Integral equation method for evaluation of eddy-current impedance of a tilted, surface-breaking crack

An integral equation method for solving the eddy-current nondestructive evaluation problem for a flat, tilted, and surface-breaking crack in a conducting half-space is presented. The method involves use of a half-space Green's tensor and the Bowler potential. This potential describes the jump in the electric field over the crack and is expanded in basis functions related to the Chebyshev polynomials, being a more analytical approach than the commonly used boundary element method. In the method, the scatterer defines a transformation operator to be applied on the incoming field. This is practical in simulations of the eddy-current inspection where this operator is independent of the position of the probe. The numerical calculations of the change in impedance due to the crack are compared to a Finite Element model of the problem and good agreement is found.