Assessing Fatigue Failure Probability for Structural Components under Deterministic and Stochastic Loading Taking into Account the Initial Crack Size Scatter

Abstract

An analytical approach that provides obtaining conservative estimates for the probability of fatigue brittle failure in the structural components of technical systems taking into account the scatter in the initial size of cracklike defects described by an exponential probabilistic distribution is presented. The operational loading is considered both as a deterministic process (with the loading cycles of constant amplitude and frequency) and as a random one (a steady-state narrowband Gaussian random loading). The crack growth kinetics is described on the basis of the modified Paris equation that takes into account the effects of the stress ratio (the loading cycle asymmetry). The parameters of the Paris law are considered as deterministic quantities. An example of the assessment of fatigue failure probability for an element of a linear pipeline section containing an axial crack on the inner surface and loaded by an internal pressure is presented. A comparative analysis of the results obtained with and without taking into account the random nature of the operational loading is performed. It is shown that neglecting the random nature of the operational loading leads to nonconservative estimates obtained for the fatigue failure probability, which can differ by an order of magnitude from calculation data taking into account the stochastic nature of the loading process. The developed method can be used in the implementation of probabilistic and risk-based approaches to providing strength, service life, and safety for technical systems under real operation conditions and in adjusting standard operating programs in terms of choosing the frequency and scope of nondestructive testing.