Universality Classes in Constrained Crack Growth

Abstract

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.

Local dynamics of a randomly pinned crack front: a numerical study

“…We study in this paper the crackling dynamics in the fiber bundle model [20][21][22]. We find quantitative consistency with the experimental measurements.…”

“…In Gjerden et al [22], we presented evidence for two scaling regimes in the model we study here. For small values of the scaled elastic constant e-or equivalently large length scales-we found a roughness exponent ζ + = 0.39 ± 0.04, which is consistent with the flucutating line model.…”

“…Section 3.1 continues the analysis from Gjerden et al [22] of the roughness of the crack front. In Gjerden et al [22], we measured the roughness locally using the average wavelet coefficient method [26,27].…”

“…Section 3.1 continues the analysis from Gjerden et al [22] of the roughness of the crack front. In Gjerden et al [22], we measured the roughness locally using the average wavelet coefficient method [26,27]. Here we base our analysis on the variance of the front, again finding two regimes: a small-scale regime consistent with ordinary gradient percolation and a large-scale regime consistent with the fluctuating line model.…”

“…By refining the model proposed by Batrouni et al [20] and Gjerden et al [21], consisting of fibers clamped between a hard and a soft block and with a gradient in the breaking thresholds, we have identified two scaling regimes for the roughness of the advancing crack front [22]. On large scales we recover the roughness seen in the reanalysis of experimental data by Santucci et al [8], ζ + = 0.39 ± 0.04, consistent with the fluctuating line model.…”