Analytical solution for magnetic field of cylindrical defect in eddy current nondestructive testing

In metal components, a defect frequently causes the failure of the components and results in serious accidents consequently. Eddy current nondestructive testing method is one of the most effective testing approaches to quantitatively monitor the defects both in non-ferrite metal and in ferrite metal. Therefore, knowledge of the magnetic field is necessary to deeply understand the mechanism of eddy current nondestructive technique in defect characterization. In this paper, an analytical expression for the magnetic field for a cylindrical defect in metal in eddy current testing system is proposed by solving the partial differential equations. Firstly, a conductive metal plate with a cylindrical defect is modeled for the cylindrical coil with rectangular cross-section, and the analytical expression to the magnetic potential vector is obtained. Then, the series form expressions are extended to calculate the axial component of magnetic induction intensity B-z and is computed on the MATLAB platform. Finally, a finite element model is setup to validate the proposed analytical expression for the magnetic field. The results show that the magnetic field calculated by the analytical method is in good agreement with that calculated by finite element method, and the calculation efficiency of the analytical method is higher than that of FEM. The proposed expressions not only can be readily used to investigate the quantitative relationship of the cylindrical defects in a conductive metal, but also it is expected to be extended to seek the theoretical expression for the elliptic defect and also for the natural defect in key structures (e.g. oil pipe, rail track, iron bridge, oil tank, ocean ship) by using (pulsed) eddy current nondestructive technique.