Size scaling of failure strength with fat-tailed disorder in a fiber bundle model

Kádár, Viktória; Danku, Zsuzsa; Kun, Ferenc

doi:10.1103/physreve.96.033001

Cited by 12 publications

(10 citation statements)

References 34 publications

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“…To investigate the evolution of fracture processes leading to ultimate failure, we use a generic fiber bundle model (FBM) which has proven successful in reproducing both the constitutive response and the intermittent bursting dynamics of heterogeneous materials on the macro-and microscales, respectively 60,61 . The model is composed of N parallel fibers, similar to a rope, which have a linearly elastic behavior.…”

Section: Disorder Driven Transition Between Brittle Quasi-brittle Amentioning

confidence: 99%

Record statistics of bursts signals the onset of acceleration towards failure

Kádár

Pál

Kun

2020

Sci Rep

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Forecasting the imminent catastrophic failure has a high importance for a large variety of systems from the collapse of engineering constructions, through the emergence of landslides and earthquakes, to volcanic eruptions. Failure forecast methods predict the lifetime of the system based on the time-to-failure power law of observables describing the final acceleration towards failure. We show that the statistics of records of the event series of breaking bursts, accompanying the failure process, provides a powerful tool to detect the onset of acceleration, as an early warning of the impending catastrophe. We focus on the fracture of heterogeneous materials using a fiber bundle model, which exhibits transitions between perfectly brittle, quasi-brittle, and ductile behaviors as the amount of disorder is increased. Analyzing the lifetime of record size bursts, we demonstrate that the acceleration starts at a characteristic record rank, below which record breaking slows down due to the dominance of disorder in fracturing, while above it stress redistribution gives rise to an enhanced triggering of bursts and acceleration of the dynamics. The emergence of this signal depends on the degree of disorder making both highly brittle fracture of low disorder materials, and ductile fracture of strongly disordered ones, unpredictable.

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Section: Disorder Driven Transition Between Brittle Quasi-brittle Amentioning

confidence: 99%

Record statistics of bursts signals the onset of acceleration towards failure

Kádár

Pál

Kun

2020

Sci Rep

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“…We could explain this interesting effect based on the extrem order statistics of the strength of single fibers, i.e. we pointed out that the bundle strength increases until the strongest fiber dominates the ultimate failure of the system [38]. For sufficiently small systems, at high cutoffs ε max , the strongest fiber can be so strong that it can keep the entire load on the system.…”

Section: Fiber Bundle Model With Fat-tailed Disordermentioning

confidence: 98%

“…In Ref. [38] we have shown that for fat tailed distri- Fig. 11 is presented in such a way that along the horizontal axis the system size N is rescaled with λ µ .…”

Section: Size Dependent Avalanche Statisticsmentioning

confidence: 99%

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

Kádár

Kun

2019

Phys. Rev. E

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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.

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“…Note that the fracture strength σ c and ε c of FBMs depend on the system size N even in the mean field limit [27][28][29]. Although the convergence is rapid, strictly speaking the above expressions give the bundle strength in the limit of infinite system size.…”

Section: Macroscopic Responsementioning

confidence: 99%

Avalanche dynamics in higher-dimensional fiber bundle models

2018

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We investigate how the dimensionality of the embedding space affects the microscopic crackling dynamics and the macroscopic response of heterogeneous materials. Using a fiber bundle model with localized load sharing computer simulations are performed from 1 to 8 dimensions slowly increasing the external load up to failure. Analyzing the constitutive curve, fracture strength and avalanche statistics of bundles we demonstrate that a gradual crossover emerges from the universality class of localized behavior to the mean field class of fracture as the embedding dimension increases. The evolution between the two universality classes is described by an exponential functional form. Simulations revealed that the average temporal profile of crackling avalanches evolves with the dimensionality of the system from a strongly asymmetric shape to a symmetric parabola characteristic for localized stresses and homogeneous stress fields, respectively.

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Size scaling of failure strength with fat-tailed disorder in a fiber bundle model

Cited by 12 publications

References 34 publications

Record statistics of bursts signals the onset of acceleration towards failure

Record statistics of bursts signals the onset of acceleration towards failure

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

Avalanche dynamics in higher-dimensional fiber bundle models

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