Model of transverse electrical conductivity of metal matrix composites above liquid nitrogen temperatures

Abstract

The present theories of transverse electrical conductivity of metal matrix composites (MMCs) containing nonconducting continuous cylindrical fibres are inadequate to predict experimental measurements. In this paper, we present a model of transverse electrical conductivity that predicts experimental data reasonably well for the case of an MMC material reinforced with nonconducting or poorly conducting continuous fibres. lt is based on the concept that transverse conductivity consists of two contributions: the electrical resistivity of the bulk material modified by periodic variations in the bulk cross-section due to the presence of nonconducting fibres; and a disturbance in electron transport due to nonuniformity in the electric field, caused by the presence of the fibres, that extends some distance away from and all around the fibres. To calculate this nonuniformity, we use the well-known solution of the potential field for a conducting cylinder in a uniform electric field and invert it so that it becomes a problem of nonconducting filaments in a conducting matrix. This gives a value of the transverse electrical resistivity for boron/aluminium (B/Al) containing 60 vol% fibre in nearly exact agreement with experimental data. The theory is compared to a modified capacitance model developed by Keller [1] for dielectric materials. The model discussed in this paper does not predict the trans-verse electrical resistivity of MMCs reinforced with very small-diameter fibres (Gr/Al, Al2O3, etc.) where the fibres are randomly distributed in a plane normal to their longitudinal axis. This problem will be discussed in a companion paper.