Probabilistic modeling for reliability assessment of biaxial fatigue-induced crack growth in rail-mounted gantry main girder
Accurately assessing the probabilistic reliability of rail-mounted gantry main girder under biaxial fatigue-induced crack growth remains a critical challenge in port machinery. Traditional methods often struggle to characterize the coupled effects of multiaxial loading, accumulative plasticity, and stochastic crack propagation, leading to significant statistical deviations. In order to overcome these shortcomings, the present work introduces a new probabilistic framework that combines non‑dimensional interference theory with stochastic fracture mechanics. The methodology leverages applied mathematical techniques to model crack growth as a random process, incorporating uncertainties in initial defect distributions, material properties, and biaxial loading spectra. First, finite element simulations extract stress responses under biaxial alternating loads, while rainfall counting and Goodman’s correction derive equivalent load spectra. Second, a continuous probability distribution model for fatigue life is established by combining the material P-S-N curve with sample aggregation theory, enabling precise quantification of crack growth rates under variable amplitude stresses. Finally, the reliability of Q235 steel and 7075 aluminum alloy rail-mounted gantry main girder is evaluated through probabilistic failure assessments based on the Failure Assessment Diagram (FAD)and Weibull stress criteria. Results demonstrate that the proposed approach not only mitigates statistical biases from traditional load-equivalent analyses but also achieves a unified probabilistic characterization of fatigue life under biaxial coupling conditions. This research highlights the utility of mathematical modeling in advancing structural reliability analysis, providing a robust tool for risk-informed design and maintenance of port machinery structures.