Issue
EPL
Volume 81, Number 5, March 2008
Article Number 54005
Number of page(s) 6
Section Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics
DOI http://dx.doi.org/10.1209/0295-5075/81/54005
Published online 19 February 2008
EPL, 81 (2008) 54005
DOI: 10.1209/0295-5075/81/54005

Universality class of fiber bundles with strong heterogeneities

R. 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

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$\leqslant$$\alpha$$\leqslant$1 of fibers is unbreakable, while the remaining 1-$\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.

PACS
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.

© EPLA 2008