On the Compatibility Between Elastically Distorted Austenite and Martensite in NiTi

The cubic B2 to monoclinic B19’ martensitic transformation in NiTi shape memory alloys proceeds by the nucleation and propagation of habit plane interfaces that remain undistorted and unrotated by the transformation. Due to incompatibility of austenite and martensite lattices in NiTi, the interfaces form between austenite and twinned martensite as described by Phenomenological Theory of Martensite Crystallography (PTMC). This have been assumed also for stress-induced martensitic transformation where, however, interfaces with single martensite variant have been frequently reported. On this account, we propose a different solution of strain compatibile habit planes by considering the effect of elastic deformation of both lattices due to external stress. Using modified PTMC theory, we evaluate the magnitudes and orientations of the critical uniaxial stress in tension and compression for which strain compatible habit plane interfaces with a single variant of martensite can form. The calculated stress is too high, but considering the pre-transformation softening of the C’ elastic constant for the {110}A⟨110⟩A austenite shear mode, the critical stress decreases down to 500 MPa. For such situation, we analyse orientation dependence and tension-compression asymmetry of required C’ softening, and the orientations of strain compatible habit planes that are compared with available experimental results. All calculations, including source code and interactive graphs, are available for download.