Numerical Study of the Asymptotics of Material Damage in the Vicinity of a Crack Front during Creep

Abstract

This paper presents and discusses the results of finite element calculations of the continuity and stress fields (in a coupled formulation) near a creep crack front performed to determine the asymptotic distributions of stresses and continuity (damage) near the notch edge. The shape of the material damage region during creep growth ahead of the notch tip is determined for various values of material constants. An analysis of the radial stress distributions obtained in the finite element calculations shows that damage accumulation changes the asymptotic behavior of stresses near the crack tip in a power-law creeping material. It is shown that in the absence of damage accumulation, the numerical solution of the problem approaches the Hutchinson–Rice–Rosengren asymptotics, whereas accounting for damage accumulation affects the stress field near the notch or crack. The characteristic sizes of the regions of dominance of various asymptotics near the crack tip can be determined using finite-element radial distributions of stresses and continuity.