Damage Scaling Laws at Crack Tip in Disordered Materials

We investigate the damage mechanisms governing crack propagation in disordered solids using random lattice models. Our simulations reveal two successive damage scaling laws at the crack tip, characterized by the coefficient of variation of the critical damage density. Close to the crack tip, the scaling exponent is ∼-0.5, transitioning to ∼-0.25 at larger distances. This transition uncovers a crack-tip equiprobable damage zone (EDZ), whose size increases with material disorder. Within the EDZ, damage exhibits statistical uniformity and the critical damage density is well approximated by a binomial distribution, reflecting the intrinsic stochasticity of fracture in disordered materials. These findings provide new physical insights into crack-tip damage and demonstrate how material disorder regulates crack propagation.