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<\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.
Keywords
Cite
@article{arxiv.0802.2695,
title = {Universality class of fiber bundles with strong heterogeneities},
author = {R. C. Hidalgo and K. Kovacs and I. Pagonabarraga and F. Kun},
journal= {arXiv preprint arXiv:0802.2695},
year = {2009}
}