Vector potential integral formulation for eddy-current probe response to cracks

A boundary integral vector potential formulation has been developed to evaluate eddy-current interactions with three-dimensional finite cracks in conductors. The approach is compared with an electric field integral equation method also used for solving crack problems in eddy-current nondestructive evaluation. An important advantage of the vector potential integral formulation is that the kernel has a weak singularity, but a drawback is that two unknown functions must be found on the crack surface. One of these functions, the current dipole density, represents the effect of the crack in terms of an induced source, and the other function is a solution of the two-dimensional Laplace equation. By contrast, the source density alone is needed for a complete solution of the electric field integral equation. In order to determine the surface Laplacian for finite cracks of arbitrary shape, a general numerical solution utilizing the boundary element technique is introduced. Numerical predictions of the eddy-current probe response to a crack give good agreement with experimental measurements, supporting the validity of the formulation.