Internal material damping of polymer matrix composites under off-axis loading

Abstract

The objective of this paper is to determine theoretically the material damping of short fibre-reinforced polymer matrix composites. The major damping mechanism in such composites is the viscoelastic behaviour of the polymer matrix. The analysis was carried out by developing a finite-element program which is capable of evaluating the stress and strain distribution of short fibre composites under axial loading (see Fig. 1a). Using the concept of balance of force we can express the modulusE x along the loading direction as a function of the mechanical properties of the fibre and matrix materials, fibre aspect ratio,l/d, loading angle,θ, and fibre volume fraction,V f. Then we apply the elastic-viscoelastic correspondence principle to replace all the mechanical properties of the composite, fibre and matrix materials such asE x,E f,E m,G m, by the corresponding complex moduli such asE x ′ +iE x ″ , andE f ′ +iE f ″ . After separation of the real and imaginary parts, we can expressE ' x/t' andE x t" as functions of the fibre aspect ratio,l/d, loading angle,θ, stiffness ratio,E f/E m, fibre volume fraction,V f, and damping properties of the fibre and matrix materials such asη f andη m. Numerical results of the composite storage modulus,E x ′ , loss modulus,E x ″ , and loss factor (damping),η C, are plotted as functions of parameters such asl/d,θ,V f, and are discussed in terms of variations ofl/d,θ, andE f/E m, in detail. It is observed that for a given composite, there exist optimum values ofl/d andθ at whichE x ″ andη c are maximized. The results of this paper can be used to optimize the performance of composite structures.