This book delivers a comprehensive overview of the methods of Integrated Computational Materials Engineering (ICME), and provides clear examples to demonstrate the multiscale modeling methodology. It walks beginners through the various aspects of modeling and simulation related to materials processing. Moreover, it captures important constitutive relations and the material constants for those relations for different materials in a single collection. Many established engineering graduates who need to catch up on this topic will find what they need in this text.

FOREWORD xiii

PREFACE xv

ACKNOWLEDGMENTS xix

**1 AN INTRODUCTION TO INTEGRATED COMPUTATIONAL MATERIALS ENGINEERING (ICME) 1**

1.1 Background / 2

1.2 The Application of Multiscale Materials Modeling via ICME / 2

1.3 History of Multiscale Modeling / 4

1.3.1 Bridging between Scales: A Difference of Disciplines / 6

1.4 ICME for Design / 22

1.4.1 Design Optimization / 23

1.4.2 Metamodeling Approaches / 26

1.4.3 Design with Uncertainty Analysis / 27

1.5 ICME for Manufacturing / 29

1.6 Summary / 29

References / 31

**2 MACROSCALE CONTINUUM INTERNAL STATE VARIABLE (ISV) PLASTICITY–DAMAGE THEORY AND MULTISTAGE FATIGUE (MSF) 45**

2.1 Introduction / 45

2.2 Stress / 46

2.3 Kinematics of Deformation and Strain / 54

2.4 Continuum Theory Constitutive Equations / 58

2.4.1 Thermodynamics of the ISV Constitutive Equations / 62

2.4.2 Kinetics of the ISV Constitutive Equations / 66

2.4.3 Continuum Theory ISV Constitutive Equations with Discrete Structures/Defects / 73

2.4.4 Guidelines for the Development of an ISV / 74

2.5 Multistage Fatigue (MSF) Modeling / 75

2.6 Bridging Strategies for the Macroscale and the Mesoscale / 80

2.6.1 Downscaling: Defi ning the Macroscale Constraints for the Mesoscale Analysis / 80

2.6.2 Upscaling: Using Design of Experiments (DOE) for Mesoscale Analysis / 80

2.7 Experimental Exploration, Calibration, and Validation at the Macroscale / 85

2.8 Summary / 87

References / 88

**3 MESOSCALE ANALYSIS: CONTINUUM THEORY METHODS WITH DISCRETE FEATURES/METHODS 98**

3.1 Kinematics of Crystal Plasticity / 100

3.2 Kinetics of Crystal Plasticity / 104

3.3 Crystal Orientations and Elasticity / 108

3.4 Upscaling: Bridging the Crystal Level to the Polycrystalline Continuum Level / 110

3.4.1 Upscaling for Plasticity / 111

3.4.2 Upscaling for Damage/Fracture / 119

3.4.3 Upscaling for Fatigue / 120

3.5 Downscaling from Crystal Plasticity to Dislocation Dynamics / 122

3.5.1 Plasticity / 122

3.5.2 Damage / 122

3.5.3 Fatigue / 122

3.6 Experimental Exploration, Calibration, and Validation at the Mesoscale / 123

3.7 Summary / 123

References / 123

**4 DISCRETE DISLOCATION DYNAMICS SIMULATIONS 128**

4.1 Introduction / 128

4.2 Metal Plasticity Modeling / 129

4.3 Dislocation Mechanics Basics / 131

4.3.1 Geometrical Attributes of Dislocations / 131

4.3.2 Dislocation Motion / 132

4.3.3 Dislocation Motion and Plastic Strain / 134

4.3.4 Dislocations Reactions / 135

4.4 Modeling Discrete Dislocations / 135

4.4.1 Dislocation Equation of Motion / 136

4.4.2 Evaluation of Fdislocation / 137

4.4.3 Evaluation of Fself / 138

4.5 Boundary Conditions / 139

4.6 Upscaling for Plasticity / 140

4.6.1 Upscaling for the Macroscopic Plastic Strain / 140

4.6.2 Upscaling: Bridging the Dislocation Level to the Macroscale Continuum Level Stresses and Strains / 140

4.6.3 Upscaling for Work Hardening / 143

4.7 Downscaling from DD to Atomistics / 143

4.8 Summary / 144

References / 144

**5 ATOMISTIC MODELING METHODS 146**

5.1 EAM Potentials / 147

5.2 MEAM Potentials / 148

5.3 Upscaling: Bridging the Atomic Level to the Dislocation Density Level and the Continuum Level / 153

5.3.1 Continuum Quantities for Upscaling / 153

5.3.2 Upscaling for Plasticity / 155

5.3.3 Upscaling for Damage / 156

5.3.4 Upscaling for Fatigue / 157

5.3.5 Downscaling from Atomistics to Electronics Structures Calculations / 157

5.4 Summary / 159

References / 159

**6 ELECTRONIC STRUCTURE CALCULATIONS 164**

6.1 Introduction / 164

6.2 Why Quantum Mechanics? / 165

6.3 Theoretical Background / 166

6.4 Postulates of Quantum Mechanics / 168

6.5 Prior to Density Functional Theory (DFT) / 170

6.6 DFT / 175

6.7 Upscaling: Bridging the Electron Level to the Atom Level / 176

6.7.1 Cohesive Energy / 177

6.7.2 Lattice Parameter / 178

6.7.3 Bulk Moduli / 178

6.7.4 Elastic Constants / 179

6.7.5 Vacancy Formation Energies / 180

6.7.6 Interstitial Defects / 180

6.7.7 Surface Formation Energies / 181

6.7.8 Surface Adsorption Energies / 181

6.7.9 Stacking Fault Energies / 182

6.7.10 GSFE Curve / 183

6.8 Summary / 184

Bibliography / 184

Cited References / 184

Uncited References / 185

**7 CASE STUDY: FROM ATOMS TO AUTOS: A REDESIGN OF A CADILLAC CONTROL ARM 187**

7.1 Introduction / 187

7.1.1 Material: Cast A356 Aluminum Alloy / 189

7.1.2 Modeling Philosophy / 189

7.2 Macroscale Microstructure–Property Internal State Variable (ISV) Plasticity–Damage Model / 195

7.2.1 Kinematics of the Macroscale Model / 196

7.2.2 Void Nucleation, Growth, and Coalescence Aspects of the Macroscale Model / 200

7.2.3 Elastic—Plastic Aspects of Macroscale Continuum Model / 205

7.2.4 Macroscale Continuum Model Summary / 209

7.3 Bridges 1 and 5: Electronics Structure Calculations: Connections to the Atomic Scale and Macroscale Continuum Level / 211

7.3.1 Atomistic Level Downscaling Requirements / 213

7.4 Bridges 2 and 6: Nanoscale Atomistic Simulations: Connections to the Microscale and Macroscale / 216

7.4.1 Atomistic Simulation Preliminaries / 217

7.4.2 Aluminum–Silicon Interface Structure and Model Sensitivity / 218

7.4.3 Aluminum–Silicon Interface Debonding / 224

7.4.4 Role of Vacancy-Type Defects / 226

7.4.5 Upscaling: Comparison of Continuum Decohesion Models for the Microscale Simulations / 229

7.5 Bridges 3 and 7: Microscale Finite Element Simulations: Connections to the Mesoscale and Macroscale / 233

7.5.1 Design of Experiment Parameters for Void–Crack Nucleation at the Microscale / 236

7.5.2 DOE Methodology / 238

7.5.3 Micromechanical DOE Results Using FEA / 240

7.5.4 Validation Experiments / 244

7.5.5 Bridge 6: From Microscale to Macroscale Modeling: Void/Crack Nucleation / 245

7.5.6 Summary of Bridges Related to the Microscale / 247

7.6 Bridges 4 and 8: Mesoscale 1 Finite Element Simulations: Connections to the Mesoscale 2 and Macroscale / 247

7.6.1 Mesoscale 1 Finite Element Simulation Setup and Results for the Realistic Microstructures / 251

7.6.2 Bridge 8: From Mesoscale 1 to Macroscale Modeling: Pore Coalescence / 258

7.6.3 Summary of Bridges Related to the Mesoscale 1 Finite Element Simulations / 258

7.7 Bridge 9: Mesoscale 2 Finite Element Simulations (Idealized Porosity): Connections to the Macroscale / 259

7.7.1 Mesoscale 2 Finite Element Simulation Setup and Results for the Idealized Porosity / 260

7.7.2 Pore Coalescence Parametric Study / 260

7.7.3 Temperature Effects on Pore Coalescence / 266

7.7.4 Bridge 9: From Mesoscale 2 to Macroscale Modeling: Pore Coalescence / 275

7.7.5 Summary of Bridges Related to Mesoscale 2 Idealized Porosity Simulations / 276

7.8 Bridge 10: Macroscale Material Model: Connections to the Macroscale Finite Element Simulations / 276

7.8.1 Summary of Bridge Information from the Lower Length Scales into the Macroscale Continuum Model / 277

7.8.2 Hierarchical Multiscale Macroscale Continuum ISV Theory: Calibration and Validation / 278

7.8.3 Model Calibration of the Continuum ISV Model / 279

7.8.4 Model Validation of the Macroscale Continuum ISV Model / 286

7.8.5 Summary of Bridges Related to the Macroscale Simulations / 303

7.9 Predictive Modeling of Structural Components for the Case Study of the Cast A356 Aluminum Alloy / 303

7.9.1 Weapons Carrier Analysis / 304

7.9.2 Automotive Control Arm Analysis / 306

7.10 Design Optimization with Uncertainty of the Automotive Control Arm / 310

7.10.1 Conventional Design Optimization Method / 311

7.10.2 Design Optimization Employing Surrogate (Metamodel) Modeling with Probabilistics (Reliability) under Uncertainty with the Macroscale Continuum ISV Model that Included the Hierarchical Multiscale Analysis and Associated Microstructures from the Different Length Scales / 312

7.11 Summary / 327

References / 328

**8 CASE STUDY: A MICROSTRUCTURE–PROPERTY MULTISTAGE FATIGUE (MSF) ANALYSIS OF A CADILLAC CONTROL ARM 340**

8.1 Introduction to the Mechanisms of Fatigue in Cast Alloys / 340

8.2 Macroscale MSF Model / 346

8.2.1 Incubation / 346

8.2.2 MSC Regime / 347

8.3 Macroscale MSF Modeling Bridges (Upscaling and Downscaling) / 350

8.3.1 Bridge 7: Atomistic Simulations for Determining the Crack Driving Force Coeffi cient for the MSC Growth Rate in the Macroscale MSF Model / 352

8.3.2 Bridge 9 Mesoscale Finite Element Simulations for the Nonlocal Plasticity Parameter in the Incubation Equation: Connections to the Macroscale / 354

8.3.3 Bridge 10 Mesoscale Finite Element Simulations for the MSC: Connections to the Macroscale / 363

8.3.4 Bridge 12: Macroscale MSF Model Calibration / 366

8.4 Summary / 373

Bibliography / 374

Cited References / 374

Uncited References / 377

**9 CASE STUDY: CONDUCTING A STRUCTURAL SCALE METAL FORMING FINITE ELEMENT ANALYSIS STARTING FROM ELECTRONICS STRUCTURES CALCULATIONS USING ICME TOOLS 379**

9.1 Introduction / 379

9.2 Modeling Philosophy / 380

9.3 Bridge 1: Electronics Principles to Atomistic Simulation Connection / 382

9.3.1 Atomistic Model Calibration Using the Modified Embedded Atom Method (MEAM) Potential / 382

9.3.2 Atomistic Model Validation Using the MEAM Potential / 382

9.4 Bridge 2: Atomistic Simulation to Dislocation Density Simulation Connection / 386

9.5 Bridge 3: Dislocation Density to CP Simulation Connection / 391

9.5.1 Model Calibration of Hardening Equations / 391

9.5.2 Model Validation of the Hardening Equations / 396

9.6 Bridge 9: CP to Macroscale Continuum Simulation Connection / 398

9.7 Bridge 12: Macroscale Continuum Model to the Structural Scale Simulation of the Sheet Forming Problem / 402

9.8 Summary / 404

References / 406

**10 THE NEAR FUTURE: ICME FOR THE CREATION OF NEW MATERIALS AND STRUCTURES 410**

10.1 Integrating Process, Structure, Property, and Performance / 410

10.2 Energy / 417

10.3 Infrastructure / 419

10.4 Transportation / 419

10.5 Nano- and Microstructures/Small Devices / 419

10.6 Summary / 421

References / 422

INDEX 425