Continuum Scale Simulation of Engineering Materials Fundamentals - Microstructures - Process Applications

by Raabe, Dierk; Roters, Franz; Barlat, Fré; dé; ric; Chen, Long-Qing

• ISBN13: 9783527307609
• ISBN10: 3527307605
• Edition: 1st
• Format: Hardcover
• Copyright: 2004-08-06
• Publisher: Wiley-VCH

Summary

Everything the reader needs to know about this hot topic in materials research -- from the fundamentals to recent applications. This book addresses graduate students and professionals in materials science and engineering as well as materials-oriented physicists and mechanical engineers, providing them with information needed to judge which simulation method to use for which kind of modeling/simulation problem.

Author Biography

<b>Professor Dierk Raabe</b> received his Ph.D. (1992) and habilitation (1997) at RWTH Aachen, Germany, in the fields of Physical Metallurgy and Metal Physics. He is currently Director and Executive at the Max-Planck Institut f&#252;r Eisenforschung, D&#252;sseldorf, Germany, after working some time as researcher at Carnegie Mellon University, USA, the High Magnetic Field Laboratory in Tallahassee, USA, and serving as senior researcher and lecturer at the Institut f&#252;r Metallkunde und Metallphysik, RWTH Aachen, Germany. His research fields are computer simulation of materials, composites, textures, and micromechanics, in which he authored more than 100 papers in peer-reviewed magazines and three books. He teaches various courses on computational materials science, materials mechanics, history of metals, and textures at RWTH Aachen (Germany) and at Carnegie Mellon University Pittsburgh (USA). His work was already awarded with several prizes, among them the Adolf-Martens Award, Masing Award, Heisenberg Award, and the Leibniz Award. <p> <b>Dr. Franz Roters</b> studied Physics in Braunschweig, where he got his diploma degree in 1993. From 1994 to 1998 he was scientist at the Institute for Metal Physics and Physical Metallurgy at the RWTH Aachen. He got his PhD. degree in 1999 in the field of constitutive modelling of aluminium. From 1999 till 2000 he was researcher at the R&amp;D centre of VAW (today Hydro Aluminium Deutschland GmbH) in Bonn. Since 2000 he is senior scientist at the Max-Planck-Institut f&#252;r Eisenforschung in D&#252;sseldorf, where he is the leader of the research group &#8220;Theory and Simulation&#8221; in the department for Microstructure Physics and Metal Forming. Dr. Roters published more than 30 papers in the field of constitutive modelling and simulation of forming. He is head of the Technical Committee &#8220;Computersimulation&#8221; of the Deutsche Gesellschaft f&#252;r Materialkunde e.V. (DGM). <p> <b>Professor Long-Qing Chen</b> is teaching Materials Science and Engineering at Penn State. He received his B.S. in Ceramics from Zhejiang University in China in 1982, a M.S. in Materials Science and Engineering from State University of New York at Stony Brook in 1985, and a Ph.D. degree in Materials Science and Engineering from MIT in 1990. He worked with Armen G. Khachaturyan as a postdoc at Rutgers University from 1990 to 1992. Professor Chen joined the Department of Materials Science and Engineering at Penn State as an assistant professor in 1992 and was promoted to associate professor in 1998. His main research interests include materials theory and computational materials science. Professor Chen received the Young Investigator Award from the Office of Naval Research (ONR) in 1995, the research creativity award from the National Science Foundation (NSF) in 1999, the Wilson Award for Excellence in Research in the College of Earth and Mineral Sciences in 2000, and the University Faculty Scholar Medal at Penn State in 2003. <p> <b>Dr. Fr&#233;d&#233;ric Barlat</b> received a PhD in Mechanics from the &#8220;Institut National Polytechnique de Grenoble,&#8221; France, in 1984. The same year, he joined Alcoa Technical Center; Pittsburgh, Pennsylvania, USA, the research facility of Alcoa Inc. (formerly the Aluminum Company of America). Dr. Barlat is currently a technology specialist in their materials science division. He is responsible for conceptualizing, importing and implementing mathematical models that predict the mechanical behavior of materials for long-term development applications in the areas of metal plasticity, fracture and material performance. His work is used for the design of alloys and processes in support of Alcoa's major business units, including packaging, automotive and aerospace. Dr. Barlat is also an invited professor at the University of Aveiro&#8217;s Center for Mechanical Technology and Automation, Portugal, where he directs activities on the fundamentals of plasticity and forming. He has actively participated in the scientific committees of various international conferences, has been a regular reviewer in a number of scientific journals and serves as a member of the Advisory Board of the International Journal of Plasticity. Dr. Barlat is published as an author or co-author in approximately 80 papers of peer-reviewed scientific journals and has delivered more than 60 technical presentations at conferences worldwide. In 1995, he was the honored recipient of the ASM Henry Marion Howe Medal of the Material Society for the best technical paper published in Metallurgical Transactions A. He holds three US patents with co-inventors from Alcoa Inc. and Kobe Steel, Ltd., Japan.

Table of Contents

Preface	xxi
List of Contributors	xxiii
I Fundamentals and Basic Methods	1	(248)
Computer Simulation of Diffusion Controlled Phase Transformations	3	(34)
A. Schneider
G. Inden
Introduction	3	(2)
Numerical Treatment of Diffusion Controlled Transformations	5	(10)
Diffusion	5	(3)
Boundary Conditions	8	(6)
Cell Size	14	(1)
Typical Applications	15	(18)
LE, LENP and PE in Fe-Mn-C	15	(2)
LE, LENP and PE in Fe-Si-C	17	(3)
PE in Fe-Ni-C	20	(1)
Effect of Traces on the Growth of Grain Boundary Cementite	21	(1)
Continuous Cooling	22	(1)
Competitive Growth of Phases: Multi-Cell Calculations	23	(3)
Gas-Metal-Reactions: Carburization	26	(7)
Outlook	33	(4)
References	34	(3)
Introduction to the Phase-Field Method of Microstructure Evolution	37	(20)
I.-Q. Chen
Introduction	37	(1)
Origin of the Model	38	(1)
Theoretical Fundamentals of the Method	38	(9)
Representation of a Microstructure	38	(2)
Thermodynamics of Microstructures	40	(6)
The Evolution Equations	46	(1)
Advantages and Disadvantages of the Method	47	(1)
Typical Fields of Applications and Examples	47	(2)
Summary and Opportunities	49	(8)
References	51	(6)
Cellular, Lattice Gas, and Boltzmann Automata	57	(20)
D. Raabe
Cellular Automata	57	(10)
Introduction	57	(1)
Formal Description and Classes of Cellular Automata	58	(2)
Cellular Automata in Materials Science	60	(1)
Recrystallization Simulations with Cellular Automata	61	(6)
Cellular Automata for Fluid Dynamics	67	(6)
Introduction	67	(1)
The HPP and FHP Lattice Gas Cellular Automata	67	(3)
The Lattice Boltzmann Automaton	70	(3)
Conclusions and Outlook	73	(4)
References	74	(3)
The Monte Carlo Method	77	(38)
A. D. Rollett
P. Manohar
Introduction	77	(1)
History of the Monte Carlo Method	77	(8)
Ising and Potts Models	78	(2)
Metropolis Algorithm	80	(1)
n-fold Way Algorithm	81	(4)
Description of the Monte Carlo Method for Grain Growth & Recrystallization	85	(7)
Discretization of Microstructure	85	(1)
Evolution of the Microstructure	86	(1)
Inert Particles	87	(1)
Lattices	87	(2)
Boundary Conditions	89	(1)
Parallelization of the Monte Carlo Algorithm	89	(3)
Nucleation in Recrystallization	92	(1)
Initialization of MC Simulations	93	(1)
Verification of the Monte Carlo Model	94	(3)
Scaling of Simulated Grain Size to Physical Grain Size	97	(1)
Recrystallization Kinetics in the Monte Carlo model	98	(1)
Results of Simulation of Recrystallization by Monte Carlo Method	99	(11)
Abnormal Grain Growth	99	(1)
Static Recrystallization	99	(2)
Grain Growth in the Presence of Particles	101	(1)
Recrystallization in the Presence of Particles	101	(2)
Texture Development	103	(2)
Texture	105	(4)
Dynamic Recrystallization	109	(1)
Summary	110	(5)
References	111	(4)
Crystal Plasticity	115	(30)
P. R. Dawson
Introduction	115	(1)
Theoretical Background	115	(9)
Mechanical Response of Single Crystals	115	(5)
Lattice Orientation Distributions for Polycrystals	120	(2)
Mechanical Response of Polycrystals	122	(2)
Macroscopic Criteria for Anisotropic Strength	124	(8)
Generalities	124	(2)
Yield Surfaces Defined by Expansions	126	(1)
Yield Surfaces Defined by Hyperplanes	127	(2)
Isoparametric Flow Surface	129	(2)
Direct Polycrystal Plasticity Implementation	131	(1)
Numerical Implementations	132	(2)
Balance Laws	132	(1)
Finite Element Formulations	132	(2)
Applications	134	(5)
Application to Explosive Forming	134	(1)
Application to the Limiting Dome Height Test	135	(4)
Bending of a Curved Component	139	(1)
Summary	139	(6)
References	141	(4)
Yield Surface Plasticity and Anisotropy	145	(40)
F. Barlat
O. Cazacu
M. Zyczkowski
D. Banabic
J. W. Yoon
Introduction	145	(1)
Classical Plasticity Theory	146	(8)
Isotropic Yield Conditions for Perfect Plasticity	146	(3)
Flow Rules	149	(1)
Subsequent Yield Surfaces during Plastic Hardening	150	(2)
Anisotropic Plasticity	152	(1)
Direct Generalizations of Isotropic Yield Conditions	153	(1)
Material Structure and Plastic Anisotropy	154	(7)
Texture	154	(2)
Dislocations	156	(4)
Porosity and Second Phases	160	(1)
Yield Functions for Metals and Alloys	161	(8)
Quadratic Yield Functions	161	(1)
Non-Quadratic Yield Functions	162	(3)
Yield Functions in Polar Coordinates	165	(1)
Other Anisotropic Yield Functions	165	(1)
BBC2000 Yield Criterion	165	(2)
Yld2000-2d Yield Criterion	167	(1)
CB2001 Yield Criterion	167	(2)
Strain Rate Potentials	169	(1)
Application to Sheet Forming and Formability	169	(8)
Mechanical testing	169	(3)
Analysis and Treatment of the Test Results	172	(2)
Application to 3103-O Aluminum Alloy Sheet Sample	174	(1)
Plastic Flow Localization	174	(1)
Cup Drawing Simulation	175	(2)
Conclusions	177	(8)
References	178	(7)
Artificial Neural Networks	185	(16)
E. Broese
H.-U. Loffer
Introduction	185	(1)
Basic Terms	186	(1)
Fields of Application	186	(1)
Pattern Recognition/Classification	186	(1)
Empirical Modeling	186	(1)
Implementation	187	(1)
Software	187	(1)
Hardware	188	(1)
Types of Artificial Neural Networks	188	(6)
Multilayer Perceptron	188	(3)
Radial Basis Function Networks	191	(2)
More Network Types	193	(1)
Kinds of Learning	194	(1)
Unsupervised Learning	194	(1)
Supervised Learning	194	(1)
Reinforcement Learning	194	(1)
Bayesian Learning	195	(1)
Application Details	195	(3)
Network Type Selection and Configuration	195	(1)
Input Selection	196	(1)
Data Preprocessing and Input Scaling	196	(1)
Prevention of Overfitting	196	(1)
Optimization of Training Parameters	197	(1)
Diagnostics of the Internal State	197	(1)
Future Prospects	198	(3)
References	198	(3)
Multiscale Discrete Dislocation Dynamics Plasticity	201	(30)
H. M. Zbib
M. Hiratani
M. Shehadeh
Introduction	201	(2)
Theoretical Fundamentals of the Method	203	(11)
Kinematics and Geometric Aspects	203	(1)
Kinetics and Interaction Forces	203	(1)
Dislocation Equation of Motion	204	(4)
The Dislocation Stress and Force Fields	208	(2)
The Stochastic Force and Cross-slip	210	(2)
Modifications for Long-Range Interactions: The Super-Dislocation Principle	212	(1)
Evaluation of Plastic Strains	213	(1)
The DD Numerical Solution: An Implicit-Explicit Integration Scheme	213	(1)
Integration of DD and Continuum Plasticity	214	(3)
Continuum Elasto-Viscoplasticity	214	(1)
Modifications for Finite Domains	215	(2)
Typical Fields of Applications and Examples	217	(8)
Evolution of Dislocation Structure during Monotonic Loading	218	(2)
Dislocation Crack Interaction: Heterogeneous Deformation	220	(3)
Dislocations Interaction with Shock Waves	223	(2)
Summary and Concluding Remarks	225	(6)
References	226	(5)
Physically Based Models for Industrial Materials: What For?	231	(18)
Y. Brechet
Introduction	231	(1)
Recent Trends in Modelling Materials Behavior	231	(6)
Analytical Models	232	(1)
Computer Simulations	233	(2)
Materials Modelling and Materials Design: Some Examples	235	(1)
Sophisticated Statistical Analysis	236	(1)
Some Examples of Physically Based Models for Industrial Materials	237	(8)
Recovery of Aluminum Alloys	237	(3)
Competition Between Recrystallization and Precipitation	240	(3)
Optimizing Casting Process in Precipitation Hardenable Alloys	243	(2)
Perspectives	245	(4)
References	247	(2)
II Application to Engineering Microstructures	249	(398)
Modeling of Dendritic Grain Formation During Solidification at the Level of Macro- and Microstructures	251	(20)
M. Rappaz
A. Jacot
Ch.-A. Gandin
Introduction	251	(3)
Pseudo-Front Tracking Model	254	(3)
Primary Phase Formation	254	(2)
Secondary Phases Formation	256	(1)
Coupling with Thermodynamic Databases	257	(1)
Primary Phase Formation	257	(1)
Secondary Phases Formation	258	(1)
Cellular Automaton -- Finite Element Model	258	(3)
Nucleation Law	259	(1)
Growth Law	259	(1)
Coupling of CA and FE Methods	260	(1)
Results and Discussion	261	(5)
PFT Model	261	(3)
CAFE Model	264	(2)
Conclusion	266	(5)
References	267	(4)
Phase-Field Method Applied to Strain-dominated Microstructure Evolution during Solid-State Phase Transformations	271	(26)
L.-Q. Chen
S. Y. Hu
Introduction	271	(1)
Phenomenological Description of Solid State Phase Transformations	272	(2)
Phase-Field Model of Solid State Phase Transformations	274	(2)
Elastic Energy of a Microstructure	276	(1)
Bulk Microstructures with Periodic Boundary Conditions	276	(2)
A Single Crystal Film with Surface and Substrate Constraint	278	(1)
Elastic Coupling of Structural Defects and Phase Transformations	279	(1)
Phase-Field Model Applied to Solid State Phase Transformations	280	(1)
Isostructural Phase Separation	280	(2)
Precipitation of Cubic Intermetallic Precipitates in a Cubic Matrix	282	(2)
Structural Transformations Resulting in a Point Group Symmetry Reduction	284	(2)
Ferroelectric Phase Transformations	286	(2)
Phase Transformation in a Reduced Dimensions: Thin Films and Surfaces	288	(2)
Summary	290	(7)
References	292	(5)
Irregular Cellular Automata Modeling of Grain Growth	297	(12)
K. Janssens
Introduction	297	(1)
Irregular Cellular Automata	297	(1)
The Concept	297	(1)
Shapeless or Point Cellular Automata	298	(1)
Irregular Shapeless Cellular Automata for Grain Growth	298	(6)
Curvature Driven Grain Growth	299	(3)
In the Presence of Additional Driving Forces	302	(2)
A Qualitative Example: Static Annealing of a Cold Rolled Steel	304	(3)
The Deformation Model	304	(1)
The Annealing Model	305	(2)
Conclusion	307	(2)
References	307	(2)
Topological Relationships in 2D Trivalent Mosaics and Their Application to Normal Grain Growth	309	(18)
R. Brandt
K. Lucke
G. Abbruzzese
J. Svoboda
Introduction	309	(3)
Individual Grains and their Distributions (One-Grain Model)	312	(2)
Definition of Parameters	312	(1)
The Grain Sizes and Shapes and their Distributions	313	(1)
The Coordination and its Distributions	314	(1)
Topological Relationships of Trivalent Mosaics	314	(3)
Grain Boundaries (GBs) and Triple Points (TPs)	314	(1)
The Geometry of the GB (Function pij)	315	(1)
Size Correlations of Nearest Neighbor Grains (Function kij)	315	(1)
Space Filling (Function qij)	316	(1)
Cases of Randomness	317	(2)
Abbruzzese--Lucke Equations (ALE, Full Randomness)	317	(1)
Weaire--Aboav Equation (WAE, Partial Randomness)	317	(2)
Curvature Driven GG	319	(4)
Direct Simulations	319	(1)
Simulations by the Statistical Theory	320	(3)
Summarizing Remarks	323	(4)
References	325	(2)
Motion of Multiple Interfaces: Grain Growth and Coarsening	327	(16)
B. Nestler
Introduction	327	(2)
The Diffuse Interface Model	329	(2)
Free Energies	331	(2)
Numerical Simulations	333	(7)
Grain Growth and Coarsening	334	(1)
Multicomponent Multiphase Solidification	335	(5)
Outlook	340	(3)
References	341	(2)
Deformation and Recrystallization of Particle-containing Aluminum Alloys	343	(18)
B. Radhakrishnan
G. Sarma
Background	343	(5)
Formation of Deformation Zones	344	(1)
Formation and Growth of Particle Stimulated Nuclei	345	(3)
Computational Approach	348	(1)
Simulations	349	(1)
Results and Discussion	350	(8)
Microstructure and Kinetics	350	(5)
Texture	355	(3)
Summary	358	(3)
References	359	(2)
Mesoscale Simulation of Grain Growth	361	(14)
D. Kinderlehrer
J. Lee
I. Livshits
S. Ta'asan
Introduction	361	(4)
Discretization	365	(1)
Numerical Implementation	366	(3)
Numerical Results	369	(1)
Conclusion	370	(5)
References	371	(4)
Dislocation Dynamics Simulations of Particle Strengthening	375	(22)
V. Mohles
Introduction	375	(2)
Simulation Method	377	(5)
Basis of the Method	377	(1)
Dislocation Segmentation	378	(1)
Dislocation Self-Interaction	379	(2)
Simulation Procedure and Accuracy	381	(1)
Particle Arrangement	382	(2)
Strengthening Mechanisms	384	(9)
Dispersion Strengthening	384	(2)
Order Strengthening	386	(2)
Lattice Mismatch Strengthening	388	(5)
Summary and Outlook	393	(4)
References	393	(4)
Discrete Dislocation Dynamics Simulation of Thin Film Plasticity	397	(16)
B. von Blanckenhagen
P. Gumbsch
Thin Film Plasticity	397	(2)
Simulation of Dislocations in Thin Films	399	(3)
Boundary Conditions	400	(2)
Thin Film Deformation, Models and Simulation	402	(11)
Mobility Controlled Deformation	402	(1)
Source Controlled Deformation	403	(6)
References	409	(4)
Discrete Dislocation Dynamics Simulation of Crack-Tip Plasticity	413	(16)
A. Hartmaier
P. Gumbsch
Introduction	413	(1)
Model	414	(5)
Crack-Tip Plasticity	419	(2)
Scaling Relations	421	(3)
Discussion	424	(1)
Conclusions	425	(4)
References	425	(4)
Coarse Graining of Dislocation Structure and Dynamics	429	(16)
R. LeSar
J. M. Rickman
Introduction	429	(1)
Dynamics of Discrete Dislocations	430	(1)
Dislocation Dynamics Methods	430	(1)
Phase-Field Methods	430	(1)
Static Coarse-Grained Properties	431	(8)
Continuous Dislocation Theory	432	(3)
Extensions to the Continuous Theory	435	(4)
Dynamic Coarse-Grained Properties	439	(2)
Conclusions	441	(4)
References	442	(3)
Statistical Dislocation Modeling	445	(14)
R. Sedlacek
Introduction	445	(3)
One-parameter Models	448	(3)
Phenomenological Model	448	(2)
Materials Science Approach	450	(1)
Multi-parameter Models	451	(4)
Various Approaches	451	(2)
Composite Framework	453	(2)
Conclusions	455	(4)
References	456	(3)
Taylor-Type Homogenization Methods for Texture and Anisotropy	459	(14)
P. Van Houtte
S. Li
O. Engler
Introduction	459	(1)
Local Constitutive Laws (Mesoscopic Scale)	460	(2)
The Taylor Ambiguity	462	(1)
Full Constraints (FC) Taylor Theory	463	(1)
Classical Relaxed Constraints (RC) Models	464	(1)
Multi-grain RC Models	465	(4)
Introduction	465	(1)
The Lamel Model	466	(1)
The Advanced Lamel Model	467	(2)
The Grain Interaction (GIA) Model	469	(1)
Validation of the Models	469	(1)
Conclusions	469	(4)
References	471	(2)
Self Consistent Homogenization Methods for Texture and Anisotropy	473	(28)
C. N. Tome
R. A. Lebensohn
Introduction	473	(2)
Viscoplastic Selfconsistent Formalism	475	(8)
Local Constitutive Behavior and Homogenization	475	(2)
Green Function Method and Fourier Transform Solution	477	(1)
Viscoplastic Inclusion and Eshelby Tensors	478	(2)
Interaction and Localization Equations	480	(1)
Selfconsistent Equations	481	(1)
Secant, Tangent and Intermediate Approximations	482	(1)
Algorithm	482	(1)
Implementation of a Texture Development Calculation	483	(4)
Kinematics	483	(2)
Hardening	485	(1)
Twinning Reorientation	486	(1)
Applications	487	(8)
Tension and Compression of FCC	487	(1)
Torsion (Shear) of FCC	488	(4)
Twinning and Anisotropy of HCP Zr	492	(1)
Compression of Olivine (MgSiO4)	493	(2)
Further Selfconsistent Models and Applications	495	(6)
References	497	(4)
Phase-field Extension of Crystal Plasticity with Application to Hardening Modeling	501	(12)
B. Svendsen
Introduction	501	(1)
Basic Considerations and Results	502	(4)
The Case of Small Deformation	506	(1)
Simple Shear of a Crystalline Strip	507	(6)
References	510	(3)
Generalized Continuum Modelling of Single and Polycrystal Plasticity	513	(16)
S. Forest
Introduction	513	(2)
Scope of this Chapter	513	(1)
Motivations for Generalized Continuum Crystal Plasticity	514	(1)
Generalized Continuum Crystal Plasticity Models	515	(4)
Cosserat Single Crystal Plasticity	515	(2)
Second Gradient Single Crystal Plasticity	517	(1)
Gradient of Internal Variable Approach	518	(1)
From Single to Polycrystals: Homogenization of Generalized Continua	519	(4)
Introduction to Multiscale Asymptotic Method	519	(3)
Extension of Classical Homogenization Schemes	522	(1)
Simulations of Size Effects in Crystal Plasticity	523	(3)
Constrained Plasticity in Two-Phase Single Crystals	523	(1)
Plasticity at the Crack Tip in Single Crystals	523	(1)
Grain Size Effects in Polycrystalline Aggregates	524	(2)
Conclusion	526	(3)
References	526	(3)
Micro-Mechanical Finite Element Models for Crystal Plasticity	529	(14)
S. R. Kalidindi
Introduction	529	(1)
Theoretical Background	529	(5)
Crystal Plasticity Framework	530	(1)
Total Lagrangian versus Updated Lagrangian Schemes	530	(2)
Fully Implicit Time Integration Procedures	532	(2)
Polycrystal Homogenization Theories	534	(1)
Micro-Mechanical Finite Element Models	534	(1)
Examples	535	(8)
Predictions of Deformation Textures	535	(1)
Predictions of Micro-Texture	535	(7)
References	542	(1)
A Crystal Plasticity Framework for Deformation Twinning	543	(18)
S. R. Kalidindi
Introduction	543	(3)
Slip versus Deformation Twinning	543	(1)
Major Consequences of Deformation Twinning	544	(2)
Historical Perspective	546	(2)
Twin Reorientation Schemes	547	(1)
Volume Fraction Transfer Scheme	547	(1)
Incorporation of Deformation Twinning	548	(8)
Relaxed Configuration	548	(2)
Elastic Response	550	(1)
Plastic Flow Rule	550	(2)
Evolution of Twin Rotations	552	(2)
Slip-Twin Hardening Functions	554	(2)
Examples	556	(5)
References	559	(2)
The Texture Component Crystal Plasticity Finite Element Method	561	(12)
F. Roters
Introduction	561	(1)
The Texture Component Method	561	(4)
Approximation of X-Ray Textures using Texture Components	562	(1)
Representation of Texture Components in a Crystal Plasticity FEM	562	(3)
The Crystal Plasticity Model	565	(1)
Application of the TCCP-FEM to Forming Simulation	566	(5)
R-value Prediction	566	(1)
Prediction of Earing Behavior	566	(5)
Outlook	571	(2)
References	572	(1)
Microstructural Modeling of Multifunctional Material Properties: The OOF Project	573	(16)
R. E. Garcia
A. C. E. Reid
S. A. Langer
W. C. Carter
Introduction	573	(2)
Program Overview	575	(3)
Modeling of Piezoelectric Microstructures	578	(2)
Modeling of Electrochemical Solids: Rechargeable Lithium Ion Batteries	580	(5)
The OOFTWO Project: A Preview	585	(4)
References	587	(2)
Micromechanical Simulation of Composites	589	(18)
S. Schmauder
Introduction	589	(1)
Matricity	590	(5)
Matricity Model	590	(2)
Adjusting Matricity in the Model	592	(1)
Realisation of the Adjustability of Matricity by Weighting Factors	592	(1)
Calculation of Stress-strain Curves	593	(1)
Mechanical Constants	594	(1)
Yield Stress	595	(1)
Results and Discussion	595	(9)
Comparison to Cluster Parameter	595	(9)
Conclusion	604	(3)
References	605	(2)
Creep Simulation	607	(14)
W. Blum
Introduction	607	(1)
Empirical Relations	608	(1)
Basic Dislocation Processes	609	(2)
Homogeneous Glide Activity	609	(1)
Heterogeneous Glide Activity	610	(1)
Models	611	(5)
Two-parameter Model for Homogeneous Glide	612	(2)
Composite Model for Heterogeneous Glide	614	(2)
Concluding Remarks	616	(5)
References	618	(3)
Computational Fracture Mechanics	621	(18)
W. Brocks
Introductory Remarks on Inelastic Material Behaviour	621	(2)
FE Meshes for Structures with Crack-Like Defects	623	(3)
General Aspects and Examples	623	(1)
Singular Elements for Stationary Cracks	624	(1)
Regular Element Arrangements for Extending Cracks	625	(1)
The J-Integral as Characteristic Parameter in Elasto-Plastic Fracture Mechanics	626	(3)
Foundation	626	(1)
The Domain Integral or VCE Method	627	(1)
Path Dependence of the J-Integral in Incremental Plasticity	628	(1)
The Cohesive Model	629	(4)
Fundamentals	629	(3)
Example: Simulation of Ductile Tearing in a Laser Weld	632	(1)
Summary	633	(6)
References	634	(5)
Rheology of Concentrated Suspensions: A Lattice Model	639	(8)
Y. Brechet
M. Perez
Z. Neda
J. C. Barbe
L. Salvo
Introduction	639	(1)
Behaviour of Suspensions: The Generation of Clusters	640	(3)
Conclusions	643	(4)
References	644	(3)
III Application to Engineering Materials Processes	647	(198)
Solidification Processes: From Dendrites to Design	649	(8)
J. A. Dantzig
Introduction	649	(1)
Dendritic Microstructures	650	(2)
Inverse Problems and Optimal Design	652	(2)
Conclusion	654	(3)
References	655	(2)
Simulation in Powder Technology	657	(18)
H. Riedel
T. Kraft
Introduction	657	(1)
Powder Production	658	(1)
Die Filling	658	(1)
Powder Compaction	658	(6)
The Drucker-Prager-Cap Model and Finite Element Implementations	659	(2)
Experiments to Determine the Drucker-Prager-Cap Parameters	661	(2)
Example	663	(1)
Sintering	664	(6)
Models for Solid-State Sintering	665	(2)
Liquid-Phase Sintering	667	(1)
Parameters of the Liquid-Phase Sintering Model for an Alumina Ceramic	668	(1)
Finite-Element Implementations and Applications	669	(1)
Sizing and Post-Sintering Mechanical Densification	670	(1)
Fatigue	671	(1)
Conclusions	671	(4)
References	671	(4)
Integration of Physically Based Materials Concepts	675	(12)
M. Crumbach
M. Goerdeler
M. Schneider
G. Gottstein
L. Neumann
H. Aretz
R. Kopp
B. Pustal
A. Ludwig
Through-process Modeling of Aluminum Alloy AA2024 from Solidification through Homogenization and Hot Rolling	677	(4)
Through-process Texture Modeling of Aluminum Alloy AA5182 during Industrial Multistep hot Rolling, Cold Rolling, and Annealing	681	(2)
Through-thickness Texture Evolution during Hot Rolling of an IF-Steel	683	(1)
Conclusions	684	(3)
References	684	(3)
Integrated Through-Process Modelling, by the Example of Al-Rolling	687	(18)
K. F. Karhausen
Introduction	687	(1)
Features of the Al Production Chain for Rolled Products	688	(2)
TP Modelling of the Al Process Chain for Rolled Products	690	(1)
Application of Through Process Modelling	691	(12)
Tracing of Dislocation Density	693	(6)
Tracing of Texture	699	(2)
Tracing of Microchemistry	701	(2)
Conclusions	703	(2)
References	703	(2)
Property Control in Production of Aluminum Sheet by Use of Simulation	705	(22)
J. Hirsch
K. F. Karhausen
O. Engler
Introduction	705	(1)
Optimization Strategies in Sheet Processing and Material Quality	706	(1)
Processing and Microstructure Features of Aluminum Sheet	707	(1)
Thermomechanical Simulation of Rolling Processes	708	(3)
Microstructure Evolution During hot Rolling	711	(6)
Material Properties of Industrially Processed Aluminum Sheet	717	(2)
Simulation of Anisotropic Sheet Properties	719	(4)
Strength Anisotropy	720	(1)
Tensile Test and r-Value Simulation	720	(1)
Earing During Cup Deep Drawing	721	(2)
Formability of Aluminum Sheets	723	(1)
Summary and Outlook	724	(3)
References	725	(2)
Forging	727	(18)
Y. Chastel
R. Loge
Introduction	727	(1)
Case I: Microstructure Evolution During Complex Hot Forging Sequences	728	(5)
Equations for Microstructure Evolutions	728	(2)
Integration into a Finite Element Code	730	(1)
2D Simulation Results	731	(2)
Extension to 3D Forging and Dynamic Recrystallization	733	(1)
Case II: Warm Forming of Two-Phase Steels	733	(3)
Case III: Texture Evolution in an Hexagonal Alloy	736	(4)
Calibrating the Polycrystalline Model with Simple Mechanical Tests	738	(1)
Using the Texture-Induced Anisotropic Plastic Flow to Validate the FEM Results	739	(1)
Application to Hot Forming	739	(1)
Conclusions	740	(5)
References	741	(4)
Numerical Simulation of Solidification Structures During Fusion Welding	745	(18)
V. Pavlyk
U. Dilthey
Introduction	745	(2)
Modell of Dendrite Growth under Constrained Solidification Conditions	747	(7)
Solidification Problem with the Sharp Interface	747	(1)
Numerical Solution	748	(6)
Verification of the CA-FDM Solidification Model	754	(1)
Model Application under Welding Conditions	755	(3)
Macroscopic Modelling of Solidification Conditions	755	(1)
Microscopic Simulation of Solidification Structures	756	(2)
Conclusions	758	(5)
References	760	(3)
Forming Analysis and Design for Hydroforming	763	(14)
K. Chung
Introduction	763	(3)
Ideal Forming Design Theory for Tube Hydroforming	766	(3)
Strain-Rate Potential: Srp98	769	(1)
Preform Design for Hydroforming Parts	770	(2)
Summary	772	(5)
References	772	(5)
Sheet Springback	777	(18)
R. H. Wagoner
Introduction	777	(1)
Review of Simulation Literature	778	(2)
Review of the Experimental Literature	780	(2)
Draw-Bend Springback	782	(6)
Conclusions	788	(7)
References	788	(7)
The ESI-Wilkins-Kamoulakos (EWK) Rupture Model	795	(10)
A. Kamoulakos
Background	795	(2)
The EWK Fracture Model	797	(1)
Academic Validation	798	(1)
Semi-Industrial Validation	799	(3)
Conclusions	802	(3)
References	803	(2)
Damage Percolation Modeling in Aluminum Alloy Sheet	805	(12)
M. J. Worswick
Z. T. Chen
A. K. Pilkey
D. Lloyd
Introduction	805	(2)
Experiment	807	(1)
Material -- Characterization of Second Phase Particle Fields	807	(1)
GTN-based FE Model	808	(3)
Coupled damage percolation model	811	(1)
Results	812	(2)
Discussion	814	(3)
References	816	(1)
Structure Damage Simulation	817	(12)
D. Steglich
Introduction	817	(1)
Plastic Potentials and Porosity	818	(3)
Model Parameter Identification	821	(2)
Strain Softening, Damage and Lengthscale	823	(2)
Hints for Application	825	(4)
References	826	(3)
Microstructure Modeling using Artificial Neural Networks	829	(16)
H.-U. Loffler
Introduction	829	(3)
Artificial Neural Networks in Process Simulation	832	(4)
Joint Microstructure Model and Neural Network System	836	(6)
Physical Model	836	(2)
Physical Model plus Neural Network	838	(1)
Off-line System, on-line System and in-line System	839	(2)
Results from Hot Strip Mills	841	(1)
Conclusions	842	(3)
References	843	(2)
Index	845