Strain-Rate Sensitivity, Relaxation Behavior, and Complex Moduli of a Class of Isotropic Viscoelastic Composites

Abstract

A micromechanical principle is developed to determine the strain-rate sensitivity, relaxation behavior, and complex moduli of a linear viscoelastic composite comprised of randomly oriented spheroidal inclusions. First, by taking both the matrix and inclusions as Maxwell or Voigt solids, it is found possible to construct a Maxwell or a Voigt composite when the Poisson ratios of both phases remain constant and the ratios of their shear modulus to shear viscosity (or their bulk counterparts) are equal; such a specialized composite can never be attained if either phase is purely elastic. In order to shed some light for the obtained theoretical structure, explicit results are derived next with the Maxwell matrix reinforced with spherical particles and randomly oriented disks. General calculations are performed for the glass/ED-6 system, the matrix being represented by a four-parameter model. It is found that, under the strain rates of 10−7/hr and 10−6/hr, randomly oriented disks and needles at 20 percent of concentration both give rise to a very stiff, almost linear, stress-strain behavior, whereas inclusions with an aspect ratio lying between 0.1 and 10 all lead to a softer nonlinear response. The relaxation behavior of the composite reinforced with spherical particles is found to be more pronounced than those reinforced with other inclusion shapes, with disks giving rise to the least stress relaxation. The real and imaginary parts of the overall complex moduli are also established, and found that, as the frequency increases, the real part of the complex bulk and shear moduli would approach their elastic counterparts, whereas for the imaginary part, the increase shows two maxima, and then drops to zero as the frequency continues to increase. Finally, the complex bulk modulus is examined in light of the Gibiansky and Milton bounds, and it is found that, for all inclusion shapes considered, this modulus always lies on or within the bounds.