System-size-dependent avalanche statistics in the limit of high disorder

Abstract

We investigate the effect of the amount of disorder on the statistics of breaking bursts during the quasi-static fracture of heterogeneous materials. We consider a fiber bundle model where the strength of single fibers is sampled from a power law distribution over a finite range, so that the amount of materials' disorder can be controlled by varying the power law exponent and the upper cutoff of fibers' strength. Analytical calculations and computer simulations, performed in the limit of equal load sharing, revealed that depending on the disorder parameters the mechanical response of the bundle is either perfectly brittle where the first fiber breaking triggers a catastrophic avalanche, or it is quasi-brittle where macroscopic failure is preceded by a sequence of bursts. In the quasibrittle phase, the statistics of avalanche sizes is found to show a high degree of complexity. In particular, we demonstrate that the functional form of the size distribution of bursts depends on the system size: for large upper cutoffs of fibers' strength, in small systems the sequence of bursts has a high degree of stationarity characterized by a power law size distribution with a universal exponent. However, for sufficiently large bundles the breaking process accelerates towards the critical point of failure which gives rise to a crossover between two power laws. The transition between the two regimes occurs at a characteristic system size which depends on the disorder parameters.

Record statistics of bursts signals the onset of acceleration towards failure

“…5(a). The underlying mechanism of the emergence of the crossover of the distribution of record sizes is the crossover of the entire burst size distribution 69 , similar to the so-called b-value anomaly observed for event magnitude distributions in geosystems 32,70,71 .…”

From Nucleation to Percolation: The Effect of System Size when Disorder and Stress Localization Compete

“…When we combine both the effects of stress release range and disorder strength, the model produces rich relaxation dynamics with different modes of failure − abrupt, non abrupt, nucleating, and random in space [48]. The avalanche statistics as well as the effect of system sizes has also been discussed recently in the context of fiber bundle model [49,50]. Moreover, the record statistics in the avalanche statistics and study of elastic energy has been observed to be a vital key to predicting an upcoming failure [51].…”