Semi‐analytical computation of a quasi‐static field induced by a 3D eddy current probe scanning a 2D layered conductor with parallel rough interfaces

Abstract

This paper deals with the fast computation of the quasi‐static fields induced in a conductor with a locally perturbed shape along the longitudinal axis and extruded along the transversal one. Besides, the material is composed of several homogeneous layers with parallel faces. The method used here is based on writing Maxwell's equations in a curvilinear system, which leads to a more simple expression of boundary conditions. The validity of this method for the computation of quasi‐static fields induced by an eddy current probe in a conductive half‐space with a rough surface has been proved recently, and we propose here to complete this innovative formalism in order to solve an eddy current non‐destructive testing (ECNDT) configuration with a rough surface conductive medium composed of several homogeneous layers with parallel faces. This extension allows to tackle new ECNDT configurations such as homogeneous media constituted by rough interfaces. Moreover, it provides sufficient solutions for non‐homogeneous conductive parts presenting a depth‐varying (i.e., along the direction of the normal local vector with respect to the surface) material property, which can be approximated by a piecewise constant function by introducing multiple thin homogeneous layers. Copyright © 2014 John Wiley & Sons, Ltd.

Fast Computation of the Fields Diffracted by a Multi-Layered Conductor With Non-Parallel Rough Interfaces. Application to Eddy-Current Non-Destructive Testing Simulation

“…The S-matrix algorithm described in [3] leads to an efficient computation of the amplitudes b + 0 and b − N for a layered medium as shown in Fig. 2.…”

“…The differential system (2) translated in the Fourier domain becomes an eigenvalue problem [3]. Since the problem is discretized in a matrix system, the eigenvalues denoted by λ p for each medium p are obtained and we denote by ψ p and φ p the eigenvectors corresponding to the functionsˆ p (u, v) and p (u, v), respectively.…”

“…The source-free covariant Maxwell equations are now considered as well as the constitutive relationships. According to the second-order vector potential formalism for nonorthogonal curvilinear systems [3], the electromagnetic fields 0018-9464 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.…”

“…In this way, boundary conditions, thus containing all the internal interactions occurring in the specimen are easily written analytically without any mesh and lead to the computation of all the coefficients of the modal expansions. in the extension of the previous modal formalism [3] to tackle more complex cases of planar layered conductors presenting non-parallel rough interfaces. The strategy is almost similar excepted that for non-parallel interfaces, each profile must be associated with its own non-orthogonal basis.…”

“…More recently, this approach has been coupled with a recursive and stable algorithm [3] to consider a layered conductor presenting several parallel rough interfaces. By associating the same change of coordinates for all interfaces, the solutions of Maxwell equations, expressed in a covariant form, are expanded in a sum of eigenfunctions forwardly depending on the analytical expression of the interface.…”