This paper examines the influence of the cross-sectional aspect ratio (the thickness-to-width ratio, denoted by α) and volume concentration, c1, of 2-D randomly oriented elliptic cylinders on the overall anisotropic creep and complex moduli of a viscoelastic composite. 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 transversely isotropic creep compliances are then examined as the cross-sectional shape of the elastic elliptic cylinders changes from a circular one (α = 1) to that of a long, thin ribbon (α → 0). Along all five loading directions the ribbon-reinforced composite consistently gives rise to the strongest creep resistance, and as the aspect ratio increases the creep resistance also continues to weaken, with the traditional circular fibers providing the poorest reinforcement. The real and imaginary parts of the five independent complex moduli are also investigated as a function of α and c1, and the loading frequency ω. It is found that the real parts of the complex moduli all increase with increasing ω, and as ω → ∞ these moduli all approach their respective elastic moduli. The imaginary parts of the complex moduli show two distinct trends; one is marked by a monotonic decrease with increasing c1, and the other shows an initial increase before it decreases to zero. Finally, the complex plane/strain bulk moduli associated with various cross-sectional shapes are examined in light of the Gibiansky-Milton bounds, and it is found that all the theoretical results lie literally on the boundary of the bounds.
All Science Journal Classification (ASJC) codes
- Ceramics and Composites
- complex moduli
- creep behavior
- polymer-matrix composites