Small scale yielding near a crack in plane strain: A finite element analysis

Abstract

This paper presents an incremental elastic-plastic finite element solution to the problem of small scale yielding near a crack in plane strain for a non-hardening material. Emphasis is placed on the design of finite elements which allow accurate reproduction, in a numerical solution, of the detailed structure of the near crack tip stress and strain fields, as understood from previous analytical studies of crack tip singularities. Numerical results are presented for: location of the elastic-plastic boundary, angular distribution of the strength of the strain singularity, crack tip opening displacement, stress distribution ahead of the crack, and angular variation of stresses at the tip. The latter results verify Rice's prediction of the Prandtl field in providing the limiting stress distribution as r → 0.