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Deformation of Shape-Memory Materials

Published online by Cambridge University Press:  25 February 2011

Richard D. James
Richard D. James*
Affiliation:
Department of Aerospace Engineering and Mechanics, 107 Akerman Hall, University of Minnesota, Minneapolis, MN 55455
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Abstract

We present an overview of a theory of martensitic transformations developed by J. M. Ball and the author, and additional related results by Bhattacharya, Chu and Collins and Luskin and Kinderlehrer. This theory is in a form that is amenable to detailed numerical computations of microstructure. We describe the energy minimizing microstructures of a single crystal under applied displacements and under detailed dead loading. The relation of the theory to the crystallographic theory of martensite is presented.

A consequence of the theory is the sensitivity of the patterns of microstructure to the precise lattice parameters. In the case of the wedge-like microstructure studied by Bhattacharya, it is found that this microstructure is only possible as a coherent, energy minimizing microstructure if very restrictive conditions on the lattice parameters are satisfied. Materials that exhibit the wedge satisfy this relation closely. The analysis suggests that optimal shape-memory behavior may be related to relations of this type.

The theory has a relation to the work of Khachaturyan, Roitburd and Shatalov. We compare and contrast the two approaches. We present results that suggest that any approach based on the kinematics of linear elasticity will make serious quantitative errors in the prediction of microstructure.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 246: Symposium M – Shape-Memory Materials and Phenomena--Fundamental Aspects and Applications , 1991 , 81
Copyright
Copyright © Materials Research Society 1992

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References

1. Ball, J. M. and James, R. D., Arch. Ration. Mech. Anal. 100, 13 (1987); Phil. Trans. Royal Soc. Lond. (1991), in press.CrossRefGoogle Scholar
2. Barsch, G., Horovitz, B. and Krumhansl, J., Phys. Rev. Lett. 59, 1251 (1987); Phys. Rev. B43 1021 (1991).CrossRefGoogle Scholar
3. Bhattacharya, K., Acta.metall.mater. 39, 2431(1991).CrossRefGoogle Scholar
4. Collins, C. and Luskin, M., Partial Differential Equations and Continuum Models of Phase Transitions, Lecture Notes in Physics 344 (ed. Rascle, M., Serre, D., and Slemrod, M.). Springer-Verlag, 34 (1989); also C. Collins, Thesis, University of Minnesota (1990).Google Scholar
5. Ericksen, J. L. Arch. Ration. Mech. Anal. 73, 99 (1980).CrossRefGoogle Scholar
6. James, R. D. Metastability and Incompletely Posed Problems, IMA Vol. 3 (ed. Antman, S., Ericksen, J.L., Kinderlehrer, D., Müller, I.), 147–176 (1987) Springer-Verlag.CrossRefGoogle Scholar
7. James, R. D. and Kinderlehrer, D. Partial Differential Equations and Continuum Models of Phase Transitions (ed. Rascle, M., Serre, D., and Slemrod, M.), 51–84 (1989) Springer-Verlag.Google Scholar
8. Khachaturyan, A. G., Soviet Physics-Solid State 8, 2163 (1967); Theory of Structural Transformations in Solids. John Wiley and Sons(1983).Google Scholar
9. Khachaturyan, A. G., and Shatalov, G.A., Soviet Physics JETP 29, 557(1969).Google Scholar
10. Kohn, R. V., Trans. 7th Army Conf. on Applied Mathematics and Computing (ed. Dressel, F.(1989));Continuum Mech. and Thermodyn 3, 193(1991).Google Scholar
11. Kohn, R. V. and Miiller, S., Phil. Mag.,to appear.Google Scholar
12. Pitted, M., J. Elasticity 14, 175 (1984); J. Elasticity 15, 3 (1985).Google Scholar
13. Roitburd, A. L., Kristallografiya, p. 567 ff.(1967); Solid State Physics 33, 317 (1978).Google Scholar