Unified scenario for the morphology of crack paths in two-dimensional disordered solids

A combined experimental and numerical investigation of the roughness of intergranular cracks in two-dimensional disordered solids is presented. We focus on brittle materials for which the characteristic length scale of damage is much smaller than the grain size. Surprisingly, brittle cracks do not follow a persistent path with a roughness exponent $\ensuremath{\zeta}\ensuremath{\approx}0.6--0.7$ as reported for a large range of materials. Instead, we show that they exhibit monoaffine scaling properties characterized by a roughness exponent $\ensuremath{\zeta}=0.50\ifmmode\pm\else\textpm\fi{}0.05$, which we explain theoretically from linear elastic fracture mechanics. Our findings support the description of the roughening process in two-dimensional brittle disordered solids by a random walk. Furthermore, they shed light on the failure mechanism at the origin of the persistent behavior with $\ensuremath{\zeta}\ensuremath{\approx}0.6--0.7$ observed for fractures in other materials, suggesting a unified scenario for the geometry of crack paths in two-dimensional disordered solids.