The order of singularities and the stress intensity factors near corners of regular polygonal holes

Abstract

A new method was developed for the calculation of the order of singularity (SO) and the respective stress intensity factor (SIF) near corners of regular polygonal holes perforated in elastic plates submitted to an overall tension at infinity. For the solution of the problem the Muskhelishvili potential function ϑ(z) was determined for an infinite plate weakened by a respective regular polygonal hole with rounded-off corners under tension. For each rounded off corner a virtual singular point was defined inside the hole along the bisector of the angle of the apex and at a distance depending on the radius of curvature of the corner. Then, the stress concentration factors (SCF) at the apices of these rounded-off corners were evaluated when their respective radii of curvature tended to zero. The corresponding stress-singularity and the SIF were afterwards derived, by correlating the SCF and the distance of the virtual singular point for each corner. By conveniently selecting the number of terms of the series development of ϑ(z) the method can approach the real values for SO and SIF to any desired degree of accuracy. A comparison of the stress field around and near a corner of a polygonal hole in an infinite plate when this corner is submitted to mode-I deformation and a V-notch in an infinite plate under tension indicated the similarities between the two affine problems.