Stresses near narrow rectangular notches, with rounded corners, in beams in bending

Abstract

The results of finite element calculations have been used to show that an analytical solution for the stresses in the vicinity of crack-like notches with elliptical and hyperbolic shaped ends gives accurate results for narrow, semi-circular ended notches. It is also shown that the peak stresses can be obtained from the stress intensity factor for an equivalent crack and the notch tip radius. Finite element solutions for narrow, rectangular notches with rounded corners, have also been used to show that the peak stresses in such notches can be obtained by using a notch shape factor to modify the peak stress values for semi-circular notches. The shape factor depends only on the notch width to corner radius ratio.