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Register a new userFrom nucleation to percolation: when disorder strength and stress localization compete
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Subhadeep Roy
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The spatial correlation during a failure event of a one-dimensional fiber bundle model is studied when three main parameters guiding the dynamics of the model is tuned: the fluctuation of local strength ($beta$), range of stress relaxation ($gamma$), and size of the bundle ($L$). Both increasing disorder strength and stress release range favor rupture events, random in space like percolation. An increase in system size on the other hand nucleating failure. At an intermediate disorder strength and stress release range, when these two parameters compete, the failure process shows avalanches and precursor activities. A complex phase diagram on the $beta-gamma-L$ plane is presented showing different failure modes - nucleation, avalanche, and percolation, depending on the spatial correlation observed during the failure process.
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A phase diagram for a one dimensional fiber bundle model is constructed with a continuous variation in two parameters guiding dynamics of the model: strength of disorder and system size. We monitor the successive events of fiber rupture in order to understand the spatial correlation associated with it. We observe three distinct regions with increasing disorder strength. (I) Nucleation - a crack propagates from a particular nucleus with very high spatial correlation and causes global failure; (II) Avalanche - the rupture events show precursors activities with a number of bursts. (III) Percolation - the rupture events are spatially uncorrelated like a percolation process. As the size of the bundle is increased, it favors the nucleating failure. In the thermodynamic limit, we only observe a nucleating failure unless the disorder strength is infinitely high.
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We study the dynamical aspects of a statistical-mechanical model for fracture of heterogeneous media: the fiber bundle model with various interaction range. Although the model does not include any thermal activation process, the system exhibits creep-like behaviors under a constant load being slightly above the critical value. These creep-like behaviors comprise three stages: in the primary and tertiary stages, the strain rate exhibits power-law behaviors with time, which are well described by the Omori-Utsu and the inverse Omori laws, respectively, although the exponents are larger than those typically observed in experiments. A characteristic time that defines the onset of power-law behavior in the Omori-Utsu law is found to decrease with the strength of disorder in the system. The analytical solution, which agrees with the above numerical results, is obtained for the mean-field limit. Beyond the mean-field limit, the exponent for the Omori-Utsu law tends to be even larger but decreases with the disorder in the system. Increasing the spatial range of interactions, this exponent is found to be independent of disorder and to converge to the mean-field value. In contrast, the inverse Omori law remains independent of the spatial range of interaction and the disorder strength.
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