Multi-dimensional constitutive modeling of SMA during unstable pseudoelastic behavior

A multi-dimensional continuum-level constitutive model of shape memory alloys exhibiting pseudoelastic behavior has been developed in this paper. The current model is an extension of the one-dimensional model previously developed by the authors, which consists of a constitutive relation and a transformation evolution rule (kinetic relation). The constitutive relation is constructed based on the gradient of a transformation potential function (effective stress), and the kinetics of transformation are expressed based on a set of transformation surfaces in stress-temperature space. The constitutive relation allows for the reorientation of the transformation strain tensor according to the current state of stress. The model is used to simulate the localized deformation and transformation front propagation in NiTi strip under quasi-static extension. Special attention has been paid to the multi-axiality of the stress state at the transformation front during the forward and reverse transformations. It is shown that the ability of the model to consider the reorientation of the transformation strain tensor results in full recovery of transformation strain upon unloading, and a uniform distribution of stress in the transformed areas in spite of the localization of transformation. It also produces a stress gradient that dictates the direction of the transformation front propagation during both the forward and reverse transformations.