Loading...Metal Forming and Finite Element Method
SHIRO KOBAYASHI
SOO-IK OH
TAYLAN ALTAN
CONTENTS
Symbols, xiii
1. Introduction, 1
1.1 Process Modeling, 1
1.2 The Finite-Element Method, 3
1.3 Solid Formulation and Flow Formulation, 4
1.4 Metal Forming and the Finite-Element Method, 5
References, 6
2. Metal-Forming Processes, 8
2.1 Introduction, 8
2.2 A Metal-Forming Operation as a System, 8
2.3 Classification and Description of Metal-Forming Processes, 11
References, 24
3. Analysis and Technology in Metal Forming, 26
3.1 Introduction, 26
3.2 Flow Stress of Metals, 28
3.3 Friction in Metal Forming, 30
3.4 Temperatures in Metal Forming, 33
3.5 Impression and Closed-Die Forging, 35
3.6 Hot Extrusion of Rods and Shapes, 36
3.7 Cold Forging and Extrusion, 39
3.8 Rolling of Strip, Plate, and Shapes, 41
3.9 Drawing of Rod, Wire, Shapes, and Tubes, 45
3.10 Sheet-Metal Forming, 47
References, 52
4. Plasticity and Viscoplasticity, 54
4.1 Introduction, 54
4.2 Stress, Strain, and Strain-Rate, 54
4.3 The Yield Criteria, 58
4.4 Equilibrium and Virtual Work-Rate Principle, 61Contents
4.5 Plastic Potential and Flow Rule, 63
4.6 Strain-Hardening, Effective Stress, and Effective Strain, 66
4.7 Extremum Principles, 68
4.8 Viscoplasticity, 70
References, 72
vm Contents IX
9.3 Compression of Solid Cylinders and Heading of Cylindrical Bars,
153
9.4 Ring Compression, 159
9.5 Evaluation of Friction at Tool-Workpiece Interface, 163
9.6 Forging and Cabbaging, 165
References, 172
5. Methods of Analysis, 73
5.1 Introduction, 73
5.2 Upper-Bound Method, 74
5.3 Hill’s General Method, 78
5.4 The Finite-Element Method, 83
5.5 Concluding Remarks, 88
References, 88
10. Steady-State Processes of Extrusion and Drawing, 174
10.1 Introduction, 174
10.2 Method of Analysis, 174
10.3 Bar Extrusion, 176
10.4 Bar Drawing, 178
10.5 Multipass Bar Drawing and Extrusion, 183
10.6 Applications to Process Design, 186
6. The Finite-Element Method—Part I, 90 References, 187
6.1 Introduction, 90
6.2 Finite-Element Procedures, 90
6.3 Elements and Shape Function, 94
6.4 Element Strain-Rate Matrix, 101
6.5 Elemental Stiffness Equation, 108
References, 110
7. The Finite-Element Method—Part II, 111
7.1 Numerical Integrations, 111
7.2 Assemblage and Linear Matrix Solver, 115
7.3 Boundary Conditions, 117
7.4 Direct Iteration Method, 121
7.5 Time-Increment and Geometry Updating, 123
7.6 Rezoning, 126
7.7 Concluding Remarks, 129
References, 129
11. Sheet-Metal Forming, 189
11.1 Introduction, 189
11.2 Plastic Anisotropy, 190
11.3 In-plane Deformation Processes, 192
11.4 Axisymmetric Out-of-plane Deformation, 195
11.5 Axisymmetric Punch-Stretching and Deep-Drawing Processes,
201
11.6 Sheet-Metal Forming of General Shapes, 206
11.7 Square-Cup Drawing Process, 210
11.8 Nonquadratic Yield Criterion, 217
References, 220
12. Thermo-Viscoplastic Analysis, 222
12.1 Introduction, 222
12.2 Viscoplastic Analysis of Compression of a Solid Cylinder, 223
12.3 Heat Transfer Analysis, 225
12.4 Computational Procedures for Thermo-Viscoplastic Analysis,
8. Plane-Strain Problems, 131
8.1 Introduction, 131
8.2 Finite-Element Formulation, 131
8.3 Closed-Die Forging with Flash, 133
8.4 Sheet Rolling, 137
8.5 Plate Bending, 141
8.6 Side Pressing, 148
References, 149
227
12.5 Applications, 229
12.6 Concluding Remarks, 240
References, 242
13. Compaction and Forging of Porous Metals, 244
13.1 Introduction, 244
13.2 Yield Criterion and Flow Rules, 245
13.3 Finite-Element Modeling and Numerical Procedures, 246
13.4 Simple Compression, 249
13.5 Axisymmetric Forging of Flange-Hub Shapes, 253
9. Axisymmetric Isothermal Forging, 151
9.1 Introduction, 151
9.2 Finite-Element Formulation, 151x Contents Contents XI
13.6 Axisymmetric Forging of Pulley Blank, 256
13.7 Heat Transfer in Porous Materials, 259
13.8 Hot Pressing Under the Plane-Strain Condition, 262
13.9 Compaction, 266
References, 272
A.3 Input and Output Files, 340
A.4 Input Preparations, 340
A.5 Description of the Major Variables, 342
A.6 Program Listing, 343
A.7 Example Solution, 364
Index, 371
14. Three-Dimensional Problems, 275
14.1 Introduction, 275
14.2 Finite-Element Formulation, 276
14.3 Block Compressions, 278
14.4 Square-Ring Compression, 284
14.5 Simplified Three-Dimensional Elements, 287
14.6 Analysis of Spread in Rolling and Flat-Tool Forging, 289
14.7 Concluding Remarks, 295
References, 296
15. Preform Design in Metal Forming, 298
15.1 Introduction, 298
15.2 Method for Design, 298
15.3 Shell Nosing at Room Temperature, 301
15.4 Plane-Strain Rolling, 305
15.5 Axially Symmetric Forging, 309
15.6 Hot Forming, 315
15.7 Concluding Remarks, 318
References, 320
16. Solid Formulation, Comparison of Two Formulations, and
Concluding Remarks, 321
16.1 Introduction, 321
16.2 Small-Strain Solid Formulation, 321
16.3 Large Deformation: Rate Form, 323
16.4 Large Deformation: Incremental Form, 326
16.5 Comparison with Rigid-Plastic (Flow) Solutions, 327
16.6 Concluding Remarks, 334
References, 335
Appendix. The FEM Code, SPID (Simple Plastic Incremental
Deformation), 338
A.l Introduction, 338
A.2 Program Structure, 339
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