Simplified Model for the Influence of Inclusion Aspect Ratio on the Stiffness of Aligned Reinforced Composites

Abstract

A simplified model for the Young’s Modulus of aligned composites possessing spheroidal inclusions, of any aspect ratio α, is developed herein based on a triply periodic array of parallelpiped inclusions. The Young’s Modulus of continuous unidirectional fiber composites (α→∞), particulate composites (α = 1) and periodically bilaminated composites (α = 0) are obtained as limiting cases based on the Parallel-Series and Series-Parallel schemes of analyses. A reinforcing parameter, R, of the inclusion is then identified from the limiting cases such that R ∊ [0,1]. By curve-fitting for a relationship between the reinforcement parameter and the inclusion aspect ratio for α∊ [0,∞], the Young’s Modulus for aligned short fiber composites (α > 1) and aligned flake composites (α < 1) are obtained. For verification, the present model at limiting cases (α =0, 1, ∞) were reduced to other simple models and/or compared with experimental results. For nonlimiting cases (α <1, α > 1), comparison with other theoretical models show reasonable agreement.