Probabilistic strength analysis of fibre bundle structures

Methods for computing the asymptotic tensile strength distribution of a bundle of a finite number of fibres are presented for a variety of situations. The individual fibres are assumed to display random variations in load-extension behaviour over and above the usual variations in breaking elongation. Random fibre slack effects (resulting from uneven clamping and variations in fibre length) are shown to cause an additional loss in bundle strength over that already caused by variations in fibre breaking elongation. Bundles constructed of more than one generic type of elastic fibre in fixed blend ratios are shown to suffer strength losses over bundles constructed of only one fibre type. The method of approach differs from that used by other workers who have treated a special case, namely the classic fibre bundle problem. The solution evolves from reducing the problem to that of a Gaussian process boundary crossing problem, using recent advances in the theory of weak convergence of probability measures.