Evaluation of transformation region around crack tip in shape memory alloys

When an edge cracked shape memory alloy (SMA) plate is loaded, phase transformation around the crack tip results in a non-homogeneous region composed of austenite and martensite phases that affects its fracture behavior. In this work, the size of the phase transformation region surrounding the tip of an edge crack in a thin SMA plate is calculated analytically using a transformation function that governs forward phase transformation, together with crack tip asymptotic stress equations. Stress intensity factors required in the asymptotic equations are obtained from a least squares fit of full displacement field, calculated using finite elements, to asymptotic near-tip opening displacement equation. The present work predicts the size and shape of the transformation region in closed form. For comparison purposes, the region is also calculated using ABAQUS with user defined material subroutines (UMAT) for plane strain and plane stress. Transformation regions calculated analytically and computationally are plotted with experimental, analytical and numerical results available in the literature; the results show a good agreement with the experimental results.