•A damage model is proposed for SAC305 based on irreversible entropy generation.•Damage evolution is more associated with strain rate rather than temperature.•Relationship between microstructure and mechanical degradation is elucidated.•Thermal energy and fatigue damage induce morphology evolution and crack formation. Low-cycle thermal-mechanical fatigue loadings induce progressive and permanent degradation of mechanical properties of lead-free solder materials, and thus reduce the fatigue life of electronic devices. In this study, damage evolution and accumulation of Sn-3.0Ag-0.5Cu (SAC305), the most successfully commercialized lead-free solder material, was investigated by performing strain-controlled fatigue tests at different temperatures (288–373 K) and strain rates (0.001–0.004 s−1). Unlike existing empirical models, a fatigue damage model was proposed based on entropy generation related to the thermodynamic nature of fatigue damage. To be intrinsic to entropy generation, the proposed model was calibrated with the peak stress degradation at different temperatures and strain rates. Our findings showed that the damage parameter is closely related to temperature and strain rate and monotonically increases from 0 to 1 during the low-cycle fatigue loading, which unveiled the fact regarding the irreversibility of the internal entropy generation. For the first time, the damage evolution is found to be more associated with the applied strain rate than the temperature. By observations using an optical microscopy, the physical damage mechanism is elucidated for SAC305 solder by correlating microstructures and damage evolutions. The evolving dendritic β-Sn phase and the surrounding Sn-Ag-Cu ternary eutectic network also explained the effects of temperature and strain rate based on the energy dissipation. Our proposed damage model reconciled the damage accumulation of SAC305 solder subjected to the low-cycle fatigue loading, which is readily adopted to predict the fatigue life of the electronic packaging structures. Display omitted