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 stress stationary crack in an elastic–perfectly plastic solid. The crack tip sector configuration consists of a centered fan ahead of the crack tip and an elastic sector in the angular range 39.126°≤θ≤180°. The angular distributions of the crack tip stress field are continuous and the corresponding asymptotic deformation field is kinematically admissible. This crack tip stress field is verified 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 functions which measure the strengths of the 1/r strain singularity in the centered fan.