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.

A unidirectional composite is modeled as a two-dimensional cartesian square lattice of infinite width and finite thickness. Circular fiber cross sections, each contained completely within a lattice square and touching on all four sides, are placed at random within the lattice according to the fiber volume fraction. Percolation, in this system, is shown to be very sensitive to the lattice thickness. To be regarded as infinitely thick a lattice must be at least 150 fiber diameters across, and for a typical ply thickness of 20 fiber diameters the critical fiber fraction for percolation is shifted by 26% from the infinite lattice value of 0.46 to a smaller value of 0.34.

A single ply of unidirectional graphite/epoxy composite is modeled by both a two-dimensional Cartesian square and a close packed triangular lattice of fibers of infinite width and finite thickness. All fiber cross-sections are cir cular (of the same diameter) and those fibers with centers located at adjacent points on the lattice will contact at the midpoint. From these contacts con duction paths are formed across the latice. To generate randomness, the cir cular fiber cross-sections are removed at random from the lattice, leaving va cant sites of insulating matrix material, until a certain fiber fraction is reached. Lattice conductivities are calculated for both models at various fiber fractions and lattice thicknesses. Good agreement is obtained when the asymptotic conductivity versus thickness curves are compared with ex perimental data.

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