In this paper we describe an analytical methodology for calculating Stress Intensity Factors (SIF) on planar embedded cracks with an arbitrarily shaped front. The approach is based on a first order expansion of the celebrated integral of Oore-Burns and the actual shapes of three-dimensional planar flaws are analysed in terms of homotopy transformations of a reference disk. The solution is proposed in terms of Fourier series and the first order approximation of the coefficients is given independently from the homotopy transformations. The comparison with numerical results, taken from scientific literature, indicates that the proposed equation is very accurate when the flaw presents a small deviation from the circular shape. Finally, the closed form solution is used to predict the SIF of many types of convex and non-convex planar flaws present in engineering components such as welded structures or casting components.
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