Analytical method for determining the elastoplastic interface of a circular hole subjected to biaxial tension-compression loads

Abstract

Based on the Tresca yield criterion, an analytical method is proposed to determine the elastoplastic interface around a circular hole in an infinite plate subjected to biaxial tension-compression loads at infinity. Comparing with the plastic region formed under the action of biaxial tension-tension or biaxial compression- compression loads, the characteristic of the plastic regions is that they cannot completely surround the hole and there may be two or four nonintersecting plastic regions around the hole. In both cases, the conformal mapping is employed to map the elastic region in the physical plane onto the outer region of a unit circle in the image plane, which transforms this kind of plane elastoplastic problem into a problem of mapping. According to the stress continuity conditions on the elastoplastic interface and the stress boundary conditions on the elastic part of the circular hole, a set of nonlinear equations containing the mapping function coefficients is established. The problem can be further transformed into an optimization problem determined by the differential-evolution algorithm. The correctness of the presented method is verified by numerical method. The influence of loads and material constant on the size and shape of the plastic regions is discussed in detail.