Grain Boundaries and Crystalline Plasticity E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 423

Veröffentlichungsjahr: 2013

Beschreibung

The main purpose of this book is to put forward the fundamental role of grain boundaries in the plasticity of crystalline materials. To understand this role requires a multi-scale approach to plasticity: starting from the atomic description of a grain boundary and its defects, moving on to the elemental interaction processes between dislocations and grain boundaries, and finally showing how the microscopic phenomena influence the macroscopic behaviors and constitutive laws. It involves bringing together physical, chemical and mechanical studies. The investigated properties are: deformation at low and high temperature, creep, fatigue and rupture.

Leseprobe

Table of Contents

Preface

Chapter 1: Grain Boundary Structures and Defects

1.1. Equilibrium structure of grain boundaries

1.2. Crystalline defects of grain boundaries

1.3. Conclusion

1.4. Bibliography

Chapter 2: Elementary Grain Boundary Deformation Mechanisms

2.1. Dislocation in close proximity to a grain boundary

2.2. Elastic interaction between dislocations and grain boundaries: image force

2.3. Short range (or core) interaction between dislocations and grain boundaries

2.4. Relaxation of stress fields associated with extrinsic dislocations

2.5. Relationships between elementary interface mechanisms and mechanical behaviors of materials

2.6. Bibliography

Chapter 3: Grain Boundaries in Cold Deformation

3.1. Introduction

3.2. Plastic compatibility and incompatibility of deformation at grain boundaries

3.3. Internal stresses in polycrystal grains

3.4. Modeling local mechanical fields using the finite element method (FEM)

3.5. Hall-Petch’s law, geometrically necessary dislocations

3.6. Sub-grain boundaries and grain boundaries in deformation and recrystallization

3.7. Conclusion

3.8. Bibliography

Chapter 4: Creep and High Temperature Plasticity: Grain Boundary Dynamics

4.1. Introduction

4.2. Grain boundaries and grain growth

4.3. Grain boundaries and creep: mechanisms and phenomenological laws

4.4. Grain boundaries and superplasticity

4.5. Prospects: creep of nanograined materials

4.6. Bibliography

Chapter 5: Intergranular Fatigue

5.1. Introduction

5.2. Low temperature intergranular fatigue

5.3. High temperature fatigue

5.4. Conclusion

5.5. Acknowledgements

5.6. Bibliography

Chapter 6: Intergranular Segregation and Crystalline Material Fracture

6.1. Grain boundaries and fracture

6.2. Intergranular segregation

6.3. Segregation and intergranular fracture

6.4. Intergranular fracture induced by liquid metals

6.5. General conclusion

6.6. Bibliography

APPENDICES

Appendix 1: Bicrystallography and Topological Characterization of Interfacial Defects

Appendix 2: Appendices of Chapter 3

A2.1. Notations

A2.2. Infinitesimal deformations

A2.3. Finished transformations

A2.4. Incompatibility in finished transformations

A2.5. Calculation of the geometrically necessary dislocation densities

List of Authors

Index

First published 2011 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

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© ISTE Ltd 2011

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Library of Congress Cataloging-in-Publication Data

Grain boundaries and crystalline plasticity / edited by Louisette Priester.

p. cm.

Includes bibliographical references and index.

ISBN 978-1-84821-327-2

1. Grain boundaries--Mathematical models. 2. Crystalline interfaces. 3. Dislocations in crystals. I. Priester, Louisette.

QC173.458.C78G77 2011

660'.284298-dc23

2011034862

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN: 978-1-84821-327-2

Preface

This book highlights the significant role played by the grain boundaries in the plastic behavior of crystalline materials. The need to understand this role increases with the development and the use of materials (metals, ceramics, etc.) with submicron sized grains. From well-established models to new experimental and simulation approaches, this book gives the state of the art on the relationship between the “grain boundary” object and its contribution to the mechanical properties of a material. The authors, amongst the best experts in the various fields addressed, give readers a comprehensive overview of their specialties, from the theoretical basics to the recent developments due to the appearance of new techniques.

Starting from the behavior of a grain boundary then going back to the contribution of a grain boundary network to the plasticity of a polycrystalline set, requires a multi-scale approach. This approach begins with the description of the grain boundary on an atomic scale and then details the elementary reactions – on a nano- and microscopic scale – between point defects, dislocations and grain boundaries, and finally takes an interest in the material behaviors – on mesoscopic and macroscopic scales – and in the laws ruling these behaviors. The project also requires coupling of physical, chemical and mechanical approaches.

These various approaches are discussed without excessive mathematical formality and are supported by many references. The presentation of the definitions, mechanisms and theoretical models is followed by the description of experiments and numerical simulations, which support the models. The examples cover various types of crystalline materials: metals and metal alloys, ceramics, semiconductors, etc. The properties involved are: hot and cold deformation, creep, fatigue and fracture.

Each chapter holds stand-alone interest and is a good reference to acquire basic knowledge in a specific field, at the discretion of the reader. However, only reading the book as a whole provides the reader with an understanding of the role of the grain boundary in crystalline plasticity. The book is divided into six chapters:

– Chapter 1 discusses the basic notions of grain boundaries: their geometry, their structures and their defects. This chapter focuses on intergranular dislocations, which are deformation vectors;

– Chapter 2 details the elementary processes involved between dislocations and grain boundaries during deformation and the relaxation of the resulting stresses;

– Chapter 3 describes deformation and the stress states in the boundaries and in their vicinity during deformation; it discusses the material behavior as a function of the grain size and it quickly tackles recrystallization phenomena;

– Chapters 4 to 6 successively discuss:

1) the role of the grain boundaries in creep and in high temperature plasticity with an extension to the superplasticity phenomenon,

2) the behavior of the boundaries subjected to high and low temperature fatigue efforts on bi- and polycrystals, with a few key-elements: iron, stainless steel, copper, superalloys, etc.,

3) the response of grain boundaries to the fracture with particular focus on the effect of segregation on intergranular brittleness, but also focusing on embrittlement caused by liquid metals.

Providing an understanding of the influence of grain boundaries on crystalline plasticity has not yet been the subject of a dedicated book, although the subject constitutes a challenge for controlling material performances.

Louisette PRIESTER

University of Paris Sud 11

September 2011

Chapter 1

Grain Boundary Structures and Defects1

1.1. Equilibrium structure of grain boundaries

A grain boundary is an interface between two crystals of the same structure. The mechanical properties of industrial materials are driven, not only by the properties of their component crystals, but also by those of the boundaries between those crystals, in particular the structure and chemical composition of the boundaries. The structural materials are generally polycrystalline and their mechanical properties are directly linked not only to the grain size but also to the grain boundaries. Moreover, since materials used in the electronics industry are to be as free from defects as possible, then it is no less true that complex manufacturing processes introduce stresses which are most often released by defects, among them dislocations, twins and also grain boundaries.

These grain boundary “objects” are therefore encountered in numerous materials; their structures and their mechanical, chemical and electrical properties have for decades been the subject of in-depth studies and they are becoming of fundamental importance in the new so-called nanomaterials. Before describing the defects found in grain boundaries during mechanical or chemical processes, we will, in this section, present three approaches which have been used in order to describe equilibrium boundaries; the purely geometric approach, the dislocation approach, historically the first, and finally the structural unit approach originally based on energy calculations. Here, two reference works are recommended: [PRI 06] and [SUT 95].

1.1.1. Geometric description and elements of bicrystaiography

1.1.1.1. Degrees of freedom

A grain boundary is defined geometrically using nine parameters, or degrees of freedom: six parameters define the interface operation, which links two adjacent crystals, and three define the interface plane. Of these nine parameters, five are said to be macroscopic and four are said to be microscopic. In cubic systems, where the operation of grain orientation is always rotational, the three macroscopic parameters defining this operation are the angle of rotation θ and the directional cosines of the rotation axis [u v w]; the final two macroscopic parameters are those which define the orientation of the interface plane given by its normal. The four microscopic parameters are, on the one hand, three parameters which define the translation between grains (translation within the boundary plane and expansion perpendicular to the boundary) and, on the other, the parameter which enables the interface to be positioned along the normal to the boundary plane. These microscopic parameters are, in fact, “energy” parameters, generally defined from the calculated atomic structure which is the most energetically stable and/or experimentally observed using electron microscopy. In non-cubic materials, the interface operation is not a simple rotation, but is often accompanied by a deformation.

1.1.1.2. Tilt, twist, mixed, symmetrical and asymmetrical grain boundaries

In the interests of simplification, this terminology is used to define grain boundaries according to the relative orientations of the rotation axis [u v w] with respect to the boundary plane {h k l}.

A grain boundary is said to be a tilt boundary if the axis [u v w] is contained within the boundary plane, a twist boundary if the axis [u v w] is perpendicular to the plane and mixed if the axis is inclined. Boundaries are said to be symmetrical if the plane between two grains, for instance 1 and 2, can be defined by the expression {h k l}= {h k l}, otherwise they are said to be asymmetrical.