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...
Brittle fractures of inhomogeneous materials like rocks, concrete, or ceramics are of two types: Nominally brittle and driven by the propagation of a single dominant crack or quasi-brittle and resulting from the accumulation of many microcracks. The latter goes along with acoustic noise, whose analysis has revealed that events form aftershock sequences obeying characteristic laws reminiscent of those in seismology. Yet, their origin lacks explanation. Here we show that such a statistical organization is not only specific to the multi-cracking situations of quasi-brittle failure and seismology, but also rules the acoustic events produced by a propagating crack. This simpler situation has permitted us to relate these laws to the overall scale-free distribution of inter-event time and energy and to uncover their selection by the crack speed. These results provide a comprehensive picture of how acoustic events are organized upon material failure in the most fundamental of fracture states: single propagating cracks.
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