Probabilistic models for fatigue crack growth prediction
Creators: name: Wang, Teng
Publisher: name: University of British Columbia
Year: 2023

description: Fatigue cracks pose a critical threat to the structural integrity of mechanical and structural components. In damage tolerance design philosophy, it is allowed that an in-service component has growing fatigue cracks, as long as the cracks can be reliably detected during scheduled inspections, and will not cause the failure of the component in a catastrophic manner. In this context, the accurate prediction of fatigue crack growth is crucial to ensure the reliability of in-service components while reducing maintenance costs. This thesis research aims to develop a set of probabilistic models for fatigue crack growth prediction considering a variety of uncertainty factors. First, to model the material uncertainty of individual structure, a probabilistic model for the fatigue crack growth prediction is proposed based on a closed-form solution. In this model, the stress intensity factor is related to the crack length and load condition through the finite element model. The material parameters and model error are regarded as random variables. Based on conjugate Bayesian analysis, a closed-form solution is derived to update the posterior distribution of the material parameters according to the crack growth observation. Given the posterior distribution, a modified Paris–Erdogan equation is adopted to predict the crack growth in a probabilistic view. The effectiveness of the model is validated based on the fatigue experimental data of a set of aluminum alloy specimens. Second, to consider multi-source prior knowledge, a probabilistic model for the fatigue crack growth prediction with hybrid prior is proposed. This model comprises two inference steps. In the first inference step, a set of candidate priors are input. Then, the Monte Carlo integration is adopted in the calculation of the posterior belief of each candidate prior. In the second inference step, the particle filter is extended to conduct the Bayesian inference with a hybrid prior. Numerical studies on the spur gear tooth show integrating multiple priors can increase the robustness of the fatigue crack growth prediction. Last but not least, to consider crack location randomness on a pipe component, a probabilistic model is proposed for the fatigue crack prediction based on the localization of the right and left crack tips. A real-world application of pipeline fatigue crack prediction is specified. In this model, the guided-wave sensor network is adopted for the crack tip localization where the probabilistic of detection and measurement accuracy are calculated first. Then, the finite element model is established for stress intensity factor calculation. To conduct a Monte Carlo analysis, a data-driven model is built as the surrogate of the finite element model. Finally, the crack growth is predicted based on the state space model, with the findings from the guided-wave sensor network. The research outcomes in this thesis contribute to fatigue crack growth prediction in different aspects. The probabilistic model with a closed-form solution enables an accurate and computationally efficient prediction considering the material uncertainty. The probabilistic model with a hybrid prior model increases the robustness of fatigue crack growth prediction by integrating multi-source prior. The probabilistic model considering the crack location randomness can be used for the prediction of crack growth when the crack location is random to some degree.