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.

We propose a volume integral equation formulation for eddy-current nondestructive evaluation of ferromagnetic tubes affected by volumetric defects. We solve the system of integral equations (introduced into the model by application of Green's theorem) by the method of moments for both fictitious electric and magnetic currents within the defects, and calculate variations of impedance of the probes by the reciprocity theorem. We have made thorough comparisons of our results with finite-element-method simulations and with experimental data as well.

We present a development on an existing model for the electromagnetic interaction of a coil with a conductive cylinder. We can now calculate analytically both the electromagnetic field and the impedance of arbitrarily positioned probe coils. This is possible by using an appropriate expansion of cylindrical eigenfunctions in terms of eigenfunctions of the Cartesian coordinate system. The extended model is useful in simulating eddy current inspections of cylindrical structures under conditions of probe tilt as well as inspections with special coil orientations like the rotating probe coil.

Magnetic losses in a ferromagnetic lamination can be separated into three contributions. Bertotti theoretically assessed this distribution at the end of the 20th century in the Statistical Theory of Losses (STL), triggering significant progress in understanding the dissipation mechanisms. Recent studies have shown the possibility of reconstructing a hysteresis cycle from the high-frequency Barkhausen noise signal. Applying STL to the Barkhausen noise cycles has never been done before. Still, it could help establish a parallel with the measurement of the magnetization cycle versus frequency and the energy loss. However, STL analysis in its ultimate description requires sinusoidal flux density, while Barkhausen noise measurements are usually done with a constant excitation slope. Multiple magnetic flux density control methods were described in the literature and are reviewed in this manuscript. However, the Barkhausen noise context, requiring high-frequency sampling during the magnetization cycle, is more constraining. Therefore, specific performance criteria were considered, followed by numerical tests to determine the most adapted method to a Barkhausen STL description. Eventually, the Proportional Iterative Learning Control (P-ILC) gave the highest satisfaction rate and was chosen for experimental tests. Some of these experimental results are provided in the manuscript discussion together with suggestions for convergence speed improvement. It is, for instance, recommended to increase the gain near saturation, where the system response is poor.

The complex impedance of an air-cored coil in a conductive tube with eccentric inner and outer cylindrical surfaces is calculated. The analytic expressions for the induced fields and the impedance variation due to the eddy-current flow inside the tube wall are derived using a second-order potential approach. The addition theorem of Bessel functions is employed to perform the transition between the local coordinate systems that conform to the boundaries of the structure. Although the model can be used for any coil shape and orientation, we focus our study on the configuration of a bobbin coil with axis parallel to the axes of the tube surfaces, but not necessarily coinciding with either of them. The results of the presented analysis are verified by a finite-element-method (FEM) solution.

A semianalytical solution to the eddy-current induction problem in a conducting, nonmagnetic plate near a cylindrical through-hole is derived by means of the second-order vector potential and the domain truncation technique. The construction of a solution, which simultaneously satisfies the field continuity across the cylindrical surface of the hole and the planar interfaces of the plate, proves to be a very challenging problem, and thus, a special superposition of partial subsolutions is proposed. The presented solution is part of a more general development aiming at the calculation of the probe interaction with material flaws located in the vicinity of the hole by means of the integral equation formalism. These tasks will be the subject of a future paper. The comparison of the semianalytical results against both finite-element simulations as well as experimental data demonstrates excellent agreement.