An energy-based physics–data fusion model for thermomechanical fatigue life prediction of directionally solidified superalloys

This study investigates the thermomechanical fatigue (TMF) behaviour and life prediction of directionally solidified nickel-based superalloys under different mechanical stress levels. TMF tests were first performed to obtain cyclic stress–strain responses and fatigue lives, and the associated fracture surfaces and microstructural evolution were characterised to identify the dominant damage and failure mechanisms at different stages. On this basis, a thermo-mechanically coupled TMF constitutive model incorporating anisotropic yielding and damage evolution was established. The classical Zamrik energy model was subsequently modified by embedding a nonlinear damage evolution law into the energy framework, introducing the viscoplastic energy dissipated per cycle as the driving variable, and explicitly accounting for the effects of phase angle and temperature, thereby yielding an energy-based TMF life-prediction relation. In parallel, a Transformer–LSTM network was constructed to learn a nonlinear mapping from multivariate time-series data to life-related features. Building on these developments, an energy-driven physics–data fusion life-prediction approach was proposed, in which the energy parameter predicted by the data-driven model is supplied to the modified Zamrik model for TMF life assessment. The results show that, under various loading conditions, most lives predicted by the fusion model fall within a two-fold dispersion band about the experimental data, with a generally conservative bias. The proposed approach combines high prediction accuracy with clear physical interpretability and provides a promising tool for TMF life evaluation and engineering design of nickel-based superalloy components.