Improvements on Evaluation Functions of a Probabilistic Fracture Mechanics Analysis Code for Reactor Pressure Vessels

In Japan, a probabilistic fracture mechanics (PFM) analysis code PASCAL was developed for structural integrity assessment of reactor pressure vessels (RPVs) considering neutron irradiation embrittlement and pressurized thermal shock (PTS) events. By reflecting the latest knowledge and findings, the evaluation functions are continuously improved and have been incorporated into PASCAL4 which is the most recent version of the PASCAL code. In this paper, the improvements made in PASCAL4 are explained in detail, such as the evaluation model of warm prestressing (WPS) effect, evaluation function of confidence levels for PFM analysis results by considering the epistemic and aleatory uncertainties in probabilistic variables, the recent stress intensity factor (KI) solutions, and improved methods for KI calculations when considering complicated stress distributions. Moreover, using PASCAL4, PFM analysis examples considering these improvements are presented.

Methodology and Warm Prestressing Effect for Pressurized Thermal Shock Analysis in Nuclear Power Plant

One potential challenge to the integrity of the reactor pressure vessel (RPV) in a pressurized water reactor is posed by pressurized thermal shock (PTS). Therefore, the safety of the RPV with regard to neutron embrittlement has to be analyzed. In this paper, the procedure and method for the structural integrity analysis of RPV subjected to PTS is presented. The FAVOR code is applied to calculate the probabilities for crack initiation and failure by considering crack distributions based on cracks observed in the Shoreham and PVRUF RPVs in the U.S. A local approach to fracture, i.e. the σ*-A* model is used to predict the warm prestressing (WPS) effect on the RPV integrity. The results show that the remaining stress contributes to the WPS effect, whereas the increase of fracture toughness is not completely attributed to the remaining stress. The modeled load paths predict a material toughness increase of 30-100%.

Statistical Analysis and Monte-Carlo Simulations of Warm Prestressing of Pre-Cracked Small Single Edge Notch Bend Specimens

Warm prestressing is widely acknowledged as being able to enhance material toughness, especially in steels that exhibit lower shelf cleavage fracture. The enhancement in toughness has a significant impact on the integrity of pressure vessels, particularly during severe loading conditions, such as pressurised thermal shock. In this paper, we undertake detailed statistical analyses of experimental data provided via a comprehensive programme of fracture tests at UJV (Ústav jaderného výzkumu Řež a.s.). A warm prestressing model, developed by Chell, is used to predict the change in toughness probabilistically, using Monte-Carlo methods to predict the distribution in toughness following different warm prestressing cycles. The results obtained from this model are also compared to predictions made by the Wallin approach. Experimental data was generated, at UJV for WWER 440 RPV steel, using small single-edge-notched bend SEN(B) specimens (or pre-cracked Charpy) across a range of different fracture temperatures, warm pre-stress temperatures, and levels of preload, in both as-received and irradiated conditions. In this paper, experimental data obtained only from tests on unirradiated specimens were statistically treated. A three parameter Weibull distribution was used to map the scatter observed in the virgin toughness. The statistical significance of increase in apparent fracture toughness due to warm prestressing was evaluated using the Mann-Whitney test. It was further shown by Monte-Carlo simulations that the Chell and Wallin models provide slightly conservative predictions of the resulting fracture toughness. Both, the experimentally measured and predicted values of the resulting fracture toughness, depend on the specific tests conditions, especially on the level of preload.

Further Predictions of Fracture Experiments of a Pre-Cracked Pressurised Thermal Shock Disk (PTS-D) Specimen Under Warm Prestressing Loading Cycles

Finite element analyses have been performed to investigate the effects of warm prestressing (WPS) of a pre-cracked PTS-D (Pressurized Thermal Shock Disk) specimen. Three basic types of WPS loading cycles were used in the analyses: LUCF (Load-Unload-Cool-Fracture) cycle; LCF (Load-Cool-Fracture) cycle; and LCTF (Load-Cool-Transient-Fracture) cycle. The analyses aimed to predict the fracture toughness enhancements due to WPS using different analysis methods and to make comparisons with the experimental work conducted by the Belgium SCK-CEN organisation under the European NESC VII project. The finite element results were used to derive the enhanced fracture toughness by three different engineering methods: (1) Chell’s displacement superposition method; (2) the local stress matching method; and (3) Wallin’s empirical formula. The enhanced fracture toughness was evaluated at the deepest point of the semi-elliptical crack based on three different levels of as-received fracture toughness of 43.96, 65.94, and 86.23 MPam1/2, which correspond to probabilities of failure of 5%, 50% and 95%, respectively. The predicted fracture loads were compared with the experimental fracture loads for the three WPS loadings cycles. The results show good agreement.

The Combined Effects of Residual Stress and Warm Prestressing on Cleavage Fracture in Steels

Residual stresses (RS) appear in most engineering structures, either because they have been deliberately introduced or they are a by-product of the manufacturing process. Since RS play an important role in increasing and decreasing the possibility of failure, it is necessary that their effect on the integrity of the structure is understood. In the presence of RS, many components are subjected to a variety of prior loading histories. One such case is often associated with warm prestressing (WPS), where the component is subjected to some form of preloading at a temperature higher than operating conditions. The aim here was to explore how WPS, together with RS, might influence the subsequent fracture conditions for cleavage fracture. First, a model for WPS is reconsidered so that it could be used for Monte Carlo (MC) simulations of WPS. Results are compared with experimental data. The model is then adopted to consider the effects of long range residual stress created in fracture samples through an initial misfit. This is done by fitting the sample into a structure, with the new system subsequently being subjected to WPS conditions. The advantage of the system model is that it facilitates the systematic prediction of the interrelationship and interaction between the applied loads and the misfit (or residual) stresses. The results show that tensile RS act to enhance the effects of WPS, and the WPS cycle, in itself, can act to relax the initial residual stress.