A probabilistic approach to leak-before-break in CANDU pressure tubes

The leak-before-break (LBB) assessment of pressure tubes is intended to demonstrate that in the event of through-wall cracking of the tube, there will be sufficient time followed by the leak detection, for a controlled shutdown of the reactor prior to the rupture of the pressure tube. CSA Standard N285.8 (2005, “Technical Requirements for In-Service Evaluation of Zirconium Alloy Pressure Tubes in CANDU Reactors,” Canadian Standards Association) has specified deterministic and probabilistic methods for LBB assessment. Although the deterministic method is simple, the associated degree of conservatism is not quantified and it does not provide a risk-informed basis for the fitness for service assessment. On the other hand, full probabilistic methods based on simulations require excessive amount of information and computation time, making them impractical for routine LBB assessment work. This paper presents an innovative, semiprobabilistic method that bridges the gap between a simple deterministic analysis and complex simulations. In the proposed method, a deterministic criterion of CSA Standard N285.8 is calibrated to specified target probabilities of pressure tube rupture based on the concept of partial factors. This paper also highlights the conservatism associated with the current CSA Standard. The main advantage of the proposed approach is that it retains the simplicity of the deterministic method, yet it provides a practical, risk-informed basis for LBB assessment.

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Probabilistic Leak Before Break

Volume 6B: Materials and Fabrication ◽

10.1115/pvp2018-84056 ◽

2018 ◽

Author(s):

L. Stefanini ◽

F. J. Blom

Keyword(s):

Fracture Toughness ◽

Yield Stress ◽

Master Curve ◽

Structural Integrity ◽

Probabilistic Approach ◽

Leakage Rate ◽

Critical Crack ◽

Critical Crack Length ◽

Integrity Assessment ◽

Leak Before Break

In this study a probabilistic Leak-Before-Break (LBB) analysis was carried out based on the R6 FAD Option 1 assessment method. The method uses the material fracture toughness and yield stress in order to determine, deterministically, a Critical Crack Length (CCL) and a Leakage Rate (LR) through a crack. In order to define the fracture toughness of the material, the Master Curve approach was used accordingly to BS7910:2013 Annex J. Initially, deterministic analyses were carried out and the fracture toughness and yield stress were set to 190 MPa√m and 158 MPa, respectively. In order to implement a probabilistic approach, the yield stress and fracture toughness were introduced as stochastic parameter. The Fracture toughness was generated using a Weibull distribution to match the Master Curve. The distribution was built such that 190 MPa√m represents the 5% probability fracture toughness. The Yield stress (0.2% proof strength) was generated using a normal distribution with standard deviation 10.35 MPa such that the average value was 175 MPa and the lower bound (5% of probability of occurrence) was 158 MPa. The choice of building the distribution as above mentioned was justified by the fact that in structural integrity assessment the lower 5% is generally used for material parameters. Thus, once a Detectable Leakage Rate (DLR) was determined, it was possible to assign an implicit probability of failure to the deterministic case. The calculations were then extended by using several LR formulas. The calculations were carried out making use of the probabilistic software RAP++ coupled to MATLAB. The probabilities of failure were calculated with regard to a postulated DLR and a DLRSF corrected with a safety factor of 10. The probabilities of failure for the DLRSF were proved to be 9 to 15 times higher than for the postulated DLR case, which leads to the opportunity of conservatism reduction.

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The role of leak-before-break in assessments of flaws detected in CANDU pressure tubes

International Journal of Pressure Vessels and Piping ◽

10.1016/0308-0161(90)90090-5 ◽

1990 ◽

Vol 43 (1-3) ◽

pp. 23-37 ◽

Cited By ~ 6

Author(s):

H.W. Wong ◽

V.K. Bajaj ◽

G.D. Moan ◽

M. Huterer ◽

C.O. Poidevin

Keyword(s):

Pressure Tubes ◽

Leak Before Break

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A Probabilistic Approach to Leak Before Break Demonstration

Volume 6: Materials and Fabrication, Parts A and B ◽

10.1115/pvp2008-61207 ◽

2008 ◽

Author(s):

Peter Dillstro¨m

Keyword(s):

Residual Stresses ◽

Conditional Probability ◽

Flow Rate ◽

Probabilistic Approach ◽

Fracture Probability ◽

Center Crack ◽

Diameter Pipe ◽

Probability Of Fracture ◽

Leak Before Break ◽

Crack Position

Recently, the Swedish Nuclear Power Inspectorate has developed guidelines on how to demonstrate the existence of Leak Before Break (LBB). The guidelines define the steps that must be fulfilled to get a conservative assessment of LBB acceptability. In this paper, a complementary probabilistic LBB approach is defined and implemented into the software ProLBB. The main conclusions, from the study presented in this paper, are summarized below. • The probabilistic approach developed in this study was applied to different piping systems in both Boiler Water and Pressurised Water Reactors. The present study shows that the conditional probability of fracture is in general small for the larger diameter pipes when evaluated as function of leak flow rate. However, when evaluated as function of fraction of crack length around the circumference, then the larger diameter pipes will belong to the ones with the highest conditional fracture probabilities. • The total failure probability, corresponding to the product between the leak probability and the conditional fracture probability, will be very small for all pipe geometries. • The influence from an off-center crack position on the conditional probability of fracture is not important when assuming a uniform distribution. This is because the result is dominated totally by the center crack position. However, if the crack position is treated as a deterministic parameter, the conditional probability of fracture is strongly dependent on the position of the crack, especially for large off-center cracks. • The weld residual stresses have quite an impact on the resulting fracture probabilities, especially for smaller cracks. The influence from the weld residual stresses on the calculation of leakage flow rate is largest for a thin-walled pipe. The influence from the weld residual stresses on the calculation of fracture probability is largest for one of the thick-walled pipes. • In the formal sensitivity analyses, it is shown that the standard deviation of the yield strength has the strongest influence on the conditional fracture probability. • This study has given an indication of the relation between the deterministic LBB-criteria and the corresponding conditional fracture probability. As expected, it is easier to fulfil the deterministic LBB-margins for a large diameter pipe compared to a small diameter pipe.

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Leak-before-break experiments on heat-treated Zr-2·5 wt% Nb pressure tubes

International Journal of Pressure Vessels and Piping ◽

10.1016/0308-0161(90)90091-u ◽

1990 ◽

Vol 43 (1-3) ◽

pp. 39-56 ◽

Cited By ~ 6

Author(s):

M.H. Koike ◽

T. Takahashi ◽

H. Baba

Keyword(s):

Heat Treated ◽

Pressure Tubes ◽

Leak Before Break

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Pilot Study for Uncertainty Analysis in Probabilistic Fitness-for-Service Evaluations of Zr-2.5Nb Pressure Tubes: Identification of Influential Variables

Volume 1B: Codes and Standards ◽

10.1115/pvp2018-85010 ◽

2018 ◽

Author(s):

Christopher Manu ◽

Suresh Datla ◽

Leonid Gutkin

Keyword(s):

Sensitivity Analysis ◽

Pilot Study ◽

Uncertainty Analysis ◽

Pressure Tube ◽

Output Variable ◽

Probabilistic Evaluation ◽

Pressure Tubes ◽

Relative Change ◽

Leak Before Break

Canadian Nuclear Standard CSA N285.8, “Technical requirements for in-service evaluation of zirconium alloy pressure tubes in CANDU® reactors”(1), permits the use of probabilistic methods when performing assessments of the reactor core. A non-mandatory annex has been proposed for inclusion in the CSA Standard N285.8, to provide guidelines for performing uncertainty analysis in probabilistic fitness-for-service evaluations within the scope of this Standard, such as the probabilistic evaluation of leak-before-break. The proposed annex outlines the general approach to uncertainty analysis as being comprised of the following major activities: identification of influential variables, characterization of uncertainties in influential variables, and subsequent propagation of these uncertainties through the evaluation framework or code. The application of the proposed guidelines for uncertainty analysis was exercised by performing a pilot study for one of the evaluations within the scope of the CSA Standard N285.8, the probabilistic evaluation of leak-before-break based on a postulated through-wall crack. The pilot study was performed for a representative CANDU reactor unit using the recently developed computer code P-LBB that complies with requirements of Canadian Nuclear Standard N286.7 for quality assurance of analytical, scientific, and design computer programs for nuclear power plants. This paper discusses the approach used and the results obtained in the first stage of this pilot study, the identification of influential variables. The proposed annex considers three approaches for identifying influential variables, which may be used separately or in combination: analysis of probabilistic evaluation outputs, sensitivity analysis and expert judgment. In this pilot study, local sensitivity analysis was used to identify and rank the influential variables. For each input variable in the probabilistic evaluation of leak-before-break, the local sensitivity coefficient was determined as the relative change in the output variable associated with a relative change of a small magnitude in the input variable. Each input variable was also varied across a large range to assess the linearity of the relationship between the input variable and the output variable. All relevant input variables were ranked according to the absolute value of their sensitivity coefficients to identify the influential variables. On the basis of the results obtained, the pressure tube wall thickness was found to be the most influential variable in the probabilistic evaluation of leak-before-break based on a postulated through-wall crack, followed by the fracture toughness of Zr-2.5Nb pressure tube material and the pressure tube inner diameter. The results obtained at this stage were then used at the second stage of this pilot study, the uncertainty characterization of influential variables, as discussed in the companion paper PVP2018-85011.

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VERLIFE: Unified Procedure for Lifetime Assessment of Components and Piping in WWER NPPs During Operation—Updating and Further Development

Volume 1: Codes and Standards ◽

10.1115/pvp2009-77392 ◽

2009 ◽

Author(s):

Milan Brumovsky

Keyword(s):

European Union ◽

Probabilistic Approach ◽

Pressure Vessels ◽

The European Union ◽

Break Zone ◽

Fatigue Evaluation ◽

Design And Manufacture ◽

Further Development ◽

Leak Before Break ◽

Reactor Pressure

VERLIFE – “Unified Procedure for Lifetime Assessment of Components and Piping in WWER NPPs during Operation” was developed within the 5th Framework Program of the European Union in 2003 and later upgraded within the 6th Framework Program project “COVERS – Safety of WWER NPPs” of the European Union in 2008. This Procedure has to fill the gap in original Soviet/Russian Codes and Rules for WWER type NPPs, as these codes were developed only for design and manufacture and were not changed since their second edition in 1989. VERLIFE Procedure is based on these Russian codes but incorporates also new developments in research, mainly in fracture mechanics, and also some principal approaches used in PWR codes. To assure that VERLIFE Procedure will remain a living document, new 3-year IAEA project (in close co-operation with another project 6th Framework Program of the European Union “NULIFE – Plant Life Management of NPPs”) has started in 2009. Within this project, upgrading/updating of the VERLIFE procedure is prepared together with the extension by following procedures: - Lifetime of reactor pressure vessel internals. - Leak-before-break concept for WWER NPPs. - No-break-zone for WWER NPPs. - Probabilistic approach for failure and lifetime assessment of WWER reactor pressure vessels and primary piping (including Risk-informed ISI). - Thermal fatigue evaluation. Final document, after its approval by expert groups of the IAEA and NULIFE, will be issued as “IAEA Guidelines for Integrity and Lifetime Assessment of Components and Piping in WWER NPPs”. The paper will describe these main principles and also future plans.

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Exploratory Analysis to Estimate Axial Fracture Toughness for Zr-2.5Nb Pressure Tubes Using Test Data From Small Curved Compact Specimens

Volume 1A: Codes and Standards ◽

10.1115/pvp2017-66116 ◽

2017 ◽

Author(s):

Steven X. Xu ◽

Kim Wallin

Keyword(s):

Fracture Toughness ◽

Prediction Model ◽

Test Data ◽

Late Life ◽

Exploratory Analysis ◽

Pressure Tube ◽

Life Conditions ◽

Pressure Tubes ◽

Axial Fracture ◽

Leak Before Break

Zr-2.5Nb pressure tubes are in-core, primary coolant containment of CANDU(1) nuclear reactors. Technical requirements for in-service evaluation of pressure tubes are provided in the Canadian Standards Associate (CSA) N285.8. These requirements include the evaluation of service conditions for protection against fracture of operating pressure tubes and demonstration of leak-before-break. Axial fracture toughness for pressure tubes is a key input in the evaluation of fracture protection and leak-before-break. The 2015 Edition of CSA N285.8 provides a pressure tube axial fracture toughness prediction model that is applicable to pressure tubes late life conditions. The fracture toughness prediction model in CSA N285.8-15 is based on rising pressure burst tests performed on pressure tube sections with axial cracks under simulated pressure tube late life conditions. Due to the associated high cost of testing and high consumption of pressure tube material, it is not practical to perform a large number of fracture toughness burst tests. On the other hand, more fracture toughness data is required to improve the existing pressure tube axial fracture toughness prediction model. There is strong motivation to estimate pressure tube axial fracture toughness using test data from small specimens. The estimated pressure tube fracture toughness using test data from small specimens can fill the gaps in the burst test toughness data, as well as provide information on material variability and data scatter. Against this background, an exploratory analysis of estimating pressure tube axial fracture toughness using test data from small curved compact specimens has been performed and is described in this paper. The estimated values of pressure tube axial fracture toughness using the test data from small curved compact specimens are compared with the measured toughness from burst tests of pressure tube sections with axial cracks to check the feasibility of this approach.

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