Estimating the Elastic Modulus through the Thickness Direction of a Uni-direction Lamina which Possesses Transverse Isotropic Property

Abstract

This investigation presents three formulae of the material constants. A simple method is applied to determine the material properties of a unidirectional lamina (UD) in the through-thickness direction. The mechanical characteristics of an orthotropic composite material generally require nine parameters: three Young's moduli; three shear moduli; and three Poisson's ratios. Most studies concentrate on two orthogonal axial moduli, a shear modulus and a Poisson's ratio in the plane of the lamina. Four material parameters were adopted in those works instead of nine. Some cases in many studies are based on three-dimension modeling, making the nine material constants necessary, as the four material parameters cannot satisfy such cases. However, the material constants through the thickness direction cannot easily be measured experimentally. In this work, the relationships between the nine mechanical properties are revealed by the wave equations of an orthotropic material. Two restrictions in the study are considered: first, the suitable cases are limited to UD possessing the transverse isotropic property; second, the distribution of the fibers in the cross-section of UD laminate must be uniform. On the base, the shear modulus and the Poisson ratio through the thickness direction of the UD material can be computed from the simple relationships.