Asymptotic Distributions for the Failure of Fibrous Materials Under Series-Parallel Structure and Equal Load-Sharing

Abstract

Asymptotic distributions are obtained for both the strength and the time to failure of a fibrous material for which mild bonding or friction exists between fibers. The analysis is based on the chain-of-bundles probability model, and equal load sharing is assumed for the nonfailed fiber elements in each bundle. Asymptotic results are obtained for the difficult but useful case where k, the number of bundles in the chain, grows very rapidly with respect to n, the number of fibers in each bundle. For both strength and time to failure, a classical extreme value distribution is found to be the asymptotic distribution, and the parameters are given in terms of certain fiber properties. The results apply to long, flexible fibrous structures such as yarns and cables.