The most recent solutions of near crack line fields for mode III cracks

Abstract

The assumption of the small scale yielding theory that the elastic field is moved to some place along the crack line has been abandoned in this paper. In the plastic region, the particular solutions of the stress field and the displacement field which previous works adopted have not been taken but the general solutions of the near crack line plastic field have been obtained. By matching the plastic field with the precise elastic field (but not the elastic K-dominant field) at the elastic-plastic boundary, completely new and precise solutions of the near crack line field for a mode III stationary crack in an infinite body in an elastic-perfectly plastic material have been found, and through a reasonable assumption, analytical solutions for a mode III stationary crack in a finite body have also been obtained. The analyses of this paper are not confined by the small scale yielding conditions, and no assumptions are made. The solutions of this paper are therefore suitable not only under the condition that the plastic region is sufficiently small but also under the condition that the plastic region is relatively large.