Impedance of a coil near an imperfectly layered metal structure: The layer approximation

Abstract

Changes in the impedance of a coil next to a one-dimensional layered conductor due to three-dimensional changes in the conductivity are studied. Eddy current probes are often used to inspect layered one-dimensional, nonmagnetic metal structures whose electrical conductivity varies primarily with depth beneath the surface. We present a perturbation method, the ‘‘layer approximation,’’ which yields simple and readily evaluated formulas for changes in the impedance of a small coil due to localized three-dimensional variations in the conductivity. The layer approximation is constructed to be accurate when the conductivity change due to the defect is small or the defect is nearly one-dimensional. The impedance is calculated and reported for a variety of defects in layered metal structures: voids, inclusions, interfacial roughness, and fasteners. We test the ‘‘robustness’’ of the layer approximation using an extreme case, a flat-bottom hole in an aluminum plate, as a ‘‘benchmark.’’ Both experimental measurements and more exact theoretical calculations are reported. Impedance measurements were made with a Hewlett–Packard 4194A impedance analyzer for a right-cylindrical flat-bottom hole in a 1-mm-thick 2024 aluminum alloy plate; the hole was on the side opposite to the coil. Frequencies were varied from 2.5 to 50 kHz. We also calculated the change in the impedance for this benchmark problem using the numerically exact volume integral method. For this benchmark problem, the layer approximation is in good agreement with experiment and more exact theory.

Numerical modeling of pulsed eddy current techniques for detection of corrosion and cracks

“…Satveli, Moulder, Wang and Rose [2] have recently developed a new perturbation method for computing the change in impedance induced by a three-dimensional defect in layered metallic structures. The layer approximation assumes that the defect is not crack like, that it localized, and that either the relative change in conductivity introduced by the defect is very small or that the sample is nearly one dimensional in the region where coil's electric field is significant.…”

“…Recently a new swept frequency based layer approximation technique was developed by Satveli, Moulder and Rose [2] for modeling the detection of corrosion in multi-layered aircraft structures. Their approach was based on an absolute comparison of measurement to the solution for the change in impedance of an air-core probe when placed on the defective layered metallic surface.…”

“…Bowler and Harrison [5] have reported on detection of corrosion using pulsed eddy current techniques. Beissner and Fisher [6,7] studied the application of pulsed eddy current [2][3] for detection and characterization of small cracks in titanium based jet engine alloys.…”

“…This is simpler and faster than frequency domain approaches, and the pulsed eddy current equipment developed for defect detection is less expensive than alternative approaches and easily portable. We take the layer approximation theory [2] for corrosion and the boundary integral method [3] for cracks as the basis for computing the change in impedance of the coil and then compute the transient voltagecurrent response for step-function excitation of the coil. Considerable effort has been made to reduce the computational complexity of calculations of the change in impedance of the coil.…”

Finite element and meshless methods in NDT applications

“…By applying Laplacetransform technique, Ludwig, Bowler and others have developed theoretical solutions for modeling of pulsed eddy currents in conducting half-space [35]- [37]. In the mean time, eddy currents techniques were widely applied to the detection of corrosion and cracks in multilayered aircraft structures in the Center for Nondestructive Evaluation at Iowa State University [38] [39]. In the next section, we will present several two-dimensional EFG models for multifrequency eddy current and pulsed eddy current testing.…”