Exact solutions of near crack line fields for mode I crack under plane stress condition in an elastic-perfectly plastic solid

Abstract

The near crack line analysis method has been used in the present paper. The classical small scale yielding conditions have been completely abandoned in the analyses and one inappropriate matching condition used to be used at the elasticplastic boundary has been corrected. The reasonable solution of the plastic stresses near the crack line region has been established. By matching the plastic stresses with the exact elastic stresses at the elastic-plastic boundary, the plastic stresses, the length of the plastic zone and the unit normal vector of the elastic-plastic boundary near the crack line region have been obtained for a mode I crack under uniaxial tension, as well as a mode I crack under biaxial tension, which shows that for both conditions the plastic stress components σ_v and σ_2v, the length of the plastic zone and the unit normal vector of the elastic-plastic boundary are quite the same while the plastic stress σ_x is different.