  We study fracture processes within a stochastic fiber-bundle model where it
is assumed that after the failure of a fiber, each intact fiber obtains a
random fraction of the failing load. Within a Markov approximation, the
breakdown properties of this model can be reduced to the solution of an
integral equation. As examples we consider two different versions of this model
that both can interpolate between global and local load redistribution. For the
strength thresholds of the individual fibers, we consider a Weibull
distribution and a uniform distribution, both truncated below a given initial
stress. The breakdown behavior of our models is compared with corresponding
results of other fiber-bundle models.
