Evaluation of the magnetic field near a crack with application to magnetic particle inspection

In this paper, the magnetic field at the mouth of a crack in ferromagnetic steel is determined by means of a two-dimensional, linear model. The solution is found by employing an analytical method in which one complex variable is transformed into another by means of a mapping function. An approximate boundary condition, based on the fact that the steel permeability is much larger than that of free space, is used. In this way, three representations of a crack are treated: narrow and open cracks and a semi-elliptical indentation. The mapping function transforms these shapes into a half-plane geometry for which the solution is easily obtained. The advantage of this analytical approach is that the results are readily accessible without the need for a large numerical code. Example calculations are compared with each other and with calculations based on a former theory. This work has application in electromagnetic non-destructive evaluations: eddy-current testing, flux leakage measurements and, most directly, magnetic particle inspection. (author)