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

In situations where the electrical skin depth δ is small compared with a typical crack dimension l, substantial progress has been achieved in recent years in modeling surface electromagnetic fields and the perturbations that are produced in them by surface-breaking flaws [1,2,3]. The development of an unfolding theory at UCL for thin-skin surface fields was based on the approximation that the electric and magnetic field vectors E and H are essentially tangential to the surface of the material in the surface skin. It was motivated by the desire to measure fatigue cracks in ferrous materials used in large-scale steel structures such as offshore oil rigs [2], and the method to which it was applied was the a.c. field measurement technique. Auld et al [4,5] later adapted the unfolding approach in considering thin-skin field models for the eddy current method, and their major concern was with applications to non-ferrous materials used in airframe and aero-engine manufacture. For acfm work, the unfolding theory leads to a surface Laplacian field on both the metal surface and the crack face and information on the crack presence is deduced by measuring perturbations in the surface field. Auld’s model for eddy currents also has a plane Laplacian field on the crack face, but it is assumed that the crack produces no change in the field on the metal surface. Field lines in the unfolded plane for both models are shown schematically in Figure 1(b,c) for the case when the interrogating field is uniform and the crack is semi-circular. Auld’s model has been described as a Born type of approximation from an analogy with wave scattering theory which ignores the scattered field when calculating scattering cross-sections.