Stability of thermally-induced martensitic transformations in bi-atomic crystals

Shape memory alloys (SMAs), such as equi-atomic NiTi, exhibit two remarkable properties: the shape memory effect and pseudoelasticity. The shape memory effect is the ability of the material to erase relatively large mechanically induced strains (up to 8%) by moderate increases in temperature (~ 10 - 20°C). Pseudoelasticity refers to the ability in a somewhat higher temperature regime to accommodate these strains during loading and recover upon unloading (via a hysteresis loop). The underlying mechanism is a reversible martensitic (displacive) transformation between solid-state phases, often occurring near room temperature. The transformation can be induced by changes in temperature or by changes in stress due to the strong thermo-mechanical coupling.



Previous work in this area has focused on phenomenological characterization of the continuum energy density, W. Physically several phases can coexist. Unfortunately constructing a phenomenological energy density is exceedingly difficult, even for the case of two coexisting phases. Thus, a new nano-scale based approach is proposed. It consists of deriving the continuum energy density function W(F,q) (where F is the lattice’s uniform deformation gradient and q is the temperature) from temperature-dependent atomic pair-potential functions. As a first approximation to the transformation mechanism, uniform strain equilibrium solutions and their stability are investigated, as a function of temperature, for perfect bi-atomic crystals subjected to hydro-static pressure. The model is then extended to include atomic “shuffles” (as seen in actual materials) and the resulting equilibrium solutions (and their stability) are investigated.