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Journal Articles

High temperature mechanical properties and microstructure in 9Cr or 12Cr oxide dispersion strengthened steels

Mitsuhara, Masatoshi*; Kurino, Koichi*; Yano, Yasuhide; Otsuka, Satoshi; Toyama, Takeshi*; Onuma, Masato*; Nakashima, Hideharu*

Tetsu To Hagane, 109(3), p.189 - 200, 2023/03

 Times Cited Count:0 Percentile:0(Metallurgy & Metallurgical Engineering)

Oxide Dispersion Strengthened (ODS) ferritic steel, a candidate material for fast reactor fuel cladding, has low thermal expansion, good thermal conductivity, and excellent resistance to irradiation damage and high temperature strength. The origin of the excellent high-temperature strength lies in the dispersion of fine oxides. In this study, creep tests at 700 or 750$$^{circ}$$C, which are close to the operating temperatures of fast reactors, and high-temperature tensile tests at 900 to 1350 $$^{circ}$$C, which simulate accident conditions, were conducted on 9Cr ODS ferritic steels, M11 and MP23, and 12Cr ODS ferritic steel, F14, to confirm the growth behavior of oxides. In the M11 and F14 creep test samples, there was little oxide growth or decrease in number density from the initial state, indicating that dispersion strengthening by oxides was effective during deformation. After creep deformation of F14, the development of dislocation substructures such as dislocation walls and subgrain boundaries was hardly observed, and mobile dislocations were homogeneously distributed in the grains. The dislocation density increased with increasing stress during the creep test. In the high-temperature ring tensile tests of MP23 and F14, the strength of both steels decreased at higher temperatures. In MP23, elongation decreased with increasing test temperature from 900 to 1100 $$^{circ}$$C, but increased at 1200 $$^{circ}$$C, decreased drastically at 1250 $$^{circ}$$C, and increased again at 1300 $$^{circ}$$C. In F14, elongation decreased with increasing temperature. It was inferred that the formation of the $$delta$$-ferrite phase was responsible for this complex change in mechanical properties of MP23 from 1200 to 1300 $$^{circ}$$C.

JAEA Reports

Evaluation of tensile and creep properties on 9Cr-ODS steel claddings

Yano, Yasuhide; Hashidate, Ryuta; Tanno, Takashi; Imagawa, Yuya; Kato, Shoichi; Onizawa, Takashi; Ito, Chikara; Uwaba, Tomoyuki; Otsuka, Satoshi; Kaito, Takeji

JAEA-Data/Code 2021-015, 64 Pages, 2022/01

JAEA-Data-Code-2021-015.pdf:2.6MB

From a view point of practical application of fast breeder reactor cycles, which takes advantage of safety and economic efficiency and makes a contribution of volume reduction and mitigation of degree of harmfulness of high-level radioactive waste, it is necessary to develop fuel cladding materials for fast reactors (FRs) in order to achieve high-burnup. Oxide dispersion strengthened (ODS) steel have been studied for use as potential fuel cladding materials in FRs owing to their excellent resistance to swelling and their high-temperature strength in Japan Atomic Energy Agency. It is very important to establish the materials strength standard in order to apply ODS steels as a fuel cladding. Therefore, it is necessary to acquire the mechanical properties such as tensile, creep rupture strength tests and so on. In this study, tensile and creep rupture strengths of 9Cr-ODS steel claddings were evaluated using by acquired these data. Because of the phase transformation temperature of 9Cr-ODS steel, temperature range for the evaluation was divided into two ones at AC1 transformation temperature of 850$$^{circ}$$C.

Journal Articles

Evaluation of multiaxial low cycle creep-fatigue life for Mod.9Cr-1Mo steel under non-proportional loading

Nakayama, Yuta*; Ogawa, Fumio*; Hiyoshi, Noritake*; Hashidate, Ryuta; Wakai, Takashi; Ito, Takamoto*

ISIJ International, 61(8), p.2299 - 2304, 2021/08

 Times Cited Count:4 Percentile:33.99(Metallurgy & Metallurgical Engineering)

This study discusses the creep-fatigue strength for Mod.9Cr-1Mo steel at a high temperature under multiaxial loading. A low-cycle fatigue tests in various strain waveforms were performed with a hollow cylindrical specimen. The low cycle fatigue test was conducted under a proportional loading with a fixed axial strain and a non-proportional loading with a 90-degree phase difference between axial and shear strains. The low cycle fatigue tests at different strain rates and the creep-fatigue tests at different holding times were also conducted to discuss the effects of stress relaxation and strain holding on the failure life. In this study, two types of multiaxial creep-fatigue life evaluation methods were proposed: the first method is to calculate the strain range using Manson's universal slope method with considering a non-proportional loading factor and creep damage; the second method is to calculate the fatigue damage by considering the non-proportional loading factor using the linear damage law and to calculate the creep damage from the improved ductility exhaustion law. The accuracy of the evaluation methods is much better than that of the methods used in the evaluation of actual machines such as time fraction rule.

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

Study on fracture behaviour of through-wall cracked elbow under displacement control load

Machida, Hideo*; Koizumi, Yu*; Wakai, Takashi; Takahashi, Koji*

Nihon Kikai Gakkai M&M 2019 Zairyo Rikigaku Kanfarensu Koen Rombunshu (Internet), p.OS1307_1 - OS1307_5, 2019/11

This paper describes the fracture test and fracture analysis of a pipe under displacement control load. In order to grasp the fracture behavior of the circumferential through-wall cracked pipe, which is important in evaluating the feasibility of leak before break (LBB) in sodium cooled reactor piping, a fracture test in case of a circumferential throughwall crack in the weld line between an elbow and a straight pipe was carried out. From this test, it was found that no pipe fracture occurs in the displacement control loading condition even if a large circumferential through-wall crack (180$$^{circ}$$) was assumed. The fracture analysis of the pipe was carried out using Gurson's parameters set based on the tensile test results of the tested pipe material. The analytic results agree well with the test results, and it was found that it will be possible to predict the fracture behavior of sodium cooled reactor piping.

JAEA Reports

Prototype fast breeder reactor Monju; Its history and achievements

Tsuruga Comprehensive Research and Development Center

JAEA-Technology 2019-007, 159 Pages, 2019/07

JAEA-Technology-2019-007.pdf:19.09MB
JAEA-Technology-2019-007-high-resolution1.pdf:42.36MB
JAEA-Technology-2019-007-high-resolution2.pdf:33.56MB
JAEA-Technology-2019-007-high-resolution3.pdf:38.14MB
JAEA-Technology-2019-007-high-resolution4.pdf:48.82MB
JAEA-Technology-2019-007-high-resolution5.pdf:37.61MB

This report summarizes the history and achievements of the prototype fast breeder reactor Monju. The development of Monju started in 1968 as a prototype reactor following the experimental fast reactor Joyo. The development covers all the activity related to the fast reactor; plant design, mockup tests, construction, operation, and plant management. This report summarizes the history and achievements for 11 technical areas: history and principal achievements, design and construction, operation test, plant safety, core physics, fuel, plant system, sodium technology, materials and mechanical design, plant management, and trouble management.

Journal Articles

Effect of local plastic component on crack opening displacement and on J-integral of a circumferential penetrated crack

Machida, Hideo*; Arakawa, Manabu*; Wakai, Takashi

Proceedings of 27th International Conference on Nuclear Engineering (ICONE-27) (Internet), 8 Pages, 2019/05

This paper describes the effect of local plastic component on J-integral and crack opening displacement (COD) evaluation of a circumferential penetrated crack, applicable to the leak before break (LBB) assessment for sodium cooled fast reactor (SFR) components. J-integral COD evaluation methods are generally formulated as a summation of elastic and plastic components, and so far many evaluation formulae based on these two components have been proposed. However, strictly, the plastic component consists of local plastic and fully plastic components. Many of the conventional evaluation methods often consider only the fully plastic component as the plastic component. The reason for this is that the effect of the local plastic component is much smaller than that of the fully plastic component excluding materials with extremely small work hardening. In contrast, for materials with high yield stress and small work hardening, such as modified 9Cr-1Mo steel which is one of the candidate materials for SFR piping, the effect of the local plastic component on J-integral and COD cannot be ignored. Therefore, the authors propose formulae taking the effect of local plastic component on J-integral and COD into account, based on finite element analysis (FEA) results, so that it is easy to apply to crack evaluation. The formulae will be employed in the guidelines on LBB assessment for SFR components published from Japan Society of Mechanical Engineers (JSME).

Journal Articles

Study on creep damage assessment method for Mod.9Cr-1Mo steel by sampling creep testing with thin plate specimen

Kanayama, Hideyuki*; Hiyoshi, Noritake*; Ogawa, Fumio*; Kawabata, Mie*; Ito, Takamoto*; Wakai, Takashi

Zairyo, 68(5), p.421 - 428, 2019/05

This study presents creep damage assessment method for Mod. 9Cr-1Mo steel by sampling creep testing with thin plate specimen. Tensile creep rupture tests were performed using three different sizes of specimen under two different test environments to verify the creep testing with the thin plate specimen. Time to rupture of Mod. 9Cr-1Mo steel using three different sizes were almost same. In addition, there was no effect of environment on time to rupture. Pre-damaged thin plate specimens were machined from a bulk specimen's gage section that pre-damage test was performed with. Pre-damage based on life fraction rule were 8%, 16% and 25%. No effect of the process of machining pre-damaged specimen on time to rupture was confirmed by verification tests in same test condition as pre-damage test. Stress acceleration creep rupture tests were performed to estimate creep damage assessment. Creep damage assessment by stress acceleration creep rupture tests was sufficiently accurate estimate. Creep damage assessments by Vickers hardness and lath width were compared with the assessment by stress acceleration creep rupture tests to study applicability of these methods.

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:15 Percentile:86.05(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

Improvement of penetrate crack length evaluation method for LBB assessment of sodium-cooled fast reactor components

Wakai, Takashi; Machida, Hideo*; Arakawa, Manabu*

Nihon Kikai Gakkai 2018-Nendo Nenji Taikai Koen Rombunshu (DVD-ROM), 5 Pages, 2018/09

According to the fitness for service code of Sodium-Cooled fast Reactor (SFR), the volumetric tests as in-service inspection can be replaced with continuous leak monitoring, where the Leak Before Break (LBB) is demonstrated, because the primary stress caused by internal pressure is not significant in SFR components. Basically, if the detectable crack length and the penetrated crack length are sufficiently smaller than the unstable critical crack length, it can be concluded that LBB is successfully demonstrated. The authors had already proposed a simplified method to calculate the penetrated crack length both of the circumferential and axial cracks in the pipe as a function of pipe geometry, fatigue crack growth characteristics and loading conditions. However, some problems in the method have been pointed out in the process of the reviewing by the JSME code committee. This study describes an improved method to calculate the penetrated crack length.

Journal Articles

Development of a crack opening displacement assessment procedure considering change of compliance at a crack part in thin wall pipes made of modified 9Cr-1Mo steel

Wakai, Takashi; Machida, Hideo*; Arakawa, Manabu*; Yanagihara, Seiji*; Suzuki, Ryosuke*; Matsubara, Masaaki*

Proceedings of 26th International Conference on Nuclear Engineering (ICONE-26) (Internet), 9 Pages, 2018/07

This paper studies crack opening displacement (COD) evaluation methods used in Leak-Before-Break (LBB) assessment of Sodium cooled Fast Reactor (SFR) pipe. For SFR pipe, the continuous leak monitoring will be adopted as an alternative to a volumetric test of the weld joints under conditions that satisfy LBB. The sodium pipes are made of ASME Gr.91 (modified 9Cr-1Mo steel). Thickness of the pipes is small, because the internal pressure is very small. Modified 9Cr-1Mo steel has a relatively large yield stress and small work hardening coefficient comparing to the austenitic stainless steels which are currently used in the conventional plants. In order to assess the LBB behavior of the sodium pipes made of modified 9Cr-1Mo steel, the coolant leak rate from a through wall crack must be estimated properly. Since the leak rate is strongly related to the crack opening displacement (COD), an appropriate COD assessment method must be established to perform LBB assessment. However, COD assessment method applicable for SFR pipes - having thin wall thickness and made of small work hardening material - has not been proposed yet. Thus, a COD assessment method applicable to such a pipe was proposed in this study. In this method, COD was calculated by classifying the components of COD; elastic, local plastic and fully plastic. In addition, the verification of this method was performed by comparing with the results of a series of four-point bending tests using modified 9Cr-1Mo steel pipe having a circumferential through wall notch. As a result, in some cases, COD were over-estimated especially for large cracks. Although the elastic component of COD is still over-estimated for large cracks, leak evaluation from small cracks is much more important in LBB assessment. Therefore, this study recommends that only the elastic component of COD should be adopted in LBB assessment of SFR pipes.

Journal Articles

Proposal of simplified J-integral evaluation method for a through wall crack in SFR pipe made of Mod.9Cr-1Mo steel

Wakai, Takashi; Machida, Hideo*; Arakawa, Manabu*; Kikuchi, Koichi*

Proceedings of ASME Symposium on Elevated Temperature Applications of Materials for Fossil, Nuclear, and Petrochemical Industries, 7 Pages, 2018/04

A simplified J-integral evaluation method applicable to unstable failure analysis in Leak Before Break (LBB) assessment of Sodium-cooled Fast Reactor (SFR) in Japan was proposed. Mod.9Cr-1Mo steel is supposed to be a candidate material for the coolant systems of SFR in Japan. This steel has relatively high yield strength and poor fracture toughness comparing to those of conventional austenitic stainless steels. In addition, SFR pipe has small thickness and large diameter. As a J-integral evaluation method for circumferential through-wall crack in a cylinder, EPRI has proposed a fully plastic solution method. However, the geometry of SFR pipe and material characteristics of Mod.9Cr-1Mo steel exceed the applicable range of EPRI's method. Therefore, a series of elastic, elasto-plastic and plastic finite element analyses (FEA) were performed for a pipe with a circumferential through-wall crack to propose a J-integral evaluation method applicable to such loading conditions. J-integrals obtained from the FEA were resolved into elastic, local plastic and fully plastic components. Each component was expressed as a function of analytical parameter, such as pipe geometries, crack size, material characteristics and so on. As a result, a simplified J-integral evaluation method was proposed. The method enables to conduct 2 parameter failure analysis using J-integral without any fracture mechanics knowledge.

Journal Articles

Study of the calculation method for the elastic follow-up coefficient by inelastic analysis

Watanabe, Sota*; Kubo, Koji*; Okajima, Satoshi; Wakai, Takashi

Nihon Kikai Gakkai M&M 2017 Zairyo Rikigaku Kanfarensu Koen Rombunshu (Internet), p.581 - 585, 2017/10

no abstracts in English

Journal Articles

Study on the seismic buckling evaluation method for Mod. 9Cr-1Mo steel cylindrical vessel

Okafuji, Takashi*; Miura, Kazuhiro*; Sago, Hiromi*; Murakami, Hisatomo*; Kubo, Koji*; Sato, Kenichiro*; Wakai, Takashi; Shimomura, Kenta

Nihon Kikai Gakkai M&M 2017 Zairyo Rikigaku Kanfarensu Koen Rombunshu (Internet), p.591 - 595, 2017/10

no abstracts in English

Journal Articles

Thermodynamic study of gaseous CsBO$$_{2}$$ by Knudsen effusion mass spectrometry

Nakajima, Kunihisa; Takai, Toshihide; Furukawa, Tomohiro; Osaka, Masahiko

Journal of Nuclear Materials, 491, p.183 - 189, 2017/08

 Times Cited Count:8 Percentile:61.27(Materials Science, Multidisciplinary)

One of the main chemical forms of cesium in the gas phase during severe accidents of light water reactor is expected to be cesium metaborate, CsBO$$_{2}$$, by thermodynamic equilibrium calculation considering reaction with boron. But accuracy of the thermodynamic data of gaseous metaborate, CsBO$$_{2}$$(g), has been judged as poor quality. Thus, Knudsen effusion mass spectrometric measurement of CsBO$$_{2}$$ was carried out to obtain reliable thermodynamic data. The evaluated values of standard enthalpy of formation of CsBO$$_{2}$$(g), $$Delta$$$$_{f}$$H$$^{circ}$$$$_{298}$$(CsBO$$_{2}$$,g), by the 2nd and 3rd law treatments are -700.7$$pm$$10.7 kJ/mol and -697.0$$pm$$10.6 kJ/mol, respectively, and agree with each other within the errors, which suggests our data are reliable. Further, it was found that the existing data of the Gibbs energy function and the standard enthalpy of formation agreed well with the values evaluated in this study, which indicates the existing thermodynamic data are also reliable.

Journal Articles

Thermal fatigue test on dissimilar welded joint between Gr.91 and 304SS

Wakai, Takashi; Kobayashi, Sumio; Kato, Shoichi; Ando, Masanori; Takasho, Hideki*

Proceedings of 25th International Conference on Nuclear Engineering (ICONE-25) (CD-ROM), 7 Pages, 2017/07

This paper describes a thermal fatigue test on a structural model with a dissimilar welded joint. In the present design of JSFR, there may be dissimilar welded joints between ferritic and austenitic steels especially in IHX and SG. Creep-fatigue is one of the most important failure modes in JSFR components. However, the creep-fatigue damage evaluation method has not been established for dissimilar welded joint. To investigate the evaluation method, structural test will be needed for verification. Therefore, a thermal fatigue test on a thick-wall cylinder with a circumferential dissimilar welded joint between Mod.9Cr-1Mo steel and 304SS was performed. Since the coefficients of thermal expansion of these steels were significantly different, buttering layer of Ni base alloy was installed between them. After the completion of the test, deep cracks were observed at the HAZ in 304SS, as well as at HAZ in Mod.9Cr-1Mo steel. There were many tiny surface cracks in BM of 304SS. According to the fatigue damage evaluation based on the finite element analysis results, the largest fatigue damage was calculated at HAZ in 304SS. Large fatigue damage was also estimated at BM of 304SS. Fatigue cracks were observed at HAZ and BM of 304SS in the test, so that analytical results are in a good agreement with the observations. However, though relatively small fatigue damage was estimated at HAZ in Mod.9Cr-1Mo steel, deep fatigue cracks were observed in the test. To identify the cause of such a discrepancy between the test and calculations, we performed a series of finite element analyses. Some metallurgical investigations were also performed.

Journal Articles

Preparation for a new experimental program addressing core-material-relocation behavior during severe accident with BWR design conditions; Conduction of preparatory tests applying non-transfer-type plasma heating technology

Abe, Yuta; Sato, Ikken; Ishimi, Akihiro; Nakagiri, Toshio; Nagae, Yuji

Proceedings of 24th International Conference on Nuclear Engineering (ICONE-24) (DVD-ROM), 7 Pages, 2016/06

A new experimental program using non-transfer type plasma heating is under consideration in JAEA to clarify the uncertainty on core-material relocation (CMR) behavior of BWR. In order to confirm the applicability of this new technology, authors performed preparatory plasma heating tests using small-scale test pieces (107 mm $$times$$ 107 mm $$times$$ 222 mmh). Based on these preliminary results, an excellent perspective in terms of applicability of the non-transfer plasma heating technology to the SA (Severe Accident) experimental study was obtained. Furthermore, JAEA is preparing for the next step intermediate-scale preparatory tests in 2016 using ca. 50 rods and a control blade that would not only confirm its technical applicability, but also some insights relevant to the issue on CMR itself.

Journal Articles

Collapse evaluation of double notched stainless pipes subjected to combined tension and bending

Suzuki, Ryosuke*; Matsubara, Masaaki*; Yanagihara, Seiji*; Morijiri, Mitsugu*; Omori, Atsushi*; Wakai, Takashi

Procedia Materials Science, 12, p.24 - 29, 2016/00

 Times Cited Count:2 Percentile:74.36(Engineering, Mechanical)

In this study, the plastic collapse strength of asymmetry multiple circumferential notched stainless steel pipes subjected to combined axial tension and bending is investigated experimentally and is compared with the theoretical plastic collapse strength. In addition, the potential is discussed for the simplification of structural integrity evaluation of multiple cracked piping. The integrity of the asymmetry multiple circumferential notched stainless steel pipes subjected to combined axial tension and bending can be evaluated conservatively using the theoretical plastic collapse strength for the pipe with multiple notches calculated based on the elastic-perfectly plastic model.

Journal Articles

A Study on evaluation method of penetrate crack length for LBB assessment of fast reactor pipes

Wakai, Takashi; Machida, Hideo*; Sato, Kenichiro*

Nihon Kikai Gakkai M&M 2015 Zairyo Rikigaku Kanfarensu Koen Rombunshu (Internet), 3 Pages, 2015/11

This paper describes a through-wall crack length evaluation procedure applicable to Leak Before Break (LBB) assessment of Japan Sodium cooled Fast Reactor (JSFR) pipes made of Mod.9Cr-1Mo steel. In LBB assessment of JSFR pipes, it is required to calculate virtual through-wall crack length, though the crack growth is quite small under design condition. Generally, it is known that the through-wall crack length depends on loading condition, namely the load ratio between tensile and bending and that the length under pure bending load condition is largest. This study proposes a simplified method to evaluate the through-wall crack length both for axial and circumferential cracks as a function of load ratio and fatigue crack growth characteristics. Using the method, through-wall crack length can be predicted as far as we know the loading condition and material properties.

Journal Articles

J-integral evaluation method for a through wall crack in thin-walled large diameter pipes made of Mod.9Cr-1Mo steel

Wakai, Takashi; Machida, Hideo*; Arakawa, Manabu*; Sato, Kenichiro*

Nihon Kikai Gakkai 2015-Nendo Nenji Taikai Koen Rombunshu (DVD-ROM), 5 Pages, 2015/09

This paper describes a J-integral evaluation procedure applicable to unstable failure analysis for a circumferential through wall crack in a pipe. Japan Sodium cooled Fast Reactor (JSFR) pipes are made of Mod.9Cr-1Mo steel. The fracture toughness of the material is inferior to that of conventional austenitic stainless steels. In addition, JSFR pipe has small thickness and large diameter and displacement controlled load is predominant. Therefore, the load balance in such piping system changes by crack extension and 2 parameter method using J-integral is applicable to unstable failure analysis for the pipes under such conditions. As a J-integral evaluation method for circumferential through wall crack in a cylinder, EPRI has proposed a fully plastic solution method. However, the geometry of JSFR pipe and material characteristics of Mod.9Cr-1Mo steel exceed the applicable range of EPRI's method. Therefore, a series of elastic, elastoplastic and plastic finite element analyses (FEA) were performed for a pipe with a circumferential through-wall crack to establish a J-integral evaluation method applicable to such conditions. J-integrals obtained from the FEA were resolved into elastic, local plastic and fully plastic components. Each component was expressed as a function of analytical parameter, such as pipe geometries, crack size, material characteristics and so on. As a result, a simplified J-integral evaluation method was proposed.

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