Stress intensity factors for elliptical surface cracks in round bars with different stress concentration coefficient

Stress intensity factors (SIFs) of elliptical surface cracks in notched tensile round bars are calculated by using three-dimensional finite element analysis (FEA) models with singular 20-node elements arranged around the crack tip. Systematic analyses are performed for semi-circular type, V-type and U-type annular notches with theoretical stress concentration coefficient K_t ranging from 1-5. It is shown that the SIFs are strongly dependent on K_t, and the influence of notch geometry is negligibly weak for a given stress concentration coefficients in the analyzed range. An empirical expression for the SIF as a function of crack geometry and K_t is then obtained by fitting the numerical results. Comparison of present results with available numerical results in the literature shows good agreement. Application of the empirical expression to a screw bolt yields good coincidence with experimental results of SIFs by using a modified James-Anderson method. Therefore, the empirical expression of SIFs can be used conveniently in integrity assessment of various notched bars, at least in the analyzed range in this paper.