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Microstructure of Martensite: Why it forms and how it gives rise to the shape-memory effect [Kõva köide]

(, Professor of Mechanics and Materials Science, California Institute of Technology)
  • Formaat: Hardback, 300 pages, kõrgus x laius x paksus: 247x174x20 mm, kaal: 732 g, numerous figures, tables and halftones; 2pp colour plates
  • Sari: Oxford Series on Materials Modelling 2
  • Ilmumisaeg: 06-Nov-2003
  • Kirjastus: Oxford University Press
  • ISBN-10: 0198509340
  • ISBN-13: 9780198509349
  • Formaat: Hardback, 300 pages, kõrgus x laius x paksus: 247x174x20 mm, kaal: 732 g, numerous figures, tables and halftones; 2pp colour plates
  • Sari: Oxford Series on Materials Modelling 2
  • Ilmumisaeg: 06-Nov-2003
  • Kirjastus: Oxford University Press
  • ISBN-10: 0198509340
  • ISBN-13: 9780198509349
Bhattacharya (mechanics and materials science, California Institute of Technology) shares what he has learned and found interesting about materials, mostly metal alloys, that after being deformed, revert to their original shape under certain conditions. (He includes a wire with the book that exhibits the behavior under the conditions he describes.) Here he explores why certain materials form the intricate patterns in their microstructure that characterize martensites, what kinds of materials form such a microstructure, and what if any is the link between the microstructure and the shape-memory effect. He assumes only a college-level knowledge of mathematics. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)

Martensites are crystalline solids that display dazzling patterns at the microscopic scales. This microstructure gives rise to unusual macroscopic properties like the shape-memory effect. Starting with the crystalline structure, this book describes a theoretical framework for studying martensites and uses the theory to explain why these materials form microstructure. The macrostructure consequences of the microstructure are subsequently discussed. Complete with a piece of shape-memory wire and numerous examples from real materials, this book represents a successful case study in multiscale modeling, giving a clear understanding of the link between microstructure and macrostructure properties. Beautifully written, in a most clear and pedagogical manner, it holds appeal for a broad audience. On the one hand, it introduces modern modeling techniques to those trained in materials science, mechanics and physics and shows how these techniques can be used in real-world problems. On the other hand, it introduces physical phenomena to those trained in mathematics, and demonstrates how such phenomena give rise to interesting mathematical problems.

Arvustused

There is certainly great need for this book. There is nothing quite like it. * Robert V. Kohn, Courant Institute of Mathematical Sciences * Bhattacharya has described the modern theory in the clearest and most pedagogical way that I have seen. It will be a very valuable addition to the literature on martensite. * Adrian P. Sutton FRS, University of Oxford * Bhattacharya explains in simple terms various ideas that only otherwise are available in the mathematical literature and completely unaccessible to a materials scientist... There is no comparable text out there. * Richard D. James, University of Minnesota * A remarkable effort of the author is that of presenting an issue that usually requires nontrivial mathematical techniques in a format accessible not only to experts. * Mathematical Reviews, 2007 * Bhattacharya is one of the top researchers in this field and perhaps the finest expositor of this material that I know. * Rohan Abeyaratne, Massachusetts Institute of Technology *

1 Introduction 1(16)
1.1 Invitation
1(3)
1.2 Introduction
4(4)
1.3 Overview
8(3)
1.4 Omissions
11(4)
1.5 Related Reviews and Books
15(2)
2 Review of Continuum Mechanics 17(12)
2.1 Vectors and Matrices
17(3)
2.2 Deformation
20(2)
2.3 Deformation Gradient
22(4)
2.4 Rotation and Stretch
26(1)
2.5 Kinematic Compatibility
27(2)
3 Continuum Theory of Crystalline solids 29(17)
3.1 Bravais Lattice
29(3)
3.2 Deformation of Lattices and Symmetry
32(2)
3.3 Lattice-Continuum Link: The Cauchy-Born Hypothesis
34(2)
3.4 Energy Density in Crystalline Solids
36(2)
3.5 Symmetry of Deformable Lattices: Ericksen-Pitteri Neighborhood
38(5)
3.6 Multi-lattice
43(3)
4 Martensitic Phase Transformation 46(20)
4.1 Martensitic Phase Transformation; Bain or Transformation Matrix
46(12)
4.2 Energy Density
58(2)
4.3 Material Symmetry: Variants of Martensite
60(2)
4.4 Frame-indifference: Energy Wells
62(2)
4.5 Summary of the Energy Density
64(1)
4.6 Multiple Transformations
65(1)
5 Twinning in Martensite 66(20)
5.1 Deformation Involving One Variant
66(1)
5.2 Deformation Involving Two Variants
67(1)
5.3 Interpretation as a Twin
68(1)
5.4 Solution of the Twinning Equation and Classification of Twins
69(5)
5.5 Cubic to Tetragonal Transformation
74(1)
5.6 Cubic to Orthorhombic Transformation
75(3)
5.7 Cubic to Monoclinic-I Transformation
78(2)
5.8 Parallel Twins
80(1)
5.9 Zig-zag Twins
81(2)
5.10 Crossing Twins
83(3)
6 Origin of Microstructure 86(19)
6.1 Simplified Example in One Dimension
87(2)
6.2 Simplified Example in Two Dimensions
89(4)
6.3 Example in Three Dimensions: Fine Twins
93(3)
6.4 Weakly Converging Sequences and Fine Microstructure
96(2)
6.5 Relaxed Energy Density
98(4)
6.6 Length-scale of the Microstructure
102(3)
7 Special Microstructures 105(26)
7.1 Austenite-Martensite Interface
106(15)
7.1.1 Cubic to Tetragonal Transformation
114(3)
7.1.2 Cubic to Orthorhombic Transformation
117(1)
7.1.3 Cubic to Monoclinic-I Transformation
117(1)
7.1.4 Remarks
118(3)
7.2 Twins within Twins
121(3)
7.3 Wedge-like Microstructure
124(7)
7.3.1 Cubic to Tetragonal Transformation
127(1)
7.3.2 Cubic to Orthorhombic Transformation
128(3)
8 Analysis of Microstructure 131(12)
8.1 Average Compatibility Conditions or the Minors Relations
131(10)
8.2 Gradient Young Measure
141(2)
9 The Shape-Memory Effect 143(16)
9.1 Self-accommodation
144(7)
9.1.1 Cubic Austenite
146(2)
9.1.2 Tetragonal Austenite
148(2)
9.1.3 Self-accommodating Plate Group
150(1)
9.2 Recoverable Strains under Load Control
151(3)
9.2.1 Uniaxial Loading
151(2)
9.2.2 Biaxial Loading
153(1)
9.3 Recoverable Strains under Displacement Control
154(5)
10 Thin Films 159(19)
10.1 A Theory of Thin Films
161(4)
10.2 Deformations with One Variant or Phase
165(1)
10.3 Deformations with Two Variants or Two Phases: Interface Conditions
166(3)
10.4 Martensite-Martensite Interface
169(1)
10.5 Austenite-Martensite Interface
170(1)
10.6 Tents and Tunnels
171(7)
11 Geometrically Linear Theory 178(26)
11.1 Linearized Kinematics
178(3)
11.2 Geometrically Linear Theory for Martensitic Phase Transformations
181(4)
11.3 Some Microstructures and Comparisons
185(9)
11.3.1 Twinning
185(4)
11.3.2 Austenite-Martensite Interface
189(3)
11.3.3 Wedge-like Microstructure
192(1)
11.3.4 Zig-zag Twins
192(2)
11.4 Recoverable Strains under Displacement Control
194(6)
11.5 Self-accommodation
200(1)
11.6 Recoverable Strains under Load Control
201(1)
11.7 Accuracy of the Geometrically Linear Theory
202(2)
12 Piecewise Linear Elasticity 204(20)
12.1 Piecewise Quadratic Energy
204(5)
12.2 Stress Due to Incompatible Phase Arrangement
209(4)
12.3 Relaxed Energy Density
213(6)
12.4 A Modified Variational Principle
219(3)
12.5 Connection to Homogenization Theory and Optimal Design
222(2)
13 Polycrystals 224(43)
13.1 Examples
227(11)
13.1.1 Bi-crystal
227(7)
13.1.2 Triple Junction
234(4)
13.2 Polycrystals
238(2)
13.3 Recoverable Strains under Displacement Control
240(3)
13.4 Recoverable Strains under Load Control
243(4)
13.5 The Consequence of Symmetry
247(2)
13.6 The Consequences of Texture
249(12)
13.7 Energy Minimization and Recoverable Strain
261(6)
Appendix 267(5)
Bibliography 272(15)
Index 287


Kaushik Bhattacharya is Professor of Mechanics and Materials Science at the California Institute of Technology. He received a NSF Young Investigator Award in 1994, the Charles Lee Powell Award in 1997 and in 2002, was invited to take part in the Frontiers of Engineering Symposium organised by the National Academy of Engineering. He is a member of various editorial boards.