John C. Moulder

Review of Advances in Quantitative Eddy Current Nondestructive Evaluation

A comprehensive review of advancements in eddy current (EC) modeling is presented. This paper contains three main sections: a general treatise of EC theory, the thin skin EC forward modeling, and the EC inverse problem. (1) The general treatise of eddy current theory begins with an exposition of the reciprocity formulas for evaluating probe impedance changes, which are derivable from first principles. Two versions of the reciprocity formulas, one with a surface integral and the other with a volume integral, are given. Any particular type of defect, as well as both one-port and two-port probes, can be treated. Second, a brief account of analytical and numerical methods for calculating the field distributions is presented. Third, theory of probe/material interactions with various defect types is described. (2) The paper then proceeds to the forward modeling section, which contains a detailed treatment of the eddy current forward problem for surface breaking cracks and EDM notches in the thin skin approximation. (3) The inverse problem section begins with a general review of commonly used inversion methods, exemplified by selected references from the literature, followed by more detailed examinations of EC inversions for surface breaking cracks and slots. The last part of this section is devoted to the inverse problem for layered structures. Although being a review in nature, the paper contains a number of new accounts for time-domain eddy current interactions. In particular, a modification is proposed to the reciprocity formula in order to take a better account of pulsed eddy current signals.

Thickness and Conductivity of Metallic Layers from Pulsed Eddy Current Measurements

Coatings and surface treatments find a wide range of technological applications; they can provide wear resistance, oxidation and corrosion protection, electrical contact or isolation and thermal insulation. Consequently, the ability to determine the thickness of coated metals is important for both process control and in-service inspection of parts. Presently ultrasonic, thermal, and eddy current inspection methods are used, depending on the circumstances. A number of commercial instruments for determining the thickness of nonconducting coatings on metal substrates are based on the fact that the impedance change of the coil decreases exponentially with the distance of the coil from the metal (the lift-off effect). However, these instruments are not suitable for determining the thickness of metal layers on conducting substrates.

Eddy-current signal analysis and inversion for semielliptical surface cracks

A scalar potential formulation of the δZ formula for the change in impedance of an eddy-current probe caused by a surface-breaking flaw is developed. The resulting formula is evaluated using a finite-difference method, which permits calculation of δZ for semielliptical flaws. The numerical results are checked by comparing calculations for rectangular-shaped flaws to previous calculations using an analytical solution for this geometry. Theoretical results are then verified by comparison with measurements on semielliptical fatigue cracks and EDM notches in aluminum alloy specimens using air-core eddy-current probes. An inversion method that compares features of the flaw profile, obtained by scanning the eddy-current probe along the length of the flaw, to a theoretical inversion chart (McFetridge chart) is demonstrated using the experimental data.

Impedance of coils over layered metals with continuously variable conductivity and permeability: Theory and experiment

The frequency‐dependent impedance of right‐cylindrical air‐core eddy‐current probes over thick metal plates whose conductivity and permeability vary as a function of depth in the near‐surface region have been studied both experimentally and theoretically. Measurements of probe impedance were made from 1 kHz to 1 MHz using an impedance analyzer. Precision‐wound air‐core coils were used for testing the theory, and commercial eddy‐current probes were used to connect with industrial practice. The samples were of two types. First, to model a continuous profile, otherwise uniform plates of metal covered with many thin, discrete layers of other metals were considered. Second, as a practical example, case‐hardened titanium plates, whose near‐surface conductivity varies smoothly and continuously as a function of depth, were considered. Two theoretical results are presented for continuously varying profiles. First, an exact closed‐form solution (within the quasistatic approximation) is reported for the impedance of...

Inductance of a coil on a thick ferromagnetic metal plate

We study the frequency-dependent inductance of a small air-cored coil of wire placed flat upon various ferromagnetic metal plates. The change in the complex inductance of the coil, measured with an HP 4193A impedance analyzer, is reported for frequencies between 1 kHz and 1 MHz. The metal plates consisted of commercially pure (99.7% and 99.9%) Ni, commercially pure (99.9%) Fe, and a suite of medium carbon steels. For the steel plates, inductance changes were consistent with a simple half-space model that treats the metal as a continuum defined by a conductivity /spl sigma/ and a relative initial-permeability /spl mu/ where these material parameters are isotropic, local, and uniform throughout the plate. The inductance changes for Ni and Fe could not be fit to the half-space model for any values of /spl sigma/ and /spl mu/, but were consistent with a model that assumes a thin (/spl sim/10 /spl mu/m) surface layer with a significantly reduced permeability-a dead layer. We tested the existence of the hypothetical dead layer in several ways. We found that the inductance increased when the surface was chemically etched (presumably eroding the dead layer) and decreased when the surface was mechanically polished (presumably increasing the dead layer). We also found that the inductance of the Fe and Ni samples decreased substantially over the course of days and months when exposed to air.

Scanned pulsed eddy current instrument for nondestructive inspection of aging aircraft

The aging of commercial and military aircraft fleets in the US has led to increased emphasis on detecting accumulated damage such as corrosion and wide-spread fatigue damage in multi-layer airframe structures. Eddy currents are the method of choice for this task, since they can penetrate multiple layers whether or not the layers are mechanically bonded. We have developed a new pulsed eddy-current instrument that is fast, rugged, portable, and relatively inexpensive to build. It has the ability to acquire wide- bandwidth information that can quantitatively characterize the thickness of multi-layered airframe structures. The instrument can also detect cracks growing from fastener holes in the second or third layers of a lap-joint structure. The probe is mounted in a rugged scanner that easily attaches to an aircraft. Data from the instrument are presented to the user in two formats: an instantaneous A- scan of the time-domain pulsed eddy-current signal and a C- scan image of the scanned area. The C-scan image can be time-gated to provide images representing signals form various depths and to discriminate against signals from fasteners or other interfering features. We describe the instrument in detail and provide examples of its use to detect both corrosion and second-layer cracks.

LOW FREQUENCY, PULSED EDDY CURRENTS FOR DEEP PENETRATION

Using eddy-currents to detect flaws buried deeply in a conducting material has always been a difficult problem. This is due in part to the fact that deep penetration requires low frequencies so that the skin depth is large enough for the eddy-currents to penetrate into the material the depth of the flaw. Also, low frequency eddy-current methods are beset with difficulties in probe design. In order to achieve the large inductance needed to operate at frequencies below 1 kHz, a large number of turns is needed, adding to the resistance of the coil and reducing the energy available to couple into the test piece. One solution is to use pulsed eddy-current methods, which operate efficiently and effectively with low inductance coils.

Magnetic Permeability and Eddy-Current Measurements

The calculation of the impedance of a right-cylindrical air-core coil placed next to a flat plate of a uniform polycrystalline metal alloy is a canonical problem in quantitative eddy-current inspection. Cheng [1] and Dodd and Deeds [2] proposed a widely-used solution for a coil next to a semi-infinite half-space of metal, which agrees quantitatively with impedance measurements made for a wide variety of thick but nonmagnetic metal plates. Said plates were assumed to have a uniform and frequency-independent conductivity, σ. The same authors proposed a similar solution for ferromagnetic metals (such as iron, steel and nickel), characterized by both a uniform σ and a nontrivial uniform permeability ¼.

Pulsed Eddy-Current Measurements of Corrosion-Induced Metal Loss: Theory and Experiment

Corrosion is one of the most important factors limiting life-extension of aircraft in both commercial and military fleets. Non-destructive methods for characterizing damage caused by hidden corrosion in layered structures such as aircraft lap-splices are, consequently, a high priority for commercial airlines and the Department of Defense. A considerable effort is underway to develop new eddy-current techniques for detecting and characterizing hidden corrosion. Eddy-currents have the advantage of penetrating into subsurface layers and therefore being sensitive to their condition, whether or not the layers are mechanically bonded. In contrast, ultrasonic techniques require a mechanical bond between layers for the ultrasonic energy to penetrate to the second or third layers. Both time-domain [1,2] (pulsed) and frequency-domain [3,4] (continuous wave) methods are under development.

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

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 measurement...