A numerical procedure for interaction integrals developed for curved cracks of general shape in 3-D

This study presents a numerical procedure for the evaluation of interaction energy integrals used to extract mixed-mode stress intensity factors. The interaction energy integral is expressed as a domain integral, and the proposed numerical procedure delivers accurate results for three-dimensional cracks with curved crack fronts and curved crack surfaces for a rather general set of integration domains. It is clearly shown that, when the curvature of the crack surface becomes sufficiently large, special care must be taken in the evaluation of both the volume and the area integrals involved. To improve the accuracy in the evaluation of the former, a composite rule for the Gaussian quadrature scheme is employed. Four benchmark geometries with available analytical solutions are considered. Firstly, mesh design parameters for planar cracks with straight and curved crack fronts are established. Secondly, non-planar cracks with straight and curved crack fronts are employed to examine the accuracy of the numerical procedure.