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

摘要

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.