Interface propagation in fiber bundles: local, mean-field and intermediate range-dependent statistics

Abstract

The fiber bundle model is essentially an array of elements that break when sufficient load is applied on them. With a local loading mechanism, this can serve as a model for a one-dimensional interface separating the broken and unbroken parts of a solid in mode-I fracture. The interface can propagate through the system depending on the loading rate and disorder present in the failure thresholds of the fibers. In the presence of a quasi-static drive, the intermittent dynamics of the interface mimic front propagation in disordered media. Such situations appear in diverse physical systems such as mode-I crack propagation, domain wall dynamics in magnets, charge density waves, contact lines in wetting etc. We study the effect of the range of interaction, i.e. the neighborhood of the interface affected following a local perturbation, on the statistics of the intermittent dynamics of the front. There exists a crossover from local to global behavior as the range of interaction grows and a continuously varying 'universality' in the intermediate range. This means that the interaction range is a relevant parameter of any resulting physics. This is particularly relevant in view of the fact that there is a scatter in the experimental observations of the exponents, in even idealized experiments on fracture fronts, and also a possibility in changing the interaction range in real samples.

Flory-like Statistics of Fracture in Fiber Bundle Model as obtained via Kolmogorov Dispersion for Turbulence: A conjecture

“…To probe the estimate in Eq. ( 7) in lower dimensions, we recall that in numerical estimates of the avalanche size distribution for a two-dimensional interface propagation in the fiber bundle model, δ ≈ 1.5 [15,16], which is consistent with Eq. ( 7) with d = 2 (considering a fixed rate of load increase, rather than following a quasi-static increase).…”

Fracture of a model cohesive granular material

“…Crack propagation in cohesive granular media is a complex problem, given all the possible routes for breaking a cemented aggregate [15][16][17] (e.g. grains crushing, cement breaking, or bonds fully or partially detaching) and the discrete nature of granular materials leading to force chains, 18 strain localization, 19 or catastrophic failure, 20 for example. While corresponding experiments on plasticity and fracture of model systems exist for some cohesive 16,[21][22][23] or non-cohesive 24,25 granular materials, they are still rare.…”

Survivability of Suddenly Loaded Arrays of Micropillars

“…It is worth noting that the segment is shifted towards higher values of with respect to its counterpart [ 17 ], which is related to quasi-statically loaded systems [ 31 , 32 , 33 ]. This can be explained as follows.…”

“…A discrete analogue of the stress-intensity drop, the so-called range variable (RV) load transfer rule [ 17 , 31 , 32 , 33 ], is suitable when dealing with cascading processes on networks. This is also the case of load-induced cascades of crushing pillars.…”