Mode I crack tip fields with incomplete crack tip plasticity in plane stress

The Mode I asymptotic crack tip stress field is developed for a plane stres s stationary crack in an elastic-perfectly plastic solid. The crack tip sec tor configuration consists of a centered fan ahead of the crack tip and an elastic sector in the angular range 39.126 degrees less than or equal to th eta less than or equal to 180 degrees. The angular distributions of the cra ck tip stress field are continuous and the corresponding asymptotic deforma tion field is kinematically admissible. This crack tip stress field is veri fied by comparison with a small-scale yielding finite element solution. It is inferred from the finite element results that the in-plane components of the asymptotic strain field are continuous at all angles around the crack tip. Closed form empirical expressions are obtained for the amplitude funct ions which measure the strengths of the 1/r strain singularity in the cente red fan. (C) 1999 Elsevier Science Ltd. All rights reserved.