Effects of fiber length and fiber orientation distributions on the tensile strength of short-fiber-reinforced polymers

This paper presents an analytical method considering the effects of fiber length and fiber orientation distributions for predicting the tensile strength (TS) of short-fiber-reinforced polymers (SFRP). Two probability density functions are used for modelling the distributions of fiber length and fiber orientation. The strength of SFRP is derived as a function of fiber length and fiber orientation distribution taking into account the dependences of the ultimate fiber strength and the critical fiber length on the inclination angle and the effect of inclination angle on the bridging stress of oblique fibers. Then the effects of the mean fiber length, the most probable length (mode length), the critical fiber length, the mean fiber orientation, the most probable fiber orientation and the fiber orientation coefficient on the tensile strength of SFRP have been studied in detail. This model provides the necessary information to determine what fiber length distribution, what fiber orientation distribution and what interfacial adhesion are required to achieve a desired composite strength. The present theory is then applied to existing experimental results and the agreement is found to be satisfactory.