Development of the curvilinear coordinate method for the computation of quasi‐static fields induced by an eddy current probe scanning a 3D conductor of complex shape characterized by an arbitrary 2D surface

Abstract

This paper deals with the development of a semi-analytical model for the fast computation of the quasi-static field induced by any eddy current probe in a 3D conductor of complex shape. The workpiece is considered as a planar half-space mock-up with an interface air conductor characterized by an arbitrary 2D surface a(x, y). The curvilinear coordinate method consists in introducing a change of coordinates to be able to write analytically and easily the boundary conditions at the interface air-metal. Due to the novel generalized metric space, the covariant form of Maxwell equations must be considered. The curvilinear coordinate method is widely used in the optical community for the analysis the diffraction phenomenon on gratings. The method has been applied recently for eddy current calculations in the planar case for 2.5D configurations characterized by a 3D eddy current probe and a 2D layered stratified conducting media. By an extension to 3D problems, this work constitutes the preliminary task for the development of a complete numerical model, which has the capability to address very complex eddy current nondestructive testing configurations such as a stratified layered media constituted by a set rough interfaces. For that purpose, the modal formalism is described for the first time in the 3D case, and several numerical experiments show the validity and the efficiency of the fast numerical model in comparison to the finite element method. KEYWORDS computational electromagnetics, covariant form of Maxwell equations, eddy current nondestructive testing, rough surfaces 1 Int J Numer Model. 2018;31:e2219.wileyonlinelibrary.com/journal/jnm

Investigation of layer interface model of multi-layer structure using semi-analytical and FEM analysis for eddy current pulsed thermography

“…We take also the assumption of variable separation: so . The modal representation of the field depends on the truncation orders and of the FT. Numerically, each component is a matrix of dimension L, with Depending on the nature of the considered anisotropic layer, the modal decomposition is presented in [12].…”

“…In the meantime, CEA LIST has recently developed a new semi-analytical method for the computation of the 3D primary fields induced by an eddy current probe in a homogeneous conductor presenting a local perturbation of the geometry [11]. This approach is an extension of the curvilinear coordinate method (CCM), which is efficient for the computation of the fields scattered by 2D diffraction gratings enlightened by a plane wave or perfectly conductive random surfaces [12,13].…”

Special issue: The 10th International Symposium on Electric and Magnetic Fields (EMF 2016)

“…Four broad topics were covered during this 10th edition of the symposium. The first major topic considers the mathematical modelling of electromagnetic problems in view of their eventual numerical solution on computers, with contributions on the modelling of electromagnetic forces, high‐temperature superconductors, eddy current problems,() and high‐frequency Maxwell/transport phenomena . The second major topic treats the numerical modelling of the electromagnetic behavior of electric and magnetic materials, with contributions on the modelling of magnetoelectric multilayer laminate composites, the magneto‐elastic behavior of steel sheets, the effect of mechanical stresses on Graphene‐based devices, and the effect of temperature on static magnetic hysteresis .…”