Contents 1 Metal Forming and Machining Processes... 1 1.1 Introduction.. 1 1.2 Metal Forming...... 2 1.2.1 Bulk Metal Forming.... 2 1.2.2 Sheet Metal Forming Processes... 17 1.3 Machining.. 23 1.3.1 Turning...... 24 1.3.2 Milling. 28 1.3.3 Some Other Machining Processes... 30 1.4 Summary 31 1.5 References.. 31 2 Review of Stress, Linear Strain and Elastic Stress-Strain Relations... 33 2.1 Introduction.... 33 2.2 Index Notation and Summation Convention...... 35 2.3 Stress.. 41 2.3.1 Stress at a Point...... 41 2.3.2 Analysis of Stress at a Point.... 52 2.3.3 Equation of Motion....... 61 2.4 Deformation........ 64 2.4.1 Linear Strain Tensor...... 65 2.4.2 Analysis of Strain at a Point..... 75 2.4.3 Compatibility Conditions..... 82 2.5 Material Behavior..... 84 2.5.1 Elastic Stress-Strain Relations for Small Deformations... 85 2.6 Summary...... 93 2.7 References.... 94 3 Classical Theory of Plasticity.. 95 3.1 Introduction.. 95 3.2 One-Dimensional Experimental Observations on Plasticity. 97 3.3 Criteria for Initial Yielding of Isotropic Materials.. 107
xii Contents 3.3.1 von Mises Yield Criterion.... 108 3.3.2 Tresca Yield Criterion...... 110 3.3.3 Geometric Representation of Yield Criteria.... 111 3.3.4 Convexity of Yield Surfaces.... 114 3.3.5 Experimental Validation.. 115 3.4 Incremental Strain and Strain Rate Measures..... 121 3.4.1 Incremental Linear Strain Tensor..... 121 3.4.2 Strain Rate Tensor.... 125 3.4.3 Relation Between Incremental Linear Strain Tensor and Strain Rate Tensor...... 130 3.5 Modeling of Isotropic Hardening or Criterion for Subsequent Isotropic Yielding.... 134 3.5.1 Strain Hardening Hypothesis.... 136 3.5.2 Work Hardening Hypothesis.... 138 3.5.3 Experimental Validations..... 138 3.6 Plastic Stress-Strain and Stress-Strain Relations for Isotropic Materials... 141 3.6.1 Associated Flow Rule... 143 3.6.2 Elastic-Plastic Incremental Stress-Strain Relations for Mises Material... 151 3.6.3 Elastic-Plastic Incremental Stress-Strain Rate Relation for Mises Material... 153 3.6.4 Viscoplasticity and Temperature Softening... 157 3.7 Objective Stress Rate and Objective Incremental Stress Tensors 161 3.7.1 Jaumann Stress Rate and Associated Objective Incremental Stress Tensor.... 163 3.8 Unloading Criterion....... 168 3.9 Eulerian and Updated Lagrangian Formulations for Metal Forming Processes... 170 3.9.1 Equation of Motion in Terms of Velocity Derivatives... 170 3.9.2 Incremental Equation of Motion... 172 3.9.3 Eulerian Formulation for Metal Forming Problems... 173 3.9.4 Updated Lagrangian Formulation for Metal Forming Problems... 182 3.10 Eulerian Formulation for Machining Processes... 188 3.11 Summary.. 192 3.12 References..... 193 4 Plasticity of Finite Deformation and Anisotropic Materials and Modeling of Fracture and Friction.... 195 4.1 Introduction..... 195 4.2 Kinematics of Finite Deformation and Rotation... 197 4.3 Constitutive Equation for Eulerian Formulation When the Rotation Is Not Small... 207 4.3.1 Solution Procedure.... 210 4.4 Kinematics of Finite Incremental Deformation and Rotation... 212
Contents xiii 4.5 Constitutive Equation for Updated Lagrangian Formulation for Finite Incremental Deformation and Rotation..... 219 4.6 Anisotropic Initial Yield Criteria.... 223 4.6.1 Hill s Anisotropic Yield Criteria..... 226 4.6.2 Plane Stress Anisotropic Yield Criterion of Barlat and Lian... 227 4.6.3 A Three-Dimensional Anisotropic Yield Criterion of Barlat and Co-workers... 229 4.6.4 A Plane Strain Anisotropic Yield Criterion....... 236 4.7 Elastic-Plastic Incremental Stress-Strain and Stress-Strain Rate Relations for Anisotropic Materials.... 239 4.7.1 Elastic-Plastic Incremental Stress-Strain Relation for Anisotropic Materials... 239 4.7.2 Elastic-Plastic Incremental Stress-Strain Rate Relation for Anisotropic Materials... 243 4.8 Kinematic Hardening... 247 4.9 Modeling of Ductile Fracture...... 252 4.9.1 Porous Plasticity Model of Berg and Gurson... 252 4.9.2 Void Nucleation, Growth and Coalescence Model (Goods and Brown, Rice and Trace and Thomason Model)... 253 4.9.3 Continuum Damage Mechanics Models... 257 4.9.4 Phenomenological Models... 262 4.10 Friction Models.... 265 4.10.1 Wanheim and Bay Friction Model.... 266 4.11 Summary.. 268 4.12 References.... 269 5 Finite Element Modeling of Metal Forming Processes Using Eulerian Formulation. 273 5.1 Introduction. 273 5.2 Background of Finite Element Method... 274 5.2.1 Pre-processing... 274 5.2.2 Developing Elemental Equations... 285 5.2.3 Assembly Procedure... 292 5.2.4 Applying Boundary Conditions... 295 5.2.5 Solving the System of Equations... 296 5.2.6 Post-processing... 296 5.3 Formulation of Plane-Strain Metal Forming Processes.. 297 5.3.1 Governing Equations and Boundary Conditions... 298 5.3.2 Non-Dimensionalization... 301 5.3.3 Weak Formulation... 302 5.3.4 Finite Element Formulation... 304 5.3.5 Application of Boundary Conditions... 311 5.3.6 Estimation of Neutral Point... 313 5.3.7 Formulation for Strain Hardening... 315 5.3.8 Modification of Pressure Field at Each Iteration... 316 5.3.9 Calculation of Secondary Variables... 318
xiv Contents 5.3.10 Some Numerical Aspects... 319 5.3.11 Typical Results and Discussion... 320 5.4 Formulation of Axisymmetric Metal Forming Processes...322 5.5 Formulation of Three-Dimensional Metal Forming Processes... 331 5.6 Incorporation of Anisotropy... 331 5.7 Elasto-Plastic Formulation... 334 5.8 Summary.... 341 5.9 References... 341 6 Finite Element Modeling of Metal Forming Processes Using Updated Lagrangian Formulation... 345 6.1 Introduction... 345 6.2 Application of Finite Element Method to Updated Lagrangian Formulation. 347 6.2.1 Governing Equations... 347 6.2.2 Integral Form of Equilibrium Equation... 349 6.2.3 Finite Element Formulation...351 6.2.4 Evaluation of the Derivative... 356 6.2.5 Iterative Scheme... 365 6.2.6 Determination of Stresses... 368 6.2.7 Divergence Handling Techniques... 371 6.3 Modeling of Axisymmetric Open Die Forging by Updated Lagrangian Finite Element Method... 372 6.3.1 Domain and Boundary Conditions... 374 6.3.2 Cylindrical Arc Length Method for Displacement Control Problems... 377 6.3.3 Friction Algorithm... 380 6.3.4 Convergence Study and Evaluation of Secondary Variables... 382 6.3.5 Validation of the Finite Element Formulation... 382 6.3.6 Typical Results... 384 6.3.7 Residual Stress Distribution... 388 6.3.8 Damage Distribution, Hydrostatic Stress Distribution and Fracture... 393 6.4 Modeling of Deep Drawing of Cylindrical Cups by Updated Lagrangian Finite Element Method... 396 6.4.1 Domain and Boundary Conditions... 399 6.4.2 Contact Algorithm... 405 6.4.3 Typical Results... 406 6.4.4 Anisotropic Analysis, Ear Formation and Parametric Studies... 408 6.4.5 Optimum Blank Shape... 416 6.5 Summary... 419 6.6 References... 420 7 Finite Element Modeling of Orthogonal Machining Process... 425 7.1 Introduction. 425
Contents xv 7.2 Domain, Governing Equations and Boundary Conditions for Eulerian Formulation... 426 7.2.1 Domain...... 426 7.2.2 Governing Equations... 428 7.2.3 Boundary Conditions... 429 7.3 Finite Element Formulation... 431 7.3.1 Integral Form..... 431 7.3.2 Approximations for Velocity Components and Pressure.. 433 7.3.3 Finite Element Equations... 436 7.3.4 Application of Boundary Conditions, Solution Procedure and Evaluation of Secondary Quantities...... 440 7.4 Results and Discussion... 442 7.4.1 Validation of the Formulation.... 444 7.4.2 Parametric Studies...... 444 7.4.3 Primary Shear Deformation Zone, Contours of Equivalent Strain Rate and Contours of Equivalent Stress...... 445 7.5 Summary..... 447 7.6 References....... 448 8 Background on Soft Computing... 451 8.1 Introduction.. 451 8.2 Neural Networks... 452 8.2.1 Biological Neural Networks. 453 8.2.2 Artificial Neurons. 454 8.2.3 Perceptron: The Learning Machine.. 458 8.2.4 Multi-Layer Perceptron Neural Networks. 462 8.2.5 Radial Basis Function Neural Network.... 469 8.2.6 Unsupervised Learning. 471 8.3 Fuzzy Sets.... 472 8.3.1 Mathematical Definition of Fuzzy Set.. 473 8.3.2 Some Basic Definitions and Operations... 474 8.3.3 Determination of Membership Function... 476 8.3.4 Fuzzy Relations... 480 8.3.5 Extension Principle... 481 8.3.6 Fuzzy Arithmetic.... 482 8.3.7 Fuzzy Sets vs Probability....... 483 8.3.8 Fuzzy Logic... 484 8.3.9 Linguistic Variables and Hedges... 484 8.3.10 Fuzzy Rules... 486 8.3.11 Fuzzy Inference. 486 8.4 Genetic Algorithms... 491 8.4.1 Binary Coded Genetic Algorithms.... 492 8.4.2 Real Coded Genetic Algorithms... 497 8.5 Soft Computing vs FEM... 498 8.6 Summary.. 499 8.7 References.... 500
xvi Contents 9 Predictive Modeling of Metal Forming and Machining Processes Using Soft Computing... 503 9.1 Introduction.. 503 9.2 Design of Experiments and Preliminary Study of the Data... 504 9.3 Preliminary Statistical Analysis... 508 9.3.1 Correlation Analysis... 508 9.3.2 Hypothesis Testing... 509 9.3.3 Analysis of Variance... 515 9.3.4 Multiple Regression... 518 9.4 Neural Network Modeling... 522 9.4.1 Selection of Training and Testing Data... 523 9.4.2 Deciding the Processing Functions... 525 9.4.3 Effect of Number of Hidden Layers... 525 9.4.4 Effect of Number of Neurons in the Hidden Layers... 525 9.4.5 Effect of Spread Parameter in Radial Basis Function Neural Network. 526 9.4.6 Data Filtration... 528 9.4.7 Lower and Upper Estimates... 528 9.5 Prediction of Dependent Variables Using Fuzzy Sets... 533 9.6 Prediction Using ANFIS... 535 9.7 Computation with Fuzzy Variables... 539 9.8 Summary... 545 9.9 References... 546 10 Optimization of Metal Forming and Machining Processes 549 10.1 Introduction.. 549 10.2 Optimization Problems in Metal Forming. 550 10.2.1 Optimization of Roll Pass Scheduling...... 551 10.2.2 Optimization of Rolls 554 10.2.3 Optimization of Wire Drawing and Extrusion.. 554 10.2.4 A Brief Review of Other Optimization Studies in Metal Forming.. 556 10.3 Optimization Problems in Machining.. 559 10.3.1 A Brief Review of Optimization of Machining Processes... 559 10.3.2 Optimization of Multipass Turning Process. 563 10.3.3 Online Determination of Equations for Machining Performance Parameters.. 569 10.4 Summary.. 573 10.5 References 573 11 Epilogue 579 11.1 References 583 Index... 585
http://www.springer.com/978-1-84800-188-6