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 quasi-brittle 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.

arXiv comment10 pages, 12 figures, revtex

References in corpus (17)

• Predictability of catastrophic events: material rupture, earthquakes, turbulence, financial crashes and human birth
• First-Order Transition in the Breakdown of Disordered Media
• Tri-critical behavior in rupture induced by disorder
• Burst avalanches in solvable models of fibrous materials
• Scaling and universality in rock fracture
• Crossover Behavior in Burst Avalanches of Fiber Bundles: Signature of Imminent Failure
• Subcritical statistics in rupture of fibrous materials: Experiments and model
• Avalanches in wood compression
• Crackling noise during failure of alumina under compression: effect of porosity
• Crossover behavior in failure avalanches
• Modes of failures in disordered solids
• From Brittle to Ductile Fracture in Disordered Materials
• Universality class of fiber bundles with strong heterogeneities
• Experimental study of the effect of disorder on subcritical crack growth dynamics
• Brittle to Ductile Transition in a Fiber Bundle with Strong Heterogeneity
• Size scaling of failure strength with fat-tailed disorder in a fiber bundle model
• Disorder induced brittle to quasi-brittle transition in fiber bundles

Cited by in corpus (4)

• Record statistics of bursts signals the onset of acceleration towards failure
• Size scaling of failure strength at high disorder
• From nucleation to percolation: the effect of system size when disorder and stress localization compete
• From nucleation to percolation: the effect of system size and system disorder