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We investigate the effect of the amount of disorder on the statistics ofbreaking bursts during the quasi-static fracture of heterogeneous materials. Weconsider a fiber bundle model where the strength of single fibers is sampledfrom a power law distribution over a finite range, so that the amount ofmaterials' disorder can be controlled by varying the power law exponent and theupper cutoff of fibers' strength. Analytical calculations and computersimulations, performed in the limit of equal load sharing, revealed thatdepending on the disorder parameters the mechanical response of the bundle iseither perfectly brittle where the first fiber breaking triggers a catastrophicavalanche, or it is quasi-brittle where macroscopic failure is preceded by asequence of bursts. In the quasi-brittle phase, the statistics of avalanchesizes is found to show a high degree of complexity. In particular, wedemonstrate that the functional form of the size distribution of bursts dependson the system size: for large upper cutoffs of fibers' strength, in smallsystems the sequence of bursts has a high degree of stationarity characterizedby a power law size distribution with a universal exponent. However, forsufficiently large bundles the breaking process accelerates towards thecritical point of failure which gives rise to a crossover between two powerlaws. The transition between the two regimes occurs at a characteristic systemsize which depends on the disorder parameters.

System-size-dependent avalanche statistics in the limit of high disorder