On the influence of the shape of randomly oriented, non-conducting inclusions in a conducting matrix on the effective electrical conductivity

摘要

The influence exerted by the shape of randomly oriented non-conducting inclusions on the electrical conductivity of a metal is investigated using the aluminum-silicon eutectic alloy. By varying the time and temperature of heat treatment after solidification, the shape of the silicon inclusions is varied between plate-like and close-to-spherical. The influence of the geometry of the inclusions on the resistivity of the composite is separated from the influence of varying amounts of silicon in solid solution by centering the analysis on the temperature coefficient of the electrical resistivity rather than on the resistivity itself. The experimentally determined influence of inclusion geometry at fixed volume fraction on resistivity is compared to analytical predictions by extending the dilute solution for random-oriented spheroids using either the Maxwell/Mori-Tanaka approach or the differential effective medium approach. As a third predictive scheme, the three-phase self-consistent scheme for randomly oriented ellipsoids developed by Miloh and Benveniste is used. It is shown that the differential scheme and the three-phase self-consistent model capture the experimental results quite well, while the Maxwell/Mori-Tanaka approach underestimates both the resistivity and the influence exerted by the inclusion aspect ratio.