Scaling and dynamics of an interfacial crack front

Pure and Applied Geophysics, 2003

The propagation of an interfacial crack through a weak plane of a transparent Plexiglas block is studied experimentally. The toughness is controlled artificially by a sand blasting procedure, and fluctuates locally in space like uncorrelated random noise. The block is fractured in mode I at low speed (10 À7 À 10 À4 m/s). The crack front is observed optically with a microscope and a high resolution digital camera. During the propagation, the front is pinned by micro-regions of high toughness and becomes rough. Roughness of the crack front is analyzed in terms of self-affinity. The in-plane roughness exponent is shown to be 0:63 AE 0:05. Experimental results are compared to a numerical model. The model reproduces the self-affine behavior of the crack front, i.e., long-range correlations of the roughness. Analogies between mode I and mode III are presented in order to discuss implications of the experimental results for creeping faults. Accordingly, correlations of the slip pattern are shown to exist over scales substantially larger than the asperity sizes.

Europhysics Letters (epl), 2010

Using a multi-resolution technique, we analyze large in-plane fracture fronts moving slowly between two sintered Plexiglas plates. We find that the roughness of the front exhibits two distinct regimes separated by a crossover length scale $\delta^*$. Below $\delta^*$, we observe a multi-affine regime and the measured roughness exponent $\zeta_{\parallel}^{-} = 0.60\pm 0.05$ is in agreement with the coalescence model. Above $\delta^*$, the fronts are mono-affine, characterized by a roughness exponent $\zeta_{\parallel}^{+} = 0.35\pm0.05$, consistent with the fluctuating line model. We relate the crossover length scale to fluctuations in fracture toughness and the stress intensity factor.

Physical Review Letters, 2006

The propagation of an interfacial crack along a heterogeneous weak plane of a transparent Plexiglas block is followed using a high resolution fast camera. We show that the fracture front dynamics is governed by local and irregular avalanches with very large size and velocity fluctuations. We characterize the intermittent dynamics observed, i.e., the local pinnings and depinnings of the crack front by measuring the local waiting time fluctuations along the crack front during its propagation. The deduced local front line velocity distribution exhibits a power law behavior, Pv / v ÿ with 2:55 0:15, for velocities v larger than the average front speed hvi. The burst size distribution is also a power law, PS / S ÿ with 1:7 0:1. Above a characteristic length scale of disorder L d 15 m, the avalanche clusters become anisotropic providing an estimate of the roughness exponent of the crack front line, H 0:66.

Journal of Computer-Aided Materials Design, 2007

The roughness of the crack front of an interfacial crack propagating along a weak plane in a heterogeneous disordered medium has been repeatedly studied both experimentally and numerically. For an interfacial toughness varying randomly on the interface, the front is self-affine. Quite often, however, the calculated roughness exponent differs from the experimental estimate. Several theoretical models have been employed up to now in the numerical simulations (elastic line depinning, random fuse and spring or beam models). In this paper we present finite element simulations (FEA) of the macroscopic mode-I static propagation of a crack front along a planar interface of an elastic or elastic-plastic coating adhered to a rigid substrate. The interfacial elements separate obeying a cohesive law, their toughness spatially fluctuating at random. The cohesive elements here employed allow for taking into account local I + II + III mixed-opening mode, i.e., allow for mode mixity at the local level. Our results indicate that for a given macroscopic toughness the crack front roughness is strongly sensitive to both the local cohesive law and the local fracture criterion.

Physica A: Statistical Mechanics and its Applications, 1999

We discuss the in uence of spatially correlated quenched noise on the wandering exponent of the crack-front line during slow in-plane crack propagation. For a uniform noise, the wandering exponent in the stastically stationary regime is = 0:35 ± 0:02, while the dynamic exponent is z = 0:75 ± 0:02. For short-range Gaussian correlations, the wandering exponent is shown to be = 0:50 ± 0:03 in the small uctuation limit and = 0:35 ± 0:02 in the large uctuation limit which can be shown to be consistent with the uniform case. In the case of long-range correlations, characterized by a self-a ne exponent t , the wandering exponent is shown to scale as = t + 1 for a wide range of t between −1:0 and +1:0. These results are discussed with reference to recent experiments of slow in-plane crack propagation between two annealed Plexiglas blocks. (J.-P. Vilotte) 0378-4371/99/$ -see front matter c 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 -4 3 7 1 ( 9 9 ) 0 0 1 5 5 -7

Europhysics Letters (EPL), 2006

The dynamics of planar crack fronts in heterogeneous media is studied using a recently proposed stochastic equation of motion that takes into account nonlinear effects. The analysis is carried for a moving front in the quasi-static regime using the Self Consistent Expansion. A continuous dynamical phase transition between a flat phase and a dynamically rough phase, with a roughness exponent ζ = 1/2, is found. The rough phase becomes possible due to the destabilization of the linear modes by the nonlinear terms. Taking into account the irreversibility of the crack propagation, we infer that the roughness exponent found in experiments might become history-dependent, and so our result gives a lower bound for ζ.

Physical Review Letters, 2011

We study the spatiotemporal dynamics of a crack front propagating at the interface between a rigid substrate and an elastomer. We first characterize the kinematics of the front when the substrate is homogeneous and find that the equation of motion is intrinsically nonlinear. We then pattern the substrate with a single defect. Steady profiles of the front are well described by a standard linear theory with nonlocal elasticity, except for large slopes of the front. In contrast, this theory seems to fail in dynamical situations, i.e., when the front relaxes to its steady shape, or when the front pinches off after detachment from a defect. More generally, these results may impact the current understanding of crack fronts in heterogeneous media.

2002

We show that the roughness exponent zeta of an in-plane crack front slowly propagating along a heterogeneous interface embeded in a elastic body, is in full agreement with a correlated percolation problem in a linear gradient. We obtain zeta=nu/(1+nu) where nu is the correlation length critical exponent. We develop an elastic brittle model based on both the 3D Green function in an elastic half-space and a discrete interface of brittle fibers and find numerically that nu=1.5, We conjecture it to be 3/2. This yields zeta=3/5. We also obtain by direct numerical simulations zeta=0.6 in excellent agreement with our prediction. This modelling is for the first time in close agreement with experimental observations.

Physical Review B, 1992

We report on experimental investigations of the propagation of cracks in the brittle plastic polymethyl methacrylate (PMMA). Velocity measurements with resolution an order of magnitude better than previous experiments reveal the existence of a critical velocity (330+30 m/s) at which the velocity of the crack tip begins to oscillate, the dynamics of the crack abruptly change, and a periodic pattern is formed on the crack surface. Beyond the critical point the amplitude of the oscillations depends linearly on the mean velocity of the crack. The existence of this instability may explain the failure of theoretical predictions of crack dynamics and provides a mechanism for the enhanced dissipation observed experimentally in the fracture of brittle materials.