Eddy-current induction in a uniaxially anisotropic plate

Abstract

A theoretical model is presented to describe the time-harmonic electromagnetic induction of eddy currents in a uniaxially anisotropic plate. The model assumes that the plate is nonmagnetic and that the axis of uniaxial anisotropy is horizontal (i.e., lying in a plane parallel to the surface of the plate). The fields and currents induced by a general magnetic source are obtained by formulating the problem in terms of reduced electromagnetic potentials (Hertzian potentials) and making extensive use of integral transforms. Closed-form expressions for the reduced potentials are given explicitly, enabling the induced fields to be calculated in all regions provided the free-space source fields are known. The change in probe-coil impedance ΔZ due to eddy-current induction is considered in detail, and an explicit closed-form expression for ΔZ is derived for the general case. This general theory is illustrated by calculating ΔZ for a cylindrical air-cored coil when (i) the coil axis is normal to the surface of the plate and (ii) the coil axis is tangential to the surface of the plate. The validity of these calculations was established by performing a series of measurements of ΔZ using an aluminum-alloy sheet unidirectionally reinforced with boron fibers. The results of the theoretical calculations are in excellent agreement with experiment. The significance of the results for the nondestructive characterization of metal-matrix composite materials is discussed.