Stress intensity factors in three-dimensional planar cracks subjected to uniform tensile stress

In this paper we present a closed-form solution for mode I Stress Intensity Factors (SIF) in three-dimensional planar flaws based on homotopy transformations of a disk. The SIF is given for each point of the crack border under the hypothesis of an isolated crack under tensile loading. The solution is proposed in terms of the Fourier series and the first order approximation of the coefficients is given using the explicit form. The results indicate that the proposed equation is very accurate when the flaw is a small deviation from a circle. Our solution is used to predict the SIF of many types of planar flaws and the results are compared with numerical predictions taken from the literature.