Theory and computation for the microstructure near the interface between twinned layers and a pure variant of martensite

We report results on a finite element simulation of a needle-like martensitic microstructure observed in biaxial loading experiments conducted by Chu and James on single crystals of the shape-memory alloy Cu-14 at.% Al-3.9 at.% Ni. This microstructure was observed near an interface between twinned layers of two variants and a pure variant of martensite. We used a geometrically nonlinear theory of martensite to model and compute the complex microstructure by energy minimization with a boundary condition that is compatible with the microstructure. Our computational model has yielded multiple metastable states that depend on the initial state of our energy-minimizing iteration. The simulated twinned layers form branches and bend as they approach the laminate-single variant interface in good agreement with the experiment of Chu and James.