A geometrical theory for eddy-current non-destructive evaluation

Abstract

In eddy-current non-destructive evaluation, an electromagnetic field is induced in a metal by means of an eddy–current probe and the presence of a flaw is indicated by a change in probe impedance. In order to predict the impedance change, it is necessary to calculate the electromagnetic field in the region of the flaw. We present a new method, based on the geometrical theory of diffraction, by which approximate analytical solutions for the electromagnetic field near to a crack can be calculated for intermediate and high frequencies. Two-dimensional field solutions are found for (i) a buried crack and (ii) a surface-breaking crack in a conducting half-space. The fields are constructed using solutions which satisfy the field equations exactly but approximate the boundary conditions. The degree to which the predicted fields match the required boundary values on the plane of the crack and the air––conductor interface plane is assessed and very good agreement is obtained for cracks whose edges lie half a skin–depth or more below the conductor surface. The impedance change due to the crack is calculated in closed form.