Probabilistic analysis of off-center cracks in cylindrical structures

This paper presents a probabilistic methodology for fracture-mechanics analysis of off-center cracks in pipes subject to pure bending moment. It is based on: (1) a new analytical approximation of the J-integral; (2) statistical models of uncertainties in loads, material properties, and crack geometry; and (3) standard computational methods of structural reliability theory. The proposed analytical equations were applied to a probabilistic fracture-mechanics analysis of off-center cracks in pipes. The second-order reliability method was used to determine the probabilistic characteristics of the J-integral and failure probability based on the initiation of crack growth. Numerical examples are presented to illustrate the proposed methodology. The results show that the failure probability strongly depends on the off-center crack angle and is generally lower than that of a pipe with a symmetrically centered crack. Hence, simplifying an off-center crack by a symmetrically centered crack can produce significant conservatism in predicting failure probabilities. In addition, uncertainty in the off-center crack angle, if it exists, can increase the failure probability of pipes.

[1]  K. Young,et al.  AMERICAN SOCIETY OF MECHANICAL ENGINEERS. , 1880, Science.

[2]  R. Rackwitz,et al.  Quadratic Limit States in Structural Reliability , 1979 .

[3]  R. Rackwitz,et al.  Structural reliability under combined random load sequences , 1978 .

[4]  Y Ibrahim.  Reliability analysis of uncertain dynamic systems , 1990 .

[5]  Sharif Rahman,et al.  ELASTIC-PLASTIC ANALYSIS OF OFF-CENTER CRACKS IN CYLINDRICAL STRUCTURES , 2000 .

[6]  Gery Wilkowski,et al.  Deterministic and probabilistic evaluations for uncertainty in pipe fracture parameters in leak-before-break and in-service flaw evaluations , 1996 .

[7]  Hid N. Grouni,et al.  Methods of structural safety , 1986 .

[8]  J. Hammersley.  SIMULATION AND THE MONTE CARLO METHOD , 1982 .

[9]  A. Harbitz.  An efficient sampling method for probability of failure calculation , 1986 .

[10]  M. Hohenbichler,et al.  Improvement Of Second‐Order Reliability Estimates by Importance Sampling , 1988 .

[11]  Clifford Goodman,et al.  American Society of Mechanical Engineers , 1988 .

[12]  G. M. Wilkowski,et al.  Effects of off-centered cracks and restraint of induced bending caused by pressure on the crack-opening-area analysis of pipes☆ , 1996 .

[13]  R. Rackwitz,et al.  New light on first- and second-order reliability methods , 1987 .

[14]  Frederick W. Brust,et al.  Assessment of short through-wall circumferential cracks in pipes. Experiments and analysis: March 1990--December 1994 , 1995 .

[15]  A. M. Hasofer,et al.  Exact and Invariant Second-Moment Code Format , 1974 .

[16]  Sharif Rahman,et al.  A stochastic model for elastic-plastic fracture analysis of circumferential through-wall-cracked pipes subject to bending , 1995 .

[17]  G. M. Wilkowski,et al.  Probabilistic pipe fracture evaluations for leak-rate-detection applications , 1995 .

[18]  Gery Wilkowski,et al.  Refinement and evaluation of crack-opening-area analyses for circumferential through-wall cracks in pipes , 1995 .