Assessment of the probability of the fatigue fracture of structural components subjected to deterministic and stochastic loading taking into account the scatter in the initial crack size

An analytical approach which provides conservative estimates of the probability of fatigue brittle fracture of structural components of technical systems taking into account the scatter of the initial dimensions of crack-like defects described by the exponent probabilistic distribution is presented. The operational loading is considered both as deterministic (with loading cycles of constant amplitude and frequency) and random (stationary narrow-band Gaussian random loading) process. The crack growth kinetics is described by the modified Paris equation that takes into account the stress ratio effects. The parameters of the Paris law are considered deterministic values. An example of the assessment of the probability of fatigue failure of tubular structural component with an axial crack on the inner surface of a tube subjected to 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 carried out. It is shown that neglection of the random nature of the operational loading leads to non-conservative estimates of the fatigue failure probability, which may differ by an order of magnitude compared to the calculation data obtained with allowance for the stochastic nature of the loading process. The developed method can be used in the implementation of probabilistic and risk-based approaches to ensuring strength, service life and safety of technical systems in real operation conditions and in adjusting standard operation programs in terms of choosing the frequency and scope of non-destructive testing.

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