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Journal Articles

Alloy design and characterization of a recrystallized FeCrAl-ODS cladding for accident-tolerant BWR fuels; An Overview of research activity in Japan

Ukai, Shigeharu; Sakamoto, Kan*; Otsuka, Satoshi; Yamashita, Shinichiro; Kimura, Akihiko*

Journal of Nuclear Materials, 583, p.154508_1 - 154508_24, 2023/09

 Times Cited Count:0 Percentile:95.21(Materials Science, Multidisciplinary)

Journal Articles

Dislocation-climbing bypass over dispersoids with different lattice misfit in creep deformation of FeCrAl oxide dispersion-strengthened alloys

Ukai, Shigeharu; Yamashita, Shinichiro

Journal of Materials Research and Technology, 16, p.891 - 898, 2022/01

 Times Cited Count:7 Percentile:87.71(Materials Science, Multidisciplinary)

The creep strain rate of FeCrAl oxide dispersion-strengthened alloys, as a promising accident-tolerant fuel (ATF) cladding of the light-water reactors, is accelerated in YAlO$$_{3}$$ dispersoids by two to three orders of magnitude compared with Y$$_{4}$$Zr$$_{3}$$O$$_{12}$$ dispersoid at 1273K and even occurs at an applied stress less than threshold stress for dislocation detachment. Two approaches were carried out to interpret new findings and to clarify their mechanism. By optimizing the relaxation of the dislocation line energy at the dispersoid interface, numerical analyses proved the accelerated dislocation-climbing in the YAlO$$_{3}$$ dispersoids. The other is a more atomistic approach. The climbing force on the dislocation induced by the stress field around the dispersoid was analyzed in terms of the Peach-Koehler relationship. The accelerated creep strain rate in YAlO$$_{3}$$ dispersoids is attributed to a larger climbing force induced by larger lattice misfit with less coherency in YAlO$$_{3}$$ dispersoid.

Journal Articles

Effects of thermal aging on the mechanical properties of FeCrAl-ODS alloy claddings

Yano, Yasuhide; Tanno, Takashi; Otsuka, Satoshi; Kaito, Takeji; Ukai, Shigeharu*

Materials Transactions, 62(8), p.1239 - 1246, 2021/08

 Times Cited Count:3 Percentile:35.36(Materials Science, Multidisciplinary)

The FeCrAl-ODS alloy claddings were manufactured and Vickers hardness, ring tensile tests and TEM observations of these claddings were performed to investigate the effects of thermal aging at 450 $$^{circ}$$C for 5,000 and 15,000 h. The age-hardening of all FeCrAl-ODS alloy cladding was found. In addition, the significant increase in tensile strength was accompanied by much larger loss of ductility. It was suggested that this age-hardening behavior was attributed to the (Ti, Al)-enriched phase ($$beta$$' phase) and the $$alpha$$' phase precipitates (content of Al is $$<$$ 7 wt%). In comparison with FeCrAl-ODS alloys with almost same chemical compositions, there was significant age-hardening in both alloys. However, the extrusion bar with no-recrystallized structures was keeping good ductility. It was suggested that this different behavior of reduction ductility was attributed to the effects of grain boundaries, dislocation densities and specimen preparation direction.

Journal Articles

Orientation dependence of yield strength in a new single crystal-like FeCrAl oxide dispersion strengthened alloy

Aghamiri, S. M. S.*; Sugawara, Naoya*; Ukai, Shigeharu; Ono, Naoko*; Sakamoto, Kan*; Yamashita, Shinichiro

Materials Characterization, 176, p.111043_1 - 111043_6, 2021/06

Advanced oxidation-resistant FeCrAl ODS alloys were developed via the control of composition-processing conditions for the accident tolerant fuel (ATF) cladding. For the first time, a single-crystal like recrystallized FeCrAl ODS alloy was achieved with a unique crystallographic texture of 110-plane and 211-direction and a high number density of fine nanoscale oxide particles. Evaluation of yield strengths at different temperatures showed higher values in transverse (T) direction than longitudinal (L) direction. The crystal orientation dependence of the yield strength up to 800$$^{circ}$$C was attributed to lower value of Schmid factor in transverse direction. Accordingly, the critical resolved shear stress of this practical class of advanced materials was calculated in various temperatures.

Journal Articles

Solid-solution strengthening by Al and Cr in FeCrAl oxide-dispersion-strengthened alloys

Ukai, Shigeharu*; Yano, Yasuhide; Inoue, Toshihiko; Sowa, Takashi*

Materials Science & Engineering A, 812, p.141076_1 - 141076_11, 2021/04

 Times Cited Count:11 Percentile:74.45(Nanoscience & Nanotechnology)

FeCrAl oxide dispersion strengthened alloys are promising materials for accident tolerant fuels for light water reactors (LWRs). In these alloys, Al and Cr are key elements with important synergistic effects: enhancement of the formation of oxidation-resistant Al$$_{2}$$O$$_{3}$$ phase by Cr addition and suppression of the formation of the embrittling Cr-rich $$alpha$$' phase by Al addition. The solid-solution strengthening resulting from Al and Cr co-addition was investigated in this study. The solid-solution strengthening resulting from Al and Cr co-addition was investigated in this study. The Al and Cr contents were systematically varied from 9-16 at.% and 10-17 at.%, respectively, and tensile tests were conducted at 298 K, 573 K and 973 K in the as-annealed condition. The solid solution strengthening increased linearly, 20 MPa per 1 at.% Al and 5 MPa per 1 at.% Cr, at the typical LWR operational temperature of 573 K. The conventional Fleischer-Friedel and Labusch theories cannot explain this level of solid-solution strengthening. It was shown that Suzuki's double kink theory for screw dislocations reasonably predicts the solid solution strengthening by Al and Cr as well as the inverse dependency on the absolute temperature and linear dependency on the Al and Cr content.

Journal Articles

High-temperature creep deformation in FeCrAl-oxide dispersion strengthened alloy cladding

Ukai, Shigeharu; Kato, Shoichi; Furukawa, Tomohiro; Otsuka, Satoshi

Materials Science & Engineering A, 794, p.139863_1 - 139863_13, 2020/09

 Times Cited Count:33 Percentile:95.13(Nanoscience & Nanotechnology)

The FeCrAl-oxide dispersion strengthened (ODS) alloy is the promising cladding material for the accident-tolerant fuel (ATF) of the light water reactors (LWR). Ring-creep tests for FeCrAl-ODS alloy cladding were carried out at 973 K and 1273 K. The dislocation detachment stress from the dispersoid was derived by considering the dislocation-dispersoid elastic interaction and the dislocation relaxation effect by climb motion. When the applied stress exceeds the dislocation detachment stress, dislocations overcome the dispersoids with the reduced values of the stress exponent. When the stress is lower than the dislocation detachment stress, grain boundary sliding (GBS) is dominant factor for the low strain rate creep deformation at 1273 K. Based on those findings, new constitutive equations for creep deformation were constructed, which is applicable to low stress, low strain rate and high temperature conditions encountered at the reactor sever accident.

Journal Articles

Oxide dispersion strengthened steels

Ukai, Shigeharu*; Ono, Naoko*; Otsuka, Satoshi

Comprehensive Nuclear Materials, 2nd Edition, Vol.3, p.255 - 292, 2020/08

Fe-Cr-based oxide dispersion strengthened (ODS) steels have a strong potential for high burnup (long-life) and high-temperature applications typical for SFR fuel cladding. Current progress in the development of Fe-Cr-based ODS steel claddings is reviewed, including their relevant mechanical properties, e.g. tensile and creep rupture strengths in the hoop directions. In addition, this paper reviewed the current research status on corrosion resistant Fe-Cr-Al-based ODS steel claddings, which are greatly paid attention recently as the accident tolerant fuel claddings for the light water reactor (LWR) and also as the claddings of the lead fast reactors (LFR) utilizing Pb-Bi eutectic (LBE) coolant.

Journal Articles

Anomalous small-angle X-ray scattering (ASAXS) study of irradiation-induced nanostructure change in Fe-ion beam irradiated oxide dispersion-strengthened (ODS) steel

Kumada, Takayuki; Oba, Yojiro; Motokawa, Ryuhei; Morooka, Satoshi; Tominaga, Aki; Tanida, Hajime; Shobu, Takahisa; Konno, Azusa; Owada, Kenji*; Ono, Naoko*; et al.

Journal of Nuclear Materials, 528, p.151890_1 - 151890_7, 2020/01

 Times Cited Count:1 Percentile:12.47(Materials Science, Multidisciplinary)

We have developed an anomalous small-angle X-ray scattering (ASAXS) diffractometer in SPring-8 to investigate irradiation-induced nanostructural change in ion-beam irradiated stainless steel. A thermally-aged MA956 stainless steel sample displays power-law scattering that follows the Porod law at the magnitude of scattering vector, Q, below 0.5 nm$$^-1$$ and an overlapped shoulder around 0.7 nm$$^-1$$. After the ion-beam irradiation, the intensity of the shoulder remained unchanged, whereas that of the power-law scattering nearly doubled. This result indicates that none of the structural parameters of the Cr-rich nanoprecipitates, such as the number density, size, and interface roughness, were changed by the irradiation.

Journal Articles

Microstructure and texture evolution and ring-tensile properties of recrystallized FeCrAl ODS cladding tubes

Aghamiri, S. M. S.*; Sowa, Takashi*; Ukai, Shigeharu*; Ono, Naoko*; Sakamoto, Kan*; Yamashita, Shinichiro

Materials Science & Engineering A, 771, p.138636_1 - 138636_12, 2020/01

 Times Cited Count:25 Percentile:90.87(Nanoscience & Nanotechnology)

Oxide dispersion strengthened (ODS) FeCrAl ferritic steels are being developed as potential accident tolerance fuel cladding materials for the light water reactors (LWRs) due to significant improvement in steam oxidation by alumina forming scale and good mechanical properties up to high temperatures. In this study, the microstructural characteristics and tensile properties of the two FeCrAl ODS cladding tubes with different extrusion temperatures of 1100$$^{circ}$$C and 1150$$^{circ}$$C were investigated during processing conditions. While the hot extruded sample showed micron sized elongated grains with strong $$alpha$$-fiber in $$<$$110$$>$$ texture, cold pilger rolling process change the microstructure to submicron/micron size grain structure along with texture evolution to both $$alpha$$-fiber ($$<$$110$$>$$ texture) and $$gamma$$-fiber ({111} texture) via crystalline rotations. Subsequently, final annealing resulted in evolution of microstructure to large grain recrystallized structure starting at recrystallization temperature of $$sim$$810-850$$^{circ}$$C. Two distinct texture development happened in recrystallized cladding tubes, i.e., only large elongated grains of (110) $$<$$211$$>$$ texture following extrusion temperature of 1100$$^{circ}$$C; and two texture components of (110) $$<$$211$$>$$ and {111} $$<$$112$$>$$ following higher extrusion temperature of 1150$$^{circ}$$C. The different texture development and retarding of recrystallization progress in 1100$$^{circ}$$C-extruded cladding tubes were attributed to higher distribution of oxide particles.

Journal Articles

Stability of $$gamma$$' precipitates in nickel based oxide dispersion-strengthened superalloys under high-temperature and heavy irradiation conditions

Konno, Azusa; Ono, Naoko*; Ukai, Shigeharu*; Kondo, Sosuke*; Hashitomi, Okinobu*; Kimura, Akihiko*

Materials Transactions, 60(11), p.2260 - 2266, 2019/11

 Times Cited Count:1 Percentile:6.35(Materials Science, Multidisciplinary)

A stability of cuboidal $$gamma$$' phase under heavy irradiation was studied for newly developed Ni-based Oxide Dispersion Strengthened (ODS) superalloy as a candidate for the core structural materials in VHTR or GFR. The ion irradiation was applied at 873K, 1073K, 1273K and the dose was 100 dpa. The $$gamma$$' phase remained the cuboidal shape at 873K but got out of the shape at 1073K after irradiation. Those growths can be explained by the Nelson-Hudson-Mazey (NHM) model. For the result of 1273K irradiation, however, huge $$gamma$$' phase appeared in the whole irradiated area at the post irradiation-observation. This behavior is interpreted in terms of disordering of the ordered $$gamma$$' phase due to cascade collision, and thus increasing Gibbs free energy of the disordered phase induces a change of the element distribution inside the irradiated area. The ordered $$gamma$$' phase was reproduced from the disordered state at the cooling after ion irradiation.

Journal Articles

Overview of accident-tolerant fuel R&D program in Japan

Yamashita, Shinichiro; Ioka, Ikuo; Nemoto, Yoshiyuki; Kawanishi, Tomohiro; Kurata, Masaki; Kaji, Yoshiyuki; Fukahori, Tokio; Nozawa, Takashi*; Sato, Daiki*; Murakami, Nozomu*; et al.

Proceedings of International Nuclear Fuel Cycle Conference / Light Water Reactor Fuel Performance Conference (Global/Top Fuel 2019) (USB Flash Drive), p.206 - 216, 2019/09

After the nuclear accident at Fukushima Daiichi Power Plant, research and development (R&D) program for establishing technical basis of accident-tolerant fuel (ATF) started from 2015 in Japan. Since then, both experimental and analytical studies necessary for designing a new light water reactor (LWR) core with ATF candidate materials are being conducted within the Japanese ATF R&D Consortium for implementing ATF to the existing LWRs, accompanying with various technological developments required. Until now, we have accumulated experimental data of the candidate materials by out-of-pile tests, developed fuel evaluation codes to apply to the ATF candidate materials, and evaluated fuel behavior simulating operational and accidental conditions by the developed codes. In this paper, the R&D progresses of the ATF candidate materials considered in Japan are reviewed based on the information available such as proceedings of international conference and academic papers, providing an overview of ATF program in Japan.

Journal Articles

Ultra-high temperature creep rupture and transient burst strength of ODS steel claddings

Yano, Yasuhide; Sekio, Yoshihiro; Tanno, Takashi; Kato, Shoichi; Inoue, Toshihiko; Oka, Hiroshi; Otsuka, Satoshi; Furukawa, Tomohiro; Uwaba, Tomoyuki; Kaito, Takeji; et al.

Journal of Nuclear Materials, 516, p.347 - 353, 2019/04

 Times Cited Count:13 Percentile:85.03(Materials Science, Multidisciplinary)

9Cr-ODS steel claddings consisting of tempered martensitic matrix, showed prominent creep rupture strength at 1000 $$^{circ}$$C, which surpassed that of heat-resistant austenitic steels although creep rupture strength of tempered martensitic steels is generally lower than that of austenitic steels at high temperatures. The measured creep rupture strength of 9Cr-ODS steel claddings at 1000 $$^{circ}$$C was higher than that from extrapolated creep rupture trend curves formulated using data at temperatures from 650 to 850 $$^{circ}$$C. This superior strength seemed to be owing to transformation of the matrix from the $$alpha$$-phase to the $$gamma$$-phase. The transient burst strengths for 9Cr-ODS steel were much higher than those for 11Cr-ferritic/martensitic steel (PNC-FMS). Cumulative damage fraction analyses suggested that the life fraction rule can be used for the rupture life prediction of 9Cr-ODS steel and PNC-FMS claddings in the transient and accidental events with a certain accuracy.

Journal Articles

Ion irradiation effects on FeCrAl-ODS ferritic steel

Kondo, Keietsu; Aoki, So; Yamashita, Shinichiro; Ukai, Shigeharu*; Sakamoto, Kan*; Hirai, Mutsumi*; Kimura, Akihiko*

Nuclear Materials and Energy (Internet), 15, p.13 - 16, 2018/05

 Times Cited Count:15 Percentile:85.51(Nuclear Science & Technology)

Radiation hardening and microstructural evolution of ion irradiated 12Cr-6Al ODS ferritic steel was studied. Ion irradiation experiments were performed using Fe ions up to the nominal displacement damage of 20 dpa at the irradiation temperature was 300$$^{circ}$$C. The monotonical increase of radiation hardening with dose was confirmed by experimentally obtained hardness data. The radiation hardening was also calculated theoretically by introducing the microstructural character examined by TEM into the dispersed barrier hardening model. The results showed a good agreement with the experimentally obtained data up to 5 dpa, while a slight discrepancy was found between theoretical and experimental hardness values at 20 dpa. Radiation hardening was mainly caused by irradiation-induced defect clusters below the irradiation dose of 5 dpa. As the irradiation dose increased toward 20 dpa, an additional influence of the radiation appeared, which was assumed to be induced by $$alpha$$' phase transformation.

Journal Articles

Technical basis of accident tolerant fuel updated under a Japanese R&D project

Yamashita, Shinichiro; Nagase, Fumihisa; Kurata, Masaki; Nozawa, Takashi; Watanabe, Seiichi*; Kirimura, Kazuki*; Kakiuchi, Kazuo*; Kondo, Takao*; Sakamoto, Kan*; Kusagaya, Kazuyuki*; et al.

Proceedings of 2017 Water Reactor Fuel Performance Meeting (WRFPM 2017) (USB Flash Drive), 10 Pages, 2017/09

In Japan, the research and development (R&D) project on accident tolerant fuel and other components (ATFs) of light water reactors (LWRs) has been initiated in 2015 for establishing technical basis of ATFs. The Japan Atomic Energy Agency (JAEA) has coordinated and carried out this ATF R&D project in cooperation with power plant providers, fuel venders and universities for making the best use of the experiences, knowledges in commercial uses of zirconium-base alloys (Zircaloy) in LWRs. ATF candidate materials under consideration in the project are FeCrAl steel strengthened by dispersion of fine oxide particles(FeCrAl-ODS) and silicon carbide (SiC) composite, and are expecting to endure severe accident conditions in the reactor core for a longer period of time than the Zircaloy while maintaining or improving fuel performance during normal operations. In this paper, the progresses of the R&D project are reported.

Journal Articles

Overview of Japanese development of accident tolerant FeCrAl-ODS fuel claddings for BWRs

Sakamoto, Kan*; Hirai, Mutsumi*; Ukai, Shigeharu*; Kimura, Akihiko*; Yamaji, Akifumi*; Kusagaya, Kazuyuki*; Kondo, Takao*; Yamashita, Shinichiro

Proceedings of 2017 Water Reactor Fuel Performance Meeting (WRFPM 2017) (USB Flash Drive), 7 Pages, 2017/09

This paper will show the overview of current status of development of accident tolerant FeCrAl-ODS fuel claddings for BWRs (boiling water reactors) in the program sponsored and organized by the Ministry of Economy, Trade and Industry (METI) of Japan. This program is being carried out to create the technical basis for the practical use of the accident tolerant fuels and the other components in LWRs through multifaceted activities. In the development of FeCrAl-ODS fuel claddings both the experimental and the analytical studies have been performed. The acquisition and accumulation of key material properties of FeCrAl-ODS fuel claddings were conducted by using bar, sheet and tube shaped FeCrAl-ODS materials fabricated in this program to support the evaluations in the analytical studies. A neutron irradiation test was also started in the ORNL High Flux Isotope Reactor (HFIR) to examine the effect of neutron irradiation on the mechanical properties.

Journal Articles

Ultra-high temperature tensile properties of ODS steel claddings under severe accident conditions

Yano, Yasuhide; Tanno, Takashi; Oka, Hiroshi; Otsuka, Satoshi; Inoue, Toshihiko; Kato, Shoichi; Furukawa, Tomohiro; Uwaba, Tomoyuki; Kaito, Takeji; Ukai, Shigeharu*; et al.

Journal of Nuclear Materials, 487, p.229 - 237, 2017/04

 Times Cited Count:32 Percentile:96.87(Materials Science, Multidisciplinary)

Ultra-high temperature ring tensile tests were carried out to investigate the tensile behavior of oxide dispersion strengthened (ODS) steel claddings and wrapper materials under severe accident conditions; temperatures ranged from room temperature to 1400$$^{circ}$$C which is near the melting point of core materials. The experimental results showed that tensile strength of 9Cr-ODS steel claddings was highest in the core materials at the ultra-high temperatures between 900 and 1200$$^{circ}$$C, but that there was significant degradation in tensile strength of 9Cr-ODS steel claddings above 1200$$^{circ}$$C. This degradation was attributed to grain boundary sliding deformation with $$gamma$$/$$delta$$ transformation, which was associated with reduced ductility. On the other hand, tensile strength of recrystallized 12Cr-ODS and FeCrAl-ODS steel claddings retained its high value above 1200 $$^{circ}$$C unlike the other tested materials. Present study includes the result of "R&D of ODS ferritic steel fuel cladding for maintaining fuel integrity at the high temperature accident condition" entrusted to Hokkaido University by the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT).

Journal Articles

Evaluation on tolerance to failure of ODS ferritic steel claddings at the accident conditions of fast reactors

Uwaba, Tomoyuki; Yano, Yasuhide; Otsuka, Satoshi; Naganuma, Masayuki; Tanno, Takashi; Oka, Hiroshi; Kato, Shoichi; Kaito, Takeji; Ukai, Shigeharu*; Kimura, Akihiko*; et al.

Proceedings of 2017 International Congress on Advances in Nuclear Power Plants (ICAPP 2017) (CD-ROM), 7 Pages, 2017/04

Tolerance of fast rector fuel elements to failure in the typical accident conditions was evaluated for the oxide-dispersion-strengthened (ODS) ferritic steel claddings that are candidate of the cladding material for advanced fast reactors. The evaluation was based on the cladding creep damage, which was quantified by the cumulative damage fractions (CDFs). It was shown that the CDFs of the ODS ferritic steel cladding were substantially lower than the breach limit of 1.0 in the loss of flow and transient over power conditions until a passive reactor shutdown system operates.

Journal Articles

Consideration of the oxide particle-dislocation interaction in 9Cr-ODS steel

Ijiri, Yuta*; Ono, Naoko*; Ukai, Shigeharu*; Yu, H.*; Otsuka, Satoshi; Abe, Yosuke; Matsukawa, Yoshitaka*

Philosophical Magazine, 97(13), p.1047 - 1056, 2017/02

 Times Cited Count:2 Percentile:11.64(Materials Science, Multidisciplinary)

The interaction between oxide particles and dislocations in a 9Cr-ODS ferritic steel is investigated by both static and in-situ TEM observation under dynamic straining conditions and room temperature. The measured obstacle strength ($$alpha$$) of the oxide particles was no greater than 0.80 and the average was 0.63. The dislocation loops around some coarsened particles were also observed. The calculated obstacle strength by a stress formula of the Orowan interaction is nearly equaled to the average experimental value. Not only cross-slip system but also the Orowan interaction should be considered as the main interaction mechanism between oxide particles and dislocation in 9Cr-ODS ferritic steel.

Journal Articles

Oxide dispersion-strengthened/ferrite-martensite steels as core materials for Generation IV nuclear reactors

Ukai, Shigeharu*; Otsuka, Satoshi; Kaito, Takeji; de Carlan, Y.*; Ribis, J.*; Malaplate, J.*

Structural Materials for Generation IV Nuclear Reactors, p.357 - 414, 2017/00

 Times Cited Count:61 Percentile:99.22

Oxide dispersion strengthened (ODS) steels are the most promising candidate materials for fuel cladding of generation IV nuclear reactors. The progress and current status for development of ODS/FM(ferrite-martensite) steels conducted mainly in Japan and France are overviewed. The chemical compositions of ODS/FM steels are listed. Fabrication routes of cladding tube are mentioned for ferrite-type ODS steels using recrystallized process and martensite-type one using $$alpha$$-$$gamma$$ phase transformation. The optimized process is identical for both countries. Joining process between cladding and end-plug has been also developed by using the pressurized resistance upset welding method. The improvements brought by ODS/FM steels in high-temperature strength and irradiation resistance are verified.

Journal Articles

Effect of the dilation caused by helium bubbles on edge dislocation motion in $$alpha$$-iron; Molecular dynamics simulation

Abe, Yosuke; Tsuru, Tomohito; Shi, S.*; Ono, Naoko*; Ukai, Shigeharu*

Journal of Nuclear Science and Technology, 53(10), p.1528 - 1534, 2016/10

 Times Cited Count:10 Percentile:71.93(Nuclear Science & Technology)

Various types of nanometric defects such as voids and helium (He) bubbles produced by high energy neutron irradiations are known to degrade the mechanical properties of irradiated materials. In this study, we have evaluated the obstacle strength of He bubbles to the mobility of an edge dislocation in $$alpha$$-iron for 2 and 4 nm bubbles with He-to-vacancy (He/V) ratios ranging from 0 to 1 at 300 and 500 K, by molecular dynamics simulation. Results showed that as the He/V ratio increases, the obstacle strength needed for the release of a dislocation from the bubble becomes stronger up to a moderate He/V ratio, and a further increase in the He/V ratio leads to weakening of the obstacle strength. For He/V = 1, the obstacle strengths are $$10-30%$$ weaker than those at moderate He/V ratios depending on the bubble size and temperature. The extent of obstacle strength was found to be correlated with the dilation caused by He bubbles depending on the bubble size, He/V ratio, and temperature.

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