A geometrical theory for eddy-current non-destructive evaluation

Abstract

In eddy-current non-destructive evaluation, an electromagnetic field is induced in a metal by means of an eddy-current probe and the presence of a flaw is indicated by a change in probe impedance. In order to predict the impedance change, it is necessary to calculate the electromagnetic field in the region of the flaw. We present a new method, based on the geometrical theory of diffraction, by which approximate analytical solutions for the electromagnetic field near to a crack can be calculated for intermediate and high frequencies. Two-dimensional field solutions are found for (i) a buried crack and (ii) a surface-breaking crack in a conducting half-space. The fields are constructed using solutions which satisfy the field equations exactly but approximate the boundary conditions. The degree to which the predicted fields match the required boundary values on the plane of the crack and the air-conductor interface plane is assessed and very good agreement is obtained for cracks whose edges lie half a skin-depth or more below the conductor surface. The impedance change due to the crack is calculated in closed form.

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

“…11 At the crack mouth the expansion functions have a finite value to admit a finite value of the jump in electric field. Inserting the sum of the expansions of the Green's tensor (8) and (10) and the expansion of the unknown (13) into the integral Eq. 7, projecting the result on the Chebyshev functions and taking a Fourier transform in y yields…”

“…4 Harfield and Bowler 5 give a closed form expression for the change in electromagnetic impedance of a conductor due to the presence of an infinitely long, perpendicular surface-breaking crack in a normally incident, uniform electric field. The perturbed electromagnetic field was more accurately calculated using Wiener-Hopf technique than Auld et al 6 A similar problem is considered by Kahn et al 7 Harfield and Bowler 8 develop a method based on geometrical theory of diffraction (GTD) for eddy-current nondestructive evaluation. Lewis et al 9 investigate thin skin electromagnetic scattering of a semi-elliptical surface-breaking crack in an infinite halfplane interrogated by a uniform surface current.…”