Damage process of a fiber bundle with a strain gradient.

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 modeled as two rigid blocks glued together by a thin elastic interface. The interface is discretized by parallel fibers with random failure thresholds, which become 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 of 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 23 and saturates for strongly disordered bundles.