Generalization of Galin's problem to frictional materials and discontinuous stress fields

Abstract

An analytical solution for the determination of the form of the plastic zone in the vicinity of a circular hole in inhomogeneous stress fields is discussed. Already in 1946 Galin arrived at a solution to a related problem of an infinite plate with a circular aperture in stretching and bending. Around the aperture, the material behaves perfectly plastically, obeying Tresca's yield criterion. However, in Galin's solution the explicit condition for the general balance of forces in bending has been omitted. This paper presents a correction to Galin's error by means of a modified analytical approach. An extension of the problem, by applying Coulomb's yield criterion in the plastic zone and assuming continuous or discontinuous stress distributions at the elastoplastic interface is also considered. The results are illustrated by some numerical examples and supplemented by an experiment.