The Application of Finite Element Method Analysis to Eddy Current NDE

The Finite Element Method for the computation of eddy current fields is presented. The method is described for geometries with a one component eddy current field. The use of the method for the calculation of the impedance of eddy current sensors in the vicinity of defects is shown. An example is given of the method applied to a C-magnet type sensor positioned over a crack in a plane conducting material. INTRODUCTION Eddy current NDE techniques detect defects in a conducting material by using a sensor which induces currents in the material, and then observing the changes in the impedance of the sensor in the vicinity of the defect. The theoretical analysis of the relation between the defect properties and the impedance change requires the solution of Maxwell's equations to determine the current fields in the material. For most practical problems, the geometry is too difficult for closed form analytic solutions, and numerical solutions are required. The most promising numerical technique for computation of eddy current fields is the Finite Element Method. This method has long been used in stress analysis and heat flow problems (Ref. 1), and in recent years has been applied to the computation of eddy current fields in electrical machines (Ref. 2). The method has also been used to investigate a problem in magnetostatic NDE (Ref. 3), but has not been applied to eddy current NDE, which is a time varying field problem. In this paper, the Finite Element Method for the computation of eddy current fields is presented. The method is described for geometries with one component eddy current field, for which the problem reduces to the solution of the two-dimensional diffusion equation. The use of the method for the calculation of the impedance of eddy current sensors is explained. An application of the technique to the case of a C-magnet type sensor over a crack in a plane conducting material is shown. Derivation of the Diffusion Equation for OneComponent Vector Potentials In eddy current testing, the frequencies are usually low enough that the displacement current term in Maxwell's equations is negligible. Under this assumption, Maxwell's equations become