Many components which are routinely tested using eddy-current methods suffer from the build-up of surface deposits. It is important to assess the effect of surface deposits because the defect signal in an eddy-current probe may be reduced, even to the point where defect detection is impossible. Here, the impedance change in a probe due to a surface crack in a half-space conductor is calculated taking into account a layer of conducting and/or permeable material on the conductor surface. The calculation is performed in the thin-skin regime, in which the electromagnetic skin-depth in the conductor is assumed to be much smaller than the dimensions of the crack. In this regime, an analytical approach can be adopted in which a scalar potential obeys Laplace's equation on the planar domain of the crack. The effect of the surface layer enters the formulation in the boundary condition on the potential along the line of the crack mouth. This boundary condition is written as an integral equation using Green's theorem, and the Green's function kernel takes account of the surface layer. Example calculations are performed for a long crack in a conductor with a surface layer of various thickness, conductivity and permeability.
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