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Skin effect

When eddy currents are induced in a conductor, they generate their own magnetic field, regardless of the depth at which they circulate. This induced field opposes the primary magnetic field, reducing the intensity of the eddy currents as depth increases. This phenomenon is known as the skin effect. The penetration depth of eddy currents decreases as the conductor’s electrical conductivity, magnetic permeability, or the excitation frequency increases. By convention, the standard penetration depth is defined as the depth at which the eddy current density has decreased to 36.8% (or 1/e) of its surface value, where e = 2.718 is the base of the natural logarithm. The standard penetration depth δ (in millimeters) is given by: δ = 50√(ρ / (f μr)) where: ρ is the electrical resistivity in µΩ·cm, f is the excitation frequency in Hz, μr is the relative magnetic permeability of the material compared to air. For non-magnetic materials (and vacuum), μr = 1. The above equation applies only to a material of infinite thickness (thickness > 5δ) and to a plane electromagnetic wave, such as that produced by a large-diameter coil. Since these conditions rarely apply in practice, the equation should be seen as an approximation of the actual penetration depth. In thin-walled tubes, such as steam generator tubes, eddy currents are confined to the tube wall. As a result, part of the magnetic field extends beyond the wall, leading to a higher eddy current density within the tube than the standard penetration depth equation would predict.

Sources

  1. “Samson, R. (1999). Eddy current hybrid probe with movable magnetic field altering member. United States Patent US5926020A.
  2. Bisiaux, B., Réboud, C., Prémél, D., Pichenot, G., & Lesselier, D. (2006). Simulation of 3D eddy current testing of tubes with external probes: modelling approach and experimental validations. Proceedings of ECNDT 2006, paper We.2.3.1, pp. 1–8.
  3. Demaldent, E., Réboud, C., Sollier, T., & Cattiaux, G. (2014). Efficient simulation of steam generator tube inspection with the PlusPoint eddy-current probe. 11th European Conference on Non-Destructive Testing (ECNDT 2014) / e-Journal of Nondestructive Testing, Vol. 19(12), article id.”
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Figures 1 and 2 illustrate the decay and phase shift of eddy currents with depth.