Avalanche Statistics of Interface Crack Propagation in Fiber Bundle Model: Characterization of Cohesive Crack

Abstract

This paper considers a model of crack propagation taking place at the interface between a rigid support and an elastic plate. The interface is modeled using a fiber bundle model (i.e., describing a damage behavior using a discrete set of elastic brittle elements having a random strength). This paper studies the fluctuations of the force required to propagate the crack along the interface. The statistics of avalanches, defined as a series of elements that are broken simultaneously under a load that decreases with the crack advance, are studied numerically and analytically. Local fiber breakage kinetics is related to a correlation length, which sets the size of a fracture process zone.

Interface crack propagation in porous and time-dependent materials analyzed with discrete models

“…It corresponds for instance to diffusion controlled dissolution processes. Interpreting the results in [11], it is shown that the size of the fracture process zone increases with increasing porosity in accordance with experimental observations [12]. The creep -fracture interaction is analyzed in the second part of the paper.…”

“…There are also a number of studies that may be placed among the two extremes that global and local load-sharing rules constitute. Among them is the study by Delaplace et al [11], who constructed an hierarchically connected fiber bundle model. They have worked out analytically and numerically the statistics of avalanches in a system whose geometry mimics the propagation of crack front at the interface between a rigid support and an elastic beam.…”

“…As shown in [11], this simplified model has the same statistical properties as the one where an elastic beam is connected with elastic-perfectly brittle fibers to the rigid substratum. We are not going to derive again the complete results obtained by the authors of [11] who used analytical solutions and analyzed the distribution of avalanches. We will recall just the main useful results, and in particular the motivations for using a simplified approach, with a fixed beam profile (2) instead of a deformable one.…”

“…It is the so-called ZIP model developed in [11]. We consider the two examples depicted in the above paragraphs, namely the case of a material whose porosity increases and the case of creepfracture interaction.…”

Local dynamics of a randomly pinned crack front: a numerical study

“…In order to follow the crack front as the breakdown process develops, we implement the "conveyor belt" technique [21,34]. We illustrate this technique in Figure 2.…”