On the electrical conductivity of metal matrix composites containing high volume fractions of non-conducting inclusions Original Research Article

Different predictive models—the Maxwell mean field approach, the differential effective medium scheme, the 2- and 3-phase self-consistent, and 3-point model—for the electrical conductivity of two-phase materials are assessed based on electrical conductivity measurements of metal matrix composites with non-conducting inclusions produced by gas pressure infiltration. The volume fraction of non-conducting phase, namely equiaxed or angular alumina particles of various sizes and size-distributions embedded in a matrix of pure aluminum, is varied between 40 and 70 vol.-%. For a given volume fraction, the equiaxed particles yield consistently higher conductivity than their angular counterparts, by as much as 40%. The Maxwell/Mori-Tanaka estimate and the 3-phase self-consistent model are consistently too high for the case of equiaxed particles (approximated by spheres), while for this particle shape the 3-point bounds for the limiting case of symmetric cell materials and the differential scheme give good agreement. For angular particles, approximated by randomly oriented oblate spheroids, only the differential scheme yields accurate predictions, whereas the Maxwell mean-field approach largely, and the 3-phase self-consistent approach for randomly oriented spheroids slightly, overestimate the effective conductivity. The 3-point bound for symmetric cell materials with spheroidal cells also overestimates the effective conductivity significantly. Overall, the differential scheme is found to exhibit very good predictive capacity over the ranges of geometry and volume fractions covered in this study, unlike all other models examined.