Approximation Method for the Calculation of Stress Intensity Factors for the Semi-elliptical Surface Flaws on Thin-Walled Cylinder

  • Jang Chang-Heui (Department of Nuclear and Quantum Engineering, Korea Advanced Institute of Science and Technology)
  • Published : 2006.03.01


A simple approximation method for the stress intensity factor at the tip of the axial semielliptical cracks on the cylindrical vessel is developed. The approximation methods, incorporated in VINTIN (Vessel INTegrity analysis-INner flaws), utilizes the influence coefficients to calculate the stress intensity factor at the crack tip. This method has been compared with other solution methods including 3-D finite element analysis for internal pressure, cooldown, and pressurized thermal shock loading conditions. For these, 3-D finite-element analyses are performed to obtain the stress intensity factors for various surface cracks with t/R=0.1. The approximation solutions are within $\pm2.5%$ of the those of finite element analysis using symmetric model of one-forth of a vessel under pressure loading, and 1-3% higher under pressurized thermal shock condition. The analysis results confirm that the approximation method provides sufficiently accurate stress intensity factor values for the axial semi-elliptical flaws on the surface of the reactor pressure vessel.


  1. ASME, 1995, Analysis of Flaws, ASME B&PV Code Sec. XI, App. A
  2. Dickson, T. L., 1994, FAVOR : A Fracture Analysis Code For Nuclear Reactor Pressure Vessels, Release 9401, ORNL/NRC/LTR/94/1
  3. Jang, C. H. et al., 2000, VINTlN : Vessel Integrity Analysis Inner Flaws, KEPRI Report TM.00NP 10.P2000.350
  4. Jang, C. H., Moonn, H. R., Jeong, I. S. and Hong, S. Y., 2001a, 'Development of The Improved Probabilistic Fracture Mechanics Analysis Code : VINTlN,' In 2001 KNS Spring Meeting, Cheju, Korea
  5. Jang, C. H., Moonn, H. R. and Jeong, I. S., 2001b, 'Stress Intensity Factor Calculation For The Semi-Elliptical Surface Flaws On The Thin-Wall Cylinder Using Influence Coefficients,' In 2001 KSME Spring Meeting, Cheju, Korea
  6. Keeney, J. A. and Bryson, J. W., 1995, 'Stress Intensity Factor Influence Coefficients For Semi-elliptical Inner Surface Flaws In Clad Pressure Vessels,' Fracture Mechanics, Vol. 26, pp. 430-443
  7. Kim, Y. J., Kim, H. G. and Im, S., 2001, 'Mode Decomposition of Three-Dimensional Mixed-Mode Cracks Via Two-State Integrals,' Int. J. Solids and Structures, Vol. 38, pp. 6405-6426
  8. Moonn, H. R. and Jang, C. H., 2001, 'Comparison of Stress Intensity Factors For Longitudinal Semi-Elliptical Surface Cracks In Cylindrical Pressure Vessels,' In 2001 KSME Spring Meeting, Cheju, Korea
  9. Raju, I. S. and Newman, J. C., 1982, 'Stress Intensity For Internal Surface Cracks In Cylindrical Vessels,' ASME Journal of Pressure Vessel Technology, Vol. 104, pp. 293-298
  10. Shih, C. F., Moran, B. and Nakamura, T., 1986, 'Energy Release Rate Along A Three-Dimensional Crack Front In Thermally Stressed Body,' Int. J. of Fracture, Vol. 30, pp. 79 -102
  11. Simonen, F. A. et al., 1986, VISA-II A Computer Code For Predicting The Probability of Reactor Vessel Failure, NUREG/CR-4486
  12. Timoshenko, S., 1940, Theory of Plate and Shells, New York : McGraw-Hill
  13. USNRC, 1982, NRC Staff Evaluation of Pressurized Thermal Shock, SECY82-465
  14. Wang, X. and Lambert, S. B., 1996, 'Stress Intensity Factors And Weight Functions For Longitudinal Semi-Elliptical Surface Cracks In Thin Pipes,' International Journal of Pressure Vessel & Piping, Vol. 65, pp. 75-87
  15. Wu, X. and Carlsson, A. J., 1991, Weight Functions and Stress Intensity Factor Solutions, Oxford : Pergamon Press