Physics-informed multiscale deep learning for fatigue–creep crack growth prediction in proton exchange membranes

Proton exchange membranes (PEMs) play a vital role in PEM fuel cells, and their service life is significantly affected by crack propagation driven by the combined effects of cyclic loading and time-dependent creep. Predicting fatigue–creep crack growth remains difficult because the underlying mechanisms interact across several length scales and involve highly nonlinear behavior. To address this challenge, a physics-informed multiscale deep learning framework is developed for the prediction of fatigue–creep crack growth in proton exchange membranes. The proposed methodology combines fracture mechanics principles with a hybrid deep learning architecture, allowing physically meaningful relationships and complex data-driven patterns to be represented simultaneously. Classical fracture mechanics equations are employed to describe the individual fatigue and creep damage contributions, whereas mesoscale characteristics, including the crack-tip plastic zone size, are introduced to account for multiscale phenomena. These physical relationships are incorporated into the learning process through a physics-informed loss function, ensuring that the neural network captures crack growth behavior while remaining consistent with governing physical laws. Experimental data obtained from Nafion membranes under fatigue–creep conditions are utilized for model training and validation. Results demonstrate that embedding physical knowledge into the learning framework substantially enhances predictive accuracy and improves generalization capability compared with conventional machine learning (ML) approaches and purely empirical models. In addition, feature importance analysis highlights the respective influences of stress intensity factor range, stress ratio, hold duration, and plastic zone size on fatigue–creep interactions. Overall, the developed framework provides a robust approach for predicting fatigue–creep damage and offers deeper understanding of the multiscale degradation processes that control membrane durability in fuel cell applications.