Boundary integral equations are developed for the electromagnetic field on the surface of an arbitrary, three-dimensional flaw in a conducting medium in the presence of a known incident field. A boundary element technique for the numerical solution of these equations is then presented and applied to the computation of eddy current flow around a rectangular slot.

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A solution is presented for the boundary value problem posed by a current-carrying coil of arbitrary shape in air above the plane surface of a conductor of semi-infinite extent. Two special cases are also treated: a circularly-symmetric coil at an arbitrary tilt angle with respect to the surface normal, and an infinitesimal coil, a magnetic dipole, also at an arbitrary tilt angle. Numerical results are presented for dipole orientations parallel and perpendicular to the surface.

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The electric-current perturbation technique consists of establishing an electric-current flow in the material to be examined and then detecting localized perturbations of this current flow at inhomogeneities such as inclusions or cracks. The current perturbation is sensed by using a small noncontacting probe to detect the associated magnetic-flux perturbation at the surface of the specimen. In the work reported here, analysis of the electric-current perturbation signals was based on an analytic solution for the change in current density caused by a slot of infinite length and finite depth. Comparisons were made with experimental data for electric-discharge machining (EDM) slots of various depths in Incology 901 where the electric current was introduced by ohmic contact. Excellent agreement between theory and experiment was obtained for deep slots, although the model predicts a more rapid decrease in signal amplitude with decreasing slot depth than is experimentally observed. Additional measurements made with fatigue cracks show that cracks as small as 0.45 mm in length are easily detected. It was concluded that the technique is not only a sensitive method for flaw detection, but also offers the possibility of determining flaw characteristics through analysis of signal shapes and amplitudes.