·Table of Contents ·Computer Processing and Simulation | Eddy current assessment of Hydrogen content in Zirconium based alloysA. LoisUniversidad 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 |
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.
Material | Conductivity Si/m | Conductivity % IACS |
100% IACS | 58.0·10^{6} | 100 |
Standard 1 | 58.47·10^{6} | 100.57 |
Standard 2 | 17.39·10^{6} | 29.91 |
Standard 3 | 5.405·10^{6} | 9.296 |
Standard 4 | 2.036·10^{6} | 3.502 |
Standard 5 | 0.554·10^{6} | 0.953 |
Zry-4[1] | 1.392·10^{6} | 2.39 |
ZrH1.59[6] | 1.32·10^{6} | 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 | 1.359·10^{6} | 0.926·10^{6} | 1.308·10^{6} | 1.344·10^{6} | 1.420·10^{6} |
1A | 1.6 ± 0.2 | 2.317 | 1.563 | 1.347·10^{6} | 0.909·10^{6} | 1.303·10^{6} | 1.341·10^{6} | 1.421·10^{6} |
3C | 4.9 ± 0.5 | 2.289 | 1.514 | 1.331·10^{6} | 0.880·10^{6} | 1.288·10^{6} | 1.330·10^{6} | 1.390·10^{6} |
4C | 7.3 ± 0.7 | 2.284 | 1.489 | 1.328·10^{6} | 0.866·10^{6} | 1.285·10^{6} | 1.325·10^{6} | 1.382·10^{6} |
3B | 12 ±1 | 2.233 | 1.397 | 1.298·10^{6} | 0.812·10^{6} | 1.282·10^{6} | 1.309·10^{6} | 1.373·10^{6} |
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 |
where
The constants l_{1}, l_{2}, r_{1}, r_{2}, 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.
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.
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.
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