Mode I stress intensity factors for semi-elliptical fatigue cracks in curved round bars

Some cyclically loaded components such as mooring chains can develop fatigue cracks in locations where the shape of the part is equivalent to that of a curved or bent round bar. Here we consider a semi-elliptical crack growing from the surface of a curved round bar. This geometry can for example represent a chain link segment with a crack located at its inner-or outer radius. The surface crack can be either almond shaped, sickle shaped or straight-fronted. Stress intensity factors (SIFs) over the fronts of such crack geometries are in the present work investigated for several elementary mode I stress distributions. Finite element analysis and linear elastic fracture mechanics methods are used to develop semi-analytical solutions for the SIF at any point on the crack front. Effects of relative bar curvature on numerical results are demonstrated. Relative to otherwise identical cracks in straight bars, SIFs for cracks in the curved bars considered here are found to differ by up to 8%. With an offshore mooring chain model as a case example, the estimation of SIFs for cracks in a complex residual stress field is furthermore demonstrated using a cubic polynomial stress approximation.