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

International audienceSemi-analytical models developed at Cea List for the simulation of Eddy current non-destructivetesting are currently based on the volume integral equation formalism. This method is very effective forcanonical geometries such as planes or cylinders since the analytical expressions of Green’s dyads areknown. This approach requires three steps: the computation of the quasi-static fields induced by the probein the workpiece without flaw, the determination of the interaction between the primary field and the defectand finally, the calculation of the response of the eddy current sensor, resulting from this interaction. Inorder to generalize this approach to more complex configurations, in this paper, we focus on the firststep: the computation of quasi-static fields induced by an eddy current probe in a conductor with a roughsurface. The semi-analytical model we generalize here is based on Maxwell’s equations, written in a nonorthogonal coordinate system resulting in the writing of the boundary conditions at the interface by usinga simple analytical expression. Starting from the second-order vector-potential formalism dedicated tonon-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 determinedby applying boundary conditions at the complex interface. First numerical results, obtained considering aspecific configuration, are compared to other Finite Element data