Based on an extension of the fiber bundle model we investigate numerically the motion of a crack front through a weak plane separating a soft and an infinitely stiff block. We find that there are two regimes. At large scales the motion is consistent with the pinned elastic line model and we find a roughness exponent equal to 0.39±0.04 characterizing it. At smaller scales, coalescence of holes dominates the motion, giving a roughness exponent consistent with 2/3, the gradient percolation value. The length of the crack front is fractal in this regime. Its fractal dimension is 1.77±0.02, consistent with the hull of percolation clusters, 7/4. This suggests that the crack front is described by two universality classes: on large scales, the pinned elastic line one and on small scales, the percolation universality class.

We study numerically the failure of an interface joining two elastic materials under load using a fiber bundle model connected to an elastic half space. We find that the breakdown process follows the equal load sharing fiber bundle model without any detectable spatial correlations between the positions of the failing fibers until localization sets in. Depending on the elastic constant describing the elastic half space, localization sets in before or after the critical load causing the interface to fail completely is reached. There is a crossover between failure due to localization and failure without spatial correlations when tuning the elastic constant, not a phase transition as has been proposed earlier. Also, contrary to earlier claims based on models different from ours, we find that a finite fraction of fibers must fail before the critical load is attained, even in the extreme localization regime, i.e., for very small elastic constant. We furthermore find that the critical load remains finite for all values of the elastic constant in the limit of an infinitely large system.

We investigate numerically the dynamics of crack propagation along a weak plane using a model consisting of fibers connecting a soft and a hard clamp. This bottom-up model has previously been shown to contain the competition of two crack propagation mechanisms: coalescence of damage with the front on small scales and pinned elastic line motion on large scales. We investigate the dynamical scaling properties of the model, both on small and large scale. The model results compare favorable with experimental results on stable crack propagation between sintered PMMA plates.

We compare experimental observations of a slow interfacial crack propagation along an heterogeneous interface to numerical simulations using a soft-clamped fiber bundle model. The model consists of a planar set of brittle fibers between a deformable elastic half-space and a rigid plate with a square root shape that imposes a non-linear displacement around the process zone. The non-linear square-root rigid shape combined with the long range elastic interactions is shown to provide more realistic displacement and stress fields around the crack tip in the process zone and thereby significantly improving the predictions of the model. Experiments and model are shown to share a similar self-affine roughening of the crack front both at small and large scales and a similar distribution of the local crack front velocity. Numerical predictions of the Family-Viscek scaling for both regimes are discussed together with the local velocity distribution of the fracture front.