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Article Dans Une Revue Physical Review Letters Année : 2006

Local waiting time fluctuations along a randomly pinned crack front

Résumé

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 ˆ 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 ˆ 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 ˆ 0:66. The physics community has recently paid a lot of attention to the study of damaging processes [1-3]. This interest is motivated not only by the practical benefits to many engineering domains, but also from a more fundamental point of view, by the diverse challenging questions brought forward, in particular, in statistical physics [4]. The role of heterogeneities during crack propagation is of central importance since they induce local pinnings of the crack front and subsequently trigger a very complex history of the fracture in the material. One of the consequences of this phenomenology is the roughness of fracture surfaces left by the crack. Indeed, cracks in heterogeneous media exhibit a self-affine morphology, with long range correlations. The associated roughness exponent was found to be very robust for different materials, over a broad range of length scales [5-11], and was further conjectured to be universal [7,8]. A recent work [2,12] suggests that the origin of these self-affine long range correlations comes from the elastic interactions within the damage zone and proposes a link between the roughness exponent and the critical exponent for the correlation length of the damage clusters. More generally, front propagation in random media has become a challenging problem related to the dynamics of interfaces in many different physical systems theoretically connected, such as crack fronts [11], magnetic domain walls [13], or wetting contact lines [14-16], where elasticity and disorder compete to shape the interface. In order to shed some light on the interactions between the crack front and material heterogeneities, a simplification to a two dimensional configuration-an interfacial crack-has been proposed both experimentally [17,18] and theoretically [12,19]. The interfacial configuration provides a higher resolution since all locations of the crack front belong to the same plane. Moreover, using a transparent material and a high resolution fast camera, the detailed complex crack dynamics can be captured, following the crack front with a high precision both in time and space [20]. So far experiments have been focused on the fracture front line morphology leading to the estimated roughness exponent ˆ 0:55 0:03 [17], followed up by a longer study showing ˆ 0:63 0:03 [18]. First attempts have been recently performed to analyze the interfacial crack front dynamics [20,21]. These studies have shown that the fracture front propagation is intermittent and can be described in terms of a Family-Vicsek scaling [22] with a roughness ˆ 0:6 and a dynamic exponent ˆ 1:2 0:2. In this Letter, we study a system first studied experimentally by Schmittbuhl and Måløy [17,20]. Whereas previous studies focused on the morphology of the inter-facial crack [17], we focus on the local crack dynamics, and on the distribution in both time and space of the waiting time during pinning events. To address this problem , we introduce a new analysis procedure in order to study the local waiting time fluctuations. The improved experimental techniques and resolution allow us to show that the dynamics of the fracture front is driven by local irregular avalanches with very large size and velocity fluctuations, and anisotropic shapes whose scaling is directly linked to the self-affine scaling of the crack front itself. This new set of experiments also confirms earlier results on such systems [17,20]. We describe here experiments where two Plexiglas plates are annealed together to create a single block with a weak interface [17]. The plates are of dimensions: 32 cm 14 cm 1 cm and 34 cm 12 cm 0:4 cm, and annealed together at 205 C under several bars of normal pressure. Before annealing, both plates are sand-blasted on one side with 50 m steel particles or 100 m glass beads. Sandblasting introduces a random topography which induces local toughness fluctuations during the an-nealing procedure. We have measured the profile of a sandblasted Plexiglas surface, using a white light interfer-ometry technique (performed at SINTEF-Oslo laboratory) and found that the local irregularities have a characteristic PRL 96,
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hal-00107346 , version 1 (29-10-2018)

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Knut Jørgen Måløy, Stephane Santucci, Jean Schmittbuhl, Renaud Toussaint. Local waiting time fluctuations along a randomly pinned crack front. Physical Review Letters, 2006, 96 (4), pp.045501. ⟨10.1103/PhysRevLett.96.045501⟩. ⟨hal-00107346⟩
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