Eddy-current non-destructive evaluation is commonly performed at relatively high frequencies at which the skin depths are significantly smaller than the dimensions of a typical crack. A thin-skin analysis of eddy currents is presented in which the electromagnetic fields on the crack faces are described in terms of a potential which obeys a two-dimensional Laplace equation. Solutions of this equation for defects in both magnetic and non-magnetic materials are determined by applying thin-skin boundary conditions at the crack perimeter. The impedance change of an eddy-current coil due to the defect is then calculated by numerical evaluation of one-dimensional integrals over the line of the crack mouth, the impedance integrals having been derived with the aid of a reciprocity relationship. Theoretical predictions are compared with experimental data for long, uniformly deep slots in aluminium and mild steel and good agreement between theory and experiment is obtained.

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Crack detection using eddy-current nondestructive testing is often carried out at frequencies such that the skin depth of the induced current is much smaller than the crack dimensions. The induced current then flows in a thin skin at the conductor surface and at the faces of a surface crack. In the case of a crack that acts as an impenetrable barrier to electric current, the electromagnetic field at the crack surface can be represented, at an arbitrary frequency, in terms of a potential which satisfies a two-dimensional Laplace equation. The boundary conditions required in the solution of the Laplace equation have not yet been determined for the general case, but we have derived approximate boundary conditions which are applicable in the thin-skin regime. The conditions derived are valid for cracks in materials of arbitrary permeability. From the harmonic solutions of the Laplace equation, the impedance change of the excitation coil due to the defect has been calculated for cracks in aluminum and ferromagnetic steel. Comparisons between predictions and experimental measurements on rectangular slots show good agreement, thus corroborating the theory and the numerical calculations.

The change in electromagnetic impedance of a conductor due to the presence of a long, perpendicular surface-breaking crack in a normally incident, uniform electric field is calculated in closed form in the high-frequency limit. At high frequencies, where the skin depth is much smaller than the depth of the crack, the fields near the edge and corners of the crack are effectively decoupled. This means that the solution may be formulated as the sum of contributions from the corners, faces, and edge of the crack. Simple analytical expressions for the electric field are found and used to calculate the impedance due to the crack in the high-frequency limit without resorting to numerical methods.

Eddy-current probe impedance variations due to interactions with planar cracks have been calculated for the thin-skin regime. In this regime, the skin depth of the induced current is small compared to the crack depth and length, allowing approximations to be made. The approximations have been used by others to show that the thin-skin field at the surface of a crack is governed by a potential satisfying the two-dimensional (2-D) Laplace equation. In fact, the transverse magnetic potential at the crack face, defined with respect to the normal to this surface, satisfies a 2-D Laplace equation at an arbitrary skin depth. However, thin-skin boundary conditions applied at the crack perimeter greatly simplify the problem. Solutions of the Laplace problem for semielliptical cracks have been found by conformal mapping to a rectangular region. The surface potential in the rectangular domain is expressed as a Fourier series expansion and the coefficients of the series determined from the boundary conditions. Curved crack profiles of a general class, including semielliptic cracks as a special case, have been approximated by using ordered elliptical epicycles, a representation that retains the ability to map the crack domain to a rectangle. The probe impedance change due to a crack has been expressed in terms of the transverse magnetic potential and calculated from a line integral. Predictions of the probe impedance variations with position and frequency have been compared with an analytical solution for a semicircular crack and with experimental coil impedance measurements on semielliptical and epicyclic slots. Good agreement is observed in all comparisons.