Abstract
The fuel safety and performance of high-temperature gas-cooled reactor (HTGR) are dependent on the integrity and geometric parameter of Tri-structural Isotropic (TRISO) coated particle. Micro X-ray computed tomography (CT) was used for nondestructive testing and three-dimensional measurement of the particle components which are composed of kernel, buffer layer, inner pyrolytic carbon layer (IPyC), silicon carbide (SiC) layer, and outer pyrolytic carbon (OPyC) layer. The thickness distribution and volume of kernel and coating layers are obtained by constructing 3D volume rendering of TRISO particle. Mean thickness of each layer is calculated for comparison with design value. A comparison between two-dimensional and three-dimensional measurement results is also made. It is found that the thickness distribution of all layers approximately obeys Gaussian distribution. Deviation of the thickness of kernel and coating layers between 3D measurement result and design value is 7.88%, -25.63%, -45.50%, 13.87%, and 14.73%, respectively. The deviation will affect the failure probability of TRISO particle. Obvious difference of the OPyC mean thickness between 3D measurement and 2D measurement is found, which proves that the proposed 3D measurement provides comprehensive information of the particle. However, 2D and 3D measured thickness of the kernel and IPyC layer tend to be similar.
1. Introduction
Tri-structural Isotropic (TRISO) coated particles are the fuel form for high-temperature gas-cooled reactor (HTGR) as well as other reactor forms [1, 2] due to its stability to retain fission product at even 1600°C [3]. It is composed of kernel, buffer layer, inner pyrolytic carbon (IPyC) layer, silicon carbide (SiC) layer, and outer pyrolytic carbon (OPyC) layer. Conventionally, TRISO is deemed to possess ideal sphericity without considering manufacturing uncertainties. However, the integrity and geometric shape of each layer are important for the safety and performance of the TRISO particle. Quality control of TRISO is extremely rigorous [4, 5]. For example, temperature distribution is affected by layer thickness. Inner CO pressure-induced stress on SiC layer is directly dependent on the diameter and volume of kernel, the volume of buffer layer, and the thickness of SiC layer. The shape of IPyC and OPyC layer has an effect on the radiation shrinkage and creep. In the case that the coating is aspherical, the pressure-induced asphericity will contribute to local stresses, which could reduce failure limits of the particle. Fundamentally, thickness distribution and the volume of the particle will affect its failure probability. Therefore, strict testing and evaluation for TRISO particle are necessary before operation.
Traditional testing method for TRISO is grind and polishing. The particle cross-section is observed using a scanning electron microscope [6, 7], which is a 2D measurement with several shortcomings, like high cost and production of radioactive wastes. One effective alternative is X-ray technique, which is nondestructive testing without causing radioactive wastes. It is desirable to utilize nondestructive characterization techniques to replace destructive methods for easy automation [8]. Beam hardening is the main problem of X-ray CT. Although it can be reduced by increasing photon energy, the contrast difference between coating layers is also mitigated [9].
2D measurement of the particle thickness was ascertained by extracting the boundary of each layer with phase contrast imaging [10, 11]. Mean thickness of each layer was calculated from 3D volume rendering of the particle [3, 9]. First 3D reconstruction from an irradiated PYCASSO particles [12] was obtained. Successful nondestructive testing with X-ray imaging was also applied to fuel pebble of HTGR [13, 14]. In this paper, advanced micro-CT setup was employed for thickness distribution measurement and asphericity calculation. SiC maximum curvature and the volume of each layer are calculated. Obvious deviation between measured thickness and design value is found, which will affect the safety and performance of TRISO particle during operation. Especially for the region with reduced thickness, the particle will be easier to be broken in terms of the pressure vessel model.
2. Method
2.1. Micro-CT
The specimen was scanned using 1081 views over 360° with a Zeiss Xradia microXCT 400 scanner for collection of 833 slices in total. Cone-beam acquisition was utilized and a Hamamatsu X-ray source was employed for the microXCT. The Xradia microXCT 400 with a 20X objective was operated at 60 kV and 10 W. Source-to-object distance (SOD) was 37 mm and object-to-detector distance (ODD) was 8 mm. Voxels were 1.12 microns. After data acquisition, the 16 bit TIFF images were reconstructed by Xradia Reconstructor. The raw data scan is shown in Figure 1(a), and a CT slice after using edge-preserving filter [3] is shown in Figure 1(b).
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2.2. Dimensional Measurement
Amira is a powerful software platform for 3D visualization, manipulation, and data analysis with different image processing tools and simulation modules. After thresholding segmentation of each layer, 3D volume rendering of a particle is obtained with Amira 5.4.3. The volume and thickness distribution of kernel and each layer were computed using modules in Amira. For thickness distribution, at each vertex, the module records the distance along the vertex perpendicular to the normal intersection with the nearest triangle. For volume measurement, the module computes the total number of voxels times the input single voxel size. SiC curvature is closely related to its stress during operation in terms of the pressure vessel model. Maximum curvature was calculated using module GetCurvature. The algorithm works by supposing the surface locally by a quadric form. The principal curvature values and directions of principal curvature are equal to the eigenvalues and to the eigenvectors of the quadric form.
3. Results
3.1. 3D Measurement for Thickness and Volume
Figure 2(a) shows 3D volume rendering of kernel and coating layers. Figure 2(b) is the triangulated 3D volume rendering of SiC layer whose surface is composed of a number of small faces and nodes. Figure 3 shows the diameter/thickness distribution of kernel and each coating layer. Y axis in Figure 3, the count, is the surface scalar field, which is equal to the number of nodes/vertexes as shown in Figure 2(b). The count represents thickness frequency in the histogram.
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Mean thickness, standard deviation, and root mean square (RMS) of thickness were calculated automatically in Amira 5.4.3 according to the thickness distribution as shown in Table 1. Deviation was calculated to show the discrepancy between mean thickness and ideal design parameter. The thickness distribution of kernel and coating layers is supposed to obey Gaussian distribution for asphericity calculation. The mean thickness and standard deviation are considered as same μ and σ of Gaussian distribution, respectively. Confidence coefficient is chosen as 95%. Thus, μ±2σ are the maximum and minimum thickness. Asphericity is maximum thickness divided by minimum thickness. The volume of kernel and coating layers is shown in Table 2. Figures 4 and 5 represent the comparison of thickness and volume between measured and ideal design value.
SiC maximum curvature distribution is represented in Figure 6. Y axis in Figure 6 is surface scalar field. The mean value, deviation, and root mean square of SiC curvature are 0.0244, 0.0126, and 0.0275, respectively.
3.2. Two-Dimensional Measurement for Thickness
A two-dimensional measurement of the central slices was also obtained as shown in Table 3 for comparison with the 3D measurement. Figure 7(a) is a digital radiograph (DR) image of the particle, which is used for manual 2D measurement in ImageJ. Figure 7(b) shows 3D rendering of 3 slices closest to the equatorial plane of TRISO. It is assumed as 2D measurement due to the very thin axis thickness compared with radial thickness. The 2D measurement is very similar to the traditional grind and polishing method. Figure 8 shows diameter/thickness distribution of kernel and coating layers. Mean thickness, standard value, and root mean square (RMS) are given in Table 3.
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A comparison between 2D measurement, 3D measurement of the thickness, and the design thickness is made as shown in Figure 9. Mean thickness of 2D and 3D measurement is used for the analysis.
4. Discussion
All thickness distributions obtained by 2D and 3D measurement approximately obey Gaussian distribution. The thickness of kernel and SiC layer under both measurements is greater than design thickness, while that of other layers is less than design value. The thickness of IPyC with both 2D and 3D measurement has the greatest deviation compared with that of other layers. In 2D measurement, the deviation of OPyC is the smallest, while kernel diameter is the closest to design diameter in 3D measurement. The deviation of kernel, buffer, and IPyC with both 2D and 3D measurement is similar, while a significant difference of SiC and OPyC deviation between them can be seen in Figure 9. 2D measurement of SiC and OPyC is close to design thickness, especially OPyC, while the deviation with 3D measurement is bigger than that with 2D measurement. This reveals that 3D measurement is more comprehensive than 2D measurement as the whole asphericity is analyzed. The SiC layer is aspherical due to the nonuniform distribution of its curvature. It can be predicted that maximum stress concentration will take place at the maximum curvature as shown in Figure 6. The pressure vessel (a spherical model) will easily fail at these maximum stress points, reducing the accuracy of the thin wall model in PANAMA (a German code for simulating the performance of the TRISO particle) [15]. Using finite element method to calculate stress of SiC layer might well be more appropriate than mean stress in the thin wall model.
In 2D measurement of the central slices, the mask of buffer and IPyC layer was segmented with the assistance of manual correction due to the similarity of gray values between them. This method depends on the visual intelligence of a human and error is unavoidable [11]. When calculating layer thickness in Amira 5.4.3, both radial and axial thickness are calculated. Thus, there are two peaks of distribution in original graph, but axial thickness is much less than radial thickness which will make it easy to manually divide them.
Several holes occurred in the 3D volume rendering of buffer, reducing the accuracy of measured volume and thickness in 3D measurement. This is due to beam hardening in spite of the correction algorithm. It can be seen in Tables 1 and 3 that the thickness of buffer with 3D measurement is still close to that of 2D measurement. Considering the feature of void volume of buffer, it is hard to conclude whether the measured volume is smaller or bigger than the ideal measured value. Further study will be focused on acquisition of slices with better image quality and beam hardening reduction.
Comprehensive 3D geometric testing of one particle can be obtained by computed tomography (CT) imaging but it is time-consuming. For large numbers of particles, digital radiography is recommended as this technique is fast-imaging and economic in terms of large samples. In the future, digital radiography might replace traditional method which is grinding, polishing, and observation using a microscope. Both of the nondestructive thickness measurement results were compared in the paper. We believe testing with tomographic imaging is more comprehensive than that with digital radiography.
5. Conclusion
In this paper, 2D and 3D measurement were used for a TRISO particle. Micro-CT was employed for raw slice acquisition and then slices were reconstructed for 3D volume rendering. The volume and thickness distribution of kernel and coating layers were obtained. Mean thickness, standard deviation, and RMS were calculated for deviation analysis between measured and design value. The thickness discrepancy of kernel and coating layers between 3D measurement result and design value is 7.88%, -25.63%, -45.50%, 13.87%, and 14.73%, respectively. The design value is the ideal TRISO thickness as shown in Table 1. The deviation will have an effect on the failure probability of the particle. Finally, a comparison between measured thickness with 2D and 3D measurement was made, proving that 3D measurement is more comprehensive and accurate than 2D measurement.
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was jointly supported by the National Natural Science Foundation of China (No. 61571262, No. 11575095, No. 61171115) and National Key Research and Development Program (No. 2016YFC010 5406). The authors would like to thank High-Resolution X-Ray CT Facility, University of Texas, for the support of experiments and Prof. Bing Liu in INET for providing the surrogate TRISO particle. Discussions with Mr. Stephen Conway and Prof. Uwe Ewert are appreciated.