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 [K. J. Måløy et al., Phys. Rev. Lett. 96, 045501 (2006)10.1103/PhysRevLett.96.045501]. In this description, the quasistatic 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.

We report in situ atomic force microscopy experiments which reveal the presence of nanoscale damage cavities ahead of a stress-corrosion crack tip in glass. Their presence might explain the departure from linear elasticity observed in the vicinity of a crack tip in glass. Such a ductile fracture mechanism, widely observed in the case of metallic materials at the micrometer scale, might be also at the origin of the striking similarity of the morphologies of fracture surfaces of glass and metallic alloys at different length scales.

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We investigate the scaling properties of postmortem fracture surfaces in silica glass and glassy ceramics. In both cases, the 2D height-height correlation function is found to obey Family-Viseck scaling properties, but with two sets of critical exponents, in particular, a roughness exponent zeta approximately 0.75 in homogeneous glass and zeta approximately 0.4 in glassy ceramics. The ranges of length scales over which these two scalings are observed are shown to be below and above the size of the process zone, respectively. A model derived from linear elastic fracture mechanics in the quasistatic approximation succeeds to reproduce the scaling exponents observed in glassy ceramics. The critical exponents observed in homogeneous glass are conjectured to reflect the damage screening occurring for length scales below the size of the process zone.

The self-affine properties of postmortem fracture surfaces in silica glass and aluminum alloy were investigated through the 2D height-height correlation function. They are observed to exhibit anisotropy. The roughness, dynamic, and growth exponents are determined and shown to be the same for the two materials, irrespective of the crack velocity. These exponents are conjectured to be universal.

International audienceDepth averaged conservation equations are written for granular surface flows. Their application to the study of steady surface flows in a rotating drum allows to find experimentally the constitutive relations needed to close these equations from measurements of the velocity profile in the flowing layer at the center of the drum and from the flowing layer thickness and the static/flowing boundary profiles. The velocity varies linearly with depth, with a gradient independent of both the flowing layer thickness and the static/flowing boundary local slope. The first two closure relations relating the flow rate and the momentum flux to the flowing layer thickness and the slope are then deduced. Measurements of the profile of the flowing layer thickness and the static/flowing boundary in the whole drum explicitly give the last relation concerning the force acting on the flowing layer. Finally, these closure relations are compared to existing continuous models of surface flows

Stress enhancement in the vicinity of brittle cracks makes the macro-scale failure properties extremely sensitive to the micro-scale material disorder. Therefore: (i) Fracturing systems often display a jerky dynamics, socalled crackling noise, with seemingly random sudden energy release spanning over a broad range of scales, reminiscent of earthquakes; (ii) Fracture surfaces exhibit roughness at scales much larger than that of material micro-structure.Here, I provide a critical review of experiments and simulations performed in this context, highlighting the existence of universal scaling features, independent of both the material and the loading conditions, reminiscent of critical phenomena. I finally discuss recent stochastic descriptions of crack growth in brittle disordered media that seem to capture qualitatively -and sometimes quantitatively -these scaling features.Submitted to: J. Phys. D: Appl. Phys. arXiv:0907.3353v2 [cond-mat.stat-mech]

Dynamic fracture experiments were performed in PMMA over a wide range of velocities and reveal that the fracture energy exhibits an abrupt 3-folds increase from its value at crack initiation at a well-defined critical velocity, below the one associated to the onset of micro-branching instability. This transition is associated with the appearance of conics patterns on fracture surfaces that, in many materials, are the signature of damage spreading through the nucleation and growth of microcracks. A simple model allows to relate both the energetic and fractographic measurements. These results suggest that dynamic fracture at low velocities in amorphous materials is controlled by the brittle/quasi-brittle transition studied here.PACS numbers: 46.50.+a, 62.20.M-, 61.43.-j Dynamic fracture drives catastrophic material failures. Over the last century, a coherent theoretical framework, the so-called Linear Elastic Fracture Mechanics (LEFM) has developed and provides a quantitative description of the motion of a single smooth crack in a linear elastic material [1]. LEFM assumes that all the mechanical energy released during fracturing is dissipated at the crack tip. Defining the fracture energy Γ as the energy needed to create two crack surfaces of a unit area, the instantaneous crack growth velocity v is then selected by the balance between the energy flux and the dissipation rate Γv. This yields [1]:where c R and E are the Rayleigh wave speed and the Young modulus of the material, respectively, and K(c) is the Stress Intensity Factor (SIF) for a quasi-static crack of length c. K depends only on the applied loading and specimen geometry, and characterizes entirely the stress field in the vicinity of the crack front. Equation (1) describes quantitatively the experimental results for dynamic brittle fracture at slow crack velocities [2]. However, large discrepancies are observed in brittle amorphous materials at high velocities [3][4][5][6]. In particular (i) the measured maximum crack speeds lie in the range 0.5 − 0.6c R , i.e. far smaller than the limiting speed c R predicted by Eq. (1) and (ii) fracture surfaces become rough at high velocities (see [3,4] for reviews). It has been argued [7] that experiments start to depart from theory above a critical v b ≃ 0.4c R associated to the onset of micro-branching instabilities [8]: for v > v b the crack motion becomes a multi-cracks state. This translates into (i) a dramatic increase of the fracture energy Γ at v b , due to the increasing number of micro-branches propagating simultaneously and (ii) a non-univocal relation between Γ and v [7]. The micro-branching instability hence yielded many recent theoretical efforts [9]. However, a number of puzzling observations remain at smaller velocities. In particular, even for velocities much lower than v b , (i) the measured dynamic fracture energy is generally much higher than that at crack initiation [7,[10][11][12] and (ii) fracture surfaces roughen over length scales much larger than the microstructure scale ("mist" patterns...