# Modeling of Metal Forming and Machining Processes: by Finite Element and Soft Computing Methods

Springer Science & Business Media, May 14, 2008 - Technology & Engineering - 590 pages
The use of computational techniques is increasing day by day in the manufacturing sector. Process modeling and optimization with the help of computers can reduce expensive and time consuming experiments for manufacturing good quality products. Metal forming and machining are two prominent manufacturing processes. Both of these processes involve large deformation of elasto-plastic materials due to applied loads. In metal forming, the material is plastically deformed without causing fracture. On the other hand, in machining, the material is deformed till fracture, in order to remove material in the form of chips. To understand the physics of metal forming and machining processes, one needs to understand the kinematics of large deformation (dependence of deformation and its rate on displacement) as well as the constitutive behavior of elasto-plastic materials (dependence of internal forces on deformation and its rate). Once the physics is understood, these phenomena have to be converted to mathematical relations in the form of differential equations. The interaction of the work-piece with the tools/dies and other surroundings also needs to be expressed in a mathematical form (known as the boundary and initial conditions). In this book, the first four chapters essentially discuss the physics of metal forming and machining processes. The physical behavior of the work-piece during the processes is modeled in the form of differential equations and boundary and initial conditions.

### What people are saying -Write a review

User Review - Flag as inappropriate

THIS IS A VERY GOOD BOOK TO SOLVE OUR PROBLEN IN ENGG WORKSHOP.

### Contents

 Metal Forming and Machining Processes 1 12 Metal Forming 2 122 Sheet Metal Forming Processes 17 13 Machining 23 131 Turning 24 132 Milling 28 133 Some Other Machining Processes 30 14 Summary 31
 57 ElastoPlastic Formulation 334 58 Summary 341 Finite Element Modeling of Metal Forming Processes Using Updated Lagrangian Formulation 345 62 Application of Finite Element Method to Updated Lagrangian Formulation 347 622 Integral Form of Equilibrium Equation 349 623 Finite Element Formulation 351 624 Evaluation of the Derivative 356 625 Iterative Scheme 365

 Review of Stress Linear Strain and Elastic StressStrain Relations 33 22 Index Notation and Summation Convention 35 23 Stress 41 232 Analysis of Stress at a Point 52 233 Equations of Motion 61 24 Deformation 64 241 Linear Strain Tensor 65 242 Analysis of Strain at a Point 75 243 Compatibility Conditions 82 25 Material Behavior 84 251 Elastic StressStrain Relations for Small Deformation 85 26 Summary 93 27 References 94 Classical Theory of Plasticity 95 32 OneDimensional Experimental Observations on Plasticity 97 33 Criteria for Initial Yielding of Isotropic Materials 107 331 von Mises Yield Criterion 108 332 Tresca Yield Criterion 110 333 Geometric Representation of Yield Criteria 111 334 Convexity of Yield Surfaces 114 335 Experimental Validation 115 34 Incremental Strain and Strain Rate Measures 121 342 Strain Rate Tensor 125 343 Relation Between Incremental Linear Strain Tensor and Strain Rate Tensor 130 35 Modeling of Isotropic Hardening or Criterion for Subsequent Isotropic Yielding 134 351 Strain Hardening Hypothesis 136 352 Work Hardening Hypothesis 138 36 Plastic StressStrain and StressStrain Rate Relations for Isotropic Materials 141 361 Associated Flow Rule 143 362 ElasticPlastic Incremental StressStrain Relation for Mises Material 151 363 ElasticPlastic StressStrain Rate Relation for Mises Material 153 364 Viscoplasticity and Temperature Softening 157 37 Objective Stress Rate and Objective Incremental Stress Tensors 161 371 Jaumann Stress Rate and Associated Objective Incremental Stress Tensor 163 38 Unloading Criterion 168 39 Eulerian and Updated Lagrangian Formulations for Metal Forming Processes 170 392 Incremental Equation of Motion 172 393 Eulerian Formulation for Metal Forming Problems 173 394 Updated Lagrangian Formulation for Metal Forming Problems 182 310 Eulerian Formulation for Machining Processes 188 311 Summary 192 312 References 193 Plasticity of Finite Deformation and Anisotropic Materials and Modeling of Fracture and Friction 195 42 Kinematics of Finite Deformation and Rotation 197 43 Constitutive Equation for Eulerian Formulation When the Rotation Is Not Small 207 431 Solution Procedure 210 44 Kinematics of Finite Incremental Deformation and Rotation 212 45 Constitutive Equation for Updated Lagrangian Formulation for Finite Incremental Deformation and Rotation 219 46 Anisotropic Initial Yield Criteria 223 461 Hills Anisotropic Yield Criteria 226 462 Plane Stress Anisotropic Yield Criterion of Barlat and Lian 227 463 A ThreeDimensional Anisotropic Yield Criterion of Barlat and Coworkers 229 464 A Plane Strain Anisotropic Yield Criterion 236 47 ElasticPlastic Incremental StressStrain and StressStrain Rate Relations for Anisotropic Materials 239 472 ElasticPlastic StressStrain Rate Relation for Anisotropic Materials 243 48 Kinematic Hardening 247 49 Modeling of Ductile Fracture 252 492 Void Nucleation Growth and Coalescence Model Goods and Brown Rice and Tracy and Thomason Model 253 493 Continuum Damage Mechanics Models 257 494 Phenomenological Models 262 410 Friction Models 265 4101 Wanheim and Bay Friction Model 266 411 Summary 268 412 References 269 Finite Element Modeling of Metal Forming Processes Using Eulerian Formulation 273 52 Background of Finite Element Method 274 522 Developing Elemental Equations 285 523 Assembly Procedure 292 524 Applying Boundary Conditions 295 525 Solving the System of Equations 296 53 Formulation of PlaneStrain Metal Forming Processes 297 531 Governing Equations and Boundary Conditions 298 532 NonDimensionalization 301 533 Weak Formulation 302 534 Finite Element Formulation 304 535 Application of Boundary Conditions 311 536 Estimation of Neutral Point 313 537 Formulation for Strain Hardening 315 538 Modification of Pressure Field at Each Iteration 316 539 Calculation of Secondary Variables 318 5310 Some Numerical Aspects 319 5311 Typical Results and Discussion 320 54 Formulation of Axisymmetric Metal Forming Processes 322 55 Formulation of ThreeDimensional Metal Forming Processes 331
 626 Determination of Stresses 368 627 Divergence Handling Techniques 371 63 Modeling of Axisymmetric Open Die Forging by Updated Lagrangian Finite Element Method 372 631 Domain and Boundary Conditions 374 632 Cylindrical Arc Length Method for Displacement Control Problems 377 633 Friction Algorithm 380 634 Convergence Study and Evaluation of Secondary Variables 382 636 Typical Results 384 637 Residual Stress Distribution 388 638 Damage Distribution Hydrostatic Stress Distribution and Fracture 393 64 Modeling of Deep Drawing of Cylindrical Cups by Updated Lagrangian Finite Element Method 396 641 Domain and Boundary Conditions 399 642 Contact Algorithm 405 643 Typical Results 406 644 Anisotropic Analysis Ear Formation and Parametric Studies 408 645 Optimum Blank Shape 416 65 Summary 419 66 References 420 Finite Element Modeling of Orthogonal Machining Process 425 72 Domain Governing Equations and Boundary Conditions for Eulerian Formulation 426 722 Governing Equations 428 723 Boundary Conditions 429 73 Finite Element Formulation 431 732 Approximations for Velocity Components and Pressure 433 733 Finite Element Equations 436 734 Application of Boundary Conditions Solution Procedure and Evaluation of Secondary Quantities 440 74 Results and Discussion 442 741 Validation of the Formulation 444 743 Primary Shear Deformation Zone Contours of Equivalent Strain Rate and Contours of Equivalent Stress 445 75 Summary 447 76 References 448 Background on Soft Computing 450 82 Neural Networks 452 821 Biological Neural Networks 453 822 Artificial Neurons 454 The Learning Machine 458 824 MultiLayer Perceptron Neural Networks 462 825 Radial Basis Function Neural Network 469 826 Unsupervised Learning 471 83 Fuzzy Sets 472 831 Mathematical Definition of Fuzzy Set 473 832 Some Basic Definitions and Operations 474 833 Determination of Membership Function 476 834 Fuzzy Relations 480 835 Extension Principle 481 836 Fuzzy Arithmetic 482 837 Fuzzy Sets vs Probability 483 838 Fuzzy Logic 484 8310 Fuzzy Rules 486 First or Last of Maxima 491 841 Binary Coded Genetic Algorithms 492 842 Real Coded Genetic Algorithms 497 85 Soft Computing vs FEM 498 86 Summary 499 87 References 500 Predictive Modeling of Metal Forming and Machining Processes Using Soft Computing 503 92 Design of Experiments and Preliminary Study of the Data 504 93 Preliminary Statistical Analysis 508 932 Hypothesis Testing 509 933 Analysis of Variance 515 934 Multiple Regression 518 94 Neural Network Modeling 522 941 Selection of Training and Testing Data 523 942 Deciding the Processing Functions 525 945 Effect of Spread Parameter in Radial Basis Function Neural Network 526 946 Data Filtration 528 95 Prediction of Dependent Variables Using Fuzzy Sets 533 96 Prediction Using ANFIS 535 97 Computation with Fuzzy Variables 539 98 Summary 545 99 References 546 Optimization of Metal Forming and Machining Processes 548 102 Optimization Problems in Metal Forming 550 1021 Optimization of Roll Pass Scheduling 551 1022 Optimization of Rolls 554 1024 A Brief Review of Other Optimization Studies in Metal Forming 556 103 Optimization Problems in Machining 559 1032 Optimization of Multipass Turning Process 563 1033 Online Determination of Equations for Machining Performance Parameters 569 104 Summary 573 Epilogue 579 111 References 583 Index 584 Copyright