Asymptotic Stress Field of a Mode I Crack in a Nolinear-Hardening Damage Material.

Abstract

The effects of the local damage field on the asymptotic crack-tip stress field of a Mode I crack in a nonlinear-hardening material are discussed. Three kinds of the damage distribution 1-(D/Dcr)=h (θ) rm 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 relation by means of the effective stress concept of continuum damage mechanics. For a given strain hardening exponent n of the power hardening equation, the exponent p of the resulting asymptotic stress fields σu∝γp is found to be governed by the exponent m of the power-law damage distribution. When m increases, p is found to increase from a singular (negative) HRR exponent p=-1/(n+1) to a nonsingular (positive) value, which coincides with the previous analytical result for a Mode III crack in a linear elastic-damage material. A sufficient condition M>1/n for the nonsingular crack-tip stress is obtained for both plane stress and plane strain states. The effects of the strain hardening exponent n and the stress states on the p-m-n relation are discussed in some details. The damage effects on θ-distribution of the asymptotic stress fields are also discussed.