Eddy-current interaction with an ideal crack. I. The forward problem

The impedance of an eddy-current probe changes when the current it induces in an electrical conductor is perturbed by a flaw such as a crack. In predicting the probe signals, it is expedient to introduce idealizations about the nature of the flaw. Eddy-current interaction is considered with an ideal crack having a negligible opening and acting as a impenetrable barrier to electric current. The barrier gives rise to a discontinuity in the electromagnetic field that has been calculated by finding an equivalent electrical source distribution that produces the same effect. The choice of source is between a current dipole layer or a magnetic dipole layer; either will give the required jump in the electric field at the crack. Here a current dipole layer is used. The strength of the equivalent source distribution has been found by solving a boundary integral equation with a singular kernel. From the solution, the probe impedance due to the crack has been evaluated. Although analytical solutions are possible for special cases, numerical approximations are needed for cracks of arbitrary shape. Following a moment method scheme, numerical predictions have been made for both rectangular and semielliptical ideal cracks. These predictions have been compared with experiments performed on narrow slots used to simulate ideal cracks. Good agreement has been found between the calculations and the measurements.