Two-dimensional approach towards a probabilistic model of fatigue cracking of an industrial pipeline

The subject addressed in this paper concerns the constantly developing methods of determining the fatigue strength of industrial pipelines. The description of semi-elliptical crack propagation proposed in the paper applies a deterministic model based on a modified Paris' formula, which became the basis for developing a probabilistic model, being the subject of this publication. Based on a differential equation, a Fokker-Plank parabolic partial equation was derived, which describes a crack development in a probabilistic sense, at the same time taking into account deterministic model relationships. A solution of the equation is a two-dimensional normal distribution of crack propagations. A manner of estimating the distribution parameters is also stated. Having a distribution of probability with known parameters, in the case of an assumed probability of exceeding the permissible crack length, the fatigue life of model elements cut-out from industrial pipelines was estimated.