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Register a new userFrom nucleation to percolation: the effect of system size and system disorder
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Subhadeep Roy
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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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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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