The electromagnetic field around a subsurface flaw in a metal

This work is a theoretical investigation into the detection and measurement in metals of flaws that do not break the surface, with the use of AC electric fields. The flaw is modelled by a semi-infinite slot, which is perpendicular to the surface and whose top edge is at a finite distance below the surface. The electromagnetic field is governed by Maxwell's equations and the skin depth of the field is assumed to be large compared to the ligament remaining between the top edge of the crack and the metal surface. Matched asymptotic expansions are used to describe the field mathematically and numerical results are presented, illustrating the variation of the potential difference on the surface of a number of metals with different-size ligaments in them. Good agreement is obtained from comparisons with some results using a Fourier-series technique. It is found that the maximum centreline voltage signal is obtained if measurements of the potential difference are made at a phase of approximately — 1/4π compared to the upstream signal.