Asymptotic crack tip stress, rotation pseudo-stress and dislocation fields for mixed mode I and II cracks in elastic perfectly plastic solids

Abstract

Nemat-Nasser and Obata (Mech. Mater. 3 (1984) 235) have pointed out that asymptotic stress fields can be constructed around the tip of a general mixed mode I and II crack in elastic perfectly plastic solids with use of elastic sectors whose stress magnitude is below the yield stress. When elastic sectors which are below the yield stress exist the rotation pseudo-stress within an elastic sector is logarithmic singular with distance r from the crack tip. It must also be logarithmic singular within a plastic fan sector that is adjacent to an elastic sector. The areal dislocation density field within a plastic fan adjacent is, therefore, singular as ( r 0/ r)ln( r 0/ r). To justify the existence of below yield stress elastic sectors it is necessary to show that the logarithmic singular stress field produced by the crack plane surface dislocation distribution is canceled by another logarithmic singular stress field produced by the areal dislocation distributions within the fan plastic sectors. This is done so explicitly in this paper.