Hierarchical Bayesian modeling to quantify fracture limit uncertainty of high-burnup advanced fuel cladding tubes under loss-of-coolant accident conditions

成川 隆文; 濱口 修輔*; 高田 孝*; 宇田川 豊

Nuclear Engineering and Design, 411, p.112443_1 - 112443_12, 2023/09

https://doi.org/10.1016/j.nucengdes.2023.112443

For realizing a highly reliable fracture limit evaluation of fuel cladding tubes during loss-of-coolant accidents (LOCAs) in light-water reactors, we developed a method to quantify the fracture limit uncertainty of high-burnup advanced fuel cladding tubes. This method employs a hierarchical Bayesian model that can quantify uncertainty even with limited experimental data. The fracture limit uncertainty was quantified as a probability using the amount of oxidation (Equivalent cladding reacted: ECR) and the initial hydrogen concentration (the hydrogen concentration in the fuel cladding tubes before the LOCA-simulated tests) as explanatory variables. We divided the regression coefficients of this model into a hierarchical structure with an overall average term common to all types of fuel cladding tubes and a term representing differences among various types of fuel cladding tubes. This hierarchical structure enabled us to quantify the fracture limit uncertainty through the effective use of prior knowledge and data, even for high-burnup advanced fuel cladding tubes with a small number of data points. The fracture limits representing a 5% fracture probability with 95% confidence of the high-burnup advanced fuel cladding tubes evaluated by the hierarchical Bayesian model were higher than 15% ECR for the initial hydrogen concentrations of up to 700-900 wtppm and restraint loads below 535 N. These fracture limits were comparable to the limit of the unirradiated Zircaloy-4 cladding tube, indicating that the burnup extension and use of the advanced fuel cladding tubes do not significantly lower the fracture limit of fuel cladding tubes. Further, we proposed a method to reduce the fracture limit uncertainty by using non-binary data, instead of the binary data, depending on the condition of the fuel cladding tube specimens after performing the LOCA-simulated test, thereby increasing the amount of information in the data.

Behavior of high-burnup BWR UO fuel with additives under reactivity-initiated accident conditions

三原 武; 垣内 一雄; 谷口 良徳; 宇田川 豊

Journal of Nuclear Science and Technology, 60(5), p.512 - 525, 2023/05

https://doi.org/10.1080/00223131.2022.2122616

Fuels with additives are expected to provide enhanced fuel performance in fission gas retention owing to their large grain size, which elongates fission gas migration path. To investigate behavior of the fuels during a reactivity-initiated accident (RIA), RIA-simulated experiments OS-1 and LS-4 were performed on ADOPT (chromia- and alumina-doped UO) fuel of 64 GWd/t and chromia-doped UO fuel of 48 GWd/t, respectively. The OS-1 rod failed at a fuel enthalpy increase of 160 J/g due to pellet-cladding mechanical interaction failure, which was the lowest failure limit among the test results ever obtained at the NSRR on high-burnup fuels from 40 to 65 GWd/tU. Comparison of the hydride morphologies in the cladding metallic layer between the rods subjected to the past NSRR tests suggests the contribution of radially oriented hydrides during base irradiation to the low failure limit. The LS-4 rod survived for a peak fuel enthalpy increase of 549 J/g, which resulted in cladding deformation of 2.4% in the residual hoop strain and FGR of 1.4%-6.1%. Whereas the low fission gas release exhibits the effect of additives, the cladding deformation is within the range explained by the deformation mechanism essentially identical to those recognized for high-burnup undoped fuels.

Engineering formulation of the irradiation growth behavior of zirconium-based alloys for light water reactors

垣内 一雄; 天谷 政樹; 宇田川 豊

Journal of Nuclear Materials, 573, p.154110_1 - 154110_7, 2023/01

https://doi.org/10.1016/j.jnucmat.2022.154110

The irradiation growth behavior of coupon specimens prepared from improved Zr-based alloys for light-water reactor fuel cladding, which have various additive elements and fabrication conditions, was investigated by conducting an irradiation test at 573 and 593 K under typical PWR coolant conditions up to a fast-neutron fluence of 7.810 (n/cm , E 1 MeV) in the Halden reactor in Norway. Based on the dimensional change data measured at interim and final inspections, the amounts of irradiation growth of the improved Zr-based alloys were formulated from the viewpoint of engineering. The trends of the parameters which express the effects of additive elements on irradiation growth behavior were in good agreement with those previously reported, and it was found that the amount of irradiation growth can be expressed by using a summation rule of the effect of each additive element on irradiation growth.

Evaluation of anisotropic elastic and plastic parameters of Zircaloy-4 fuel cladding from biaxial stress test data and their application to a fracture mechanics analysis

Li, F.; 三原 武; 宇田川 豊

Journal of Nuclear Science and Technology, 59(12), p.1455 - 1464, 2022/12

https://doi.org/10.1080/00223131.2022.2062474

The mechanical properties of fuel cladding near the elastic limit are essential in considering its failure limit during a pellet-cladding mechanical interaction phase under reactivity-initiated accident (RIA) conditions. The mechanical properties of a Zircaloy-4 cladding tube, such as orthotropic elasticity and anisotropic constants for Hill's plasticity law, were evaluated based on the biaxial stress test data, focusing on the equivalent plastic strain up to ~2.5%. Samples with various fabrication conditions, such as cold-worked, recrystallized, and stress relieved after cold-work with Q-factors of 2, 3, and 4 were investigated. The cold worked samples and recrystallized samples showed high yield stress and Young's modulus, respectively. The evaluated mechanical properties of the stress relieved samples revealed a limited impact of Q-factors on mechanical behavior, including their anisotropic feature. The derived mechanical properties were applied to evaluate the fracture mechanics parameter, J-integral, based on failure limit data from biaxial-expansion-due-to-compression tests on precracked tubes. This evaluation produced systematically lower J-integral values of the stress relieved tube than previously evaluated based on the failure limit data from in-pile RIA-simulated tests.

Mechanical property evaluation with nanoindentation method on Zircaloy-4 cladding tube after LOCA-simulated experiment

垣内 一雄; 山内 紹裕*; 天谷 政樹; 宇田川 豊; 北野 剛司*

Proceedings of TopFuel 2022 (Internet), p.409 - 418, 2022/10

In order to examine the influence of cladding microstructural changes upon the mechanical property of the fuel cladding under LOCA conditions in a more direct and quantitative manner, the nanoindentation method has been applied to Zircaloy-4 cladding specimens after LOCA simulated tests (about 1473 K, ECR 20%, quench at 973 K after slow cooling); results for two specimens taken from the rupture opening part and secondary hydriding part were compared. In addition to hardness and Young's modulus, the plastic work fraction that corresponds to the relative ductility was evaluated from the load-displacement curve. The plastic work fraction at the secondary hydriding part was found to be obviously lower than that at the rupture opening part and closer to that in -Zr(O) layers beneath the outer surface. This result from the nanoindentation method agrees with the conventional knowledge about low ductility at the secondary hydriding part.

Irradiation growth behavior and effect of hydrogen absorption of Zr-based cladding alloys for PWR

垣内 一雄; 天谷 政樹; 宇田川 豊

Annals of Nuclear Energy, 171, p.109004_1 - 109004_9, 2022/06

https://doi.org/10.1016/j.anucene.2022.109004

In order to understand the dimensional stability of the fuel rod during long-term use in commercial LWRs, an irradiation growth testing in the Halden reactor of Norway was conducted on various fuel cladding materials including the improved Zr alloy. In this paper, the effect of hydrogen, which was absorbed in the cladding tube due to corrosion, on the irradiation growth behavior was evaluated. Comparison between the specimens with or without pre-charged hydrogen revealed that the effect of hydrogen absorption, accelerating irradiation growth, became significant when the hydrogen content exceeded the hydrogen solubility limit in the corresponding irradiation temperature. Analysis based on this understanding derived growth acceleration effect (0.060.01)%/100 ppm, whose denominator is defined as the amount of absorbed hydrogen involved in hydride precipitation under irradiation as a relevant parameter.

Follow-up experimental study on causes of the low-enthalpy failure observed in the reactivity-initiated-accident-simulated test on LWR additive fuels

三原 武; 垣内 一雄; 谷口 良徳; 宇田川 豊

Proceedings of TopFuel 2021 (Internet), 10 Pages, 2021/10

Test OS-1, the reactivity-initiated-accident (RIA) -simulated test on 64 GWd/tU high burnup fuel with ADOPT (chromia-and-alumina-doped UO) pellets resulted in a failure at the lowest fuel enthalpy increase among the tests ever performed at the NSRR on high burnup fuels from 40 to 65 GWd/tU. Roles of both fuel pellets and cladding behaviours in this remarkable observation are being investigated. A comparative RIA-simulated test OS-2 was thus performed on undoped fuel that had been base-irradiated in the identical fuel assembly with the OS-1 rod. The transient records acquired during Test OS-2 indicated that the rod survived without fuel failure. Radially projected hydride lengths in the cladding metallic layer were evaluated from the metallograph images observed in the vicinity of the OS-2 test rod and compared with other failure test cases. The comparison suggested that the hydride morphologies affected the low failure limit of the OS-1 rod and also explains the survival of the OS-2 rod, to some extent. Nevertheless, as the OS-2 rod survived 100 J/g higher peak fuel enthalpy than the OS-1 failure limit, further experimental and analytical studies are desired to pursue other possible causes: additional loading specific to ADOPT pellets, difference in the pellet/cladding bonding condition, and so on.

Simulation of the effect of radially oriented hydride precipitates on failure limit of high-burnup BWR fuel cladding under PCMI loading

谷口 良徳; 三原 武; 宇田川 豊

Proceedings of TopFuel 2021 (Internet), 10 Pages, 2021/10

Scattering of hydride precipitates in a fuel cladding tube was simply modeled by mapping of multiple cracks in finite element system based on the image-processed hydride morphologies observed in post-test cladding samples and the mechanical interactions of these cracks were simulated by damage mechanics calculation. This is a part of ongoing efforts to analyze the effect of the radially oriented hydride precipitates in the cladding tube on the fuel-failure limit observed in Test OS-1: a reactivity-initiated accident (RIA)-simulated test on the BWR fuel with additives irradiated to 64 GWd/tU, which resulted in a fuel failure with the lowest failure limit among the tests ever performed at the NSRR for high burnup BWR rods. The LS-1 test fuel rod, with similar burnup to the OS-1 rod, was selected as another RIA-simulated test rod to be compared with. Sensitivity was examined for damage model parameters, which dominate strain level at which a finite element becomes softened and finally loses its load-carrying capacity, and two sets of plasticity model parameters calibrated for irradiated and unirradiated materials. In the calculation, large stress concentration occurred in the regions between the tips of two adjacent cracks, and one pair of such cracks, typically one of the longest radial cracks existing in the outer periphery of the cladding, then linked to form a longer crack. The simulated macroscopic circumferential strain at failure of the OS-1 cladding model was lower than that of the LS-1 cladding model by about 40% or more. Limited sensitivity of the damage and plasticity model parameters, observed for the investigated range, suggests that the reduction of failure strain primarily reflects the difference in crack distributions between the two simulated rods. The results support the interpretation that the radially oriented hydrides contributed to the low PCMI-failure limit observed in Test OS-1.

燃料挙動解析コードFEMAXI-8の燃料結晶粒内ガス移行モデル改良

宇田川 豊; 田崎 雄大

JAEA-Data/Code 2021-007, 56 Pages, 2021/07

JAEA-Data-Code-2021-007.pdf:5.05MB

FEMAXI-8は、軽水炉燃料の通常運転時及び過渡条件下の挙動解析を目的として日本原子力研究開発機構が開発・整備を進めてきたFEMAXIコードの最新バージョンとして、2019年3月に公開された。本報告では、公開以降新たに整備を進めた、燃料結晶粒内核分裂生成物(FP)ガスバブルの多群/非平衡モデルについてまとめた。結晶粒内で様々なサイズを持って分布しているFPガスバブルを単一の大きさのガスバブルにより近似していた従来のモデルに対し、このモデルでは、バブルサイズに関する2群以上の群構造と非平衡な挙動の双方を表現することが出来る。これによって、妥当なオーダーのガスバブル圧力算定が可能となるなど、主に過渡的な挙動の再現性改善が見込めると共に、粒内FPガスバブル挙動についてより厳密な記述が可能となり、FP挙動モデリング全体としての高度化余地が拡大している。今回のモデル整備では、まず、任意の群数や空間分割に対応する粒内FP挙動解析モジュールを開発した。次に、FEMAXI-8上で容易に運用可能な2群モデルとして扱うため、同モジュールとFEMAXI-8間のインタフェースを開発し、両者を接続した。これによりFEMAXI-8から利用可能となった2群モデルについては改めて検証解析を実施した。多群/非平衡モデル適用時にも一定の性能を確保できるモデルパラメータを決定し、公開パッケージ向けに整備した。

燃料挙動解析コードFEMAXI-8の開発と公開; 信頼性向上と燃料分野での利用拡大に向けて

宇田川 豊

日本原子力学会誌ATOMO, 62(10), p.555 - 559, 2020/10

https://doi.org/10.3327/jaesjb.62.10_555

核燃料や燃料被覆管のふるまいに係る研究で得られた知見やデータは、燃料挙動解析コードにモデルとして集約され、燃料設計や安全評価に活用されている。著者らは、国産/公開の燃料挙動解析コードとして産官学で広く利用されてきたFEMAXIの最新バージョンFEMAXI-8を開発した。FPガス移行挙動モデル等のモデル高度化および機能拡充を進めるとともに、燃料分野における産官学の研究開発をより強力にサポートする技術基盤とすべく、体系的検証による性能評価を経て、一定の信頼性が確認された標準モデルセットを提供した。2019年3月の公開に至るまでの取組みを概説する。