Abstract
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.
References
Bhattacharya, K.: Microstructure of Martensite: Why It Forms and How It Gives Rise to the Shape-Memory Effect. Oxford University Press (2003)
Carlsson, A.E.: Solid State Physics. Chapter Beyond Pair Potentials in Elemental Transition Metals and Semiconductors, vol. 43, pp. 1–91. Academic Press (1990)
Chadwick, P., Ogden, R.W.: Definition of elastic moduli. Arch. Ration. Mech. Anal. 44(1), 41–53 (1971)
Duerig, T.W., Melton, K.N., Stockel, D., Wayman, C.M.: Engineering Aspects of Shape Memory Alloys. Butterworth-Heinemann (1990)
Elliott, R.S.: Multiscale bifurcation and stability of multilattices. J. Computer-aided Mat. Des. doi:10.1007/s10820-007-9075-8 (2008)
Elliott, R.S., Shaw, J.A., Triantafyllidis, N.: Stability of pressure-dependent, thermally-induced displacive transformations in bi-atomic crystals. Int. J. Solids Struct. 39(13–14), 3845–3856 (2002)
Elliott, R.S., Shaw, J.A., Triantafyllidis, N.: Stability of thermally-induced martensitic transformations in bi-atomic crystals. J. Mech. Phys. Solids 50(11), 2463–2493 (2002)
Elliott, R.S., Shaw, J.A., Triantafyllidis, N.: Stability of crystalline solids—II: application to temperature-induced martensitic phase transformations in bi-atomic crystals. J. Mech. Phys. Solids 54(1), 161–192 (2006)
Elliott, R.S., Triantafyllidis, N., Shaw, J.A.: Stability of crystalline solids—I: continuum and atomic-lattice considerations. J. Mech. Phys. Solids 54(1), 193–232 (2006)
Ericksen, J.L.: The Cauchy and Born Hypothesis for Crystals, in Phase Transformations and Material Instabilities in Solids. Academic Press (1984)
Friesecke, G., Theil, F.: Validity and failure of the Cauchy-Born hypothesis in a two-dimensional mass-spring lattice. J. Nonlinear Sci. 12(5), 445–478 (2002)
Girifalco, L.A., Weizer, V.G.: Application of the morse potential function to cubic metals. Phys. Rev. 114(3), 687–690 (1959)
Huang, K., Born, M.: Dynamical Theory of Crystal Lattices. Oxford University Press (1962)
Huang, X., Ackland, G.J., Rabe, K.M.: Crystal structures and shape-memory behavior of NiTi. Nat. Mater. 2(5), 307–311 (2003)
Huang, X., Bungaro, C., Godlevsky, V., Rabe, K.M.: Lattice instabilities of cubic NiTi from first principles. Phys. Rev. B-Condensed Matter 65(1), 014108/1–5 (2002)
Janssen, T., Tjon, J.A.: Microscopic model for incommensurate crystal phases. Phys. Rev. B 25(6), 3767–3785 (1982)
Laing, P.G., Ferguson, A.B., Hodges, E.S.: Tissue reaction in rabbit muscle exposed to metallic implants. J. Biomed. Materi. Res. 1(1), 135–149 (1967)
Milstein, F.: Mechanical stability of crystal lattices with 2-body interactions. Phys. Rev. B 2(2), 512–517 (1970)
Milstein, F.: Morse function description of anharmonicity in pressure-volume relations of cubic metals. Phys. Status Solidi B-Basic Res. 48(2), 681–688 (1971)
Milstein, F., Hill, R.: Theoretical properties of cubic-crystals at arbitrary pressure—I density and bulk modulus. J. Mech. Phys. Solids 25(6), 457–477 (1977)
Milstein, F., Hill, R.: Theoretical properties of cubic-crystals at arbitrary pressure—II shear moduli. J. Mech. Phys. Solids 26(4), 213–239 (1978)
Milstein, F., Hill, R.: Divergences among the Born and classical stability-criteria for cubic-crystals under hydrostatic loading. Phys. Rev. Letters 43(19), 1411–1413 (1979)
Milstein, F., Hill, R.: Theoretical properties of cubic-crystals at arbitrary pressure–III stability. J. Mech. Phys. Solids 27(3), 255–279 (1979)
Otsuka, K., Wayman, C.M.: Shape Memory Materials. Cambridge University Press (1998)
Pitteri, M., Zanzotto, G.: Continuum Models for Phase Transitions and Twinning in Crystals. Applied Mathematics, vol. 19. CRC Press (2002)
Putters, J.L.M., Sukul, D.M.K., de Zeeuw, G.R., Bijma, A., Besselink, P.A.: Comparative cell culture effects of shape memory metal <Nitinol®>, nickel and titanium: a biocompatibility estimation. Eur. Sur. Res. 24(6), 378–382 (1992)
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)
Riks, E.: Incremental approach to the solution of snapping and buckling problems. Int. J. Solids Struct. 15(7), 529–551 (1979)
Soliqo, D., Zanzotto, G., Pitteri, M.: Non-generic concentrations for shape-memory alloys; the case of CuZnAl. Acta Mater. 47(9), 2741–2750 (1999)
Truskinovsky, L., Vainchtein, A.: Quasicontinuum modelling of short-wave instabilities in crystal lattices. Philos. Mag. 85(33–34), 4055–4065 (2005)
Watah, J.C., O’Dell, N.L., Singh, B.B., Ghazi, M., Whitford, G.M., Lockwood, P.E.: Relating nickel induced tissue inflammation to nickel release in vivo. J. Biomed. Materi. Res. 58(5), 537–544 (2001)
Zhorovkov, M.F., Kulagina, V.V.: Phonon anomalies and martensitic transitions in BCC materials. Russ. Phys. J. 36(10), 917–923 (1993)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Guthikonda, V.S., Elliott, R.S. Stability and Elastic Properties of the Stress-Free B2 (CsCl-type) Crystal for the Morse Pair Potential Model. J Elasticity 92, 151–186 (2008). https://doi.org/10.1007/s10659-008-9155-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10659-008-9155-3