Numerical Modelling of Material Deformation Processes

I. Introduction to Plasticity Theory.- 1 Classical Plasticity.- 1.1 General Theory.- 1.2 Plane Strain - The Slip-Line Field.- 1.3 Velocity Discontinuities.- 1.4 Stress Discontinuities.- 1.5 Limit Analysis.- 1.6 Instability.- 2 Finite Deformation of Solids.- 2.1 Introduction.- 2.2 Configurations.- 2.3 Metric Structure in the Current Configuration ?.- 2.4 Metric Structure in the Initial Configuration ?.- 2.5 Stresses.- 2.6 Covariant Derivatives and Gauss Theorem.- 2.7 Infinitesimal Volume Equilibrium Equations.- 2.8 The Virtual Work Principle - Conjugated Virtual Strains.- 2.9 Strains.- 2.10 Discretized Equilibrium Equations.- 2.11 Solution of the Discretized Equilibrium Equations.- 2.12 Conclusions.- 3 Isotropic Plasticity.- 3.1 Introduction.- 3.2 Constitutive Equations and Isotropy.- 3.3 Incompressibility and Planar Representation.- 3.4 The Yield Surface and Plastic Potential.- 3.5 The Tresca and von Mises Yield Criteria.- 3.6 Isotropic Plastic and Viscoplastic Equations.- 3.7 Isotropic Elastoplastic Equations.- 3.8 Finite Deformation Increments.- 4 Anisotropic Plasticity.- 4.1 Introduction.- 4.2 Examples of the Plastic Anisotropy of Engineering Materials.- 4.3 The Fundamental Plastic Anisotropy of Crystalline Materials.- 4.4 Anisotropic Polycrystalline Materials.- 4.5 Analytical Expressions for Anisotropic Yield Loci.- II. Review of Numerical Techniques in Material Deformation Processes.- 5 The Upper Bound Method.- 5.1 Introduction.- 5.2 The Upper Bound Theorem.- 5.3 Deformation Power (P1).- 5.4 Power Dissipation due to Velocity Discontinuities (P2).- 5.5 Power Dissipation due to Friction (P3).- 5.6 Upper Bound Solutions for Axisymmetric Problems.- 5.7 UBET.- 5.8 Conclusion.- 6 Boundary-Element Analysis of Forming Processes.- 6.1 Introduction.- 6.2 The Behaviour of Non-Newtonian Materials.- 6.3 Governing Equations.- 6.4 Boundary Integral Methods.- 6.5 Applications to Forming Problems.- 6.6 Conclusion.- 7 The Rigid-Plastic Finite-Element Method for Simulation of Deformation Processing.- 7.1 Introduction.- 7.2 History of the Rigid-Plastic Finite-Element Method.- 7.3 Theory.- 7.4 Finite-Element Implementation.- 7.5 Special Numerical Features of Deformation Processing Codes.- 7.6 Coupled Thermal and Deformation Processing.- 7.7 Conclusion.- 8 The Viscoplastic Approach for the Finite-Element Modelling of Metal-Forming Processes.- 8.1 Introduction.- 8.2 Constitutive Equations for a Viscoplastic Material.- 8.3 The Thermomechanical Formulation.- 8.4 The Steady-State Problem.- 8.5 Incremental Processes.- 8.6 Conclusion.- 9 The Elastic-Plastic Finite-Element Method.- 9.1 Introduction.- 9.2 Incremental Methodology.- 9.3 Discretization.- 9.4 Elastic-Plastic Formulation.- 9.5 FE Solution.- 9.6 Examples.- 9.7 Conclusions.- III. Specialized Applications and Topics.- 10 Numerical Modelling of Forging.- 10.1 Introduction.- 10.2 Finite-Element Plasticity.- 10.3 Forging Applications.- 10.4 Conclusions.- 11 Rolling Process Modelling.- 11.1 Introduction.- 11.2 Mathematical Models.- 11.3 Conclusions.- 12 Extrusion and Drawing.- 12.1 Introduction.- 12.2 Method of Modelling.- 12.3 Extrusion.- 12.4 Drawing.- 12.5 Conclusion.- 13 Numerical Modelling of Sheet Metal-Forming Problems.- 13.1 Introduction.- 13.2 Introductory Concepts.- 13.3 Solid Approach: Basic Equations for Nonlinear Deformation of Porous Metals.- 13.4 Rigid-Plastic/Viscoplastic Model: Flow Approach.- 13.5 Finite-Element Discretization: Computational Aspects.- 13.6 Viscous Shell Approach.- 13.7 Contact and Friction.- 13.8 Use of Constant Spatial Velocity Field.- 13.9 Inclusion of Elastic Effects in the Viscous Voided Shell Formulation.- 13.10 Examples.- 13.11 Conclusion.- 14 Forming of Metal Matrix Composites.- 14.1 Introduction.- 14.2 Consolidation and Deformation of Metal Matrix Composites.- 14.3 Application of the Finite-Element Method to Metal-Forming.- 14.4 Equivalent Material with Orthotropic Properties.- 14.5 Effect of Fibre Arrangement on Transverse Compression Deformation.- 14.6 Micromechanical Finite-Element Analysis of Fibre-Matrix Interfacial Stresses.- 14.7 Conclusions.- Appendix. Plane-Strain Orthotropic Formulation.- 15 Finite-Element Analysis of the Superplastic Forming of Thin Sheet Components.- 15.1 Introduction.- 15.2 Governing Equations.- 15.3 Finite-Element Discretization.- 15.4 Solution Procedures.- 15.5 Applications.- 15.6 Conclusions.- 16 Fracture in Forming Processes.- 16.1 Introduction.- 16.2 Criteria for Ductile Fracture.- 16.3 Predictions of Ductile Fracture Using the Finite-Element Method.- 16.4 Conclusions.- IV. Computer Integrated Systems.- 17 Integration of Numerical Modelling and CAD/CAM Systems.- 17.1 Introduction.- 17.2 Typical Tasks.- 17.3 Multilevel Approach.- 17.4 Interface Problems.- 17.5 Summary.- 18 Application of Knowledge-Based Techniques.- 18.1 Introduction.- 18.2 Application of Numerical Modelling and Knowledge-Based Systems.- 18.3 Design of Parts and Process Sequences in Cold Forging.- 18.4 Application of KBS in Hot Forging.- 18.5 Applications in Sheet-Metal Forming.- 18.6 Applications in FEM Modelling of Forming Processes.