On phase connectivity descriptions in modeling viscoelasticity of fiber or sphere reinforced composites

We consider composites exhibiting different scales of heterogeneities and some hierarchical phase connectivities, referred to as “composites of composites.” Following literature suggestions, and as an alternative to the use of complicated pattern-based models, effective elastic or viscoelastic moduli of such structures, with spherical (isotropic) or fiber-like (transverse isotropic) symmetry are estimated following a stepwise homogenization procedure. The steps are chosen according to the successive identified heterogeneity scales, making use, at each step, of the simplest n-layered (n=3 or 4) sphere or fiber inclusion model accounting for the scale dominant connectivity features. We quantitatively check the sensitivity of such an estimate process to the chosen simplifications for the morphology description, on comparing different choices for morphologies typical of nonuniformly reinforced matrices. The comparison first investigates, in elasticity, the effects of volume fractions of phases and of stiffnesses ranging over several orders, as well as phase connectivity permutations for 3-phase arrangements. One then compares several estimates obtained for the effective complex longitudinal modulus of a typical fiber reinforced polymer morphology using the correspondence principle for its viscoelasticity. The material description is compared to experiment, which for the morphological characteristics is the most important.