Contents Metal Forming and Machining Processes Review of Stress, Linear Strain and Elastic Stress-Strain Relations 3 Classical Theory of Plasticity

Transcription

1 Contents 1 Metal Forming and Machining Processes Introduction Metal Forming Bulk Metal Forming Sheet Metal Forming Processes Machining Turning Milling Some Other Machining Processes Summary References Review of Stress, Linear Strain and Elastic Stress-Strain Relations Introduction Index Notation and Summation Convention Stress Stress at a Point Analysis of Stress at a Point Equation of Motion Deformation Linear Strain Tensor Analysis of Strain at a Point Compatibility Conditions Material Behavior Elastic Stress-Strain Relations for Small Deformations Summary References Classical Theory of Plasticity Introduction One-Dimensional Experimental Observations on Plasticity Criteria for Initial Yielding of Isotropic Materials.. 107

2 xii Contents von Mises Yield Criterion Tresca Yield Criterion Geometric Representation of Yield Criteria Convexity of Yield Surfaces Experimental Validation Incremental Strain and Strain Rate Measures Incremental Linear Strain Tensor Strain Rate Tensor Relation Between Incremental Linear Strain Tensor and Strain Rate Tensor Modeling of Isotropic Hardening or Criterion for Subsequent Isotropic Yielding Strain Hardening Hypothesis Work Hardening Hypothesis Experimental Validations Plastic Stress-Strain and Stress-Strain Relations for Isotropic Materials Associated Flow Rule Elastic-Plastic Incremental Stress-Strain Relations for Mises Material Elastic-Plastic Incremental Stress-Strain Rate Relation for Mises Material Viscoplasticity and Temperature Softening Objective Stress Rate and Objective Incremental Stress Tensors Jaumann Stress Rate and Associated Objective Incremental Stress Tensor Unloading Criterion Eulerian and Updated Lagrangian Formulations for Metal Forming Processes Equation of Motion in Terms of Velocity Derivatives Incremental Equation of Motion Eulerian Formulation for Metal Forming Problems Updated Lagrangian Formulation for Metal Forming Problems Eulerian Formulation for Machining Processes Summary References Plasticity of Finite Deformation and Anisotropic Materials and Modeling of Fracture and Friction Introduction Kinematics of Finite Deformation and Rotation Constitutive Equation for Eulerian Formulation When the Rotation Is Not Small Solution Procedure Kinematics of Finite Incremental Deformation and Rotation

3 Contents xiii 4.5 Constitutive Equation for Updated Lagrangian Formulation for Finite Incremental Deformation and Rotation Anisotropic Initial Yield Criteria Hill s Anisotropic Yield Criteria Plane Stress Anisotropic Yield Criterion of Barlat and Lian A Three-Dimensional Anisotropic Yield Criterion of Barlat and Co-workers A Plane Strain Anisotropic Yield Criterion Elastic-Plastic Incremental Stress-Strain and Stress-Strain Rate Relations for Anisotropic Materials Elastic-Plastic Incremental Stress-Strain Relation for Anisotropic Materials Elastic-Plastic Incremental Stress-Strain Rate Relation for Anisotropic Materials Kinematic Hardening Modeling of Ductile Fracture Porous Plasticity Model of Berg and Gurson Void Nucleation, Growth and Coalescence Model (Goods and Brown, Rice and Trace and Thomason Model) Continuum Damage Mechanics Models Phenomenological Models Friction Models Wanheim and Bay Friction Model Summary References Finite Element Modeling of Metal Forming Processes Using Eulerian Formulation Introduction Background of Finite Element Method Pre-processing Developing Elemental Equations Assembly Procedure Applying Boundary Conditions Solving the System of Equations Post-processing Formulation of Plane-Strain Metal Forming Processes Governing Equations and Boundary Conditions Non-Dimensionalization Weak Formulation Finite Element Formulation Application of Boundary Conditions Estimation of Neutral Point Formulation for Strain Hardening Modification of Pressure Field at Each Iteration Calculation of Secondary Variables

4 xiv Contents Some Numerical Aspects Typical Results and Discussion Formulation of Axisymmetric Metal Forming Processes Formulation of Three-Dimensional Metal Forming Processes Incorporation of Anisotropy Elasto-Plastic Formulation Summary References Finite Element Modeling of Metal Forming Processes Using Updated Lagrangian Formulation Introduction Application of Finite Element Method to Updated Lagrangian Formulation Governing Equations Integral Form of Equilibrium Equation Finite Element Formulation Evaluation of the Derivative Iterative Scheme Determination of Stresses Divergence Handling Techniques Modeling of Axisymmetric Open Die Forging by Updated Lagrangian Finite Element Method Domain and Boundary Conditions Cylindrical Arc Length Method for Displacement Control Problems Friction Algorithm Convergence Study and Evaluation of Secondary Variables Validation of the Finite Element Formulation Typical Results Residual Stress Distribution Damage Distribution, Hydrostatic Stress Distribution and Fracture Modeling of Deep Drawing of Cylindrical Cups by Updated Lagrangian Finite Element Method Domain and Boundary Conditions Contact Algorithm Typical Results Anisotropic Analysis, Ear Formation and Parametric Studies Optimum Blank Shape Summary References Finite Element Modeling of Orthogonal Machining Process Introduction. 425

5 Contents xv 7.2 Domain, Governing Equations and Boundary Conditions for Eulerian Formulation Domain Governing Equations Boundary Conditions Finite Element Formulation Integral Form Approximations for Velocity Components and Pressure Finite Element Equations Application of Boundary Conditions, Solution Procedure and Evaluation of Secondary Quantities Results and Discussion Validation of the Formulation Parametric Studies Primary Shear Deformation Zone, Contours of Equivalent Strain Rate and Contours of Equivalent Stress Summary References Background on Soft Computing Introduction Neural Networks Biological Neural Networks Artificial Neurons Perceptron: The Learning Machine Multi-Layer Perceptron Neural Networks Radial Basis Function Neural Network Unsupervised Learning Fuzzy Sets Mathematical Definition of Fuzzy Set Some Basic Definitions and Operations Determination of Membership Function Fuzzy Relations Extension Principle Fuzzy Arithmetic Fuzzy Sets vs Probability Fuzzy Logic Linguistic Variables and Hedges Fuzzy Rules Fuzzy Inference Genetic Algorithms Binary Coded Genetic Algorithms Real Coded Genetic Algorithms Soft Computing vs FEM Summary References

6 xvi Contents 9 Predictive Modeling of Metal Forming and Machining Processes Using Soft Computing Introduction Design of Experiments and Preliminary Study of the Data Preliminary Statistical Analysis Correlation Analysis Hypothesis Testing Analysis of Variance Multiple Regression Neural Network Modeling Selection of Training and Testing Data Deciding the Processing Functions Effect of Number of Hidden Layers Effect of Number of Neurons in the Hidden Layers Effect of Spread Parameter in Radial Basis Function Neural Network Data Filtration Lower and Upper Estimates Prediction of Dependent Variables Using Fuzzy Sets Prediction Using ANFIS Computation with Fuzzy Variables Summary References Optimization of Metal Forming and Machining Processes Introduction Optimization Problems in Metal Forming Optimization of Roll Pass Scheduling Optimization of Rolls Optimization of Wire Drawing and Extrusion A Brief Review of Other Optimization Studies in Metal Forming Optimization Problems in Machining A Brief Review of Optimization of Machining Processes Optimization of Multipass Turning Process Online Determination of Equations for Machining Performance Parameters Summary References Epilogue References 583 Index

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