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Shape Memory Alloys PDF

152 Pages·1996·8.93 MB·English
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CISM COURSES AND LECTURES Series Editors: The Rectors of CISM Sandor Kaliszky -Budapest Mahir Sayir -Zurich Wilhelm Schneider -Wien The Secretary General of CISM Giovanni Bianchi - Milan Executive Editor Carlo Tasso - Udine The series presents lecture notes, monographs, edited works and proceedings in the field of Mechanics, Engineering, Computer Science and Applied Mathematics. Purpose of the series is to make known in the international scientific and technical community results obtained in some of the activities organized by CISM, the International Centre for Mechanical Sciences. INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES COURSES AND LECTURES -No. 351 SHAPE MEMORY ALLOYS M.FREMOND LAB. DES MATERIAUX ET STRUCTURES DU GENIE CIVIL S. MIYAZAKI UNIVERSITY OF TSUKUBA ~ Springer-Verlag Wien GmbH Le spese di stampa di questa volume sono in parte coperte da contributi del Consiglio Nazionale delle Ricerche. This volume contains 99 illustrations This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. © 1996 by Springer-Verlag Wien Originally published by Springer-Verlag Wien New York in 1996 In order to make this volume available as economically and as rapidly as possible the authors' typescripts have been reproduced in their original forms. This method unfortunately has its typographical limitations but it is hoped that they in no way distract the reader. ISBN 978-3-211-82804-5 ISBN 978-3-7091-4348-3 (eBook) DOI 10.1007/978-3-7091-4348-3 PREFACE The thermal and mechanical properties of shape memory alloys are puzzling: thermal actions induce large deformations. In some sense thermal actions are equivalent to mechanical actions. This equivalence is the basic tool for many practical applications. The complete description of the shape memory alloys involves physics, metallurgy, crystallography, mechanics and even mathematics to deal with the predictive theories describing their behaviour. This book consisting of two chapters is devoted to the crystallographic and thermomechanical properties and to the macroscopic modelling of the shape memory alloys. It results from part of the lectures given by professors Fremond, James, Miyazaki and Muller during a session of the Centre International des Sciences Mecaniquesfrom October4 to October 8, 1993. The first chapter describes the thermomechanical macroscopic theory. Shape memory alloys are mixtures of many phases: martensites and austenite. The composition of the mixtures vary: the martensites and the austenite which have different mechanical properties transform into one another. The phase changes can be produced either by thermal actions or by mechanical actions. The striking and well known properties of shape memory alloys results from these links between mechanical and thermal actions. The macroscopic modelling is based on thermodynamics involving internal quantities. It gives a macroscopic theory which can be used for engineering purposes, for example to describe the evolution of structures made of shape memory alloys. Some of the internal quantities which are chosen, the phase volume fractions for instance, are submitted to constraints (for instance their actual value is between 0 and 1 ). It is shown that most of the macroscopic properties of shape memory alloys result from a careful treatment of these constraints. The thermomechanical modelling uses continuum thermodynamics and some elementary notions of convex analysis as basic tools. The second chapter describes the experimental works on the crystallographic and thermomechanical properties. Recent development of shape memory alloys is reviewed, emphasis being placed on the Ti-Ni, Cu-based and ferrous alloys which are considered as practical materials for applications among many shape memory alloys. Crystal structures of the parent and martensitic phases are described, and the crystallography of the martensitic transformations is also briefly explained. The origin of the shape memory effect and the shape memory mechanisms are discussed on the basis of the crystal structure and the crystallography of the martensitic transformations. Since an applied stress also induces the martensitic transformations, successive stages of the stress-induced martensitic transformations are reviewed briefly in Cu-based and Ti-Ni alloys, which show martensite-to-martensite transformations upon loading. Then, the transformation and mechanical characteristics of the shape memory alloys are reviewed in detail,· i.e. phase diagrams, transformation temperatures, transformation process, stress-induced transformation, aging effects, cycling effects, fracture, fatigue, grain refinement, two-way shape memory effect, and so on. Recent development of sputter-deposited Ti-Ni thin films is also introduced. The authors wish that this book would be a good guide and introduction for the readers to the study of shape memory alloys. M. Fremond S. Miyazaki CONTENTS Page Preface Shape Memory Alloy A Thermomechanical Macroscopic Theory by M. Fremond 1. Introduction ................................................................................................ 3 2. Description of a Material. The State Quantities .......................................... .3 3. Principle of Virtual Power without Micoscopic Velocities ......................... 3 4. Principle of Virtual Power with Microscopic Velocities ............................ .4 5. The Energy Balance .................................................................................... 6 6. The Second Principle of Thermodynamics ................................................. 6 7. Constitutive Laws when there are no Constraint on the Internal Quantities ........................................................................... 7 8. Constitutive Laws When There are Constraints on the Internal Quantities ........................................................................... 9 9. Shape Memory Alloys. A Macroscopic Theory ....................................... 16 10. Evolutions of Structures Made of Shape Memory Alloys ..................... 60 11. Conclusion ............................................................................................. 60 12. Appendix ................................................................................................ 61 13. References .............................................................................................. 66 Development and Characterization of Shape Memory Alloys by S. Miyazaki Abstract ........................................................................................................ 69 1. Introduction .............................................................................................. 71 2. Fundamental Aspects of Shape Memory Alloys ..................................... 72 3. Development of Shape Memory Alloys ................................................... 92 4. Prospects in Applications of Shape Memory Alloys .............................. 142 References .................................................................................................. 143 SHAPE MEMORY ALLOY A THERMOMECHANICAL MACROSCOPIC THEORY M. Fremond Lab. des Materiaux et Structures du Genie Civil, Champs sur Marne, France A Thermomechanical Macroscopic Theory 3 1. Introduction. Shape memory alloys are mixtures of many martensites and of austenite. The composition of the mixture varies : the matensites and the austenite transform into one another. These phase changes can be produced either by thermal actions or by mechanical actions. The striking and well known properties of shape memory alloys results from these links between mechanical and thermal actions [4], [15], [26]. Shape memory alloys can be studied at the microscopic level by describing the microstructures of the constitutive crystals, [7], [17], [28]. They can also be studied by using statistical thermodynamics of a lattice of particles [3] [23]. Thermodynamics involving internal quantities is an other tool to study shape memory alloys at the macroscopic level, [1], [2], [5], [6], [9], [18], [19], [22] [25], [27], [29]. It is the one we have chosen [10], [11]. It gives a macroscopic theory which can be used for engineering purposes, for example to describe the evolution of structures made of shape memory alloys. The internal quantities we choose, the phase volume fractions, are submitted to constraints (for instance their actual value is between 0 and 1). We show that most of the properties of shape memory alloys result from a careful treatment of these constraints [ 10], [ 12]. The first paragraphs 1 to 8 describe the thermodynamical quantities, the free energy and the pseudo-potential of dissipation. They give also the basic tools for macroscopic modelling. The p~agraph 9 is devoted to the macroscopic description of shape memory alloys. Basic definitions and properties of convex analysis are given in the appendix 12. 2. Description of a material. The state quantities. The state quantities are the basic quantities which describe the equilibrium and the evolution of a material. Their choice depends on the sophistication of the model we are searching for. Thus their choice depends on the scientist or the engineer concerned. When the state quantities are constant with respect to the time, we say that the material is at an equilibrium. Thus the notion of equilibrium is subjective : it depends on the sophistication of the description. The set of the state quantities is denoted by E. It usually contains quantities describing the deformations and the ·temperature. The other quantities of E are often called internal quantities. 3. Principle of Virtual P¢wer without micoscopic velocities. This is the classical situation. Let ? be the linear space of the macroscopic virtual velocities, n be the domain of R3 occupied by the structure we consider at the time t. The principle of virtual power [ 14] is (1), '1 D c. Q, 'VVEV, A(D,V) = P;(D,V) + Pe(D,V). where D is a subdomain of n. The virtual power of the acceleration forces is A(D,V) = JpyVdQ, where y is the acceleration and p the density. The virtual power of the internal forces is P;(D,V) =-Jcr:D(V)dQ, 4 M. Fremond where D(V) = (Dij(V) = ~Vi,j+Yj,i)) are the strain rates and cr = (crij) the stresses. The virtual power of the external forces is the sum of the power of the at a distance forces, Jr.vdn. where f is the volumetric external force, and of the power of the contact forces fT.Vdr, ()D where T is the contact external force. The virtual power of the external forces is Pe(D,V) = fr.Vctn + fT.Vdr. D CJD It is classical [ 14] to get the equations of the movement from the principle ( 1) , = (2), P'Y divcr + f, in D, = (3), cr.N T, in CJD, where N is the outwards normal unit vector to D. 4. Principle of Virtual Power with microscopic velocities. When the state quantities include internal quantities, the evolution of those quantities can result from microscopic movements. We think that the power of the microscopic movements can be taken into account in the power of the internal forces [13]. Let ~ be an internal quantity, for instance a volumetric proportion of austenite in a shape memory alloy, the volumetric proportion of a constituent in a mixture, the damage in a piece of concrete [13], the intensity of adhesion between two pieces [16], [32], the volume fraction of unfrozen water in a soil in winter. .. The only macroscopic quantity which is related to the micoscopic movements or velocities is ~ which describes their macroscopic effects i.e. the evolution of ~· Thus we choose as actual power of the internal forces J j d~ d~ d~ P;(D,U,dt) =- cr:D(U)d.Q- {Bdt + H.graddt}d.Q, and as virtual power of the internal forces, J J V'(V,c)eVxC, P;(D,V,c) =- cr:D(V)d.Q- {Be+ H. grade }d.Q, where C is the linear space of the virtual microscopic velocities. The elements (V ,c) of VxC are function of x, (V (x),c(x)).

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This book consists of two chapters. The first chapter deals with the thermomechanical macroscopic theory describing the transformation and deformation behavior of shape memory alloys. The second chapter deals with the extensive and fundamental review of the experimental works which include crystallo
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