Effects of fiber length and orientation distribution on the elastic modulus of short fiber reinforced thermoplastics

Abstract

AbstractA method including the effects of fiber length and orientation distribution to predict elastic moduli of short fiber reinforced thermplastics (FRTP) is presented. The fiber length distribution in FRTP has an asymmetric character with a tail at the long fiber end. Statistical distribution functions such as Weibull or log‐normal can be used to represent this kind of distribution. Orientation distribution of fibers in FRTP can be characterized by a single parameter exponential function, \documentclass{article}\pagestyle{empty}\begin{document}$F(\theta) = \frac{{1 - \lambda \theta }}{{1 - e^{ - \frac{\P}{2}\lambda } }}$\end{document}. A large λ indicates a highly oriented material whereas small λ represents a quasi‐isotropic material. As fiber length and orientation distribution functions have been characterized, the elastic moduli of FRTP can be predicted. First, the mean elastic moduli of unidirectional plies are predicted through the fiber length distribution. Then the stacking sequence of laminate is assumed to be as the fiber orientation distribution of FRTP, and the overall elastic moduli of FRTP are estimated based on the laminate‐plate method.