Failure modes investigation of pipe structure under excessive seismic loading
公開日:
カテゴリ: 第12回
The University of Tokyo Md Abdullah Al BARI Non-Member The University of Tokyo Toshiaki KOKUFUDA Non-Member The University of Tokyo Yamato KATSURA Non-Member The University of Tokyo Takuya SATO Non-Member The University of Tokyo Kazuyuki DEMACHI Member The University of Tokyo Naoto KASAHARA Member
１. INTRODUCTION
The concept of nuclear safety has changed a lot after Fukushima. Before Fukushima, severe accident was a part of beyond design basis accident and the designers only considered design basis accidents prior to design. But after Fukushima, beyond design basis accident also included as design basis, so the designer need to consider beyond design basis accident during their design (explain later). The following table 1 and 2 represents the design and beyond design basis cases after and before 2012. Though the beyond design basis accidents are included in the design basis as design extension condition but the prevention technique for design extension condition and design basis accident are different. For design extension condition the prevention approach is best estimation whereas for design basis accident, the approach is conservative. From the structural point of view, to prevent design extension conditions or in other words to make the design resistant against design extension condition, designers need to know the failure modes of the specific component under extreme loading. One of the extreme loading is excessive seismic loading. There are several studies on failure mode under seismic loading and more or less it is found that low cycle fatigue failure, collapse, ratcheting and the combinations of these are the probable modes of failure. But the occurrence conditions of these failure modes are still not clear.
Table 1 IAEA NS-R-1 (2000) Operational states Accident conditions Normal operation Anticipated operational occurrence Design basis accidents Beyond Design basis accidents Plant status Accident management Table 2 IAEA SSR-2/1 (2012) Operational states Accident conditions Normal operation Anticipated operational occurrence Design basis accidents (Conservative evaluation) Beyond Design basis accidents (best estimation) Plant status (consider in design) The objective of this research is to clarify the occurrence condition of failure modes under seismic loading. In this paper the first stage research is presented. In first stage the seismic Md Abdullah Al BARI, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8654 E-mail: md.abdullahbari@gmail.com - 392 - Base acce. Mass loading is applied on a beam structure to clarify the occurrence condition of ratcheting and collapse with literature review. 2. Literature Survey For identification of different types of failure mode caused by seismic loading is done mostly by experimental evaluation. Preliminary vibration test result showed that the probable failure modes are collapse, buckling and low cycle fatigue [1]. On the other hand EPRI test result showed fatigue ratchet and ratchet buckling are the fundamental failure modes for pipe structure [2]. In preliminary vibration test, loading conditions had two different patterns. One was sudden acceleration for investigating effects of the maximum peak acceleration and another was continuous sinusoidal wave around natural vibration frequency. The tests were done on elbow pipe section. The result showed that continuous loading always lead to crack initiation and propagation around few hundred of cycles and on the other hand, plastic deformation was observed under sudden acceleration. In EPRI test total thirty two specimens (mostly pipe structure of different geometry) were tested under dynamic loading until failure. The input seismic loads were much greater than actual seismic load with different maximum peak acceleration and frequencies. The result was interesting, it has seen that no collapse was occurred and for thirty specimens the failure mode was fatigue ratchet and other two specimens failure occurred because of ratchet buckling. From the above literature survey it has been clear that due to seismic loading ratchet, collapse and low cycle fatigue are the fundamental cause of failure of pipe structure. 3. NUMERICAL STUDY To clarify failure modes authors have planned step by step experimental and numerical analysis. First step is to do vibration test on simple beam structure. The experiment has done in Kasahara laboratory, University of Tokyo. The numerical simulation of the beam structure is done by FINAS/FINAS STAR (Finite element nonlinear structural analysis system) software. Here in this paper the numerical analysis of simple beam structure for ratchet and collapse analysis is discussed. 3.1 NUMERICAL ANALYSIS OF RATCHETING Ratcheting effect, namely the cyclic accumulation of plastic deformation, occurs when the structure is subjected to a primary load with a secondary cyclic load if the applied loads are high enough to make the structure yield. The renowned ratcheting is thermal ratcheting, but the analysis of seismic ratcheting is new. In this work it is tried to find the occurrence condition of seismic ratcheting in a cantilever beam model by putting seismic acceleration at the base of the model. Also it is tried to find whether the seismic load is behave like secondary or primary. To do that the following beam configuration shown in Table 3 and Fig.1 is used in simulation. Table 3 Geometry and material properties of beam Geometry Material Length Thickness Width Elastic Modulus Density Yield stress 140 mm 6 mm 13 mm 15250 MPa 11.34gm/cm3 5 MPa Fig. 1 The model beam for numerical analysis At the top node of the beam extra 4 different masses (0.1kg, 0.2 kg, 0.3 kg and 0.4 kg) was loaded to check the effect of maximum mass on the occurrence condition of ratcheting. The bottom node was fixed and a sinusoidal wave of different acceleration was put on this node. It was observed that ratchet deformation in vertically downward direction occurred due to the primary stress which is the stress caused by weight moment and secondary repetitive seismic stress due to inertia moment of the top mass. Time history response analysis was carried out whereas the elastic perfectly plastic stress strain constitutive equation was used. The frequency used in the analysis is twice the natural frequency of the model. One of the analysis results for 0.2kg showed that 5000gal acceleration has not occurred ratcheting deformation but 6000gal has occurred ratcheting deformation (Fig. 2). Occurrence condition of ratcheting, red dots indicated ratcheting whereas blue dots are not (Fig. 3). - 393 - -2024681900/01/090 0.2 0.4 0.6 0.8 1 1.2 1.4 Deflection[mm] Time[s] 6000gal 5000gal Fig. 2 Analysis results of deformation of ratcheting 0500100015002000250030000 200 400 600 800 Moment by seismic loading [Nmm] Moment by weight [Nmm] 赤：進行性変形発生青：進行性変形未発生 Fig. 3 Occurrence condition of ratcheting caused by seismic load Fig. 4 Thermal ratcheting occurrence condition (Bree diagram [3]) The renowned Bree diagram (Fig. 4) is the occurrence condition for thermal ratchetting [3]. Horizontal axis expressed the primary pressure stress and vertical axis represents secondary thermal stress. Compared the Bree diagram with seismic ratchetting diagram it has seen that for the both the occurrence condition line has similar shape and also it has seen that ratcheting deformation is less likely to occur at high thermal loads which is similar in the case of seismic load. Since the similarity is found between the stress caused by seismic load and thermal load, authors thought that stress caused by the seismic load is also characterized as secondary stress manner. 3.2 NUMERICAL ANALYSIS OF COLLAPSE Collapse is the excessive deformation of the structure, it occurs when the load doesn’t satisfy the equilibrium condition. In other words due to stress the stiffness of structure reduces gradually with the deformation and resulting in complete loss of stiffness. For collapse analysis similar beam model was also used like ratcheting. The same material and geometrical properties were used along with the same 4 masses at the top node. The only difference was the input wave. The shape of acceleration wave was half sinusoidal (Fig. 5) but for ratcheting it was full sinusoidal wave. Also the frequency used in the case is natural frequency which is different from ratcheting analysis. The reason of using half sinusoidal wave was that half sinusoidal wave is similar to sudden pulse type wave and collapse is prone to occur for pulse type wave than continuous full sinusoidal wave. Fig. 5 Input pulse type acceleration for collapse The analysis result of deformation for 0.2kg weight showed that for 10000 gal the collapse didn’t occur because the deformation was not stable but for 15000 gal it occurred because the deformation saturate at the point which is almost the maximum possible deformation of this beam and also the deformation didn’t increase by increasing the value of acceleration (Fig. 6). The mass-maximum acceleration curve - 394 - 0500100015002000250030003500400045000 100 200 300 400 500 600 Moment by seismic load[N-mm] Moment by gravity [N-mm] 0500001000001500002000002500003000003500000 0.1 0.2 0.3 0.4 0.5 Maximum acceleration [mm/s^2] Mass [kg] (Fig. 7) showed that more the top mass the less the seismic load is needed to occur collapses. The occurrence condition of collapse has also found similar behaviour like ratchetting (Fig. 8). Alike ratchetting the stress by weight which is primary stress has more impact on occurrence of collapse than stress by seismic load, though the occurrence condition line for collapse is not as straight as for ratchetting. Fig. 6 Analysis results of deformation of collapse Fig. 7 Effect of maximum acceleration and mass on collapse Fig. 8 Occurrence condition of collapse caused by seismic load 4. CONCLUSION After the Fukushima nuclear accident, it is high time to robust the nuclear facility in such a way that core melting can be prevented in any circumstances. Earthquake is one of the major threats for any type of structure at any time. To make the heavy“ “Failure modes investigation of pipe structure under excessive seismic loading “ “Md Abdullah Al BARI,Toshiaki KOKUFUDA ,Yamato KATSURA, Takuya SATO,Kazuyuki DEMACHI ,Naoto KASAHARA
１. INTRODUCTION
The concept of nuclear safety has changed a lot after Fukushima. Before Fukushima, severe accident was a part of beyond design basis accident and the designers only considered design basis accidents prior to design. But after Fukushima, beyond design basis accident also included as design basis, so the designer need to consider beyond design basis accident during their design (explain later). The following table 1 and 2 represents the design and beyond design basis cases after and before 2012. Though the beyond design basis accidents are included in the design basis as design extension condition but the prevention technique for design extension condition and design basis accident are different. For design extension condition the prevention approach is best estimation whereas for design basis accident, the approach is conservative. From the structural point of view, to prevent design extension conditions or in other words to make the design resistant against design extension condition, designers need to know the failure modes of the specific component under extreme loading. One of the extreme loading is excessive seismic loading. There are several studies on failure mode under seismic loading and more or less it is found that low cycle fatigue failure, collapse, ratcheting and the combinations of these are the probable modes of failure. But the occurrence conditions of these failure modes are still not clear.
Table 1 IAEA NS-R-1 (2000) Operational states Accident conditions Normal operation Anticipated operational occurrence Design basis accidents Beyond Design basis accidents Plant status Accident management Table 2 IAEA SSR-2/1 (2012) Operational states Accident conditions Normal operation Anticipated operational occurrence Design basis accidents (Conservative evaluation) Beyond Design basis accidents (best estimation) Plant status (consider in design) The objective of this research is to clarify the occurrence condition of failure modes under seismic loading. In this paper the first stage research is presented. In first stage the seismic Md Abdullah Al BARI, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8654 E-mail: md.abdullahbari@gmail.com - 392 - Base acce. Mass loading is applied on a beam structure to clarify the occurrence condition of ratcheting and collapse with literature review. 2. Literature Survey For identification of different types of failure mode caused by seismic loading is done mostly by experimental evaluation. Preliminary vibration test result showed that the probable failure modes are collapse, buckling and low cycle fatigue [1]. On the other hand EPRI test result showed fatigue ratchet and ratchet buckling are the fundamental failure modes for pipe structure [2]. In preliminary vibration test, loading conditions had two different patterns. One was sudden acceleration for investigating effects of the maximum peak acceleration and another was continuous sinusoidal wave around natural vibration frequency. The tests were done on elbow pipe section. The result showed that continuous loading always lead to crack initiation and propagation around few hundred of cycles and on the other hand, plastic deformation was observed under sudden acceleration. In EPRI test total thirty two specimens (mostly pipe structure of different geometry) were tested under dynamic loading until failure. The input seismic loads were much greater than actual seismic load with different maximum peak acceleration and frequencies. The result was interesting, it has seen that no collapse was occurred and for thirty specimens the failure mode was fatigue ratchet and other two specimens failure occurred because of ratchet buckling. From the above literature survey it has been clear that due to seismic loading ratchet, collapse and low cycle fatigue are the fundamental cause of failure of pipe structure. 3. NUMERICAL STUDY To clarify failure modes authors have planned step by step experimental and numerical analysis. First step is to do vibration test on simple beam structure. The experiment has done in Kasahara laboratory, University of Tokyo. The numerical simulation of the beam structure is done by FINAS/FINAS STAR (Finite element nonlinear structural analysis system) software. Here in this paper the numerical analysis of simple beam structure for ratchet and collapse analysis is discussed. 3.1 NUMERICAL ANALYSIS OF RATCHETING Ratcheting effect, namely the cyclic accumulation of plastic deformation, occurs when the structure is subjected to a primary load with a secondary cyclic load if the applied loads are high enough to make the structure yield. The renowned ratcheting is thermal ratcheting, but the analysis of seismic ratcheting is new. In this work it is tried to find the occurrence condition of seismic ratcheting in a cantilever beam model by putting seismic acceleration at the base of the model. Also it is tried to find whether the seismic load is behave like secondary or primary. To do that the following beam configuration shown in Table 3 and Fig.1 is used in simulation. Table 3 Geometry and material properties of beam Geometry Material Length Thickness Width Elastic Modulus Density Yield stress 140 mm 6 mm 13 mm 15250 MPa 11.34gm/cm3 5 MPa Fig. 1 The model beam for numerical analysis At the top node of the beam extra 4 different masses (0.1kg, 0.2 kg, 0.3 kg and 0.4 kg) was loaded to check the effect of maximum mass on the occurrence condition of ratcheting. The bottom node was fixed and a sinusoidal wave of different acceleration was put on this node. It was observed that ratchet deformation in vertically downward direction occurred due to the primary stress which is the stress caused by weight moment and secondary repetitive seismic stress due to inertia moment of the top mass. Time history response analysis was carried out whereas the elastic perfectly plastic stress strain constitutive equation was used. The frequency used in the analysis is twice the natural frequency of the model. One of the analysis results for 0.2kg showed that 5000gal acceleration has not occurred ratcheting deformation but 6000gal has occurred ratcheting deformation (Fig. 2). Occurrence condition of ratcheting, red dots indicated ratcheting whereas blue dots are not (Fig. 3). - 393 - -2024681900/01/090 0.2 0.4 0.6 0.8 1 1.2 1.4 Deflection[mm] Time[s] 6000gal 5000gal Fig. 2 Analysis results of deformation of ratcheting 0500100015002000250030000 200 400 600 800 Moment by seismic loading [Nmm] Moment by weight [Nmm] 赤：進行性変形発生青：進行性変形未発生 Fig. 3 Occurrence condition of ratcheting caused by seismic load Fig. 4 Thermal ratcheting occurrence condition (Bree diagram [3]) The renowned Bree diagram (Fig. 4) is the occurrence condition for thermal ratchetting [3]. Horizontal axis expressed the primary pressure stress and vertical axis represents secondary thermal stress. Compared the Bree diagram with seismic ratchetting diagram it has seen that for the both the occurrence condition line has similar shape and also it has seen that ratcheting deformation is less likely to occur at high thermal loads which is similar in the case of seismic load. Since the similarity is found between the stress caused by seismic load and thermal load, authors thought that stress caused by the seismic load is also characterized as secondary stress manner. 3.2 NUMERICAL ANALYSIS OF COLLAPSE Collapse is the excessive deformation of the structure, it occurs when the load doesn’t satisfy the equilibrium condition. In other words due to stress the stiffness of structure reduces gradually with the deformation and resulting in complete loss of stiffness. For collapse analysis similar beam model was also used like ratcheting. The same material and geometrical properties were used along with the same 4 masses at the top node. The only difference was the input wave. The shape of acceleration wave was half sinusoidal (Fig. 5) but for ratcheting it was full sinusoidal wave. Also the frequency used in the case is natural frequency which is different from ratcheting analysis. The reason of using half sinusoidal wave was that half sinusoidal wave is similar to sudden pulse type wave and collapse is prone to occur for pulse type wave than continuous full sinusoidal wave. Fig. 5 Input pulse type acceleration for collapse The analysis result of deformation for 0.2kg weight showed that for 10000 gal the collapse didn’t occur because the deformation was not stable but for 15000 gal it occurred because the deformation saturate at the point which is almost the maximum possible deformation of this beam and also the deformation didn’t increase by increasing the value of acceleration (Fig. 6). The mass-maximum acceleration curve - 394 - 0500100015002000250030003500400045000 100 200 300 400 500 600 Moment by seismic load[N-mm] Moment by gravity [N-mm] 0500001000001500002000002500003000003500000 0.1 0.2 0.3 0.4 0.5 Maximum acceleration [mm/s^2] Mass [kg] (Fig. 7) showed that more the top mass the less the seismic load is needed to occur collapses. The occurrence condition of collapse has also found similar behaviour like ratchetting (Fig. 8). Alike ratchetting the stress by weight which is primary stress has more impact on occurrence of collapse than stress by seismic load, though the occurrence condition line for collapse is not as straight as for ratchetting. Fig. 6 Analysis results of deformation of collapse Fig. 7 Effect of maximum acceleration and mass on collapse Fig. 8 Occurrence condition of collapse caused by seismic load 4. CONCLUSION After the Fukushima nuclear accident, it is high time to robust the nuclear facility in such a way that core melting can be prevented in any circumstances. Earthquake is one of the major threats for any type of structure at any time. To make the heavy“ “Failure modes investigation of pipe structure under excessive seismic loading “ “Md Abdullah Al BARI,Toshiaki KOKUFUDA ,Yamato KATSURA, Takuya SATO,Kazuyuki DEMACHI ,Naoto KASAHARA