The longitudinal electrical conductivity of metal matrix composites at cryogenic temperature in the presence of a longitudinal magnetic field

In this paper we use the results of Part I to derive two integral expressions for the electrical conductivity of metal matrix composite materials when a magnetic field, B, is added to a small electric field also parallel to fibres. One expression applies to strong magnetic fields meaningR ₀/a < 1, whereR ₀ =m ^* v _F/eB when the Fermi velocity is perpendicular to the magnetic field. WhenB , the integral expression reduces to the well known conductivity value = ₀(1 -V _f), where ₀ is the bulk matrix conductivity andV _f is the fibre volume fraction. For weak magnetic fields,R ₀/a > 1, then the electrical conductivity is expressed by the sum of two integrals. When B 0, the electrical conductivity reduces to the integral expression obtained in our earlier results when there is only a longitudinal electric field. In this paper we correct an incorrect derivation of the composite conductivity in the absence of a magnetic field published earlier J. Mater. Sci.21 (1986) 2409].