Through-thickness elastic constants of composite laminates

Abstract

This article presents relationships for the through-thickness elastic constants of composite laminates, needed for modelling three-dimensional stress problems. Using the individual ply elastic constants together with the in-plane laminate elastic constants (from laminate theory) results in explicit relationships for, ν13, ν23, E3, G13 and G23. The Poisson’s ratio and Young’s modulus expressions apply to all laminate types. The shear modulus relationships apply to balanced laminates, but are extendable to other laminate types. Relationships are developed here for angle-ply, cross-ply and quasi-isotropic laminates. Results are presented for glass/epoxy and carbon/epoxy laminates, above and below the resin Tg. The importance of coupling stresses and their influence on ν13, ν23 and E3 is underlined. It is shown, for instance, that equating the laminate through-thickness modulus to the individual ply value can result in a significant under-estimate.