Ultrafine-grained aluminum alloys (UFG AA) show great potential in the design of fatigue-resistant lightweight alloys, and the methodology to assess low-cycle fatigue (LCF) life remains to be studied. In this work, a micromechanics-based LCF life prediction model is presented by conducting crystal plasticity finite element simulation (CPFEM). The fatigue indicator parameter (FIP) of maximum accumulated equivalent plastic strain energy, modulated by triaxiality, is developed to assess the material damage in the microstructure. Particularly, a new multiaxial strain parameter is proposed by considering the combined influence of the mean strain and non-proportional cyclic additional hardening effect, and then directly embedding into the cyclic J-integral. Finally, the reformulated Manson-Coffin relationship is theoretically constructed by correlating the crack tip opening displacement to the crack propagation equation. The results show the scatter fatigue life of UFG AA6061 is not only related to the inhomogeneous evolution of plastic deformation but also to the local stress state. Since the proposed approach considers both the deformation mechanisms at the micro-scale and the corresponding macroscopic responses, it can predict the LCF life of UFG AA with reasonable accuracy.

Hull structures endure severe corrosion-fatigue damage under the coupled effect of marine corrosive environments and alternating loads, posing great challenges to structural reliability assessment. Existing methods suffer from unclear multi-scale corrosion-fatigue coupling mechanisms and poor adaptability to small-sample data. To address these issues, this study proposes an intelligent corrosion-fatigue life prediction framework with a core focus on AI mathematical modeling, integrating physical prior mathematical models, Long Short-Term Memory (LSTM) residual learning mathematics, and Extended Kalman Filter (EKF) optimal estimation mathematics. First, a mathematical model of the Stress Concentration Factor (SCF) based on surface roughness parameters was established by quantifying the micro-notch effect of corroded hull surfaces, and coupled with the Paris crack growth equation to construct a physical prior mathematical model that quantitatively describes the crack propagation law. Second, an LSTM residual network mathematical model was developed to fit the nonlinear deviation between experimental logarithmic fatigue life and physical prior predictions, with the loss function defined as mean squared error for joint optimization of network weights, physical parameters, and fusion coefficients. Finally, an EKF-based online update mathematical framework was designed. Model parameters were vectorized into a dynamic state vector, and sequential small-sample data from new corrosion states were used to drive recursive updates of state equations and observation equations, realizing adaptive parameter correction. Validation on four hull structural steel datasetswith four corrosion levels shows that the proposed model relying on rigorous AI mathematical modelling achieves superior performance, which providing a reliable mathematical tool for corrosion-fatigue life assessment of hull structures.