Semi-analytical computation of a quasi-static field induced by an eddy current probe in a conductor with a rough surface^*

¹ CEA, LIST, Laboratoire de Simulation et Modélisation, 91191 Gif-sur-Yvette Cedex, France
² Institut Pascal, Université Blaise Pascal, France

^a e-mail: francois.caire@cea.fr

Received: 27 September 2012
Revised: 4 December 2012
Accepted: 10 April 2013
Published online: 6 November 2013

Abstract

Semi-analytical models developed at Cea List for the simulation of Eddy current non-destructive testing are currently based on the volume integral equation formalism. This method is very effective for canonical geometries such as planes or cylinders since the analytical expressions of Green’s dyads are known. This approach requires three steps: the computation of the quasi-static fields induced by the probe in the workpiece without flaw, the determination of the interaction between the primary field and the defect and finally, the calculation of the response of the eddy current sensor, resulting from this interaction. In order to generalize this approach to more complex configurations, in this paper, we focus on the first step: the computation of quasi-static fields induced by an eddy current probe in a conductor with a rough surface. The semi-analytical model we generalize here is based on Maxwell’s equations, written in a non-orthogonal coordinate system resulting in the writing of the boundary conditions at the interface by using a simple analytical expression. Starting from the second-order vector-potential formalism dedicated to non-orthogonal curvilinear coordinate systems, two scalar potentials are expressed as a modal expansion, satisfying the outgoing wave condition. Finally, the coefficients of the modal expansion are determined by applying boundary conditions at the complex interface. First numerical results, obtained considering a specific configuration, are compared to other Finite Element data.