  We study the failure properties of fiber bundles when continuous rupture goes
on due to the application of external load on the bundles. We take the two
extreme models: equal load sharing model (democratic fiber bundles) and local
load sharing model. The strength of the fibers are assumed to be distributed
randomly within a finite interval. The democratic fiber bundles show a solvable
phase transition at a critical stress (load per fiber). The dynamic critical
behavior is obtained analytically near the critical point and the critical
exponents are found to be universal. This model also shows elastic-plastic like
nonlinear deformation behavior when the fiber strength distribution has a lower
cut-off. We solve analytically the fatigue-failure in a democratic bundle, and
the behavior qualitatively agrees with the experimental observations. The
strength of the local load sharing bundles is obtained numerically and compared
with the existing results. Finally we map the failure phenomena of fiber
bundles in terms of magnetic model (Ising model) which may resolve the
ambiguity of studying the failure properties of fiber bundles in higher
dimensions.
