Vector-potential boundary-integral evaluation of eddy-current interaction with a crack

In eddy-current nondestructive evaluation, an excitation coil, used to induce current in a conductor, changes impedance in the presence of a crack. The impedance change can be calculated from a knowledge of the coil parameters, the excitation frequency, and the crack geometry. Two boundary integral formulations of the problem are compared. The first formulation uses an electric field integral equation, and the second expresses the magnetic vector potential in integral form using an integral kernel with a weaker singularity. The vector potential formulation, presented here for the first time, leads to a more complicated equation but has a singular kernel that is easier to deal with. In addition, the new approach opens up a number of possibilities for further analytical developments. An example calculation is performed for a long, surface-breaking crack, and the results are compared to available analytical solutions. Very good agreement is found between the numerical solution of the integral equation and the analytical results.