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 |  موضوع: كتاب Modeling of Metal Forming and Machining Processes الثلاثاء 14 يوليو 2020, 11:29 pm | |
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أخوانى فى الله
أحضرت لكم كتاب
Modeling of Metal Forming and Machining Processes
by Finite Element and Soft Computing Methods
Prakash M. Dixit , Uday S. Dixit
و المحتوى كما يلي :
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 212Contents 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 . 318xiv 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 . 425Contents 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 500xvi 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
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