The aim of this book is to understand and describe the martensitic phase transformation and the process of martensite platelet reorientation. These two key elements enable the author to introduce the main features associated with the behavior of shape-memory alloys (SMAs), i.e. the one-way shape-memory effect, pseudo-elasticity, training and recovery. Attention is paid in particular to the thermodynamical frame for solid materials modeling at the macroscopic scale and its applications, as well as to the particular use of such alloys the simplified calculations for the bending of bars and their torsion. Other chapters are devoted to key topics such as the use of the crystallographical theory of martensite for SMA modeling, phenomenological and statistical investigations of SMAs, magneto-thermo-mechanical behavior of magnetic SMAs and the fracture mechanics of SMAs. Case studies are provided on the dimensioning of SMA elements offering the reader an additional useful framework on the subject. Contents 1. Some General Points about SMAs. 2. The World of Shape-memory Alloys. 3. Martensitic Transformation. 4. Thermodynamic Framework for the Modeling of Solid Materials. 5.
Use of the CTM to Model SMAs. 6. Phenomenological and Statistical Approaches for SMAs. 7. Macroscopic Models with Internal Variables. 8. Design of SMA Elements: Case Studies. 9. Behavior of Magnetic SMAs. 10. Fracture Mechanics of SMAs. 11. General Conclusion. Appendix 1. Intrinsic Properties of Rotation Matrices. Appendix 2. Twinning Equation Demonstration. Appendix 3. Calculation of the Parameters a, n and Q from the Twinning Equation. Appendix 4. Twinned Austenite/Martensite Equation. About the Authors Christian Lexcellent is Emeritus Professor at the Ecole National Superieure de Mecanique et des Microtechniques de Besancon and a researcher in the Department of Applied Mechanics at FEMTO-ST in France. He is a specialist in the mechanics of materials and phase transition and has taught in the subjects of mechanics of continuum media and shape memory alloys. He is also a member of the International Committee of ESOMAT.
Professor Christian Lexcellent U.F.R. Sciences and Technics, Laboratory of Applied Mechanics, University of Franche-Comt , Besan on, France.
Foreword xiii Preface xv Chapter 1. Some General Points about SMAs 1 1.1. Introduction 1 1.2. Why are SMAs of interest for industry? 2 1.3. Crystallographic theory of martensitic transformation 5 1.4. Content of this book 8 Chapter 2. The World of Shape-memory Alloys 11 2.1. Introduction and general points 11 2.2. Basic metallurgy of SMAs, by Michel Morin 12 2.3. Measurements of phase transformation temperatures 27 2.4. Self-accommodating martensite and stress-induced martensite 28 2.5. Fatigue resistance 29 2.6. Functional properties of SMAs 35 2.7. Use of NiTi for secondary batteries 42 2.8. Use of SMAs in the domain of civil engineering 42 Chapter 3. Martensitic Transformation 49 3.1. Overview of continuum mechanics 49 3.2. Main notations for matrices 50 3.3. Additional notations and reminders 51 3.4. Kinematic description 57 3.5. Kinematic compatibility 61 3.6. Continuous theory of crystalline solids 62 3.7. Martensitic transformation 67 3.8. Equation governing the interface between two martensite variants Mi/Mj or the twinning equation 70 3.9. Origin of the microstructure 73 3.10. Special microstructures 76 3.11. From the scale of the crystalline lattice to the mesoscopic and then the macroscopic scale 84 3.12. Linear geometric theory 88 3.13. Chapter conclusion 95 Chapter 4. Thermodynamic Framework for the Modeling of Solid Materials 97 4.1. Introduction 97 4.2. Conservation laws 98 4.3. Constitutive laws 103 Chapter 5. Use of the CTM to Model SMAs 109 5.1. Introduction 109 5.2. Process of reorientation of the martensite variants in a monocrystal 109 5.3. Process of creation of martensite variants in a monocrystal: pseudoelastic behavior 118 5.4. Prediction of the surfaces for the austenite martensite phase transformation 122 Chapter 6. Phenomenological and Statistical Approaches for SMAs 129 6.1. Introduction 129 6.2. Preisach models 130 6.3. First-order phase transitions and Falk s model 132 6.4. Constitutive framework of the homogenized energy model 142 6.5. Conclusion 154 Chapter 7. Macroscopic Models with Internal Variables 157 7.1. Introduction 157 7.2. RL model 159 7.3. Anisothermal expansion 173 7.4. Internal variable model inspired by micromechanics 181 7.4.1. Introduction 181 7.5. Elastohysteresis model: formalism and digital implantation 223 7.6. Conclusion 233 Chapter 8. Design of SMA Elements: Case Studies 235 8.1. Introduction 235 8.2. Strength of materials -type calculations for beams subject to flexion or torsion 235 8.3. Elements of calculations for SMA actuators 245 8.4. Case studies 251 Chapter 9. Behavior of Magnetic SMAs 261 9.1. Introduction 261 9.2. Some models of the thermo-magneto-mechanical behavior of MSMAs 262 9.3. Crystallography of Ni-Mn-Ga 265 9.4. Model of the magneto-thermo-mechanical behavior of a monocrystal of magnetic shape-memory alloy 270 9.5. Conclusion 293 Chapter 10. Fracture Mechanics of SMAs 295 10.1. Introduction 295 10.2. The elastic stress field around a crack tip 296 10.3. Prediction of the phase transformation surfaces around the crack tip (no curvature at the crack tip) 311 10.4. Prediction of the phase transformation surfaces around the crack tip (curvature at the crack tip) 322 10.5. Some experimental results about fracture of SMAs 325 10.6. Problem of delamination between a SMA and an elastic solid 329 Chapter 11. General Conclusion 337 11.1. Resolved problems 337 11.2. Unresolved problems 338 11.3. Suggestions for future directions 339 Appendix 1. Intrinsic Properties of Rotation Matrices (see Chapter 3) 341 A1.1. Characterization of rotations 342 Appendix 2. Twinning Equation Demonstration (see Chapter 3) 345 A2.1. Question 345 A2.2. Solution 345 Appendix 3. Calculation of the Parameters a, n and Q from the Twinning Equation (see Chapter 3) 349 A3.1. Problem 349 A3.2. Statement 349 A3.3. Solution 350 Appendix 4. Twinned Austenite/Martensite Equation (see Chapter 3) 355 A4.1. Proposition 1 355 A4.2. Proposition 2 355 A4.3. Theorem 356 Bibliography 359 Index 377