Thin-skin electromagnetic fields in the neighbourhood of surface-breaking cracks in metals

Abstract

Electromagnetic non-destructive evaluation techniques are widely used to detect and size surface-breaking cracks in metal structures and components. The precise distribution of the electromagnetic field around such a crack depends on the frequency of the applied field, the material properties of the metal and the crack geometry. In many situations, the skin depth of the electromagnetic field in the metal is small compared with the crack dimensions. If this is the case, the crucial parameter that determines the way the electromagnetic field in air couples to the field in the metal is m = μ 0 l / μδ , where μ and μ 0 are the metal and free space permeabilities respectively and l / δ is the ratio of the crack length scale l to the skin depth δ . If the metal is ferromagnetic, m can take a wide range of values and the distribution of the electromagnetic field around the crack is very different in the two limiting cases m = 0 and m ≫ 1. In the first case, the magnetic flux emerging from the crack is directed into the metal surface whereas in the second case, the flux is directed into free space. In this work, the distribution of the electromagnetic field around a surface-breaking crack is determined for arbitrary values of m . The theory is developed for cracks of general shape and numerical calculations of the free-space components of the magnetic field are made for rectangular and semi-elliptical shaped cracks. The numerical predictions are found to be in good agreement with experimental measurements of the magnetic field above a rectangular slot, cut in a flat plate of mild steel.