Ductile crack analysis by a cohesive damage zone model

Abstract

A cohesive damage zone model of the Dugdale-Barenblatt type is presented to explore the effects of microscopic damage on a macroscopic crack in ductile materials. A semi-infinite macrocrack in a power-law plastic material under antiplane shear (mode III) is considered. The microscopic damage is assumed to occur in the form of dispersed microcracks which are localized into a narrow strip directly ahead of a macrocrack tip. By using the analytical result of the J-integral for a periodic array of collincar cracks in a power-law solid and by applying a homogenization technique, the effective mechanical property of the damage zone is obtained. Then, the effect of damage on the fracture initiation toughness is analyzed. Under the small-scale damage condition and by the use of an approximate and constant average shear stress within the damage zone, the size of the damage zone at the initiation of macrocrack growth is estimated. For small-scale damage and small-scale yielding, a nonlinear first order differential equation for the crack resistance curve is derived, where the hypothesis of constant crack tip opening angle (CTOA) during the stable crack growth is adopted. Numerical results are presented and discussed to reveal the effects of microscopic damage on the resistance and tearing modulus of a macrocrack.