Computational Methods for Microstructure-Property Relationships (eBook)

Preface 
8 
Contents 
14 
Contributors 
16 
Microstructure--Property--Design Relationships in the Simulation Era: An Introduction 20
1 Microstructure--Property--Design Relationships and Structural Materials Engineering 20
2 Computational Materials Science for Microstructure 23
3 Integrated Computational Materials Engineering 25
3.1 Materials Readiness and the Evolving Microstructure--Properties--Design Paradigm 25
3.2 Accelerated Insertion of Materials, Virtual Aluminum Castings, and the ICME Paradigm 28
3.3 The Evolving Needs for Materials Data 30
3.4 ICME: Lessons Learned 31
4 Multiscale Materials Modeling, Materials Systems Simulation Science, and Virtual Materials Systems 32
4.1 Microstructure--Property Representation and Simulation 33
4.2 Single-Crystal Turbine Blades: An Emerging Case Study 35
4.2.1 A Prototype Challenge 35
4.2.2 Deficiencies in the Processing--Properties--Design Paradigm 37
4.2.3 A Look Forward 39
4.3 Advanced Engineering Design: A Virtual Materials Systems Paradigm 42
5 The Present Book 44
References 45
Serial Sectioning Methods for Generating 3D Characterization Data of Grain- and Precipitate-Scale Microstructures 49
1 Introduction 49
2 Serial Sectioning 52
3 Automated Serial Sectioning Instrumentation 55
3.1 Alkemper--Voorhees Micromiller 55
3.2 RoboMet.3D 58
3.3 Focused Ion Beam--Scanning Electron Microscopes 59
4 Data Processing and Segmentation 64
5 Summary Comments: Future Developments and Needs 66
References 68
Digital Representation of Materials Grain Structure 71
1 Introduction 71
2 Challenges and Previous Work 74
2.1 Characterization 74
2.2 Modeling 74
3 Explicit Representation of Structure 75
3.1 Reconstruction and Feature Identification 77
3.1.1 Image Alignment and Stacking 77
3.1.2 Feature Segmentation and Clean-Up 79
3.2 Feature Surface Representation and Mesh Generation 82
3.2.1 Voxel-Based Mesh 83
3.2.2 CAD-Based Surface Fitting 84
3.2.3 Direct Image-Based Meshing 85
3.2.4 Surface Area/Line Tension-Based Smoothing Methods 86
4 Statistical Representation of Structure 87
4.1 Quantitative Description of Structure 87
4.1.1 Feature Size and Volume 87
4.1.2 Feature Shape 88
4.1.3 Number of Neighbors 90
4.1.4 Correlations between Parameters 91
4.1.5 Crystallographic Texture 93
4.1.6 Interface Character Distribution 94
4.1.7 N-Point Statistics 96
4.1.8 Limitations/Concerns when Using Statistical Descriptors 97
4.2 Synthetic Structure Builders 98
4.2.1 Representative Feature Generation 98
4.2.2 Feature Placement 101
4.3 Measures of Goodness 102
4.3.1 Size(s) 102
4.3.2 Shape(s) 103
4.3.3 Neighborhood(s) 105
4.3.4 Boundary Character(s) 105
5 Inference of 3D Structure 106
5.1 Link Between 2D and 3D Structure 106
5.2 Probable Set Generation 107
5.2.1 Monte Carlo Histogram Fitting 107
5.2.2 Domain Constraint 109
5.3 Limitations and Possibilities 111
6 Comments on Complex Microstructures 112
7 Conclusions 113
References 114
Multiscale Characterization and Domain Partitioning for Multiscale Analysis of Heterogeneous Materials 116
1 Introduction 117
2 Reconstructing High-Resolution Microstructures from Low-Resolution Micrographs 122
2.1 Resolution Augmentation Problem 123
2.2 Wavelet-based Interpolation in the WIGE Algorithm 124
2.2.1 A Brief Discussion of Wavelet Basis Functions 124
2.2.2 Wavelet Interpolated Indicator Functions 126
2.3 Gradient-based Probabilistic Enhancement of Interpolated Images in the WIGE Algorithm 129
2.3.1 Accounting for Relative Locations of the Calibrating and Simulated Micrographs 133
2.3.2 A Validation Test for the WIGE Algorithm 133
3 Binary Image Processing for Noise Filtering 136
4 Functions for Microstructure Characterization 138
4.1 Size Descriptors 138
4.2 Shape Descriptors 139
4.3 Spatial Distribution Descriptors 140
4.3.1 Covariance Function 141
4.3.2 Cluster Index 141
4.3.3 Cluster Contour 143
4.4 Characterization of the W319 Microstructure 144
4.5 Identification of Effective Spatial Distribution Descriptors 145
5 Domain Partitioning: A Preprocessor for Multiscale Modeling 148
5.1 Statistical Homogeneity and Homogeneous Length Scale (LH) 149
5.2 Multiscale Domain Partitioning Criteria 150
6 Numerical Execution of the MDP Method on the W319 Alloy 152
7 Multiscale Analysis with the MDP Based Preprocessor 155
7.1 Identification of the RVE Size for Homogenization 157
7.2 Level-1 and Level-2 Analysis with LE-VCFEM 160
7.3 Multiscale Analysis of Ductile Failure 162
8 Conclusions 162
References 164
Coupling Microstructure Characterization with Microstructure Evolution 168
1 Introduction 168
2 Fundamentals of Phase Field Method 169
2.1 Description of Microstructure 169
2.2 Governing Equations 170
2.3 Interface Property and Curvature 173
2.4 Growth and Coarsening 174
2.5 Long-Range Elastic Interactions 175
2.6 Quantitative Phase Field Simulation and Length Scale 177
2.7 Multicomponent Diffusion 179
2.8 Multiphase-Field Model 180
3 Model Input 181
3.1 CALPHAD Free Energy 181
3.2 Pseudobinary and Pseudoternary Systems 183
3.3 CALPHAD Free Energy for Multiphase Systems 183
3.4 Free Energy for Grain Growth 185
3.5 Chemical Mobility of Diffusion 186
3.6 Fast Diffusion Path (Boundary Diffusion) 186
3.7 Boundary Mobility 187
3.8 Input from Experiment Image as Initial Microstructure 188
4 Numerical Algorithms 188
5 Examples of Application 191
5.1 Exploration of Mechanisms of Microstructural Evolution 191
5.2 Extracting Materials Parameters by Evolving Experimental Images 194
5.3 Texture Evolution During Grain Growth 196
5.4 Physics-Based Repair of Experimental Microstructure Data Set 201
5.5 Generation of Digital Microstructures 204
6 Summary 208
References 209
Representation of Materials Constitutive Responses in Finite Element-Based Design Codes 215
1 Introduction 215
2 Code Survey 217
2.1 Code Classifications 217
2.2 Specific Capabilities 221
2.3 User Material Models 223
3 Material Modeling in Engineering Design Practice 224
3.1 Material Modeling: Strong Points of the Major Codes 225
3.2 Material Modeling: Shortcomings and Challenges 227
4 Microscopic vs. Macroscopic Behaviors and Models for Metallic Materials 230
4.1 FEM-based Modeling of Macroscopic Deformation Behaviors 232
4.1.1 Generic Modeling with a Homogeneous Bulk Continuum Medium as an MRP 232
4.1.2 Polycrystal Modeling with a Grain Aggregate as an MRP 234
4.1.3 Polycrystal Modeling with a Single Crystal as an MRP 236
4.1.4 Final Remarks on Macroscopic Modeling Approaches 237
4.2 Numerical Approaches for Linking Microscopic and Macroscopic Behaviors 238
4.2.1 Coarse Graining from Dislocation Behaviors 238
4.2.2 Grain Level Constitutive Modeling based upon Discrete Dislocation Dynamics Simulations 239
4.2.3 Unit Cell Modeling 240
5 User-Defined Material Constitutive Models for Crystal Plasticity 243
5.1 Determination of an MRP 244
5.2 Strain Rate Sensitivity and Hardening Laws: Intrinsic Flow Responses 245
5.3 NonDimensional Analytical Modeling, 3D FEM Modeling, and Designing the Simulation Geometry and Boundary Conditions 246
6 Concluding Remarks 248
References 249
Accounting for Microstructure in Large Deformation Models of Polycrystalline Metallic Materials 255
1 Introduction 256
2 Experimental 260
2.1 Tantalum Material 260
2.2 Experiments 260
3 Material Modeling 260
3.1 Nomenclature 263
3.2 Continuum-Based Material Modeling 263
3.2.1 Continuum Constitutive Model 263
3.2.2 Continuum Model Material Parameter Evaluation 267
3.2.3 Continuum Model Results 269
3.3 Polycrystal-Based Material Modeling 272
3.3.1 Isotropic Constitutive Model 274
3.3.2 Single Crystal Constitutive Model 275
3.3.3 Crystal Material Parameters for Tantalum 277
3.3.4 Numerical 279
3.3.5 Polycrystal Model Results 281
4 Discussion 284
5 Conclusion 289
References 289
Dislocation Mediated Continuum Plasticity: Case Studies on Modeling Scale Dependence, Scale-Invariance, and Directionality of Sharp Yield-Point 293
1 Introduction 293
2 Field Dislocation Dynamics Theory 298
3 Effects of Sample Size on Mechanical Response 303
4 Intermittency of Crystal Plasticity: Scale Invariance and Transport Effects 309
5 Internal Stresses and Anisotropy of Mechanical Behavior 316
6 Conclusions 322
References 323
Dislocation-Mediated Time-Dependent Deformation in Crystalline Solids 326
1 Introduction 326
2 Broad Phenomenology and Commonality in Creep and Plasticity 327
3 Mobility-Controlled Dislocation Creep 332
3.1 Peierls Friction-Controlled Deformation 332
3.2 Climb-Controlled Creep 334
3.2.1 Pure Dislocation Climb 334
3.2.2 Harper--Dorn Creep 336
3.2.3 Jog-Dragging-Controlled Creep 336
3.3 Solute Drag Creep 342
3.4 Reordering Controlled Creep at Intermediate Temperatures in Superalloys 347
4 Obstacle-Controlled Dislocation Creep 348
4.1 Postulates for Modeling Obstacle-Controlled Creep 349
4.2 Limiting Solution Methods 352
4.3 Scaling Assumptions 352
4.3.1 Basic Material Parameters 352
4.3.2 Obstacles 353
4.4 Examples of Use of the Obstacle Controlled Creep Approach 356
4.4.1 A Model for Temperature-Dependent Strength at Fixed Structure Applied to Oxide Dispersion Strengthened (ODS) Alloys 356
4.4.2 Pure Metal Behavior and the Role of Structural Change 361
4.4.3 Other High Temperature Engineered Alloys 364
4.5 A General Approach to Obstacle-Controlled Strengthening 369
5 Conclusions 371
References 372
Modeling Heterogeneous Intragrain Deformations Using Finite Element Formulations 377
1 Introduction 377
2 Crystal Elastoplasticity Model Equations 379
2.1 Lattice Orientations and Orientation Distributions 379
2.2 Crystal-Scale Elastic and Plastic Behaviors 380
3 Crystal Elastoplasticity Simulation Methodology 383
4 Lattice Misorientations from Geometrically Necessary Dislocations 384
4.1 Intragrain Lattice Misorientations 384
4.2 Misorientations Developed Under Tension of an FCC Polycrystal 386
5 Extending the Kinematic Model for Incomplete Slip 392
6 Simulation Methodology for Nonlocal Crystal Constitutive Equations 395
7 Yield Asymmetry From Long-Range Strains Associated with Excess Dislocations 396
7.1 Bending of a Thin Foil 396
7.2 Development of Asymmetries from Long Range Strain Gradients 398
8 Discussion 403
9 Summary and Conclusions 405
References 405
Full-Field vs. Homogenization Methods to Predict Microstructure--Property Relations for Polycrystalline Materials 407
1 Introduction 408
2 Models 410
2.1 Viscoplastic Self-Consistent Formalism 410
2.1.1 Local Constitutive Behavior and Homogenization 411
2.1.2 Interaction and Localization Equations 416
2.1.3 Self-Consistent Equations 416
2.1.4 Linearization Assumptions 417
2.1.5 Second-Order Formulation 418
2.1.6 Numerical Implementation 422
2.2 FFT-Based Formalism 424
2.2.1 Periodic Unit Cell: Green Function Method 424
2.2.2 FFT-Based Algorithm 426
3 Results 428
3.1 Validation of the Full-Field Formulation Using an Analytical Result 428
3.2 Validation of Mean-Field Formulations Using Full-Field Computations 432
3.3 Overall Texture Development Predictions Using Mean-Field Approaches 437
3.4 Local Texture Development Predictions Usingthe FFT-Based Full-Field Approach 440
4 Conclusions 446
References 448
Appendix: Calculation of Effective Moduli Derivatives 451
A.1 Calculation of Bkj(s)/Mu(r) 451
A.2 Calculation of ij/Muv(r) 452
A.3 Calculation of Ejo/Mu(r) 453
A.4 Calculation of /Mu(r) 453
A.5 Calculation of S/ 454
Stochastic Upscaling for Inelastic Material Behavior from Limited Experimental Data 456
1 Introduction 457
2 Basic Notation and Assumptions 460
3 Parametric Formulation of Material Plasticity 464
4 Nonparametric Modeling of Cep 469
5 Numerical Illustration 475
6 Conclusion 478
References 479
DDSim: Framework for Multiscale Structural Prognosis 482
1 Prologue: 2025 482
2 Introduction 483
3 DDSim Architecture 484
4 DDSim Level I: Reduced-Order, Probabilistic, Low-Fidelity Life Prediction and Initial Screening 488
4.1 Application of DDSim Level I to Example Problem 491
5 DDSim Level II: High-Fidelity, MLC Growth Simulation 495
5.1 Input and the FRANC3D/NG Loop 497
5.2 Application of DDSim Level II to Example Problem 498
6 DDSim Level III: High-Fidelity, MSC Growth Simulation 501
6.1 Generation of a Microstructural Model 502
6.2 Level III Input and Operations 503
6.3 Application of DDSim Level III to Example Problem 505
7 Conclusions 506
References 507
Modeling Fatigue Crack Nucleation Using Crystal Plasticity Finite Element Simulations and Multi-time Scaling 510
1 Introduction 510
2 Grain Level Dwell Fatigue Crack Nucleation Model based on Crystal Plasticity Finite Element Simulations 513
2.1 Experimental Observations on Crack Evolution 514
2.1.1 Crack Detection and Monitoring in Tests on / Forged Ti-6242 515
2.2 The Crystal Plasticity Finite Element Model (CPFEM) 516
2.2.1 Crystal Plasticity Constitutive Model 516
2.3 Representation of Microstructural Images in CPFEM 520
2.4 A Nonlocal Crack Nucleation Criterion from CPFE Variables 523
2.4.1 Limitations of a Purely Stress based Crack Nucleation Criterion 523
2.4.2 Nonlocal Nucleation Criterion Incorporating Soft Grain Dislocation Pile-Up 524
2.4.3 Implementation of the Nonlocal Nucleation Criterion 526
2.5 Calibration and Validation of the Nucleation Criterion 529
2.5.1 Calibration of Rc for / Forged Ti-6242 530
2.5.2 Predictions of Crack Nucleation in MS2 and MS3 531
3 A Novel Multi-time Scaling Method for Cyclic Crystal Plasticity FE Simulations 532
3.1 Review of Some Accelerated Time Integration Methods 533
3.1.1 Extrapolation based Methods 533
3.1.2 Block Integration Methods 535
3.1.3 Asymptotic Expansion Based Methods 536
3.1.4 Methods on Homogenization of Almost Periodic Functions 540
3.2 Wavelet Transformation based Multi-time Scaling Methodology for Cyclic Plasticity 541
3.2.1 Brief Overview of Wavelet Basis Functions 544
3.2.2 Coarse (Cycle) Scale Evolutionary Constitutive Relations 549
3.2.3 Coarse (Cycle) Scale Crystal Plasticity Finite Element Equations 549
3.3 WATMUS Adaptivity for Accuracy and Efficiency 551
3.3.1 Evolving and Active Wavelet Basis Functions 551
3.3.2 Coarse (Cycle Scale) Integration Step Size Control 554
3.4 Numerical Examples Solved with the WATMUS Algorithm 555
3.4.1 One-Dimensional Elastic-Viscoplastic Problem 555
3.4.2 3D Crystal Plasticity FE Simulation Under Cyclic Loading 557
4 Conclusions 559
References 564
Challenges Below the Grain Scale and Multiscale Models 568
1 Introduction 568
2 Advances in Experimental Methods 569
2.1 Onset of Plasticity Modeling 573
2.2 Analysis of Slip Around Indentation as a tie to Dislocation Mechanisms 576
2.3 Micro-Uniaxial Tests 578
3 Multiscale Framework 579
4 The Dislocation Dynamics (DD) Method 581
4.1 Kinematics and Geometric Aspects 581
4.2 Kinetics and Interaction Forces 582
4.3 Dislocation Equation of Motion 583
4.4 Dislocation Mobility Function 583
4.5 Dislocation Collisions 584
4.6 Discretization of Dislocation Equation of Motion 584
4.7 The Dislocation Stress and Force Fields 586
4.8 Evaluation of Plastic Strains 588
4.9 The DD Numerical Solution 589
5 Integration of DD and Continuum Plasticity 590
5.1 Modifications for Finite Domains 591
5.1.1 Interactions with External Free Surfaces 591
5.1.2 Interactions with Interfaces 591
6 Problems with Size Effects and the DD Approach 593
6.1 Size Effect in Nanolaminate Metallic Composites 594
6.1.1 Dislocation near an Interface 594
6.1.2 Strengthening in Nanolaminate Metallic Composites 596
6.2 Size Effect in Micropillars 596
References 599
Emerging Methods for Matching Simulation and Experimental Scales 604
1 Current Design Practice 604
2 Physical Constitutive Behavior 608
2.1 Limitations of the Current Practices 611
3 Need for New Design Tools 613
4 Multiscale Testing Methodology: From Coarse to Fine Scales 615
4.1 Advances and Needs 615
4.2 Advanced Test Techniques at the Conventional Scale 616
4.2.1 Measurements 616
4.2.2 Load Simulation 617
4.3 Advanced Test Techniques using Subscale Specimens 618
4.4 Advanced Tests at the Grain Level 620
5 What's Next? 624
References 625
Simulation-Assisted Design and Accelerated Insertion of Materials 629
1 Introduction: Systems Engineering and Materials Design 630
2 Recent Advances in Integrating Materials Simulation and Product Design 632
3 Multiscale Materials Modeling and Simulation: Purposes and Utility 639
3.1 Hierarchical and Concurrent Multiscale Modeling 640
3.2 Materials Design and the Need for Top-Down Methods 645
4 Hierarchical Decision-Making in Materials Design 646
5 Future Prospects: Challenges and Opportunities 653
6 Conclusion 655
References 656
Index 660