- Email: [email protected]
Evaluation of breach characteristics of fast reactor fuel pins during steady state irradiation
Nuclear Engineering and Design 370 (2020) 110894
Contents lists available at ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Evaluation of breach characteristics of fast reactor fuel pins during steady state irradiation Hiroshi Oka a, *, Takeji Kaito a, Yoshihisa Ikusawa b, Satoshi Ohtsuka a a b
Oarai Research and Development Institute, Japan Atomic Energy Agency, 4002 Narita-cho, Oarai-machi, Ibaraki 311-1393, Japan Nuclear Fuel Cycle Engineering Laboratories, Japan Atomic Energy Agency, 4-33 Muramatsu, Tokai-mura, Ibaraki 319-1194, Japan
A R T I C L E I N F O
A B S T R A C T
Keywords: Fast reactor fuel pins In-reactor creep rupture strength Cumulative damage fraction EBR-2 reactor Fuel pin breach
This study evaluates the reliability of a cumulative damage fraction (CDF) analysis for the prediction of fuel pin breach in fast rector using experimentally obtained fuel pin breach data for the first time. Six breached fuel pins with austenitic stainless steel cladding were obtained from steady state irradiation in the Experimental Breeder Reactor II. Post irradiation examinations revealed that fission gas pressure was the main cause of creep damage in cladding, and that the stress contribution from fuel-cladding-mechanical-interaction was negligible. CDFs evaluated for these pins using in-reactor creep rupture equation, taking into account the irradiation history of cladding temperature and hoop stress due to fission gas pressure, were in the range of 0.7 to 1.4 at the occurrence of breach. This shows clearly that fuel pin breach occurs when the CDF approaches 1.0. On the other hand, the CDFs derived from thermal control creep equation showed the value less than that from the in-reactor creep rupture equation. These results indicate that CDF analysis would be a reliable method for the prediction of fuel pin breach when appropriate material strength and environmental effects, i.e. the in-reactor creep rupture equation, are used.
1. Introduction In a fast reactor core fuel, creep damage due to the internal pressure of the fission gas is one of the causes of breach for cladding material. In the design analysis of fuel pins, the cumulative damage fraction (CDF) is applied to predict the fuel pin breach. The CDF is a method of evaluating the life of materials and is calculated based on the creep strength of materials. This method integrates creep damage introduced into mate rial at a certain temperature and stress, and the CDF value of 1.0 means material failure. The CDF method has been used to analyze the behavior of fast reactor fuel pins (Uwaba et al., 2012, 2010; Rawers, 1984; Kaito and Mizuno, 1997). Uwaba et al. (2010) performed CDF evaluation for high burnup fuel pins irradiated in the Fast Flux Test Facility (FFTF) where cladding was austenitic stainless steel. Fuel pins were irradiated under steady state conditions and attained their respective peak pellet burnups of 147 and 162 GWd/t without any indication of fuel pin breach. The evaluated CDFs were in the order of 10− 4–10− 2 at the end of irradiation, indicating a sufficient safety margin against fuel pin breach. Since the fuel pins subjected to the above analysis did not breach at the end of irradiation, it is not confirmed experimentally that the pins actually breach when the
CDF reaches 1.0. There have been no studies based on the data regarding an actual occurrence of fuel pin breach. Fuel pin irradiation was conducted in the Experimental Breeder Reactor II (EBR-II) as a part of the run-beyond-cladding-breach (RBCB) testing program in a collaborative effort involving the Power Reactor and Nuclear Fuel Development Corporation of Japan (currently the Japan Atomic Energy Agency) and the United States Department of Energy in the 1980′ s. In the K2A and K2B tests of the RBCB program, 20% cold-worked (CW) D9 alloy, which is a titanium-modified variant of austenitic 316 stainless steel (Puigh and Hamilton, 1987; Pitner et al., 1995; Makenas, 1986), was used for cladding material. In order to simulate breach at mid-life burnups, the cladding in the region near the top of the fuel column was locally pre-thinned and the size of the plenum volume was reduced. Since the primary purpose of the RBCB-K2A and K2B tests was to study the behavior of fuel pins after breach, including the formation of fuel-sodium reaction products (FSRP), reactor opera tion continued after fuel pin breach. In this study, CDF was evaluated for six fuel pins that breached during steady state irradiation in the RBCB-K2A and K2B tests. The relationship between the CDF values and the actual occurrence of fuel pin breach was investigated for the first time in order to evaluate the
* Corresponding author currently at: Faculty of Engineering, Hokkaido University, Japan. E-mail addresses: [email protected] (H. Oka), [email protected] (T. Kaito). https://doi.org/10.1016/j.nucengdes.2020.110894 Received 9 April 2020; Received in revised form 5 October 2020; Accepted 6 October 2020 Available online 1 November 2020 0029-5493/© 2020 Elsevier B.V. All rights reserved.
H. Oka et al.
Nuclear Engineering and Design 370 (2020) 110894
reliability of CDF analysis for predicting the fuel pin breach. For this reason, the fuel pin behavior after breach is outside the scope of this study.
Table 2 Specifications for the fuel pin of RBCB-K2A and K2B test. Test series Fuel Fuel composition (Pu / Pu + U) Fuel O/M Fuel pellet diameter Fuel Pellet density Fuel smeared density Fuel column length Cladding material Outer diameter Inner diameter Plenum position Plenum size
2. Experimental 2.1. Description of the irradiation tests Steady state irradiation tests (K2A and K2B) (Kaito and Mizuno, 1997) with 20%CW D9 alloy cladding (Puigh and Hamilton, 1987; Pit ner et al., 1995; Makenas, 1986) were conducted in the EBR-II. The chemical composition of D9 alloy is shown in Table 1. The fuel pins were 5.84 mm in diameter and 1016 mm in length; and the cladding wall thickness was 0.38 mm. The pins contained uranium-plutonium mixed oxide (Pu/(Pu + U) = 25 wt%) pellets, with a pellet density of ~90% T. D., an overall smeared density of 85.5% T.D., and an initial oxygen to metal (O/M) ratio of 1.96. The detailed specifications for the fuel pins are given in Table 2. Test pins (designed to breach at mid-life) were modified by a com bination of locally pre-thinning the cladding region near the top of the fuel column and by reducing the size of the fission gas plenum. The K2A test pins were thinned to a residual thickness of about 0.10 mm while the residual thickness of the K2B test pins was about 0.15 mm in order to induce breaches at about 4 and 6 at.% burnup, respectively. Data on the measured residual thickness of the pre-thinned regions of the K2A and K2B test pins are given in Table 3. The plenum size of the test pins was reduced to 3.3 cm3, compared to that of the environmental pins of 7.2 cm3. Thinning was performed by electrode discharge machining of an area of 6.35 mm long and 1.0 mm wide in the outer surface of the cladding. The position of the pre-thinned area was located at x/L = 0.95 (L: column length). A photograph of a typical thinned area and a crosssection through a tested thinned area are shown in Fig. 1. Loading diagrams for the two tests are shown in Fig. 2. In the RBCBK2A test, seven test pins were loaded in the center of the subassembly. The pre-thinned areas were loaded in the same direction. Irradiation started in September 1982. Table 4 shows the irradiation conditions of the respective fuel pins. Peak linear heat rate was 360 ~ 366 W/cm at the start of irradiation. The coolant temperature at an elevation corre sponding to the pre-thinned area was 609 to 639 ◦ C. The cladding temperature at the same elevation was 615 to 656 ◦ C. The power history for the center pin in the K2A and the K2B tests is shown in Fig. 3. The time of the fuel pin breach was estimated based on cover gas signal and tag-gas analysis. The six out of the seven test pins resulted in the fuel pin breach.
(–) (–) (mm) (%TD) (%TD) (mm) (mm) (mm) (cm3)
K2A
K2B
UO2-PuO2 0.250 1.96 4.94 90.4 85.5 342.9 D9, 20%CW 5.84 5.08 upper part 3.3
UO2-PuO2 0.250 1.96 4.94 90.4 85.5 342.9 D9, 20%CW 5.84 5.08 upper part 3.3
Table 3 Residual Cladding Thickness of Pre-thinned Area for the Test Pins. Test
Fuel pin No.
Thickness (mm)
K2A
AKB-21 AKB-22 AKB-23 AKB-24 AKC-25 AKC-26
0.112 0.109 0.112 0.112 0.145 0.152
K2B
2.2. Post irradiation examinations of the fuel pins Post irradiation examinations (PIE), e.g. visual examination, axial profilometry, gamma scanning, and ceramography (optical metallog raphy) etc., were performed on the set of test pins and selected sibling pins soon after each irradiation test in Argonne National LaboratoryWest (currently Idaho National Laboratory). In this study, the visual examination results are presented for the test pins, while axial profil ometry and ceramography results are presented for the selected sibling pin. Besides primary stress due to internal fission gas pressure, stress due to fuel-cladding-mechanical-interaction (FCMI) can also damage clad ding. Since the irradiation test continued after fuel pin breach and the FSRP formed, it is very difficult to determine the inner condition of breached pins (the presence or absence of FCMI) from the PIE results.
Fig. 1. Appearance of the pre-thinned area of the cladding for the test pins.
Table 1 Chemical composition (wt%) of D9-type alloy. C 0.039
Si
Mn
P
S
Ni
Cr
Mo
Co
B
N
Cu
Ti
V
0.80
2.03
<0.005
0.004
15.77
13.70
1.65
<0.01
<0.0005
0.004
<0.01
0.34
0.01
2
H. Oka et al.
Nuclear Engineering and Design 370 (2020) 110894
Fig. 3. Power history for center pin in the K2A and K2B tests.
Fig. 2. Loading diagrams of test pins of interest in this study.
K2A test. At the end of the K2A test, AKB-21 and AKB-24 showed large cracks through the pre-thinned area, which are 35 and 29 mm in length, respectively. The three pins (AKB-22, AKB-23, and AKC-25) were fission-gas leakers at the end of the K2A test. The breaches in these pins were assumed to be very small pin-holes. The intact AKC-26 and pinhole-damaged AKC-25 were continuously irradiated throughout the K2B test. At the end of the K2B test, both pins exhibited large cracks of about 40 mm in length; and fuel-sodium re action product appeared to protrude slightly out of the cladding split and to be cracked longitudinally. Fig. 5 shows the visual appearance of AKC25 and AKC-26 after the K2B test. In this study, fuel-sodium reaction product is out of scope. Fig. 6 shows the axial profilometry of the sibling pin AKA-10 with no significant increase of fuel pin diameter. In particular, no significant increase in the outer diameter was observed at the upper core part where the breach occurred in the breached pins. Fig. 7 shows a cross section of the sibling pin at an elevation of 327 mm from core bottom, where the pre-thinned area for the breached pins was located. It was confirmed that a radial gap of about 50 μm remained between the fuel pellet and the cladding. From the above results, it was revealed that the stress contribution from FCMI was likely to be negligible in the breach of the fuel pins. In other words, it was confirmed that within the irradiation condition of this study, only creep damage due to increased internal pressure from accumulated fission gas contributed to the fuel pin breach. Taking into account the cladding temperature, fuel burnup, and O/M ratio of fuel pellet, fuel-cladding-chemical-interaction (FCCI) (Maeda, 2012) is expected to occur under the irradiation condition of this study. As shown in Fig. 7, a roughened surface was found on the inner surface of the cladding, presumably due to FCCI. Although no detailed mea surement of cladding thickness was made on ceramography, thickness
Table 4 Irradiation conditions of the fuel pins of interest. Fuel pin No.
Peak linear heat rate*1 (W/cm)
Cladding temperature*1 (◦ C)
Time of pin breach*2 (EFPD*3)
Peak burn-up*4 (at.%)
AKB-21 AKB-22 AKB-23 AKB-24 AKC-25 AKC-26
364 366 364 362 360 360
656 650 628 656 635 615
213 219 221 198 223 294
5.2 5.5 5.5 4.9 5.4 6.5
*1 at the start of irradiation. *2 estimation based on cover gas signal, tag-gas analysis, and the results of PIE. *3 EFPD: Effective Full Power Day. *4 at the pin breach.
Instead of the breached pins, a sibling pin (AKA-10) that was irradiated in the same subassembly was also examined in order to assess whether or not FCMI occurred and contributed to breach. Axial profilometry and ceramography were performed for the AKA-10 sibling pin. The axial profilometer measurement was made using laser profilometer. The axial diameter profile was averaged from measurement in three orientations (0, 60, and 120◦ ). For the ceramography, the AKA-10 sibling pin was transversely sectioned and prepared by grinding and then polishing with 1 μm and 0.25 μm diamond paste. 2.3. Results of PIE Fig. 4 shows the visual appearance of AKB-21 through AKC-25 after 3
H. Oka et al.
Nuclear Engineering and Design 370 (2020) 110894
Fig. 4. Visual appearance of AKB-21 through AKC-25 after the K2A test.
Fig. 6. Axial profilometry of sibling pin AKA-10.
for the axial position of pre-thinned area, with the data of irradiation history. In order to evaluate the CDF value, an in-reactor creep rupture equation of D9 alloy was created. In-reactor creep rupture data (Puigh and Hamilton, 1987) which were obtained from the Materials Open Test Assembly (MOTA) experiment in the FFTF were used. The stress and Larson-Miller parameter (LMP) were read from the figure in the litera ture (Puigh and Hamilton, 1987); and the rupture times were deter mined from the LMP and the irradiation temperature. From the obtained data set, the in-reactor creep rupture equation was determined as follows: / LMP = (T + 273.15)(5.66 + logtR ) 103 = 36.657 − 42.667(logσH ) + 22.137(logσH )2 − 3.9469(logσH )3
(2)
where T, tR and σ H are temperature (◦ C), time to rupture (h) and hoop stress (MPa), respectively. For the low stress side; σ H < 100 MPa, a tangent line was drawn at a position where the stress was 100 MPa in the curve of Eq. (2), and the following equation was obtained by extrapo lating the tangent line; / LMP = (T + 273.15)(5.66 + logtR ) 103 = 11.260 − 1.4825(logσH ) (3)
Fig. 5. Visual appearance of AKC-25 and AKC-26 after the K2B test.
reduction by FCCI needs to be considered in this study.
Fig. 8 shows the creep rupture Eqs. (2) and (3) (solid line) together with the in-reactor creep rupture data plot of FFTF/MOTA. Although there is some variation in the data on the low stress side, it can be seen that the creep rupture equation and the FFTF/MOTA data set are in good agreement. The in-reactor creep rupture equation covers the range of the irradiation temperature and time for the K2A and K2B tests. Reduction in cladding thickness due to FCCI was considered. Since the chemical composition of D9 alloy was similar to that of 316 stainless steel, the nominal FCCI curve based on the design curve of modified type 316 stainless steel (PNC316) was used for FCCI evaluation. The design curve of PNC316 was developed by covering the FCCI data of driver fuel
3. CDF calculations CDFs for the creep damage on the breached pins were evaluated by the following equation; ∫t dt CDF = (1) 0 tR where t is the testing time and tR is the rupture time at a given stress and temperature (Rawers, 1984; Kramer et al., 1993). CDFs were calculated 4
H. Oka et al.
Nuclear Engineering and Design 370 (2020) 110894
Fig. 7. Cross section of sibling pin AKA-10 at the elevation of 327 mm (x/L = 0.95).
Fig. 8. In-reactor creep rupture equation obtained from the data of FFTF/MOTA. Fig. 9. FCCI curve used for CDF calculation.
of experimental fast reactor Joyo whose cladding was PNC316. The FCCI curve used for CDF evaluation is the one drawn with the solid lines in Fig. 9: this curve gives the 35 µm lower corrosion depth than that given by the design curve, which can represent a non-conservative nominal behavior of FCCI. It was determined that FCCI starts at a local burnup of 1.6 at%, increases linearly with time during irradiation, and saturates at 65 μm beyond a local burnup of 6.4 at%.
Fission gas pressure was evaluated based on the initial gas amount, fission gas release rate and plenum volume. For the fission gas release rate, the design curve for Joyo driver fuel, which was empirically determined based on the data of MOX fuel irradiated in Joyo (Mizuno et al., 1992; Maeda et al., 2005), was used. The curve shows that the 5
H. Oka et al.
Nuclear Engineering and Design 370 (2020) 110894
fission gas release rate increases with the pin averaged burnup, and then reaches 100% at burnup of 7.5 at%. The curve is considered appropriate because the curve covers the fission gas release rate data of EBR-II (Cox, 1969). The influence of sodium corrosion on the outer surface of the clad ding tube may be considered. In the present study, the effect of sodium corrosion was included in the in-reactor creep rupture equation ob tained above. In addition, regarding the cladding temperature, nominal values were used assuming no hot spots. Cladding hoop stress was estimated by the thin-walled cylinder approximation. The wall thickness of the pre-thinned area was used in the calculation, and the loss of thickness due to FCCI was taken into account. 4. Results and discussion 4.1. CDF evaluation and failure probability CDF values obtained for the test pins are shown in Table 5. Fig. 10 shows the calculated hoop stress for each test pin as a function of the irradiation time. The hoop stress increases exponentially with increasing irradiation time. This is due to both an increase in the fission gas release and a decrease in cladding wall thickness by FCCI. The hoop stress at the time of breach occurrence was estimated to be about 128 to 192 MPa. For the K2B test pins (AKC-25 and 26), the increase rate of hoop stress was slower than it was for the other fuel pins. This is because the initial thickness of the K2B pins was large compared to the K2A pins. Fig. 11 shows the evaluated CDFs as a function of EFPD for the test pins. As shown in Fig. 11, the logarithm of CDF increases substantially linearly with increasing irradiation time. This indicates that the creep damage accumulated more rapidly at the end of the lifetime of fuel pins. The evaluated CDFs for the test pins were in the range of 0.7 to 1.4 at the occurrence of breach. This is significant because it empirically confirms that the fuel pin breach is likely to occur when the CDF approaches 1.0. It is important to note that at every six pins with different degrees of burnup, every CDF value was close to 1.0 and did not exceed 1.0 by an order of magnitude. This means that the CDF analysis would be a reli able method for the prediction of fuel pin breach. Weibull distribution analysis was performed to clarify the relation ship between CDF value and failure probability (Pitner et al., 1995). The obtained Weibull plot is illustrated in Fig. 12. The following general equation was used for the Weibull distribution analysis (Datsiou and Overend, 2018): ( ( )) 1 ln ln = mlnt − lnα (4) 1 − F(t)
Fig. 10. Histories of calculated hoop stress for each test pins.
where t, F(t), and α are the CDF value, the failure probability, and constant, respectively. The failure probability was estimated by the mean rank method: F(t)i =
i n+1
Fig. 11. Histories of CDF for each test pins.
was liner, and the following liner formula was obtained:
(5)
Y = 2.864 X − 0.5357
where n is the total number of tested specimens. F(t)i means the cumu lative frequency of the i-th data extracted from n data. As shown in Fig. 12, the relationship between CDF values and the failure probability
From this equation, the failure probability when the CDF approaches 1.0 is estimated to be about 0.45, meaning that almost half of the fuel pins are breached. This result suggests that the integrity of the fuel pin can be evaluated by creep damage of cladding caused by fission gas internal pressure. The Eq. (6) is significant because it is obtained based on data from the fuel pin irradiation, and it describes the probability of fuel pin breach for fast reactor.
Table 5 Obtained CDF value for the test pins at the pin breach. Pin No.
FCCI (μm)
Hoop stress (MPa)
CDF
AKB-21 AKB-22 AKB-23 AKB-24 AKC-25 AKC-26
30 31 32 26 32 48
170 187 177 147 127 192
1.3 1.4 0.8 1.0 0.7 1.3
(6)
4.2. CDF evaluation in particular condition In the design study of fuel pin, the design creep stress, SR, is used in the CDF calculations. The SR takes into consideration the scattering of creep test data, in which the rupture time is set to be one-third. It 6
H. Oka et al.
Nuclear Engineering and Design 370 (2020) 110894
irradiation and sodium corrosion on the CDF and the failure probability, CDF evaluation was performed using thermal control creep equation of D9 alloy instead of the in-reactor creep equation. The thermal control creep equation was created by tracing the lines from the figure in literature (Puigh and Hamilton, 1987). The created curve is drawn in Fig. 8. The calculated CDFs for the 6 test pins are shown in Table 6 and the calculated CDFs for AKC-26 are shown in Fig. 14. The CDF values are about 30 ~ 80% of the nominal values at the pin breach due to the environmental effects having been ignored. Comparing the in-reactor and thermal control stress rupture behaviors, the in-reactor data exhibit shorter rupture lives than the thermal control data for longer exposure times (Puigh and Hamilton, 1987). As increasing hoop stress at longer life, CDFs were dominated by longer side behavior; and this ex plains why the CDF of thermal control has the steep slope as shown in Fig. 14. Since CDF evaluation using the thermal control creep equation is underestimated, it is important to experimentally obtain the in-reactor creep rupture equation and use it in CDF evaluation. It can be said that the CDF analysis would be a reliable method for the prediction of fuel pin breach when appropriate material strength and environmental effects are adopted. The corrosion depth due to FCCI has relatively large experimental scattering according to a number of past studies. Thus, the influence of FCCI depth on the CDF value and the failure probability was also investigated. CDFs were calculated assuming no reduction of cladding wall thickness due to FCCI. The results are also shown in Table 6 and Fig. 15 for AKC-26. The CDF values were about 60 ~ 80% of the nominal value, but they did not differ by more than one order of magnitude. Although it depends on the specific irradiation conditions of each test pin, the effect of FCCI on the CDF calculation is not significant compared to that of creep equation. Fig. 15 also shows the CDF result derived from SR assuming no reduction of cladding by FCCI. The irradiation time where the CDF derived from SR reaches 1.0 is about 239 EFPD, which is corresponding to the CDF value of 0.33 for the nominal creep equation assuming no corrosion by FCCI. This implies that the safety margin of SR has room to be rationalized in the case assuming no thickness reduction by FCCI.
Fig. 12. Relationship between CDF and failure probability.
corresponds to the lower bound of the variations in the creep rupture data of the modified type 316 stainless steel cladding (Uwaba et al., 2010). Here, SR of D9 alloy was obtained by setting the rupture time in the in-reactor creep equation to one-third because D9 alloy is an austenitic stainless steel and its creep rupture data variation is consid ered to be the same as that of the modified type 316 stainless steel. Fig. 13 shows the CDF result derived from the SR compared to that from nominal in-reactor creep strength for the case of AKC-26. From Fig. 13, it is found that the irradiation time at which the CDF derived from SR reaches 1.0 is about 221 EFPD. The CDF value at the irradiation time of 221 EFPD in the case of nominal creep is 0.33, which is consistent with the rupture time setting of one-third. The corresponding failure proba bility when CDF is 0.33 is 0.02 from Eq. (5), which is small. The small failure probability derived from SR implies that the safety margin of SR has room to be rationalized. These findings will probably contribute to the rationalization of the fuel pin design and, consequently, the pro longation of the fuel pin lifetimes. In order to estimate environmental effects such as neutron
5. Conclusions Six in-reactor fuel pin breaches were obtained in the RBCB testing program performed in EBR-II. The CDFs of each breached pin were calculated using the in-reactor creep rupture equation, taking into ac count the irradiation history of cladding temperature, the reduction of wall thickness due to FCCI, and hoop stress due to fission gas pressure. The in-reactor creep rupture equation was obtained from the literature data, i.e. in-reactor creep rupture data of D9 alloy irradiated in FFTF. Each parameter used for CDF evaluation is nominal value thus the re sults obtained here are not conservative. It was concluded that the fuel pin breach resulted from creep damage due to internal pressure from accumulated fission product gas within the irradiation condition of this study. The CDFs of the breached fuel pins evaluated by nominal in-reactor creep strength were in the range of 0.7 Table 6 CDFs and failure probabilities calculated by thermal control equation or without FCCI consideration. Pin No.
AKB-21 AKB-22 AKB-23 AKB-24 AKC-25 AKC-26
Fig. 13. Comparison of CDF between nominal condition and design stress condition for the AKC-26 pin. 7
Evaluation using thermal control creep equation of D9 instead of the in-reactor creep equation
Evaluation without wall thickness reduction caused by FCCI
CDF
Failure probability
CDF
Failure probability
0.9 1.1 0.4 0.5 0.2 0.7
0.35 0.54 0.04 0.08 0.01 0.19
0.9 0.9 0.5 0.7 0.5 0.7
0.35 0.35 0.08 0.19 0.08 0.19
H. Oka et al.
Nuclear Engineering and Design 370 (2020) 110894
using nominal values for each parameter to the degree possible. On the other hand, the CDFs derived from the thermal control creep equation were less than those from the in-reactor creep rupture equation, high lighting the importance of experimentally obtaining the in-reactor creep rupture equation and use it in the CDF evaluation. The above result indicates that the CDF analysis would be a reliable method for the prediction of fuel pin breach when appropriate material strength and environmental effects are adopted. CRediT authorship contribution statement Hiroshi Oka: Conceptualization, Methodology, Investigation, Data curation, Writing - original draft, Writing - review & editing. Takeji Kaito: Conceptualization, Investigation, Data curation, Validation, Writing - review & editing, Supervision, Resources. Yoshihisa Ikusawa: Validation, Writing - review & editing. Satoshi Ohtsuka: Writing - re view & editing, Resources. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Fig. 14. Comparison of CDF derived from nominal condition and design stress condition for the AKC-26 pin.
References Cox, C.M., 1969. Irradiation performance of uranium-plutonium oxide fuel pins. Nucl. Saf. 10, 380. Datsiou, K.C., Overend, M., 2018. Weibull parameter estimation and goodness-of-fit for glass strength data. Struct. Saf. 73, 29–41. https://doi.org/10.1016/j. strusafe.2018.02.002. Kaito, T., Mizuno, T., 1997. 1997 Fall Meeting. Atomic Energy Society of Japan, Okinawa (in Japanese). Kramer, J.M., Liu, Y.Y., Billone, M.C., Tsai, H.C., 1993. Modeling the behavior of metallic fast reactor fuels during extended transients. J. Nucl. Mater. 204, 203–211. https:// doi.org/10.1016/0022-3115(93)90218-N. Maeda, K., 2012. 3.16 – ceramic fuel-cladding interaction. In: Compr. Nucl. Mater. Elsevier, pp. 443–483. https://doi.org/10.1016/B978-0-08-056033-5.00068-9. Maeda, K., Katsuyama, K., Asaga, T., 2005. Fission gas release in FBR MOX fuel irradiated to high burnup. J. Nucl. Mater. 346 (2-3), 244–252. https://doi.org/ 10.1016/j.jnucmat.2005.06.014. Makenas, B.J., 1986. Performance of titanium stabilized D9 cladding and ducts. Int. Conf. Reliab. Fuels Liq. Met. React., pp. 3–52 to 3–61. Mizuno, T., Asaga, T., Shikakura, S., 1992. Fast reactor fuel performance and an advanced fuel design. Int. Conf. Des. Saf. Adv. Nucl. Power Plants, pp. 28.3–1–28.3–7. Pitner, A.L., Gneiting, B.C., Bard, F.E., 1995. Irradiation performance of fast flux test facility drivers using D9 alloy. Nucl. Technol. 112 (2), 194–203. Puigh, R.J., Hamilton, M.L., 1987. In-reactor creep rupture behavior of the D9 and 316 alloys. ASTM STP 956, 22–29. Rawers, J.C., 1984. Creep and transient testing of irradiated type 316 stainless steel. Mater. Sci. Eng. 68 (1), 19–34. https://doi.org/10.1016/0025-5416(84)90240-4. Uwaba, T., Sogame, M., Ito, M., Mizuno, T., Donomae, T., Katsuyama, K., 2010. Evaluation of creep damage and diametral strain of fast reactor MOX fuel pins irradiated to high burnups. J. Nucl. Sci. Technol. 47 (8), 712–720. Uwaba, T., Maeda, S., Mizuno, T., Teague, M.C., 2012. Study on the mechanism of diametral cladding strain and mixed-oxide fuel element breaching in slow-ramp extended overpower transients. J. Nucl. Mater. 429 (1-3), 149–158. https://doi.org/ 10.1016/j.jnucmat.2012.05.042.
Fig. 15. Influence of corrosion on CDF derived from nominal condition and design stress condition for the AKC-26 pin.
to 1.4 at the occurrence of breach. These results confirm that fuel pin breach occurs as the CDF approaches 1.0 when the CDF is evaluated
8
Contents lists available at ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Evaluation of breach characteristics of fast reactor fuel pins during steady state irradiation Hiroshi Oka a, *, Takeji Kaito a, Yoshihisa Ikusawa b, Satoshi Ohtsuka a a b
Oarai Research and Development Institute, Japan Atomic Energy Agency, 4002 Narita-cho, Oarai-machi, Ibaraki 311-1393, Japan Nuclear Fuel Cycle Engineering Laboratories, Japan Atomic Energy Agency, 4-33 Muramatsu, Tokai-mura, Ibaraki 319-1194, Japan
A R T I C L E I N F O
A B S T R A C T
Keywords: Fast reactor fuel pins In-reactor creep rupture strength Cumulative damage fraction EBR-2 reactor Fuel pin breach
This study evaluates the reliability of a cumulative damage fraction (CDF) analysis for the prediction of fuel pin breach in fast rector using experimentally obtained fuel pin breach data for the first time. Six breached fuel pins with austenitic stainless steel cladding were obtained from steady state irradiation in the Experimental Breeder Reactor II. Post irradiation examinations revealed that fission gas pressure was the main cause of creep damage in cladding, and that the stress contribution from fuel-cladding-mechanical-interaction was negligible. CDFs evaluated for these pins using in-reactor creep rupture equation, taking into account the irradiation history of cladding temperature and hoop stress due to fission gas pressure, were in the range of 0.7 to 1.4 at the occurrence of breach. This shows clearly that fuel pin breach occurs when the CDF approaches 1.0. On the other hand, the CDFs derived from thermal control creep equation showed the value less than that from the in-reactor creep rupture equation. These results indicate that CDF analysis would be a reliable method for the prediction of fuel pin breach when appropriate material strength and environmental effects, i.e. the in-reactor creep rupture equation, are used.
1. Introduction In a fast reactor core fuel, creep damage due to the internal pressure of the fission gas is one of the causes of breach for cladding material. In the design analysis of fuel pins, the cumulative damage fraction (CDF) is applied to predict the fuel pin breach. The CDF is a method of evaluating the life of materials and is calculated based on the creep strength of materials. This method integrates creep damage introduced into mate rial at a certain temperature and stress, and the CDF value of 1.0 means material failure. The CDF method has been used to analyze the behavior of fast reactor fuel pins (Uwaba et al., 2012, 2010; Rawers, 1984; Kaito and Mizuno, 1997). Uwaba et al. (2010) performed CDF evaluation for high burnup fuel pins irradiated in the Fast Flux Test Facility (FFTF) where cladding was austenitic stainless steel. Fuel pins were irradiated under steady state conditions and attained their respective peak pellet burnups of 147 and 162 GWd/t without any indication of fuel pin breach. The evaluated CDFs were in the order of 10− 4–10− 2 at the end of irradiation, indicating a sufficient safety margin against fuel pin breach. Since the fuel pins subjected to the above analysis did not breach at the end of irradiation, it is not confirmed experimentally that the pins actually breach when the
CDF reaches 1.0. There have been no studies based on the data regarding an actual occurrence of fuel pin breach. Fuel pin irradiation was conducted in the Experimental Breeder Reactor II (EBR-II) as a part of the run-beyond-cladding-breach (RBCB) testing program in a collaborative effort involving the Power Reactor and Nuclear Fuel Development Corporation of Japan (currently the Japan Atomic Energy Agency) and the United States Department of Energy in the 1980′ s. In the K2A and K2B tests of the RBCB program, 20% cold-worked (CW) D9 alloy, which is a titanium-modified variant of austenitic 316 stainless steel (Puigh and Hamilton, 1987; Pitner et al., 1995; Makenas, 1986), was used for cladding material. In order to simulate breach at mid-life burnups, the cladding in the region near the top of the fuel column was locally pre-thinned and the size of the plenum volume was reduced. Since the primary purpose of the RBCB-K2A and K2B tests was to study the behavior of fuel pins after breach, including the formation of fuel-sodium reaction products (FSRP), reactor opera tion continued after fuel pin breach. In this study, CDF was evaluated for six fuel pins that breached during steady state irradiation in the RBCB-K2A and K2B tests. The relationship between the CDF values and the actual occurrence of fuel pin breach was investigated for the first time in order to evaluate the
* Corresponding author currently at: Faculty of Engineering, Hokkaido University, Japan. E-mail addresses: [email protected] (H. Oka), [email protected] (T. Kaito). https://doi.org/10.1016/j.nucengdes.2020.110894 Received 9 April 2020; Received in revised form 5 October 2020; Accepted 6 October 2020 Available online 1 November 2020 0029-5493/© 2020 Elsevier B.V. All rights reserved.
H. Oka et al.
Nuclear Engineering and Design 370 (2020) 110894
reliability of CDF analysis for predicting the fuel pin breach. For this reason, the fuel pin behavior after breach is outside the scope of this study.
Table 2 Specifications for the fuel pin of RBCB-K2A and K2B test. Test series Fuel Fuel composition (Pu / Pu + U) Fuel O/M Fuel pellet diameter Fuel Pellet density Fuel smeared density Fuel column length Cladding material Outer diameter Inner diameter Plenum position Plenum size
2. Experimental 2.1. Description of the irradiation tests Steady state irradiation tests (K2A and K2B) (Kaito and Mizuno, 1997) with 20%CW D9 alloy cladding (Puigh and Hamilton, 1987; Pit ner et al., 1995; Makenas, 1986) were conducted in the EBR-II. The chemical composition of D9 alloy is shown in Table 1. The fuel pins were 5.84 mm in diameter and 1016 mm in length; and the cladding wall thickness was 0.38 mm. The pins contained uranium-plutonium mixed oxide (Pu/(Pu + U) = 25 wt%) pellets, with a pellet density of ~90% T. D., an overall smeared density of 85.5% T.D., and an initial oxygen to metal (O/M) ratio of 1.96. The detailed specifications for the fuel pins are given in Table 2. Test pins (designed to breach at mid-life) were modified by a com bination of locally pre-thinning the cladding region near the top of the fuel column and by reducing the size of the fission gas plenum. The K2A test pins were thinned to a residual thickness of about 0.10 mm while the residual thickness of the K2B test pins was about 0.15 mm in order to induce breaches at about 4 and 6 at.% burnup, respectively. Data on the measured residual thickness of the pre-thinned regions of the K2A and K2B test pins are given in Table 3. The plenum size of the test pins was reduced to 3.3 cm3, compared to that of the environmental pins of 7.2 cm3. Thinning was performed by electrode discharge machining of an area of 6.35 mm long and 1.0 mm wide in the outer surface of the cladding. The position of the pre-thinned area was located at x/L = 0.95 (L: column length). A photograph of a typical thinned area and a crosssection through a tested thinned area are shown in Fig. 1. Loading diagrams for the two tests are shown in Fig. 2. In the RBCBK2A test, seven test pins were loaded in the center of the subassembly. The pre-thinned areas were loaded in the same direction. Irradiation started in September 1982. Table 4 shows the irradiation conditions of the respective fuel pins. Peak linear heat rate was 360 ~ 366 W/cm at the start of irradiation. The coolant temperature at an elevation corre sponding to the pre-thinned area was 609 to 639 ◦ C. The cladding temperature at the same elevation was 615 to 656 ◦ C. The power history for the center pin in the K2A and the K2B tests is shown in Fig. 3. The time of the fuel pin breach was estimated based on cover gas signal and tag-gas analysis. The six out of the seven test pins resulted in the fuel pin breach.
(–) (–) (mm) (%TD) (%TD) (mm) (mm) (mm) (cm3)
K2A
K2B
UO2-PuO2 0.250 1.96 4.94 90.4 85.5 342.9 D9, 20%CW 5.84 5.08 upper part 3.3
UO2-PuO2 0.250 1.96 4.94 90.4 85.5 342.9 D9, 20%CW 5.84 5.08 upper part 3.3
Table 3 Residual Cladding Thickness of Pre-thinned Area for the Test Pins. Test
Fuel pin No.
Thickness (mm)
K2A
AKB-21 AKB-22 AKB-23 AKB-24 AKC-25 AKC-26
0.112 0.109 0.112 0.112 0.145 0.152
K2B
2.2. Post irradiation examinations of the fuel pins Post irradiation examinations (PIE), e.g. visual examination, axial profilometry, gamma scanning, and ceramography (optical metallog raphy) etc., were performed on the set of test pins and selected sibling pins soon after each irradiation test in Argonne National LaboratoryWest (currently Idaho National Laboratory). In this study, the visual examination results are presented for the test pins, while axial profil ometry and ceramography results are presented for the selected sibling pin. Besides primary stress due to internal fission gas pressure, stress due to fuel-cladding-mechanical-interaction (FCMI) can also damage clad ding. Since the irradiation test continued after fuel pin breach and the FSRP formed, it is very difficult to determine the inner condition of breached pins (the presence or absence of FCMI) from the PIE results.
Fig. 1. Appearance of the pre-thinned area of the cladding for the test pins.
Table 1 Chemical composition (wt%) of D9-type alloy. C 0.039
Si
Mn
P
S
Ni
Cr
Mo
Co
B
N
Cu
Ti
V
0.80
2.03
<0.005
0.004
15.77
13.70
1.65
<0.01
<0.0005
0.004
<0.01
0.34
0.01
2
H. Oka et al.
Nuclear Engineering and Design 370 (2020) 110894
Fig. 3. Power history for center pin in the K2A and K2B tests.
Fig. 2. Loading diagrams of test pins of interest in this study.
K2A test. At the end of the K2A test, AKB-21 and AKB-24 showed large cracks through the pre-thinned area, which are 35 and 29 mm in length, respectively. The three pins (AKB-22, AKB-23, and AKC-25) were fission-gas leakers at the end of the K2A test. The breaches in these pins were assumed to be very small pin-holes. The intact AKC-26 and pinhole-damaged AKC-25 were continuously irradiated throughout the K2B test. At the end of the K2B test, both pins exhibited large cracks of about 40 mm in length; and fuel-sodium re action product appeared to protrude slightly out of the cladding split and to be cracked longitudinally. Fig. 5 shows the visual appearance of AKC25 and AKC-26 after the K2B test. In this study, fuel-sodium reaction product is out of scope. Fig. 6 shows the axial profilometry of the sibling pin AKA-10 with no significant increase of fuel pin diameter. In particular, no significant increase in the outer diameter was observed at the upper core part where the breach occurred in the breached pins. Fig. 7 shows a cross section of the sibling pin at an elevation of 327 mm from core bottom, where the pre-thinned area for the breached pins was located. It was confirmed that a radial gap of about 50 μm remained between the fuel pellet and the cladding. From the above results, it was revealed that the stress contribution from FCMI was likely to be negligible in the breach of the fuel pins. In other words, it was confirmed that within the irradiation condition of this study, only creep damage due to increased internal pressure from accumulated fission gas contributed to the fuel pin breach. Taking into account the cladding temperature, fuel burnup, and O/M ratio of fuel pellet, fuel-cladding-chemical-interaction (FCCI) (Maeda, 2012) is expected to occur under the irradiation condition of this study. As shown in Fig. 7, a roughened surface was found on the inner surface of the cladding, presumably due to FCCI. Although no detailed mea surement of cladding thickness was made on ceramography, thickness
Table 4 Irradiation conditions of the fuel pins of interest. Fuel pin No.
Peak linear heat rate*1 (W/cm)
Cladding temperature*1 (◦ C)
Time of pin breach*2 (EFPD*3)
Peak burn-up*4 (at.%)
AKB-21 AKB-22 AKB-23 AKB-24 AKC-25 AKC-26
364 366 364 362 360 360
656 650 628 656 635 615
213 219 221 198 223 294
5.2 5.5 5.5 4.9 5.4 6.5
*1 at the start of irradiation. *2 estimation based on cover gas signal, tag-gas analysis, and the results of PIE. *3 EFPD: Effective Full Power Day. *4 at the pin breach.
Instead of the breached pins, a sibling pin (AKA-10) that was irradiated in the same subassembly was also examined in order to assess whether or not FCMI occurred and contributed to breach. Axial profilometry and ceramography were performed for the AKA-10 sibling pin. The axial profilometer measurement was made using laser profilometer. The axial diameter profile was averaged from measurement in three orientations (0, 60, and 120◦ ). For the ceramography, the AKA-10 sibling pin was transversely sectioned and prepared by grinding and then polishing with 1 μm and 0.25 μm diamond paste. 2.3. Results of PIE Fig. 4 shows the visual appearance of AKB-21 through AKC-25 after 3
H. Oka et al.
Nuclear Engineering and Design 370 (2020) 110894
Fig. 4. Visual appearance of AKB-21 through AKC-25 after the K2A test.
Fig. 6. Axial profilometry of sibling pin AKA-10.
for the axial position of pre-thinned area, with the data of irradiation history. In order to evaluate the CDF value, an in-reactor creep rupture equation of D9 alloy was created. In-reactor creep rupture data (Puigh and Hamilton, 1987) which were obtained from the Materials Open Test Assembly (MOTA) experiment in the FFTF were used. The stress and Larson-Miller parameter (LMP) were read from the figure in the litera ture (Puigh and Hamilton, 1987); and the rupture times were deter mined from the LMP and the irradiation temperature. From the obtained data set, the in-reactor creep rupture equation was determined as follows: / LMP = (T + 273.15)(5.66 + logtR ) 103 = 36.657 − 42.667(logσH ) + 22.137(logσH )2 − 3.9469(logσH )3
(2)
where T, tR and σ H are temperature (◦ C), time to rupture (h) and hoop stress (MPa), respectively. For the low stress side; σ H < 100 MPa, a tangent line was drawn at a position where the stress was 100 MPa in the curve of Eq. (2), and the following equation was obtained by extrapo lating the tangent line; / LMP = (T + 273.15)(5.66 + logtR ) 103 = 11.260 − 1.4825(logσH ) (3)
Fig. 5. Visual appearance of AKC-25 and AKC-26 after the K2B test.
reduction by FCCI needs to be considered in this study.
Fig. 8 shows the creep rupture Eqs. (2) and (3) (solid line) together with the in-reactor creep rupture data plot of FFTF/MOTA. Although there is some variation in the data on the low stress side, it can be seen that the creep rupture equation and the FFTF/MOTA data set are in good agreement. The in-reactor creep rupture equation covers the range of the irradiation temperature and time for the K2A and K2B tests. Reduction in cladding thickness due to FCCI was considered. Since the chemical composition of D9 alloy was similar to that of 316 stainless steel, the nominal FCCI curve based on the design curve of modified type 316 stainless steel (PNC316) was used for FCCI evaluation. The design curve of PNC316 was developed by covering the FCCI data of driver fuel
3. CDF calculations CDFs for the creep damage on the breached pins were evaluated by the following equation; ∫t dt CDF = (1) 0 tR where t is the testing time and tR is the rupture time at a given stress and temperature (Rawers, 1984; Kramer et al., 1993). CDFs were calculated 4
H. Oka et al.
Nuclear Engineering and Design 370 (2020) 110894
Fig. 7. Cross section of sibling pin AKA-10 at the elevation of 327 mm (x/L = 0.95).
Fig. 8. In-reactor creep rupture equation obtained from the data of FFTF/MOTA. Fig. 9. FCCI curve used for CDF calculation.
of experimental fast reactor Joyo whose cladding was PNC316. The FCCI curve used for CDF evaluation is the one drawn with the solid lines in Fig. 9: this curve gives the 35 µm lower corrosion depth than that given by the design curve, which can represent a non-conservative nominal behavior of FCCI. It was determined that FCCI starts at a local burnup of 1.6 at%, increases linearly with time during irradiation, and saturates at 65 μm beyond a local burnup of 6.4 at%.
Fission gas pressure was evaluated based on the initial gas amount, fission gas release rate and plenum volume. For the fission gas release rate, the design curve for Joyo driver fuel, which was empirically determined based on the data of MOX fuel irradiated in Joyo (Mizuno et al., 1992; Maeda et al., 2005), was used. The curve shows that the 5
H. Oka et al.
Nuclear Engineering and Design 370 (2020) 110894
fission gas release rate increases with the pin averaged burnup, and then reaches 100% at burnup of 7.5 at%. The curve is considered appropriate because the curve covers the fission gas release rate data of EBR-II (Cox, 1969). The influence of sodium corrosion on the outer surface of the clad ding tube may be considered. In the present study, the effect of sodium corrosion was included in the in-reactor creep rupture equation ob tained above. In addition, regarding the cladding temperature, nominal values were used assuming no hot spots. Cladding hoop stress was estimated by the thin-walled cylinder approximation. The wall thickness of the pre-thinned area was used in the calculation, and the loss of thickness due to FCCI was taken into account. 4. Results and discussion 4.1. CDF evaluation and failure probability CDF values obtained for the test pins are shown in Table 5. Fig. 10 shows the calculated hoop stress for each test pin as a function of the irradiation time. The hoop stress increases exponentially with increasing irradiation time. This is due to both an increase in the fission gas release and a decrease in cladding wall thickness by FCCI. The hoop stress at the time of breach occurrence was estimated to be about 128 to 192 MPa. For the K2B test pins (AKC-25 and 26), the increase rate of hoop stress was slower than it was for the other fuel pins. This is because the initial thickness of the K2B pins was large compared to the K2A pins. Fig. 11 shows the evaluated CDFs as a function of EFPD for the test pins. As shown in Fig. 11, the logarithm of CDF increases substantially linearly with increasing irradiation time. This indicates that the creep damage accumulated more rapidly at the end of the lifetime of fuel pins. The evaluated CDFs for the test pins were in the range of 0.7 to 1.4 at the occurrence of breach. This is significant because it empirically confirms that the fuel pin breach is likely to occur when the CDF approaches 1.0. It is important to note that at every six pins with different degrees of burnup, every CDF value was close to 1.0 and did not exceed 1.0 by an order of magnitude. This means that the CDF analysis would be a reli able method for the prediction of fuel pin breach. Weibull distribution analysis was performed to clarify the relation ship between CDF value and failure probability (Pitner et al., 1995). The obtained Weibull plot is illustrated in Fig. 12. The following general equation was used for the Weibull distribution analysis (Datsiou and Overend, 2018): ( ( )) 1 ln ln = mlnt − lnα (4) 1 − F(t)
Fig. 10. Histories of calculated hoop stress for each test pins.
where t, F(t), and α are the CDF value, the failure probability, and constant, respectively. The failure probability was estimated by the mean rank method: F(t)i =
i n+1
Fig. 11. Histories of CDF for each test pins.
was liner, and the following liner formula was obtained:
(5)
Y = 2.864 X − 0.5357
where n is the total number of tested specimens. F(t)i means the cumu lative frequency of the i-th data extracted from n data. As shown in Fig. 12, the relationship between CDF values and the failure probability
From this equation, the failure probability when the CDF approaches 1.0 is estimated to be about 0.45, meaning that almost half of the fuel pins are breached. This result suggests that the integrity of the fuel pin can be evaluated by creep damage of cladding caused by fission gas internal pressure. The Eq. (6) is significant because it is obtained based on data from the fuel pin irradiation, and it describes the probability of fuel pin breach for fast reactor.
Table 5 Obtained CDF value for the test pins at the pin breach. Pin No.
FCCI (μm)
Hoop stress (MPa)
CDF
AKB-21 AKB-22 AKB-23 AKB-24 AKC-25 AKC-26
30 31 32 26 32 48
170 187 177 147 127 192
1.3 1.4 0.8 1.0 0.7 1.3
(6)
4.2. CDF evaluation in particular condition In the design study of fuel pin, the design creep stress, SR, is used in the CDF calculations. The SR takes into consideration the scattering of creep test data, in which the rupture time is set to be one-third. It 6
H. Oka et al.
Nuclear Engineering and Design 370 (2020) 110894
irradiation and sodium corrosion on the CDF and the failure probability, CDF evaluation was performed using thermal control creep equation of D9 alloy instead of the in-reactor creep equation. The thermal control creep equation was created by tracing the lines from the figure in literature (Puigh and Hamilton, 1987). The created curve is drawn in Fig. 8. The calculated CDFs for the 6 test pins are shown in Table 6 and the calculated CDFs for AKC-26 are shown in Fig. 14. The CDF values are about 30 ~ 80% of the nominal values at the pin breach due to the environmental effects having been ignored. Comparing the in-reactor and thermal control stress rupture behaviors, the in-reactor data exhibit shorter rupture lives than the thermal control data for longer exposure times (Puigh and Hamilton, 1987). As increasing hoop stress at longer life, CDFs were dominated by longer side behavior; and this ex plains why the CDF of thermal control has the steep slope as shown in Fig. 14. Since CDF evaluation using the thermal control creep equation is underestimated, it is important to experimentally obtain the in-reactor creep rupture equation and use it in CDF evaluation. It can be said that the CDF analysis would be a reliable method for the prediction of fuel pin breach when appropriate material strength and environmental effects are adopted. The corrosion depth due to FCCI has relatively large experimental scattering according to a number of past studies. Thus, the influence of FCCI depth on the CDF value and the failure probability was also investigated. CDFs were calculated assuming no reduction of cladding wall thickness due to FCCI. The results are also shown in Table 6 and Fig. 15 for AKC-26. The CDF values were about 60 ~ 80% of the nominal value, but they did not differ by more than one order of magnitude. Although it depends on the specific irradiation conditions of each test pin, the effect of FCCI on the CDF calculation is not significant compared to that of creep equation. Fig. 15 also shows the CDF result derived from SR assuming no reduction of cladding by FCCI. The irradiation time where the CDF derived from SR reaches 1.0 is about 239 EFPD, which is corresponding to the CDF value of 0.33 for the nominal creep equation assuming no corrosion by FCCI. This implies that the safety margin of SR has room to be rationalized in the case assuming no thickness reduction by FCCI.
Fig. 12. Relationship between CDF and failure probability.
corresponds to the lower bound of the variations in the creep rupture data of the modified type 316 stainless steel cladding (Uwaba et al., 2010). Here, SR of D9 alloy was obtained by setting the rupture time in the in-reactor creep equation to one-third because D9 alloy is an austenitic stainless steel and its creep rupture data variation is consid ered to be the same as that of the modified type 316 stainless steel. Fig. 13 shows the CDF result derived from the SR compared to that from nominal in-reactor creep strength for the case of AKC-26. From Fig. 13, it is found that the irradiation time at which the CDF derived from SR reaches 1.0 is about 221 EFPD. The CDF value at the irradiation time of 221 EFPD in the case of nominal creep is 0.33, which is consistent with the rupture time setting of one-third. The corresponding failure proba bility when CDF is 0.33 is 0.02 from Eq. (5), which is small. The small failure probability derived from SR implies that the safety margin of SR has room to be rationalized. These findings will probably contribute to the rationalization of the fuel pin design and, consequently, the pro longation of the fuel pin lifetimes. In order to estimate environmental effects such as neutron
5. Conclusions Six in-reactor fuel pin breaches were obtained in the RBCB testing program performed in EBR-II. The CDFs of each breached pin were calculated using the in-reactor creep rupture equation, taking into ac count the irradiation history of cladding temperature, the reduction of wall thickness due to FCCI, and hoop stress due to fission gas pressure. The in-reactor creep rupture equation was obtained from the literature data, i.e. in-reactor creep rupture data of D9 alloy irradiated in FFTF. Each parameter used for CDF evaluation is nominal value thus the re sults obtained here are not conservative. It was concluded that the fuel pin breach resulted from creep damage due to internal pressure from accumulated fission product gas within the irradiation condition of this study. The CDFs of the breached fuel pins evaluated by nominal in-reactor creep strength were in the range of 0.7 Table 6 CDFs and failure probabilities calculated by thermal control equation or without FCCI consideration. Pin No.
AKB-21 AKB-22 AKB-23 AKB-24 AKC-25 AKC-26
Fig. 13. Comparison of CDF between nominal condition and design stress condition for the AKC-26 pin. 7
Evaluation using thermal control creep equation of D9 instead of the in-reactor creep equation
Evaluation without wall thickness reduction caused by FCCI
CDF
Failure probability
CDF
Failure probability
0.9 1.1 0.4 0.5 0.2 0.7
0.35 0.54 0.04 0.08 0.01 0.19
0.9 0.9 0.5 0.7 0.5 0.7
0.35 0.35 0.08 0.19 0.08 0.19
H. Oka et al.
Nuclear Engineering and Design 370 (2020) 110894
using nominal values for each parameter to the degree possible. On the other hand, the CDFs derived from the thermal control creep equation were less than those from the in-reactor creep rupture equation, high lighting the importance of experimentally obtaining the in-reactor creep rupture equation and use it in the CDF evaluation. The above result indicates that the CDF analysis would be a reliable method for the prediction of fuel pin breach when appropriate material strength and environmental effects are adopted. CRediT authorship contribution statement Hiroshi Oka: Conceptualization, Methodology, Investigation, Data curation, Writing - original draft, Writing - review & editing. Takeji Kaito: Conceptualization, Investigation, Data curation, Validation, Writing - review & editing, Supervision, Resources. Yoshihisa Ikusawa: Validation, Writing - review & editing. Satoshi Ohtsuka: Writing - re view & editing, Resources. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Fig. 14. Comparison of CDF derived from nominal condition and design stress condition for the AKC-26 pin.
References Cox, C.M., 1969. Irradiation performance of uranium-plutonium oxide fuel pins. Nucl. Saf. 10, 380. Datsiou, K.C., Overend, M., 2018. Weibull parameter estimation and goodness-of-fit for glass strength data. Struct. Saf. 73, 29–41. https://doi.org/10.1016/j. strusafe.2018.02.002. Kaito, T., Mizuno, T., 1997. 1997 Fall Meeting. Atomic Energy Society of Japan, Okinawa (in Japanese). Kramer, J.M., Liu, Y.Y., Billone, M.C., Tsai, H.C., 1993. Modeling the behavior of metallic fast reactor fuels during extended transients. J. Nucl. Mater. 204, 203–211. https:// doi.org/10.1016/0022-3115(93)90218-N. Maeda, K., 2012. 3.16 – ceramic fuel-cladding interaction. In: Compr. Nucl. Mater. Elsevier, pp. 443–483. https://doi.org/10.1016/B978-0-08-056033-5.00068-9. Maeda, K., Katsuyama, K., Asaga, T., 2005. Fission gas release in FBR MOX fuel irradiated to high burnup. J. Nucl. Mater. 346 (2-3), 244–252. https://doi.org/ 10.1016/j.jnucmat.2005.06.014. Makenas, B.J., 1986. Performance of titanium stabilized D9 cladding and ducts. Int. Conf. Reliab. Fuels Liq. Met. React., pp. 3–52 to 3–61. Mizuno, T., Asaga, T., Shikakura, S., 1992. Fast reactor fuel performance and an advanced fuel design. Int. Conf. Des. Saf. Adv. Nucl. Power Plants, pp. 28.3–1–28.3–7. Pitner, A.L., Gneiting, B.C., Bard, F.E., 1995. Irradiation performance of fast flux test facility drivers using D9 alloy. Nucl. Technol. 112 (2), 194–203. Puigh, R.J., Hamilton, M.L., 1987. In-reactor creep rupture behavior of the D9 and 316 alloys. ASTM STP 956, 22–29. Rawers, J.C., 1984. Creep and transient testing of irradiated type 316 stainless steel. Mater. Sci. Eng. 68 (1), 19–34. https://doi.org/10.1016/0025-5416(84)90240-4. Uwaba, T., Sogame, M., Ito, M., Mizuno, T., Donomae, T., Katsuyama, K., 2010. Evaluation of creep damage and diametral strain of fast reactor MOX fuel pins irradiated to high burnups. J. Nucl. Sci. Technol. 47 (8), 712–720. Uwaba, T., Maeda, S., Mizuno, T., Teague, M.C., 2012. Study on the mechanism of diametral cladding strain and mixed-oxide fuel element breaching in slow-ramp extended overpower transients. J. Nucl. Mater. 429 (1-3), 149–158. https://doi.org/ 10.1016/j.jnucmat.2012.05.042.
Fig. 15. Influence of corrosion on CDF derived from nominal condition and design stress condition for the AKC-26 pin.
to 1.4 at the occurrence of breach. These results confirm that fuel pin breach occurs as the CDF approaches 1.0 when the CDF is evaluated
8