Research Papers: Design and Analysis

Use of the Failure Assessment Diagram to Evaluate the Safety of the Reactor Pressure Vessel

[+] Author and Article Information
Mingya Chen

Suzhou Nuclear Power Research Institute,
No.1788, Xihuan Road,
Suzhou, Jiangsu 215004, China
e-mail: chenmingya@cgnpc.com.cn;

Feng Lu, Rongshan Wang

Suzhou Nuclear Power Research Institute,
No.1788, Xihuan Road,
Suzhou, Jiangsu 215004, China

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received May 14, 2014; final manuscript received November 17, 2014; published online February 24, 2015. Assoc. Editor: Allen C. Smith.

J. Pressure Vessel Technol 137(5), 051203 (Oct 01, 2015) (8 pages) Paper No: PVT-14-1080; doi: 10.1115/1.4029191 History: Received May 14, 2014; Revised November 17, 2014; Online February 24, 2015

Analysis of multiple failure modes is the key element of the integrity evaluation of the nuclear reactor pressure vessel (RPV). While the simple single-criterion failure code provides the guidance for structural integrity, the guidance ignores the interaction between fast fracture and plastic collapse. In this paper, the differences between the reserve factor (RF) in the R6 two-criteria failure procedure and the safety coefficient (SC) in the single-criterion failure code were compared. Based on 3D finite element (FE) analyses, the option 3 failure assessment diagram (FAD) of the beltline of the RPV was established according to the R6 basic route and alternative approaches, respectively. Also, the nonconservation of the secondary stress correction parameter ρ was reviewed. In this paper, it was shown that the effect of crack sizes on the FAD is considered to be limited, and the influence of the thermal stress on the FAD is obvious in the transition region of the failure assessment curve (FAC). The FAD only considering the mechanical load encloses the FAD considering the thermal–mechanical load for the Lr smaller than 1, but it is contrary when the Lr is bigger than 1. It is not enough to just satisfy the requirement in the IWB-3612 of the ASME code because the risk of plastic-collapse failure is ignored. And in this study, the maximum nonconservation of the fracture toughness RF is more than 7% due to the approximate value of ρ. Accordingly, the accurate method in the R6 procedure should be used in the integrity assessment of the RPV under the faulted transient.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Cravero, S., and Ruggieri, C., 2006, “Structural Integrity Analysis of Axially Cracked Pipelines Using Conventional and Constraint-Modified Failure Assessment Diagrams,” Int. J. Pressure Vessels Piping, 83, pp. 607–617. [CrossRef]
Kamaya, M., and Machida, H., 2010, “Reference Stress Method for Evaluation of Failure Assessment Curve of Cracked Pipes in Nuclear Power Plants,” Int. J. Pressure Vessels Piping, 87(1), pp. 66–73. [CrossRef]
ASME, 2010, Fracture Toughness Criteria for Protection Against Failure, ASME, New York, Sec. XI, App. G.
RCC-M, 2007, Design and Construction Rules for Mechanical Components of PWR Nuclear Islands, Subsec. Z. Annex Z G Fast Fracture Resistance, Paris, France, Sec. I.
Dowling, A. R., and Townley, C. H. A., 1975, “The Effects of Defects on Structural Failure: A Two-Criteria Approach,” Int. J. Pressure Vessels Piping, 3(2), pp. 77–107. [CrossRef]
Harrinson, R. P., Loosemore, K., and Milne, I., 1976, “Assessment of the Integrity of Structures Containing Defects,” Central Electricity Generating Board Report, UK.
R6 Revision 4, 2000, Assessment of the Integrity of Structures Containing Defects, Basic Procedures, British Energy, London, UK, Chap. I.
SINTAP, 1999, “Structural Integrity Assessment Procedure for European Industry,” Final Procedure, European Union Brite-Euram Programme, Project No. BE95-1426, Contact No. BRPR-CT95-0024.
API, 2000, American Petroleum Institute, “Recommended Practice for Fitness-for-Service,” API RP-579, Washington, DC.
Wang, G. Z., Liu, G. H., and Chen, J. H., 2001, “Effects of Precracked Specimen Geometry on Local Cleavage Fracture Stress of Low Alloy Steel,” Int. J. Fract., 112(2), pp. 183–196. [CrossRef]
Huh, N. S., and Kim, Y. J., 2001, “Effect of Nozzle Geometry on Leak-Before-Break Analysis of Pressurized Piping,” Eng. Fract. Mech., 68(16), pp. 1709–1722. [CrossRef]
International Atomic Energy Agency, 2010, “Pressurized Thermal Shock in Nuclear Power Plants: Good Practices for Assessments,” IAEA, Vienna, Austria,
Qian, G., and Niffenegger, M., 2013, “Procedures, Methods and Computer Codes for the Probabilistic Assessment of Reactor Pressure Vessels Subjected to Pressurized Thermal Shocks,” Nucl. Eng. Des., 258, pp. 35–50. [CrossRef]
Li, F., and Modarres, M., 2005, “Probabilistic Modeling for Fracture Mechanic Studies of Reactor Vessels With Characterization of Uncertainties,” Nucl. Eng. Des., 235(1), pp. 1–19. [CrossRef]
ASME, 2010, Acceptance Criteria Based on Applied Stress Intensity Factor, ASME, New York, Sec. XI IWB-3612.
R6 Revision 4, 2000, Assessment of the Integrity of Structures Containing Defects, Alternative Approaches, British Energy, London, UK, Chap. III.
Dickson, T. L., Bass, B. R., and Williams, P. T., 2000, “Validation of a Linear-Elastic Fracture Methodology for Postulated Flaws Embedded in the Wall of a Nuclear Reactor Pressure Vessel,” Proceedings of the ASME Pressure Vessel and Pipings, PVP Vol. 403, pp. 145–150.
Nanstadt, R. K., Keeney, J. A., and McCabe, D. E., 1993, “Preliminary Review of the Bases for the KIC Curve in the ASME Code,” Report No. ORNL/NRC/LTR/93—15.
Marshall, W., 1982, “An Assessment of the Integrity of PWR Pressure Vessels,” Second Report by a Study Group Under the Chairmanship of Dr W. Marshall, UKAEA.
Chen, M. Y., Lu, F., Wang, R. S., and Ren, A., 2014, “Structural Integrity Assessment of the Reactor Pressure Vessel Under the Pressurized Thermal Shock Loading,” Nucl. Eng. Des., 272, pp. 84–91. [CrossRef]
Niffenegger, M., and Reichlin, K., 2012, “The Proper Use of Thermal Expansion Coefficientsin Finite Element Calculations,” Nucl. Eng. Des., 243, pp. 356–359. [CrossRef]
Lee, T. J., Choi, J. B., Kim, Y. J., and Park, Y. W., 2002, “A Parametric Study on Pressure Temperature Limit Curve Using 3D Finite Element Analyses,” Nucl. Eng. Design., 214(1-2), pp. 73–81. [CrossRef]
Qian, X. D., Robert, H., Dodds, J., Yin, S. J., and Bass, R., 2008, “Cleavage Fracture Modeling of Pressure Vessels Under Transient Thermo-Mechanical Loading,” Eng. Fract. Mech., 75(14), pp. 4167–4189. [CrossRef]
Gong, N., Wang, G. Z., Xuan, F. Z., and Tu, S. T., 2012, “Effects of Initial Crack Location on Failure Assessment Curves in Dissimilar Metal Weld Joints in Nuclear Power Plants,” Pressure Vessel Technol., 134(6), pp. 1–7. [CrossRef]
ASME, 2010, Rules for Construction of Nuclear Facility Components,” ASME, New York, Sec. III.


Grahic Jump Location
Fig. 1

Schematic diagram of the FAD

Grahic Jump Location
Fig. 2

Flow chart of the paper

Grahic Jump Location
Fig. 4

Calculation of the RF

Grahic Jump Location
Fig. 5

Calculation the failure probability

Grahic Jump Location
Fig. 6

The inner surface crack model

Grahic Jump Location
Fig. 7

Three-dimensional mesh of the vessel containing a surface crack (a/t = 0.15)

Grahic Jump Location
Fig. 8

Temperature histories of the transients

Grahic Jump Location
Fig. 9

Plastic-collapse loads of the flawed structure

Grahic Jump Location
Fig. 11

The assessment points of the normal transient

Grahic Jump Location
Fig. 12

The assessment points of the faulted transient

Grahic Jump Location
Fig. 13

Comparation of Je and J

Grahic Jump Location
Fig. 14

The elastic hoop stress at 3600 s and 7200 s of the faulted transient

Grahic Jump Location
Fig. 15

FAD considering the influence of the thermal stress

Grahic Jump Location
Fig. 16

Comparison of the ρ parameter




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In