Probabilistic Fatigue Damage Assessment for Small Crack Growth

Fatigue and fracture are typical random phenomena due to various uncertainty sources, including material property, initial flaw and crack shape, structural configuration and geometry around crack tip, load fluctuation, and other environmental factors. As contrast to the most commonly used probabilistic fatigue growth models, which are built based on simplified fatigue crack growth law, a framework of probabilistic fracture mechanics based fatigue damage assessment methodology for small crack propagation is presented here. The proposed modeling is developed based on a comprehensive fatigue crack growth model, which accounts the effect of crack aspect ratio, stress ratio, and crack closure and retardation. Due to the complicated nature of the fatigue damage modeling adopted, a high non-linear limit state function with discontinuity resulted from physical domain jumping and overlapping are encountered. The advanced fast probability integration techniques in conjunction with response surface methodology and Monte Carlo simulation are used and the accuracy of the analysis is verified. The interface between probabilistic analysis package and the deterministic fracture mechanics analysis program is developed for the purpose of uncertainty propagation. The probability of failure of fatigue damage is computed first. The statistical characteristics of estimated fatigue life and critical crack size are obtained and presented through CDF/PDF curves. The sensitivity analysis is also performed, which provides an indication of the order of importance for the random variables considered. The results of the study have shown robustness and efficiency of the probabilistic analysis to deal with the real world challenge of uncertainty modelling, propagation, and quantification. Currently, possibility to combine the subject probabilistic damage assessment methodology with reliability updating techniques is under the investigation. The successfulness of the presented research activity will address an important issue of quantitative risk analysis for aging structures subjected to accumulative material damage.