Abstract
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.
Highlights
Predicting the remaining fatigue life of a round bar component containing a surface crack is a well-known engineering problem that is relevant to a vast range of different industries
This stress distribution can in the case of a straight bar under tension loading be reduced to a uniform tensile stress σz = σ0, or for a straight bar under bending load reduced to a linear bending stress σz = σ1(1 – 2y/ D)
The polynomial fits all have a coefficient of determination R2 of 0.9999 or higher, while their relative errors compared to the finite element analysis (FEA) results are no higher than 3.2%
Summary
Predicting the remaining fatigue life of a round bar component containing a surface crack is a well-known engineering problem that is relevant to a vast range of different industries. In order to model the growth of a semi-elliptical fatigue crack as a linear elastic fracture mechanics problem, the stress intensity factor (SIF) associated with the crack front must be evaluated. The evaluation of SIFs associated with almond shaped cracks in straight round bars under tension and bending loads is a subject that has been addressed in a number of publications [8,9,10,11,12]. A few of the various closed-form solutions found in literature do readily allow for SIFs to be evaluated at arbitrary crack front positions Solutions addressing both almond- and sickle shaped cracks in curved round bars appear to be hard to find. Effect of bar curvature on SIFs and some implications for fatigue cracks in a typical offshore mooring chain link are addressed
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