Eddy-current losses due to a surface crack in conducting material

Abstract

Calculations are reported for the spatial distribution of magnetic fields in the neighborhood of a long surface crack in a conductor, where a uniform ac magnetic field is applied parallel to the length of the crack. The problem is resolved into tractable parts consisting of the cases of eddy currents near a semi‐infinite crack with a sharp tip and eddy currents near a square corner. The semi‐infinite crack problem is solved exactly by a modification of Sommerfeld’s diffraction theory and the corner problem is treated by a Green’s function obtained by the method of images. The composite solution is valid for a crack of depth equal to four times the electromagnetic skin depth or greater. From the solution, the Poynting vector is calculated and its integral over the surface computed. The change in power dissipation relative to the ’’uncracked’’ surface is given in a simple form.