Universality class of fiber bundles with strong heterogeneities

Abstract

We study the effect of strong heterogeneities on the fracture of disordered materials using a fiber bundle model. The bundle is composed of two subsets of fibers, i.e. a fraction 0<α<1 of fibers is unbreakable, while the remaining 1-αfraction is characterized by a distribution of breaking thresholds. Assuming global load sharing, we show analytically that there exists a critical fraction of the components α_c which separates two qualitatively different regimes of the system: below α_c the burst size distribution is a power law with the usual exponent τ=5/2, while above α_c the exponent switches to a lower value τ=9/4 and a cutoff function occurs with a diverging characteristic size. Analyzing the macroscopic response of the system we demonstrate that the transition is conditioned to disorder distributions where the constitutive curve has a single maximum and an inflexion point defining a novel universality class of breakdown phenomena.

References in corpus (2)

• Statistical Models of Fracture
• Effect of discontinuity in threshold distribution on the critical behaviour of a random fiber bundle

Cited by in corpus (7)

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• A random fiber bundle with many discontinuities in the threshold distribution
• Slip avalanches in a fiber bundle model
• Disorder induced brittle to quasi-brittle transition in fiber bundles
• System-size-dependent avalanche statistics in the limit of high disorder
• Crackling noise in three-point bending of heterogeneous materials
• Failure process of fiber bundles with random misalignment