Stress singularity at the corner point of 3-D surface crack under Mode II loading

Abstract

The point where the front of a 3-D crack intersects a free surface is called "corner point". The ordinary elastic crack tip stress singularity of γ λ is λ=-0.5. However, with regard to the stress singularity at the corner point there are several different theories. This paper concerns the detailed analysis of the stress singularity at the corner point for a through crack and a semi-circular crack under Mode II loading. According to the theories by Benthem and others, not only K II but also K III has a non- zero value at a corner point which, however, contradicts the stress-free boundary condition of the free surface. The FEM analysis of the present study based on the careful meshing and accurate determination of singularity (λ) answers this paradox on the corner point singularity. The answer is that, although the value of K III increases as the crack front approaches the corner point, the domain of non-zero value of K III decreases to an infinitesimal value and accordingly the influence of K III can be ignored at the corner point. Similarly, the domain of the singular stress field with λ≠-0.5 and λ=-0.6∼-0.5 also decreases as the crack front approaches the corner point. These conclusions should be considered when fracture criterion at a corner point under mixed-mode loadings is used.