Effect of Reference Loads on Fracture Mechanics Analysis of Surface Cracked Pipe Based on Reference Stress Method

참조응력법에 입각한 표면균열배관의 파괴역학 해석 -참조하중의 영향 분석-

  • Published : 2004.05.01


To investigate relevance of the definition of the reference stress to estimate J and $C^{*}$ for surface crack problems, this paper compares FE J and $C^{*}$ results for surface cracked pipes with those estimated according to the reference stress approach using various definitions of the reference stress. Pipes with part circumferential inner surface crack and finite internal axial crack are considered, subject to internal pressure and global bending. The crack depth and aspect ratio are systematically varied. The reference stress is defined in four different ways using (i) the local limit load, (ii) the global limit load, (iii) the global limit load determined from the FE limit analysis, and (iv) the optimized reference load. It is found that the reference stress based on the local limit load gives overall excessively conservative estimates of J and $^{*}$. Use of the global limit load clearly reduces the conservatism, compared to that of the local limit load, although it can provide sometimes non-conservative estimates of J and $^{*}$. The use of the FE global limit load gives overall non-conservative estimates of J and $^{*}$. The reference stress based on the optimised reference load gives overall accurate estimates of J and $^{*}$, compared to other definitions of the reference stress. Based on the present finding, general guidance on the choice of the reference stress for surface crack problems is given.


Reference Stress Method;Surface Cracked Pipe;J-integral;C$^{*}$-integral


  1. Webster, G.A. and Ainsworth, R.A., 1994, 'High Temperature Component Life Assessment,' Chapman & Hall
  2. Miller, A.G., 1988, 'Review of Limit Loads of Structures Containing Defects,' International Journal of Pressure Vessels & Piping, Vol. 32, pp. 191-327
  3. 2001, 'ABAQUS Version 6.2-1. User's manual,' Hibbitt,Karlson & Sorensen, Inc.
  4. Lei, Y., 2001, 'J-Integral and Limit Load Analysis of a Semi-Elliptical Surface Crack in a Plate under Combined Tensile and Bending Load, Part II-Bending Load,' Report E/REP/ATEC/0024/GEN/01, British Energy Generation Ltd.
  5. Kim, Y.J., Kim, J.S., Park, Y.J. and Kim, Y.J., 2004, 'Elastic-Plastic Fracture Mechanics Method for Finite Internal Axial Surface Cracks in Pipes,' Engineering Fracture Mechanics, Vol. 71, pp. 925-944
  6. Kim, Y.J., Kim, J.S., Lee, Y.Z. and Kim, Y.J., 2002, 'Non-Linear Fracture Mechanics Analyses of Part Circumferential Surface Cracked Pipes,' International Journal of Fracture, Vol. 116(4), pp. 347-375
  7. Shim, D.J., Kim, Y.J., Kim, Y.J., Hwang, S.S. and Kim, J.S., 2003, 'Plastic Limit Load Solutions for Circumferential Surface Cracked Cylinders Under Combined Loading,' Transaction of the KSME (A), Vol. 27, No. 9, pp. 1469-1476
  8. Lei, Y. and Budden, P.J., 2002, 'J and Limit Load Analysis of Semi-Elliptical Surface Cracks in Plates Under Tension,' Proc. ECF 14- Fracture Mechanics beyond 2000, EMAS Publishing, pp. 341-348
  9. Shim, D.J., Huh, N.S., Kim, Y.J. and Kim, Y.J., 2003, 'Plastic Limit Pressure for Cracked Pipes Using Finite Element Limit Analyses,' Transaction of the KSME (A), Vol. 27, No. 1, pp. 26-33
  10. 1999, SINTAP Final Procedure, Brite Euram Project, BE95-1426
  11. Miller, A.G., 1988, 'J Estimation for Surface Defects; Further Results,' CEGB Memorandum TPRD/B/SM/SF95/M88, Central Electrical Generating Board
  12. Kim, Y.J., 2000, 'Reference Stress Based J Estimation for Surface Crack Assessments: Global Versus Local Limit Loads,' British Energy Report, E/REP/GEN/0010/00, British Energy Generation Ltd.
  13. 2001, 'R6 : Assessment of the Integrity of Structures Containing Defects,' Revision 4, British Energy Generation Ltd.
  14. 2000, 'API 579 : Recommended Practice for Fitness-for-Service,' First Edition, American Petroleum Institute
  15. Ainsworth, R.A., 1984, 'The Assessment of Defects in Structures of Strain Hardening Materials,' Engineering Fracture Mechanics, Vol. 19, pp. 633-642