Microstructure of macrointerfaces in shape-memory alloys

Shape-memory alloys exhibit a rich microstructure, characterized by large regions containing relatively regular laminates mixing different martensitic variants. Macrointerfaces separate these regions, and are often composed of arrays of needle-shaped martensitic domains. We formulate a model for the geometry of arrays of needles and present numerical simulations, appropriate for two compound twinned variants of martensite in a plane stress setting. One important ingredient is a new class of polyconvex energy densities with cubic symmetry, that is able to reproduce the austenitic elastic constants of the relevant materials. The energy-minimizing needle geometry is determined with tools from shape optimization. Our main finding is the "transparency effect'', which characterizes the effect of needles on domain boundaries located in front of their tip. Our numerical results are in good agreement with experimental observations.