An analytical calculation is presented for the response of an air-cored eddy-current probe to a surface-breaking metal fatigue crack in a flat plate, modelled as a region of zero conductivity, infinitely long and uniformly deep, in a homogeneous, conducting half-space. The problem is formulated in terms of the magnetic scalar potential, subject to surface impedance boundary conditions, with a line source to represent the crack. Solutions are found using spatial Fourier transforms. The theory is valid for both ferromagnetic and non-magnetic metals, providing that the electromagnetic penetration depth is small compared with the crack depth. The signal is expressed in terms of two integrals which, in general, must be evaluated numerically. Specific computations have been performed for a circular, single-coil probe.
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A. M. Lewis (1992) studied this question.
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