Shape-memory Alloys Handbook

Shape-memory Alloys Handbook......Page 1
Shape-memory Alloys Handbook......Page 2
Table of Contents......Page 4
Foreword......Page 11
Preface......Page 13
1.1. Introduction......Page 15
1.2. Why are SMAs of interest for industry?......Page 16
1.3. Crystallographic theory of martensitic transformation......Page 19
1.4.2. Content of this book......Page 22
2.1. Introduction and general points......Page 24
2.2.1. Copper-based shape-memory alloys......Page 25
2.2.2. Cu-Zn-Al......Page 27
2.2.3. Cu-Al-Ni......Page 29
2.2.4. Cu-Al-Be......Page 31
2.2.5. The phenomena of aging, stabilization and fatigue......Page 32
2.2.7. Ti-Ni-based alloys......Page 34
2.2.8. Ti-Ni alloy......Page 35
2.2.9. Ti-Ni-X alloys......Page 36
2.2.10. Elaboration......Page 37
2.2.12. Final heat treatments......Page 38
2.2.14. Biocompatibility of SMAs......Page 39
2.3. Measurements of phase transformation temperatures......Page 40
2.4. Self-accommodating martensite and stress-induced martensite......Page 41
2.5.1. Causes of degradation of the properties......Page 42
2.5.3. Results......Page 43
2.6.1. The pseudo-elastic effect......Page 48
2.6.2. One-way shape-memory effect......Page 50
2.6.3. Recovery stress......Page 53
2.6.4. Double shape-memory effect: training......Page 54
2.8. Use of SMAs in the domain of civil engineering......Page 55
3.1.1. Main notations for vectors......Page 61
3.2. Main notations for matrices......Page 62
3.3.2. Rotation matrix......Page 63
3.3.4. Positive definite symmetric matrices......Page 66
3.3.5. Polar decomposition......Page 67
3.4.1. Strain gradient......Page 69
3.4.2. Dilatation and strain tensors......Page 70
3.4.3. Transformation of an element of volume or surface see Figure 3.2......Page 72
3.5. Kinematic compatibility......Page 73
3.6. Continuous theory of crystalline solids......Page 74
3.6.1. Bravais lattices......Page 75
3.6.2. Deformation of lattices and symmetry......Page 76
3.6.3. Link between lattices and the continuous medium: Cauchy?Born hypothesis......Page 77
3.6.4. Energy density in crystalline solids......Page 78
3.7.2. Martensitic transformation: Bain matrix or transformation matrix......Page 79
3.8. Equation governing the interface between two martensite variants M2 IM3 or the "twinning equation"......Page 82
3.8.1. Cubic - quadratic transformation......Page 84
3.9. Origin of the microstructure......Page 85
3.9.1. Simplified one-dimensional case......Page 86
3.9.2. Simplified two-dimensional case......Page 87
3.10.1 Austenite-martensite interface......Page 88
3.10.2. Phenomenological theory of martensite......Page 89
3.10.3. Crystallographic theory of martensite......Page 92
3.11. From the scale of the crystalline lattice to the mesoscopic and then the macroscopic scale......Page 96
3.11.1. Approach at the level of the crystalline lattice......Page 97
3.11.3. Mesoscopic approach......Page 98
3.12. Linear geometric theory......Page 100
3.12.1. Linearized kinematics......Page 101
3.12.2. Linear geometric theory for phase transformation......Page 103
3.12.3. Some microstructures and comparison......Page 104
3.13. Chapter conclusion......Page 107
4.1. Introduction......Page 108
4.2.1. Concept of a material system......Page 109
4.2.2. Concept of a particulate derivative......Page 110
Euler variables......Page 111
4.2.4. Motion balance equation......Page 112
4.2.5. Energy balance: first law of thermodynamics......Page 113
4.3. Constitutive laws......Page 114
4.3.1. Clausius-Duhem inequality......Page 115
5.2. Process of reorientation of the martensite variants in a monocrystal......Page 119
5.2.1. Internal variable model of the thermomechanical behavior of an SMA monocrystal......Page 121
5.2.2. Experimental procedure and results obtained......Page 123
5.2.3. Modeling of the experiments......Page 124
5.3.1. Modeling the pseudoelastic behavior of the monocrystal......Page 128
5.3.2. Traction curves......Page 130
5.4.1. Case of a monocrystal......Page 132
5.4.2. Case of a polycrystal......Page 134
6.1. Introduction......Page 138
6.2. Preisach models......Page 139
6.3.1. Falk’s model......Page 141
6.3.2. Extension of Falk’s model......Page 145
6.3.3. Description of hysteresis loops......Page 146
6.3.4. Phase domains with moving boundaries......Page 147
6.3.4.1. Development of the model......Page 148
6.3.4.3. Irreversible deformations......Page 149
6.3.5.2. Experimental validation......Page 150
6.4. Constitutive framework of the homogenized energy model......Page 151
6.4.1.1. Helmholtz and Gibbs free energies......Page 153
6.4.1.2. Local stress-strain relation with negligible thermal activation......Page 154
6.4.1.3. Local stress-strain relation with thermal activation......Page 156
6.4.2. Thermal change......Page 157
6.4.3. Macroscopic model......Page 158
6.4.4.1. Simulation of the model......Page 159
6.4.4.2. Characterization of the materials......Page 161
6.5. Conclusion......Page 163
7.1. Introduction......Page 165
7.2.1. Reversible R model......Page 167
7.2.2. RL model with a hysteresis loop [MUL 89]......Page 170
7.2.2.1. Heat equation......Page 173
7.2.3. Extension to reversible phase transformation: austenite=.R phase for NiTi [LEX 94]......Page 174
7.2.4. Multiaxial isothermal behavior......Page 176
7.3. Anisothermal expansion [LEC 96] [LEX 06a]......Page 181
7.3.1. Kinetics of phase transformation or reorientation......Page 184
7.3.1.1. Application of the RL model......Page 188
7.4.2. Chemisky et al.’s model [CHE 11]......Page 189
7.4.2.1. Mechanisms of deformation considered......Page 190
7.4.2.2. Internal variables and physical limitations......Page 191
7.4.2.3. Thermodynamic potential......Page 192
7.4.2.5. Asymmetry between traction and compression......Page 196
7.4.2.6. Application to thermomechanical stresses......Page 198
7.4.2.7. Criticism of Chemisky et al.’s model......Page 202
7.4.3. Kelly and Bhattacharya’s model [KEL 08, KEL 12]......Page 203
7.4.4.1. Kinematics and limitations......Page 206
7.4.4.2. Equations of the model......Page 209
7.4.5.1. Hard constraints......Page 212
7.4.5.2. Flexible, adjustable constraints......Page 213
7.4.6.1. One-dimensional case......Page 214
7.4.6.2. Two- or three-dimensional case......Page 217
7.4.6.3. Transformation criterion......Page 219
7.4.6.7. Parameters of the model......Page 220
7.4.7. Traction and compression for an isotropic material......Page 221
7.4.8. Pure shearing of an isotropic material......Page 222
7.4.9.1. Isotropic materials......Page 223
7.4.9.2. Anisotropic material......Page 224
7.4.9.3. Proportional loads applied in different directions......Page 225
7.4.9.4. Non-proportional loading......Page 227
7.4.10. Digital implantation......Page 228
7.5.2.1. Formalism in finite transformations......Page 231
7.5.2.3. Calculation of the reversible stress......Page 233
7.5.2.4. Hysteresis stress: discrete memory......Page 235
7.5.2.5. Temperature dependency......Page 236
7.5.3.1. Modeling of homogenous tests......Page 237
7.5.3.3. Simulation of non-homogeneous isothermal tests......Page 240
7.6. Conclusion......Page 241
8.2.1. Beam with a rectangular cross-section, subject to pure flexion: theoretical study......Page 243
8.2.2. Experimental and theoretical validation [REJ 02]......Page 249
8.2.3. Solving pure torsion problem: relation between the twisting torque C and the unitary angle of torsion a......Page 250
8.3.1. tress/position diagram: temperature parameterization......Page 253
8.3.4. Flexion of a beam......Page 256
8.3.5. Comparison of the different modes of loading......Page 257
8.3.6. A few remarks about the duration of heating and cooling of SMAs......Page 258
8.4.1.1. Statement......Page 259
8.4.2.1. Statement......Page 260
8.4.3.1. Statement......Page 262
8.4.3.2. Brief solution......Page 263
8.4.4.1. Statement......Page 264
8.4.5.1. Statement [PAT 01]......Page 265
8.4.5.2. Solution......Page 267
9.1. Introduction......Page 269
9.2.1. O’Handley and Murray et al.'s model......Page 270
9.2.4. Original approaches......Page 271
9.2.5. Overlaps between these approaches......Page 272
9.3.1. The different phases and variants......Page 273
9.3.2. Rearrangement and transformation......Page 274
9.3.3. Calculations of microstructures......Page 275
9.4. Model of the magneto-thermo-mechanical behavior of a monocrystal of magnetic shape-memory alloy......Page 278
9.4.2. Choice of the representative elementary volume......Page 279
9.4.3. Expression of chemical energy......Page 281
9.4.5. Expression of mechanical energy......Page 282
9.4.6.1. General aspects......Page 283
9.4.6.2. Magnetization of martensite: axis of easy magnetization......Page 284
9.4.6.5. Mixture law......Page 285
9.4.7. General expression of the free energy......Page 286
9.4.8.1. Thermodynamic forces......Page 287
9.4.9.1. Example with two variants Figures 9.11 and 9.12......Page 289
9.4.9.3. Generalization to the three variants and the austenitic phase......Page 291
9.4.10. Heat balance equation......Page 292
9.4.11.1. Differential scanning calorimetry......Page 293
9.4.11.5. Reliability of the model......Page 294
9.4.12. Application: creation of a “push/pull? actuator......Page 300
9.5. Conclusion......Page 301
10.1. Introduction......Page 303
10.2.1. Basic modes of fracture and stress intensity factors......Page 304
10.2.2.1. Basic equations for plane elasticity......Page 305
10.2.2.3. Representation of the Airy function as a complex potential......Page 307
10.2.2.4. Stresses and displacements......Page 308
10.2.3.1. Symmetrical problems mode I......Page 309
10.2.3.2. Antisymmetric problems mode II......Page 310
10.2.4.1. Mode I fracture......Page 312
10.2.4.2. The solution near to the crack tip......Page 314
10.2.4.3. Mode II fracture......Page 315
10.2.4.4. Mode III fracture......Page 317
10.2.4.5. Case study: specimen of finite dimensions: effects of size......Page 318
10.3. Prediction of the phase transformation surfaces around the crack tip no curvature at the crack tip [LEX 11]......Page 319
10.3.2. Mode II......Page 322
10.3.3. Mode III......Page 325
10.3.4. Mixed Mode I + II: analytical prediction of the transformation surfaces......Page 326
10.4. Prediction of the phase transformation surfaces around the crack tip curvature p at the crack tip......Page 330
10.4.1. Applications......Page 332
10.5. Some experimental results about fracture of SMAs......Page 333
10.6. Problem of delamination between a SMA and an elastic solid [LAY 12]......Page 337
11.1. Resolved problems......Page 344
11.2. Unresolved problems......Page 345
11.3. Suggestions for future directions......Page 346
Appendix 1: Intrinsic Properties of Rotation Matrices see Chapter 3......Page 347
A1.1. Characterization of rotations......Page 348
A2.2. Solution......Page 350
A3.2. Statement......Page 354
A3.3. Solution......Page 355
A3.3.3. Case 3......Page 358
A3.3.4. Case 4......Page 359
A4.2. Proposition 2......Page 360
A4.3. Theorem......Page 361
Bibliography......Page 363
Index......Page 380