Determination of elastic T-stress along three-dimensional crack fronts using an interaction integral

Abstract

We introduce an effective computational method, based on an interaction integral, to evaluate elastic T-stress along three-dimensional crack fronts. Using this technique, T-stress distributions of various three-dimensional geometries are determined from finite element calculations. The computed results show that the through-thickness variation of T-stress along the crack front of edge-cracked plates is relatively small under both tension and bending load conditions. The deviation from the corresponding two-dimensional results increases with increasing relative crack length and with decreasing relative plate thickness. The increase in T-stress with decreasing thickness results from the inherent positive biaxiality of thin elastic plates. Furthermore, the value of three-dimensionally computed T-stress in these through-crack geometries increases with increasing Poisson's ratio. The T-stress distribution is also calculated along the curved crack front of a surface-flawed plate. For the particular geometry considered, the maximum T-stress along the crack front is located at the mid-point of the crack front, and there is a greater variation of T-stress along the crack front under bending loads than in tension.