Universality class of fiber bundles with strong heterogeneities

TL;DR

This paper investigates how strong heterogeneities in fiber bundles influence fracture behavior, revealing a critical threshold that changes the universality class of the failure process and alters burst size distributions.

Contribution

It analytically identifies a critical fraction of unbreakable fibers that separates two regimes with different burst size exponents, defining a new universality class of breakdown.

Findings

Below critical fraction, burst size distribution follows a power law with exponent 5/2.

Above critical fraction, the exponent shifts to 9/4 with a diverging cutoff.

The transition depends on the shape of the macroscopic constitutive curve.

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<\alpha<1 of fibers is unbreakable, while the remaining 1-\alpha fraction is characterized by a distribution of breaking thresholds. Assuming global load sharing, we show analytically that there exists a critical fraction of the components \alpha_c which separates two qualitatively different regimes of the system: below \alpha_c the burst size distribution is a power law with the usual exponent \tau=5/2, while above \alpha_c the exponent switches to a lower value \tau=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.