An analytical characterization of the anisotropy of the elastic modulus of misaligned short-fiber-reinforced polymers

Short-fiber-reinforced polymers (SFRP) are very attractive because of their ease of fabrication, relatively low cost and mechanical properties which are superior to those of relevant polymer resins. Owing to the partial orientation distribution of the fibers in final components, SFRP composites show direction-dependence, namely anisotropy in their mechanical properties. The fiber-length distribution (FLD) and the fiber-orientation distribution (FOD) in SFRP composites play an important role in determining the composite mechanical properties. In the present paper, the FLD and the FOD are modelled with suitable probability density functions and the laminate analogy approach is used to derive the expression of the elastic modulus of SFRP as a function of any given direction, the FLD and the FOD. The direction-dependence, i.e. the anisotropy, of the elastic modulus of SFRP has been studied in detail by taking into consideration the effects of the FLD and the FOD. The present theory is applied to existing experimental results, and the agreement is found to be very satisfactory.