Shape Memory Alloys: Modeling and Engineering Applications

446 Pages·2008·14.23 MB·English

by  P.K. Kumar

Shape Memory Alloys
Dimitris C. Lagoudas
Editor
Shape Memory Alloys
Modeling and Engineering Applications
123
Editor
DimitrisC.Lagoudas
DepartmentofAerospaceEngineering
TexasA&MUniversity
CollegeStation
TX,USA
ISBN:978-0-387-47684-1 e-ISBN:978-0-387-47685-8
DOI:10.1007/978-0-387-47685-8
LibraryofCongressControlNumber:2007942944
(cid:2)c 2008SpringerScience+BusinessMedia,LLC
Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten
permissionofthepublisher(SpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork,NY
10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnec-
tionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orby
similarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.
Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyare
notidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubject
toproprietaryrights.
Printedonacid-freepaper
9 8 7 6 5 4 3 2 1
springer.com
To all of our loved ones.
Preface
It all started with a trip to Red River...
Coauthors, families, and colleagues enjoy a working vacation in the Sangre de
Cristo Mountains of New Mexico, March 2006.
As technical conversations on modeling, characterization and applications
of shape memory alloys (SMAs) were blending with the view of the white
snowy peaks surrounding Red River, New Mexico, it became clear to our
research group that a consistent and comprehensive text on SMAs would be
very helpful to future students interested in performing research in this field.
Many communication barriers could be eliminated and access to the substan-
tial body of research discussed in the literature would be increased. In this
way, a working vacation became the motivating factor behind a challenging
research project.
This book has been written with contributions from three of my current
Ph.D. students, Luciano Machado, Parikshith Kumar and Darren Hartl, and
three former Ph.D. students, Pavlin Entchev, Peter Popov and Bjo¨rn Kiefer.
These latter three coauthors were still members of the Shape Memory Alloy
Research Team (SMART), or in close proximity, when we started the project
of writing this book more than a year and a half ago. The work of a seventh
former Ph.D. student, Siddiq Qidwai, is also included in this book. The task
of putting forth a sequence of topics on shape memory alloys (SMAs) that
VIII Preface
forms a coherent learning path seemed natural, given the diversity of topics
covered by their Ph.D. work.
In the first chapter, Parikshith describes the basic properties and appli-
cations of SMAs, followed by the second chapter on thermomechanical char-
acterization and material parameter identification presented by Darren. The
thermomechanical constitutive modeling and closed form solutions are cov-
ered in the third chapter by Luciano, while the numerical implementation
and finite element analysis examples are presented in the fourth chapter by
Siddiq and Darren. The incorporation of transformation induced plasticity is
discussedinchapterfivebyPavlinandanextendedmodelforSMAsaccount-
ing both for phase transformation and reorientation is described in the sixth
chapter by Peter. Finally, Bjo¨rn introduces modeling of magnetic SMAs in
the seventh chapter.
Even though the seven chapters cover a wide variety of topics and discuss
different aspects of modeling of SMAs, there are many specialized considera-
tionsthathavebeenleftoutduetospacelimitations.Thereaderwillhopefully
gain enough background to be able to seek additional sources of information
and appreciate the complexity of the constitutive response of SMAs and the
importance of modeling in the design and analysis of engineering systems.
The work of many other graduate and undergraduate student members of
my research group has been valuable in writing this book. In particular, the
helpprovidedbyAmnayaAwasthi,KrishnenduHaldar,JesseMooney,Justin
Schick and Francis Phillips is greatly appreciated. The many various tasks
performed by these individuals were coordinated in a large part by Darren
Hartl, who also helped with the overall compilation of the manuscript. The
proofreadingservicesofGarySeidel,OlivierBertacchini,BrentVolk,Matthew
Kuester, Jack Vincent, Pam McConal, Alex McCord and Natasha, Georgia
and Magda Lagoudas are also appreciated. Finally, the inspiration provided
by my colleagues at Texas A&M University and elsewhere, and the financial
support provided by the Department of Defense, NASA, NSF and industry
partners over the years to sustain the SMART research team is gratefully
acknowledged.
Texas A&M University
College Station, Texas Dimitris C. Lagoudas
December 2007 Editor
Contents
Preface ....................................................... VII
List of Symbols ...............................................XVII
1 Introduction to Shape Memory Alloys
(by P. K. Kumar and D. C. Lagoudas).................... 1
1.1 Introduction: Overview of Active Materials ................ 1
1.2 Shape Memory Alloys - A Brief History ................... 4
1.3 Phenomenology of Phase Transformation in Shape Memory
Alloys................................................. 5
1.4 Shape Memory Effect ................................... 11
1.5 Pseudoelasticity ........................................ 13
1.6 Cyclic Behavior of SMAs ................................ 15
1.7 Transformation Induced Fatigue in SMAs.................. 17
1.8 Crystallography of Martensitic Transformation ............. 19
1.9 Effect of Alloying on the Transformation Behavior of SMAs.. 23
1.9.1 NiTi-Based Alloys ................................ 23
1.9.2 Copper-Based Alloys.............................. 26
1.9.3 Iron-Based Alloys ................................ 28
1.9.4 Additional SMAs................................. 28
1.10 SMAs as Active Materials — Applications ................. 29
1.10.1 Aerospace Applications ........................... 30
1.10.2 Medical Applications ............................. 35
1.10.3 Transportation Applications ....................... 39
1.10.4 Other Applications ............................... 39
1.11 Summary.............................................. 40
1.12 Problems.............................................. 41
References ................................................. 43
X Contents
2 Thermomechanical Characterization of Shape Memory
Alloy Materials
(by D. J. Hartl and D. C. Lagoudas)...................... 53
2.1 Introduction ........................................... 53
2.1.1 Review of SMA Characterization Methods........... 54
2.1.2 Shape Memory Alloy Specimens.................... 55
2.2 Thermomechanical Material Properties of SMAs
for Engineering Applications ............................. 60
2.2.1 Thermoelastic Properties.......................... 64
2.2.2 Critical Stress and Temperature States for
Transformation (Phase Diagram)................... 65
2.2.3 Transformation Strain Properties and Hardening ..... 67
2.3 Experimental Characterization Process.................... 68
2.3.1 Overview of the General Thermomechanical
Characterization Process .......................... 69
2.3.2 Illustration of the General Characterization
Process ......................................... 69
2.4 Experimental Considerations Unique to SMA
Thermomechanical Characterization ...................... 82
2.4.1 Influence of Total Material History on Shape Memory
Behavior ........................................ 82
2.4.2 Comparison of Test Specimen to Intended Application
Component...................................... 84
2.4.3 Importance of Mechanical and Thermal
Loading Rates ................................... 85
2.4.4 Stochastic Variation in Material Response ........... 88
2.5 Examples of SMA Characterization ....................... 88
2.5.1 Example 1. Characterization of NiTi Wire Intended
for Pseudoelastic Application ...................... 89
2.5.2 Example 2. Characterization of NiTi Wire for
Determination of Stochastic Variation............... 93
2.5.3 Example 3. Characterization of Ni60Ti40 (wt%) Plate
Intended for Actuation Application ................. 95
2.6 Simple SMA Application Design and Empirical
1-D Analysis........................................... 102
2.6.1 Application Design Considerations.................. 103
2.6.2 Experimentally-Based 1-D Material Model........... 105
2.7 Summary.............................................. 109
2.8 Problems.............................................. 109
References ................................................. 117
3 Thermomechanical Constitutive Modeling of SMAs
(by L. G. Machado and D. C. Lagoudas).................. 121
3.1 Introduction ........................................... 121
3.2 Brief Review of Continuum Mechanics .................... 122
3.2.1 Kinematics of SMAs .............................. 122
Contents XI
3.2.2 Conservation (Balance) Laws ...................... 123
3.2.3 Constitutive Equations in the Presence of Internal
State Variables................................... 126
3.3 Constitutive Modeling of SMAs .......................... 131
3.3.1 Choice of Internal State Variables .................. 132
3.3.2 Kinematic Assumptions ........................... 132
3.3.3 Thermomechanical Constitutive Assumptions
for SMAs........................................ 133
3.3.4 Thermomechanical Coupling in SMAs............... 142
3.4 Unification of Different SMA Constitutive Models .......... 145
3.5 Analytical Solutions and 1-D Examples ................... 150
3.5.1 1-D Reduction of the SMA Constitutive Model....... 150
3.5.2 Example Solutions for Various Thermomechanical
Loading Paths ................................... 152
3.5.3 Application of the Smooth Hardening Model to a
Nonlinear Oscillator .............................. 167
3.6 Brief Overview of Other Thermomechanical Constitutive
Models for SMAs....................................... 171
3.7 Summary.............................................. 180
3.8 Problems.............................................. 180
References ................................................. 182
4 Numerical Implementation of an SMA Thermomechanical
Constitutive Model Using Return Mapping Algorithms
(by M. A. Siddiq Qidwai, D. J. Hartl
and D. C. Lagoudas)...................................... 189
4.1 Introduction ........................................... 189
4.2 Continuum Tangent Moduli Tensors ...................... 191
4.3 Return Mapping Algorithms ............................. 193
4.3.1 A General View of Thermoelastic Prediction-
Transformation Correction Return Mapping ......... 193
4.3.2 Closest Point Projection Return Mapping
Algorithm ....................................... 196
4.3.3 Convex Cutting Plane Return Mapping Algorithm.... 203
4.3.4 Summary and Comparison of Algorithms............ 205
4.4 Numerical Examples .................................... 206
4.4.1 SMA Uniaxial Thermomechanical Loading Cases ..... 208
4.4.2 SMA Actuated Beam ............................. 209
4.4.3 SMA Torque Tube................................ 212
4.4.4 SMA Actuated Variable Geometry Jet Engine
Chevron......................................... 215
4.4.5 SMA Medical Stent............................... 219
4.5 Summary.............................................. 221
4.6 Problems.............................................. 221
References ................................................. 229