This paper describes the requirements for securing the reliability of pipes with a circumferential surface flaw when they are used continually without repair. In the Rules on Fitness-for-Service (the Rules on FFS) of the Japan Society of Mechanical Engineers (JSME), limitations for flaw angle and flaw depth, and the safety margin for fracture evaluation are prescribed to ensure structural integrity during the evaluation period. In addition, for continued use without repair, three successive inspections are conducted and the prediction of flaw size is reviewed. The influence of these rules on the fracture probability when applying the limit load analysis was evaluated. From these evaluations, the flaw depth limitation and improvement of the safety factor are ineffective in improving the reliability of fracture evaluation, and the most influential factor is the prediction accuracy of flaw size. To improve the prediction accuracy of flaw size, it is important to review the predicted flaw size to envelop its actual size at the end of the evaluation period using the results of successive inspections. Based on this examination, the framework of the rules of the successive inspections and flaw evaluation incorporating the revision of the flaw size at the end of the evaluation period was proposed.

This study was carried out to establish crack opening displacement (COD) evaluation methods used in Leak-Before-Break (LBB) assessment of thin-walled large-diameter pipes of the Sodium cooled Fast Reactors (SFRs). For the pipes of SFR, 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 thin walled large diameter pipe made of modified 9Cr-1Mo steel 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 overestimated especially for large cracks. Although the elastic component of COD, δ EE , 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, δ EE , should be adopted in LBB assessment of SFR pipes.

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. Furthermore, in SFR, primary stresses are insignificant and displacement controlled secondary stresses are predominant. Therefore, the load balance in such piping system changes by crack extension and R6 (2-parameter) method (hereinafter “2-parameter method”) [1] using J-integral is applicable to unstable failure analysis for the pipes under such loading 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 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 method using J-integral without any fracture mechanics knowledge.

This paper describes examinations of the screening criteria of fracture assessment methods for pipes having a circumferential surface flaw. The failure mode screening criteria for ferritic steel pipes are defined in Appendix E-11 of the Rules on Fitness-for-service for Nuclear Power Plants [1] (hereinafter, the FFS Codes) of the Japan Society of Mechanical Engineers (JSME) and ARTICLE C-4000 of ASME Section XI [2] (hereinafter, ASME Sec. XI). However, these screening criteria were assessed under limited conditions; they are not intended for detailed evaluation. Essentially, the fracture mode depends on a stress-strain curve, a J-R curve, flaw shape (length and depth), pipe shape (R/t), etc. First, among these parameters, these that have a large effect on fracture strength evaluation were selected. The important parameters for fracture strength are a stress-strain curve, a J-R curve, flaw depth. Next, failure modes according to these parameters were classified. Finally, a screening method to determine whether the failure mode is Limit Load (LL) or Elastic-Plastic Fracture Mechanics (EPFM) for all pipe materials was proposed. The proposed method is a general method not limiting the applicable pipe materials.

Based on the lessons learned from the Fukushima nuclear power plant accident, it is recognized the importance of the risk assessment and mitigation for failure consequences to avoid catastrophic failure of pressure equipment during severe accidents (SA) and excessive earthquake. The objectives of structural design (from the first layer to the third layer of the defense-in-depth) is strength confirmation under assumed loading conditions. On the other hand, ones of risk assessment and mitigation (the forth layer of the defense-in-depth) is prediction of realistic failure scenarios. Through investigation of failure locations and modes of main components under both severe accident and excessive earthquake, different failure modes from DBE(Design Basis Events) were identified for BDBE(Beyond Design Basis Events). To clarify these modes, the failure mechanisms were studied with some strength experiments. For most of failure modes, their dominant parameters are inelastic strain rather than stress. So that large scale inelastic analysis methods were studied and extended to very high temperature and large strain. By using above results, this paper has proposed the new structural analysis approach for risk assessment under BDBE. This is the extension of “design by analysis” concept. However it is clearly different from design approach from next viewpoints. (1) Additional failure modes to design condition Such additional failure modes induced by excessive loadings are considered for as local failure, creep rupture, creep buckling, ratcheting collapse and so on. (2) Identification of dominant failure modes Design codes require conservative evaluation against all of assumed failure modes. On the other hand, risk assessment needs adequate failure scenarios, where failure locations, modes and their order are important. For that reason, dominant failure modes have to be identified. To identify dominant modes, failure mode map concept was proposed. (3) Best estimation To estimate realistic accident phenomena, the best estimation is required. Therefore, dominant strength parameters and criteria without safety margins should be adopted. Through strength mechanism investigations, plastic and creep strain are recognized as more dominant parameters than stress for many failure modes. So that realistic inelastic analyses are recommended for BDBE.

Some of the important lessons learned from Fukushima Daiichi nuclear power plant accident are that mitigation of failure consequences and prevention of catastrophic failure are essential to combat severe accidents (SA) and excessive earthquake conditions that correspond to design extension conditions (DEC). To improve mitigation measures and accident management, clarification of failure behaviors depending on locations is premised under DEC such as SA and earthquakes. Design extension conditions induce some failure modes that are different from those in design conditions. The best estimation for these failure modes is necessary in order to prepare countermeasures and management. A prerequisite for conducting best estimation is to clarify the failure modes with the ultimate structural strength under extreme loads due to very high temperatures, pressure, and great earthquakes. The authors attempt to clarify unclear failure mechanisms caused by extreme loading under DEC using numerical simulation. In this paper, the relationships between failure modes and extreme loading were studied through numerical simulation using the cylinder and half-spherical model that assumes the bottom of the reactor pressure vessel (RPV) (e.g. Lower Formed Head, Instrument Tube, Gide Tube, Nozzle). This bottom structure of RPV is estimated to be under high temperature and pressure conditions due to the relocation of the molten corium. This heat loading causes major deformation of the bottom head due to creep, which leads to RPV failure. On the other hand, there is a possibility that structural discontinuities (e.g. Gide Tube Nozzle) may fail in advance. In order to recognize actual failure modes, the authors had to study the basic relationship between failure modes and load conditions in the failure mode map. This failure mode map is being considered for use as initial simple structural in beyond design basis events (BDBE) and DEC.

This paper describes examinations of the requirements for fracture toughness of piping materials to establish Leak-Before-Break (LBB) behaviors. One of the important elements in establishing LBB is the fracture toughness of the materials. The fracture toughness might vary greatly due to inappropriate material management. Some representative fracture toughness properties of piping materials are plane strain fracture toughness ( K Ic or J Ic ) and fracture resistance curve (J-R curves). Requirements to establish LBB were examined focusing on these two properties. Although it is easy to obtain plane strain fracture toughness (it can, for example, be estimated using the Charpy impact test, etc.), trying to predict ductile fracture strength based only on plane strain fracture toughness will likely result in underestimating the strength. In the LBB Codes of the Japan Society of Mechanical Engineers (JSME), the elastic-plastic fracture mechanics (EPFM) have been defined for the material that shows ductile fracture behaviors. The LBB Codes set the ratio of the plastic collapse strength and ductile fracture strength ( P b ′/P b-cr ) as 1.5 or less. Therefore, requirements for the fracture resistance of the piping materials to have the same fracture strength as the LBB Codes were examined. The examinations have shown that the slope of the fracture resistance curve is as important as the plane strain fracture toughness ( J Ic ). In order to achieve the same ductile fracture strength with EPFM defined in the LBB Codes, the fracture resistance of the pipe materials should be controlled plane strain fracture toughness ( J Ic ) and fracture resistance curve. Materials with high fracture toughness should be used, especially when employing thin-walled or high yield stress pipes.

As the important lessons learned from the Fukushima-nuclear power plant accident, mitigation of failure consequences and prevention of catastrophic failure became essential against severe accident and excessive earthquake conditions. To improve mitigation measures and accident management, clarification of failure behaviors with locations is premise under design extension conditions such as severe accidents and earthquakes. Design extension conditions induce some different failure modes from design conditions. Furthermore, best estimation for these failure modes are required for preparing countermeasures and management. Therefore, this study focused on identification of failure modes under design extension conditions. To observe ultimate failure behaviors of structures under extreme loadings, new experimental techniques were adopted with simulation materials such as lead and lead-antimony alloy, which has very small yield stress. Postulated failure modes of main components under design extension conditions were investigated according three categories of loading modes. The first loading mode is high temperature and internal pressure. Under this mode, ductile fracture and local failure were investigated. At the structural discontinuities, local failure may become dominant. The second is high temperature and external pressure loading mode. Buckling and fracture were investigated. Buckling occurs however hardly break without additional loads or constraints. The last loading is excessive earthquake. Ratchet deformation, collapse, and fatigue were investigated. Among them, low-cycle fatigue is dominant.

As the important lessons learned from Fukushima-nuclear power plant accident, mitigation of failure consequences and prevention of catastrophic failure were strongly recognized against severe accidents (SA) and excessive earthquake conditions. To improve mitigation measures and accident management, clarification of failure behaviors with locations is premised under design extension conditions (DEC) such as severe accidents and earthquakes. Design extension conditions induce some different failure modes from design conditions. Furthermore, the best estimation for these failure modes is required for preparing countermeasures and management. Therefore, this study focused on identification failure modes under design extension conditions. To realize best estimation, it is prerequisite to clarify failure modes with ultimate structural strength under extreme loadings such as very high temperature, pressure and great earthquakes. The authors attempt to clarify unclear failure mechanisms by extreme loadings under DEC using numerical simulations. In this paper, relations between failure modes and extreme loadings were investigated by the numerical simulation using the cylindrical model which is a typical structure of nuclear reactor structures (for example, Formed Head, Nozzle, Instrument Tube, Guide Tube, Support Skirt, etc.). Moreover, it was shown that failure modes change with an effect of structural discontinuities. Local failure dominates than ductile fracture at locally constraint portions where stress triaxiality becomes high.

This paper describes the safety factors used for fracture assessments of pipes having circumferential surface flaws. The “Fitness-For-Services Codes (the FFS Codes)” of the Japan Society of Mechanical Engineers (JSME) restrict the depths of flaws according to their angles to prevent pipes with flaws from being fracture. Past restrictions were determined based on deterministic evaluations. In fracture assessments of pipes having flaws, however, the effects of measurement errors in flaw dimensions and of variations on material strength must be taken into account. Thus, we evaluated the effects of such variations on fracture assessments of pipes having flaws, and examined safety factors for giving failure probability (or reliability) equal, irrespective of the cracking angles. We found out that failure probability is heavily dependent on the measurement accuracy of flaw depths and material strength (flow stress). In view of this finding, we examined and proposed a simple approach which meets the target reliability without conducting complex evaluations by the Monte Carlo method and reliability evaluation methods (e.g., first-order second-moment method (FOSM)).

As the important lessons learned from Fukushima-nuclear power plant accident, preparation based on Probabilistic Risk Assessment (PRA) with adequate scenario is strongly recognized as essential countermeasures against severe accidents, which are possible in nuclear plants. IAEA requires design extension conditions (DEC) for considering severe accidents. From a view point of structural design, the strength evaluation approach for DEC is somewhat different from conventional one for design basis accident (DBA). There are additional failure modes by extreme loadings under DEC. Best estimation with possible scenarios is necessary for PRA and planning of accident management (AM). This paper introduces study plan on failure modes and their mechanisms by extreme loadings under DEC. First step is the list-up of possible failure modes which should be assumed for extreme loadings such as very high temperature, high pressure and great earthquakes. Next is clarification of failure mechanism and relevant limit strength. One of examples is the failure modes of structural discontinuities under high pressure such as ductile fracture and local failure. Another example is ones of pipes under severe earthquake such as collapse and low cycle fatigue. To clarify above questions, such different scale tests were planned and conducted as the fundamental tests with simulated materials, structural element tests and structural tests. Preliminary results of above tests and next plans are explained.

This paper shows the technical basis of revision to the JSME Fitness-for-Service Code (the FFS code) for flaw evaluation methods of pipes which have a very shallow circumferential flaw. When a flaw in a pipe is very small, the allowable stress between the FFS code and the JSME Design and Construction Code (the design code) is mismatched. Fracture strength of a pipe with small flaw depends on the tensile strength accompanied by large deformation. Therefore, fracture mechanics is not applicable in such a case. This mismatch has been resolved for an axial crack assessment by improving definition of flow stress for shallow crack. In this study, the authors investigated this mismatch in the allowable stress in the flaw assessment for a pipe with a circumferential crack. Some past fracture test results of pipes showed that flawed pipes did not fracture at the flaw section when the circumferential flaw size was small and they failed by oval deformation or plastic buckling. Allowable stress for such behavior has been incorporated in some existing design codes as a restriction for plastic collapse. Through the reevaluation of the existing piping fracture test results, the applicability of fracture evaluation methods defined in the FFS code was examined for the case that flaw size was very small. As a result, the fracture evaluation method based on flow stress was found not to be applicable when flaw size was very small, and the failure criterion in this case depended on the collapse strength accompanying with ovalization. Revisions of the FFS code reflecting these examination results were proposed in this paper.

This paper describes the outline of the guidelines on structural reliability evaluation for the passive components of the fast breeder reactor (FBR). The guidelines are now being prepared by the task force for the system based code in the Japan society of mechanical engineers in order to contribute to reducing differences in evaluated structural reliability by evaluators. They consist of five chapters, which are “General rules”, “Reliability evaluation”, “Failure scenario setting”, “Modeling”, and “Failure probability calculation”, respectively. In the chapter of “Reliability evaluation”, the general procedures of reliability evaluation are explained. Detailed procedures at each step are explained in the following chapters in the guidelines. Evaluation procedures for accumulation damage and crack propagation due to creep-fatigue interaction which is a typical degradation phenomenon in FBR are also provided in the appendix of the guidelines. In addition, some examples of random variables are prepared as standard input data for structural reliability evaluation.

In the System Based Code (SBC), a reliability target is defined according to the importance of components (risk and/or failure probability), and the grade of material, design, manufacture and maintenance are chosen to satisfy the reliability target. Therefore, a reliability assessment of the components plays an important role in the concept of SBC. In the reliability assessment guidelines of SBC under development in JSME, the Load and Resistance Factor Design (LRFD) method and the Monte Carlo method will be applied to reliability assessment. Along with a development plan of the SBC, examination of the target reliability according to the importance of components and preparation of the LRFD methods and assessment of partial safety factor for some failure modes are underway. Until now, the LRFD methods have been developed for burst due to internal pressure, plastic collapse due to membrane and bending stress, fatigue, plastic collapse of a pipe having a circumferential crack, and buckling of a thin wall cylinder. This paper describes the action plans for the development of the reliability assessment methods and examination results till date.

This paper is the first one of the series of four papers that describe ongoing activities in the Japan Society of Mechanical Engineers (JSME) and the American Society of Mechanical Engineers (ASME) on the elaboration of the System Based Code (SBC) concept aiming at its application to nuclear structural codes and standards. This paper includes a brief introduction to the SBC concept and the technical features of structural evaluation methodologies that are being developed for use in the SBC concept; Load and Resistance Factor Design based reliability assessment methods and the JSME guidelines for reliability evaluation of static components of sodium-cooled fast reactors. Also described is the ongoing collaboration of JSME and ASME at the Joint Task Group for System Based Code established in the ASME Boiler and Pressure Vessel Code Committee which is developing alternative rules for ASME B&PV Code Section XI Division 3, inservice inspection requirements for liquid metal reactor components.

This paper reports the results of the study on the failure modes and limit loads of piping in nuclear power plants subjected to cyclic seismic loading. By investigating the past fracture tests and earthquake resistance tests, it became clear that dominant failure mode of piping was fatigue, and the effect of ratchet strain was negligible. Until now, the stress generated with the acceleration of an earthquake was classified into the primary stress. However, the relationship between the input acceleration and the seismic response displacement of the pipe observed from earthquake resistance tests is non-linear, and increasing rate of displacement is lower than that of input acceleration in elastic-plastic stress condition. Therefore, the seismic loading can be treated as displacement controlled loading. To evaluate the reliability-based critical acceleration, a limit state function was defined taking the variations in the fatigue strength or some parameters into consideration. By using the limit state function, the reliability was evaluated for the typical piping of boiling water reactor (BWR) plants subjected to cyclic seismic loading, and a partial safety factors were calculated. Based on these results, a fatigue curve corresponding to the target reliability was proposed.

Limit state design was newly developed in order to apply the margin exchange which is one of the innovative concepts of the System Based Code (SBC). It was shown that limit state design method is applicable to plant design instead of current design criteria. In this report, working example of a reactor vessel of a Fast Reactor subject to thermal load is conducted to demonstrate this concept. As the result allowable stress was increased by changing the acceptance criteria from current design criteria to limit state design criteria.

This paper describes the efficiency of the deployment of rotational stiffness evolution model in the critical crack size evaluation for Leak Before Break (LBB) assessment of Sodium cooled Fast Reactor (SFR) pipes. The authors have developed a critical crack size evaluation method for the thin-walled large diameter pipe made of modified 9Cr-1Mo steel. In this method, since the SFR pipe is mainly subjected to displacement controlled load caused by thermal expansion, the stress at the crack part is estimated taking stiffness evolution due to crack into account. The stiffness evolution is evaluated by using the rotational spring model. In this study, critical crack sizes for several pipes having some elbows were evaluated and discuss about the effect of the deployment of the stiffness evolution model at the crack part on critical crack size. If there were few elbows in pipe, thermal stress at the crack part was remarkably reduced by considering the stiffness evolution. In contrast, in the case where the compliance of the piping system was small, the critical crack size could be estimated under displacement controlled condition. As a result, the critical crack size increases by employing the model and LBB range may be expected to be enlarged.

Not only nonmandatory Appendix C, “Evaluation of Flaws in Piping,” in ASME Boiler & Pressure Vessel Code Section XI but also Appendix E-9, “Elastic-Plastic Fracture Mechanics Evaluation,” in the JSME Rules on Fitness-for-Service for Nuclear Power Plants use the load multiplier Z-factor that is applied to elastic-plastic fracture mechanics evaluation for a circumferential flaw of austenitic stainless steel piping and ferritic steel piping. The Z-factor is defined as the ratio of the limit load to the load at fracture load. Basically, the Z-factor equations were conservatively formulated by using the Z-factors for circumferential through-wall flaws. However, the Codes require flaw evaluation for circumferential surface flaws. Accordingly, Z-factors for circumferential surface flaws should be developed to have the consistency. Therefore Z-factor equations of austenitic stainless steel piping and ferritic steel piping have been developed for circumferential surface flaws.