From Creep Damage Mechanics to Homogenization Methods (eBook)

Preface 6
Selected Papers of the Main Achievements of Professor Nobutada Ohno 10
Contents 12
Contributors 15
1 Thermo-Electro-Mechanical Properties of Interpenetrating Phase Composites with Periodic Architectured Reinforcements 19
1.1 Introduction 20
1.2 Architecture and Numerical Analysis Assumptions 23
1.2.1 Architectures 23
1.2.2 Governing Equations and Boundary Conditions 24
1.2.3 Analytical Models for Calculating Effective Properties 26
1.3 Results and Discussions 27
1.3.1 Effective Thermal/Electrical Conductivity 27
1.3.2 Effective Elastic Properties 29
1.4 Manufacturability 33
References 35
2 A Continuum Damage Model Based on Experiments and Numerical Simulations---A Review 37
2.1 Introduction 38
2.2 Continuum Damage Model 39
2.2.1 Kinematics 39
2.2.2 Constitutive Equations 41
2.3 Uniaxial Tension Tests 44
2.4 Numerical Analyses on the Micro-Scale 45
2.5 Experiments and Numerical Simulations with Biaxially Loaded Specimens 48
2.6 Conclusions 52
References 52
3 The Multiplicative Decomposition of the Deformation Gradient in Plasticity---Origin and Limitations 54
3.1 Introduction 54
3.2 One-Dimensional Considerations 56
3.3 Basic Facts for a Deforming Continuous Body 62
3.4 A Short Historical Overview 64
3.5 Lagrangean Formulations with Plastic Strain 68
3.6 Formulations with Unstressed Configurations 71
3.7 Director Triads and Isoclinic Configurations 78
References 80
4 Effect of Biaxial Work Hardening Modeling for Sheet Metals on the Accuracy of Forming Limit Analyses Using the Marciniak-Kuczy?ski Approach 84
4.1 Introduction 85
4.2 Constitutive Model 87
4.3 Experimental Methods 90
4.3.1 Test Material 90
4.3.2 Biaxial Tensile Testing Methods 90
4.3.3 Measurement of Forming Limit Strains, Stresses, and Plastic Work per Unit Volume 95
4.4 Material Modeling 96
4.4.1 Results of Biaxial Tensile Tests 96
4.4.2 Isotropic Hardening Model 97
4.4.3 Differential Hardening Model 98
4.5 Forming Limit Analysis 102
4.5.1 Conditions of Analysis 102
4.5.2 Results and Discussion 103
4.6 Conclusions 106
References 110
5 Three-Dimensional FE Analysis Using Homogenization Method for Ductile Polymers Based on Molecular Chain Plasticity Model Considering Craze Evolution 113
5.1 Introduction 114
5.2 Material Models for Ductile Polymers 116
5.2.1 Configurations with Damage 116
5.2.2 Model for Glassy Phase 117
5.2.3 Model for Crystalline Phase 119
5.2.4 Homogenization Method 120
5.3 Material Response Law 120
5.3.1 Inelastic Response Law for Glassy Phase 120
5.3.2 Hardening Law for Crystalline Phase 122
5.4 Craze Evolution Equation 122
5.5 FE Simulation and Discussion 123
5.5.1 Analysis with Specimen Model for Glassy Polymer 123
5.5.2 Single-Phase Analysis for Crystalline Phase 127
5.5.3 Multiscale Analysis for Ductile Polymers 130
5.6 Conclusions 133
References 134
6 Inelastic Deformation and Creep-Fatigue Life of Plate-Fin Structures 136
6.1 Introduction 137
6.2 Outline of a Plate-Fin Heat Exchanger 138
6.3 Elastic-Plastic Homogenization Analysis of Unit Cell Model 139
6.4 Uniaxial Strength Tests with Small Plate-Fin Specimens 144
6.4.1 Tensile and Creep Tests 144
6.4.2 Fatigue Tests 146
6.4.3 Comparison with FEM Results 149
6.5 Thermal Fatigue Test of Plate-Fin Structure 151
6.5.1 Method and Results of Thermal Fatigue Test 151
6.5.2 Fatigue Life Prediction Based on Homogenization FEM Analysis 153
6.6 Conclusions 156
References 157
7 Review on Spatio-Temporal Multiscale Phenomena in TRIP Steels and Enhancement of Its Energy Absorption 158
7.1 Introduction 159
7.2 Constitutive Model for TRIP Steel 162
7.2.1 Macroscopic Model 162
7.2.2 A Bridging Method Between the Spatial Scales and Microscopic Model 164
7.3 Validation by Experiments 167
7.3.1 Macroscopic Model 167
7.3.2 Analyzes of Micrographs to Discuss the Microstructural Change 168
7.4 Obtained Results and Discussions 169
7.4.1 Spatial Multiscale Phenomena 169
7.4.2 Temporal Multiscale Phenomenon on the Energy Absorption Characteristic 171
7.5 Summary 174
References 174
8 Methods for Creep Rupture Analysis---Previous Attempts and New Challenges 177
8.1 Introduction 177
8.1.1 Uniaxial Creep Tests---Tool for Initial Material Characterization 179
8.1.2 Multiaxial Creep Tests---Advanced Characterization of Materials 179
8.1.3 New Concepts of Creep Analysis 180
8.2 Previous Attempts of Creep Analysis---Selected Examples of Uniaxial and Biaxial Tests 180
8.2.1 Analysis of Prior Deformation Effect on Creep Under Uniaxial Loading Conditions 180
8.2.2 Creep Tests Under Complex Stress States 183
8.3 A Short Survey on Advances in Modelling of Creep Damage Development 189
8.4 New Attempts for Damage Development During Creep 194
8.4.1 Experimental Details 194
8.4.2 Experimental Results and Discussion 198
8.5 Concluding Remarks 209
References 210
9 Strain Gradient Plasticity: A Variety of Treatments and Related Fundamental Issues 213
9.1 Introduction 213
9.2 Basic Relations Unchanged from Classical J2 Theory 214
9.3 Introduction of Plastic Strain Gradient into Yield Condition 215
9.4 Different Treatments of Strain Gradient Plasticity 216
9.4.1 Treatment 1: Eq. (??) is Simply an Extra Balance Law 217
9.4.2 Treatment 2: A Virtual Work Principle with Higher-Order Quantities Is Introduced as the Major Premise 218
9.4.3 Treatment 3: A Variational Principle Is Utilized 220
9.4.4 Treatment 4: Eq. (??) is Merely a Constitutive Relation 222
9.5 Computational Aspects 224
9.5.1 Finite Element Procedure 224
9.5.2 Numerical Issues 224
9.6 Discussion 227
9.6.1 Plastic Dissipation 228
9.6.2 Large Strains 229
9.6.3 Crystal Plasticity 230
9.7 Conclusions 230
References 231
10 Effects of Fiber Arrangement on Negative Poisson's Ratio of Angle-Ply CFRP Laminates: Analysis Based on a Homogenization Theory 233
10.1 Introduction 234
10.2 Analysis Method 235
10.2.1 Modeling of Angle-Ply CFRP Laminates 235
10.2.2 Homogenization Theory for Nonlinear Time-Dependent Composites 236
10.3 Analysis 237
10.3.1 Analysis Conditions 237
10.3.2 Results of Analysis: Macroscopic Stress-Strain Relationships 239
10.3.3 Results of Analysis: Elastic-Viscoplastic Poisson's Ratios 240
10.3.4 Results of Analysis: Microscopic Mechanisms 242
10.4 Conclusions 243
References 244
11 Modeling of Internal Damage Evolution of Piezoelectric Ceramics Under Compression-Compression Fatigue Tests 245
11.1 Introduction 245
11.2 Experimental Results 248
11.3 Modeling of Fatigue Damage Evolution 250
11.4 Concluding Remarks 252
References 253
12 Analysis of Inelastic Behavior for High Temperature Materials and Structures 255
12.1 Introduction 255
12.2 High-Temperature Inelasticity in Structural Materials 256
12.2.1 Uni-axial Stress State 256
12.2.2 Multi-axial and Stress State Effects 273
12.3 High-Temperature Inelasticity in Structures 279
12.3.1 Steam Transfer Line 281
12.3.2 Two-Bar System Under Thermo-Mechanical Loading 287
12.4 Microstructural Features and Length Scale Effects 291
12.5 Temporal Scale Effects 296
12.6 Modeling Approaches 297
12.7 Conclusions and Recommendations 303
References 305
13 Onset of Matrix Cracking in Fiber Reinforced Polymer Composites: A Historical Review and a Comparison Between Periodic Unit Cell Analysis and Analytic Failure Criteria 313
13.1 Introduction 314
13.2 A Brief Historical Review of Matrix Crack Modeling 315
13.2.1 Analytic Failure Criterion 315
13.2.2 Micromechanics of Matrix Cracks 317
13.2.3 Unit Cell Analysis 318
13.3 Comparison Between Analytic Criteria and Periodic Unit Cell Analysis 319
13.4 Conclusions and Remarks 329
References 329
14 Swelling-Induced Buckling Patterns in Gel Films with a Square Lattice of Holes Subjected to In-Plane Uniaxial and Biaxial Pretensions 332
14.1 Introduction 333
14.2 Inhomogeneous Field Theory 335
14.3 Numerical Modeling 337
14.4 Results and Discussion 339
14.4.1 Uniaxial Pretension 339
14.4.2 Biaxial Pretension 343
14.4.3 Dependence on Unit Cell Size 346
14.5 Conclusions 346
References 347
15 A Method to Evaluate Creep Properties of Solder Alloys Using Micro Indentation 348
15.1 Introduction 348
15.2 Experimental Discussions 350
15.2.1 Experimental Method 350
15.2.2 Experimental Results 351
15.3 The Indentation Test Including the Constant Depth Process 354
15.4 Method-FE Model 356
15.5 Principal Stress Plane Caused by the Indentation Test 357
15.5.1 Identification of the Principal Stress Plane 357
15.5.2 Method to Determine the New Reference Area 359
15.6 Evaluation of the Creep Deformation Considering the Principal Stress Plane 362
15.6.1 Behavior of the Plastic Depth in the Constant Depth Process 362
15.6.2 The Method to Evaluate the Steady-State Creep 363
15.7 Conclusion 367
References 368
16 The Behavior of the Graded Cellular Material Under Impact 370
16.1 Introduction 370
16.2 Finite Element Simulation of the Graded Honeycomb Structure 372
16.3 Analytical Modeling of the Deformation Process in the Graded Cellular Rod 376
16.4 Experimental Work on the Foam Block with Varying Cross-Section 380
16.5 Conclusion 388
References 389
17 Fracture Mechanics at Atomic Scales 391
17.1 Introduction 391
17.2 Fracture Criterion for Mechanical Instability in Arbitrary Atomic Structures 393
17.3 Simplified Evaluation of Fracture Criterion for Large-Scale Atomic Structures 398
17.4 Recent Advances of Instability Criteria for Complicated Systems 402
17.5 Conclusions 406
References 406
18 Radiation Damage Evolution in Ductile Materials 409
18.1 Introduction 409
18.2 Constitutive Relations 411
18.3 Kinetics of Evolution of Radiation Induced Damage 413
18.4 Analytical Solutions for the Problem of Periodic Irradiation Combined with Cyclic Axial Loads 418
18.5 Concluding Remarks 422
References 423
19 Capabilities of the Multi-mechanism Model in the Prediction of the Cyclic Behavior of Various Classes of Metals 424
19.1 Introduction 425
19.2 Experimental Procedure 426
19.2.1 Materials, Specimens and Experimental Device 426
19.2.2 Tests Performed in Earlier Work 428
19.3 Numerical Simulations 429
19.3.1 Constitutive Equations of the MM Model 429
19.3.2 Identification of the Material Parameters 433
19.3.3 Summary of the Qualitative Capabilities of the MM Model 439
19.3.4 Thermodynamic Consistency of the Model with the Identified Parameters 439
19.3.5 Simulation of the Stress Controlled Experiments of Taleb (2013a) 440
19.4 Discussion 445
19.5 Concluding Remarks 447
References 447
20 Phase-Field Modeling for Dynamic Recrystallization 451
20.1 Introduction 452
20.2 MPF-DRX Model 455
20.2.1 Deformation 455
20.2.2 DRX Grain Growth 457
20.2.3 DRX Grain Nucleation 458
20.2.4 Simulations 459
20.3 MPFFE-DRX Model 461
20.4 Conclusions 465
References 465
21 Mechanical Properties of Shape Memory Alloy and Polymer 470
21.1 Introduction 470
21.2 Thermomechanical Properties and Modeling of Shape Memory Alloy 472
21.2.1 Constitutive Relationship for Martensitic Transformation 472
21.2.2 Transformation Kinetics of Martensitic Transformation 472
21.2.3 Constitutive Relationship Containing Martensitic and R-Phase Transformations 473
21.2.4 Transformation Kinetics of R-Phase Transformation 474
21.2.5 Stress-Strain Curves and Transformed Region 475
21.2.6 Results and Discussion of Modeling 475
21.2.7 Conditions for Progress of Phase Transformation and Subloop-Deformation Behavior 481
21.3 Thermomechanical Properties and Modeling of Shape Memory Polymer 485
21.3.1 Linear Constitutive Equation 485
21.3.2 Nonlinear Constitutive Equation 485
21.3.3 Dependence of Coefficients on Temperature 486
21.3.4 Results and Discussion of Modeling 487
21.4 Conclusion 495
References 495
22 Constitutive Model of Discontinuously-Reinforced Composites Taking Account of Reinforcement Damage and Size Effect and Its Application 497
22.1 Introduction 497
22.2 Load Carrying Capacity of a Broken Ellipsoidal Inhomogeneity 499
22.2.1 Intact Ellipsoidal Inhomogeneity 499
22.2.2 Broken Ellipsoidal Inhomogeneity 500
22.3 An Incremental Damage Model of Discontinuously-Reinforced Composites 503
22.3.1 Properties of Constituent Materials 504
22.3.2 Modeling of Progressive Damage of Reinforcements 506
22.3.3 Formulation 507
22.3.4 Cumulative Probability of the Cracked Reinforcements 510
22.3.5 Equivalent Stress of the Matrix in Composite 511
22.3.6 Cracking Damage and Debonding Damage of Reinforcements 512
22.4 Influence of Reinforcement Damage on Stress-Strain Response of Composites 513
22.4.1 Elastic Stress-Strain Response 513
22.4.2 Elastic-Plastic Stress-Strain Response 514
22.5 Consideration of Particle Size Effects 515
22.5.1 Particle Size Effect on Deformation 516
22.5.2 Particle Size Effect on Debonding Damage 517
22.5.3 Composites Containing Various Sized Particles 518
22.6 Influence of Debonding Damage and Particle Size in Particulate-Reinforced Composites 519
22.6.1 Composites Containing Constant Sized Particles 519
22.6.2 Composites Containing Various Sized Particles 521
22.7 Finite Element Method Based on the Constitutive Model 523
22.8 An Elastic-Plastic Singular Field Around a Crack-Tip in Particulate-Reinforced Composites 525
22.8.1 Numerical Procedure 525
22.8.2 Elastic-Plastic Singular Field Around a Crack-Tip 528
22.9 Summary 532
References 533
23 A Study of Metal Fatigue Failure as Inherent Features of Elastoplastic Constitutive Equations 536
23.1 Introduction 536
23.2 Smooth Elastoplastic Equations with Asymptotic Loss of the Stress-Bearing Capacity Upto Failure 538
23.3 Fatigue Failure Under Uniaxial Cyclic Loadings 541
23.4 Numerical Results 543
23.5 Concluding Remarks 545
References 546
24 Maximization of Strengthening Effect of Microscopic Morphology in Duplex Steels 548
24.1 Introduction 548
24.2 Finite Element Analysis Method for Periodic Microstructures 550
24.2.1 Boundary Value Problem on a Microscale 550
24.2.2 Setting of Analysis Condition 551
24.3 Strengthening Effect of Microscopic Morphology in Duplex Steels 551
24.3.1 Simulations and Experiments 552
24.3.2 Results and Discussions 553
24.4 Maximization of Morphologic Strengthening Effect 555
24.4.1 Computational Approach 555
24.4.2 Demonstration and Discussion 558
24.5 Conclusion 560
References 561
25 Molecular Dynamics Simulations on Local Lattice Instability at Mode I Crack Tip in BCC Iron 563
25.1 Introduction 564
25.2 AES Evaluation in FS Potential Function 565
25.3 Simulation Procedure 566
25.4 Results and Discussion 567
25.4.1 Stress--Strain Curves and Deformation Behavior 567
25.4.2 Change in Negative AES Atoms 570
25.4.3 Change in Eigenvalue of AES 572
25.5 Conclusion 575
References 576
26 Modeling of Large-Strain Cyclic Plasticity Including Description of Anisotropy Evolution for Sheet Metals 577
26.1 Introduction 577
26.2 Framework of Combined Anisotropic-Kinematic Hardening Model 579
26.3 Cyclic Plasticity Model to Describe the Bauschinger Effect and Workhardening Stagnation: Yoshida-Uemori Model 581
26.4 Description of Evolution of Anisotropy 585
26.5 Concluding Remarks 588
References 589
27 A New Kinematic Hardening Rule Describing Different Plastic Moduli in Monotonic and Cyclic Deformations 592
27.1 Introduction 593
27.2 Constitutive Model 594
27.2.1 Main Equations 594
27.2.2 Modified Chaboche's Kinematic Hardening Rule 595
27.3 Simulation and Discussion 598
27.3.1 Determination of Material Parameter 599
27.3.2 Simulation and Discussion 600
27.4 Conclusions 605
References 605