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Nondestructive evaluation (NDE) is to materials and structures as CAT-scanning is to the human body--an attempt to look inside without opening it. As in CAT-scanning, modern NDE requires sophisticated mathematical software to perform the mathematical "inversion" operations that allow one to infer the internal state of a structure from external measurments. In this note we will show how VIC-3D® fulfills this need. In reading this example, keep in mind that the data could be taken with a conventional impedance analyzer, such as the HP4194A. For higher frequencies, up to 180MHz,or so, the HP4915A series can be used. There is nothing exotic about the instrumentation; the exotic stuff is in VIC-3D®.

Figure 1. Thermal barrier coating workpiece

The nondestructive evaluation (NDE) of high-temperature coatings is one of the important factors in achieving a high-level of structural integrity in advanced gas turbines. This problem is of great interest to users of gas turbines, including power utilities. Not only are the "established" public utilities relying more and more heavily on combustion turbines for power generation, but the independent producers that have emerged since deregulation are relying exclusively on land-based engines, and they can ill afford a blade failure.

Victor Technologies, LLC has been performing research into the nondestructive characterization of in-service high-temperature metallic (such as MCrAlY) coatings applied by vacuum plasma spray on Ni-based superalloy turbine blades. When new, such coatings are not diffusive -- they present quite sharp interfaces with the base metal; the interdiffusion layer is thin (~10µm) as compared to the coating thickness(>100µm) (see G. Antonelli, M. Ruzzier, and F. Necci, "Thickness Measurement of MCrAlY High-Temperature Coatings by Frequency Scanning Eddy Current Technique," Presented at the ASME 97-GT-1 International Gas Turbine & Aeroengine Congress & Exhibition, Orlando, Florida, June 2 to June 5, 1997.)

Coatings, such as MCrAlY, possess physical and chemical properties quite similar to those of the Ni-superalloys. This means that the electrical conductivity may vary by only 3% to 10% between the two metals. Thus, part of the challenge is to develop an eddy-current-based algorithm that is able to resolve such small changes. A further challenge arises because it is found that the coating may become ferromagnetic with use, which means that the algorithm must also determine magnetic permeabilities, as well as electrical conductivities. Finally, the blade curvature must ultimately be taken into account.

  In the problem displayed here, we reconstruct a two-layer system, in which there are four variables to be reconstructed, the conductivity and permeability of each layer. The top layer is 0.2 mm thick, and the bottom layer is an infinite substrate. The data comprise ten impedance measurements at frequencies, 1E5, 2E5, 4E5, 8E5, 1.6E6, 5E7, 6.25E7, 7.5E7, 8.75E7, and 1.E8 Hz. The data were corrupted by the addition of zero-mean random noise, with a variance of 0.01. This is probably a rather large variance, but it allows us to demonstrate the algorithm, anyway. The left-hand portion of the figure shows the original structure, and the right-hand shows the reconstruction, using the data just described. Clearly, eddy-current measurements can allow the simultaneous determination of conductivities and permeabilities with excellent precision.