A probabilistic approach to the description of the crack kinetics and fatigue failure of structural components with allowance for the effect of crack retardation after overloads

Abstract

A probabilistic approach to assessing fatigue strength and cyclic life based on Wheeler’s model is presented. The approach provides the possibility of estimating the probability of failure of the structural component under consideration, with allowance for the effect of crack retardation after the overload. The initial crack size, the parameters of the Paris equation, and the exponent of the crack retardation power function are assumed random parameters. The kinetics of a fatigue crack is described by cycle-by-cycle integration of the Paris equation written in finite differences. The probabilistic estimate is performed using the Monte Carlo statistical simulation method by repeatedly solving the Cauchy problem for various combinations of the values of random model parameters that are generated under the adopted laws of the probability distributions of those parameters. The probabilistic distributions of random parameters are selected proceeding from the level of the uncertainty of the problem using available statistical data without taking into accounting for data on the actual state of a particular structural component in real operation conditions. A computer code in Matlab environment has been developed for statistical description of the fatigue crack growth in structural components which allows accounting for the effect of crack retardation. An example of assessing the probability of the fatigue failure of a pipeline component with a longitudinal crack on the inner surface loaded by the internal pressure which varies according to a periodic law with a constant amplitude is presented for single tensile overload of the pipeline component. The dependencies of the fatigue failure probability on the number of loading cycles for various combinations of model parameters were obtained. The sensitivity of the fatigue failure probability under a given number of loading cycles to changes of the values of structural parameters was assessed.