Interface compatibility and hysteresis in shape memory materials are affected by lattice distortions from applied stresses

Significant effort has been put into designing shape-memory materials that can survive many cycles without functional or structural fatigue. A component of the design process is the condition defining perfect interface compatibility between the austenite and martensite lattices (λ₂ = 1). In this paper, we evaluate the traditional mathematical theories of martensite under applied stresses, which distort the lattice compatibility through elastic strains. In NiTi we find that elastic distortions resulting from applied stresses influence the interface compatibility to a degree of impacting the material's functional abilities. Combining our results with empirical relationships connecting interface compatibility to transformation hysteresis we show that the model matches reasonably to a number of experimental results in the literature in which hysteresis changes under applied loads. We also apply these theories to a shape-memory ceramic (zirconia), which suggests a large orientation-dependence and asymmetric behavior in tension and compression. In both systems, we find that variant selection plays a large role in whether interface compatibility will improve or worsen under stress.