Simple stress intensity factor expressions for surface cracks in smooth and notched round bars

Mode I stress intensity factors (SIFs), , of elliptical-arc surface cracks in metallic smooth and notched round bars are analysed. For such cracked structural components under elementary Mode I stress distributions acting on the crack faces, the SIF values have been computed in previous works by employing three-dimensional finite element analysis (FEA) models, with 20-node finite elements arranged around the crack front. In the present paper, simple expressions depending on the crack geometry parameters are determined by fitting the above numerical results. Several crack configurations have been examined in such FEAs in order to yield expressions of engineering interest. Then such simple expressions allow us to compute approximated values of SIF for complex Mode I stress distributions acting on the crack faces. As an example, the proposed procedure is applied to two residual stress distributions found in the literature. Finally, the crack propagation under cyclic tension together with residual stresses is analysed by employing SIF values obtained from both FEAs and the above simple expressions, respectively.