Ghosh / Dimiduk Computational Methods for Microstructure-Property Relationships

1. Auflage 2010
ISBN: 978-1-4419-0643-4
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 790 Seiten

Computational Methods for Microstructure-Property Relationships introduces state-of-the-art advances in computational modeling approaches for materials structure-property relations. Written with an approach that recognizes the necessity of the engineering computational mechanics framework, this volume provides balanced treatment of heterogeneous materials structures within the microstructural and component scales. Encompassing both computational mechanics and computational materials science disciplines, this volume offers an analysis of the current techniques and selected topics important to industry researchers, such as deformation, creep and fatigue of primarily metallic materials. Researchers, engineers and professionals involved with predicting performance and failure of materials will find Computational Methods for Microstructure-Property Relationships a valuable reference.

Autoren/Hrsg.

Ghosh, Somnath

Dimiduk, Dennis

Inhaltsverzeichnis

1;Preface
;8
2;Contents
;14
3;Contributors
;16
4;Microstructure--Property--Design Relationships in the Simulation Era: An Introduction;20
4.1;1 Microstructure--Property--Design Relationships and Structural Materials Engineering;20
4.2;2 Computational Materials Science for Microstructure;23
4.3;3 Integrated Computational Materials Engineering;25
4.3.1;3.1 Materials Readiness and the Evolving Microstructure--Properties--Design Paradigm;25
4.3.2;3.2 Accelerated Insertion of Materials, Virtual Aluminum Castings, and the ICME Paradigm;28
4.3.3;3.3 The Evolving Needs for Materials Data;30
4.3.4;3.4 ICME: Lessons Learned;31
4.4;4 Multiscale Materials Modeling, Materials Systems Simulation Science, and Virtual Materials Systems;32
4.4.1;4.1 Microstructure--Property Representation and Simulation;33
4.4.2;4.2 Single-Crystal Turbine Blades: An Emerging Case Study;35
4.4.2.1;4.2.1 A Prototype Challenge;35
4.4.2.2;4.2.2 Deficiencies in the Processing--Properties--Design Paradigm;37
4.4.2.3;4.2.3 A Look Forward;39
4.4.3;4.3 Advanced Engineering Design: A Virtual Materials Systems Paradigm;42
4.5;5 The Present Book;44
4.6;References;45
5;Serial Sectioning Methods for Generating 3D Characterization Data of Grain- and Precipitate-Scale Microstructures;49
5.1;1 Introduction;49
5.2;2 Serial Sectioning;52
5.3;3 Automated Serial Sectioning Instrumentation;55
5.3.1;3.1 Alkemper--Voorhees Micromiller;55
5.3.2;3.2 RoboMet.3D;58
5.3.3;3.3 Focused Ion Beam--Scanning Electron Microscopes;59
5.4;4 Data Processing and Segmentation;64
5.5;5 Summary Comments: Future Developments and Needs;66
5.6;References;68
6;Digital Representation of Materials Grain Structure;71
6.1;1 Introduction;71
6.2;2 Challenges and Previous Work;74
6.2.1;2.1 Characterization;74
6.2.2;2.2 Modeling;74
6.3;3 Explicit Representation of Structure;75
6.3.1;3.1 Reconstruction and Feature Identification;77
6.3.1.1;3.1.1 Image Alignment and Stacking;77
6.3.1.2;3.1.2 Feature Segmentation and Clean-Up;79
6.3.2;3.2 Feature Surface Representation and Mesh Generation;82
6.3.2.1;3.2.1 Voxel-Based Mesh;83
6.3.2.2;3.2.2 CAD-Based Surface Fitting;84
6.3.2.3;3.2.3 Direct Image-Based Meshing;85
6.3.2.4;3.2.4 Surface Area/Line Tension-Based Smoothing Methods;86
6.4;4 Statistical Representation of Structure;87
6.4.1;4.1 Quantitative Description of Structure;87
6.4.1.1;4.1.1 Feature Size and Volume;87
6.4.1.2;4.1.2 Feature Shape;88
6.4.1.3;4.1.3 Number of Neighbors;90
6.4.1.4;4.1.4 Correlations between Parameters;91
6.4.1.5;4.1.5 Crystallographic Texture;93
6.4.1.6;4.1.6 Interface Character Distribution;94
6.4.1.7;4.1.7 N-Point Statistics;96
6.4.1.8;4.1.8 Limitations/Concerns when Using Statistical Descriptors;97
6.4.2;4.2 Synthetic Structure Builders;98
6.4.2.1;4.2.1 Representative Feature Generation;98
6.4.2.2;4.2.2 Feature Placement;101
6.4.3;4.3 Measures of Goodness;102
6.4.3.1;4.3.1 Size(s);102
6.4.3.2;4.3.2 Shape(s);103
6.4.3.3;4.3.3 Neighborhood(s);105
6.4.3.4;4.3.4 Boundary Character(s);105
6.5;5 Inference of 3D Structure;106
6.5.1;5.1 Link Between 2D and 3D Structure;106
6.5.2;5.2 Probable Set Generation;107
6.5.2.1;5.2.1 Monte Carlo Histogram Fitting;107
6.5.2.2;5.2.2 Domain Constraint;109
6.5.3;5.3 Limitations and Possibilities;111
6.6;6 Comments on Complex Microstructures;112
6.7;7 Conclusions;113
6.8;References;114
7;Multiscale Characterization and Domain Partitioning for Multiscale Analysis of Heterogeneous Materials;116
7.1;1 Introduction;117
7.2;2 Reconstructing High-Resolution Microstructures from Low-Resolution Micrographs;122
7.2.1;2.1 Resolution Augmentation Problem;123
7.2.2;2.2 Wavelet-based Interpolation in the WIGE Algorithm;124
7.2.2.1;2.2.1 A Brief Discussion of Wavelet Basis Functions;124
7.2.2.2;2.2.2 Wavelet Interpolated Indicator Functions;126
7.2.3;2.3 Gradient-based Probabilistic Enhancement of Interpolated Images in the WIGE Algorithm;129
7.2.3.1;2.3.1 Accounting for Relative Locations of the Calibrating and Simulated Micrographs;133
7.2.3.2;2.3.2 A Validation Test for the WIGE Algorithm;133
7.3;3 Binary Image Processing for Noise Filtering;136
7.4;4 Functions for Microstructure Characterization;138
7.4.1;4.1 Size Descriptors;138
7.4.2;4.2 Shape Descriptors;139
7.4.3;4.3 Spatial Distribution Descriptors;140
7.4.3.1;4.3.1 Covariance Function;141
7.4.3.2;4.3.2 Cluster Index;141
7.4.3.3;4.3.3 Cluster Contour;143
7.4.4;4.4 Characterization of the W319 Microstructure;144
7.4.5;4.5 Identification of Effective Spatial Distribution Descriptors;145
7.5;5 Domain Partitioning: A Preprocessor for Multiscale Modeling;148
7.5.1;5.1 Statistical Homogeneity and Homogeneous Length Scale (LH);149
7.5.2;5.2 Multiscale Domain Partitioning Criteria;150
7.6;6 Numerical Execution of the MDP Method on the W319 Alloy;152
7.7;7 Multiscale Analysis with the MDP Based Preprocessor;155
7.7.1;7.1 Identification of the RVE Size for Homogenization;157
7.7.2;7.2 Level-1 and Level-2 Analysis with LE-VCFEM;160
7.7.3;7.3 Multiscale Analysis of Ductile Failure;162
7.8;8 Conclusions;162
7.9;References;164
8;Coupling Microstructure Characterization with Microstructure Evolution;168
8.1;1 Introduction;168
8.2;2 Fundamentals of Phase Field Method;169
8.2.1;2.1 Description of Microstructure;169
8.2.2;2.2 Governing Equations;170
8.2.3;2.3 Interface Property and Curvature;173
8.2.4;2.4 Growth and Coarsening;174
8.2.5;2.5 Long-Range Elastic Interactions;175
8.2.6;2.6 Quantitative Phase Field Simulation and Length Scale;177
8.2.7;2.7 Multicomponent Diffusion;179
8.2.8;2.8 Multiphase-Field Model;180
8.3;3 Model Input;181
8.3.1;3.1 CALPHAD Free Energy;181
8.3.2;3.2 Pseudobinary and Pseudoternary Systems;183
8.3.3;3.3 CALPHAD Free Energy for Multiphase Systems;183
8.3.4;3.4 Free Energy for Grain Growth;185
8.3.5;3.5 Chemical Mobility of Diffusion;186
8.3.6;3.6 Fast Diffusion Path (Boundary Diffusion);186
8.3.7;3.7 Boundary Mobility;187
8.3.8;3.8 Input from Experiment Image as Initial Microstructure;188
8.4;4 Numerical Algorithms;188
8.5;5 Examples of Application;191
8.5.1;5.1 Exploration of Mechanisms of Microstructural Evolution;191
8.5.2;5.2 Extracting Materials Parameters by Evolving Experimental Images;194
8.5.3;5.3 Texture Evolution During Grain Growth;196
8.5.4;5.4 Physics-Based Repair of Experimental Microstructure Data Set;201
8.5.5;5.5 Generation of Digital Microstructures;204
8.6;6 Summary;208
8.7;References;209
9;Representation of Materials Constitutive Responses in Finite Element-Based Design Codes;215
9.1;1 Introduction;215
9.2;2 Code Survey;217
9.2.1;2.1 Code Classifications;217
9.2.2;2.2 Specific Capabilities;221
9.2.3;2.3 User Material Models;223
9.3;3 Material Modeling in Engineering Design Practice;224
9.3.1;3.1 Material Modeling: Strong Points of the Major Codes;225
9.3.2;3.2 Material Modeling: Shortcomings and Challenges;227
9.4;4 Microscopic vs. Macroscopic Behaviors and Models for Metallic Materials;230
9.4.1;4.1 FEM-based Modeling of Macroscopic Deformation Behaviors;232
9.4.1.1;4.1.1 Generic Modeling with a Homogeneous Bulk Continuum Medium as an MRP;232
9.4.1.2;4.1.2 Polycrystal Modeling with a Grain Aggregate as an MRP;234
9.4.1.3;4.1.3 Polycrystal Modeling with a Single Crystal as an MRP;236
9.4.1.4;4.1.4 Final Remarks on Macroscopic Modeling Approaches;237
9.4.2;4.2 Numerical Approaches for Linking Microscopic and Macroscopic Behaviors;238
9.4.2.1;4.2.1 Coarse Graining from Dislocation Behaviors;238
9.4.2.2;4.2.2 Grain Level Constitutive Modeling based upon Discrete Dislocation Dynamics Simulations;239
9.4.2.3;4.2.3 Unit Cell Modeling;240
9.5;5 User-Defined Material Constitutive Models for Crystal Plasticity;243
9.5.1;5.1 Determination of an MRP;244
9.5.2;5.2 Strain Rate Sensitivity and Hardening Laws: Intrinsic Flow Responses;245
9.5.3;5.3 NonDimensional Analytical Modeling, 3D FEM Modeling, and Designing the Simulation Geometry and Boundary Conditions;246
9.6;6 Concluding Remarks;248
9.7;References;249
10;Accounting for Microstructure in Large Deformation Models of Polycrystalline Metallic Materials;255
10.1;1 Introduction;256
10.2;2 Experimental;260
10.2.1;2.1 Tantalum Material;260
10.2.2;2.2 Experiments;260
10.3;3 Material Modeling;260
10.3.1;3.1 Nomenclature;263
10.3.2;3.2 Continuum-Based Material Modeling;263
10.3.2.1;3.2.1 Continuum Constitutive Model;263
10.3.2.2;3.2.2 Continuum Model Material Parameter Evaluation;267
10.3.2.3;3.2.3 Continuum Model Results;269
10.3.3;3.3 Polycrystal-Based Material Modeling;272
10.3.3.1;3.3.1 Isotropic Constitutive Model;274
10.3.3.2;3.3.2 Single Crystal Constitutive Model;275
10.3.3.3;3.3.3 Crystal Material Parameters for Tantalum;277
10.3.3.4;3.3.4 Numerical;279
10.3.3.5;3.3.5 Polycrystal Model Results;281
10.4;4 Discussion;284
10.5;5 Conclusion;289
10.6;References;289
11;Dislocation Mediated Continuum Plasticity: Case Studies on Modeling Scale Dependence, Scale-Invariance, and Directionality of Sharp Yield-Point;293
11.1;1 Introduction;293
11.2;2 Field Dislocation Dynamics Theory;298
11.3;3 Effects of Sample Size on Mechanical Response;303
11.4;4 Intermittency of Crystal Plasticity: Scale Invariance and Transport Effects;309
11.5;5 Internal Stresses and Anisotropy of Mechanical Behavior;316
11.6;6 Conclusions;322
11.7;References;323
12;Dislocation-Mediated Time-Dependent Deformation in Crystalline Solids;326
12.1;1 Introduction;326
12.2;2 Broad Phenomenology and Commonality in Creep and Plasticity;327
12.3;3 Mobility-Controlled Dislocation Creep;332
12.3.1;3.1 Peierls Friction-Controlled Deformation;332
12.3.2;3.2 Climb-Controlled Creep;334
12.3.2.1;3.2.1 Pure Dislocation Climb;334
12.3.2.2;3.2.2 Harper--Dorn Creep;336
12.3.2.3;3.2.3 Jog-Dragging-Controlled Creep;336
12.3.3;3.3 Solute Drag Creep;342
12.3.4;3.4 Reordering Controlled Creep at Intermediate Temperatures in Superalloys;347
12.4;4 Obstacle-Controlled Dislocation Creep;348
12.4.1;4.1 Postulates for Modeling Obstacle-Controlled Creep;349
12.4.2;4.2 Limiting Solution Methods;352
12.4.3;4.3 Scaling Assumptions;352
12.4.3.1;4.3.1 Basic Material Parameters;352
12.4.3.2;4.3.2 Obstacles;353
12.4.4;4.4 Examples of Use of the Obstacle Controlled Creep Approach;356
12.4.4.1;4.4.1 A Model for Temperature-Dependent Strength at Fixed Structure Applied to Oxide Dispersion Strengthened (ODS) Alloys;356
12.4.4.2;4.4.2 Pure Metal Behavior and the Role of Structural Change;361
12.4.4.3;4.4.3 Other High Temperature Engineered Alloys;364
12.4.5;4.5 A General Approach to Obstacle-Controlled Strengthening;369
12.5;5 Conclusions;371
12.6;References;372
13;Modeling Heterogeneous Intragrain Deformations Using Finite Element Formulations;377
13.1;1 Introduction;377
13.2;2 Crystal Elastoplasticity Model Equations ;379
13.2.1;2.1 Lattice Orientations and Orientation Distributions;379
13.2.2;2.2 Crystal-Scale Elastic and Plastic Behaviors;380
13.3;3 Crystal Elastoplasticity Simulation Methodology;383
13.4;4 Lattice Misorientations from Geometrically Necessary Dislocations;384
13.4.1;4.1 Intragrain Lattice Misorientations;384
13.4.2;4.2 Misorientations Developed Under Tension of an FCC Polycrystal;386
13.5;5 Extending the Kinematic Model for Incomplete Slip;392
13.6;6 Simulation Methodology for Nonlocal Crystal Constitutive Equations;395
13.7;7 Yield Asymmetry From Long-Range Strains Associated with Excess Dislocations;396
13.7.1;7.1 Bending of a Thin Foil;396
13.7.2;7.2 Development of Asymmetries from Long Range Strain Gradients;398
13.8;8 Discussion;403
13.9;9 Summary and Conclusions;405
13.10;References;405
14;Full-Field vs. Homogenization Methods to Predict Microstructure--Property Relations for Polycrystalline Materials;407
14.1;1 Introduction;408
14.2;2 Models;410
14.2.1;2.1 Viscoplastic Self-Consistent Formalism;410
14.2.1.1;2.1.1 Local Constitutive Behavior and Homogenization;411
14.2.1.2;2.1.2 Interaction and Localization Equations;416
14.2.1.3;2.1.3 Self-Consistent Equations;416
14.2.1.4;2.1.4 Linearization Assumptions;417
14.2.1.5;2.1.5 Second-Order Formulation;418
14.2.1.6;2.1.6 Numerical Implementation;422
14.2.2;2.2 FFT-Based Formalism;424
14.2.2.1;2.2.1 Periodic Unit Cell: Green Function Method;424
14.2.2.2;2.2.2 FFT-Based Algorithm;426
14.3;3 Results;428
14.3.1;3.1 Validation of the Full-Field Formulation Using an Analytical Result;428
14.3.2;3.2 Validation of Mean-Field Formulations Using Full-Field Computations;432
14.3.3;3.3 Overall Texture Development Predictions Using Mean-Field Approaches;437
14.3.4;3.4 Local Texture Development Predictions Usingthe FFT-Based Full-Field Approach;440
14.4;4 Conclusions;446
14.5;References;448
14.6;Appendix: Calculation of Effective Moduli Derivatives;451
14.6.1;A.1 Calculation of Bkj(s)/Mu(r) ;451
14.6.2;A.2 Calculation of ij/Muv(r) ;452
14.6.3;A.3 Calculation of Ejo/Mu(r) ;453
14.6.4;A.4 Calculation of /Mu(r) ;453
14.6.5;A.5 Calculation of S/;454
15;Stochastic Upscaling for Inelastic Material Behavior from Limited Experimental Data;456
15.1;1 Introduction;457
15.2;2 Basic Notation and Assumptions;460
15.3;3 Parametric Formulation of Material Plasticity;464
15.4;4 Nonparametric Modeling of Cep;469
15.5;5 Numerical Illustration;475
15.6;6 Conclusion;478
15.7;References;479
16;DDSim: Framework for Multiscale Structural Prognosis;482
16.1;1 Prologue: 2025;482
16.2;2 Introduction;483
16.3;3 DDSim Architecture;484
16.4;4 DDSim Level I: Reduced-Order, Probabilistic, Low-Fidelity Life Prediction and Initial Screening;488
16.4.1;4.1 Application of DDSim Level I to Example Problem;491
16.5;5 DDSim Level II: High-Fidelity, MLC Growth Simulation;495
16.5.1;5.1 Input and the FRANC3D/NG Loop;497
16.5.2;5.2 Application of DDSim Level II to Example Problem;498
16.6;6 DDSim Level III: High-Fidelity, MSC Growth Simulation;501
16.6.1;6.1 Generation of a Microstructural Model;502
16.6.2;6.2 Level III Input and Operations;503
16.6.3;6.3 Application of DDSim Level III to Example Problem;505
16.7;7 Conclusions;506
16.8;References;507
17;Modeling Fatigue Crack Nucleation Using Crystal Plasticity Finite Element Simulations and Multi-time Scaling;510
17.1;1 Introduction;510
17.2;2 Grain Level Dwell Fatigue Crack Nucleation Model based on Crystal Plasticity Finite Element Simulations;513
17.2.1;2.1 Experimental Observations on Crack Evolution;514
17.2.1.1;2.1.1 Crack Detection and Monitoring in Tests on / Forged Ti-6242;515
17.2.2;2.2 The Crystal Plasticity Finite Element Model (CPFEM);516
17.2.2.1;2.2.1 Crystal Plasticity Constitutive Model ;516
17.2.3;2.3 Representation of Microstructural Images in CPFEM;520
17.2.4;2.4 A Nonlocal Crack Nucleation Criterion from CPFE Variables;523
17.2.4.1;2.4.1 Limitations of a Purely Stress based Crack Nucleation Criterion;523
17.2.4.2;2.4.2 Nonlocal Nucleation Criterion Incorporating Soft Grain Dislocation Pile-Up;524
17.2.4.3;2.4.3 Implementation of the Nonlocal Nucleation Criterion;526
17.2.5;2.5 Calibration and Validation of the Nucleation Criterion;529
17.2.5.1;2.5.1 Calibration of Rc for / Forged Ti-6242;530
17.2.5.2;2.5.2 Predictions of Crack Nucleation in MS2 and MS3;531
17.3;3 A Novel Multi-time Scaling Method for Cyclic Crystal Plasticity FE Simulations;532
17.3.1;3.1 Review of Some Accelerated Time Integration Methods;533
17.3.1.1;3.1.1 Extrapolation based Methods;533
17.3.1.2;3.1.2 Block Integration Methods;535
17.3.1.3;3.1.3 Asymptotic Expansion Based Methods;536
17.3.1.4;3.1.4 Methods on Homogenization of Almost Periodic Functions;540
17.3.2;3.2 Wavelet Transformation based Multi-time Scaling Methodology for Cyclic Plasticity;541
17.3.2.1;3.2.1 Brief Overview of Wavelet Basis Functions;544
17.3.2.2;3.2.2 Coarse (Cycle) Scale Evolutionary Constitutive Relations;549
17.3.2.3;3.2.3 Coarse (Cycle) Scale Crystal Plasticity Finite Element Equations;549
17.3.3;3.3 WATMUS Adaptivity for Accuracy and Efficiency;551
17.3.3.1;3.3.1 Evolving and Active Wavelet Basis Functions;551
17.3.3.2;3.3.2 Coarse (Cycle Scale) Integration Step Size Control;554
17.3.4;3.4 Numerical Examples Solved with the WATMUS Algorithm;555
17.3.4.1;3.4.1 One-Dimensional Elastic-Viscoplastic Problem;555
17.3.4.2;3.4.2 3D Crystal Plasticity FE Simulation Under Cyclic Loading;557
17.4;4 Conclusions;559
17.5;References;564
18;Challenges Below the Grain Scale and Multiscale Models;568
18.1;1 Introduction;568
18.2;2 Advances in Experimental Methods;569
18.2.1;2.1 Onset of Plasticity Modeling;573
18.2.2;2.2 Analysis of Slip Around Indentation as a tie to Dislocation Mechanisms;576
18.2.3;2.3 Micro-Uniaxial Tests;578
18.3;3 Multiscale Framework;579
18.4;4 The Dislocation Dynamics (DD) Method;581
18.4.1;4.1 Kinematics and Geometric Aspects;581
18.4.2;4.2 Kinetics and Interaction Forces;582
18.4.3;4.3 Dislocation Equation of Motion;583
18.4.4;4.4 Dislocation Mobility Function;583
18.4.5;4.5 Dislocation Collisions;584
18.4.6;4.6 Discretization of Dislocation Equation of Motion;584
18.4.7;4.7 The Dislocation Stress and Force Fields;586
18.4.8;4.8 Evaluation of Plastic Strains;588
18.4.9;4.9 The DD Numerical Solution;589
18.5;5 Integration of DD and Continuum Plasticity;590
18.5.1;5.1 Modifications for Finite Domains;591
18.5.1.1;5.1.1 Interactions with External Free Surfaces;591
18.5.1.2;5.1.2 Interactions with Interfaces;591
18.6;6 Problems with Size Effects and the DD Approach;593
18.6.1;6.1 Size Effect in Nanolaminate Metallic Composites;594
18.6.1.1;6.1.1 Dislocation near an Interface;594
18.6.1.2;6.1.2 Strengthening in Nanolaminate Metallic Composites;596
18.6.2;6.2 Size Effect in Micropillars;596
18.7;References;599
19;Emerging Methods for Matching Simulation and Experimental Scales;604
19.1;1 Current Design Practice;604
19.2;2 Physical Constitutive Behavior;608
19.2.1;2.1 Limitations of the Current Practices;611
19.3;3 Need for New Design Tools;613
19.4;4 Multiscale Testing Methodology: From Coarse to Fine Scales;615
19.4.1;4.1 Advances and Needs;615
19.4.2;4.2 Advanced Test Techniques at the Conventional Scale;616
19.4.2.1;4.2.1 Measurements;616
19.4.2.2;4.2.2 Load Simulation;617
19.4.3;4.3 Advanced Test Techniques using Subscale Specimens;618
19.4.4;4.4 Advanced Tests at the Grain Level;620
19.5;5 What's Next?;624
19.6;References;625
20;Simulation-Assisted Design and Accelerated Insertion of Materials;629
20.1;1 Introduction: Systems Engineering and Materials Design;630
20.2;2 Recent Advances in Integrating Materials Simulation and Product Design;632
20.3;3 Multiscale Materials Modeling and Simulation: Purposes and Utility;639
20.3.1;3.1 Hierarchical and Concurrent Multiscale Modeling;640
20.3.2;3.2 Materials Design and the Need for Top-Down Methods;645
20.4;4 Hierarchical Decision-Making in Materials Design;646
20.5;5 Future Prospects: Challenges and Opportunities;653
20.6;6 Conclusion;655
20.7;References;656
21;Index;660