On the strength of classical fibres and fibre bundles

Abstract

This paper discusses tensile strength distributions for fibres (called classical fibres ) whose strength is independent of the rate of loading. Reasons are presented for expecting, in the absence of all other information, that the tensile strength of long classical libres from a common stationary source should obey the W eibull distribution. The statistical theory of the strength of bundles of classical fibres, as developed by Daniels is applied to infinite bundles composed of fibres which obey the Weibull distribution. It is found that the ratio of the tensile strength (units of force at break per initial unit area) of a bundle to the mean tensile strength of the constituent filaments decreases montonically with increasing dispersion in the strength of the constituent filaments. In general, the tensile strength of a large bundle has the same order of magnitude, but is less than the mean strength of the component filaments. Previous calculations have yielded this conclusion for fibres with a special time-dependence to their tensile strength ; here it is shown that the conclusion also applies to classical fibres.