Asymptotic stress field of a mode III crack in a nonlinear-hardening damage material or in a creep damage material

Abstract

The effects of local damage fields on the asymptotic stress field of a Mode III crack in a nonlinear -hardening material or in a creep material are discussed. Two kinds of the damage distribution 1-D = li(0)(r/r)M represented by a power function of radius r from the crack-tip are postulated for the damage variable D, and the damage effects are included into the power-hardening law or the Norton creep law by means of the effective stress concept of continuum damage mechanics. For a given strain hardening exponent n of the power-hardening law or of the Norton creep law, the exponent ρ of the resulting asymptotic stress fields ́̈αrp is found to be governed by the exponent m of the power-law damage distribution. It is elucidated that when the exponent of damage distribution m increases, the exponent p of the stress field increase from a singular (negative) HRR exponent p= -1/(n+1) to a nonsingular (positive) value.