Interfacial Microstructures in Martensitic Transitions: From Optical Observations to Mathematical Modeling

We present a construction of a mathematical model of an interfacial microstructure (i.e., microstructure forming at the phase interface between austenite and martensite) in a single crystal of Cu-Al-Ni shape memory alloy. In the first part of the article, the experiment is briefly outlined and the compatibility of the experimentally observed microstructures is analyzed, showing that the observed X-interfaces cannot be compatible without the presence of elastic strains. Then, the elastic strains in the microstructure are evaluated by finite element method, whereby the elastic coefficients of finely microstructured regions are obtained by homogenization. The significant influence of the choice of the geometry on the numerical results is shown and discussed.