Deterministic method for predicting the strength distribution of a fibre bundle

Owing to the non-strain hardening plastic behaviour of the aluminium matrix and the weak fibre/matrix interface, it has been shown that the strength of a carbon fibre-reinforced aluminium matrix composite made by diffusion bonding of prepreg layers can be derived from the corresponding fibre bundle strength. Application of Coleman's model to predict bundle strength leads to the conclusion that the composite must break when 15% of the fibres are broken. This greatly overestimates the experimental composite strength. Overestimations made by using the Coleman model are due to some implicit assumptions which are not valid in the case under consideration and which may consequently not describe our material. A new approach is proposed for the calculation of the strength distribution of a fibre bundle, based on the same fracture mechanism (fibres fracture progressively until the catastrophic fracture) but without restrictive assumptions. The real interpolated experimental fibre strength distribution (and not the Weibull distribution) is taken into account to predict bundle strength. The proposed method clearly shows the limit of strength prediction, in term of bundle size (number of fibres and gauge length). The risk of making predictions following the Weibull distribution out of the range of the observations (through single-fibre tensile tests) is demonstrated.