Damage field and stress singularity of a mode III creep crack in steady-state growth

Abstract

The effects of a damage field on the stress singularity of a mode III creep crack in steady-state growth are discussed in the framework of continuum damage mechanics. The asymptotic stress field and damage field are analyzed by employing semi-inverse method. A damage field for steady-state crack growth represented by an undetermined power function r' of radius r from the crack tip is assumed first, and the corresponding asymptotic stress field of a mode III creep crack is analyzed by solving a two-point boundary value problem of non-linear differential equations of order two. Then, the exponent / of the undetermined damage field is determined so that the assumed damage field may be consistent with the damage evolution equation and the resulting asymptotic stress field. Finally, the effects of creep exponent n and the exponent m of the damage evolution equation on the stress singularity exponent P are elucidated. The effects of damage field on the stress and strain rate distribution around the crack are also discussed. It was elucidated that, in the case of cracks accompanied by damage, the stress singularity at the tip of a mode III crack is weaker than that of a mode I crack.