# Eddy Current Testing Models for the Analysis of Corrosion Effects in Metal Plates

## Abstract

Direct method for the solution of eddy current testing problem for the case where an air core coil is located above a conducting two-layer plate with a flaw in the form of a cylindrical inclusion with reduced electrical conductivity is presented in the paper. Semi-analytical approach (the TREE method) is used to construct the solution of the system of equations for the components of the vector potential. The flaw is assumed to be symmetric with respect to the coil. Numerical calculations are performed using the proposed model and Comsol Multiphysics software. The obtained values of the change in impedance of the coil for both methods are found to be in a good agreement. The proposed model can be used for the assessment of the effect of corrosion in metal plates.

## Notes

### Acknowledgements

This work was partially supported by the grant 632/2014 by the Latvian Council of Science.

## References

- 1.Antimirov, M.Ya., Kolyshkin, A.A., Vaillancourt, R.: Mathematical Models for Eddy Current Testing. CRM, Montréal (1997)Google Scholar
- 2.He, Y., Tian, G., Alamin, M., Simm, A., Kackson, P.: Steel corrosion characterization using pulsed eddy current systems. IEEE Sensors J.
**12**, 2113–2120 (2012)CrossRefGoogle Scholar - 3.Koliskina, V., Kolyshkin, A.: Mathematical model for eddy current testing of metal plates with two cylindrical flaws. In: Leonowicz, Z. (ed.) Proceedings of the 15th International Conference on Environment and Electrical Engineering, pp. 374–377. Elsevier, Institute of Electrical and Electronics Engineers (2015)Google Scholar
- 4.Rodriguez, A.A., Valli, A.: Eddy Current Approximation of Maxwell Equations. Springer, New York (2010)CrossRefMATHGoogle Scholar
- 5.Skarlatos, A., Theodoulidis, T.: Solution to the eddy-current induction problem in a conducting half-space with a vertical cylindrical borehole. Proc. Roy. Soc. Lond.
**468**, 1758–1777 (2012)MathSciNetCrossRefMATHGoogle Scholar - 6.Skarlatos, A., Theodoulidis, T.: Calculation of the eddy-current flow around a cylindrical through-hole in a finite thickness plate. IEEE Trans. Magn.
**51**(9), (2015). doi:10.1109/TMAG.2015.2426676Google Scholar - 7.Tegopoulos, J.A., Kriezis, E.E.: Eddy Currents in Linear Conducting Media. Elsevier, Amsterdam (1985)Google Scholar
- 8.Theodoulidis, T.P., Kriezis, E.E.: Eddy Current Canonical Problems (with Applications to Nondestructive Evaluation). Tech Science Press, New York (2006)MATHGoogle Scholar
- 9.Touzani, R., Rappaz, J.: Mathematical Models for Eddy Currents and Electrostatics. Springer, New York (2014)CrossRefMATHGoogle Scholar