Universality class of fiber bundles with strong heterogeneitiesR. C. Hidalgo1, K. Kovács2, 3, I. Pagonabarraga4 and F. Kun2
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 in final form 18 January 2008; published March 2008
published online 19 February 2008
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 01 of fibers is unbreakable, while the remaining 1- 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 c which separates two qualitatively different regimes of the system: below c the burst size distribution is a power law with the usual exponent =5/2, while above c the exponent switches to a lower value =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.
46.50.+a - Fracture mechanics, fatigue and cracks.
62.20.M- - Structural failure of materials.
64.60.A- - Specific approaches applied to studies of phase transitions.
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