Stochastic models of fatigue crack growth

摘要

We seek to develop stochastic models with reasonable predictive ability to assist in making decisions related to the inspection, repair, and replacement of civil infrastructure subject to fatigue. It is assumed that the Paris-Erdogan equation is a suitable deterministic model of fatigue crack growth, and represents the mean tendency of a good stochastic formulation. Two models have been proposed. First is a Markovian process whose samples can reproduce satisfactorily the mean and the variance of reported test results; it can be extended to cases with high variability in loads and material properties by randomization of one parameter. Second is an arrival and growth model, based on a Poisson arrival procesB and a randomized version of the Paris-Erdogan equation; it can be useful when fatigue interacts with crack-generating processes like corrosion and freeze/thaw cycles. Due to their formulation, all these models can be directly simulated and empirical density function of the crack size at any time can be computed. Particularly interesting for maintenance purposes is the crack arrival and growth model. It is worth noting that the arrival of small cracks modifies substantially the reliability of a structure subjected to fatigue. Applications to infrastructure maintenance decisions are promising.