MATTER AND COMPLEXITY : Physics of geological processes : Fracture

Softening induced instability of a stretched cohesive granular layer.

O. Ramos, J.-C. Géminard and F. Vittoz.

H. Alarcon and F. Melo (USACH, Chile); L. Vanel (LPMCN, Lyon).

We report on a cellular pattern which spontaneously forms at the surface of a thin layer of a cohesive granular material submitted to in-plane stretching or outof-plane flexural deformation. We present a simple model in which the mechanism responsible of the instability is the "strain softening" exhibited by humid granular materials above a typical strain. Our analysis indicates that such type of instability should be observed in any system presenting a negative stress sensitivity to strain perturbations.

H. Alarcon, O. Ramos, L. Vanel, F. Vittoz, F. Melo and J.-C. Géminard., Phys. Rev. Lett. 105, (2010) 208001.
J.-C. Géminard, L. Champougny, P. Lidon and F. Melo, to appear in Phys. Rev. E.

Avalanches and clusters in planar crack front propagation

S. Santucci

Collaboration: L. Laurson, ISI, Torino (Italy) and S. Zapperi, CNR, Milano, (Italy).

We study avalanches in a model for a planar crack propagating in a disordered medium. Due to long-range interactions, avalanches are formed by a set of spatially disconnected local clusters, the sizes of which are distributed according to a power law with an exponent tau(a)=1.5. We derive a scaling relation tau(a)=2 tau-1 between the local cluster exponent tau(a) and the global avalanche exponent tau. For length scales longer than a crossover length proportional to the Larkin length, the aspect ratio of the local clusters scales with the roughness exponent of the line model. Our analysis provides an explanation for experimental results on planar crack avalanches in Plexiglas plates, but the results are applicable also to other systems with long-range interactions.

Laurson L, Santucci S, Zapperi S, Phys. Rev. E, 81 (4), 046116, 2010

Time-dependent rupture and slow crack growth: Elastic and viscoplastic dynamics

L. Vanel, S. Ciliberto, PP. Cortet, S. Santucci

We review some theoretical and experimental works describing the slow, thermally activated, growth of a crack in a solid material under stress. Theoretical approaches fall into two main classes: creep crack growth models and elastic trap models. On the one hand, creep crack growth models describe the visco-plastic flow of matter until some characteristic rupture strain is reached. This first category of models applies especially to the case of polymer rupture. On the other hand, elastic trap models assume that a rupture energy barrier is overcome by elastic stress fluctuations. While this second category of models is more restricted since it applies only to materials with brittle rupture features, it offers a framework that can be interestingly and importantly extended to the case of heterogeneous materials. Models will be discussed in the light of recent experimental works.

L. Vanel, S. Ciliberto, P. Cortet and S. Santucci, Time-dependent rupture and slow crack growth: Elastic and viscoplastic dynamics, J. Phys. D: Appl. Phys. 42 214007 (2009).

Quake Catalogs from an Optical Monitoring of an Interfacial Crack Propagation

S. Santucci

Collaboration: M. Grob, J. Schmittbuhl, R. Toussaint, L. Rivera, Institut de Physique du Globe de Strasbourg, and K. J. Måløy, Physics Dept, Oslo University, Norway

Using an experimental setup which allows to follow optically the propagation of an interfacial crack front in a heterogeneous medium, we show that the fracture front dynamics is governed by local and irregular avalanches with large velocity fluctuations. Events defined as high velocity bursts are ranked in catalogs with analogous characteristics to seismicity catalogs: time of occurrence, epicenter location and energy parameter (moment). Despite differences in the fracturing mode (opening for the experiments and shear rupture for earthquakes), in the acquisition mode and in the range of time scales, the distributions of moment and epicenter jumps in the experimental catalogs obey the same scaling laws with exponents similar to the corresponding distributions for earthquakes. The record-breaking event analysis also shows very strong similarities between experimental and real seismicity catalogs. The results suggest that the dynamics of crack propagation is controlled by the elastic interactions between microstructures within the material.

M. Grob, R. Toussaint, J. Schmittbuhl, L. Rivera, S. Santucci, K. J. Måløy, Pure appl. geophys. 166, 777 799 (2009).

Crackling dynamics in material failure as the signature of a self-organized dynamic phase transition

S. Santucci

Collaboration: D. Bonamy and L. Ponson, CEA Saclay.

We derive here a linear elastic stochastic description for slow crack growth in heterogeneous materials. This approach succeeds in reproducing quantitatively the intermittent crackling dynamics observed recently during the slow propagation of a crack along a weak heterogeneous plane of a transparent Plexiglas block [Phys. Rev. Lett. 96, 045501 (2006)]. In this description, the quasi-static failure of heterogeneous media appears as a self-organized critical phase transition. As such, it exhibits universal and to some extent predictable scaling laws, analogous to that of other systems such as, for example, magnetization noise in ferromagnets.

D. Bonamy, S. Santucci, L. Ponson, Phys. Rev. Lett. 101, 045501 (2008).