Eddy-current inspection of cracks in a multilayer conductor

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Abstract
A theoretical model is presented to describe the time-harmonic induction of eddy currents in a layered conductor containing a crack. The layered system consists of two parallel conducting plates separated by an insulating gap and it is assumed that the thickness tS of the plate containing the (through-the-thickness) crack is small compared with the electromagnetic skin depth δS. Explicit expressions for the magnetic vector potential in the absence of the crack are derived for the particular case of induction by a circular air-cored coil, and these results are used to calculate the change in coil impedance ΔZU due to the induced currents in the uncracked system. The effect of a through-the-thickness crack is represented by an equivalent distribution of current sources along the line of the crack. The form of these generalized current vortex sources is examined and explicit expressions are presented for the current density and vector potential due to a single vortex. The vortex density, and hence the induced current distribution, are obtained by solving a one-dimensional singular integral equation. This formalism is used to calculate the change in coil impedance ΔZC due to a first- or second-layer crack. Experimental measurements of ΔZ were carried out for several model systems and the theoretical calculations were found to agree with experiment to within 10% or better for tS/δS up to 0.4. The implications for the detectability of cracks using eddy-current nondestructive inspection is discussed.

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