Statistics for static strength of fibre bundles

Abstract

The failure statistics of fibre bundles are derived in terms of the defect size distribution which is a material characteristic determining the random occurrence of defects in the fibres. Two different loading cases are considered which lead to the same simple expression for the limiting strength of a bundle containing an infinite number of fibres. The first loading case leads to relatively simple statistical relations whereas the second case, which is encountered in practice, is much more involved. Because some composites are reinforced with bundles which may contain as many as 500 fibres there is a strong motivation to assess their strength using the simple asymptotic formula which is valid as the number of fibres per bundle tends to infinity. A numerical method of accurately calculating the failure probabilities of fibre bundles has been developed and numerical results are presented which show how the error of using the asymptotic formula can be assessed. The numerical results demonstrate why it is advantageous in practice to use bundles of fibres in composites, rather than single fibres.