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

Abstract

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.

Soft-Clamp Fiber Bundle Model and Interfacial Crack Propagation: Comparison Using a Non-linear Imposed Displacement

“…Recently, Gjerden et al [23,24] presented for the first time roughness exponents compatible with both the large scale and small scale values found in the experiments. Their model was a development of the soft clamp fiber bundle model [25,26] first introduced by Batrouni et al [27].…”

“…In Gjerden et al [24], the dynamical exponent is κ − = 1.47 at small scales and κ + = 0.75 at large scale. Here we obtained κ − = 0.85 and κ + = 0.6 which are rather different.…”

“…On the contrary to Gjerden et al [24], the thresholds are uniformly spatially distributed between f t min and f t max , where we have set f t min = 0 and f t max = 1. The force, f i , experienced by each individual fiber is given by the Hooke's law:…”

“…We note in particular that κ was not measured directly by Gjerden et al [24], but rather inferred from assuming that the Family-Vicsek scaling assumption holds.…”

“…Their model was a development of the soft clamp fiber bundle model [25,26] first introduced by Batrouni et al [27]. Gjerden et al implemented this model with a linear spatial gradient in the threshold distribution thereby creating a crack front whose dynamics and morphology could be compared to the experimental observations [24].…”