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Eddy current assessment of Hydrogen content in Zirconium based alloys A. Lois Universidad Tecnológica Nacional, Regional Gral. Pacheco - Argentina H. Mendonça, M. Ruch Ensayos no Destructivos y Estructurales (ENDE) - CNEA - Argentina E-mail: hmendon@cnea.gov.ar Contact

During service at high temperature or in aggressive media, metallic structures and components may suffer different types of changes or degradation. As an example, phase transformations may occur, second phases may precipitate, and in consequence the mechanical and chemical properties of the structure may change. Their behaviour will therefore differ from that considered for the design of the component. A knowledge of the amount of a second phase precipitated in a component should be an important tool in the hands of the maintenance engineer. And it would be very important to obtain this knowledge nondestructively and reliably.
Eddy current testing is an adequate method for these assessments. However, the induced voltage in an eddy current probe, the measured quantity, is actually a superposition of many variables, and contains information on lift-off, resistance, etc. In order to sort out this information, a model of the impedance plane was programmed in a PC. Use of this program would provide a method for the calculation of the conductivity of materials, taking into account the effect of specimen thickness. Adequate calibrations would allow for the nondestructive assessment of the amount of hydrogen in reactor components such as pressure and calandria tubes, a knowledge which will enable the experts to predict the degree of fragilization of those components. This type of tests should be a natural complement to the normal inspection procedures, which search for cracks and blisters.

INTRODUCTION

Metallic structures and components may suffer damage or transformations during service at high temperatures or in an aggressive environment. Such damage may include oxidisation, phase transformations, second phase precipitation, all of which alter the mechanical and chemical properties of the materials. The effect of changes in these properties on material performance must be considered both during design of the components and when analysing life extension and performance improvement. Therefore, a non-destructive method for material characterisation is a valuable tool for the engineers in charge of maintenance of facilities. Eddy current testing is a non-destructive evaluation method suitable for this task [1,2].

The interpretation of experimental results from eddy current material characterisation being by no means straight forward, the purpose of this paper is to contribute theoretical calculations which might help in the eddy currents assessment of the conductivity of thin specimens. These calculations are based in the well known model of Dodd and Deeds [3], who propose an analytical solution of the eddy current problem in a two layer conducting medium and represent their solution in the impedance plane. MATHEMATICA 2.2.3 ä [4] was used for the programming.

This work is part of a project to assess by eddy currents the thickness of the oxide layer grown on the surface of Zircaloy-4 reactor components and the amount of hydrogen incorporated by them during service. A series of Zircaloy-4 specimens with oxide layers of different thickness and different concentrations of hydrogen were prepared by controlled autoclave treatments [5]. The precipitation of platelets of zirconium hydride produce a small decrease in the conductivity of the specimens [6,7]. It has been observed that the sensitivity of eddy currents to conductivity variations is higher at rather low excitation frequencies (100 to 200 kHz for this type of alloys), at which the skin depth of the eddy currents is quite large, and the results are therefore affected by the thickness of the specimens. Experimental results from Perotti [3] were used throughout.

EXPERIMENTAL BACKGROUND

The 1 mm thick Zircaloy-4 specimens used in this work were prepared by Perotti [5] during 1998 and 1999, by controlled autoclave treatments in LiOH at 340ºC, a procedure which results in the growth of layers of zirconium oxide on the specimens and the diffusion of a large amount of hydrogen into the matrix, which precipitates as platelets of zirconium hydride. Table 1 shows the hydrogen content of the autoclave treated specimens (ATS). Two standards for conductivity calibration from Zetec were used, the conductivity of which are also listed in Table 1.

Material	Conductivity Si/m	Conductivity % IACS
100% IACS	58.0·106	100
Standard 1	58.47·106	100.57
Standard 2	17.39·106	29.91
Standard 3	5.405·106	9.296
Standard 4	2.036·106	3.502
Standard 5	0.554·106	0.953
Zry-4[1]	1.392·106	2.39
ZrH1.59[6]	1.32·106	2.27
Table 1: Conductivity and resistivity of certified standards and of Zirconium alloys and compounds

Two different eddy current equipments were used for the experimental measurements, namely a PC based MAD8Dä equipment from ect (Eddy Current Technology inc.) and a MIZ-22ä from Zetec, with a conductivity measuring device. Impedance plane lift-off curves at different frequencies were obtained with MAD8Dä, and the corresponding raw data were saved in a hard disk file. At relatively low frequencies, the slight changes in sample conductivity associated with hydrogen content can be detected, though not quantified. But the results depend strongly on the thickness of the specimens, as can be observed in the "conductivity values" obtained with the MIZ-22ä at 120 kHz, where the value determined for zircaloy-4 was lower than the tabulated value [6]. Assemblies of one ATS and a different number of blank Zircaloy-4 specimens were made, and the conductivity of each different set was measured. The values are presented in Table 2

Specimen	Hydrogen content [atoms %]	IACS % values read on MIZ-22 3 slabs	IACS % values read on MIZ-22 1 slab	Conductivity calculated from IACS% values 3 slabs [Si/m]	Conductivity calculated from IACS% values 1 slab [Si/m]	Conductivity calculated with this software from Z-plane data 3 slabs [Si/m]	Conductivity calculated with this software from Z-plane data 2 slabs [Si/m]	Conductivity calculated with this software from Z-plane data 1 slab [Si/m]
Zry-4	0.09 ± 0.01	2.337	1.593	1.359·106	0.926·106	1.308·106	1.344·106	1.420·106
1A	1.6 ± 0.2	2.317	1.563	1.347·106	0.909·106	1.303·106	1.341·106	1.421·106
3C	4.9 ± 0.5	2.289	1.514	1.331·106	0.880·106	1.288·106	1.330·106	1.390·106
4C	7.3 ± 0.7	2.284	1.489	1.328·106	0.866·106	1.285·106	1.325·106	1.382·106
3B	12 ±1	2.233	1.397	1.298·106	0.812·106	1.282·106	1.309·106	1.373·106
Table 2: "Conductivity values" of the thin hydrided specimens calculated by eddy currents at 120 kHz: IACS values measured with MIZ-22, conductivity calculated from those measured values, coductivity values calculated with the present software from data measured with ect MAD8D

CALCULATIONS

The two layer model of Dodd and Deeds [3] for the calculation of probe impedances was programmed in MATHEMATICA 2.2.3, and specific routines were written, in order to solve the inverse problem for the conductivity of the specimens. The following equation was used:

where

The constants l₁, l₂, r₁, r₂, stand for the dimensions of the probe, as shown in Figure 1, and for the calculations, they were given the corresponding values of the probe which was used for the experiments. In order to verify the programming, some calculations were made, the results of which are shown in figure 2, which represents the complex impedance plane. The full circles in Figure 2 represent the calculated probe impedances at 90 kHz, for different values of the conductivity. After that, the conductivity values of standards 5 and 4 were selected and the corresponding lift-off curves were calculated (x and white circles in figure 2). The same calculations were made for the other three frequencies used in the experimental work, namely 80, 120 and 160 kHz.

Fig 1: Scheme of experimental setup illustrating the parameters used in the calculations.

Fig 2: Calculated complex impedance plane. Full circles: calculated probe impedances at 90 kHz, for different values of the conductivity. Calculated lift-off curves for conductivity values of standards 5 (x) and 4 (white circles).

In order to analyse the experimental data with these theoretical tools, a program was written to read the raw voltages in the file generated by MAD8Dä and convert them to another format, compatible with MATHEMATICAä 2.2.3. Figure 3 represents, in an impedance plane type graph, the raw voltages measured by MAD8Dä , converted to the intermediate file and represented by MATHEMATICAä . The two extreme lift-off curves correspond to standards 5 and 4 and the closely grouped intermediate curves to the Zircaloy-4 specimens with different hydrogen content.

Fig 3: Output of MAD8D read and represented by the pesent software. Units: volts.

Actually, the data acquired with MAD8Dä and represented in Figure 3 are the corresponding voltages in the horizontal and vertical axes of the screen, not necessarily coincident with the real and imaginary components of impedance, which are the coordinate axes of Figure 2. In order to map the measured data onto the impedance plane model upon which the mathematical calculations are based, a linear transformation was proposed, the parameters of which are to be determined. Six points are necessary for this task, three of them measured and the other three, calculated. The three measured points are the induced voltages on conductivity standards 5 and 4 and the balance point. The corresponding "theoretical" values were calculated with the model. Thus, three points on the impedance plane can be fixed, and the linear transformation mapping the former into the latter can consequently be calculated. From them, the unknown conductivities can be numerically fitted.

RESULTS AND DISCUSSION

Table 2 contains the results of all the experiments and calculations. The third and fourth columns contain the IACS values read on the display of MIZ-22, obtained with the conductivity measuring device at 120 kHz with a send / receive probe. The two following columns contain the conductivity calculated from those values. In both cases, it can be observed that the conductivity dimishes as the hydrogen content of the specimens increase. This is in accordance with the fact that in a two phase material the conductivity should be a function of the amount of second phase [7]. It can also be observed that the measured conductivities on one hydrided slab and two blank Zry-4 (3 slabs) are some 40% higher than those measured on only the hydrided slabs. This clearly shows that the measured quantity is actually the conductance of the specimens.

The three columns at the right hand side of the table show the conductivity values calculated with the present software from impedance plane data acquired with MAD8D at 120 kHz, measured on one hydrided slab and two blank Zry-4 (3 slabs), one hydrided slab and one blank Zry-4 (2 slabs) and the single specimens (1 slab). As above, in all three cases, the calculated conductivity diminishes with increasing hydrogen content. However, with increasing number of slabs, the calculated conductivity decreases, the calculated values for the 3 slabs configuration being 10% lower than those for the single slabs. Further refinement of the software and of the data acquisition methods would probably ellucidate the reason of this behaviour.

CONCLUSIONS

The software that is being presented allows for an improved method for the processing of eddy current data used in the assessment of the electrical conductivity of thin specimens. Further refinements of calculation and experimental data acquisition methods are necessary, in order to reduce the effect of geometry on the calculated conductivity, which in turn is related to important properties of the materials, such as its composition.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge partial funding of this work from Research Contract 6248 RB of the International Atomic Energy Agency.

REFERENCES

1. V.S. Cecco, G. Van Drunnen, F.L. Sharp, "Manual on eddy current method", Vol.1, Chalk River Nuclear Laboratories (1981).
2. Hugo Libby, "Introduction to Electromagnetic Nondestructive Test Methods" (Wiley-Interscience, 1971).
3. C.V. Dodd, W.E. Deeds, "Analytical solutions to eddy-current probe-coil problems", J. Appl. Phys. 39, No 6, 1968, pp 2829-2838.
4. S. Wolfram, "The MATHEMATICAä Book", Third Edition, Wolfram Media and Cambridge University Press, 1996.
5. A. Perotti, "Evaluación no destructiva de capas de óxido sobre Zircaloy-4", Master Dissertation, Institute of Technology, San Martin University, Argentina, (1999).
6. P.W. Bickel, T.G. Berlincourt, "Electrical Properties of Hydrides and Deuterides of Zirconium", Phys. Rev. B, Vol. 2, No 12, 1970, pp. 4807-4813.
7. R.M. Rose, L.A. Shepard, J. Wulff, "Introducción a la Ciencia de Materiales, vol. 4: Propiedades electrónicas", (Limusa-Wiley S.A., 1968), pp. 92.

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