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

Abstract

A phase diagram for a one-dimensional fiber bundle model is constructed with a continuous variation in two parameters guiding the dynamics of the model: strength of disorder and range of stress relaxation. When the range of stress relaxation is very low, the stress concentration plays a prominent role and the failure process is nucleating where a single crack propagates from a particular nucleus with a very high spatial correlation unless the disorder strength is high. On the other hand, a high range of stress relaxation represents the mean-field limit of the model where the failure events are random in space. At an intermediate disorder strength and stress release range, when these two parameters compete, the failure process shows avalanches and precursor activities. As the size of the bundle is increased, it favors a nucleating failure. In the thermodynamic limit, we only observe a nucleating failure unless either the disorder strength is extremely high or the stress release range is high enough so that the model is in the mean-field limit. A complex phase diagram on the plane of disorder strength, stress release range, and system size is presented showing different failure modes - 1) nucleation 2) avalanche, and 3) percolation, depending on the spatial correlation observed during the failure process.

Correlation Between Avalanches and Emitted Energies During Fracture With a Variable Stress Release Range

“…The critical range that separates these two limits has been studied elsewhere [17,18]. The underlying mechanism is not only valid for the fiber bundle model [17][18][19][20] but also seen in the random fuse model [32,33] and in molecular dynamics simulations [34]. The present study is a manifestation of these two competing effects.…”

“…In the fiber bundle model, the mode of failure depends mainly on two factors: the strength of disorder in the individual failure threshold of the fibers and the range of stress release [15][16][17][18] when one such fiber is broken. Such interplay between disorder and damage nucleation not only affects the failure mode but also influences the spatial correlation during the failure process [17][18][19][20]. The range of stress release has two extreme limits, viz.…”