Crystal plasticity-guided deep learning for extrapolative prediction of cyclic behaviour

Quantifying material response under cyclic loading is crucial for fatigue life and structural reliability. Crystal Plasticity Finite Element (CPFE) methods have been widely used to simulate cyclic behaviour. However, such models require careful calibration of numerous parameters, incur substantial computational costs, and exhibit questionable predictability under cyclic loading conditions not used for calibration. Data-driven approaches also suffer from poor extrapolative and predictive capability with limited data. To address these limitations, this study proposes a crystal plasticity-guided deep learning framework combining the physical fidelity of the CPFE model with the efficiency of data-driven methods. This framework consists of a Deep Deterministic Policy Gradient (DDPG) algorithm and a Transformer model. The approach was guided by crystal plasticity behaviour, using CPFE-simulated stress as both an input to the model and a baseline for predicting experimental cyclic responses. DDPG automatically calibrated the CPFE model parameters over the first three cycles from a 100-cycle cyclic response of 316H stainless steel at a 1.2% strain range (R ratio = -1). Subsequently, Transformer learned the discrepancies between the CPFE and experimental stresses, which were then added to the CPFE-simulated stress to predict experimental cyclic responses. This approach exhibited excellent calibration performance. Furthermore, under various unseen cyclic loading conditions, the framework demonstrated high-fidelity prediction of experimental cyclic behaviour and accurately captured key cyclic deformation characteristics, including the combined isotropic–kinematic hardening and cyclic saturation. It also outperformed the CPFE model in prediction accuracy and a Transformer without crystal-plasticity guidance in extrapolative capability when trained on limited data from initial cycles.