Stability and Elastic Properties of the Stress-Free B2 (CsCl-type) Crystal for the Morse Pair Potential Model
- 177 Downloads
Solid-to-solid martensitic phase transformations are responsible for the remarkable behavior of shape memory alloys. There is currently a need for shape memory alloys with improved corrosion, fatigue, and other properties. The development of new accurate models of martensitic phase transformations based on the material’s atomic composition and crystal structure would lead to the ability to computationally discover new improved shape memory alloys. This paper explores the Effective Interaction Potential method for modeling the material behavior of shape memory alloys. In particular, an extensive parameter study of the Morse pair potential model of the stress-free B2 cubic crystal is performed. Results for the stability, potential energy, current unit cell volume, instantaneous bulk modulus, and the two instantaneous cubic shear moduli are presented and discussed. It is found that an Effective Interaction Potential model based on the Morse potential is appropriate for modeling transformations between the B2 cubic structure and the B19 orthorhombic structure, but is not likely to be capable of simulating the B2 cubic to B19′ monoclinic transformation found in the popular shape memory alloy NiTi. In fact, this conclusion may be extended to all types of pair interaction potential models.
KeywordsShape memory alloys B2 crystal Martensitic precursor behavior Morse potential
Mathematics Subject Classifications (2000)74N10 74N05 70G99 70C20 70B99
Unable to display preview. Download preview PDF.
- 1.Bhattacharya, K.: Microstructure of Martensite: Why It Forms and How It Gives Rise to the Shape-Memory Effect. Oxford University Press (2003)Google Scholar
- 2.Carlsson, A.E.: Solid State Physics. Chapter Beyond Pair Potentials in Elemental Transition Metals and Semiconductors, vol. 43, pp. 1–91. Academic Press (1990)Google Scholar
- 4.Duerig, T.W., Melton, K.N., Stockel, D., Wayman, C.M.: Engineering Aspects of Shape Memory Alloys. Butterworth-Heinemann (1990)Google Scholar
- 5.Elliott, R.S.: Multiscale bifurcation and stability of multilattices. J. Computer-aided Mat. Des. doi:10.1007/s10820-007-9075-8 (2008)
- 10.Ericksen, J.L.: The Cauchy and Born Hypothesis for Crystals, in Phase Transformations and Material Instabilities in Solids. Academic Press (1984)Google Scholar
- 13.Huang, K., Born, M.: Dynamical Theory of Crystal Lattices. Oxford University Press (1962)Google Scholar
- 24.Otsuka, K., Wayman, C.M.: Shape Memory Materials. Cambridge University Press (1998)Google Scholar
- 25.Pitteri, M., Zanzotto, G.: Continuum Models for Phase Transitions and Twinning in Crystals. Applied Mathematics, vol. 19. CRC Press (2002)Google Scholar
- 27.Ren, X., Miura, N., Zhang, J., Otsuka, K., Tanaka, K., Koiwa, M., Suzuki, T., Chumlyakov, Y.I.: A comparative study of elastic constants of Ti-Ni-based alloys prior to martensitic transformation. Mater. Sci. Eng., A Struct. Mater.: Prop. Microstruct. Process. 312(1–2), 196–206 (2001)Google Scholar