Boundary Element Simulation of Eddy Current Inspection

Abstract

Eddy current nondestructive evaluation (NDE) is a way of inspecting electrically conducting materials for the presence of flaws. The technique makes use of an eddy current field induced in the material by a coil which is scanned over the surface of the material. A flaw produces a perturbation of current flow, which is sensed as a change in the impedance of the probe. Modeling of eddy current NDE requires calculation of the unperturbed incident field, the eddy current perturbation caused by the flaw, and the resulting impedance change. Analytic methods exist for calculating the incident field; a reciprocity theorem is used to determine the impedance in terms of the field on the flaw surface, and the boundary element method (BEM) is used to calculate the flaw surface field. An approximate, scalar potential theory of the probe/flaw interaction is described, and the impedance calculation is recast in terms of the potential and its normal derivative on the flaw surface. The approximation that makes this possible is the so-called impedance boundary condition, which expresses the normal derivative of the potential in terms of tangential derivatives. Rizzo-Shippy shape functions are used to express tangential derivatives in terms of the potential at nodal points in calculating the BEM matrix. Computer codes are described for calculating the incident field, the BEM solution, and the impedance. Results are presented for a circular coil scanned over a slot in a flat plate. Comparisons with experimental data show generally good agreement, though some discrepancy exists. Additional calculations demonstrate that residual errors are caused by the failure of the impedance boundary condition at the corners of the slot, thus defining a problem on which further research is needed.