Peak stresses near narrow rectangular notches, with rounded corners, subjected to tensile and shear loading

Abstract

The finite element method is used to determine the peak stress for narrow rectangular notches, with rounded corners, for a range of notch width to corner radius ratios, under mode I, mode II, and mixed-mode loading conditions. It is shown that the specific geometry and loading conditions are unimportant and that the loading is conveniently characterized by the mode I and mode II stress-intensity factors for an equivalent crack. Superposition of peak stresses for mode I and mode II conditions allows the peak stress in a semi-circular notch to be obtained from simple equations describing the surface tangential stress distributions. A notch shape factor, which dependes only on the notch width to corner radius ratio and mode-mixity parameter, is then used to modify the peak stress values obtained for a semi-circular notch. The method provides a relatively cheap and efficient means of determining stress concentration factors for what can appear to be complex geometries and loading situations.