The effect of crack shape on the fatigue limit of three-dimensional stress concentrations

Methods of fatigue analysis for notches and other stress-concentration features are generally developed using specimens with simple two-dimensional geometries. It has been demonstrated in a previous publication [Bellett D, Taylor D, Marco S, Mazzeo E, Guillois J, Pircher T. The fatigue behaviour of three-dimensional stress concentrations. Int J Fatigue 2005; 27: 207–221], that large errors arise when these methods are applied to certain types of three-dimensional stress concentrations. In particular, it was shown that very localised stress concentrations, which are characterised by high stress gradients in all directions, give rise to very conservative fatigue-limit predictions when using standard assessment methods. We hypothesised that the reason for this error might lie in the shape of the crack which developed from the notch. In 2D, the crack growing from the root of a sharp notch tends to extend through the thickness of the specimen, whereas in 3D, cracks develop various semi-elliptical shapes. This can affect the fatigue limit, due to the existence of non-propagating cracks. Using this idea, a method was developed to predict how crack shape would affect fatigue limit in notched specimens of four different types. We were able to successfully predict which specimens would give rise to prediction errors, and which would not. Correction factors derived from this approach served to reduce the prediction errors, but not to completely eliminate them.