A Semi-Analytical Solution for the Stress Field and Stress Intensity Factor of Hole-Edge Cracks Using Improved Muskhelishvili Method

A semi-analytical solution is provided to obtain the stress intensity factors (SIFs) of hole-edge cracks with different configurations and the stress fields along the crack propagation direction in an infinite isotropic plane. The complicated solution procedure while using the Muskhelishvili method is improved by expanding an irrational mapping function into an approximate rational function so that singular integral equations could be converted to linear equations. The proposed method used to obtain the SIFs of symmetrical cracks emanating from circular or elliptical holes and a single crack emanating from a circular hole is compared with other methods in the literature. The results show that this method is universal and accurate for hole-edge cracks. In addition, the effects of the lengths of the asymmetrical cracks and the ratio of the semi-axes of the elliptical hole (a/b) on the SIFs are studied, which have not been previously reported.