  A phase diagram for a one-dimensional fiber bundle model is constructed with
a continuous variation in two parameters guiding the dynamics of the model:
strength of disorder and range of stress relaxation. When the range of stress
relaxation is very low, the stress concentration plays a prominent role and the
failure process is nucleating where a single crack propagates from a particular
nucleus with a very high spatial correlation unless the disorder strength is
high. On the other hand, a high range of stress relaxation represents the
mean-field limit of the model where the failure events are random in space. At
an intermediate disorder strength and stress release range, when these two
parameters compete, the failure process shows avalanches and precursor
activities. As the size of the bundle is increased, it favors a nucleating
failure. In the thermodynamic limit, we only observe a nucleating failure
unless either the disorder strength is extremely high or the stress release
range is high enough so that the model is in the mean-field limit. A complex
phase diagram on the plane of disorder strength, stress release range, and
system size is presented showing different failure modes - (I) nucleation, (II)
avalanche, and (III) percolation, depending on the spatial correlation observed
during the failure process.
