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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 École National Supérieure de Mécanique et des Microtechniques de Besançon 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.
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Veröffentlichungsjahr: 2013
Contents
Foreword
Preface
Chapter 1: Some General Points about SMAs
1.1. Introduction
1.2. Why are SMAs of interest for industry?
1.3. Crystallographic theory of martensitic transformation
1.4. Content of this book
Chapter 2: The World of Shape-memory Alloys
2.1. Introduction and general points
2.2. Basic metallurgy of SMAs, by Michel Morin
2.3. Measurements of phase transformation temperatures
2.4. Self-accommodating martensite and stress-induced martensite
2.5. Fatigue resistance
2.6. Functional properties of SMAs
2.7. Use of NiTi for secondary batteries
2.8. Use of SMAs in the domain of civil engineering
Chapter 3: Martensitic Transformation
3.1. Overview of continuum mechanics
3.2. Main notations for matrices
3.3. Additional notations and reminders
3.4. Kinematic description
3.5. Kinematic compatibility
3.6. Continuous theory of crystalline solids
3.7. Martensitic transformation
3.8. Equation governing the interface between two martensite variants Mi/Mj or the “twinning equation”
3.9. Origin of the microstructure
3.10. Special microstructures
3.11. From the scale of the crystalline lattice to the mesoscopic and then the macroscopic scale
3.12. Linear geometric theory
3.13. Chapter conclusion
Chapter 4: Thermodynamic Framework for the Modeling
4.1. Introduction
4.2. Conservation laws
4.3. Constitutive laws
Chapter 5: Use of the “CTM” to Model SMAs
5.1. Introduction
5.2. Process of reorientation of the martensite variants in a monocrystal
5.3. Process of creation of martensite variants in a monocrystal: pseudoelastic behavior
5.4. Prediction of the surfaces for the austenite → martensite phase transformation
Chapter 6: Phenomenological and Statistical Approaches for SMAs
6.1. Introduction
6.2. Preisach models
6.3. First-order phase transitions and Falk’s model
6.4. Constitutive framework of the homogenized energy model
6.5. Conclusion
Chapter 7: Macroscopic Models with Internal Variables
7.1. Introduction
7.2. RL model
7.3. Anisothermal expansion [LEC 96] [LEX 06a]
7.4. Internal variable model inspired by micromechanics
7.5. Elastohysteresis model: formalism and digital implantation
7.6. Conclusion
Chapter 8: Design of SMA Elements: Case Studies
8.1. Introduction
8.2. “Strength of materials”-type calculations for beams subject to flexion or torsion [REJ 99]
8.3. Elements of calculations for SMA actuators
8.4. Case studies
Chapter 9: Behavior of Magnetic SMAs
9.1. Introduction
9.2. Some models of the thermo-magneto-mechanical behavior of MSMAs
9.3. Crystallography of Ni-Mn-Ga
9.4. Model of the magneto-thermo-mechanical behavior of a monocrystal of magnetic shape-memory alloy
9.5. Conclusion
Chapter 10: Fracture Mechanics of SMAs
10.1. Introduction
10.2. The elastic stress field around a crack tip
10.3. Prediction of the phase transformation surfaces around the crack tip (no curvature at the crack tip) [LEX 11]
10.4. Prediction of the phase transformation surfaces around the crack tip (curvature ρ at the crack tip)
10.5. Some experimental results about fracture of SMAs
10.6. Problem of delamination between a SMA and an elastic solid [LAY 12]
Chapter 11: General Conclusion
11.1. Resolved problems
11.2. Unresolved problems
11.3. Suggestions for future directions
Appendix 1: Intrinsic Properties of Rotation Matrices (see Chapter 3)
A1.1. Characterization of rotations
Appendix 2: “Twinning Equation” Demonstration (see Chapter 3)
A2.1. Question
A2.2. Solution
Appendix 3: Calculation of the Parameters a, n and Q from the “Twinning” Equation (see Chapter 3)
A3.1. Problem
A3.2. Statement
A3.3. Solution
Appendix 4: “Twinned” Austenite/Martensite Equation (see Chapter 3)
A4.1. Proposition 1
A4.2. Proposition 2
A4.3. Theorem
Bibliography
Index
First published 2013 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:
ISTE Ltd27-37 St George’s RoadLondon SW19 4EUUK
www.iste.co.uk
John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USA
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© ISTE Ltd 2013
The rights of Christian Lexcellent to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.
Library of Congress Control Number: 2013930404
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN: 978-1-84821-434-7
Foreword
Shape-memory alloys (SMAs), often also qualified as “smart materials”, were discovered over 60 years ago (Au–Cd in the 1930s and NiTi alloys in the early 1960s). The first applications were for mechanical purposes. In particular, these materials “remember” their original un-deformed shape. When they are preformed at a given temperature, they recover their original shape if they are heated above this temperature. These materials are solid-state alternatives to conventional actuators, such as hydraulic, pneumatic and motor-based systems. Shape-memory alloys have applications in industrial fields including medicine and aerospace. There is another type of SMA, called a ferromagnetic shape-memory alloy (FSMA), which changes shape when subjected to strong magnetic fields. These materials are of particular interest, as their magnetic response tends to be faster and more efficient than temperature-induced responses.
In this book, Christian Lexcellent gives a detailed analysis, both physical and mechanical, of the properties of these fascinating materials. The author, who belongs to the French school of mechanics of materials, has devoted a large part of his scientific career to working on these materials and has supervised about 20 PhD students who have investigated various aspects of these alloys. Christian Lexcellent is a well-known scientist and has published many technical papers dealing with various aspects of these materials.
It is real pleasure to introduce this comprehensive book on SMAs. In his book, Christian Lexcellent has found the right balance between physical metallurgy (Chapter 2), the various mechanical and thermodynamic facets of these materials (Chapters 3, 4, 5, 6 and 7), their applications (Chapter 8) and magnetic SMAs (Chapter 9). The main chapters are characterized by the fact that all the aspects (theory and thermodynamics of phase transformation, phenomenological models, models based on internal variables) are approached. A broad overview of the literature, in addition to the authors own work, is presented.
This book covers the most important fundamental and practical aspects of SMA in a clear and logical manner, and provides a sound basis that should make it as attractive to English-speaking students, practicing engineers and researchers.
André PINEAUProfessor École des Mines ParisTechJanuary 2013
Preface
In this age of “immediacy”, in which it is often the case that people have lost the memory of their history, there are some materials which have, beyond a doubt, kept theirs.
In this context, I came to discover the wondrous world of shape-memory alloys (SMAs) in the late 1980s, while working on a project financed under a CIFRE grant with the company Aug Dcoupage in Besanon.
Our task was to create, characterize and model small elements made of copper-based SMAs, such as springs. In the end, the contract was never signed, because the company was alarmed by what it called the “exotic” or mysterious behavior of these alloys.
Therefore, Claude Oytana and I went to study under Grard Gunin in the Materials Laboratory at INSA Lyon. Thus, the first academic terms regarding these metallic alloys saw the light of day (one-way shape-memory effect, pseudo-elasticity, double-way shape memory effect, training, etc.).
Armed with this priceless knowledge, Pierre Vacher (now at the IUT Annecy) and I endured the trials and tribulations of early “hiccups” in the context of his thesis. For instance, what thermal treatment should be carried out on Cu-Zn-Al alloys under traction in order to obtain a hysteresis loop corresponding to a pseudo-elastic behavior of the alloy?
We soon came into contact with Marcel Berveiller and Etienne Patoor at the LPMM in Metz, who were more knowledgeable on the subject than we were. This contact gave rise to enriching exchanges and amicable debates which are still going on even today.
“The discovery” of the concept of training these alloys, in our small world, was an important part of what has been an epic journey.
Certain researchers have discovered mysterious treatments to make the four leaves of a clover open at ambient temperature when removed from a refrigerator. Water memory, the treasured theory of Jacques Benveniste, was compared to the shape memory of these alloys. When it was realized that a simple appropriate thermomechanical treatment was all that was required in order to train these materials, research in the field regained in rigor what it had lost in poetry.
Thus, the domain is strewn with theses: Pierre Vacher, 1991; Ccile Rogueda, 1993; Gilles Bourbon, 1994; Byong Chong Goo, Sylvain Leclercq, 1995; Hellal Benzaoui, Bertrand Gabry, Sylvain Moyne, 1998; Alexandre Vivet, 1999; Jol Abadie, James Rejzner, 2000; Christophe Bouvet, 2001; Benot Vieille, 2003; Nicolas Creton*, 2004; Pierrick Malecot, 2005; Jean-Yves Gauthier*, Frdric Thiebaud, 2007; Karine Taillard, 2008; Zoltan Palanki, Elie Gibeau, 2009; these are 19 theses about SMAs, of which two (marked *) are devoted to magnetic shape-memory alloys.
Virginie Taillebot has recently completed the coverage of the area in 2012, presenting her works on the fracture mechanics of SMAs.
We have been joined in this exalting adventure by partners such as Christian Licht, Bodgan Raniecki, Lamine Boubakar, Sylvain Calloch, Rachid Laydi for thermomechanical modeling, Jean Bernardini, Deszo Beke, Patrick Delobelle for knowledge of the materials, Nicolas Chaillet and Arnaud Hubert for the command and control of these alloys, and finally Manuel Collet and Emmanuel Foltte for the dynamic and damping responses of SMAs. This book is an attempt to reconstruct what these doctoral candidates and my colleagues have taught me about “the world of shape-memory alloys”.
Without the technical assistance of Joël Abadie and Scott Cogan at FEMTO-ST, it would have been difficult, or even impossible, to put this book together. Thanks to my status as Professor Emeritus, I have benefited from the facilities at the Department of Applied Mechanics, for which I am very thankful.
What are these alloys that we call “shape-memory alloys”?
To begin with, they are metallic alloys with two, three or even four components, with very special compositions.
There are two main families of SMAs:
These materials are called “memory” materials, meaning that they have the property of “remembering” thermomechanical treatments to which they have been subjected (traction, torsion, flexion, etc.).
Specifically, the geometric shape that they had, at high and low temperatures, constitute two states which they “remember”. This memory is developed by way of training – i.e. often by the repetition of the same thermodynamic loading: this is in terms of stress or strain imposed and/or in terms of temperature.
The physical key to “shape memory” lies in a phase transformation between a parent phase called austenite (A) and a produced phase called martensite (M). For SMAs, this phase transformation is described as thermoelastic. It involves a change of crystalline lattice between the phase A, also known as the “high temperature” phase, and a phase M, also known as the “low temperature” phase. This change is called a “martensitic transformation”. The austenite is transformed into “martensite variants” (a term which will be explained later on).
As shown by the photographs taken by Chu and James [CHU 93] of “copper-based SMAs”, the microstructure may prove very complex, which makes it difficult to analyze them (Figures 1.1 to 1.4).
Figure 1.1.Optical micrograph of a microstructure of a Cu-Al-Ni alloy: a “complex lattice”; horizontal extent 0.75 mm: reproduced with kind permission from C. Chu and R.D. James [BHA 03]
SMAs belong to the category of so-called “adaptive” materials. Not only are they useful as structural elements, appreciable for their mechanical properties such as toughness; they are also capable of fulfilling functions such as that of a sensor or an actuator.
They are very widely used in domains with high financial added value – for example:
Figure 1.2.Optical micrograph of a microstructure of a Cu-Al-Ni alloy: a “corner”-type microstructure; horizontal extent 0.75 mm: reproduced with kind permission from C. Chu and R.D. James [BHA 03]
Figure 1.3.Optical micrograph of a microstructure of a Cu-Al-Ni alloy: “cross-twinning”; horizontal extent 0.75 mm: reproduced with kind permission from C. Chu and R.D. James [BHA 03]
Figure 1.4.Optical micrograph of a microstructure of a Cu-Al-Ni alloy: “needles”; horizontal extent 0.75 mm: reproduced with kind permission from C. Chu and R.D. James [BHA 03]
However, the cost of the alloy has hitherto been a serious hindrance for potential applications in the automobile industry, because of the tight budget in terms of mechanical parts in this sector.
Indeed, this cost is very heavily dependent on the delivery state, i.e. on the metallurgic treatment, shaping and geometry of the manufactured parts.
For instance, according to information provided by Nimsis-Technologies:
At present, in France, there are three companies which supply SMAs:
Mmomtal produces its alloys using the “hot crucible” technique, which is excellent for obtaining homogeneity in the resulting composition, but causes the problem of excessive oxygen absorption. NiTiFrance uses a “cold copper crucible”, which increases the ductility of the alloy (by 15 to 30% between the two solutions) by decreasing the percentage of oxygen absorbed. Remember that titanium is highly oxyphilic, and that oxygen tends to position itself in the interstitial site in crystalline lattices, which causes an increase in the fragility of the material.
As regards the activity of Nimésis-Technologies, it covers the main sectors of applications for SMAs, satisfying the demand for sensors and actuators.
Founded a century ago in Besanon, the company “MICRO-MEGA” is an uncontested leader in endodontics. In October 2009, it was bought by a German industrial dentistry corporation. It has developed a profitable niche market in NiTi “nerve lag” for root-canal work. It is the pseudo-elasticity of the alloy which is exploited here (see Chapter 2).
One of the drawbacks to these alloys is that they have a relatively slow dynamic of use, due to the prolonged period of heat transfer. However, the use of thin films can greatly improve the situation. An operational frequency of 100 Hz has been obtained by exploiting the austenite to R phase transformation for certain NiTi based alloys [TOM 06].
With massive SMAs, even a slow dynamic does not prevent their use in development of actuators.
The specific uses of SMAs, relating to their particular properties associated with phase transformation, will be discussed in detail in Chapter 2, entitled “The world of SMAs”.
Let us first examine the crystallographic aspect of martensitic transformation. At a low temperature, the phase M (hereafter called MT – self-accommodating martensite) obtained from A by simple cooling of the alloy and therefore isotropic redistribution of the variants, may, under external stresses, produce major deformations associated with the reorientation of the martensite variants. This associated behavior is qualified as “pseudo-plastic” (Figure 1.5).
Figure 1.5.Reorientation of martensite variants under stress
“Shape memory” constitutes a particular manifestation of crystalline phase transformation, known as “martensitic phase transformation”. This is a solid-to-solid phase transformation where the parameters of the crystalline lattice change suddenly (e.g. A → M when cooled) at a specific temperature of the alloy in question. Although the change is abrupt and the distortion of the lattice is very significant, there is no diffusion and no alteration in the relative positions of the atoms during the transformation. This transformation is said to be “displacive”, of the first order (sudden change in the crystalline parameters) (see Figure 1.6).
Figure 1.6.An illustration of martensitic transformation: a) austenite, b and c) martensite variants, d) a coherent arrangement between martensite variants [BHA 03]
If the alloy is heated, it undergoes thermal expansion until the reverse transformation (M → A) occurs at another critical temperature. The difference between the two critical temperatures (A → M) and (M → A) shows that the behavior of SMAs is hysteretic. The conventional SMAs exhibit a small amount of hysteresis.
Figure 1.7 illustrates the so-called “pseudo-elastic” traction curve representing a phase transformation under stress.
Figure 1.7.The pseudo-elastic stress/strain curve
One observable characteristic of martensitic transformation is the microstructure that it causes. In a typical transformation, the austenite, which is often “cubic” has a greater degree of symmetry than the produced phase. This is shown diagrammatically in two-dimensions in Figure 1.6, where the austenite is a square (a) and the martensite a rectangle (b and c). Consequently, we have multiple martensite variants – in this case two: (b and c). The number ν of variants obtained depends on the change in symmetry during the transformation.
More specifically:
[1.1]
where Pa (Pm) is the symmetry group of A(M).
Indeed, there is no reason why the austenite crystal should transform into only one martensite variant. However, the microstructure must be consistent and may be presented in the architecture shown in Figure 1.6 (d), which is corroborated by transmission electron microscope (TEM) observations of a nickel-aluminum alloy (see the images of microstructures in Figures 1.1 to 1.4 [BHA 03]).
This need of the crystals to form mixtures of variants, while the whole must remain consistent, gives rise to complex structures which we refer to as the microstructure of the martensite.
The first widely-recognized work in French on the topic was a basic introduction to SMAs, by Patoor and Berveiller [PAT 90]. Their second book was more significant in terms of the mechanical behavior of these alloys [PAT 94].
The question of the microstructure of martensite: “why it forms and how it gives rise to the shape-memory effect” constitutes the premise of the book with the same name by Bhattacharya [BHA 03]. The first founding theorems in this theory can be attributed to Ball and James [BAL 87], [BAL 92]. The chapter on martensitic transformation (Chapter 3) will make use of their proposals about the mathematic description of the microstructure.
Wayman’s book [WAY 64] is largely used as an introduction to crystallography of martensitic transformation (CMT).
With regard to the book by Khachaturyan [KHA 83] and the review by Roytburd [ROY 78], they predate the discipline of CMT (by linear or nonlinear construction) and deal with linear geometric theory.
The monograph published by Abeyaratne and Knowles [ABE 04] consists of an introduction to the dynamics of phase transformations.
The reader will find fairly general information about SMAs and their use in Shape Memory Alloys, the book written by Japanese scientists such as Shimizu, Tadaki, Homma, Miyazaki, Otsuka, Suzuki and Sekiguchi, translated into English [FUN 87].
Structural calculations about SMAs can be found in a special edition of the Revue des lments finis (Finite Element Journal) [REF 98].
Finally, Smith [SMI 05] extended his study to intelligent systems such as ferroelectrics, ferromagnetics and of course, SMAs.
Note that these materials are not intrinsically intelligent; rather it is the usage that is made of them that can be intelligent (or not)! Also, the title Journal of Intelligent Materials and Structures may be considered to be ambiguous.
This chapter is an attempt to place shape-memory alloys in the context of physics and the mechanics of materials and to set out the key physical concepts of martensitic transformation and reorientation of martensite plates.
Chapter 2 contains a few elements on the basic metallurgy of SMAs, written by Michel Morin (MATEIS (Materials, Engineering and Science) lab at INSA in Lyon). Particular attention is paid to phase diagrams and ad hoc thermal treatments, drawing the distinction between copper-based SMAs and NiTi materials and their derivatives. The chapter closes with a description of the functional properties of SMAs (simple memory effect, pseudo-elasticity, recovering stress and training).
Chapter 3 borrows heavily from Kaushik Bhattacharya’s book, Microstructure of martensite: why it forms and how it gives rise to the shape-memory effect [BHA 03]. Following an overview of continuum mechanics, the kinematic (or Hadamard) compatibility conditions are examined, as well as the twinning equation between two martensite variants and special microstructures.
Chapter 4 defines the thermodynamic framework used for the modeling of the materials, referred to as generalized standards [HAL 75].
Chapter 5 touches on the earliest applications of the crystallographic theory of martensite on SMA monocrystals.
Chapter 6 also borrows from Chapter 5 (Model development for shape memory alloys) of Ralph Smith’s book Smart Material Systems: Model Development [SMI 05].
It consists of the description of the “all-or-nothing” Preisach models, Falk’s investigations into the deformation potential, the statistical approaches of Seelecke and Muller and Smith’s extensions of these.
Chapter 7 introduces three macroscopic models with internal variables: namely, those advanced by Raniecki and Lexcellent, referred to as the RL models; the Metz-Nancy approaches, which are more concerned with the microstructure [CHE 11]; and finally the more mathematical models put forward by Kelly and Bhattacharya [KEL 12]. An elastohysteresis model was also described [FAV 88].
In Chapter 8, “material strength”-type calculations are performed on beams in flexion or torsion and a number of distilled exercises.
Chapter 9 will examine the behavior of magnetic shape-memory alloys.
In Chapter 10, some elements of the fracture mechanics of SMAs will be set out.
A general conclusion will focus on the numerous problems which still need to be resolved in this domain of functional materials.
Although there is a common thread running throughout the book, the author has been careful to make sure that each chapter can be read independently of the others. For instance, a reader interested in metallurgy can focus on Chapter 2 and on Chapter 9 about magnetic shape-memory alloys.
The term martensite was first put forward in honor of Adolf Martens, a German metallurgist who was the first to observe this microstructure in quenched steel. Regarding SMAs, Chang and Read [CHA 51] were the first to detect a phase transformation in a Au-Cd alloy by metallographic observations and measurements of electrical resistance. Thus, pseudo-elasticity was born.
Two decades later, the shape-memory effect was observed on a bent bar of that same alloy. In 1963, Buelher et al. [BUE 63] discovered the same properties on an equiatomic NiTi alloy. In the wake of this discovery, in 1969, the world witnessed the first industrial application with the simple memory effect used on a sleeve of hydraulic lines in a fighter plane. This created a particular interest in these new materials.
Yet the process of gaining true knowledge of the material and its thermomechanical behavior was slow, and would cause difficulties in practical perennial use in the 1970s–1980s. In fact, scientific research into the topic truly began in the 1980s associated with the first experimental investigations and the earliest attempts at modeling. The first mechanical tests were, naturally, uniaxial (traction/compression) as were the models. As in the study of any solid material, multiaxial tests – proportional or otherwise – such as traction-torsion-internal pressure tests, were performed, which necessitated the development of more complex models [BOU 02, GAL 98, ORG 98a].
Finally, in the 2000s, SMAs came to include the category of “smart materials”, but it is more accurate to speak of functional materials or adaptive materials.
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