Thermo-mechanical description of phase transformation in Ni-Ti Shape Memory Alloy

Abstract

The pseudo-elasticity of Shape Memory Alloys is due to a change in volumetric fraction between the high temperature phase (Austenite) and the low temperature phase (Martensite) under a mechanical loading. When a tensile loading is considered, transformation bands occur leading to strong localization of the deformation and a strong local heating. The modeling of this strongly coupled phenomenon is discussed for a polycrystalline specimen in a multiaxial mechanical framework. Three different scales are considered: the variant scale (or phase scale), the single-crystal scale and the polycrystalline scale. The free energy of each variant is first computed from the loading and the geometrical lattice transformations associated to each variant. The volumetric fraction of each phase is then defined at the grain scale as function of their free energy. A simple averaging operation allows to estimate the deformation at the grain scale. The polycrystalline scale is not considered at present.