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Microstructure of martensite : why it forms and how it gives rise to the shape-memory effect / Kaushik Bhattacharya.

LIBRA TN731 .B53 2003 1 v. + wire
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Language:
English
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Physical Description:
xi, 288 pages : illustrations (some color) ; 25 cm.
Place of Publication:
Oxford ; New York : Oxford University Press, 2003.
Contents:
  • 2 Review of Continuum Mechanics 17
  • 2.1 Vectors and Matrices 17
  • 2.2 Deformation 20
  • 2.3 Deformation Gradient 22
  • 2.4 Rotation and Stretch 26
  • 2.5 Kinematic Compatibility 27
  • 3 Continuum Theory of Crystalline Solids 29
  • 3.1 Bravais Lattice 29
  • 3.2 Deformation of Lattices and Symmetry 32
  • 3.3 Lattice-Continuum Link: The Cauchy-Born Hypothesis 34
  • 3.4 Energy Density in Crystalline Solids 36
  • 3.5 Symmetry of Deformable Lattices: Ericksen-Pitteri Neighborhood 38
  • 3.6 Multi-lattice 43
  • 4 Martensitic Phase Transformation 46
  • 4.1 Martensitic Phase Transformation; Bain or Transformation Matrix 46
  • 4.2 Energy Density 58
  • 4.3 Material Symmetry: Variants of Martensite 60
  • 4.4 Frame-indifference: Energy Wells 62
  • 4.5 Summary of the Energy Density 64
  • 4.6 Multiple Transformations 65
  • 5 Twinning in Martensite 66
  • 5.1 Deformation Involving One Variant 66
  • 5.2 Deformation Involving Two Variants 67
  • 5.3 Interpretation as a Twin 68
  • 5.4 Solution of the Twinning Equation and Classification of Twins 69
  • 5.5 Cubic to Tetragonal Transformation 74
  • 5.6 Cubic to Orthorhombic Transformation 75
  • 5.7 Cubic to Monoclinic-I Transformation 78
  • 5.8 Parallel Twins 80
  • 5.9 Zig-zag Twins 81
  • 5.10 Crossing Twins 83
  • 6 Origin of Microstructure 86
  • 6.1 Simplified Example in One Dimension 87
  • 6.2 Simplified Example in Two Dimensions 89
  • 6.3 Example in Three Dimensions: Fine Twins 93
  • 6.4 Weakly Converging Sequences and Fine Microstructure 96
  • 6.5 Relaxed Energy Density 98
  • 6.6 Length-scale of the Microstructure 102
  • 7 Special Microstructures 105
  • 7.1 Austenite-Martensite Interface 106
  • 7.1.1 Cubic to Tetragonal Transformation 114
  • 7.1.2 Cubic to Orthorhombic Transformation 117
  • 7.1.3 Cubic to Monoclinic-I Transformation 117
  • 7.1.4 Remarks 118
  • 7.2 Twins within Twins 121
  • 7.3 Wedge-like Microstructure 124
  • 7.3.1 Cubic to Tetragonal Transformation 127
  • 7.3.2 Cubic to Orthorhombic Transformation 128
  • 8 Analysis of Microstructure 131
  • 8.1 Average Compatibility Conditions or the Minors Relations 131
  • 8.2 Gradient Young Measure 141
  • 9 The Shape-Memory Effect 143
  • 9.1 Self-accommodation 144
  • 9.1.1 Cubic Austenite 146
  • 9.1.2 Tetragonal Austenite 148
  • 9.1.3 Self-accommodating Plate Group 150
  • 9.2 Recoverable Strains under Load Control 151
  • 9.2.1 Uniaxial Loading 151
  • 9.2.2 Biaxial Loading 153
  • 9.3 Recoverable Strains under Displacement Control 154
  • 10 Thin Films 159
  • 10.1 A Theory of Thin Films 161
  • 10.2 Deformations with One Variant or Phase 165
  • 10.3 Deformations with Two Variants or Two Phases: Interface Conditions 166
  • 10.4 Martensite-Martensite Interface 169
  • 10.5 Austenite-Martensite Interface 170
  • 10.6 Tents and Tunnels 171
  • 11 Geometrically Linear Theory 178
  • 11.1 Linearized Kinematics 178
  • 11.2 Geometrically Linear Theory for Martensitic Phase Transformations 181
  • 11.3 Some Microstructures and Comparisons 185
  • 11.3.1 Twinning 185
  • 11.3.2 Austenite-Martensite Interface 189
  • 11.3.3 Wedge-like Microstructure 192
  • 11.3.4 Zig-zag Twins 192
  • 11.4 Recoverable Strains under Displacement Control 194
  • 11.5 Self-accommodation 200
  • 11.6 Recoverable Strains under Load Control 201
  • 11.7 Accuracy of the Geometrically Linear Theory 202
  • 12 Piecewise Linear Elasticity 204
  • 12.1 Piecewise Quadratic Energy 204
  • 12.2 Stress Due to Incompatible Phase Arrangement 209
  • 12.3 Relaxed Energy Density 213
  • 12.4 A Modified Variational Principle 219
  • 12.5 Connection to Homogenization Theory and Optimal Design 222
  • 13 Polycrystals 224
  • 13.1.1 Bi-crystal 227
  • 13.1.2 Triple Junction 234
  • 13.2 Polycrystals 238
  • 13.3 Recoverable Strains under Displacement Control 240
  • 13.4 Recoverable Strains under Load Control 243
  • 13.5 The Consequence of Symmetry 247
  • 13.6 The Consequences of Texture 249
  • 13.7 Energy Minimization and Recoverable Strain 261.
Notes:
  • Includes bibliographical references (pages [272]-285) and index.
  • One piece of shape-memory wire in pocket attached to inside back cover.
Local Notes:
Acquired for the Penn Libraries with assistance from the Alumni and Friends Memorial Book Fund.
ISBN:
0198509340
OCLC:
52696531
Online:
The Alumni and Friends Memorial Book Fund Home Page

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