A Lumped Energy Model for Crack Growth in Shape-Memory Materials

We construct an energy-based model to study crack growth behavior in a shape-memory alloy that undergoes a stress-induced austenite to martensite transformation. The total energy, which is the sum of the elastic energy of the specimen and loading device, the surface energy of the crack, and the energy associated with transforming austenite to martensite, depends on the applied extension, the crack length, and the martensite volume fraction. The crack length and martensite volume fraction are coupled through a transformation criteria at the crack tip. By tracking the progression of equilibrium cracks as extension increases, we show that the transformation leads to a regime of stable crack growth followed by unstable growth. These results are in agreement with experiments on both single crystal and polycrystal shape-memory alloys.