Estimation of C*-Integral for Defective Components with General Creep-Deformation Behaviors

일반 크리프 거동을 고려한 균열 구조물 C*-적분 예측

  • Published : 2002.05.01


For assessing significance of a defect in a component operating at high (creeping) temperatures, accurate estimation of fracture mechanics parameter, $C^{*}$-integral, is essential. Although the J estimation equation in the GE/EPRl handbook can be used to estimate the $C^{*}$-integral when the creep -deformation behavior can be characterized by the power law creep, such power law creep behavior is a very poor approximation for typical creep behaviors of most materials. Accordingly there can be a significant error in the $C^{*}$-integral. To overcome problems associated with GE/EPRl approach, the reference stress approach has been proposed, but the results can be sometimes unduly conservative. In this paper, a new method to estimate the $C^{*}$-integral for deflective components is proposed. This method improves the accuracy of the reference stress approach significantly. The proposed calculations are then validated against elastic -creep finite element (FE) analyses for four different cracked geometries following various creep -deformation constitutive laws. Comparison of the FE $C^{*}$-integral values with those calculated from the proposed method shows good agreements.greements.


$C^{*}$-Integral;Creep;Generalized Creep Law;Reference Stress Approach;Enhanced Reference Stress Approach


  1. Tada, H., Paris, P.C. and Irwin, G.R., 1985, 'The Stress Analysis of Cracks Handbook,' Del Research Corporation, St Louis, MI
  2. Miller, A.G. and Ainsworth, R.A., 1989, 'Consistency of Numerical Results for Power-Law Hardening Materials and the Accuracy of the Reference Stress Approximation for J,' Engineering Fracture Mechanics, Vol. 32, pp. 237-247
  3. ABAQUS Standard/User's Manual, Version 5.8, 1998, Hibbit Karlsson & Sorensen, Inc., Pawtucket, RI. USA
  4. 허남수, 김윤재, 김영진, 2001,' 원자력 배관의 파단전누설 해석을 위한 개선된 참조응력법의 수치해석적 검증,' 대한기계학회논문집 A권, 제 25권, 제 4호, pp. 741-747
  5. Hamm, C.D.(ed.), 1999, R66 AGR Materials Data Handbook, Issue 5
  6. RCC-MR, 1985, Design and Construction Rules for Mechanical Components of FBR Nuclear Islands, AFCEN, Paris
  7. Kim, Y.J., 2000, 'Evaluation of Time Dependent Contour Integrals (J and C) in Creep: Comparison of ABAQUS and BERSAFE Results, EPD/GEN/REP/0500/99, Issue 1, British Energy Generation Ltd.
  8. Miller, A.G., 1988, 'Review of Limit Loads of Structures Containing Defects,' International Journal of Pressure Vessels and Piping, Vol. 32, pp. 191-327
  9. 김윤재, 허남수, 김영진, 2001,' 원주방향 관통균열이 존재하는 배관의 J-적분 및 COD 계산을 위한 새로운 공학적 계산식,' 대한기계학회논문집 A권, 제 25 권, 제 3 호, pp. 548-553
  10. R6: Assessment of the Integrity of Structures Containing Defects, Revision3, Amendment 10, 1999, British Energy
  11. Kim, Y.J., 2001, 'Contour Integral Calculation for Generalised Creep Laws within ABAQUS,' International Journal of Pressure Vessels and Piping, Vol. 78, pp. 661-666
  12. R5: Assessment Procedure for the High Temperature Responses of Structures, Issue 2, 1998, British Energy
  13. Kumar, V., German, M.D. and Shih, C.F., 1981, 'An Engineering Approach for Elastic-Plastic Fracture Analysis,' EPRI Final Report to NP 1931
  14. Kumar, V., German, M.D., Wilkening, W.W., Andrews, W.R., deLorenzi, H.G and Mowbray, D.F., 1982, 'Estimation Technique for the Prediction of Elastic-Plastic Fracture of Structural Components of Nuclear Systems,' Combined 5th and 6th Semi-annual Report, EPRI RP-1237-1
  15. Kumar, V and German, M.D., 1988, 'Elastic-Plastic Fracture Analysis of Through-Wall and Surface Flaws in Cylinders,' EPRI Report to NP-5596
  16. Ainsworth, R.A., 1984, 'The Assessment of Defects in Structures of Strain Hardening Materials,' Engineering Fracture Mechanics, Vol. 19, pp. 633-642
  17. Riedel, H., 1987, Fracture at High Temperature, Springer-Verlag, Berlin
  18. Webster, G..A. and Ainsworth, R.A., 1994, High Temperature Component Life Assessment, Chapman & Hall, London

Cited by

  1. Estimation of C(t) -Integral Under Transient Creep Conditions for a Cracked Pipe Subjected to Combined Mechanical and Thermal Loads Depending on Loading Conditions vol.35, pp.6, 2011,