Time Dependence of Mechanical Breakdown in Bundles of Fibers. I. Constant Total Load

Abstract

A previously published phenomenological theory of the statistics and time dependence of the creep failure of oriented polymeric filaments is here applied to bundles of filaments. The mathematical apparatus of the theory of stochastic processes is used to calculate relationships between the strength of filament bundles and the strength of their component filaments. The present paper is concerned with the case in which the total load on a given bundle is maintained contant in time. Two limiting idealized cases are discussed—bundles with no interfiber friction (called ``ideal bundles'') and bundles with very strong interfiber friction (called ``tight bundles''). Only the first case is discussed rigorously. It is assumed throughout that the bundles are composed of filaments which have been randomly selected from a first-order ensemble. The principle mathematical result is that, subject to certain rather general conditions, in the limit as the numbers of filaments, N, becomes infinite the distribution of lifetimes for an ideal bundle becomes normal with a coefficient of variation that is proportional to N−½. The present theory predicts an appreciable loss in strength upon the arrangement of filaments into bundles.