Failure properties of loaded fiber bundles having a lower cutoff in fiber threshold distribution

The presence of lower cutoff in fiber threshold distribution may affect the failure properties of a bundle of fibers subjected to external load. We investigate this possibility--both in an equal load sharing (ELS) model and in a local load sharing (LLS) one using analytic as well as numerical methods. In the ELS model, the critical strength gets modified and, beyond a certain lower cutoff level, the whole bundle fails instantly (brittle failure) after the first fiber ruptures. Although the dynamic exponents for the order parameter, susceptibility, and relaxation time remain unchanged, the avalanche size distribution shows a gradual deviation from the mean field power law. A similar "instant failure" situation occurs in the LLS model at a lower cutoff level, which reduces to that of the equivalent ELS model at higher (high enough) dimensions. Also, the system size variation of the bundle's strength and the avalanche statistics show strong dependence on the lower cutoff level.