Shape Memory Alloys (eBook)

Preface 6
Contents 8
List of Symbols 15
Introduction to Shape Memory Alloys (by P. K. Kumar and D. C. Lagoudas) 19
Introduction: Overview of Active Materials 19
Shape Memory Alloys - A Brief History 22
Phenomenology of Phase Transformation in Shape Memory Alloys 23
Shape Memory Effect 29
Pseudoelasticity 31
Cyclic Behavior of SMAs 33
Transformation Induced Fatigue in SMAs 35
Crystallography of Martensitic Transformation 37
Effect of Alloying on the Transformation Behavior of SMAs 41
NiTi-Based Alloys 41
Copper-Based Alloys 44
Iron-Based Alloys 46
Additional SMAs 46
SMAs as Active Materials - Applications 47
Aerospace Applications 48
Medical Applications 53
Transportation Applications 57
Other Applications 57
Summary 58
Problems 59
References 61
Thermomechanical Characterization of Shape Memory Alloy Materials (by D. J. Hartl and D. C. Lagoudas) 70
Introduction 70
Review of SMA Characterization Methods 71
Shape Memory Alloy Specimens 72
Thermomechanical Material Properties of SMAs for Engineering Applications 77
Thermoelastic Properties 81
Critical Stress and Temperature States for Transformation (Phase Diagram) 82
Transformation Strain Properties and Hardening 84
Experimental Characterization Process 85
Overview of the General Thermomechanical Characterization Process 86
Illustration of the General Characterization Process 86
Experimental Considerations Unique to SMA Thermomechanical Characterization 99
Influence of Total Material History on Shape Memory Behavior 99
Comparison of Test Specimen to Intended Application Component 101
Importance of Mechanical and ThermalLoading Rates 102
Stochastic Variation in Material Response 105
Examples of SMA Characterization 105
Example 1. Characterization of NiTi Wire Intended for Pseudoelastic Application 106
Example 2. Characterization of NiTi Wire for Determination of Stochastic Variation 110
Example 3. Characterization of Ni60Ti40 (wt%) Plate Intended for Actuation Application 112
Simple SMA Application Design and Empirical 1-D Analysis 119
Application Design Considerations 120
Experimentally-Based 1-D Material Model 122
Summary 126
Problems 126
References 134
Thermomechanical Constitutive Modeling of SMAs (by L. G. Machado and D. C. Lagoudas) 137
Introduction 137
Brief Review of Continuum Mechanics 138
Kinematics of SMAs 138
Conservation (Balance) Laws 139
Constitutive Equations in the Presence of Internal State Variables 142
Constitutive Modeling of SMAs 147
Choice of Internal State Variables 148
Kinematic Assumptions 148
Thermomechanical Constitutive Assumptionsfor SMAs 149
Thermomechanical Coupling in SMAs 158
Unification of Different SMA Constitutive Models 161
Analytical Solutions and 1-D Examples 166
1-D Reduction of the SMA Constitutive Model 166
Example Solutions for Various Thermomechanical Loading Paths 168
Application of the Smooth Hardening Model to a Nonlinear Oscillator 183
Brief Overview of Other Thermomechanical Constitutive Models for SMAs 187
Summary 196
Problems 196
References 198
Numerical Implementation of an SMA Thermomechanical Constitutive Model Using Return Mapping Algorithms (by M. A. Siddiq Qidwai, D. J. Hartland D. C. Lagoudas) 204
Introduction 204
Continuum Tangent Moduli Tensors 206
Return Mapping Algorithms 208
A General View of Thermoelastic Prediction-Transformation Correction Return Mapping 208
Closest Point Projection Return Mapping Algorithm 211
Convex Cutting Plane Return Mapping Algorithm 218
Summary and Comparison of Algorithms 220
Numerical Examples 221
SMA Uniaxial Thermomechanical Loading Cases 223
SMA Actuated Beam 224
SMA Torque Tube 227
SMA Actuated Variable Geometry Jet Engine Chevron 230
SMA Medical Stent 234
Summary 236
Problems 236
References 244
Modeling of Transformation-Induced Plasticity in SMAs (by P. B. Entchev and D. C. Lagoudas) 247
Introduction 247
Experimental Motivation: Polycrystalline SMAs Undergoing Cyclic Loading 248
Three Dimensional Constitutive Model for SMAs Experiencing TRIP 252
Modifications Needed to Account for TRIP 253
Complete Constitutive Model for TRIP 257
Evolution of the Hysteretic Response of an SMA Undergoing Cyclic Loading 259
Modeling of Minor Hysteresis Loops 261
Estimation of Material Parameters 262
1-D Reduction of the Model 262
Material Parameters for a StableTransformation Cycle 264
Material Parameters for Cyclic Loading 270
Material Parameters for Minor Loop Modeling 271
Sample Loading Cases 271
Uniaxial Isothermal Pseudoelastic Loading 272
Uniaxial Constant Stress Thermally-Induced Transformation 272
Torsion-Compression Loading 274
Response of an SMA Torque Tube 278
Correlation with Experimental Data 280
Cyclic Behavior up to a Constant Stress or Strain 281
Experiments on Large Diameter NiTi SMA Actuators 284
Summary 288
Problems 289
References 290
Extended SMA Modeling (by P. Popov and D. C. Lagoudas) 292
Introduction 292
Experimental Results on the Transformation Temperatures of Twinned and Detwinned Martensite to Austenite. 294
Setup and Experimental Procedure 295
Modified SMA Phase Diagram 298
Austenite to Martensite (AMt, AMd) 302
Detwinning of Self-Accommodated Martensite (Mt Md) 303
Combined Austenite to Detwinned Martensite at Low Stresses 305
Description of the SMA Constitutive Model 305
Kinematic Assumptions 307
Free Energy for Polycrystalline SMAs 308
Evolution of the Rate of the Gibbs FreeEnergy Function 312
Thermodynamics and Constitutive Relations 313
Transformation Hardening Functions 314
Transformation Surfaces and Evolution Equations 316
One-Dimensional Reduction and Material Parameter Determination 318
Reduction of the Model to the Uniaxial Stress State 318
Determination of Material Parameters 321
The Uniaxial Transformation Strips and the Phase Diagram 322
Relative Position of the Transformation Surfaces 323
Numerical Examples 325
Constrained Cooling of an SMA Rod 325
Thermomechanical Loading of an SMA Thick Plate with a Cylindrical Hole 327
Summary 333
Problems 334
References 335
Modeling of Magnetic SMAs (by B. Kiefer and D. C. Lagoudas) 338
Introduction 338
Properties of Magnetic SMAs 340
Magnetic-Field-Induced Strain Response of MSMAs 340
Magnetization Response of MSMAs 346
Derivation of a Phenomenological Constitutive Model for Magnetic SMAs 354
Extended Thermodynamic Framework 354
Choice of Internal State Variables 355
Formulation of the Specific Gibbs Free Energy 357
Evolution Equations and Activation Conditions 361
MSMA Response Under Specific Magnetomechanical Loading 364
Prediction of Magnetic-Field-Induced Variant Reorientation at Constant Stress (Fixed Domain Structure) 364
Prediction of Magnetic-Field-Induced Variant Reorientation at Constant Stress (Variable Domain Structure) 382
Prediction of Stress-Induced Variant Reorientation at Constant Magnetic Field 389
Summary 397
Problems 397
References 399
Generalized Framework for Modeling of SMAs (by M. A. Siddiq Qidwai and D. C. Lagoudas) 407
Thermodynamic Potentials in the Lagrangian Formulation 407
Phase Transformation Function 408
Principle of Maximum Transformation Dissipation 409
Consequences of the Application of the Principle of Maximum Transformation Dissipation 409
Modeling of Polycrystalline SMAs: Lagrangian Formulation 411
J2 Transformation Function 413
J2-I1 Transformation Function 414
J2-J3-I1 Transformation Function 414
References 415
Numerical Solutions to Boundary Value Problems (by P. Popov) 416
Displacement-Based Finite Element Methods for Nonlinear Problems 416
Numerical Implementation of an SMA Constitutive Model 423
The Loading Step 424
Thermoelastic Prediction 426
Transformation Correction 426
Active Surfaces and Other Implementation Details 428
Algorithmic Tangent Stiffness (Jacobian) 429
References 433
Numerical Implementation of Transformation Induced Plasticity in SMAs (by P. B. Entchev and D. C. Lagoudas) 434
Summary of the SMA Constitutive Model Equations 434
Closest Point Projection Return Mapping Algorithm 435
Thermoelastic Prediction 436
Transformation Correction 437
Consistent Tangent Stiffness and Thermal Moduli Tensors 440
Summary of the Numerical Algorithm for SMA Constitutive Model with Transformation Induced Plasticity 443
References 443
Index 444