Local dynamics of a randomly pinned crack front during creep and forced propagation: An experimental study

Abstract

We have studied the propagation of a crack front along the heterogeneous weak plane of a transparent PMMA block using two different loading conditions: imposed constant velocity and creep relaxation. We have focused on the intermittent local dynamics of the fracture front, for a wide range of average crack front propagation velocities spanning over four decades. We computed the local velocity fluctuations along the fracture front. Two regimes are emphasized: a de-pinning regime of high velocity clusters defined as avalanches and a pinning regime of very low velocity creeping lines. The scaling properties of the avalanches and pinning lines (size and spatial extent) are found to be independent of the loading conditions and of the average crack front velocity. The distribution of local fluctuations of the crack front velocity are related to the observed avalanche size distribution. Space-time correlations of the local velocities show a simple diffusion growth behaviour.

Bursts of activity in collective cell migration

“…The exponent τ of the power-law distribution appears to be similar for different cell types: the fitted values (SI Appendix, Table S1) are all similar within error bars (τ ' 1.4 − 1.6) and remarkably close to the values recorded in crack-front propagation (20). As observed in moving crack fronts, the cluster distributions, and in particular the cutoff to the power-law decay, depend on the threshold c used to identify the activity (Materials and Methods and SI Appendix, Fig.…”

“…The maps reported in Fig. 1 vividly illustrate the formation of localized clusters of activity similar to those found in fracture (20) and imbibition (21). The corresponding distributions of cluster areas are reported in Fig.…”

“…The fronts show a rough structure with localized bursts of activity that is reminiscent of elastic lines moving in a pinning landscape (19)(20)(21)(22). Spatiotemporal velocity fluctuations in moving fronts can be effectively quantified by constructing activity maps, as done previously for moving crack fronts (20) and fluid imbibition through porous media (21). As discussed in Materials and Methods, from each time-lapse movie we construct a spatial map v f (x,y) measuring the velocity of the front at position (x,y) (SI Appendix, Fig.…”

“…When the front locally moves backward, we average all of the velocity values at that point. To define areas of correlated activity, we consider the spatial map of the local front velocities v f ðx, hðx, tÞÞ and define avalanches as clusters of velocities larger than an arbitrary threshold (20,21): v f ðx, hðx, tÞÞ ≥ cAEv f ae, where AEv f ae is the mean front velocity during the experiment (SI Appendix, Fig. S1C).…”

“…Hence the dynamics of an invading cell sheet is ruled by a combination of long-range internal stresses and interactions with the substrate, suggesting an analogy with driven elastic systems moving in a disordered medium such as cracks lines (19,20), imbibition fronts (21), or ferromagnetic domain walls (22). The scaling laws in these systems are usually associated with a depinning critical point that has been widely studied by simple models for interface dynamics.…”