Three-dimensional stress constraint in an elastic plate with a notch

Abstract

This paper presents analytical solutions for the three-dimensional stress distribution around typical stress concentrators in an isotropic plate of arbitrary thickness. Based on the assumption of a generalised plane-strain theory, which assumes that the through-the-thickness extensional strain is uniform in the thickness direction, an exact three-dimensional solution has been obtained for an annulus subjected to arbitrary loading along its edges. Emphasis has been placed on the through-the-thickness stress constraint, which is a pre-requisite to analysing the effect of plate thickness on the elastic–plastic deformation at a notch root. Important results are presented on the effects of the plate thickness and Poisson's ratio on the in-plane stress concentration factor and the out-of-plane stress constraint factor. By extending the theoretical method to a plate with a non-circular notch, an approximate solution has been obtained for the through-the-thickness constraint factor in a plate with a V-shaped notch having a circular tip. The present solutions have been shown to correlate well with numerical results obtained using the finite element method.