Effective elastic moduli of misoriented short-fiber composites

Abstract

This paper deals with the effective moduli of composites containing misoriented fibers. The orientation distribution of fibers in a composite can be characterized by a single parameter exponential function, F(θ) = 1—e−λπ. A large λ indicates a highly oriented material, whereas a small λ represents a quasi-isotropic material. Based on the Eshelby-Mori-Tanaka theory, the effective elastic moduli of planar orientation distribution and transversely isotropic distribution of fibers are studied. For planar orientation case, we have examined the nine independent stiffness constants of injection-molded tensile bars of poly (pheylene sulfide) reinforced with 30 and 40% by weight of carbon or glass fibers which have been measured by Choy et al. [Polymer Composites 13, 69–80 (1992)]. For the transversely isotropic orientation case, five elastic constants of a composite are derived. These moduli are given in terms of the length-diameter aspect ratio, the volume fraction, and the orientation distribution parameter λ of the short fibers. And they are given in very simple, explicit forms. Numerical results are presented to demonstrate the effects of the fiber elastic property, aspect ratio, volume fraction and orientation distribution function on composite elastic moduli. The fiber orientation distribution and aspect ratio have a more significant effect on composite longitudinal Young’s modulus than does the fiber volume fraction within the range examined.