Approximate Expressions for Three‐dimensional Notch Tip Stress Fields

The analytical solution of Sadowsky and Sternberg for the stress field around an biaxial elliptical cavity in an infinite elastic body was carefully examined. For uniaxial tension, it was found that the stress concentration factor varies very slowly along the equator of the cavity, regardless of the shape of the cavity. As was found for two dimensional notch problems, the normalized stress fields around cavities with different shapes are virtually identical within the stress concentration region and differ only slightly beyond that region. This fact permits simple, yet very accurate approximate stress equations to be developed for three dimensional notch problems by modifying the previously obtained solutions for two dimensional notch problems.