Analytical and numerical assessments of probabilities of fatigue fracture of pipeline components under internal pressure

Abstract

The paper presents analytical and numerical approaches to assessing the probability of failure of structural components of technical systems subjected to cyclic loading. The kinetics of the crack is described by the modified Paris equation. The analytical solution is based on the inverse extrapolation of the critical crack depth. In this case, the only probabilistic parameter is considered to be the initial crack depth, which is assumed to be distributed according to an exponential law. The numerical solution uses the Monte-Carlo method. The initial crack depth, fracture toughness of the structural material, and parameters C and m of the Paris equation are taken as probabilistic parameters. For the statistical description of the process of fatigue crack growth in structural components, a computer code was developed in the Matlab environment, which allows using appropriate random number generators to simulate various laws of distribution of random parameters, including the laws of uniform density, exponential law, normal law, Weibull's law, etc. An example of analytical and numerical calculation of the probability of fatigue failure of a pipeline component containing an axial crack on the inner surface and loaded with internal pressure is given. Comparison of the obtained results of analytical and numerical solutions allows us to conclude that an approximate analytical estimate of the fracture probability can be used for preliminary calculations at the design stage of structural components, as well as for obtaining a prior estimates of the fracture probability when implementing Bayesian updating procedures for specifying the fracture probability and determining the frequency of technical inspections of the condition of the components under consideration as part of the implementation of risk-oriented approaches to ensuring their strength and safety.