Estimation of the reinforcement factor ξ for calculating the transverse stiffness E2 with the Halpin-Tsai equations using the finite element method

In this work, an estimation of the reinforcement factor ξ of the Halpin-Tsai equations used to calculate the transverse stiffness E2 is provided. An improved estimation of the value ξ=2 originally proposed by Halpin and Tsai is given through a set of finite element analyses that consider randomly distributed unidirectional fibers for different volume fractions. The analysis overcomes the original hypothesis of a square array distribution of fibers in the transverse plane. It is concluded that a value of ξ=1.5 is a better estimation for the usual volume fractions found in practice for a unidirectional lamina of fiber reinforced composites.