  We study the damage process of fiber bundles in a wedge-shape geometry which
ensures a constant strain gradient. To obtain the wedge geometry we consider
the three-point bending of a bar, which is modelled as two rigid blocks glued
together by a thin elastic interface. The interface is discretized by parallel
fibers with random failure thresholds, which get elongated when the bar is
bent. Analyzing the progressive damage of the system we show that the strain
gradient results in a rich spectrum of novel behavior of fiber bundles. We find
that for weak disorder an interface crack is formed as a continuous region of
failed fibers. Ahead the crack a process zone develops which proved to shrink
with increasing deformation making the crack tip sharper as the crack advances.
For strong disorder, failure of the system occurs as a spatially random
sequence of breakings. Damage of the fiber bundle proceeds in bursts whose size
distribution shows a power law behavior with a crossover from an exponent 2.5
to 2.0 as the disorder is weakened. The size of the largest burst increases as
a power law of the strength of disorder with an exponent 2/3 and saturates for
strongly disordered bundles.
