SIMULATION OF THE PERCOLATION BEHAVIOR OF QUASI AND TRANSVERSELY ISOTROPIC SHORT-FIBER COMPOSITES WITH A CONTINUUM MODEL

This study uses a continuum model to predict the percolation threshold of composites consisting of electrically conducting fibers in an insulating matrix. The influence of preferred orientations (resulting from differences in processing conditions) on the threshold volume fractions is discussed. The model consists of an impenetrable cylindrical core surrounded by a fully penetrable soft shell. The hard core represents a physical fiber whereas the soft shell represents an effective range for electrical conduction in the otherwise insulating matrix. The simulation procedure consists of the addition of fibers to a control volume to probe the formation of a 3-D interconnected network. Finite size scaling (FSS) theory is used to predict the threshold volume fractions for infinite systems. The correlation length exponent was found to be 0.89, in agreement with values reported in our earlier study for particulate composites as well as in other literature studies. For transversely isotropic composites, the threshold values were found to be anisotropic for finite systems. However, the anisotropy vanishes as the system size becomes infinitely large. The correlation length exponent for these transversely isotropic composites was also found to be 0.89. The effect of shell thickness on the threshold volume fractions is investigated. The influence of fiber aspect ratio on percolation behavior is discussed, and the simulation results are compared with experimental results reported in the literature.