Since the accident at the Fukushima Daiichi power plant, in addition to “design to prevent accidents”, “mitigating the severe accident” has come to be emphasized. Thus, it is necessary to evaluate the actual failure mode under beyond design basis events (BDBEs). In this study, authors focus on the failure mode of piping in nuclear power plants under excessive earthquakes. The piping design of nuclear power plants has been conservative assuming that seismic load acts as load-controlled and the collapse happens by maximum acceleration. However, the test conducted by Electric Power Research Institute (EPRI) confirmed that when excessive vibration load was applied to the piping with the elbow, ratchet deformation occurred with time and eventually collapsed. Unfortunately, this failure mechanism is not clear, so it is highly important to consider the actual failure mode, namely ratchet deformation leading to collapse. Authors tried to clarify the mechanism of ratchet deformation by experiments and analyses of inputting acceleration to a beam simulating piping. According to these results, it is identified that ratchet deformation is likely to occur when the vibration load whose frequency is lower than resonance frequency is applied, and is difficult to occur on the higher frequency area. Hereafter, the ratio of the frequency of vibration load to the natural frequency of beams is referred as “frequency ratio”. In this study, half-cycle vibration load was applied to the beam, and the frequency dependence of the collapse phenomenon was investigated.

Nuclear structure’s integrity must be confirmed under severe accident conditions. However, performing structure tests using actual steels is very difficult and expensive. Therefore, the authors conducted structure tests using the lead alloy to evaluate the structure integrity under severe accident conditions. Because the strength of the lead alloy is considerably less than that of actual steels, structure tests can be conducted under low-pressure, low-temperature conditions. To quantitatively correlate the structural response of the lead alloy to that of actual steels, finite-element analyses (FEAs) must be performed. Because the inelastic constitutive equations, namely, inelastic stress–strain relationship equation, creep rupture equation, and creep strain equation, are required to perform the inelastic FEA, the authors introduced material tests using the lead alloy and, subsequently, proposed the inelastic constitutive equations based on the material test results in a previously conducted PVP conference. However, the proposed inelastic constitutive equations could not successfully express the material characteristic of the lead alloy because of large variations observed in the material tests of the lead alloy. Furthermore, the authors observed that the material characteristic of the lead alloy could be stabilized by aging. In this study, we propose the improved inelastic constitutive equations of the lead alloy on the basis of test results newly obtained from a series of material test performed using aged alloy.

As a lesson learned from the Fukushima nuclear power plant accident, the industry recognized the imporatance of mitigating accident consequences after Beyond Design Basis Events (BDBE). We propose the concept of applying fracture control to mitigate failure consequences of nuclear components under BDBE. Requirements are different between Design Basis Events (DBE) and BDBE. In the case of DBE, it requires preventing occurrence of failures, and thus, its structural approach is strengthening. On the other hand, BDBE requires mitigating failure consequences. The simple strengthening approach with DBE is inappropriate for this BDBE requirement. As the structural strengthening approach for mitigating failure consequences, we propose applying the concept of fracture control. The fundamental idea is to control the sequence of failure locations and modes. Preceding failures release loadings and prevent further catastrophic consequent failures. At the end, locations and modes of failure are limited. Absolute strength evaluation for each failure mode is not easy especially for BDBE. Fracture control, however, requires only relative strength evaluation among different locations and failure modes. Our paper discusses two sample applications of our proposed method. One is a fast reactor vessel under severe accident conditions. Our method controls the upper part of a vessel above the liquid coolant surface weaker than the lower part. This strength control maintains enough coolant even after a high pressure and high temperature condition causes failure of the reactor vessel because structural failure in the upper part releases internal pressure to protect the lower part. The other example is the piping under a large earthquake. Our proposal controls strength of supports weaker than the piping itself. When the supports fail first, natural frequencies of piping systems drop. When the natural frequencies of dominant modes are lower than the peak frequency of seismic loads, seismic loads hardly transfer to the piping and catastrophic failures such as collapse or break are avoided.

To investigate the failure behavior of piping systems under excessive seismic loads, shaking table tests on piping system models made of a simulation material have been executed. The simulation material adopted in the experiment was lead-antimony (Pb-Sb) alloy. The piping system model was composed of two elbows made of Pb-Sb alloy, one additional mass, and two fixed anchors. Input motions were sinusoidal wave. The failure modes of the piping system were examined by varying the additional mass and frequency of the input sinusoidal wave. Through the excitation tests, the failure mode which was named as “ratchet and subsequent collapse” was obtained successfully. The result which was classified as “no failure after 500 cycles” was also obtained. It was found that the occurrence of the failure depended on the ratio of the input frequency to the specimen’s natural frequency, and the ratio of additional mass weight to the limit mass weight. Though the effect of higher modes on the failure behavior was necessary to be more investigated, it seemed that the tendency of dominant failure behavior was similar to that of the single-elbow specimen investigated in the previous study. Moreover, it was confirmed that the experimental approach to use a simulation material was applicable for piping system model with multiple elbows.

In our past paper, the new fracture surface was proposed considering the effects of hydrostatic stress in an elastic-plastic region and in a creep region. In this paper, the mechanism the dominant factors of local failure were studied in an elastic-plastic region. Experimental and analytical study were made using circular plate specimens with a nozzle. The material was a lead alloy (99% Pb-1% Sb). The fracture test was performed in an elastic-plastic region at room temperature. Both ductile fracture and local failure were observed at structural discontinuities, based on the stiffness differences between attached nozzles and plates. In this study, the proposed fracture surface in an elastic-plastic region showed the fracture location accurately, for the both failure modes. It was concluded that the proposed fracture surface is available and useful in order to predict the failure mode and the failure location.

For safety improvement after Fukushima daiichi nuclear power plant accident, mitigation of accident consequence for Beyond Design Basis Events (BDBE) has become important. Authors propose application of fracture control concept for mitigation of accident consequence of nuclear plants as follows. In the case of reactor vessels under high temperature and pressure conditions, small cracks from local failure will release internal pressure and can avoid a large scale ductile fracture of general portions. For piping under excessive earthquake, repeated elastic-plastic deformation and ratchet deformation dissipate vibration energy and reduce input energy from floor. They can prevent collapse of piping systems or break of pipe wall. Strength of pipe supports can be designed lower than pipe itself. Controlling the failure of supports would lead to plastic deformation without the break. The ratio of the frequency of seismic loading to the natural frequency of the piping system would also affect the failure behavior of piping systems. This paper describes research plan and progress to realize fracture control of nuclear components. The first step is clarification of actual failure modes and their mechanisms. Next step is development of relative strength evaluation method among failure modes. The third step is proposals of failure control methods. One of example is a vessel under high pressure and high temperature loadings. Another example is pipe under excessive earthquake.

This paper studies inelastic stress-strain relationship equation and creep rupture equation and creep strain equation of 99%lead-1% antimony alloy. Under the severe accident conditions, structural materials of nuclear power plants are subjected to excessive high temperature. Although it is very essential to clarify how the structure collapses under the severe accident conditions, there’re no experimental evidences of failure modes and the failure mechanisms in such high temperatures are not clarified. However, it is very difficult and expensive to perform structural tests using actual structural materials, such as austenitic stainless steels. Therefore, the authors propose to use lead alloys instead of actual structural materials. Because the strength of such alloys is much poorer than that of the actual structural materials, failure can be observed at much low temperature and by much small load. For demonstration of analogy between the failure mechanisms of lead alloy structure at low temperature and those of the actual structures at extremely elevated temperature, numerical analyses are required. The authors proposes inelastic constitutive equations of lead alloy based on a series of material tests. Nonlinear numerical analyses, e.g. finite element analyses, can be performed using the proposed equations.

The failure mode known as local failure could occur at structure discontinuities with multiaxial stress conditions. Experiments and analyses of notched bars, which generate multiaxial stress, were conducted. The experiments showed that the tensile strength of a notched bar was stronger than that of a smooth bar. The ratio of the maximum and minimum diameter has become the important factor of this notch strengthening. In addition, the initiation of failure was observed at the inner location from the notch root. According to the analysis results, the Mises-stress became the maximum at the notch root. On the other hand, hydrostatic stress became the maximum at the inner location from the notch root, and this location corresponded to the initiation of fracture. The maximum hydrostatic stress has good correlation with the notch strengthening ratio. These facts reveal that hydrostatic stress must be taken into account for strength evaluation as a dominant factor in addition to the Mises-stress. However, only Mises-stress is considered in the present structural design code of nuclear plants. From above results, the new criterion based on fracture surface, where the coordinate plane consists of hydrostatic stress and Mises-stress, was proposed for local failure. Furthermore, this fracture surface was extended to an isochronous fracture surface in a creep region based on isochronous stress-strain curves.

This paper proposes research issues on contribution to safety enhancement for BDBE in structure and material fields. There are large difference between DBE and BDBE. Objective of DBE is prevention of accident and conservative approach is adopted such as prevention of all assumed failure modes. As for BDBE, objectives are prevention of safety function loss and mitigation of accident consequences, risk approach is expected. Since DEC is a part of BDBE, approach against DEC is different from DBE. DEC requires best estimate. Probabilistic Risk Assessment consists of best estimate plus uncertainty. For stress test, identification of the weakest portions and cliff edges become important. To realize above approach, prediction of realistic failure modes is essential. Furthermore, relative strength evaluation becomes important to predict order of failure location and their mode, even though absolute strength is not clear. After Fukushima daiichi nuclear accident, there is a tendency to apply DBE design criteria to BDBE, however, conservative criteria for design are inappropriate for best estimate. Therefore, authors proposes failure mode maps to identify realistic failure mode and its application to mitigation to accident sequences such as fracture control.

In order to investigate the failure modes of piping systems under the beyond design basis seismic loads, the authors proposed an experimental approach to use pipes made of the simulation material instead of steel pipes in the previous study. Though the ratchet-collapse (ratchet and subsequent collapse) was successfully obtained as the failure mode through the shaking table test using the pure lead (Pb) pipes as the simulation material pipe specimens, there was concern that characteristics of pure lead was somewhat extreme considering the analogy with the stress-strain relationship of steel. In order to resolve such concern, a modified experimental procedure has been developed. In the modified procedure, lead-antimony (Pb-Sb) alloy is used as the simulation material. Through the shaking table tests on single elbow pipe specimens made of Pb-Sb alloy, it is found that the typical failure mode is the ratchet and subsequent collapse, as same as the results by the shaking table tests of the Pb pipe specimens. The results indicate that the lower input frequency than the specimen’s natural frequency is prone to cause failure to the specimen, while the higher input frequency hardly causes the failure. The tendency of the global behavior of specimens is similar each other between the Pb pipe specimens and the Pb-Sb alloy specimens, but the strength of self-weight collapse of the Pb-Sb alloy pipe specimen is much higher than that of the Pb pipe specimen. Due to such higher strength of Pb-Sb alloy pipes, a prospect to conduct an excitation test on a more complicated piping system model is obtained.

In nuclear reactors, piping components are susceptible to thermal fatigue damage. This is due to the fluid temperature change along these pipelines that can generate repeated thermal loads. One of these loads is thermal stratification. Thermal stratification generates an oscillating stratified layer, which induce cyclic thermal stresses leading to fatigue damage. To evaluate thermal fatigue by thermal stratification, a frequency response function for straight pipes was developed. However, this function cannot evaluate elbow pipes under thermal stratification. Here, thermal stress generates due to bending moment that is generated by the horizontal portion unlike straight pipes. Furthermore, the elbow pipe can give rise to stress intensifications which can affect the peak stress values within the elbow. To understand the stress generation mechanism, Finite element analyses were performed. The study focused on the effect the frequency of the fluid oscillation on the stress generation mechanism. Based on the clarified mechanism, the frequency response function was improved to correspond to the thermal stratification at elbow pipes. Applicability of this function was validated through agreement with finite element simulation.

Preparation for beyond design basis events (BDBE) becomes an important issue as the lessons learned from the Fukushima nuclear accident. IAEA proposed the best estimation approach for strength evaluation under BDBE. It is required to identify dominant failure modes for best estimation approach. Ratcheting, collapse and fatigue are the probable failure modes which can occur due to dynamic loadings like the seismic load. The current studies describe an attempt to clarify occurrence conditions of such failure mode as ratcheting and collapse for pipes. Elbow pipe components have been analyzed by using the inelastic finite element method. Gravity load was the primary loads, while the base acceleration of sinusoidal waveform of different frequencies was considered as pseudo secondary load. The results have been put in a nondimensional stress parameter plot similar to the Bree diagram for thermal ratcheting, paying attention to the similarity between thermal load and dynamic load. From above results, authors have proposed the failure mode map which can evaluate the occurrence conditions of ratcheting and collapse failure mode for pipes under dynamic loadings.

Preparation for beyond design basis events (BDBE) becomes important as the lessons learned from the Fukushima Daiichi nuclear accident. The objective of strength evaluation for design basis events (DBE) is a confirmation to prevent structural failure for assumed events. For BDBE, main objectives are weak point survey, deterministic and probabilistic risk assessment, and planning of countermeasures including potable equipment and accident management. According to the above objectives, strength evaluation approach have to be different between for DBE and for BDBE. (1) DBE Conservative approach to prevent of failure. Design by analysis concept is basically adopted Assumption of hypothetical failure modes to prevent actual failure modes Stress criteria to bond actual strength Elastic analyses for conservative loading assumption Design factor to bound uncertainties (2) BDBE Best estimation of failure behavior with uncertainties to plan mitigations Identification of realistic failure modes to identify failure consequences Criteria by dominant parameters of failure phenomena Inelastic analyses for realistic loading prediction Probabilistic evaluation to quantify uncertainties. Strength evaluation concept has not yet been established for BDBE. It is necessary to discuss from basic philosophy to make sharable concepts. Adequate criteria is required to meet above concepts. Instead of stress, strain is one of candidate. New evaluation technics are desired to satisfy above criteria. This paper indicates the direction of strength evaluation for BDBE with same examples proposals. Its aims is to promote international discussions and to implement new technologies to actual countermeasures against BDBE.

For assessing possible failure of piping structures under excessive seismic loading, dynamic structural analysis methods employing advanced constitutive models need to be established. The multilayer kinematic hardening model for cyclic plasticity, which is applicable up to large strain, was proposed in the previous paper by the authors for carbon steel STS410 (JIS, Japanese Industrial Standard) to represent precisely nonlinear stress-strain relation as well as cyclic hardening, and was validated through its application to quasi-static cyclic bending tests of an elbow. In this paper, the applicability of the model to dynamic analysis of piping systems under earthquake loading is evaluated. An existing simulated earthquake excitation test of a piping system made of carbon steel STPT370 (JIS) is dealt with for validation of the finite element nonlinear dynamic analysis method using the presented model. To emphasize the advantage of this model, analyses using the conventional linear kinematic hardening model are also conducted. The results by the latter model are shown to be highly variable depending on the method of bilinear approximation of stress-strain curves. It is shown that the multilayer kinematic hardening model can predict well inelastic strains in piping systems under excessive earthquakes, which is important for the failure assessment.

Creep buckling failure of a stainless steel tube column was investigated at three temperature conditions (800, 900, and 1000 °C). 304 grade stainless steel was used as a test material in this study. In creep tests, external pressure was increased to a target value, temperature of the tube column was quickly increased to a target temperature, and failure time was measured maintaining the pressure and the temperature. Based on the experimental results of the creep buckling failure time, an empirical correlation was developed by the Larson-Miller parameter. Moreover, post buckling experiments were performed to examine buckling-induced boundary failure at extremely high temperature more than 1300 °C. Additional heating was applied to the specimen which already buckled by external pressure. In the additional heating tests, temperature was increased until boundary failure was formed on the surface of the tube columns. The results showed that the creep buckling failure time was shorter than those in other tensile stress-induced creep tests. The empirical correlation obtained by Larson-Miller parameter predicts well the creep buckling failure time. Finally, boundary failure was obtained in the post buckling under the additional heating.

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.

Piping systems are one of the central components of NPP; It is well known that the major failure mode under seismic loads is likely to be fatigue failure. Other failure modes, however, such as ratchet-buckling failure, have been reported to occur under particular conditions. It is necessary to clarify the conditions that cause different failure modes of piping systems under very high seismic motion, but experimental studies with steel pipes are difficult to achieve, mainly due to the limitations of testing facilities and safety concerns. In order to overcome such difficulties, we propose a new experimental approach that uses pipes made of a simulation material instead of steel. Lead (Pb) pipes were used for the simulation material, and shaking table tests were conducted on lead elbow pipe specimens. Results showed that ratchet-collapse and overall deformation of pipe specimens were possible failure modes. The ratchet-collapse failure mode appeared to be affected not only by input acceleration level but also by the direction of gravity, the primary constant stress level of its own weight, and the frequencies of the input motion. The dynamic behaviors of pipes in the high inelastic region where a nearly fully plastic section was assumed were quite different from those in the elastic region, and those of the steel pipes in previous studies. We demonstrate that the proposed test approach is effective for qualitatively clarifying various kinds of failure behaviors with large plasticity under excessive seismic load.