NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROGRAM OR FUNCTION, METHOD OF SOLUTION, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, TYPICAL RUNNING TIME, UNUSUAL FEATURES OF THE PROGRAM, RELATED AND AUXILIARY PROGRAMS, STATUS, REFERENCES, MACHINE REQUIREMENTS, LANGUAGE, OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED, OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHORS, MATERIAL, CATEGORIES

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Program name | Package id | Status | Status date |
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PRAISE-C | NESC1070/01 | Tested | 16-JAN-1991 |

Machines used:

Package ID | Orig. computer | Test computer |
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NESC1070/01 | CDC 7600 | CDC CYBER 830 |

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3. DESCRIPTION OF PROGRAM OR FUNCTION

PRAISE-C is a probabilistic fracture mechanics code used to estimate the probability of double-ended guillotine break (DEGB) in light water reactor piping due to the growth of cracks at welded joints. Pipe failures are considered to occur as the result of crack-like defects either introduced during fabrication, or that initiate after plant operation has begun, and that escape detection during inspections. PRAISE was developed to estimate the influence of earthquakes on the probability of failure at a weld joint in the primary coolant system of a pressurized water reactor. An initial hydrostatic proof test, pre-service non-destructive inspection, and periodic in-service inspection can be simulated. PRAISE treats the inter-arrival times of operating transients, such as system heatup and cooldown, either as constant or exponentially distributed according to observed or postulated rates. Leak rate and leak detection models are also included. Earthquakes of varying intensity and arbitrary occurence times can be modeled.

PRAISE-C extends the capabilities of PRAISE-B to include a tearing instability failure criterion for carbon steels (supplementing the original net section stress criterion used for austenitic materials), and an advanced probabilistic model of stress corrosion cracking in stainless steels (Type 304, Type 316NG "nuclear grade") used for BWR reactor coolant piping. The stress corrosion model is semi-empirical in nature, and is based on experimental and field data. The model considers crack initiation, including the number, time, and location of initiated cracks, in addition to the effect of stress corrosion on crack growth rates. Various phenomena are considered, including environment (i.e., coolant temperature, dissolved oxygen content, level of impurities), applied loads, residual stresses, material type, and degree of sensitization. By allowing cracks to initiate after reactor operationhas begun, the simulation is not restricted to the original "single crack" assumption. Consequently, crack linking (i.e., multiple small cracks joining to form a single large crack) is considered. Separate descriptions of welding residual stresses are included for small-, intermediate-, and large-diameter piping.

PRAISE-C can be readily modified by the user to accommodate longitudinal welds, as well as a wide range of crack growth relationships, failure criteria, and stress intensity factor formulations. The model could also be modified to include measures now being used on actual reactor piping to mitigate stress corrosion cracking, such as inductive heating stress improvement and weld overlay.

PRAISE-C is a probabilistic fracture mechanics code used to estimate the probability of double-ended guillotine break (DEGB) in light water reactor piping due to the growth of cracks at welded joints. Pipe failures are considered to occur as the result of crack-like defects either introduced during fabrication, or that initiate after plant operation has begun, and that escape detection during inspections. PRAISE was developed to estimate the influence of earthquakes on the probability of failure at a weld joint in the primary coolant system of a pressurized water reactor. An initial hydrostatic proof test, pre-service non-destructive inspection, and periodic in-service inspection can be simulated. PRAISE treats the inter-arrival times of operating transients, such as system heatup and cooldown, either as constant or exponentially distributed according to observed or postulated rates. Leak rate and leak detection models are also included. Earthquakes of varying intensity and arbitrary occurence times can be modeled.

PRAISE-C extends the capabilities of PRAISE-B to include a tearing instability failure criterion for carbon steels (supplementing the original net section stress criterion used for austenitic materials), and an advanced probabilistic model of stress corrosion cracking in stainless steels (Type 304, Type 316NG "nuclear grade") used for BWR reactor coolant piping. The stress corrosion model is semi-empirical in nature, and is based on experimental and field data. The model considers crack initiation, including the number, time, and location of initiated cracks, in addition to the effect of stress corrosion on crack growth rates. Various phenomena are considered, including environment (i.e., coolant temperature, dissolved oxygen content, level of impurities), applied loads, residual stresses, material type, and degree of sensitization. By allowing cracks to initiate after reactor operationhas begun, the simulation is not restricted to the original "single crack" assumption. Consequently, crack linking (i.e., multiple small cracks joining to form a single large crack) is considered. Separate descriptions of welding residual stresses are included for small-, intermediate-, and large-diameter piping.

PRAISE-C can be readily modified by the user to accommodate longitudinal welds, as well as a wide range of crack growth relationships, failure criteria, and stress intensity factor formulations. The model could also be modified to include measures now being used on actual reactor piping to mitigate stress corrosion cracking, such as inductive heating stress improvement and weld overlay.

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4. METHOD OF SOLUTION

Failure probabilities are estimated by applying Monte Carlo methods to simulate the life history of the selected weld joint. During each replication of the Monte Carlo simulation, PRAISE assumes that failure, defined as either a through-wall defect (leak) or a complete pipe severance (LOCA), results from the fatigue-induced growth of an as-fabricated interior surface circumferential defect (crack) assumed to be two-dimensional and semi-elliptical in shape. The initial crack size is selected by stratified sampling from probabilility distributions of crack depth and aspect ratio. Crack propagation rates are governed by a Paris-type relationship with separate cyclic RMS stress intensity factors for the depth and length. Both uniform through-the-wall and radial gradient thermal stresses are included in the calculation of the stress intensity factors.

Failure probabilities are estimated by applying Monte Carlo methods to simulate the life history of the selected weld joint. During each replication of the Monte Carlo simulation, PRAISE assumes that failure, defined as either a through-wall defect (leak) or a complete pipe severance (LOCA), results from the fatigue-induced growth of an as-fabricated interior surface circumferential defect (crack) assumed to be two-dimensional and semi-elliptical in shape. The initial crack size is selected by stratified sampling from probabilility distributions of crack depth and aspect ratio. Crack propagation rates are governed by a Paris-type relationship with separate cyclic RMS stress intensity factors for the depth and length. Both uniform through-the-wall and radial gradient thermal stresses are included in the calculation of the stress intensity factors.

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6. TYPICAL RUNNING TIME

The four sample problems require 3, 0.9, 0.9, and 1.6 CP hours, respectively, on a CDC7600. NESC executed the second sample problem in 2 CP hours on a CDC CYBER170/875.

The four sample problems require 3, 0.9, 0.9, and 1.6 CP hours, respectively, on a CDC7600. NESC executed the second sample problem in 2 CP hours on a CDC CYBER170/875.

NESC1070/01

NEA-DB executed the test cases included in this package (with a reduced number of replications) on a CYBER 830 computer. The following CPU times were required - case 1 (500 repl.): 5308 secs; case 2 (with 1000 repl.): 1992 secs; case 3 (1000 repl.): 1992 secs; case 4 (10000 repl.): 15032 secs.[ top ]

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8. RELATED AND AUXILIARY PROGRAMS

PRAISE-C is an updated release of the stratified Monte Carlo simulation code, PRAISE (Piping Reliability Analysis Including Seismic Events) and supersedes the PRAISE-B code previously distributed. PRAISE assumed that exactly one initial defect existed in the weld and that the earthquake of interest was the first earthquake experienced at the reactor. While retaining the "single defect" assumption, PRAISE-B extended the capabilities of PRAISE to include: the effect of stress corrosion on crack growth rates (no initiation), the contribution of welding residual stresses to the stress intensity factors, and the influence of high-cycle low-amplitude vibratory stresses.

PRAISE-C is an updated release of the stratified Monte Carlo simulation code, PRAISE (Piping Reliability Analysis Including Seismic Events) and supersedes the PRAISE-B code previously distributed. PRAISE assumed that exactly one initial defect existed in the weld and that the earthquake of interest was the first earthquake experienced at the reactor. While retaining the "single defect" assumption, PRAISE-B extended the capabilities of PRAISE to include: the effect of stress corrosion on crack growth rates (no initiation), the contribution of welding residual stresses to the stress intensity factors, and the influence of high-cycle low-amplitude vibratory stresses.

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10. REFERENCES

- E.Y. Lim:

Probability of Pipe Fracture in a Primary Coolant Loop of a PWR

Plant, Volume 9: PRAISE Computer Code User's Manual, Load

Combination Program Project I Final Report,

NUREG/CR-2189 (UCID-18967), August 1981.

- T. Loo and R.W. Mensing:

Probability of Pipe Failure in the Reactor Coolant Loops of

Combustion Engineering PWR Plants, Vol. 2: Pipe Failure Induced by Crack Growth,

NUREG/CR-3663 (UCRL-53500), September 1984.

- A. Brueckner-Foit, Th. Schmidt and J. Theodoropoulos:

A Comparison of the PRAISE Code and the PARIS Code for the Evalua- tion of the Failure Probability of Crack-containing Components

Preprint Nuclear Engineering & Design 110 (1989) 395-411

(Available from Elsever Science Publishers B.V. (North-Holland

Physics Publishing Division), Amsterdam.)

- E.Y. Lim:

Probability of Pipe Fracture in a Primary Coolant Loop of a PWR

Plant, Volume 9: PRAISE Computer Code User's Manual, Load

Combination Program Project I Final Report,

NUREG/CR-2189 (UCID-18967), August 1981.

- T. Loo and R.W. Mensing:

Probability of Pipe Failure in the Reactor Coolant Loops of

Combustion Engineering PWR Plants, Vol. 2: Pipe Failure Induced by Crack Growth,

NUREG/CR-3663 (UCRL-53500), September 1984.

- A. Brueckner-Foit, Th. Schmidt and J. Theodoropoulos:

A Comparison of the PRAISE Code and the PARIS Code for the Evalua- tion of the Failure Probability of Crack-containing Components

Preprint Nuclear Engineering & Design 110 (1989) 395-411

(Available from Elsever Science Publishers B.V. (North-Holland

Physics Publishing Division), Amsterdam.)

NESC1070/01, included references:

- G.S. Holman and C.K. Chou:Probability of Failure in BWR Reactor Coolant Piping

Vol. 1: Summary Report

NUREG/CR-4792 (UCID-20914) (March 1989).

- T.Lo, S.E. Bumpus, D.J. Chinn, R.W. Mensing, G.S. Holman:

Probability of Failure in BWR Reactor Coolant Piping

Vol. 2: Pipe Failure Induced by Crack Growth and Failure of

Intermediate Supports

NUREG/CR-4792 (UCID-20914) (March 1989).

- D.O. Harris, D.D. Dedhia, E.D. Eason, and S.D. Patterson:

Probability of Failure in BWR Reactor Coolant Piping

Vol. 3: Probabilistic Treatment of Stress Corrosion Cracking in

304 and 316NG BWR Piping Weldments

NUREG/CR-4792 (UCID-20914).

- D.O. Harris, E.Y. Lim, D.D. Dedhia, H.H. Woo, and C.K. Chou:

Fracture Mechanics Models Developed for Piping Reliability

Assessment in Light Water Reactors

Piping Reliability Project

NUREG/CR-2301 (UCID-15490) (June 1982).

- N. Storch et al.:

TV80LIB Graphics Library

LCSD-436 Rev. 0 (February 3, 1981).

- L. Eyberger:

PRAISE-C Tape Description and Implementation Information

NESC Note 89-46 (March 31, 1989).

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11. MACHINE REQUIREMENTS

The sample problem required 155,000 (octal) words of memory on a CDC CYBER170/875.

The sample problem required 155,000 (octal) words of memory on a CDC CYBER170/875.

NESC1070/01

To run the test cases on a CYBER 830 computer, 132712 words of main storage were required with an additional 21610 words of LCM.[ top ]

NESC1070/01

NOS2.5.1 (CYBER 830).[ top ]

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

Memory

must be preset to zero prior to execution.

PRAISE-C calls the LLNL TV80LIB graphics routines FRAME, MAPARAM, MAPBOX, MAPS, PLOTE, SETCH, SETCHM, TRACE, and UX80ID; these routines are not included. Suitable alternatives must be provided to obtain graphical output.

Memory

must be preset to zero prior to execution.

PRAISE-C calls the LLNL TV80LIB graphics routines FRAME, MAPARAM, MAPBOX, MAPS, PLOTE, SETCH, SETCHM, TRACE, and UX80ID; these routines are not included. Suitable alternatives must be provided to obtain graphical output.

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NESC1070/01

File name | File description | Records |
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NESC1070_01.001 | Information file | 71 |

NESC1070_01.002 | JCL and control information | 17 |

NESC1070_01.003 | PRAISE-C FORTRAN source | 8073 |

NESC1070_01.004 | Sample problem 1 | 17 |

NESC1070_01.005 | Sample problem 2 | 17 |

NESC1070_01.006 | Sample problem 3 | 17 |

NESC1070_01.007 | Sample problem 4 | 17 |

NESC1070_01.008 | Sample problem 1 output (by author) | 812 |

NESC1070_01.009 | Sample problem 2 output (by author) | 767 |

NESC1070_01.010 | Sample problem 3 output (by author) | 767 |

NESC1070_01.011 | Sample problem 4 output (by author) | 668 |

NESC1070_01.012 | Sample problem 1 output (NEA-DB) | 813 |

NESC1070_01.013 | Sample problem 2 output (NEA-DB) | 768 |

NESC1070_01.014 | Sample problem 3 output (NEA-DB) | 768 |

NESC1070_01.015 | Sample problem 4 output (NEA-DB) | 669 |

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- I. Deformation and Stress Distributions, Structural Analysis and Engineering Design Studies

Keywords: Monte Carlo method, fracture properties, light-water reactors, loss-of-coolant accident, pipes, probabilistic sys assessment, reliability, seismic effects, stress analysis.