Fluctuations of Global Energy Release and Crackling in Nominally Brittle Heterogeneous Fracture

Abstract

The temporal evolution of mechanical energy and spatially-averaged crack speed are both monitored in slowly fracturing artificial rocks. Both signals display an irregular burst-like dynamics, with power-law distributed fluctuations spanning a broad range of scales. Yet, the elastic power released at each time step is proportional to the global velocity all along the process, which enables defining a material-constant fracture energy. We characterize the intermittent dynamics by computing the burst statistics. This latter displays the scale-free features signature of crackling dynamics, in qualitative but not quantitative agreement with the depinning interface models derived for fracture problems. The possible sources of discrepancies are pointed out and discussed.Predicting when and how solids break continues to pose significant fundamental challenges [1,2]. This problem is classically addressed within the framework of continuum mechanics, which links deterministically the degradation of a solid to the applied loading. Such an idealization, however, fails in several situations. In heterogeneous solids upon slowly increasing loading for instance, the fracturing processes are sometimes observed to be erratic, with random events of sudden energy release spanning a variety of scales. Such dynamics are e.g. revealed by the acoustic emission accompanying the failure of various materials [3][4][5][6] and, at much larger scale, by the seismic activity going along with earthquakes [7,8]; A generic observation in this field is the existence of scalefree statistics for the event energy [9].These avalanche dynamics [10] have attracted much recent attention. They were originally thought to be inherent to quasi-brittle fracture, where the solid starts by accumulating diffuse damage through microfracturing events before collapsing when a macroscopic crack percolates throughout the microcrack cloud [11]. Phenomenological models such as fiber bundle models (see [12] for review) or random fuse models (see [2] for review) developed in this case reproduce qualitatively the avalanche dynamics with a minimal set of ingredients. More recently, it has been demonstrated [13] that a situation of nominally brittle fracture, involving the destabilization and propagation of a single crack, can also yield erratic dynamics. Within the linear elastic fracture mechanics (LEFM) framework, the in-plane motion of a crack front was mapped to the problem of a long-range (LR) elastic interface propagating within a two-dimensional (2D) random potential [14,15], so that the driving force selfadjusts around the depinning threshold [13]. This approach reproduces, in a simplified 2D configuration, the local and irregular avalanches evidenced in the space-time dynamics of an interfacial crack growing along a weak heterogeneous plane [16]. There exists theoretical arguments to extend this approach to the bulk fracture of real three-dimensional (3D) solids and crackling dynamics at the global (specimen) scale are anticipated [17,18]. Still, fracture experime...

Breakdown of Scaling and Friction Weakening in Intermittent Granular Flow

“…For larger avalanches however, scaling (Eq. 2) is broken: for large slips the shape takes a clear leftwards shape in agreement with what observed in seismic data [38,46] (and recently in [51]).…”

Crack growth in heterogeneous brittle solids: intermittency, crackling and induced seismicity

“…The same is to be expected here since the unloading factor k in Eq. 5 plays the same role as the demagnetization factor in the Barkhausen problem [20]. Finally a small but clear leftward asymmetry is detected (positive a in Fig.…”

“…This actually results from the nominally brittle character of the specimen fracture, so that the mechanical energy release rate per unit length, G = −dE/df = P(t)/f(t), is equal at each time step to the fracture energy, Γ, which is a material constant. For the artificial rocks considered here : Γ = 100 J/m 2 [20]. Note finally that, in addition to f (t) and P(t), the acoustic emission was collected at eight different locations via eight broadband piezoacoustic transducers (see [22] for details).…”

Interface propagation in fiber bundles: local, mean-field and intermediate range-dependent statistics

“…Apart from showing a crossover in response from small-to-large length scales, the roughness exponent measurements also show differences in these two limiting regions. The avalanche exponent can be significantly lower (1.1) than predicted (1.28) by the elastic interface model with inverse square elastic strength [33], but also there exists a large spread in the measured values of such exponents in different experiments [23]. Such a spread is not unique to the case of fracture front propagation, but is also seen in the cases of domain wall dynamics in magnetic systems [54][55][56], and fluid invasion fronts in porous media [57].…”