Crack-tip singularity in damaged materials

Abstract

The effects of the preceding damage field on the stress singularity of a growing mode III crack are investigated from the view point of Continuum Damage Mechanics (CDM). By postulating a circular damage field at the crack-tip represented by a power law function r m of radius r , analytical solutions of asymptotic stress and strain fields were first obtained. It was found that the asymptotic stress field depends on the power law exponent m of the given damage distribution, and the well known elastic singularity disappears when the damage exponent m becomes larger than 3/4. However, the strain field was ascertained to be always singular regardless of the exponent m . Then, for more general damage distributions, numerical analyses by means of the finite element method were performed, and the effects of the geometry of three local damage fields on the stress distribution around the crack-tip were elucidated. It was shown that, though the damage field behind the crack-tip gives significant influence on the stress field in front of a growing crack, the analytical solution for the circular damage field gives essentially similar stress singularity as that for more general damage distribution. The re insights into some fundamental aspects of the local approach to fracture based on CDM.