Lagoudas Shape Memory Alloys

Modeling and Engineering Applications
1. Auflage 2008
ISBN: 978-0-387-47685-8
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 436 Seiten

This book provides a working knowledge of the modeling and engineering applications of shape memory alloys (SMAs), beginning with a rigorous introduction to continuum mechanics and continuum thermodynamics as they relate to the development of SMA modeling.Modern SMAs can recover from large amounts of bending and deformation, and millions of repetitions within recoverable ranges. SMAs are used in the medical industry to create stents, in the dental industry to create dental and orthodontic archwires, and in the aerospace industry to create fluid fittings. The text presents a unified approach to the constitutive modeling of SMAs, including modeling of magnetic and high temperature SMAs.

Autoren/Hrsg.

Lagoudas, Dimitris C.

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;List of Symbols;15
4;Introduction to Shape Memory Alloys (by P. K. Kumar and D. C. Lagoudas);19
4.1;Introduction: Overview of Active Materials;19
4.2;Shape Memory Alloys - A Brief History;22
4.3;Phenomenology of Phase Transformation in Shape Memory Alloys;23
4.4;Shape Memory Effect;29
4.5;Pseudoelasticity;31
4.6;Cyclic Behavior of SMAs;33
4.7;Transformation Induced Fatigue in SMAs;35
4.8;Crystallography of Martensitic Transformation;37
4.9;Effect of Alloying on the Transformation Behavior of SMAs;41
4.9.1;NiTi-Based Alloys;41
4.9.2;Copper-Based Alloys;44
4.9.3;Iron-Based Alloys;46
4.9.4;Additional SMAs;46
4.10;SMAs as Active Materials - Applications;47
4.10.1;Aerospace Applications;48
4.10.2;Medical Applications;53
4.10.3;Transportation Applications;57
4.10.4;Other Applications;57
4.11;Summary;58
4.12;Problems;59
4.13;References;61
5;Thermomechanical Characterization of Shape Memory Alloy Materials (by D. J. Hartl and D. C. Lagoudas);70
5.1;Introduction;70
5.1.1;Review of SMA Characterization Methods;71
5.1.2;Shape Memory Alloy Specimens;72
5.2;Thermomechanical Material Properties of SMAs for Engineering Applications;77
5.2.1;Thermoelastic Properties;81
5.2.2;Critical Stress and Temperature States for Transformation (Phase Diagram);82
5.2.3;Transformation Strain Properties and Hardening;84
5.3;Experimental Characterization Process;85
5.3.1;Overview of the General Thermomechanical Characterization Process;86
5.3.2;Illustration of the General Characterization Process;86
5.4;Experimental Considerations Unique to SMA Thermomechanical Characterization;99
5.4.1;Influence of Total Material History on Shape Memory Behavior;99
5.4.2;Comparison of Test Specimen to Intended Application Component;101
5.4.3;Importance of Mechanical and ThermalLoading Rates;102
5.4.4;Stochastic Variation in Material Response;105
5.5;Examples of SMA Characterization;105
5.5.1;Example 1. Characterization of NiTi Wire Intended for Pseudoelastic Application;106
5.5.2;Example 2. Characterization of NiTi Wire for Determination of Stochastic Variation;110
5.5.3;Example 3. Characterization of Ni60Ti40 (wt%) Plate Intended for Actuation Application;112
5.6;Simple SMA Application Design and Empirical 1-D Analysis;119
5.6.1;Application Design Considerations;120
5.6.2;Experimentally-Based 1-D Material Model;122
5.7;Summary;126
5.8;Problems;126
5.9;References;134
6;Thermomechanical Constitutive Modeling of SMAs (by L. G. Machado and D. C. Lagoudas);137
6.1;Introduction;137
6.2;Brief Review of Continuum Mechanics;138
6.2.1;Kinematics of SMAs;138
6.2.2;Conservation (Balance) Laws;139
6.2.3;Constitutive Equations in the Presence of Internal State Variables;142
6.3;Constitutive Modeling of SMAs;147
6.3.1;Choice of Internal State Variables;148
6.3.2;Kinematic Assumptions;148
6.3.3;Thermomechanical Constitutive Assumptionsfor SMAs;149
6.3.4;Thermomechanical Coupling in SMAs;158
6.4;Unification of Different SMA Constitutive Models;161
6.5;Analytical Solutions and 1-D Examples;166
6.5.1;1-D Reduction of the SMA Constitutive Model;166
6.5.2;Example Solutions for Various Thermomechanical Loading Paths;168
6.5.3;Application of the Smooth Hardening Model to a Nonlinear Oscillator;183
6.6;Brief Overview of Other Thermomechanical Constitutive Models for SMAs;187
6.7;Summary;196
6.8;Problems;196
6.9;References;198
7;Numerical Implementation of an SMA Thermomechanical Constitutive Model Using Return Mapping Algorithms (by M. A. Siddiq Qidwai, D. J. Hartland D. C. Lagoudas);204
7.1;Introduction;204
7.2;Continuum Tangent Moduli Tensors;206
7.3;Return Mapping Algorithms;208
7.3.1;A General View of Thermoelastic Prediction-Transformation Correction Return Mapping;208
7.3.2;Closest Point Projection Return Mapping Algorithm;211
7.3.3;Convex Cutting Plane Return Mapping Algorithm;218
7.3.4;Summary and Comparison of Algorithms;220
7.4;Numerical Examples;221
7.4.1;SMA Uniaxial Thermomechanical Loading Cases;223
7.4.2;SMA Actuated Beam;224
7.4.3;SMA Torque Tube;227
7.4.4;SMA Actuated Variable Geometry Jet Engine Chevron;230
7.4.5;SMA Medical Stent;234
7.5;Summary;236
7.6;Problems;236
7.7;References;244
8;Modeling of Transformation-Induced Plasticity in SMAs (by P. B. Entchev and D. C. Lagoudas);247
8.1;Introduction;247
8.1.1;Experimental Motivation: Polycrystalline SMAs Undergoing Cyclic Loading;248
8.2;Three Dimensional Constitutive Model for SMAs Experiencing TRIP;252
8.2.1;Modifications Needed to Account for TRIP;253
8.2.2;Complete Constitutive Model for TRIP;257
8.2.3;Evolution of the Hysteretic Response of an SMA Undergoing Cyclic Loading;259
8.2.4;Modeling of Minor Hysteresis Loops;261
8.3;Estimation of Material Parameters;262
8.3.1;1-D Reduction of the Model;262
8.3.2;Material Parameters for a StableTransformation Cycle;264
8.3.3;Material Parameters for Cyclic Loading;270
8.3.4;Material Parameters for Minor Loop Modeling;271
8.4;Sample Loading Cases;271
8.4.1;Uniaxial Isothermal Pseudoelastic Loading;272
8.4.2;Uniaxial Constant Stress Thermally-Induced Transformation;272
8.4.3;Torsion-Compression Loading;274
8.4.4;Response of an SMA Torque Tube;278
8.5;Correlation with Experimental Data;280
8.5.1;Cyclic Behavior up to a Constant Stress or Strain;281
8.5.2;Experiments on Large Diameter NiTi SMA Actuators;284
8.6;Summary;288
8.7;Problems;289
8.8;References;290
9;Extended SMA Modeling (by P. Popov and D. C. Lagoudas);292
9.1;Introduction;292
9.2;Experimental Results on the Transformation Temperatures of Twinned and Detwinned Martensite to Austenite.;294
9.2.1;Setup and Experimental Procedure;295
9.3;Modified SMA Phase Diagram;298
9.3.1;Austenite to Martensite (AMt, AMd);302
9.3.2;Detwinning of Self-Accommodated Martensite (Mt Md);303
9.3.3;Combined Austenite to Detwinned Martensite at Low Stresses;305
9.4;Description of the SMA Constitutive Model;305
9.4.1;Kinematic Assumptions;307
9.4.2;Free Energy for Polycrystalline SMAs;308
9.4.3;Evolution of the Rate of the Gibbs FreeEnergy Function;312
9.4.4;Thermodynamics and Constitutive Relations;313
9.4.5;Transformation Hardening Functions;314
9.4.6;Transformation Surfaces and Evolution Equations;316
9.5;One-Dimensional Reduction and Material Parameter Determination;318
9.5.1;Reduction of the Model to the Uniaxial Stress State;318
9.5.2;Determination of Material Parameters;321
9.5.3;The Uniaxial Transformation Strips and the Phase Diagram;322
9.5.4;Relative Position of the Transformation Surfaces;323
9.6;Numerical Examples;325
9.6.1;Constrained Cooling of an SMA Rod;325
9.6.2;Thermomechanical Loading of an SMA Thick Plate with a Cylindrical Hole;327
9.7;Summary;333
9.8;Problems;334
9.9;References;335
10;Modeling of Magnetic SMAs (by B. Kiefer and D. C. Lagoudas);338
10.1;Introduction;338
10.2;Properties of Magnetic SMAs;340
10.2.1;Magnetic-Field-Induced Strain Response of MSMAs;340
10.2.2;Magnetization Response of MSMAs;346
10.3;Derivation of a Phenomenological Constitutive Model for Magnetic SMAs;354
10.3.1;Extended Thermodynamic Framework;354
10.3.2;Choice of Internal State Variables;355
10.3.3;Formulation of the Specific Gibbs Free Energy;357
10.3.4;Evolution Equations and Activation Conditions;361
10.4;MSMA Response Under Specific Magnetomechanical Loading;364
10.4.1;Prediction of Magnetic-Field-Induced Variant Reorientation at Constant Stress (Fixed Domain Structure);364
10.4.2;Prediction of Magnetic-Field-Induced Variant Reorientation at Constant Stress (Variable Domain Structure);382
10.4.3;Prediction of Stress-Induced Variant Reorientation at Constant Magnetic Field;389
10.5;Summary;397
10.6;Problems;397
10.7;References;399
11;Generalized Framework for Modeling of SMAs (by M. A. Siddiq Qidwai and D. C. Lagoudas);407
11.1;Thermodynamic Potentials in the Lagrangian Formulation;407
11.1.1;Phase Transformation Function;408
11.1.2;Principle of Maximum Transformation Dissipation;409
11.1.3;Consequences of the Application of the Principle of Maximum Transformation Dissipation;409
11.2;Modeling of Polycrystalline SMAs: Lagrangian Formulation;411
11.2.1;J2 Transformation Function;413
11.2.2;J2-I1 Transformation Function;414
11.2.3;J2-J3-I1 Transformation Function;414
11.3;References;415
12;Numerical Solutions to Boundary Value Problems (by P. Popov);416
12.1;Displacement-Based Finite Element Methods for Nonlinear Problems;416
12.2;Numerical Implementation of an SMA Constitutive Model;423
12.2.1;The Loading Step;424
12.2.2;Thermoelastic Prediction;426
12.2.3;Transformation Correction;426
12.2.4;Active Surfaces and Other Implementation Details;428
12.2.5;Algorithmic Tangent Stiffness (Jacobian);429
12.3;References;433
13;Numerical Implementation of Transformation Induced Plasticity in SMAs (by P. B. Entchev and D. C. Lagoudas);434
13.1;Summary of the SMA Constitutive Model Equations;434
13.2;Closest Point Projection Return Mapping Algorithm;435
13.2.1;Thermoelastic Prediction;436
13.2.2;Transformation Correction;437
13.2.3;Consistent Tangent Stiffness and Thermal Moduli Tensors;440
13.2.4;Summary of the Numerical Algorithm for SMA Constitutive Model with Transformation Induced Plasticity;443
13.3;References;443
14;Index;444