Three-dimensional fatigue crack propagation by means of first order SIF approximation

In this paper we make use of a closed-form solution for mode I Stress Intensity Factors (SIF) in three-dimensional planar flaws based on homotopy transformations of a disc. The utilised equations are very accurate when the flaw is a small deviation from a circle. Under the hypothesis of an isolated crack, the SIF at each point of the crack border is calculated to assess the crack shape after propagation. The solution is proposed in terms of the Fourier series and the crack growth rate equation is taken according to Paris' low. Many examples are proposed with the aim of predicting the final shape of different types of embedded planar flaws in butt welded joints under fatigue tensile loading.