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

1 | |

2 | |

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 |

584 | |

### Other editions - View all

### Common terms and phrases

analysis anisotropic anisotropic yield assumed boundary conditions called coefficient constitutive equation coordinate system Coulomb’s law cutting speed deformed configuration depth of cut derivative deviatoric displacement vector Dixit elastic elastic-plastic Eulerian formulation experimental expression finite element method friction fuzzy set genetic algorithms given by Equation hardening incremental deformation incremental displacement vector incremental stress interface International Journal isotropic iteration linear strain tensor machining processes material matrix membership function membership grade metal forming processes Mises neural network neurons nodal nodes normal obtained optimization output parameters plane plane strain plastic deformation prediction principal directions problem punch residual stress respect rotation shape functions shear stress sheet sheet metal forming solution stress components stress rate stress tensor stress vector stress-strain relations thickness tool Tresca updated Lagrangian formulation values variables velocity void work-piece yield criterion yield stress yield surface zero