A tensile crack in creeping solids with large damage near the crack tip

Abstract

An asymptotic analysis of stationary mode I crack in creeping solids with large damage near crack tip is conducted. To consider the damage effect, Kachanov damage evolution law is utilized and incorporated into the power-law creep constitutive equation. With the compatibility equation, a nonlinear eigenvalue problem which can be solved by numerical approaches is established. From this result, the distribution of stress and strain rate are obtained with the coupling effect of damage and creep under plane stress condition. Also the influence of material parameters on the stress is examined. According to the result, it is shown that the creep exponent n and damage parameter eta(= mu/(l + k)) have a significant effect on determining the eigenvalue s and angular distribution of stress and strain rate near the crack tip. The creep exponent n plays the role to soften and damage parameter eta plays the role to harden the material near the crack tip. The stress and strain rate show quite different behavior from those of HRR problem.