Emergent patterns of localized damage as a precursor to catastrophic failure in a random fuse network

Abstract

We study the failure of disordered materials by numerical simulations of the random fuse model. We identify emergent patterns of localized damage prior to catastrophic failure by statistically averaging the density of damage around the eventual failure nucleation point. The resulting pattern depends on fracture density and obeys the same scaling relations as would be expected for the stress field generated by a critical crack nucleating in a finite, disorder-free effective medium of varying size. The growth of this critical crack absorbs preexisting clusters according to a well-defined scaling relation. Unfortunately, in single model runs such precursory signals are not obvious. Our results imply that reliable and accurate prediction of failure in time-independent, microscopically brittle random materials in a real case is inherently problematic, and degrades with system size.

Acceleration and localization of subcritical crack growth in a natural composite material

“…We make the assumption that the characteristic extension of the fault zone controls failure in a similar manner as the length of a critical crack does in the context of fracture mechanics (for detailed discussion of this point see Ref. [13]). This allows us to relate the crack size to the number of AE events and to use the AE record for monitoring damage accumulation and predicting time-to-failure even when it is impossible to measure the crack size directly within an experiment.…”

A Beam Network Model Approach to Strength Optimization of Disordered Fibrous Materials

“…This can be understood from the different failure modes of unconnected fiber bundles and of connected beam networks: For a connected network, lateral load redistribution leads to localized damage clusters, which form as weaker‐than‐average beams fail in a correlated manner and that extend in lateral direction. In studies of random fuse networks, such damage clusters were shown to control system strength in a manner very similar to small cracks that become critical at the failure stress . Thus, we observe that in a material with low disorder, cross linking may reduce strength even if it does not introduce damage, because cross links here facilitate the formation and lateral propagation of a critical crack which is impossible as long as the system consists of unconnected fibers.…”

“…In studies of random fuse networks, such damage clusters were shown to control system strength in a manner very similar to small cracks that become critical at the failure stress. [17,18] Thus, we observe that in a material with low disorder, cross linking may reduce strength even if it does not introduce damage, because cross links here facilitate the formation and lateral propagation of a critical crack which is impossible as long as the system consists of unconnected fibers. The effect is, of course, exacerbated if in addition the cross links are associated with damage (reduction in strength) of the load-carrying fibers.…”

“…This strength in turn decreases with fiber length according to a statistical size effect: For a fiber consisting of L elements with Weibull‐distributed failure thresholds, the average fiber strength (and therefore the bundle strength) decreases as L 1/β . For a fully cross‐linked network, in contrast, the average strength decreases in inverse proportion with the logarithm of system size . Thus, for very large system sizes, the strength of a disconnected bundle (which decreases in inverse proportion with a power of L ) will always be less than that of a connected network (which decreases in inverse proportion with the logarithm of L ).…”

“…For a fully cross-linked network, in contrast, the average strength decreases in inverse proportion with the logarithm of system size. [17] Thus, for very large system sizes, the strength of a disconnected bundle (which decreases in inverse proportion with a power of L) will always be less than that of a connected network (which decreases in inverse proportion with the logarithm of L). We note, however, that for large β (low disorder) the cross-over may only occur at extremely large system sizes that are unlikely to be relevant in real-world systems.…”