Preface to Third Edition ..................................... 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
9.1 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 A 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
12.1 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 ................................. 207
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 ......................................... 275
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
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