Abstract
In this chapter, the stochastic mathematical model is developed for the thermal fatigue crack growth phenomenon in the metallic pipe of a structural component. Any stochastic fatigue crack growth model used in time-reliability analysis must include a part means for incorporating randomness in service loads, and also another one, which should include a description of statistical characteristics of crack growth under constant amplitude loadings. Time-dependent fluctuation of temperature should be correlated with time dependent fluctuation of crack growth from the deterministic crack growth law. The number of loading cycles is a discrete variable with respect to time. When time-dependent stochastic analysis is conducted, the number of loading cycles is modified into a continuous variable by introducing an average cyclic rate. By stochastic analysis of a stationary Gaussian narrow-band process, we deal with the expected value of crack growth rate and expected rate of peak crossing (or mean rate of maxima) as well, in order to assess the thermal fatigue crack growth. The uncertainties in initial crack depth and Paris’s law constants will be accounted by Monte Carlo simulation based on a properly limit state function (damage criterion). A method of crack growth assessment of linear elastic fracture mechanics (LEFM) for a stationary Gaussian narrow-band temperature fluctuation is given in this book. The model of stochastic fatigue crack growth is developed for cylindrical geometry, for which analytical solutions for temperature and associated elastic stresses were obtained in previous work. For the stochastic approach of crack growth due to random thermal fluctuations, only temporal incoherence is accounted and not any degree of spatial coherence has been taken into account.
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Radu, V. (2015). Stochastic Model for Thermal Fatigue Crack Growth. In: Stochastic Modeling of Thermal Fatigue Crack Growth. Applied Condition Monitoring, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-12877-1_4
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DOI: https://doi.org/10.1007/978-3-319-12877-1_4
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12876-4
Online ISBN: 978-3-319-12877-1
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