Verification of Probabilistic Fracture Mechanics Analysis Code PASCAL

Recent improvements of probabilistic fracture mechanics analysis code PASCAL for reactor pressure vessels

A probabilistic fracture mechanics (PFM) analysis method for pressure boundary components is useful to evaluate the structural integrity in a quantitative way. This is because the uncertainties related to influence parameters can be rationally incorporated in PFM analysis. From this viewpoint, the probabilistic approach evaluating through-wall cracking frequencies (TWCFs) of reactor pressure vessels (RPVs) has already been adopted as the regulation on fracture toughness requirements against PTS events in the U.S. As a study of applying PFM analysis to the integrity assessment of domestic RPVs, JAEA has been preparing input data and analysis models to calculate TWCFs using PFM analysis code PASCAL3. In this paper, activities have been introduced such as preparing input data and models for domestic RPVs, verification of PASCAL3, and formulating guideline on general procedures of PFM analysis for the purpose of utilizing PASCAL3. In addition, TWCFs for a model RPV evaluated by PASCAL3 are presented.

To assess the structural integrity of reactor vessels (RVs) during pressurized thermal shock (PTS) events, a deterministic fracture mechanics (DFM) approach has been widely used such as the procedure in JEAC4206-2007. On the other hand, the application of a probabilistic fracture mechanics (PFM) analysis method for the structural reliability assessment of RV has become attractive recently because uncertainties related to input parameters can be incorporated rationally. The probabilistic approach has already been adopted as the regulation on fracture toughness requirements against PTS events in the U.S. In this paper, in order to verify the applicability of a PFM method to JEAC4206-2007, deterministic and probabilistic analyses have been performed, and the effects of initial crack size defined in JEAC4206-2007 on the temperature margin obtained from DFM and the probability of crack initiation obtained from PFM have been evaluated. With regard to the PTS event variation, a stuck open valve scenario (SO) has been considered in addition to large- and small-break loss of coolant accident (LBLOCA, SBLOCA) and main steam line break (MSLB).

Improvements to a probabilistic fracture mechanics code for evaluating the integrity of a RPV under transient loading

The probabilistic fracture mechanics (PFM) analysis code PASCAL has been developed in JAERI. This code can evaluate the conditional probabilities of crack initiation and fracture of a reactor pressure vessel (RPV) under transient conditions such as pressurized thermal shock (PTS). Based on the temperature and stress distributions in the vessel wall for four cases of PTS transients in a typical 3-loop PWR, parametric PFM analyses were performed using PASCAL on the variables such as pre-service inspection method, crack geometry, fracture toughness curve and irradiation embrittlement prediction equation. The results showed that the Arakawa's model for a pre-service inspection had a significant effect on the fracture probability and reduced it by more than 3 orders of magnitude compared with no inspection case. The fracture probability calculated by the fracture toughness estimation method in Japan was about 2 orders of magnitude lower than that by the USA method. It was found that the treatment of a semi-elliptical crack after its initiation in PASCAL reduced the conservatism in a conventional method where it is transformed into an infinite length crack.

The United States Nuclear Regulatory Commission (USNRC) initiated a comprehensive project in 1999 to determine if improved technologies can provide a technical basis to reduce the conservatism in the current regulations for pressurized thermal shock (PTS) while continuing to provide reasonable assurance of adequate protection to public health and safety. A relaxation of PTS regulations could have profound implications for plant license renewal considerations. During the PTS re-evaluation study, an improved risk-informed computational methodology was developed that provides a more realistic characterization of PTS risk. This updated methodology was recently applied to three commercial PWRs. The results of this study provide encouragement that a technical basis can be established to support a relaxation of current PTS regulations. One significant model improvement applied in the PTS re-evaluation study was the development of flaw databases derived from the non-destructive and destructive examinations of material from cancelled reactor pressure vessels (RPV). Empirically-based statistical distributions derived from these databases and expert illicitation were used to postulate the number, size, and location of flaws in welded and base metal (plate and forging) regions of an RPV during probabilistic fracture mechanics (PFM) analyses of RPVs subjected to transient loading conditions such as PTS. However, limitations in the available flaw data have required assumptions to be made to complete the risk-based flaw models. Sensitivity analyses were performed to evaluate the impact of four flaw-related assumptions. Analyses addressed: 1) truncations of distributions to exclude flaws of extreme depth dimensions, 2) vessel-to-vessel differences in flaw data, 3) large flaws observed in weld repair regions, and 4) the basis for estimating the number of surface breaking flaws. None of the four alternate weld flaw models significantly impacted calculated vessel failure frequencies or invalidated the tentative conclusions derived from the USNRC PTS re-evaluation study.

The current regulations, as set forth by the United States Nuclear Regulatory Commission (NRC), to insure that light-water nuclear reactor pressure vessels (RPVs) maintain their structural integrity when subjected to planned startup (heat-up) and shutdown (cool-down) transients are specified in Appendix G to 10 CFR Part 50, which incorporates by reference Appendix G to Section XI of the ASME Code. The technical basis for these regulations contains many aspects that are now broadly recognized by the technical community as being unnecessarily conservative. During the past decade, the NRC conducted the interdisciplinary Pressurized Thermal Shock (PTS) Re-evaluation Project that established a technical basis to support a risk-informed revision to current PTS regulations (10CFR Part 50.61). Once the results of the PTS reevaluation are incorporated into a revision of the 10 CFR 50 guidance on PTS, it is anticipated that the regulatory requirements for the fracture toughness of the RPV required to withstand a PTS event (accidental loading) will in some cases be less restrictive than the current requirements of Appendix G to 10 CFR Part 50, which apply to normal operating conditions. This logical inconsistency occurs because the new PTS guidelines will be based on realistic models and inputs whereas existing Appendix G requirements contain known and substantial conservatisms. Consequently, a goal of current NRC research is to derive a technical basis for a risk-informed revision to the current requirements of Appendix G to 10 CFR Part 50 in a manner that is consistent with that used to develop the risk-informed revision to the PTS regulations. Scoping probabilistic fracture mechanics (PFM) analyses have been performed for several hundred parameterized cool-down transients to (1) obtain insights regarding the interaction of operating temperature and pressure parameters on the conditional probability of crack initiation and vessel failure and (2) determine the limits on the permissible combinations of operating temperature and pressure within which the reactor may be brought into or out of an operational condition that remains below the acceptance criteria adopted for PTS of 1 × 10−6 failed RPVs per reactor operating year. This paper discusses the modeling assumptions, results, and implications of these scoping analyses.

Integrity assessment of reactor pressure vessels (RPVs) can be performed either by deterministic fracture mechanics (DFM) or/and by probabilistic fracture mechanics (PFM) analyses. In European countries and Switzerland, only DFM analyses are required. However, in order to establish the probabilistic approach in Switzerland, the advantages and shortcomings of the PFM are investigated in the frame of a national research project. Both, the results from DFM and PFM depend strongly on the previous calculated thermal-hydraulic boundary conditions. Therefore, complete integrity analyses involving several integrated numerical codes and methods were performed for a reference pressurized water reactor (PWR) RPV subjected to pressurized thermal shock (PTS) loads. System analyses were performed with the numerical codes RELAP5 and TRACE, whereas for structural and fracture mechanics calculations, the FAVOR and ABAQUS codes were applied. Additional computational fluid dynamics analyses were carried out with ANSYS/FLUENT, and the plume cooling effect was alternatively considered with GRS-MIX. The results from the different analyses tools are compared, to judge the expected overall uncertainty and reliability of PTS safety assessments. It is shown that the scatter band of the stress intensities for a fixed crack configuration is rather significant, meaning that corresponding safety margins should be foreseen. The conditional probabilities of crack initiation and RPV failure might also differ, depending on the considered random parameters and applied rules.

Structural integrity assessments for cracked nuclear components are currently performed on the basis of deterministic fracture mechanics in accordance with the Rules on Fitness-for-Service for Nuclear Power Plant of the Japan Society of Mechanical Engineers. On the other hand, probabilistic fracture mechanics (PFM) is expected as a rational method for a structural integrity assessment because it can account for the uncertainties and scatters of various influencing factors and can evaluate quantitative values such as the failure probabilities of the components as the solutions. In the Japan Atomic Energy Agency (JAEA), a PFM analysis code PASCAL-SP was developed in order to evaluate the failure probability of nuclear pipe by taking into account aging degradation mechanisms such as inter-granular stress corrosion cracking (IGSCC) and fatigue in the boiling water reactor (BWR) environment. Recently, a number of cracks due to primary water stress corrosion cracking (PWSCC) have been detected in nickel-based alloy welds in the primary piping of pressurized water reactors (PWRs). Therefore, the structural integrity assessment for primary piping taking PWSCC into consideration has become important. This paper details the improvement of PASCAL-SP to evaluate the failure probability of primary pipe taking PWSCC into consideration. We introduce several probabilistic evaluation models such as crack initiation, crack growth and crack detection models related to PWSCC into PASCAL-SP. As numerical examples, the failure probabilities for circumferential and axial cracks in nickel-based alloy weld in pipe in the PWR primary water environment are calculated. We also evaluate the influence of non-destructive inspection on failure probabilities. On the basis of the numerical results, we conclude that the improved PASCAL-SP is useful for evaluating the failure probability of primary pipe taking PWSCC into account.

Semi-elliptical underclad cracks resulting from the fabrication process of a reactor pressure vessel (RPV) were able to be detected by non-destructive testing method. Meanwhile, after long-term operation under severe conditions, such as high temperature, high pressure, and irradiation, the RPV becomes brittle and susceptible to damage, especially when subjected to pressurised thermal shocks (PTS). Therefore, the probabilistic fracture mechanics (PFM) analysis of RPV with the crack should be applied to evaluate the operation safety. To the best of the authors' knowledge, few studies or computer codes have applied PFM analysis for such cracks. Therefore, this study conducts PFM analysis for cracks by modifying the calculation procedure of FAVOR 12.1 computer code. The results show that during the lifetime of a nuclear power plant, such cracks will not threaten the RPV's safety. Additionally, three methods were proposed to improve FAVOR 12.1's ability to perform PFM analysis for axial through-clad cracking.

Development of probabilistic fracture mechanics analysis codes for reactor pressure vessels and piping considering welding residual stress

Probabilistic fracture mechanics (PFM) analysis is expected to be a rational method for structural integrity assessment because it can consider the uncertainties of various influence factors and evaluate the quantitative values such as failure probability of a cracked component as the solution. In the Japan Atomic Energy Agency, a PFM analysis code PASCAL-SP has been developed for structural integrity assessment of piping welds in nuclear power plants (NPP). In the past few decades, a number of cracks due to primary water stress corrosion cracking (PWSCC) have been detected in nickel-based alloy welds in the primary piping of pressurized water reactors (PWRs). Thus, structural integrity assessments considering PWSCC have become important. In this study, PASCAL-SP was improved considering PWSCC by introducing several analytical functions such as the models for evaluation of crack initiation time, crack growth rate (CGR), and probability of crack detection. By using the improved version of PASCAL-SP, the failure probabilities of pipes with a circumferential crack or an axial crack due to PWSCC were numerically evaluated. Moreover, the influence of leak detection and nondestructive examination (NDE) on failure probabilities was detected. Based on the obtained numerical results, it was concluded that the improved version of PASCAL-SP is useful for evaluating the failure probability of a pipe considering PWSCC.

The International Atomic Energy Agency (IAEA) has had a series of reactor pressure vessel (RPV) structural integrity programs that started back in the 1970s. These Coordinated Research Projects most recently have focused on use of the Master Curve fracture toughness testing approach for RPV and other ferritic steel components and on the issue of pressurized thermal shock (PTS) in operating pressurized water reactors. This paper will provide the current status for these projects and discuss the implications for improved safety of key ferritic steel components in nuclear power plants (NPPs).

The Reactor Pressure Vessel (RPV) is an essential component, which is liable to limit the lifetime duration of PWR plants. The assessment of defects in RPV subjected to pressurized thermal shock (PTS) transients made at an European level generally does not necessarily consider the beneficial effect of the load history (Warm Pre-stress, WPS). The SMILE project — Structural Margin Improvements in aged embrittled RPV with Load history Effects — aims to give sufficient elements to demonstrate, to model and to validate the beneficial WPS effect. It also aims to harmonize the different approaches in the national codes and standards regarding the inclusion of the WPS effect in a RPV structural integrity assessment. The project includes significant experimental work on WPS type experiments with C(T) specimens and a PTS type transient experiment on a large component. This paper deals with the results of the PTS type transient experiment on a component-like specimen subjected to WPS- loading, the so called Validation Test, carried out within the framework of work package WP4. The test specimen consists of a cylindrical thick walled specimen with a thickness of 40mm and an outer diameter of 160mm, provided with an internal fully circumferential crack with a depth of about 15mm. The specified load path type is Load-Cool-Unload-Fracture (LCUF). No crack initiation occurred during cooling (thermal shock loading) although the loading path crossed the fracture toughness curve in the transition region. The benefit of the WPS-effect by final reloading up to fracture in the lower shelf region, was shown clearly. The corresponding fracture load during reloading in the lower shelf region was significantly higher than the crack initiation values of the original material in the lower shelf region. The post test fractographic evaluation showed that the fracture mode was predominantly cleavage fracture also with some secondary cracks emanating from major crack.

In this paper, the results of the sensitivity analyses of failure probability are presented for pressure vessel under PTS (Pressurized Thermal Shock) transient, by using our new probabilistic fracture mechanics analysis code. The pressure, the fluid temperature at the inner surface of pressure vessel and other analysis conditions are based on an international benchmark study on PTS. The temperature and stress distributions through wall thickness during transient are obtained by a heat transfer and an elasto-plastic stress analysis with FEM. The new models and methodologies introduced in our code are summarized and the effect of overlay clad and behavior of semi-elliptical crack on the failure probability are investigated especially.