Effects of fibre length and orientation distributions on the fibre pull-out energy of short fibre reinforced polymers

In this paper a theoretical study on the fibre pull-out energy is carried out for short fibre reinforced polymers (SFRP). Two probability density functions-are 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 crossing obliquely the fracture plane (i.e. the inclined strength of fibres), the fibre pull-out energy of short fibre reinforced composites is 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 and orientation distributions and interfacial properties on the fibre pull-out energy are studied in detail. The present study provides the necessary information that what fibre length distribution, what fibre orientation distribution and what interfacial properties are required to achieve a desired fibre pull-out energy and hence a desired composite toughness.