Analytical methods in eddy current non-destructive evaluation.
The two-dimensional problem of a long crack in a non-magnetic, half-space conductor
lying perpendicular to the flow of eddy-currents induced by a one-dimensional external current
sheet is studied in the context of eddy-current non-destructive evaluation. Impedance
changes due to closed, surface-breaking cracks and deep, subsurface cracks are calculated.
The Wiener-Hopf technique is used to obtain an approximate solution for the magnetic field
scattered by a subsurface crack and hence the impedance change. The solution is accurate
to within 5% for cracks whose edges lie more than one electromagnetic skin depth (8) below
the conductor surface. For the surface-breaking crack the Wiener-Hopf method yields a
high-frequency asymptotic series solution for the magnetic field. The first term corresponds
to the limit in which the field perturbations by the edge and corners of the crack are decoupled.
The impedance change in this limit is found in closed form. Use of the Wiener-Hopf
procedure in rigorously treating the open crack problem is investigated. The opening of a
deep, subsurface crack whose width is much less than 0 is found to be undetectable to first
order in the opening.
A geometrical theory of eddy-current scattering is developed, based on the optical Geometrical
Theory of Diffraction. The theory includes a procedure which accounts for multiple
scattering of the fields between the edge of a crack and its image. The method is applied
to subsurface and surface-breaking cracks, yielding solutions for a subsurface crack whose
edge lies only 0.48 below the conductor surface and for a surface-breaking crack of depth 8
Finally, perturbation theory is applied to the surface-breaking crack problem in the lowfrequency
limit, giving the impedance change for a crack of depth up to 0.40