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

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Springer Science & Business Media, May 14, 2008 - Technology & Engineering - 590 pages
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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.
 

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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
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About the author (2008)

Prof. P. M. Dixit has been actively working in the area of metal forming, machining and non-traditional machining for the past 20 years. He has published extensively in leading international journals and carried out projects in the area of metal forming and large deformation. He also teaches Metal Forming, Plasticity and FEM to postgraduate and senior undergraduate students. Prof. P.M. Dixit obtained his bachelors degree in Aeronautical Engineering from the Indian Institute of Technology, Kharagpur, in 1974. He was awarded a silver medal for securing the first rank in the Department. Subsequently, he obtained his doctoral degree in Mechanics from the University of Minnesota, Minneapolis, U.S.A, in 1979. After receiving his Ph.D. degree, Prof. Dixit taught at the Aeronautical Engineering Department of the Indian Institute of Technology, Kharagpur for 4 years (1980-1984). Since 1984, Prof. Dixit has been teaching at the Mechanical Engineering Department of the Indian Institute of Technology, Kanpur.

Prof. U. S. Dixit has more than a decade’s experience in carrying out research in the area of metal forming and machining. Apart from FEM, he uses fuzzy set theory and neural networks in his research. Before taking up a research career, he worked for four years as a machine tool designer in HMT Ltd. Pinjore, India. He has a number of publications, some of them jointly with Prof. P.M. Dixit. Prof. U. S. Dixit is currently a Professor of Mechanical Engineering at the Indian Institute of Technology in Guwahati. Prof. U. S. Dixit obtained his bachelors degree in Mechanical Engineering from the Indian Institute of Technology, Roorkee in 1987. He gained his M. Tech in Mechanical Engineering and his Ph.D. in Mechanical Engineering from the Indian Institute of Technology, Kanpur, in 1993 and 1998 respectively.