Pinning and Depinning of Crack Fronts in Heterogeneous Materials

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 $\zeta \simeq 0.78$ is recovered. At smaller length scales, the roughness exponent is close to ${\zeta }_c\simeq 0.50$. The crossover length ${\xi }_c$ separating these two regimes strongly depends on the material, and exhibits a power-law decrease with the measured crack velocity ${\xi }_c\propto v^{-\phi }$, with $\phi \simeq 1$. The exponents $\nu$ and $\beta$ characterizing the dependence of ${\xi }_c$ and $v$ upon the pulling force are shown to be close to $\nu \simeq 2$ and $\beta \simeq 2$.