Probabilistic Fracture Mechanics for Analysis of Longitudinal Cracks in Pipes Under Internal Pressure

• Published in: Journal of failure analysis and prevention 2018-12, Vol.18 (6), p.1643-1651
• Main Authors: Mechab, Belaïd, Chioukh, Nadji, Mechab, Boubaker, Serier, Boualem
• Format: Article
• Language: English
• Subjects: Characterization and Evaluation of Materials; Chemistry and Materials Science; Classical Mechanics; Computer simulation; Corrosion and Coatings; Distribution functions; Elastic analysis; Failure analysis; Finite element method; Fracture mechanics; Internal pressure; J integral; Material properties; Materials Science; Monte Carlo simulation; Pipes; Probabilistic methods; Probability density functions; Quality Control; Reliability; Reliability analysis; Reliability aspects; Reliability engineering; Safety and Risk; Shape functions; Solid Mechanics; Statistical analysis; Structural reliability; Technical Article > -Peer-Reviewed; Three dimensional analysis; Tribology; Uncertainty analysis; Yield stress
• ISSN: 1547-7029; 1728-5674; 1864-1245
• DOI: 10.1007/s11668-018-0564-8

In this paper, we present a probabilistic fracture mechanics methodology to analyze elastic and elastic–plastic fracture of semi-elliptical longitudinal cracks in pipes under internal pressure. Numerical results are acquired using three-dimensional finite element simulations. Analytical expressions are proposed with unknown coefficients obtained by nonlinear fitting to the numerical results. For the elastic case, results of the shape function using the newly proposed expression are found to be in a good agreement with those found in the literature. In the elastic–plastic case, estimates of the J -integral are presented for various ratios including crack depth to pipe thickness ( a / t ), reference stress to material yield stress ( σ ref / σ y ) and mean pipe radius to its thickness ( R m / t ). It is found that the range of applicability of the proposed expressions is extended even beyond those found in the literature. Finally, failure probability is accessed by a statistical analysis for uncertainties in loads and material properties, and structural reliability. The probability density function is estimated by the Monte Carlo Method. It is shown from the present results that the crack size is an important factor influencing the distribution function of ( J / Je ), failure and reliability rates.