Fingering in highly heterogeneous brittle interfaces

We track, by a perturbation approach, the planar propagation of a tensile circular crack pinned by a brittle periodic array of defects. We obtain two distinct propagation regimes depending on the obstacle strength: A weak pinning regime where the crack maintains a stationary equilibrium shape and a fingering regime, characterized by the continuous growth of fingers, while other part remains trapped. Correlatively, the evolution of the macroscopic fracture properties is found to be discontinuous: while the effective properties remain close to the material average values in the weak pinning regime, they dramatically drop to the weakest value in the fingering regime.