Effect of Thickness on Single Ply Percolation and Conductivity

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Abstract
A single ply of unidirectional composite is modeled as a two-dimension al close packed lattice of circular fiber cross sections of infinite width and finite thickness. To introduce randomness fibers are removed at random from the lattice, leaving vacant lattice sites of matrix material, until a certain fiber volume fraction is reached. The effect of lattice thickness on the critical fiber fraction for percolation is calculated for this random, close packed fiber model. For a typical ply thickness of 24 fiber diameters, the critical fiber fraction for percolation is reduced by 20% from the infinite lattice value of 0.45 to a smaller value of 0.36. The percolation versus thickness results of the random square lattice of fibers are compared with those of the random close packed fiber model. Experimental measure ments of the increase in electrical conductivity of a single ply of graphite/ epoxy composite with decrease in ply thickness predicted by the random close packed fiber model, are presented.