COMPUTATIONAL MATERIALS ENGINEERING Episode 1 pptx

[...]... microstructure and materials properties! Bibliography [Bra] [Bra50] [Bra 51] [Cah02] [DP05] [FS96] [GS99] [HH96] [HH04] [HR99] [LC90] [LL03] [MDC97] [Mor04] [SB95] [Set99] [Tor02] [Atl02] M A Bravais http://en.wikipedia.org/wiki/Bravais–lattice M A Bravais J Ecole Polytechnique, 19 :1 12 8, 18 50 M A Bravais J Ecole Polytechnique, 20 :10 1–278, 18 51 R W Cahn The science of dirt Nature Materials, 1: 3–4, 2002 F... Dislocation Dynamics 8.4 .1 Introduction 8.4.2 Newtonian Dislocation Dynamics 8.4.3 Viscous and Viscoplastic Dislocation Dynamics 8.5 Kinematics of Discrete Dislocation Dynamics 8.6 Dislocation Reactions and Annihilation 9 292 298 298 299 307 310 311 Finite Elements for Microstructure Evolution 9 .1 Fundamentals of Differential Equations 9 .1. 1 Introduction to Differential Equations 9 .1. 2 Solution of Partial... computational microstructure evolution: garbage-in = garbage-out (1. 1) You have been warned—we wash our hands in innocence 1. 1 Microstructures Defined The world of materials around us is amazingly diverse It is so diverse that scientists feel the need to classify materials into different types Like the authors of this book, your typical technologist classifies materials based on their technical properties Fundamental... Crystalline Materials Clarendon Press, Oxford, 19 95 J A Sethian Level Set Methods and Fast Marching Methods Cambridge University Press, Cambridge, 19 99 S Torquato Random Heterogeneous Materials: Microstructure and Macroscopic Properties SpringerVerlag, Berlin, 2002 S N Atluri and S Shen The Meshless Local Petrov-Galerkin (MLPG) Method Tech Science Press, Forsyth, GA, 2002 6 COMPUTATIONAL MATERIALS ENGINEERING. .. German physicist Rudolf Clausius (18 22 18 88) The word entropy has Greek origin and means transformation Similar to U and H , entropy S is a state function Its value is only dependent on the state variables T , P , V , N and it is independent of the way how the state was established We can therefore also write dS = 10 COMPUTATIONAL MATERIALS ENGINEERING dQ =0 T (2 .14 ) ... Finite Element Methods at the Meso- and Macroscale 9.3 .1 Introduction and Fundamentals 9.3.2 The Equilibrium Equation in FE Simulations 9.3.3 Finite Elements and Shape Functions 9.3.4 Assemblage of the Stiffness Matrix 9.3.5 Solid-State Kinematics for Mechanical Problems 9.3.6 Conjugate Stress–Strain Measures 317 317 317 320 3 21 322 322 324 324 327 329 3 31 Index 335 TABLE OF CONTENTS xi This page intentionally... correctly in 18 45, a classification published in 18 50 18 51 [Bra, Bra50, Bra 51] The lattice parameters define the length in space over which the lattice repeats itself, or in other words the volume of the unit cell of the crystal The organization of atoms on a lattice with a specific set of lattice parameters is what we call a solid state phase Going from pure metals to alloys, ceramics, polymers, and biomaterials,... during hot rolling (or any other technological process T2Tcr Tcr T2 T1 0 0.2 0.4 0.6 Molefraction X 0.8 1 B Phase Transformation Diffusion Solidification Recovery Recrystallization Deformation Grain Growth FIGURE 1- 1 Schematic of the industrial processing of a metal from its liquid phase to a sheet metal,... skip straight to the computational chapters However, if you intend to learn more about the science of polycrystalline materials but want to learn about them through their computational modeling, then this chapter will give you the bare-bones introduction to the secrets of microstructures Just remember that the one law binding any type of computational modeling is equally valid for computational microstructure... Transitions and Microstructure Evolution 7.5 Acknowledgments 219 220 222 224 226 226 228 229 229 2 31 232 232 233 236 237 238 2 41 2 41 242 245 248 249 252 253 253 Introduction to Discrete Dislocations Statics and Dynamics 8 .1 Basics of Discrete Plasticity Models 8.2 Linear Elasticity Theory for Plasticity 8.2 .1 Introduction 8.2.2 Fundamentals of Elasticity Theory 8.2.3 Equilibrium Equations 8.2.4 Compatibility . 8 2 .1. 2 The Gibbs Energy 11 2 .1. 3 Molar Quantities and the Chemical Potential 11 2 .1. 4 Entropy Production and the Second Law of Thermodynamics 12 2 .1. 5 Driving Force for Internal Processes 15 2 .1. 6. One-Dimensional Recrystallization 11 1 4.2.2 Before Moving to Higher Dimensions 11 1 4.3 +2D CA Modeling of Recrystallization 11 6 4.3 .1 CA-Neighborhood Definitions in Two Dimensions 11 6 4.3.2 The Interface. Phase Transformation 17 9 6 .1 Statistical Theory of Phase Transformation 18 1 6 .1. 1 The Extended Volume Approach—KJMA Kinetics 18 1 6.2 Solid-State Nucleation 18 5 6.2 .1 Introduction 18 5 6.2.2 Macroscopic