Eddy-Current NDE of Combustion Turbine Blade Coatings. Determination of Conductivity Profiles in the Presence of a Diffusion Process

This paper deals with the modelization of eddy-current measurements over combustion turbine blade coatings affected by depletion of aluminum. First, we model the response of an eddy-current coil over a layered metallic structure with a top over-aluminized coating by extending the analytical Uzal-Rose's model for one hyperbolic tangent conductivity profile to a conductivity profile using two hyperbolic tangents for taking inward and outward depletion of aluminum inside the coating into account. Results obtained with this model are similar to those obtained with a numerical multilayer model but with a reduced computing time.

We report experimental measurements that test an inverse method for determining the electrical properties of conducting surface layers on metals. We test the method's ability to determine the spatial variation of the near-surface electrical conductivity of flat, layered (one-dimensional) metal plates from experimental measurements of the frequency-dependent impedance of a small right-cylindrical air-core coil placed next to the metal surface and driven by an alternating current. This is an inverse problem for the diffusion equation with complex wavevector. We fit the experimental measurements to a recent closed-form analytic solution for the impedance of a conductivity profile that varies as a constant plus a hyperbolic tangent with depth into the sample. The model profile depends on three parameters, which roughly correspond to: (1) the thickness of the surface layer, (2) the change in conductivity and (3) the sharpness of the transition from surface to bulk conductivity. Data were obtained by measuring the impedance of an air-core coil for flat Cu and Ti plates that have surface layers that extend to various depths. We extended the range of the study by using simulated data, which were obtained by solving the forward problem numerically. Good estimates for the 'average' conductivity profile were obtained when the conductivity was maximum (minimum) at the surface and decreased (increased) monotonically to the bulk conductivity as a function of depth into the sample. The thickness, conductivity change and the sharpness of the profile were successfully inferred from experiment in most cases.

Because of their frequency-dependent penetration depth, eddy current measurements are capable of mapping the near-surface depth profile of the electrical conductivity. This technique can be used to nondestructively characterize the subsurface residual stress distribution in certain types of shot-peened metals, e.g., in nickel-base superalloys. For quantitative evaluation of the experimental results, analytical and computational techniques are needed to solve the direct and inverse problems, i.e., to predict the frequency-dependent apparent eddy current conductivity from the depth profile of the frequency-independent intrinsic electrical conductivity of the specimen and vice versa. Simple analytical approximations are presented for both the direct and inverse eddy current problems by exploiting two specific features of the subsurface electrical conductivity variation caused by near-surface residual stresses in shot-peened metals. First, compressive residual stresses are limited to a shallow surface region of depth, much less than typical probe coil diameters. Second, the change in electrical conductivity due to residual stresses is always very small, typically less than 1%. The proposed approximations are verified by numerical comparison to much more complicated numerical solutions.

The two main graphite ageing processes in advanced gas-cooled reactors (AGRs) are fast neutron damage and radiolytic graphite oxidation. These processes change the properties of the graphite core and lead to a reduction in the graphite density, ie a weight loss. Electrical conductivity measurement of the graphite material is among the possible methods for estimating the weight loss and hence provides a measure of the graphite ageing. The inductance spectroscopy technique using eddy current sensors has been implemented in a wide variety of NDT applications, since it enables the possibility of extracting the electrical parameters variation from eddy current measurements and examining more fully the internal material structure. In this paper we present a non-contact eddy current method for determining non-destructively the electrical conductivity gradient through 100 mm-thick graphite sections using inductive spectroscopic measurements collected by a gradiometer. The method employs the commercial finite element software COMSOL to generate the data from a model of a real profile distribution. This data is translated to the profile conductivity of the graphite test object via the solution of an inverse problem. The linear Tikhonov regularisation method and the non-linear regularised Gauss Newton technique are employed in the solution of the inverse problem. During the optimisation, the forward problem is evaluated using COMSOL. Numerical optimisation tests have been carried out for different cases of step conductivity profiles. Initial results using simulated data show that representative estimates of the conductivity profile of the modelled graphite sections have been obtained.

Because of their frequency-dependent penetration depth, eddy current measurements are capable of mapping the near-surface depth profile of the electrical conductivity. This technique is used to nondestructively characterize the subsurface residual stress and cold work distributions in shot-peened metal components. Unfortunately, the spurious surface roughness produced by the shot peening process causes an apparent loss of eddy current conductivity, thereby decreasing the accuracy of the measurements, especially in thermally relaxed specimens where the primary material effects are significantly reduced. In this paper, a numerical method is introduced based on the Rayleigh approximation for calculating the apparent eddy current conductivity loss exhibited by 1D randomly rough surfaces. The relevant boundary conditions are satisfied using the so-called point-by-point technique, and the results are first compared to the previously developed Rayleigh–Fourier technique for a 1D sinusoidal corrugation. Pseudorandom surface profiles of different autocorrelation functions are considered. It is found that the Gaussian model lends itself the best to numerical simulations, but it significantly underestimates the apparent eddy current conductivity loss expected on real shot-peened surfaces, which exhibit essentially exponential correlation function. It is also demonstrated that the Lorentzian model is numerically less stable, but physically closer to the exponential one. The latter could not be simulated reliably by the present numerical technique because of its slowly decaying high-frequency spectral components.

Because of their frequency-dependent penetration depth, eddy current measurements are capable of mapping the near-surface depth profile of the electric conductivity. This technique can be used to nondestructively characterize the subsurface residual stress distribution in certain types of shot-peened metals, e.g., in nickel-base superalloys. In this paper, a highly convergent iterative inversion procedure is presented to predict the frequency-independent intrinsic electric conductivity depth profile from the frequency-dependent apparent eddy current conductivity (AECC) spectrum. The proposed technique exploits three specific features of the subsurface electric conductivity variation caused by near-surface residual stresses in shot-peened metals. First, compressive residual stresses are limited to a shallow surface region of depth much less than typical probe coil diameters. Second, the change in electric conductivity due to residual stresses is always very small, typically less than 1%. Third, the electric conductivity depth profile is continuous and fairly smooth. The accuracy of the proposed iterative inversion procedure is one order of magnitude better than that of the previously developed simpler method (J Appl Phys 2004;96:1257).

Because of their frequency‐dependent penetration depth, eddy current measurements are capable of mapping the near‐surface depth profile of the electric conductivity. This technique can be used to nondestructively characterize the subsurface residual stress distribution in certain types of shot‐peened metals, e.g., in nickel‐base superalloys. To predict the depth‐dependent, but frequency‐independent, intrinsic electric conductivity from the frequency‐dependent apparent eddy current conductivity (AECC), a highly convergent iterative inversion procedure is presented. The proposed technique exploits three specific features of the subsurface electric conductivity variation caused by near‐surface residual stresses in shot‐peened metals. First, compressive residual stresses are limited to a shallow surface region of depth much less than typical probe coil diameters. Second, the change in electric conductivity due to residual stresses is always very small, typically less than 1%. Third, the electric conductivity profile is fairly smooth and continuous. The accuracy of the proposed iterative inversion procedure is one order of magnitude better than that of the previously developed simpler method (J. Appl. Phys. 96, 1257 2004).

Because of their frequency‐dependent penetration depth, eddy current measurements are capable of mapping the near‐surface depth profile of the electrical conductivity. This technique can be used to nondestructively characterize the subsurface residual stress distribution in certain types of shot‐peened metals, e.g., in nickel‐base superalloys. For quantitative evaluation of the experimental results, analytical and computational techniques are needed to solve the direct and inverse problems, i.e., to predict the frequency‐dependent apparent eddy current conductivity from the depth profile of the frequency‐independent intrinsic electrical conductivity of the specimen and vice versa. Simple analytical approximations are presented for both the direct and inverse eddy current problems by exploiting two specific features of the electrical conductivity variation caused by near‐surface residual stresses in shot‐peened metals. First, compressive residual stresses are limited to a shallow surface region of depth much less than typical probe coil diameters. Second, the change in electrical conductivity due to residual stresses is always very small, typically less than 1%. The proposed approximations are verified by numerical comparison to much more complicated numerical solutions.

Evaluating the conductivity distribution in isotropic polycrystalline graphite using spectroscopic eddy current technique for monitoring weight loss in advanced gas cooled reactors

This paper discusses the relationship between isothermal and adiabatic piezoresistive properties of metals. The piezoresistive effect, i.e., stress‐dependence of the electrical resistivity, can be exploited for nondestructive residual stress assessment using eddy current measurements. First, the paper establishes the relationship between the familiar isothermal piezoresistivity coefficients measured under uniaxial tension and hydrostatic pressure and the relevant isothermal electroelastic coefficients measured under uniaxial and biaxial stress conditions either by non‐directional circular or directional elliptical eddy current coils. In order to quantitatively assess the prevailing residual stress from eddy current conductivity measurements, the electroelastic coefficients must be first determined. These calibration measurements are usually conducted on a reference specimen of the material to be tested using cyclic uniaxial loads between 0.1 and 10 Hz, which is fast enough to produce adiabatic conditions. It is demonstrated that in high‐conductivity metals such calibration measurements must be corrected for the thermoelastic effect, which is always positive, i.e., it increases the conductivity in tension, when the material cools down, and reduces it in compression, when the material heats up.

Recent research results indicate that eddy current conductivity measurements can be exploited for nondestructive evaluation of subsurface residual stresses in surface-treated nickel-base superalloy components. According to this approach, first the depth-dependent electric conductivity profile is calculated from the measured frequency-dependent apparent eddy current conductivity spectrum. Then, the residual stress depth profile is calculated from the conductivity profile based on the piezoresistivity coefficient of the material, which is determined separately from calibration measurements using known external applied stresses. This paper presents new results that indicate that in some popular nickel-base superalloys the relationship between the electric conductivity profile and the sought residual stress profile is more tenuous than previously thought. It is shown that in delta-processed IN718 the relationship is very sensitive to the state of precipitation hardening and, if left uncorrected, could render the eddy current technique unsuitable for residual stress profiling in components of 36 HRC or harder, i.e., in most critical engine applications. The presented experimental results show that the observed dramatic change in the eddy current response of hardened IN718 to surface treatment is caused by very fine nanometer-scale features of the microstructure, such as γ′ and γ″ precipitates, rather than micrometer-scale features, such as changing grain size or δ phase and carbide precipitates.

The authors have recently developed a new technique for nondestructive Hall coefficient measurement based on inductive sensing of the Hall-Corbino current produced by the injection of high-frequency alternating current into the component under test. In this study, the feasibility of characterizing the combined influence of near-surface residual stress and cold work based on Hall impedance spectroscopy was investigated in shot-peened fully hardened IN718 coupons. First, a simple analytical approximation is proposed that allows the direct prediction of the measured frequency-dependent Hall impedance from the depth-dependent Hall coefficient and conductivity profiles. This approximation is based on the simplistic approximation originally developed for eddy current conductivity depth profiling that has been modified for Hall coefficient measurements. According to this approximation, Hall coefficient measurements exhibit roughly half the penetration depth of eddy current conductivity measurements taken at the same frequency. Typical depth profiles of the Hall coefficient and electric conductivity were estimated from residual stress and cold work depth profiles obtained by destructive X-ray diffraction (XRD) measurements. The corresponding Hall coefficient and electric conductivity depth profiles were determined using gauge factors obtained from experiments previously conducted to study the influence of applied stress and cold work on the Hall coefficient and electric conductivity in fully hardened IN718. These Hall coefficient and conductivity depth profiles were then used to predict the Hall impedance spectra using COMSOL FE simulations and the analytical approximation. The results of finite element simulations were in reasonable agreement with the analytical approximation and validate the predicted lower penetration depth of Hall current compared to the conduction current. Finally, the feasibility of Hall impedance measurements was demonstrated by experiments conducted between 100 kHz and 30 MHz on fully hardened IN718 coupons surface treated to three different shot-peening levels of 4A, 8A, and 12A Almen intensity.

Recent research results indicate that eddy current conductivity measurements can be exploited for nondestructive evaluation of subsurface residual stresses in surface-treated nickel-base superalloy components. According to this approach, the depth-dependent electric conductivity profile is calculated from the measured frequency-dependent apparent eddy current conductivity spectrum. Then, the residual stress depth profile is calculated from the conductivity profile based on the piezoresistivity coefficient of the material, which is determined separately from calibration measurements using the known external applied stresses. This paper reviews the basic principles, measurement procedures, advantages, and limitations of eddy current residual stress profiling.

: Recent research results indicate that eddy current conductivity measurements can be exploited for nondestructive evaluation of subsurface residual stresses in surface-treated nickel-base superalloy components. According to this approach, first the depth-dependent electric conductivity profile is calculated from the measured frequency-dependent apparent eddy current conductivity spectrum. Then, the residual stress depth profile is calculated from the conductivity profile based on the piezoresistivity coefficient of the material, which is determine separately from calibration measurements using known external applied stresses. This report presents results that indicate that in some popular nickel-base superalloys the relationship between the electric conductivity profile and the sought residual stress depth profile is more tenuous than previously thought. In particular, it is shown that in IN718 the relationship is very sensitive to the state of precipitation hardening and could render this technique unsuitable for eddy current residual stress profiling in components of 36 HRC or harder, i.e., in most critical engine applications.

We report an inverse method for determining the near-surface electrical conductivity of flat, layered (one-dimensional) metal plates from measurements of the frequency-dependent impedance of a small right-cylindrical air-core coil placed next to the metal surface and driven by an alternating current. This is an inverse problem for the diffusion equation with complex wavevector in one and a half dimensions . We use variational least-squares to fit experimentally measured impedances. The fit is based on a recent closed-form analytic solution for a model conductivity profile that varies as a constant plus a hyperbolic tangent with depth into the sample. The model profile depends on three parameters, which roughly correspond to: (1) the thickness of the surface layer, (2) the change in conductivity and (3) the shaipness of the transition from surface to bulk conductivity. Data were obtained by measuring the impedance of a 1 mm radius coil between 1 kHz and 1 MHz for five flat Cu and Ti plates whose surface layers extended to depths on the order of 0.25 mm. We extended the range of the study by using simulated data, which were obtained by solving the forward problem numerically. Good estimates for the average conductivity profile were obtained when the conductivity was maximum (minimum) at the surface and decreased (increased) monotonically to the bulk conductivity as a function of dep± into the sample. The thickness, conductivity change and the profile diffuseness were successfully inferred from experiment.