Modeling the stress-induced transformation behavior of shape memory alloy single crystals

The phenomenological theory of martensite crystallography has been used to determine habit plane/shear direction combinations for stress-induced transformation of NiTi, Cu-Ni-Al and NiAl shape memory alloys (SMA) to twin-related martensite correspondence variant pairs. By considering the habit plane/shear direction combinations as unidirectional shear systems, generalized Schmid's law is then used to predict the mechanical response of unconstrained single crystals of each SMA. Model results include axial transformation strain, and plane stress transformation surfaces as a function of crystal orientation. Comparison of the predicted mechanical response results with the habit plane/shear direction combinations reveals a link between the anisotropy and asymmetry of the mechanical response of SMA single crystals, and the crystallography of the martensitic transformation.