Preface to the Fourth Edition ................................. xii
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 Effective stress ....................................... 21
2.5 Effective strain ....................................... 22
2.6 Flow rules ............................................. 23
2.7 Normality principle .................................... 24
2.8 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 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 .................................................. 41
PROBLEMS .................................................... 41
4 Plastic 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 ti, 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 ............................................... 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 Coming ................................................ 101
7.13 Reducing the area of contact .......................... 101
NOTES OF INTEREST .......................................... 102
REFERENCES ................................................. 102
PROBLEMS ................................................... 102
8 Friction and Lubrication ................................... 106
8.1 General ............................................... 106
8.2 Experimental findings ................................. 109
8.3 Ring friction test .................................... 110
8.4 Galling ............................................... 111
8.5 Ultrasonics ........................................... 111
NOTE OF INTEREST ........................................... 111
REFERENCES ................................................. 112
PROBLEMS ................................................... 112
9 Upper-Bound Analysis ....................................... 113
9.1 Upper bounds .......................................... 113
9.2 Energy dissipation on plane of shear .................. 114
9.3 Plane-strain frictionless extrusion ................... 115
9.4 Plane-strain frictionless indentation ................. 119
9.5 Plane-strain compression .............................. 119
9.6 Another approach to upper bounds ...................... 122
9.7 A combined upper-bound analysis ....................... 123
9.8 Plane-strain drawing .................................. 124
9.9 Axisymmetric drawing .................................. 124
REFERENCES ................................................. 126
PROBLEMS ................................................... 126
10 Slip-Line Field Analysis ................................... 132
10.1 Introduction .......................................... 132
10.2 Governing stress equations ............................ 132
10.3 Boundary conditions ................................... 136
10.4 Plane-strain indentation .............................. 137
10.5 Hodographs for slip-line fields ....................... 138
10.6 Plane-strain extrusion ................................ 139
10.7 Energy dissipation in a slip-line field ............... 141
10.8 Metal distortion ...................................... 141
10.9 Indentation of thick slabs ............................ 142
10.10 Plane-strain drawing ................................. 146
10.11 Constant shear stress interfaces ..................... 150
10.12 Pipe formation ....................................... 151
NOTES OF INTEREST .......................................... 152
REFERENCES ................................................. 154
APPENDIX ................................................... 154
PROBLEMS ................................................... 157
11 Deformation-Zone Geometry .................................. 167
11.1 The Д parameter ....................................... 167
11.2 Friction .............................................. 168
11.3 Redundant deformation ................................. 168
11.4 Inhomogeneity ......................................... 170
11.5 Internal damage ....................................... 175
11.6 Residualstresses ...................................... 179
11.7 Comparison of plane-strain and axisymmetric
deformation ........................................... 182
NOTE OF INTEREST ........................................... 184
REFERENCES ................................................. 184
PROBLEMS ................................................... 184
12 Formability ................................................ 186
12.1 Ductility ............................................. 186
12.2 Metallurgy ............................................ 186
12.3 Ductile fracture ...................................... 190
12.4 Hydrostatic stress .................................... 191
12.5 Bulk formability tests ................................ 195
12.6 Formability in hot working ............................ 196
NOTE OF INTEREST ........................................... 197
REFERENCES ................................................. 197
PROBLEMS ................................................... 197
13 Bending .................................................... 199
13.1 Sheet bending ......................................... 199
13.2 Bending with super-imposed tension .................... 202
13.3 Young's modulus on unloading .......................... 204
13.4 Reducing springback ................................... 204
13.5 Neutral axis shift .................................... 204
13.6 Bendability ........................................... 206
13.7 Shape bending ......................................... 207
13.8 Forming limits in bending ............................. 208
NOTE OF INTEREST ........................................... 209
REFERENCES ................................................. 209
PROBLEMS ................................................... 209
14 Plastic Anisotropy ......................................... 212
14.1 Crystallographic basis ................................ 212
14.2 Measurement of R ...................................... 214
14.3 Hill's anisotropic plasticity theory .................. 214
14.4 Special cases of Hill's yield criterion ............... 216
14.5 Nonquadratic yield criteria ........................... 217
14.6 Calculation of anisotropy from crystallographic
considerations ........................................ 220
NOTE OF INTEREST ........................................... 221
REFERENCES ................................................. 221
PROBLEMS ................................................... 221
15 Cupping, Redrawing, and Ironing ............................ 225
15.1 Cup drawing ........................................... 225
15.2 Anisotropy effects in drawing ......................... 228
15.3 Effects of strain hardening in drawing ................ 229
15.4 Analysis of assumptions ............................... 230
15.5 Effects of tooling on cup drawing ..................... 232
15.6 Earing ................................................ 233
15.7 Redrawing ............................................. 235
15.8 Ironing ............................................... 236
15.9 Progressive forming ................................... 238
15.10 Tapered dies ......................................... 238
15.11 Drawing boxes ........................................ 240
15.12 Residual stresses .................................... 241
NOTES OF INTEREST .......................................... 242
REFERENCES ................................................. 242
PROBLEMS ................................................... 242
16 Forming Limit Diagrams ..................................... 245
16.1 Localized necking ..................................... 245
16.2 Forming limit diagrams ................................ 249
16.3 Experimental determination of FLDs .................... 250
16.4 Calculation of forming limit diagrams ................. 252
16.5 Factors affecting forming limits ...................... 255
16.6 Changing strain paths ................................. 258
16.7 Stress-based forming limits ........................... 260
NOTE OF INTEREST ........................................... 260
REFERENCES ................................................. 261
PROBLEMS ................................................... 261
17 Stamping ................................................... 263
17.1 Stamping .............................................. 263
17.2 Draw beads ............................................ 263
17.3 Strain distribution ................................... 265
17.4 Loose metal and wrinkling ............................. 266
17.5 Springback ............................................ 268
17.6 Strain signatures ..................................... 269
17.7 Die design ............................................ 270
17.8 Toughness and sheet tearing ........................... 272
17.9 General observations .................................. 274
NOTES OF INTEREST .......................................... 275
REFERENCES ................................................. 275
PROBLEMS ................................................... 275
18 Hydroforming ............................................... 277
18.1 General ............................................... 277
18.2 Free expansion of tubes ............................... 277
18.3 Hydroforming into square cross sections ............... 279
18.4 Bent sections ......................................... 281
NOTE OF INTEREST ........................................... 283
REFERENCES ................................................. 283
PROBLEMS ................................................... 283
19 Other Sheet Forming Operations ............................. 285
19.1 Roll forming ......................................... 285
19.2 Spinning .............................................. 286
19.3 Foldable shapes ....................................... 288
19.4 Incremental sheet forming ............................. 288
19.5 Shearing .............................................. 290
19.6 Flanging, hole expansion, and beading ................. 291
19.7 Hemming ............................................... 292
NOTE OF INTEREST ........................................... 293
REFERENCES ................................................. 293
PROBLEMS ................................................... 293
20 Formability Tests .......................................... 294
20.1 Cupping tests ......................................... 294
20.2 LDH test .............................................. 294
20.3 Post-uniform elongation ............................... 297
20.4 OSU formabiiity test .................................. 297
20.5 Hole expansion ........................................ 298
20.6 Hydraulic bulge test .................................. 299
20.7 Duncan friction test .................................. 300
REFERENCES ................................................. 301
PROBLEMS ................................................... 301
21 Sheet Metal Properties ..................................... 304
21.1 Introduction .......................................... 304
21.2 Surface appearance .................................... 305
21.3 Strain aging .......................................... 305
21.4 Roller leveling and temper rolling .................... 308
21.5 Properties of steels .................................. 309
21.6 Grades of low-carbon steel ............................ 309
21.7 Tailor-welded blanks .................................. 314
21.8 Special sheet steels .................................. 315
21.9 Surface treatment ..................................... 315
21.10 Stainless steels ..................................... 316
21.11 Aluminum alloys ...................................... 317
21.12 Copper and brass ..................................... 321
21.13 Hexagonal close-packed metals ........................ 322
21.14 Tooling .............................................. 323
21.15 Product uniformity ................................... 323
21.16 Scrap ................................................ 324
NOTES OF INTEREST .......................................... 324
REFERENCES ................................................. 325
PROBLEMS ................................................... 325
Index ......................................................... 327
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