Universality class of fiber bundles with strong heterogeneities
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 ac the burst size distribution is a power law with the usual exponent tau = 5/2, while above ac 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 de. ning a novel universality class of breakdown phenomena. Copyright (c) EPLA, 2008.