Investigations on critical anisotropic triaxiality at the crack tip under mixed-mode (I plus II) fracture

In this analytical study, anisotropic triaxiality, at the yield loci of the crack tip under mixed-mode (I + II) loading, has been modeled. According to the well-known M-criterion the crack of any orientation from the loading axis, initiates at a polar angle at which criticality of triaxiality occurs. Thus, the critical values of triaxiality have been obtained by statistically evaluating the proposed model for various crack inclinations. The combination of six anisotropic constants classifies the five different yield conditions, which are useful in various alloys. Hill's generalized anisotropic yield equation generates these yield conditions. The assumption of limited plastic deformation at the crack tip has been the basis of analysis. In particular, the principle of linear elastic fracture mechanics (considering small-scale yielding) holds well. Plastic zone shapes at the crack tip for various crack inclinations are plotted to supplement the results obtained from critical values of triaxiality. For both, plane stress and plane strain conditions, the analysis reveals the regions of the degree of anisotropy for particular Lankford's coefficient and vice versa where the crack initiation angles show variations.