Dislocation based fracture mechanics

$Cover image for Dislocation based fracture mechanics$

Title:

Personal Author:

Weertman, Johannes

Publication Information:

Singapore : World Scientific, 1996

ISBN:

9789810226206

Subject Term:

Fracture mechanics

Dislocations in crystals

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Summary

Author Notes

Johannes (Hans) Weertman is Walter P Murphy Professor of Materials Science and Engineering in the Department of Materials Science and Engineering at Northwestern University

Preface	p. vii
Selected Symbols List	p. xxii
Chapter 1 Griffith-Inglis Crack & Zener-Stroh-Koehler Crack	p. 1
1.1 Griffith-Inglis Crack	p. 2
1.2 Stress Fields of Griffith-Inglis Cracks	p. 5
1.2.1 Mode I Stress Field	p. 6
1.2.2 Mode II Stress Field	p. 7
1.2.3 Mode III Stress Field	p. 14
1.2.4 Mode I Near Tip Stress Field	p. 14
1.2.5 Mode II Near Tip Stress Field	p. 16
1.2.6 Mode III Near Tip Stress Field	p. 16
1.3 Elastic Displacement Fields of Griffith-Inglis Cracks	p. 17
1.3.1 Mode I Near Tip Elastic Displacement Field	p. 18
1.3.2 Mode II Near Tip Elastic Displacement Field	p. 18
1.3.3 Mode III Near Tip Elastic Displacement Field	p. 18
1.4 Fracture Stress of Griffith-Inglis Crack	p. 18
1.4.1 Energy Method	p. 19
1.4.2 Critical Crack Tip Displacement Method	p. 22
1.4.3 Dislocation Method	p. 23
1.4.4 Stress Intensity Factor	p. 24
1.4.5 J Integral	p. 25
1.4.6 Short Griffith-Inglis Crack	p. 26
1.5 Zener-Stroh-Koehler Crack	p. 27
1.6 Stress Fields of Zener-Stroh-Koehler Cracks	p. 29
1.6.1 Mode I Near Tip Stress Field	p. 30
1.6.2 Mode II Near Tip Stress Field	p. 34
1.6.3 Mode III Near Tip Stress Field	p. 35
1.7 Elastic Displacement Fields of Zener-Stroh-Koehler Cracks	p. 35
1.7.1 Mode I Near Tip Elastic Displacement Field	p. 36
1.7.2 Mode II Near Tip Elastic Displacement Field	p. 36
1.7.3 Mode III Near Tip Elastic Displacement Field	p. 36
1.8 Equilibrium Length of Zener-Stroh-Koehler Crack	p. 37
1.8.1 Short Zener-Stroh-Koehler Crack	p. 38
1.9 Equilibrium Length: ZSK Crack Subjected to an Applied Load	p. 38
1.10 Energy of ZSK Crack Under an Applied Load	p. 39
Chapter 1 Homework	p. 42
Chapter 2 Dislocation Mechanics	p. 45
2.1 Dislocation Stress Fields: Rectangular Coordinates	p. 45
2.1.1 Glide Edge Dislocation	p. 45
2.1.2 Climb Edge Dislocation	p. 46
2.1.3 Screw Dislocation	p. 47
2.1.4 Elastic Strain and Rotation Fields	p. 48
2.2 Dislocation Stress Fields: Cylindrical Coordinates	p. 48
2.2.1 Glide Edge Dislocation	p. 48
2.2.2 Climb Edge Dislocation	p. 49
2.2.3 Screw Dislocation	p. 49
2.3 Crack Plane Traction and Non-Traction Stress	p. 49
2.3.1 Crack Plane Traction Arising from a Crack Plane Dislocation Distribution	p. 49
2.3.2 Crack Plane Non-Traction Arising from a Crack Plane Dislocation Distribution	p. 50
2.4 Force on a Dislocation	p. 53
2.4.1 Extrinsic Resistance (Friction) Stress [tau subscript F] to Dislocation Motion	p. 54
2.4.2 Intrinsic Resistance (Friction) Stress [tau subscript i] to Dislocation Motion	p. 55
2.5 Dislocations and the J Integral	p. 55
2.6 Dislocation Crack Extension and Deflection Forces	p. 58
2.6.1 Dislocation Crack Extension Force	p. 58
2.6.2 Dislocation Crack Deflection Force	p. 61
2.7 Dislocations Density Fields of Non-Redundant Dislocations	p. 65
2.7.1 Antiplane Strain	p. 66
2.7.2 Plane Strain	p. 67
2.7.3 Dislocation Density from Plastic Strain	p. 70
2.7.3.1 Antiplane Strain	p. 70
2.7.3.2 Antiplane Strain, Curvilinear Coordinates	p. 71
2.7.3.3 Plane Strain	p. 74
2.7.3.4 Plane Strain, Curvilinear Coordinates	p. 78
2.7.3.5 Incremental Form	p. 80
2.7.3.6 Strain Gradient Form Dislocation Density Field in Plane Strain	p. 81
2.8 Electrical Analogy	p. 81
2.8.1 Dislocation Analogue of Point Electrical Charge	p. 84
2.9 Dislocations, the Source of Internal Stresses	p. 86
2.9.1 General Dislocation Density Field	p. 87
2.9.2 Lattice Curvature	p. 89
2.10 Edge Dislocation Stress-Strain-Rotation Field in Plane Stress	p. 89
2.10.1 Glide Edge Dislocation	p. 90
2.10.2 Climb Edge Dislocation	p. 90
2.10.3 Mode I Crack and Mode II Crack in an Elastic Foil	p. 91
2.10.4 Dislocation Crack Extension Force & Fracture Stress in Plane Stress	p. 92
2.10.5 Screw Dislocation	p. 92
2.11 Dislocations Near and on an Interface	p. 93
2.11.1 Screw Dislocation	p. 93
2.11.2 Glide Edge Dislocation	p. 93
2.11.3 Climb Edge Dislocation	p. 94
2.11.4 Comninou-Dundurs Equation	p. 94
Chapter 2 Appendix: Non-Traction Stress Jump Without(?) a Planar Dislocation Distribution	p. 96
Test of the Rule	p. 99
Chapter 2 Homework	p. 99
Chapter 3 Hilbert Transforms & Muskhelishvili Equations	p. 103
3.1 Hilbert Transforms	p. 103
3.2 Muskhelishvili Equations	p. 106
3.2.1 Determination of Muskhelishvili Equations for a Single Zone	p. 107
3.3 Determination of the Distance c to the Outer Crack Boundary	p. 110
3.4 Summary of Equations for a Single Dislocation Zone	p. 113
3.5 Solution When the Stress is Infinite at the Crack Tips	p. 114
3.6 Non-Centered Coordinate System	p. 116
3.7 Multiple Dislocation Zones	p. 117
3.7.1 Double Zone	p. 117
3.7.2 Infinite Crack Tip Stress for Symmetric Double Zone	p. 121
3.7.3 Symmetric Triple Zone	p. 122
3.8 Plane Stress	p. 123
3.9 Resolution of a Hilbert Transform Paradox with Ghost Dislocation Distributions	p. 123
Table 3.1	p. 127
Chapter 3 Homework	p. 131
Chapter 4 Bilby-Cottrell-Swinden-Dugdale (BCSD) Crack	p. 133
4.1 Bilby-Cottrell-Swinden-Dugdale (BCSD)	p. 133
4.1.1 Griffith-Inglis Crack Limit	p. 137
4.1.2 Crack Extension force of BCSD Crack	p. 137
4.1.3 Crack Tip Shielding of BCSD Crack	p. 138
4.1.4 Mixed Mode I & II BCSD Crack	p. 138
4.1.4.1 Crack Extension Force	p. 138
4.1.4.2 Crack Deflection Force	p. 138
4.2 BCSD Type Zener-Stroh-Koehler Crack	p. 139
4.2.1 Classical Limit of Zener Stroh-Koehler Crack	p. 141
4.2.2 Stressed Zener-Stroh-Koehler Crack	p. 142
4.3 Stress Fields of BCSD Cracks	p. 143
4.3.1 Mode III BCSD Crack	p. 144
4.3.2 Mode II BCSD Crack	p. 146
4.3.3 Mode I BCSD Crack	p. 147
4.4 Asymmetric Crack Solutions	p. 147
4.5 Double Slip Plane Crack Model	p. 150
4.5.1 Stationary Crack	p. 151
4.5.2 Crack Tip Stress Intensity Factor	p. 154
4.5.2.1 Short Short-Crack	p. 156
4.5.2.2 Dislocation Crack Tip Shielding and Antishielding	p. 157
4.5.3 Growing Crack	p. 158
4.5.3.1 R-Curve	p. 159
Chapter 4 Homework	p. 160
Chapter 5 Crack Tip Shielding and Antishielding by Dislocations	p. 163
5.1 Dislocation Crack Tip Shielding and Antishielding	p. 165
5.1.1 Screw Dislocations	p. 166
5.1.2 Glide Edge Dislocations	p. 167
5.1.3 Climb Edge Dislocations	p. 167
5.1.4 Stress Intensity Factor L for an Individual Dislocation	p. 168
5.1.5 Near Tip	p. 168
5.1.5.1 Screw Dislocation	p. 168
5.1.5.2 Glide Edge Dislocation	p. 168
5.1.5.3 Climb Edge Dislocation	p. 168
5.1.6 Far Crack	p. 169
5.1.6.1 Screw Dislocation	p. 169
5.1.6.2 Glide Edge Dislocation	p. 169
5.1.6.3 Climb Edge Dislocation	p. 169
5.1.7 Near Tip Radial Edge Dislocation	p. 170
5.1.8 Near Tip Azimuthal Edge Dislocation	p. 170
5.1.9 Comparison of L with Stress Fields of Griffith-Inglis and Zener-Stroh-Koehler Cracks	p. 173
5.1.10 Placing a Discrete Dislocation within the Crack	p. 174
5.2 Induced Crack Plane Dislocation Distribution B(x)	p. 174
5.2.1 Screw Dislocation Induced	p. 174
5.2.2 Glide Edge Dislocation Induced	p. 176
5.2.3 Climb Edge Dislocation Induced	p. 177
5.2.4 Near Tip	p. 177
5.2.4.1 Screw Dislocation Induced	p. 177
5.2.4.2 Glide Edge Dislocation Induced	p. 178
5.2.4.3 Climb Edge Dislocation Induced	p. 178
5.2.5 Near Tip Radial Edge Dislocation Induced	p. 178
5.2.6 Near Tip Azimuthal Edge Dislocation Induced	p. 179
5.3 Stress on Crack Plane Ahead of Crack Tip	p. 179
5.3.1 Screw Dislocation	p. 180
5.3.2 Glide Edge Dislocation	p. 180
5.3.3 Climb Edge Dislocation	p. 180
5.3.4 Near Tip	p. 181
5.3.5 Near Tip Crack Plane Dislocation arising from Near Tip Dislocation	p. 182
5.4 Impurity Atom Crack Tip Shielding and Antishielding	p. 184
5.4.1 Near Tip	p. 185
5.4.2 Far Crack	p. 186
5.5 Microcrack Shielding and Antishielding	p. 187
5.5.1 Dislocation Dipoles	p. 189
5.5.1.1 Horizontal Glide Edge Dislocation Dipole	p. 189
5.5.1.2 Vertical Glide Edge Dislocation Dipole	p. 190
5.5.1.3 Horizontal Climb Edge Dislocation Dipole	p. 190
5.5.1.4 Vertical Climb Edge Dislocation Dipole	p. 191
5.5.1.5 Horizontal Screw Dislocation Dipole	p. 191
5.5.1.6 Vertical Screw Dislocation Dipole	p. 191
5.5.2 Near Tip Stress Intensity Factors	p. 191
5.5.2.1 Horizontal Glide Edge Dislocation Dipole	p. 192
5.5.2.2 Vertical Glide Edge Dislocation Dipole	p. 192
5.5.2.3 Horizontal Climb Edge Dislocation Dipole	p. 192
5.5.2.4 Vertical Climb Edge Dislocation Dipole	p. 192
5.5.2.5 Horizontal Screw Dislocation Dipole	p. 192
5.5.2.6 Vertical Screw Dislocation Dipole	p. 193
5.6 Crack Tip Blunting by Dislocation Emission	p. 193
5.6.1 Rice-Thomson Model	p. 193
5.6.2 Model Based on Muskhelishvili Type Analysis	p. 195
5.6.3 Crack Tip Blunting	p. 198
Chapter 5 Homework	p. 199
Chapter 6 Mode III Crack in an Elastic-Plastic Solid	p. 201
6.1 Mode III Crack in an Elastic Perfectly Plastic Solid	p. 201
6.1.1 Stress Field	p. 202
6.1.2 Strain Field	p. 206
6.1.3 Dislocation Crack Extension Force and the Plastic Zone Size	p. 207
6.1.4 Crack Tip Shielding	p. 207
6.1.5 Crack Plane Dislocation Distribution	p. 208
6.1.6 Elastic Region Stress Field	p. 208
6.1.7 Boundary Conditions Summary	p. 210
6.2 Stationary Crack in a Work Hardening Solid in Small Scale Yielding	p. 211
6.2.1 Stress Solution	p. 212
6.2.2 Strain Solution	p. 214
6.2.3 Dislocation Density Field	p. 214
6.2.4 Slip Trajectories	p. 214
6.2.5 Plastic Strain from Dislocation Density Field	p. 217
6.2.6 Dislocation Crack Tip Shielding	p. 220
6.2.7 Dislocation Crack Extension Force	p. 220
6.2.8 Crack Plane Dislocation Density Distribution	p. 221
6.2.9 Net Burgers Vector of Plastic Zone Dislocations	p. 222
6.3 Mode III Crack in a Linear Work Hardening Solid with Zero Yield Stress	p. 222
6.3.1 Stress Solution	p. 223
6.3.2 Maximum Shear Stress Plane Trajectories	p. 224
6.3.3 Dislocation Density	p. 225
6.4 Mode III Crack in an Elastic Perfectly Plastic Solid in Large Scale Yielding	p. 226
6.4.1 Approximate Solution	p. 227
6.4.2 Special Problem	p. 228
6.4.3 Exact Solution	p. 230
6.4.3.1 'Pressurized' Mode III Crack	p. 235
6.5 Growing Mode III Crack in an Elastic Perfectly Plastic Solid	p. 236
6.5.1 Chitaley-McClintock Asymptotic Region	p. 238
6.5.2 Strain Field in CM Sector	p. 239
6.5.3 Strain Field in DH Sector	p. 242
6.5.4 Approximate Solution	p. 243
Chapter 6 Appendix: Iterative Solution of Special Problem	p. 249
Chapter 6 Homework	p. 256
Chapter 7 Mode II Crack in an Elastic-Plastic Solid	p. 259
7.1 Mode II Crack in an Elastic Perfectly Plastic Solid in Small Scale Yielding	p. 259
7.1.1 Plastic Zone Stress Field	p. 260
7.1.2 Asymptotic Dislocation Density Field	p. 262
7.1.2.1 Asymptotic Dislocation Density Field from Stress Field	p. 265
7.1.2.2 Asymptotic Dislocation Density Field from Strain Field	p. 265
7.1.3 Plastic Zone Strain-Rotation Field and Dislocation Density Field	p. 266
7.1.4 Plastic Zone Shape	p. 268
7.1.4.1 Dislocation Crack Extension Force and the Plastic Zone Size	p. 270
7.1.4.2 Dislocation Crack Tip Shielding	p. 270
7.1.5 Crack Plane Dislocation Distribution	p. 273
7.1.6 Elastic Region Stress Field	p. 275
7.1.6.1 Constant Stress Magnitude Contours	p. 279
7.2 Mode II Crack in a Linear Work Hardening Solid with Zero Yield Stress	p. 282
7.2.1 Stress Solution	p. 283
7.2.2 Maximum Shear Stress Plane Trajectories	p. 284
7.2.3 Rotation	p. 285
7.2.3.1 A Physical Inconsistency	p. 285
7.2.4 Solution without Reversed Slip	p. 286
7.2.4.1 Dislocation Density Field	p. 286
Chapter 7 Homework	p. 289
Chapter 8 Mode I Crack in an Elastic-Plastic Solid	p. 291
8.1 Mode I Crack in an Elastic Perfectly Plastic Solid in Small Scale Yielding	p. 291
8.1.1 Mode II Analogue Plastic Zone Stress Field	p. 292
8.1.2 Asymptotic Dislocation Density Field	p. 293
8.1.3 Plastic Zone Stress Field: Mode I Crack in an Elastic Perfectly Plastic Solid Dislocation Density Field	p. 299
8.2 Dislocation Density Field	p. 304
8.2.1 Strain-Rotation Field	p. 306
8.2.1.1 Stream Functions and Displacement Fields	p. 306
8.2.1.2 Strain-Rotation Field	p. 307
8.2.2 Dislocation Density Field	p. 308
8.3 Dislocation Crack Extension Force	p. 309
8.3.1 Transformed Dislocation Density Components	p. 310
8.3.2 Transformed Stress Components	p. 310
8.4 Dislocation Crack Tip Shielding	p. 310
8.4.1 Trajectory Equations	p. 311
8.5 Crack Plane Dislocation Distribution	p. 316
8.6 Elastic Region Stress Field	p. 316
8.6.1 Constant Stress Magnitude Contours	p. 319
8.7 Mode I Crack in a Linear Work Hardening Solid with Zero Yield Stress	p. 322
8.7.1 Stress Solution	p. 322
8.7.2 Maximum Shear Stress Plane Trajectories	p. 323
8.7.3 Rotation	p. 324
8.7.3.1 A Physical Inconsistency	p. 324
8.7.4 Solution without Reversed Slip	p. 325
8.7.4.1 Dislocation Density Field	p. 325
8.7.5 Dislocation Density Field Found from Plastic Strain Field	p. 327
8.8 Hutchinson-Rice-Rosengren (HRR) Stress-Strain Field	p. 329
8.8.1 Boundary and Symmetry Conditions	p. 330
8.8.2 HRR Stress Field	p. 332
8.8.3 HRR Strain Field	p. 333
8.8.4 HRR Strain-Strain Field for a Special Case	p. 334
8.8.5 Dislocation Density Field of the HRR Stress-Strain-Rotation Field	p. 337
8.8.6 Dislocation Density Condition	p. 338
8.8.7 Exponent Condition	p. 339
8.9 Mixed Mode I & II Stationary Crack in an Elastic Perfectly Plastic Solid	p. 342
8.9.1 Shih Asymptotic Stress Field	p. 342
8.9.2 Asymptotic Stress Field with Sector Below Yield Stress	p. 344
Chapter 8 Homework	p. 348
Chapter 9 Moving Yoffe Crack	p. 351
9.1 Dislocation Stress Fields	p. 351
9.1.1 Uniformly Moving Screw Dislocation Stress Field	p. 352
9.1.2 Uniformly Moving Glide Edge Dislocation Stress Field	p. 352
9.1.3 Uniformly Moving Climb Edge Dislocation Stress Field	p. 353
9.1.4 Dislocation and Crack Plane Traction Stresses	p. 354
9.2 Stress Fields of Moving Yoffe Cracks	p. 356
9.2.1 Mode I Crack	p. 357
9.2.2 Mode II Crack	p. 357
9.2.3 Mode III Crack	p. 358
9.2.4 Mode I Near Tip Stress Field	p. 358
9.2.5 Mode II Near Tip Stress Field	p. 359
9.2.6 Mode III Near Tip Stress Field	p. 359
9.2.7 Plane of Maximum Tensile Stress at Mode I Crack Tip	p. 360
9.2.7.1 Yoffe Crack Branching	p. 361
9.2.8 Plane of Maximum Tensile and Shear Stress at Mode II Crack Tip	p. 365
9.2.9 Plane of Maximum Shear Stress at Mode III Crack Tip	p. 370
9.3 Dislocation Density Field Equations	p. 370
9.3.1 Antiplane Strain	p. 371
9.3.2 Plane Strain	p. 372
Chapter 9 Homework	p. 372
Chapter 10 Interesting Applications	p. 373
10.1 Crevasses and Dikes	p. 373
10.1.1 Crevasses	p. 373
10.1.2 Propagation of Magma Filled Cracks	p. 379
10.1.3 Dikes	p. 380
10.2 Unstable Slippage	p. 382
10.3 Edge Cracks in Elastic Solids	p. 385
10.4 Interface Cracks	p. 391
10.5 Fatigue Crack Propagation	p. 398
10.5.1 Fatigue Crack Growth Controlled by Crack Tip Blunting	p. 398
10.5.2 Paris Law	p. 399
10.6 Redundant and Non-Redundant Dislocations	p. 402
10.6.1 Irwin-Orowan Fracture Equation	p. 405
Chapter 10 Appendix: Stress Field of a Mode I and of a Mode II Interface Crack	p. 407
Chapter 10 Homework	p. 413
Appendix A Short Table of Hilbert Transforms	p. 417
Appendix B Table of Useful Integrals for Crack Problems	p. 420
Appendix C Stress Fields of Dislocations Near or On an Interface	p. 439
C.1 Screw Dislocation	p. 439
C.1.1 Discrete Image Screw Dislocations	p. 439
C.1.2 Image Screw Interface Dislocation Distributions	p. 441
C.2 Glide Edge Dislocation	p. 442
C.2.1 Continuity Conditions	p. 443
C.2.2 Real Dislocation and Set I of Image Dislocations	p. 443
C.2.3 Set II of Image Dislocations	p. 445
C.2.4 Shear Stress Continuity	p. 446
C.2.5 Normal Stress Continuity	p. 447
C.2.6 Normal Displacement Continuity	p. 448
C.2.7 Tangential Displacement Continuity	p. 449
C.2.8 Constants	p. 450
C.3 Climb Edge Dislocation	p. 451
C.4 Dislocation at the Interface	p. 451
C.4.1 Screw Dislocation	p. 451
C.4.2 Glide Edge Dislocation	p. 451
C.4.3 Climb Edge Dislocation	p. 453
C.5 Comninou-Dundurs Equations	p. 453
C.6 Inverse Comninou-Dundurs Equations	p. 454
Appendix D Table of Useful Equations	p. 455
D.1 Stress and Strain Components	p. 455
D.1.1 Cartesian Coordinates	p. 456
D.1.2 Cylindrical Coordinates	p. 456
D.1.3 Finger and Thumb Coordinates	p. 456
D.1.4 Strain Compatibility Condition for Plane Strain	p. 457
D.2 Elastic Constants	p. 458
D.3 Stress and Strain Components in Rotated Coordinate System	p. 458
D.4 Conditions for Antiplane Strain, Plane Strain and Plane Stress	p. 460
D.5 Equations for Dynamics Equilibrium	p. 461
D.6 Non-Redundant Dislocation Density Field	p. 462
D.6.1 Cartesian Coordinates	p. 462
D.6.1.1 Frank's Rule	p. 463
D.6.2 Cylindrical Coordinates	p. 463
D.6.2.1 Frank's Rule	p. 464
D.6.3 Spherical Coordinates	p. 464
D.6.3.1 Frank's Rule	p. 465
D.6.4 Dislocation Density Relationships and Strain Compatibility Equations	p. 465
D.6.4.1 Beltrami-Michell (Strain) Compatibility Equations	p. 465
D.7 Stress-Strain-Rotation Displacement Fields in Plane Strain from Stress and Strain Functions	p. 466
D.7.1 Airy Stress Function	p. 466
D.7.2 Displacement and Rotation Field	p. 466
D.7.3 Stream Function	p. 466
D.7.4 Antiplane Strain Stress Function	p. 467
D.8 The Del Divergence, Curl and Gradient Operators	p. 467
D.8.1 Cartesian	p. 467
D.8.2 Cylindrical	p. 467
D.8.3 Spherical	p. 467
D.8.4 Cylindrical, Shifting Center	p. 468
D.9 Equations of Static Equilibrium in Shifting Center Cylindrical Coordinate System	p. 468
D.9.1 Antiplane Strain	p. 468
D.9.2 Plane Strain	p. 468
D.10 Trigonometric Relationships	p. 469
D.11 Dirac Delta Functions	p. 470
D.11.1 One Dimension	p. 470
D.11.2 Two Dimensions	p. 470
D.11.3 Three Dimensions	p. 470
D.11.4 One Dimension, Special Example	p. 471
D.12 Curves	p. 472
D.13 Surface Dislocation Density Tensor	p. 472
D.14 Single Stress Component - Dislocation Density Relationships	p. 474
D.14.1 Plane Strain	p. 474
D.14.2 Antiplane Strain	p. 474
Appendix E Derivation of the Del Gradient and other Operators for the Shifting Center Cylindrical Coordinate System	p. 475
Appendix F Orthogonal Curvilinear Coordinates	p. 481
F.1 Curvilinear Coordinates	p. 481
F.1.1 Exponential Spirals	p. 482
F.1.2 Non-exponential Spiral	p. 484
F.2 Static Equilibrium Equations	p. 487
F.2.1 Plane Strain	p. 487
F.2.2 Antiplane Strain	p. 493
F.3 Gradient [down triangle, open subscript grad], Divergence [down triangle, open subscript div] and Curl [down triangle, open subscript curl] Operators	p. 493
Appendix G Dislocations in Stress Space	p. 495
G.1 Cracks in Elastic Stress Space	p. 498
G.1.1 Zener-Stroh-Koehler Crack	p. 498
G.1.2 Griffith-Inglis Crack	p. 501
G.2 Plane Strain Stress Space	p. 503
References	p. 505
Dislocation Texts	p. 505
Fracture Texts	p. 505
Other Texts	p. 507
Review Papers	p. 508
Research Papers	p. 510
Index	p. 519

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