Theory and Computation for the Microstructure Near the Interface Between Twinned Layers and a Pure Variant of Martensite

We report results on a nite 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-14at.%Al-3:9at.%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.