Elastic–plastic problem for a circular hole plate with regard to crack initiation in elastic zone

Abstract

A plane elastic–plastic problem of stress distribution in a circular hole thin plate involving initiation and propagation of cracks in an elastic zone, is considered. It is assumed that the stress level is such that the circular hole is entirely enclosed by the plastic deformations zone. The plate material satisfies the Tresca–Saint Venant plasticity condition. It is supposed that cracks initiation and fracture of the plate material occur in the loading process in the elastic zone. Location and size of prefracture zone in the plate material are unknown in advance and are to be determined. The methods of theory of perturbations and theory of singular integral equations are used. As a crack appearance condition, we use the criterion of critical opening of prefracture zone faces. The interface of elastic and plastic deformations and also the location and sizes of crack initiation zones are found.