  We investigate the effect of the amount of disorder on the statistics of
breaking bursts during the quasi-static fracture of heterogeneous materials. We
consider a fiber bundle model where the strength of single fibers is sampled
from a power law distribution over a finite range, so that the amount of
materials' disorder can be controlled by varying the power law exponent and the
upper cutoff of fibers' strength. Analytical calculations and computer
simulations, performed in the limit of equal load sharing, revealed that
depending on the disorder parameters the mechanical response of the bundle is
either perfectly brittle where the first fiber breaking triggers a catastrophic
avalanche, or it is quasi-brittle where macroscopic failure is preceded by a
sequence of bursts. In the quasi-brittle phase, the statistics of avalanche
sizes is found to show a high degree of complexity. In particular, we
demonstrate that the functional form of the size distribution of bursts depends
on the system size: for large upper cutoffs of fibers' strength, in small
systems the sequence of bursts has a high degree of stationarity characterized
by a power law size distribution with a universal exponent. However, for
sufficiently large bundles the breaking process accelerates towards the
critical point of failure which gives rise to a crossover between two power
laws. The transition between the two regimes occurs at a characteristic system
size which depends on the disorder parameters.
