Eddy-current nondestructive inspection with thin spiral coils: Long cracks in steel

The impedance of a cylindrical coil and a planar circular spiral coil carrying an alternating current above (i) a defect-free conducting magnetic half-space and (ii) a conducting magnetic half-space containing an infinitely long slot with uniform depth and width is examined in detail. Closed-form expressions for the coil impedance in these cases are presented, based on the theories of Dodd and Deeds and Harfield and Bowler. The validity of these expressions is tested by measurements using steel plates over the frequency range 100 Hz-10 MHz. The theoretical predictions are in good agreement with experiment, with the best agreement for the smallest slot width. The results confirm that thin, flexible spiral coils offer some attractive features for eddy-current detection of cracks in metals, particularly in terms of sensitivity and potential for unobtrusive permanent attachment to the material being inspected. Approximate expressions for a spiral coil above a defect-free magnetic half-space are also given to allow easy calculation in limiting cases.