Multiscale modeling of effective electrical conductivity of short carbon fiber-carbon nanotube-polymer matrix hybrid composites

Epoxy matrix reinforced with conventional microscale short carbon fibers (SCFs) and carbon nanotubes (CNTs) form a hybrid material system where the characteristic length scales of SCFs and CNTs differ by multiple orders of magnitude. Several recent studies show that the addition of CNTs into a non-conducting polymer matrix improves both structural performance such as modulus, strength and fracture toughness and functional response such as electrical and thermal conductivities of the resulting nano-composite. In this study, a physics-based hierarchical multiscale modeling approach is presented to calculate the effective electrical conductivity of SCF-CNT-polymer hybrid composites. A dual step procedure is adopted to couple the effects of nano- and micro-scale so as to estimate the effective electrical properties of the composite. First, CNTs are dispersed into the non-conducting polymer matrix to obtain an electrically conductive CNT-epoxy composite. The effective electrical conductivity of CNT-epoxy composite is modeled using a physics-based formulation for both randomly distributed and vertically aligned cases of CNTs and the results are verified with the measured data available in the literature. In the second step, SCFs are randomly distributed in the CNT-epoxy composite and the effective electrical conductivity of the resulting SCF-CNT-epoxy hybrid composite is estimated using a micromechanics based self-consistent approach considering SCFs as microscopic inhomogeneities.