aging 199

Dynamic Strain-Aging 201

Combined Effects 202

Notes 206

References 206

Problems 206

13 Ductility and Fracture 210

Introduction 210

Ductile Fracture 212

Brittle Fracture 217

Impact Energy 220

Notes 224

References 224

Problems 225

14 Fracture Mechanics 227

Introduction 227

Theoretical Fracture Strength 227

Stress Concentration 229

Griffith Theory 230

Orowan Theory 231

Fracture Modes 231

Irwin’s Fracture Analysis 231

Plastic Zone Size 233

Thin Sheets 235

Temperature and Loading Rate 236

Metallurgical Variables 237

Fracture Mechanics in Design 237

Compact Tensile Specimens 239

Strain-Energy Release 240

The J-integral 241

Notes 242

References 243

Problems 243

Appendix Ⅰ 245

Size and Shape of the Plastic Zone at a Crack Tip 245

1 5 Viscoelasticity 247

Introduction 247

Rheological Models 247

Series Combination of a Spring and Dashpot 248

Parallel Combination of a Spring and Dashpot 249

Combined Parallel-Series Model 250

More Complex Models 251

Damping 251

Natural Decay 253

Elastic Modulus - Relaxed Versus Unrelaxed 254

Thermoelastic Effect 255

Snoek Effect in bcc Metals 256

Other Damping Mechanisms 257

References 258

Notes 258

Problems 259

16 Creep and Stress Rupture 262

Introduction 262

Creep Mechanisms 262

Temperature Dependence of Creep 266

Deformation Mechanism Maps 267

Cavitation 268

Rupture Versus Creep 269

Extrapolation Schemes 270

Alloys for High-Temperature Use 273

Notes 275

References 275

Problems 276

17 Fatigue 279

Introduction 279

Surface Observations 279

Nomenclature 281

S-N Curves 282

Effect of Mean Stress 283

The Palmgren-Miner Rule 285

Stress Concentration 286

Surfaces 288

Design Estimates 290

Metallurgical Variables 291

Strains to Failure 291

Crack Propagation 294

Cyclic Stress-Strain Behavior 296

Temperature and Cycling Rate Effects 297

Fatigue of Polymers 300

Fatigue Testing 302

Design Considerations 302

Summary 303

Notes 303

References 304

Problems 304

18 Residual Stresses 308

Introduction 308

Small-Scale Stresses 308

Bauschinger Effect 311

Nonuniform Cooling 312

Nonuniform Material 313

Stresses from Welding 313

Stresses from Mechanical Working 314

Consequences of Residual Stresses 316

Measurement of Residual Stresses 317

Relief of Residual Stresses 319

Notes 321

References 321

Problems 321

19 Ceramics and Glasses 324

Introduction 324

Elastic Properties 324

Slip Systems 325

Hardness 326

Weibull Analysis 326

Testing 329

Porosity 329

High-Temperature Behavior 331

Fracture Toughness 331

Toughening of Ceramics 334

Fatigue 335

Silicate Glasses 335

Strength of Glasses 338

Thermally Induced Stresses 339

Delayed Fracture 340

Glassy Metals 341

Notes 342

References 343

Problems 343

20 Polymers 345

Introduction 345

Elastic Behavior 345

Rubber Elasticity 350

Damping 353

Yielding 353

Effect of Strain Rate 356

Effect of Pressure 356

Crazing 361

Yielding of Fibers in Compression 363

Fracture 364

Deformation Mechanism Maps 366

Shape-Memory Effect 367

References 368

Notes 368

Problems 370

21 Composites 372

Introduction 372

Fiber-Reinforced Composites 372

Elastic Properties of Fiber-Reinforced Composites 372

Strength of Fiber-Reinforced Composites 376

Volume Fraction of Fibers 377

Orientation Dependence of Strength 378

Fiber Length 379

Failures with Discontinuous Fibers 381

Failure under Compression 382

Typical Properties 383

Particulate Composites 384

Brick-Wall Model 385

Lamellar Composites 387

Notes 388

References 389

Problems 389

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