by NISHIKAWA Hiroyuki, KATSUYAMA Jinya and ONIZAWA Kunio

Transcription

1 [ 27 p. 245s-250s (2009)] by NISHIKAWA Hiroyuki, KATSUYAMA Jinya and ONIZAWA Kunio Numerical simulations by thermal-elastic-plastic-creep analysis using finite element method (FEM) have been performed to evaluate residual stress distributions in a reactor pressure vessel (RPV) caused by weld-overlay cladding, post-weld heat treatment (PWHT), hydrostatic test, operation and pressurized thermal shock (PTS). The weld-overlay cladding gives tensile stress in the cladding layer and base metal near the cladding. Using the calculated welding residual stress, stress intensity factors (SIFs) during PTS have been computed based on the influence function method. The maximum value of SIF during PTS with weld-overlay cladding is higher than that without weld-overlay cladding. According to the structural integrity assessment procedure of an RPV against PTS, a comparison has been also made by defining a temperature margin. The result indicates that the residual stress makes the temperature margin smaller in a few degree C which may be within the range of the margin originally put in the structural integrity assessment procedure. Key Words: Finite element analysis, Reactor pressure vessel, Weld-overlay cladding, Residual stress, Structural integrity assessment 1. Introduction Austenitic stainless steel is welded on the inner surface of ferritic low alloy steel of reactor pressure vessels (RPVs) for protecting the vessel walls against the corrosion. Residual stress which corresponds to yield stress will be generated near the cladding layer due to the weld-overlay cladding. After the manufacturing process of the RPVs including weld-overlay cladding and post-weld heat treatments (PWHT), the residual stresses still remain in such dissimilar metals due to the difference between the thermal expansions. Pressurized thermal shock (PTS) is one of the most severe events to assess the structural integrity of RPVs 1, 2). Japanese codes for assessing the structural integrity of RPVs provide rules based on fracture mechanics to prevent the RPVs from nonductile fracture under PTS events 3). Welding residual stress may affect the structural integrity of the RPVs during PTS. However, there is no specific provision in the codes related to the residual stress caused by weld-overlay cladding. One must evaluate effects of the residual stress on the parameters related to fracture mechanics to assess the structural integrity of nuclear components appropriately. Numerical simulations based on finite element method (FEM) have been conducted to evaluate the welding residual stress of nuclear components by some researchers. Siegele and Brand 4) have performed experiments and FEM simulations to evaluate the stress fields of plates of RPVs due to weld-overlay cladding. The results showed that weld-overlay cladding revealed tensile stress in *Received: ** Nuclear Safety Research Center, Japan Atomic Energy Agency (JAEA) ***Member, Nuclear Safety Research Center, Japan Atomic Energy Agency (JAEA) the cladding followed by compressive stress in the base metal. The stress distribution was in agreement with the experimental results. In our previous paper, FEM simulations have been performed to evaluate the stress in a vessel wall caused by weld-overlay cladding and post-weld heat treatment (PWHT) 5). The results indicated that the tensile stress of about 400MPa remained in the cladding layer of the RPV at room temperature even after PWHT. Effects of residual stress on stress intensity factor (SIF) were also evaluated under typical PTS conditions in the study. Still, the procedures of the FEM analysis including boundary conditions, material properties and phase transformation need to be modified to simulate the weld-overlay cladding appropriately. In the present study, the analysis conditions are improved in the following points: material properties taken from the experiment and boundary conditions, conditions for hydrostatic test and operation. FEM simulations are performed to evaluate the residual stresses of an RPV. Using the result of the FEM simulations, stress intensity factors (SIFs) are computed based on the influence function method. Structural integrity assessment of an RPV against PTS is then evaluated. 2. Simulation method 2.1 FEM analysis Thermal-elastic-plastic-creep analysis has been performed using ABAQUS, which is a commercially available FEM code 6) Model geometry, material properties and boundary conditions Model geometry for the FEM analysis is shown in Fig. 1. The model is a part of the beltline region of a 3-loop RPV with 12 degree in the circumferential direction and 288mm in axial direction for saving calculation time. The inner radius of the base metal of the RPV and the thickness of base metal are 2000mm and 200mm, respectively. The thickness and the width of weld metal

2 246s NISHIKAWA et al.: Effects of Weld-overlay Cladding on the Structural Integrity of RPV during PTS Fig. 1 FEM model. (a) Overall view, (b) Enlarged view including the surface-breaking semi-elliptical flaw. are 6mm and 48mm, respectively. Elements used in this analysis are three-dimensional solid ones which have 6 nodes. The number of elements and nodes are 8920 and 10127, respectively. Shown in Fig.2 are the temperature dependencies of material properties. The relationship between stress and strain in plastic region is defined using the kinematic hardening law. Heat transfer and radiation are considered at each surface of the model using a coefficient of heat transfer of 10 W/(m 2 ) and an emissivity of 0.7. Latent heats of weld metal and base metal are defined at their melting points. Back stress and equivalent plastic strain are reset to zero above the melting point in the elastic-plastic analysis. Boundary conditions applied to the FEM model are depicted in Fig. 3. Symmetric boundary condition has been imposed on the two lateral faces to constrain the circumferential direction (Fig. 3 (a)). No constraint in the axial direction is considered in the previous study 5). In contrast, the top face and the bottom face are constrained to keep parallel in the present study (Fig. 3 (b)) Analysis cases FEM analysis cases are shown in Table 1. In Cases 0 and 1, the procedure of the analyses is composed of three steps: hydrostatic test, operation and PTS. The difference between Cases 0 and 1 is the analysis type. In Case 2, the procedure including weld-overlay cladding and PWHT are considered. In each Case, the initial state of stress-free is assumed at 20 before simulating each postulated event Analysis of weld-overlay cladding Unsteady thermal analysis has been performed to simulate temperature distributions during weld-overlay cladding. The type of weld-overlay cladding in the analysis is submerged-arc welding. Movement of a heat source is modeled by varying heat input to elements across the welding. Goldak double ellipsoid Fig. 2 Temperature dependencies of material properties. (a) Thermal conductivity, (b) Specific heat, (c) Stress-strain curves of base metal (A533B-1), (d) Stress-strain curves of weld metal (Type 308), and (e) Coefficients of thermal expansion.

3 s Fig. 4 Modified double ellipsoid model used in this study. Fig. 3 Boundary conditions in FEM analysis. (a) Top view of the FEM model, and (b) Side view of the FEM model. Table 1 Analysis cases. Fig. 5 Time histories of temperature and inner pressure during PTS (SBLOCA). model is applicable to simulate the behavior of arc welding for butt-welding joints 7). In this study, Goldak model is modified in that the double ellipsoid is divided in half, inserting the width of a bead. This modified double ellipsoid model is depicted in Fig. 4. Welding speed, heat input and heat transfer efficiency are 3.8 mm/s, 35kW and 0.85, respectively. Solution of stress and displacement is dependent on a temperature field with no inverse dependency; hence, sequentially coupled thermal-elastic-plastic analysis has been performed to obtain stress distributions. In the thermal-elastic-plastic analysis, the elements of cladding before being overlaid are considered as air Analysis of PWHT Creep analysis has been performed to simulate PWHT under the condition of 620 for 6 hours. Norton creep law has been adopted as creep constitutive equation in this analysis. The creep laws of base metal and weld metal are as follows:. e cr - = s (Base metal). e cr - = s (Weld metal) where is the equivalent creep strain rate (1/s) and s is the von- ė cr Mises equivalent stress. The constants in the equations have been taken from experiments Analysis of hydrostatic test, operation and PTS The inner pressure of 21.45MPa has been applied to the RPV to simulate a hydrostatic test. Axial tensile stress induced by the inner pressure has been applied to the top surface of the RPV. The inner pressure of 15.4MPa at the temperature of 288 has been applied to the RPV to simulate the normal operation. Thermal-elastic or thermal-elastic-plastic analysis during PTS has been performed. A transient induced by small break loss of coolant accident (SBLOCA) was selected as a PTS event. The time histories of temperature and inner pressure during SBLOCA are shown in Fig. 5. A coefficient of heat transfer to the inner surface of the RPV was kept to W/(m 2 ) as a conservative value. 2.2 Fracture mechanics analysis during PTS SIFs at the deepest point of a postulated surface-breaking semi-elliptical flaw in the axial direction have been computed based on an influence function method using the non-dimensional SIF database of PASCAL2 (PFM Analysis of Structural Components in Aging LWR version 2) 8, 9). SIFs during PTS have been obtained from the hoop stresses of the FEM results. The flaw is 16mm in depth and 64mm in length, which corresponds to the size of the postulated flaw provided in the code of the structural integrity assessment of an RPV 3). 3. Results and discussion 3.1 Stress distributions considering weld-overlay cladding Figure 6 presents through-thickness variation of residual hoop stresses after weld-overlay cladding, PWHT, hydrostatic test at room temperature and during operation in Case 2. It should be noted that the hoop stress is the opening stress for an axial flaw.

4 248s NISHIKAWA et al.: Effects of Weld-overlay Cladding on the Structural Integrity of RPV during PTS Fig. 6 Hoop stress distributions in Case 2 during the process of weldoverlay cladding, PWHT, hydrostatic test and operation. The residual stress in the range from the inner surface to about 20mm depth is tensile after weld-overlay cladding. The tensile stress in base metal near cladding ( MPa) is higher than that in the cladding ( MPa). This is due to the difference in the yield stresses as shown in Figs. 2(c) and 2(d). Compressive stress occurs in the deeper region to keep balance with the tensile stress. The hoop stress in the cladding increases by about 50MPa after PWHT as shown in Fig. 6. The stress in the base metal near the cladding decreases to about 50 70MPa as opposed to that in the cladding. In the early stage of PWHT, the plastic stress in the base metal decreases due to the creep. This behavior provides drastic decreasing of residual stress in the base metal. Tensile residual stress in cladding, whereas, is mostly due to the difference between the thermal expansions of weld and base metals. The hoop stress distribution after PWHT agrees well with the experimental results 10). After the hydrostatic test, the stress in the cladding decreases to around 120MPa due to the yield of the cladding, whereas the stress in the base metal near the cladding hardly changes. During the operating condition of 288 and 15.4MPa, the hoop stress in the base metal near the cladding increases to 230MPa. In contrast, the hoop stress in the cladding decreases to about -50MPa. This behavior is due to the higher thermal expansion of the weld metal than that of the base metal in the range of 20 and 288 as shown in Fig. 2 (e). The hoop stress without considering weld-overlay cladding (Case 1) is also shown in Fig. 6. The hoop stress in Case 2 mentioned above is higher than that of Case 1 in the range from the inner surface to 50mm depth. Fig. 7 Hoop stress distributions during PTS event. (a) Case 0, (b) Case 1, and (c) Case Stress distributions during PTS event Figure 7 shows the hoop stress distributions in Cases 0-2 during PTS event. The hoop stresses at 0s (the start of PTS), 2007s (the time to reach the maximum of the stress in the base metal near the cladding) and 3960s (the end of PTS) are shown in the figures. The hoop stresses in the base metal in Cases 0 and 1 have almost the same distribution. The stresses in Case 2 in the base metal near the cladding are higher than those in Cases 0 and 1. The differences in the hoop stress distributions would affect stress intensity factors of the postulated flaw of 16mm depth 3.3 Fracture mechanics analysis during PTS event SIFs at the deepest point of the flaw are shown in Fig. 8 as a function of time during PTS event. In each case, SIF value starts to increase at around 800s when the inner surface of the RPV starts to cool down rapidly as shown in Fig. 5. The SIF value reaches the maximum value at around 2000s. The maximum value of SIF in Case 2 (76MPam 1/2 ) is higher than those of Case 0

5 s Fig. 8 Time histories of SIFs during PTS event. Fig. 9 Comparison between SIFs and fracture toughness. (63MPam 1/2 ) and Case 1 (61MPam 1/2 ). This is attributed to the higher hoop stress of Case 2 during PTS than that of Case 1. It should be noted that the SIF value of Case 2 is higher than that of Case 0, the analysis type of which is elastic. The integrity assessment of RPVs which is provided in the Japanese code 3) has been conducted. The integrity assessment involves the computation of a SIF at the deepest point of the postulated flaw and the comparison to the fracture toughness curve at the evaluation time of an operating plant. The fracture toughness curve applied in the study is as follows: K Ic = exp{0.036(T RT NDT )} where K Ic, T and RT NDT are the fracture toughness, temperature and the reference temperature of the nil-ductile transition, respectively. The value of RT NDT at the evaluation time has been obtained from the embrittlement prediction equation established in the Japanese code 11). Figure 9 is the result of the comparison between the SIFs and the fracture toughness curve at the fast neutron fluence of 10*10 19 (n/cm 2, E>1MeV) corresponding to the 60 years operation. The Japanese code provides that an RPV is intact if a fracture toughness curve does not intersect a SIF curve. However, considering the warm pre-stress effect, the peak of a SIF curve is only important for the structural integrity assessment 12). In this study, we have defined the difference between the temperature giving the maximum of SIF and that of fracture toughness corresponding to the maximum of SIF as a temperature margin ( T) and compared the margins among analysis cases. T values obtained from results of Cases 0, 1 and 2 are 25.4, 27.5 and 22.5, respectively. The effect of residual stress is less than 5 within the cases analyzed here. The difference depends on the analysis conditions such as welding parameters, PTS transients. However, this effect is not so large when the conservatism in the integrity assessment procedure is concerned such as the size of postulated flaw, heat transfer analysis condition and so on. Therefore, the effect may be small compared with the margin originally put in the assessment procedure. Nevertheless, the consideration of residual stress caused by weld-overlay cladding is important to evaluate the failure probability of RPVs appropriately based on probabilistic fracture mechanics analysis which requires a best estimate solution without a margin. 4. Conclusion Thermal-elastic-plastic-creep analyses have been performed to evaluate residual stress distributions caused by manufacturing processes including weld-overlay cladding, PWHT, hydrostatic test and operation. The analysis results have shown higher tensile stress in cladding and the base metal near the cladding when the welding is considered. Using the results, the effect of the residual stress on stress intensity factors during a PTS event has been evaluated assuming a semi-elliptical surface flaw according to the structural integrity assessment procedure. The SIF calculated with weld-overlay cladding is higher than that without weldoverlay cladding. From the integrity assessment of an RPV the effect of weld-overlay cladding on the temperature margin T has been quantitatively evaluated and may be within the range of the margin put in the procedure of structural integrity assessment. Acknowledgements This study has been performed under the contract between Nuclear and Industrial Safety Agency of the Ministry of Economy, Trade and Industry of Japan and JAEA. References 1) D. Moinereau, G. Bezdikian and C. Faidy: International Journal of Pressure Vessels and Piping, 78, (2001), ) T. L. Dickson and S. N. M. Malik: International Journal of Pressure Vessels and Piping, 78 (2001), ) Japan Electric Association: Nuclear Standards Committee of JEA, JEAC (in Japanese) (2004). 4) D. Siegele and M. Brand: Proceedings of 2007 ASME Pressure Vessels and Piping Division Conference, PVP (2007). 5) M. Udagawa, J. Katsuyama and K. Onizawa: Proceedings of ASME Pressure Vessels and Piping Division Conference, PVP (2007). 6) Dassault Systemes Simulia Corp.: ABAQUS user's manual, version 6.7 (2007).

6 250s NISHIKAWA et al.: Effects of Weld-overlay Cladding on the Structural Integrity of RPV during PTS 7) J. Goldak, A. Chakravarti and M. Bibby: Metallurgical Transactions B, 15B (1984), ) K. Onizawa, K. Shibata, K. Osakabe and K. Tanaka: Proceedings of ASME Pressure Vessels and Piping Division Conference, PVP 2006-ICPVT (2006). 9) K. Osakabe, D. Kato, K. Onizawa and K. Shibata: JAEA-Data/Code (in Japanese) (2006). 10) M. Udagawa, J. Katsuyama and K. Onizawa: Proceedings of symposium on welding structure, Japan Welding Society (2006) (in Japanese). 11) Japan Electric Association: Nuclear Standards Committee of JEA, JEAC (in Japanese) (2004). 12) B. W. Pickles and A. Cowan: International Journal of Pressure Vessels and Piping, 14, (1983),