Solution to the eddy-current induction problem in a conducting half-space with a vertical cylindrical borehole

Abstract

The eddy-current induction problem in a conducting half-space with a vertical borehole is studied and a solution based on modal techniques is presented. Owing to the particular characteristics of the specific geometry, the straightforward application of the truncated region eigenfunction expansion method (a well-established tool for the analytical solution of such problems) presents significant difficulties. Therefore, a modified truncation approach has been adopted that treats the problem in two steps, each one based on the superposition principle. The approach proves to be very efficient and numerically robust. Results for the coil impedance are in excellent agreement with those obtained with the finite-element method. From the engineering point of view, the geometry simulates the eddy-current inspection of fastener holes in aircraft structures when coil scanning is performed from the surface. The presented solution constitutes an important step towards the development of a complete model for fastener hole crack inspections.

Direct Eddy Current Method for Volumetric Flaws of Cylindrical Shape

“…Examples of the application of the TREE method to the solution of direct eddy current testing problems with cylindrical symmetry can be found in [3], [5], [6], [7]. The case of an asymmetric infinite cylindrical flaw is considered in [8]. In the present paper we present the solution of eddy current testing problem for the case of a cylindrical flaw in a two-layer plate.…”

Calculation of Eigenvalues for Eddy Current Testing Problems

“…Determination of complex eigenvalues is one of the important steps in the TREE method (see examples in [11] and [12]). Recently asymmetric problems of eddy current testing problems were solved in [13]− [16]. Solutions were obtained using the second order vector potential formulation.…”

Simulation of Cracks Detection in Tubes by Eddy Current Testing

“…{A} ={b} (14) where [k] is the (N × N) banded symmetric complex global matrix, and {b} and {A} are the (N x 1) complex source vector and the (N × 1) complex vector of unknowns (N is the total number of nodes in the studied domain). The system is solved using in-house code developed by the authors.…”

“…And analytical solutions for the problems where the properties are constant or no can be found in the literature (see, for example (Koliskina and Volodko [12], Fan et al [13], Skarlatos and Theodoulidis, [14]). …”