Analysis of eddy-current interaction with a surface-breaking crack

Abstract

The change in electromagnetic impedance of a conductor due to the presence of a long, perpendicular surface-breaking crack in a normally incident, uniform electric field is calculated in closed form in the high-frequency limit. At high frequencies, where the skin depth is much smaller than the depth of the crack, the fields near the edge and corners of the crack are effectively decoupled. This means that the solution may be formulated as the sum of contributions from the corners, faces, and edge of the crack. Simple analytical expressions for the electric field are found and used to calculate the impedance due to the crack in the high-frequency limit without resorting to numerical methods.

Analysis of eddy current formulations in two-dimensional domains with cracks

“…Eddy current testing, for example, as a particular technique of non destructive testing, remains one of the most popular tools in the quality control of conducting test pieces, and an important number of papers in the electric engineering community, mostly based on integral equation techniques, is devoted to numerical methods for crack detection (see e.g. [11,12,14,15,27]). In a typically configuration of eddy current testing, a coil carrying an alternative current is placed in proximity to the conducting test piece.…”

A geometrical theory for eddy-current non-destructive evaluation

“…The solutions of independent 'face', 'edge' and 'corner' problems together yield that for the crack. While it has recently been shown that the solution of Kahn et al (1977) does indeed arise in the high-frequency limit of a rigorous solution in which decoupling is not assumed at the outset (Harfield & Bowler 1995b) and the impedance change has now been evaluated in closed form rather than numerically (Harfield & Bowler 1994), the solution of this fundamental problem has remained essentially unimproved. The technique introduced in this work improves the solution of Kahn et al (1977) by providing a systematic means by which the coupling between the perturbed fields at the crack edge and mouth can be evaluated.…”

“…The second contribution accounts for the fact that the current distribution is non-Laplacian at the edge of the crack (buried in the conductor) and in the corners where the crack meets the conductor surface. The 1122 N. Harfield and J. R. Bowler edge and corner contributions for a crack of finite length have been approximated by Auld (1981) from their exact values for an infinitely long crack in a uniform field (Kahn et al 1977;Harfield & Bowler 1994).…”

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

“…There have been several studies of simulating scattering of eddy-currents from cracks in a conducting half-space during recent decades, see Auld and Moulder. 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.…”