STRAIN-RATE SENSITIVITY, RELAXATION BEHAVIOR, AND COMPLEX MODULI OF ACLASS OF ISOTROPIC VISCOELASTIC COMPOSITES

A micromechanical principle is developed to determine the strain-rate sensitivity, relaxation behavior, and complex moduli of a linear visco elastic composite comprised of randomly oriented spheroidal inclusions . First, by taking both the matrix and inclusions as Maxwell or Voigt solids, if is found possible to construct a Maxwell or a Voigt composi te when the Poisson ratios of both phases remain constant and the rati os of their shear modulus to shear viscosity (or their bulk counterpar ts) are equal; such a specialized composite can never be attained if e ither phase is purely elastic. In order to shed some light for the obt ained theoretical structure, explicit results are derived next with Th e Maxwell matrix reinforced with spherical particles and randomly orie nted disks. General calculations are performed for the glass/ED-6 syst em, the matrix being represented by a four-parameter model. It is foun d that, under the strain rates of 10(-7)/hr and 10(-6)/hr, randomly or iented disks and needles at 20 percent of concentration both give rise to a very stiff, almost linear, stress-strain behavior, whereas inclu sions with an aspect ratio lying between 0.1 and 10 all lead to a soft er nonlinear response. The relaxation behavior of the composite reinfo rced with spherical particles is found to be more pronounced than thos e reinforced with other inclusion shapes, with disks giving rise to th e 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 ap proach their elastic counterparts, whereas for the imaginary part, the increase shows two maxima, and then drops to zero as the frequency co ntinues to increase. Finally, the complex bulk modulus is examined in light of the Gibiansky and Milton bounds, and if is found that, for al l inclusion shapes considered, this modulus always lies on or within t he bounds.