METAL FORMING AND THE FINITE-ELEMENT METHOD SHIRO KOBAYASHI SOO-IK OH TAYLAN ALTAN

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1 METAL FORMING AND THE FINITE-ELEMENT METHOD SHIRO KOBAYASHI SOO-IK OH TAYLAN ALTAN New York Oxford OXFORD UNIVERSITY PRESS 1989

2 CONTENTS Symbols, xiii 1. Introduction, Process Modeling, The Finite-Element Method, Solid Formulation and Flow Formulation, Metal Forming and the Finite-Element Method, 5 References, 6 2. Metal-Forming Processes, Introduction, A Metal-Forming Operation as a System, Classification and Description of Metal-Forming Processes, 11 References, Analysis and Technology in Metal Forming, Introduction, Flow Stress of Metals, Friction in Metal Forming, Temperatures in Metal Forming, Impression and Closed-Die Forging, Hot Extrusion of Rods and Shapes, Cold Forging and Extrusion, Rolling of Strip, Plate, and Shapes, Drawing of Rod, Wire, Shapes, and Tubes, Sheet-Metal Forming, 47 References, Plasticity and Yiscoplasticity, Introduction, Stress, Strain, and Strain-Rate, The Yield Criteria, Equilibrium and Virtual Work-Rate Principle, 61

3 Vlll Contents 4.5 Plastic Potential and Flow Rule, Strain-Hardening, Effective Stress, and Effective Strain, Extremum Principles, Viscoplasticity, 70 References, Methods of Analysis, Introduction, Upper-Bound Method, Hill's General Method, The Finite-Element Method, Concluding Remarks, 88 References, The Finite-Element Method Part I, Introduction, Finite-Element Procedures, Elements and Shape Function, Element Strain-Rate Matrix, Elemental Stiffness Equation, 108 References, The Finite-Element Method Part II, Numerical Integrations, Assemblage and Linear Matrix Solver, Boundary Conditions, Direct Iteration Method, Time-Increment and Geometry Updating, Rezoning, Concluding Remarks, 129 References, Plane-Strain Problems, Introduction, Finite-Element Formulation, Closed-Die Forging with Flash, Sheet Rolling, Plate Bending, Side Pressing, 148 References, Axisymmetric Isothermal Forging, Introduction, Finite-Element Formulation, 151

4 Contents 9.3 Compression of Solid Cylinders and Heading of Cylindrical Bars, Ring Compression, Evaluation of Friction at Tool-Workpiece Interface, Forging and Cabbaging, 165 References, Steady-State Processes of Extrusion and Drawing, Introduction, Method of Analysis, Bar Extrusion, Bar Drawing, Multipass Bar Drawing and Extrusion, Applications to Process Design, 186 References, Sheet-Metal Forming, Introduction, Plastic Anisotropy, In-plane Deformation Processes, Axisymmetric Out-of-plane Deformation, Axisymmetric Punch-Stretching and Deep-Drawing Processes, Sheet-Metal Forming of General Shapes, Square-Cup Drawing Process, Nonquadratic Yield Criterion, 217 References, Thermo-Viscoplastic Analysis, Introduction, Viscoplastic Analysis of Compression of a Solid Cylinder, Heat Transfer Analysis, Computational Procedures for Thermo-Viscoplastic Analysis, Applications, Concluding Remarks, 240 References, Compaction and Forging of Porous Metals, Introduction, Yield Criterion and Flow Rules, Finite-Element Modeling and Numerical Procedures, Simple Compression, Axisymmetric Forging of Flange-Hub Shapes, 253 ix

5 X Contents 13.6 Axisymmetric Forging of Pulley Blank, Heat Transfer in Porous Materials, Hot Pressing Under the Plane-Strain Condition, Compaction, 266 References, Three-Dimensional Problems, Introduction, Finite-Element Formulation, Block Compressions, Square-Ring Compression, Simplified Three-Dimensional Elements, Analysis of Spread in Rolling and Flat-Tool Forging, Concluding Remarks, 295 References, Preform Design in Metal Forming, Introduction, Method for Design, Shell Nosing at Room Temperature, Plane-Strain Rolling, Axially Symmetric Forging, Hot Forming, Concluding Remarks, 318 References, Solid Formulation, Comparison of Two Formulations, and Concluding Remarks, Introduction, Small-Strain Solid Formulation, Large Deformation: Rate Form, Large Deformation: Incremental Form, Comparison with Rigid-Plastic (Flow) Solutions, Concluding Remarks, 334 References, 335 Appendix. The FEM Code, SPID (Simple Plastic Incremental Deformation), 338 A.l Introduction, 338 A.2 Program Structure, 339

6 Contents 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 xi Index, 371

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