Crystal Plasticity Finite Element Methods E-Book

Franz Roters

• Herausgeber: Wiley-VCH
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 318

Veröffentlichungsjahr: 2011

Beschreibung

Written by the leading experts in computational materials science, this handy reference concisely reviews the most important aspects of plasticity modeling: constitutive laws, phase transformations, texture methods, continuum approaches and damage mechanisms. As a result, it provides the knowledge needed to avoid failures in critical systems udner mechanical load.
With its various application examples to micro- and macrostructure mechanics, this is an invaluable resource for mechanical engineers as well as for researchers wanting to improve on this method and extend its outreach.

Leseprobe

Contents

Notation

Preface

1: Introduction to Crystalline Anisotropy and the Crystal Plasticity Finite Element Method

Part One Fundamentals

2: Metallurgical Fundamentals of Plastic Deformation

2.1 Introduction

2.2 Lattice Dislocations

2.3 Deformation Martensite and Mechanical Twinning

3: Continuum Mechanics

3.1 Kinematics

3.2 Mechanical Equilibrium

3.3 Thermodynamics

4: The Finite Element Method

4.1 The Principle of Virtual Work

4.2 Solution Procedure - Discretization

4.3 Nonlinear FEM

5: The Crystal Plasticity Finite Element Method as a Multiphysics Framework

Part Two The Crystal Plasticity Finite Element Method

6: Constitutive Models

6.1 Dislocation Slip

6.2 Displacive Transformations

6.3 Damage

7: Homogenization

7.1 Introduction

7.2 Statistical Representation of Crystallographic Texture

7.3 Computational Homogenization

7.4 Mean-Field Homogenization

7.5 Grain-Cluster Methods

8: Numerical Aspects of Crystal Plasticity Finite Element Method Implementations

8.1 General Remarks

8.2 Explicit Versus Implicit Integration Methods

8.3 Element Types

Part Three Application

9: Microscopic and Mesoscopic Examples

9.1 Introduction to the Field of Crystal Plasticity Finite Element Experimental Validation

9.2 Stability and Grain Fragmentation in Aluminum under Plane Strain Deformation

9.3 Texture and Dislocation Density Evolution in a Bent Single-Crystalline Copper Nanowire

9.4 Texture and Microstructure Underneath a Nanoindent in a Copper Single Crystal

9.5 Application of a Nonlocal Dislocation Model Including Geometrically Necessary Dislocations to Simple Shear Tests of Aluminum Single Crystals

9.6 Application of a Grain Boundary Constitutive Model to Simple Shear Tests of Aluminum Bicrystals with Different Misorientation

9.7 Evolution of Dislocation Density in a Crystal Plasticity Model

9.8 Three-Dimensional Aspects of Oligocrystal Plasticity

9.9 Simulation of Recrystallization Using Micromechanical Results of CPFE Simulations

9.10 Simulations of Multiphase Transformation-Induced-Plasticity Steels

9.11 Damage Nucleation Example

9.12 The Grain Size Dependence in Polycrystal Models

10: Macroscopic Examples

10.1 Using Elastic Constants from ab initio Simulations for Predicting Textures and Texture-Dependent Elastic Properties of β-Titanium

10.2 Simulation of Earing during Cup Drawing of Steel and Aluminum

10.3 Simulation of Lankford Values

10.4 Virtual Material Testing for Sheet Stamping Simulations

11: Outlook and Conclusions

References

Index

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ISBN 978-3-527-32447-7

Notation

As a general scheme of notation, vectors are written as boldface lowercase letters (e. g., a b), second-order tensors as boldface capital letters (e. g., A, B), and fourthorder tensors as blackboard-bold capital letters (e. g., , ). For vectors and tensors, Cartesian components are denoted as, ai, Aij, and Aijkl respectively. The action of a second-order tensor upon a vector is denoted as Ab (in components Aijbj, with implicit summation over repeated indices) and the action of a fourth-order tensor upon a second-order tensor is designated as B (Aijkl Bkl). The composition of two second-order tensors is denoted as AB (Aij Bjl). The tensor (or dyadic) product between two vectors is denoted as a⊗b (ai bj). All inner products are indicated by a single dot between the tensorial quantities of the same order, for example, a·b (aibi) for vectors and A·B(Aij Bij) for second-order tensors. The cross-product of a vector a with a second-order tensor A, denoted by a × A, is a second-order tensor defined in components as , where is the Levi-Civita permutation matrix. The transpose, AT, of a tensor A is denoted by a superscript “T,” and the inverse, A-1, by a superscript “-1.” Additional notation will be introduced where required.

Preface

In the last 20 years, the Crystal Plasticity Finite Element Method (CPFEM) has developed into an extremely versatile tool for describing the mechanical response of crystalline materials on all length scales from single crystals to engineering parts. While this is clearly reflected by an ever increasing number of publications in scientific journals, to date there is no comprehensive monograph on the topic. To change this situation the authors have brought together their experience with CPFEM into the current book. The aim of the book is to give an overview of the wide field of models and applications in CPFEM at both small and large scales, and to give some practical advice to beginners.

The book is organized as follows: The introduction gives a comprehensive overview over the development of the application of CPFEM in the last 20 years. The first part gives an introduction into the fundamentals on which the Crystal Plasticity Finite Element Method is built. As it works in the interface of material physics, continuum mechanics and applied computer science the reader finds one chapter on each of these aspects. In the second part the Crystal Plasticity Finite Element Method is introduced in detail. First, different single crystal constitutive models are presented, including deformation mechanisms such as dislocation slip, twinning, athermal transformations, and damage. Second, in view of large scale applications, different homogenization schemes for the transition from single to polycrystals are introduced. Finally, some numerical aspects of importance for the practical implementation of CP as a material model in FEM codes are discussed. The last and by far most elaborate part of the book is concerned with application examples. Naturally, most of these examples originate from the work of the authors, plus some important examples taken from the work of other groups. The aim of this part of the book is to give an overview on the numerous potential applications of CPFEM in materials simulation and closes with an outlook of the authors on future applications of the Crystal Plasticity Finite Element Method.

Düsseldorf, April 2010

Franz Roters Philip Eisenlohr Thomas R. Bieler Dierk Raabe

Part One Fundamentals

2

Metallurgical Fundamentals of Plastic Deformation