Two-dimensional finite element model for a long rectangular eddy current surface coil

An eddy current model for predicting the electrical impedance variation of a long rectangular surface coil due to a surface breaking defect in layered conductors is reported. The method is based on transforming a three-dimensional eddy current problem into the spatial frequency domain and solving the transformed diffusion problem for a limited number of the spatial spectrum components. The transformed problem has been assumed to be quasitwo dimensional (2D) for a long rectangular surface coil and formulated in terms of a two-component transformed vector magnetic potential A and scalar electric potential <(phi)over bar>. The 2D problems have been solved with the finite element method using triangle elements. The system of algebraic equations was obtained using the Galerkin weak formulation and solved with the Gaussian elimination method. A high accuracy solution with ten spatial frequency components takes around 4 min on a Pentium 200 MHz PC. The accuracy of the solution has been tested experimentally at 200 kHz on coated stainless steel samples using a rectangular surface coil with the length-to-width ratio around 6. Agreement between theory and experiment is excellent. Discrepancies between the theory and experiment are within 15% and typically less. The method is useful for eddy current nondestructive evaluation and modeling, and can be also applied for the case of buried defects and for general multilayer coatings' problem. (C) 2000 American Institute of Physics. [S0034-6748(00)01002-9].