The fibre pull-out energy of misaligned short fibre composites

A theoretical study on the fibre pull-out energy has been carried out for short fibre-reinforced composites. Two probability density functions were introduced for modelling the fibre-length distribution and the fibre-orientation distribution. By taking into account the effect of snubbing friction between fibres and matrix at the fibre exit point during fibre pull-out, and that of the fracture stress of fibres obliquely crossing the fracture plane (i.e. the inclined strength of fibres), the fibre pull-out energy of composites has been derived as a function of fibre-length distribution and fibre-orientation distribution, as well as interfacial properties. The previously existing fibre pull-out energy theories can be deduced from the present model. The effects of fibre-length distribution, fibre-orientation distribution, interfacial properties, snubbing-friction coefficient and parameter A for determining the inclined strength of fibres on the fibre pull-out energy, have been studied in detail. The present study provides the necessary information as to which fibre-length distribution, fibre-orientation distribution and interfacial property are required to achieve a desired fibre pull-out energy and hence a desired composite toughness. High-strength fibres, a large fibre-volume fraction and a large fibre diameter for a comparatively large mean fibre length, are shown to be favourable for achieving a high fibre pull-out energy.