First order Oore–Burns integral for nearly circular cracks under uniform tensile loading

In this paper, by means of the Oore–Burns weight function, we have obtained a general explicit equation for the Stress Intensity Factors (SIFs) of a nearly circular internal crack subjected to remotely uniform tensile stress. We have expanded the crack border in Fourier series and have derived an analytic solution for the SIF at any point on the front crack, in terms of the homotopic transformation of a disk. More precisely, we have given the first order approximation of the SIF in closed form. From a theoretical point of view, the proposed equation can only be used for a small deviation from the circle, however some tests on elliptical cracks have shown that the equation also works well for slender ellipses (up to a ratio of 0.4 between the two semi-axes). Finally, as an example, we have given a suitable explicit formula for SIF derived from general equations for triangular cracks and square-like cracks.