Fracture Probability Integral Applied to Reactor Vessel Life Estimate1

2001 ◽  
Vol 123 (3) ◽  
pp. 346-354
Author(s):  
Shih-Jung Chang
Keyword(s):  
Fracture Toughness ◽  
Monte Carlo Simulation ◽  
Random Variables ◽  
Temperature Shift ◽  
Fracture Probability ◽  
Reactor Vessel ◽  
Vessel Steel ◽  
Radiation Induced ◽  
Probability Integral ◽  
Probability Of Fracture

The conventional method of fracture probability calculations such as that adopted by the NRC-sponsored PRAISE CODE and the FAVOR CODE developed in this laboratory are both based on Monte Carlo simulation. Heavy computations are required. A new method of fracture probability calculation is developed by direct probability integration. The preliminary version of the development was published in an earlier paper. More detailed development of the method is presented here. The present approach offers simple and expedient method to obtain numerical values of fracture probability. This method can be applied to problems as general as the method of Monte Carlo simulation. This approach also provides a clear physical picture on the meaning of the probability of fracture. Parametric studies are made in this paper to show the variation of the numerical values of the probabilities of fracture as a result of the change of the standard deviation of either fracture toughness or the radiation-induced temperature shift. Also, it is shown numerically that a limiting probability can be obtained if the standard deviation of the fracture toughness approaches zero that implies a deterministic fracture toughness. It confirms the theoretical proof shown in Eq. (11). The limiting probability is the simplistic probability of crack count used by this author where both toughness and temperature shift are assumed to be deterministic values. The general probability of fracture developed here is simply a generalization of the crack count, except the crack count is selected with the appropriate fracture toughness in the toughness distribution. The toughness for the problem considered here is then multiplied by the appropriate temperature shift in the distribution function of the temperature shift. Although the present development is based on linear fracture mechanics assumption and applied to the radiated reactor vessel steel, there is no difficulty in viewing the present development as a general formulation that is capable of handling as many random variables as required by the fracture model. The multiplicity of the integration corresponds to the number of random variables. The probability integral is applied in this paper to calculate the probability of fracture for the high flux isotope reactor (HFIR) vessel that has been weakened due to the radiation embrittlement. The random variables used here are the crack length, the fracture toughness, and the radiation-induced temperature shift that is needed in the parametric representation of the radiated vessel steel.

A Fracture Probability Integral for HFIR Accident Analysis

2004 ◽  
Author(s):  
Shih-Jung Chang
Keyword(s):  
Fracture Toughness ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Fracture Probability ◽  
Reactor Vessel ◽  
Operating Life ◽  
Vessel Steel ◽  
Ductile Brittle Transition Temperature ◽  
Probability Calculation ◽  
Probability Of Fracture

The state of the reactor vessel steel embrittlement as a result of neutron irradiation is reflected by its increase in ductile-brittle transition temperature (DBTT) in fracture toughness versus temperature curve. Higher DBTT implies a decrease in fracture toughness and an increase in the chance of vessel fracture in brittle fracture mode. The extent of degradation that the High Flux Isotope Reactor (HFIR) vessel has experienced is characterized by its probability of fracture that is defined as a probability count of the number of critical cracks in the reactor vessel based on a distribution of possible cracks. In this paper, the fracture probabilities under the accident pressure conditions against possible HFIR operating life are calculated for the safety analysis of the reactor vessel. Conventional methods of fracture probability calculation such as that adopted by the NRC-sponsored PRAISE CODE and the FAVOR CODE developed in this Laboratory are based on Monte Carlo simulation. Heavy computations are required. The present calculations are based on a new method of fracture probability calculation that was developed by applying direct probability integration [1]. This method offers simple and expedient procedure to obtain numerical values of fracture probability yet retains all possible features that a Monte Carlo simulation can possibly accomplish.

A Fracture Probability Integral for Pressure Vessel Life Estimate and Accident Analysis

2010 ◽  
Author(s):  
Shih-Jung Chang
Keyword(s):  
Fracture Toughness ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Integral Representation ◽  
Multiple Integral ◽  
Fracture Probability ◽  
Reactor Vessel ◽  
Remaining Life ◽  
Probability Integral ◽  
Probability Of Fracture

A multiple integral representation has been developed to analytically model the probability of failure of reactor vessel. The probability of fracture is a basic methodology for projecting for the life of a new vessel as well as to estimate the remaining life of an existing vessel. The integral representation for the probability of fracture calculation is based on the number count of critical cracks across the whole section of a vessel, based on a given calibrated crack distribution function, obtained by experimental examination of the vessel cross section. Multiple integral is implemented because of the degraded, or variable, fracture toughness and other factors representing the variable facture toughness. For example, the nuclear reactor vessel that is subjected to neutron radiation, will increase the reactor vessel steel brittleness. The effect of neutron irradiation can be calibrated by its increase in ductile-brittle transition temperature (DBTT) in fracture toughness versus temperature curve. Higher DBTT implies a decrease in fracture toughness and an increase in the chance of vessel fracture in brittle fracture mode. The extent of degradation that the High Flux Isotope Reactor (HFIR) vessel has experienced is characterized by its probability of fracture in this paper. The fracture probabilities under the accident pressure conditions against possible HFIR operating life are calculated for the safety analysis of the reactor vessel. Conventional numerical methods of fracture probability calculation such as that adopted by the NRC-sponsored PRAISE CODE and the FAVOR CODE developed in this Laboratory are based on Monte Carlo simulation. Heavy computations are required. The present method of Probability Integral has been used to verify numerical results of approximately 8–10 reports on HFIR remaining-life calculations by Cheverton using FAVOR CODE for the installation of HFIR new cold neutron source. The numerical result based on the method of Probability Integral confirms almost exactly as compared with that obtained by Monte Carlo Method adopted by FAVOR CODE. This Method of Probability Integral, because of its analytical structure, shows the clear physical interpretation of the fracture probability. It provides simple and expedient procedure to obtain numerical values of fracture probability. Moreover, it retains all possible features that the Monte Carlo Method of simulation can accomplish.

Use of Local Approach for Prediction of the Irradiation Effect on Fracture Toughness of Pressure Vessel Steel

2011 ◽  
Vol 465 ◽  
pp. 568-573
Author(s):  
Sergiy Kotrechko ◽  
Sergii Mamedov ◽  
Ivo Dlouhy ◽  
Vladislav Kozák
Keyword(s):  
Fracture Toughness ◽  
Pressure Vessel ◽  
Fracture Probability ◽  
Irradiation Effect ◽  
Pressure Vessel Steel ◽  
Local Approach ◽  
Vessel Steel ◽  
Reactor Pressure Vessel Steel ◽  
Probability Of Fracture ◽  
Reactor Pressure

Possibility of use of Local Approach (LA) to prediction of the effect of neutron irradiation on the fracture toughness of pressure vessel steel is discussed. The fundamental of new version of LA to fracture is briefly stated. Specific feature of this version of LA is that Weibull distribution is not used for description of distribution function of fracture probability. Probability of fracture is estimated by modeling of regularities of the crack nucleus formation and instability in polycrystal. Findings on simulation of fracture of reactor pressure vessel steel 2Cr-Mo-V in initial and irradiated states are presented.

Reconstitution of Compact Specimen for Irradiated Reactor Pressure Vessel Steel

2006 ◽  
Author(s):  
Toru Osaki ◽  
Hiroshi Matsuzawa
Keyword(s):  
Fracture Toughness ◽  
Plastic Deformation ◽  
Crack Opening ◽  
Crack Tip ◽  
Reactor Vessel ◽  
Compact Specimen ◽  
Pressure Vessel Steel ◽  
Vessel Steel ◽  
Original Size ◽  
Surveillance Specimens

Reconstitution in this paper means to constitute the original size compact specimen, which is made of the insert cut out from tested specimen and tubs welded to the insert. It is a promising technique to secure an adequate number of surveillance specimens for long-term operation of nuclear power plants. The fracture toughness of each reactor vessel of pressurized water reactors in Japan is measured periodically by 1/2T compact surveillance specimens, and is applied to assess the structural integrity of the reactor vessel under pressurized thermal shock loads. [1] This practice should be continued and enhanced if possible, after the full use of originally installed specimens, because its fracture toughness is lower than before. Reconstitution of irradiated 1/2T compact specimens to the original size was studied and demonstrated. Reconstituted specimens were composed of an irradiated material called an insert and un-irradiated tabs welded to the insert. It was demonstrated that the central part of the insert near the crack tip was not annealed by the thermal transient during welding if properly adjusted YAG laser welding was applied. Crack-tip opening and compliance before and after reconstitution were investigated by testing and analysis. Testing and analysis of un-irradiated specimens before reconstitution showed that the plastic deformation expanded to an area wider than 6 mm, the half width of the insert if it was a reconstituted specimen. The material had medium fracture toughness. The reconstituted specimen of the same material showed almost the same fracture toughness, although the weld could not be yielded as the insert, which could affect the crack opening. The crack opening was immune to the change of the deformation far from the crack tip. Correlation between J at 2.5 mm crack extension and plastic deformation width, and the effects of short time annealing of the insert far from the crack tip during welding were studied. Integrating the results, the conditions for reconstituting the 1/2T compact specimen were settled. The reconstituted specimen with irradiated insert designed to meet the conditions showed little change in fracture toughness.

Probability of Fracture and Life Extension Estimate of the High-Flux Isotope Reactor Vessel

1998 ◽  
Vol 120 (3) ◽  
pp. 290-296 ◽  
Author(s):  
S.-J. Chang
Keyword(s):  
Transition Temperature ◽  
Hydrostatic Pressure ◽  
Fracture Probability ◽  
Reactor Vessel ◽  
Numerical Results ◽  
Life Extension ◽  
Time Interval ◽  
High Flux ◽  
Vessel Steel ◽  
Pressure Test

The state of the vessel steel embrittlement as a result of neutron irradiation can be measured by its increase in ductile-brittle transition temperature (DBTT) for fracture, often denoted by RTNDT for carbon steel. This transition temperature can be calibrated by the drop-weight test and, sometimes, by the Charpy impact test. The life extension for the high-flux isotope reactor (HFIR) vessel is calculated by using the method of fracture mechanics that is incorporated with the effect of the DBTT change. The failure probability of the HFIR vessel is limited as the life of the vessel by the reactor core melt probability of 10−4. The operating safety of the reactor is ensured by periodic hydrostatic pressure test (hydrotest). The hydrotest is performed in order to determine a safe vessel static pressure. The fracture probability as a result of the hydrostatic pressure test is calculated and is used to determine the life of the vessel. Failure to perform hydrotest imposes the limit on the life of the vessel. The conventional method of fracture probability calculations such as that used by the NRC-sponsored PRAISE CODE and the FAVOR CODE developed in this Laboratory are based on the Monte Carlo simulation. Heavy computations are required. An alternative method of fracture probability calculation by direct probability integration is developed in this paper. The present approach offers simple and expedient ways to obtain numerical results without losing any generality. This approach provides a clear analytical expression on the physical random variables to be integrated, yet requires much less computation time. In this paper, numerical results on 1) the probability of vessel fracture, 2) the hydrotest time interval, and 3) the hydrotest pressure as a result of the DBTT increase are obtained. Limiting the probabilities of the vessel fracture as a result of hydrotest to 10−4 implies that the reactor vessel life can be extended up to 50 EFPY (100 MW) with the minimum vessel operating temperature equal to 85°F.

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