Pinning and Depinning of Crack Fronts in Heterogeneous Materials

Abstract

The fatigue fracture surfaces of a metallic alloy and the stress corrosion fracture surfaces of a silicate glass are investigated as a function of crack velocity. It is shown that in both cases there are two self-affine fracture regimes. At large enough length scales, the universal roughness index $\ensuremath{\zeta}\ensuremath{\simeq}0.78$ is recovered. At smaller length scales, the roughness exponent is close to ${\ensuremath{\zeta}}_{c}\ensuremath{\simeq}0.50$. The crossover length ${\ensuremath{\xi}}_{c}$ separating these two regimes strongly depends on the material, and exhibits a power-law decrease with the measured crack velocity ${\ensuremath{\xi}}_{c}\ensuremath{\propto}{v}^{\ensuremath{-}\ensuremath{\varphi}}$, with $\ensuremath{\varphi}\ensuremath{\simeq}1$. The exponents $\ensuremath{\nu}$ and $\ensuremath{\beta}$ characterizing the dependence of ${\ensuremath{\xi}}_{c}$ and $v$ upon the pulling force are shown to be close to $\ensuremath{\nu}\ensuremath{\simeq}2$ and $\ensuremath{\beta}\ensuremath{\simeq}2$.