Avalanches and clusters in planar crack front propagation

Abstract

We study avalanches in a model for a planar crack propagating in a disordered medium. Due to long-range interactions, avalanches are formed by a set of spatially disconnected local clusters, the sizes of which are distributed according to a power law with an exponent tau{a}=1.5. We derive a scaling relation tau{a}=2tau-1 between the local cluster exponent tau{a} and the global avalanche exponent tau . For length scales longer than a crossover length proportional to the Larkin length, the aspect ratio of the local clusters scales with the roughness exponent of the line model. Our analysis provides an explanation for experimental results on planar crack avalanches in Plexiglas plates, but the results are applicable also to other systems with long-range interactions.

Experimental study of stable imbibition displacements in a model open fracture. II. Scale-dependent avalanche dynamics

“…Interestingly, Laurson, Santucci, and Zapperi [35] could obtain a theoretical relation linking the scaling behavior of the clusters of local high velocity and the global avalanche dynamics of an interfacial crack front. However, such a relation cannot be used for the imbibition process studied here.…”

Quantitative Prediction of Effective Toughness at Random Heterogeneous Interfaces

“…While the macroscopic effective toughness is given by the mean local toughness in case of weak pinning, a systematic toughness enhancement is observed for strong pinning (the critical point of the depinning transition). A selfconsistent approximation is shown to account very accurately for this evolution, without any free parameter.Introduction -While physicists studied the scaling properties of crack [1,2] and developed an analogy between crack front propagation and the dynamical phase transition associated with the pinning/depinning of an elastic line driven through a random potential [3][4][5][6][7][8][9][10][11][12], a parallel (and independent) effort was made by mechanical engineers studying crack trapping by tough particles [13][14][15] or the effect of crack front deflection on the stress intensity factors (see e.g. [16] for a recent review).…”

“…This justifies a first order perturbative expansion around K c . The equation of evolution of the crack front thus writes [7,11,13]:…”

Role of the sample thickness in planar crack propagation

“…This is reflected also in the avalanche behavior that in the stable propagation regime follows the predictions of the interface depinning model [15,16]. Besides the theoretical implications, understanding the role of thickness in planar cracks could be interesting in view of applications for the delamination of coatings [20].…”

“…This case appears to be the ideal candidate to test the theory that envisages the crack as a line moving through a disordered medium [10,11]. For planar cracks, the problem can be mapped into a model for interface depinning with long-range forces [12][13][14][15][16][17], implying a self-affine front with a roughness exponent close to ζ = 1/3 [18,19] and avalanche propagation of the front between pinned configurations with scaling exponents predicted by the theory [14][15][16]. Such results are also of importance for applications such as the failure of the interface between a substrate and a coating, or an adhesive layer, and the propagation of indentation cracks [20].…”