Universality class of fiber bundles with strong heterogeneities

¹  AMADE, Departament de Física and Departament de Enginyeria Mecànica de la Construcció Industrial, Universitat de Girona - Ave. Montilivi s/n, E-17071 Girona, Spain
²  Department of Theoretical Physics, University of Debrecen - P.O. Box 5, H-4010 Debrecen, Hungary
³  Department of Applied Mathematics and Probability Theory, University of Debrecen P.O. Box 12, H-4010 Debrecen, Hungary
⁴  Departament de Física Fonamental, Universitat de Barcelona - Carrer Martí i Franqués 1, E-08028 Barcelona, Spain

Received: 23 August 2007
Accepted: 18 January 2008

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 0α1 of fibers is unbreakable, while the remaining 1-α 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 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.