  We study the existence of distinct failure regimes in a model for fracture in
fibrous materials. We simulate a bundle of parallel fibers under uniaxial
static load and observe two different failure regimes: a catastrophic and a
slowly shredding. In the catastrophic regime the initial deformation produces a
crack which percolates through the bundle. In the slowly shredding regime the
initial deformations will produce small cracks which gradually weaken the
bundle. The boundary between the catastrophic and the shredding regimes is
studied by means of percolation theory and of finite-size scaling theory. In
this boundary, the percolation density $\rho$ scales with the system size $L$,
which implies the existence of a second-order phase transition with the same
critical exponents as those of usual percolation.
