Inversion of voltage measurements to predict crack shape

A surface-breaking crack in a metal sheet may be detected by passing an alternating current through the sheet. The perturbations in the surface electric field, produced by the crack, may be observed by making measurements of the voltage on the metal surface. In an earlier paper, it was shown that the crack shape could be predicted from the distribution of potential along the top of the crack. This work extends the previous work to the more realistic case, where the initial data is in the form of measurements of the potential difference, rather than the potential itself. In addition, it is assumed that the strength of the upstream electric field is unknown. A Fredholm integral equation of the second kind is derived, for the potential distribution along the top of the crack, in terms of measurements of the potential difference. This equation is solved using theoretical voltage distributions derived from idealised ~ crack shapes.