Thin-skin electromagnetic fields around surface-breaking cracks in metals

Abstract

There has been a long history of the use of two electromagnetic techniques to measure surface-breaking cracks in metals. Both the alternating current potential drop (ACPD) technique and the eddy current technique have given good agreement with experimental results, even though the theoretical models on which their interpretations are based use contrasting assumptions for the boundary condition on the metal surface. The model for the ACPD technique assumes that the magnetic scalar potential satisfies the 2D Laplace equation, while eddy current modeling assumes an approximation of Born type in which the surface field is unperturbed by the presence of the crack. This paper considers a general model matching the thin-skin electromagnetic field around a surface-breaking crack to that in the free space above and shows that the two contrasting boundary conditions are extremes of a more general one. The Laplace approximation is valid for high permeability materials such as mild steel, while the Born approximation is appropriate for materials of low permeability and high conductivity such as aluminum. Experimental investigations of the magnetic fields near semielliptical cracks in mild steel and aluminum show quantitative agreement with the theory.