Fracture process of a fiber bundle with strong disorder

We investigate the effect of the amount of disorder on the fracture process of heterogeneous materials in the framework of a fiber bundle model. The limit of high disorder is realized by introducing a power law distribution of fiber strength over an infinite range. We show that on decreasing the amount of disorder by controlling the exponent of the power law the system undergoes a transition from the quasi-brittle phase where fracture proceeds in bursts to the phase of perfectly brittle failure where the first fiber breaking triggers a catastrophic collapse. For equal load sharing in the quasi-brittle phase the fat tailed disorder distribution gives rise to a homogeneous fracture process where the sequence of breaking bursts does not show any acceleration as the load increases quasi-statically. The size of bursts is power law distributed with an exponent smaller than the usual mean field exponent of fiber bundles. We demonstrate by means of analytical and numerical calculations that the quasi-brittle to brittle transition is analogous to continuous phase transitions and determine the corresponding critical exponents. When the load sharing is localized to nearest neighbor intact fibers the overall characteristics of the failure process prove to be the same, however, with different critical exponents. We show that in the limit of the highest disorder considered the spatial structure of damage is identical with site percolation-however, approaching the critical point of perfect brittleness spatial correlations play an increasing role, which results in a different cluster structure of failed elements.