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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.
R. S. Elliott, John A. Shaw, Nicolas Triantafyllidis
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