Orthotropic Creep and Complex Moduli of a Viscoelastic Composite Reinforced with Aligned Elliptic Fibers

A general micromechanical viscoelastic theory is developed to study the effective creep behavior and nine complex parameters of an orthotropic composite consisting of a viscoelastic matrix and aligned elliptic cylinders. With such a microgeometry it is first shown that two Maxwell or two Voigt constituents generally do not make a Maxwell or a Voigt composite, but under the conditions that the ratios of the shear modulus to the shear viscosity are equal for both constituents and that both Poisson's ratios remain unchanged in the course of deformation, a Maxwell and a Voigt composite can be constructed. The orthotropic creep compliances then are examined as the cross-sectional aspect ratio α (the thickness-to-width ratio) of the elastic elliptical cylinders changes from circular one (α = 1) to lamellar one (α→ 0) under six loading directions. It is found that under the three tensile loadings the composite with the lamellar structures gives rise to the strongest creep resistance. As the aspect ratio increases the tensile creep resistance also weakens, with the traditional circular fibers providing the poorest reinforcement. But the creep behaviors under the three shear loadings are sensitive to the loading direction as well. The real and imaginary parts of the nine complex moduli under a harmonic loading at low frequency are also examined as a function of the aspect ratio, the volume fraction of elastic cylinders and the loading frequency. The results show that the real parts of all these nine effective complex moduli will reach their elastic counterparts as the frequency increases. The imaginary parts, however, are dependent upon the cross-sectional shape and the loading frequency, but all of them reduce to zero when the volume concentration reaches 1 or the loading frequency increases to infinity.