Energy release rates of crack kinking by boundary condition sensitivity analysis

The energy release rate, which is the total derivative of the energy with respect to crack length, is recognized as corresponding to the shape sensitivity analysis with the crack length change represented by the tangential component of design velocity. In this paper the sensitivity formula recently developed for a changing boundary condition has been further extended to cover crack kinking under mixed mode loading. Due to difficulty in defining the velocity field at the corner, the energy release rate at the onset of crack kinking is obtained by extrapolating the energy release rates for finite length kinked cracks. A rectangular plate with a single edge slant crack under uniform tension is taken as a numerical example. The multi-region technique in the numerical implementation of the boundary integral equation is adopted to consider the asymmetry of the problem. Excellent accuracy is observed as compared with reference analytic solutions.