O-Integral evaluation for stress intensity factor of three-dimensional planar-crack with arbitrary shape

The numerical scheme of the O-integral is formulated for precisely evaluating the stress intensity factor of an embedded crack with arbitrary shape in an infinite elastic body. In this study, we evaluate the O-integral using an efficient numerical integration method by introducing an iso-parametric element and the Gauss-Legendre formula, which is typically used in the finite element method. To verify the numerical procedure introduced herein, the mode-I stress intensity factors for cracks are evaluated based on a circle, an ellipse, and a perturbated circle cracks. Result shows that the K results obtained using the proposed method are consistent with the exact solution. Therefore, fatigue crack propagation is successfully simulated using the O-integral for the elliptical crack.