Crack tip plastic zone shape for anisotropic material subjected to mode -I loading

Abstract

This paper discusses the effect of anisotropy in terms of anisotropy ratio on ductile materials subjected to mode-I type of loading. Thin plate with plane stress condition is considered for this work. σ3 is taken as zero. For considering the effect of Poisson’s ratio, σ3 = ν (σ1 + σ2) is considered. Isotropic plane strain and anisotropic plane stress condition is considered to develop mathematical relations for stress triaxiality and plastic zone around the crack tip by using Hill – von Mises’s yield criterion. The effect of poisons ratio, anisotropy ratio and stress triaxiality is shown on the size of plastic zone around the crack tip. The results were generated and are compared in the form of polar plot for plane strain condition at different Poisson’s ratio. In addition to this, the effect of anisotropy ratio on stress triaxiality is also investigated. It was observed that increase in Poisson’s ratio causes significant reduction in the size of plastic zone around the crack tip. The increase in anisotropy ratio also shows the same trend, especially for its higher values. It is observed that anisotropy plane stress problem of fracture is almost equivalent to isotropic fracture in plane strain condition.