Three-Dimensional Effective Moduli of Symmetric Laminates

Abstract

Closed-form expressions of three-dimensional effective moduli of symmetric laminates, which are based on the assumption of constant in-plane strains and constant interlaminar stresses through the thickness, had been proposed by Chou and Carleone (1972) and later re-proposed by Sun and Li (1988). This article modified the effective interlaminar shear moduli to account for the effect of stacking sequence by assuming the parabolic distribution of interlaminar shear stresses through the thickness. In this article, the effective three-dimensional moduli are also re-presented in such forms that it could be seen that several particular forms of the rule of mixture apply for individual stiffness or compliance components. As a result, four stiffness invariants and one compliance invariant are developed. The invariance is helpful in checking the reliability of measurements. The effective moduli predicted by this article are found to be in good agreement with the experimental data measured by ultrasonic methods.