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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®.

In their recent paper, "In situ NDT of Degradation of Thermal Barrier Coatings Using Impedance Spectroscopy," Materials Evaluation, March 2000, pp. 476-481, K. Ogawa, T. Shoji, I. Abe, and H. Hashimoto develop a model for the NDE of thermal barrier coating that is based on the simultaneous measurement of thickness and lift-off.

four-layer thermal barrier problem In order to understand the model, refer to the figure, which shows a three-layer system (before aging), that degenerates into a four-layer system with aging. The Y2O3-ZrO2 (Yttria Stabilized Zirconia:YSZ) thermal barrier coating is bonded to the Ni base superalloy substrate (the turbine blade) through the MCrAlY bond coat. M represents one or more of the metals Ni, Co, or Fe.

With deterioration, however, a layer is formed of certain reaction products, namely a number of oxides, including Al2O3, that result when thermal stresses corrode the bond coat. This reaction layer, together with the thermal barrier coating, are nonconducting (or are very weakly conducting when compared with the bond coat and the substrate). Hence, the thermal barrier coating effectively increases in depth with aging, but at the expense of the bond coat thickness, and it is the latter that determines the remaining life of the system.

The electrical model of Ogawa et al represents the partially conducting layers as capacitors shunted by large resistors. We will continue to model the system inductively, in the usual manner of eddy-current NDE, and will treat the thermal barrier coating, together with the reaction layer, as nonconducting. In this model, therefore, these nonconducting layers contributing to the lift-off of the probe above the conducting bond coat and substrate. The problem, therefore, is to determine the lift-off value and the thickness of the bond coat. This problem is complicated by the fact that the conductivity of the bond coat is quite close to that of the substrate, as indicated in the first Thermal Barrier Coating problem, so that electrically the two materials are similar, if neither is ferromagnetic.

Nevertheless, we have solved this problem using the same frequency range as in the first Thermal Barrier Coating problem, namely, 50MHz, 62.5MHz, 75MHz, 87.5MHz, and 100MHz. We assume that the thermal barrier coating, together with the oxide reaction layer, is 0.313mm deep, and that the bond coat is 0.087mm thick (which could correspond to operation of the turbine blade for 3000 hours at a temperature of 1273 K; see Ogawa et al).

In our model inversion calculation, we perturbed the noise by 1%, as before, and obtained a solution for the total dielectric layer thickness to be 0.3126mm, and for the thickness of the bond coat, 0.0838mm. Clearly, eddy-currents, together with the sophisticated inversion algorithm included in VIC-3D®, are well-suited to solve the problem of NDE of thermal barrier coatings.