Inversion of voltage data to predict crack shape

Abstract

Surface-breaking cracks in metal sheets may be detected by injecting alternating current into the sheet and observing the resulting nonuniformity in the surface electromagnetic field. The current is forced to flow in a thin skin near the surface of the metal with a skin depth, I)= ..f2tlyl, where (1) and Jl is the permability of the metal, o is the conductivity and ro is the angular frequency of the interrogating field. At a frequency of 6 kHz the skin depth of the field in mild steel is about 0.1 mm which is much less than the typical length scale associated with many of the surface-breaking flaws of interest. Using a thin skin approximation, therefore, Michael et al [1] showed that if a uniform current is incident on a crack in a ferrous metal, the electric field may be written as In ferrous metals at relatively low frequencies, Lewis et al [2] showed that it is a reasonable approximation to assume that both the normal and tangential components of the electric field are continuous at the crack edge and so the potential distribution in the plane of the crack is an analytic continuation of the potential distribution on the upper surface of the metal. Thus, the crack face may be 'unfolded' into the same plane as the metal surface resulting in a two dimensional boundary value problem for a single potential in a region with a partially unknown boundary, as illustrated in figure 1. Continuity of magnetic flux across the lower edge of the crack requires the potetnial to be zero along the line ABCDE while the uniform upstream field is modelled by <ll(x,y) -y as (x 2 + yZ)' 12 --+ oo y ~ 0