The volume integral method of eddy-current modeling: Verification

Abstract

The volume integral method of eddy-current modeling represents a flaw in metal as a set of electric dipoles located within volume elements or cells defining the flaw volume. Given this dipole distribution, impedance changes may be computed. The electric field of the dipole distribution is determined by an integral equation relating, by means of the electric field Green's tensor, the electric field due to the source to the total electric field in the flaw. The integral equation is solved by assuming that the total electric field is constant in each volume element, resulting in a matrix equation. The method has been programmed for use on a microcomputer. The method and computer program are verified using the analytical solution for a small spherical flaw and three sets of measured impedance data, measured by air-core coils along profiles overlying both surface-breaking and buried simulated flaws of known dimensions. Operating frequencies ranged between 900 and 4000 Hz. Generally agreement is good at lower frequencies (∼ 1000 Hz). At higher frequencies (∼ 4000 Hz), the agreement is not as good. This is thought to be due to the inability of the constant electric field approximation to model the steep electric field gradients present in the host metal at high frequency. The results are also sensitive to the method of computation of the electric field due to the source. Some improvements can and should be made to the method.