Failure of thermal barrier coating systems (TBC), the indispensable protector of gas turbine’s hot gas path components against high temperature oxidation, is governed by fully coupled reaction, diffusion and mechanics. Existing analytical and numerical approaches aim at predicting the growth of the thermally grown oxide (TGO) layer and the stress within the system, but cannot completely determine the system's lifespan. Crucially, it is acknowledged that relying on critical TGO thickness, depletion of Aluminium in the coat and stress is inconclusive calling for an integrated multiphysics-based modelling framework. In this work a fully coupled, thermodynamically-consistent framework has been developed. Besides reaction and diffusion, the critical role of previously-ignored diffusional creep is included in the modelling framework. Simulation results have been classified and presented in three sections. First, the accuracy of the model is validated by comparing the thickness of the TGO with previous numerical and experimental data. Second the evolution of stress in the system has been computed and compared with available literature data. Third, the evolution of damage within the system was examined by constructing relevant creep-fatigue damage indicators enabling to anticipate the life-time of the system. Finally, the degree of predictability of the model has been verified by comparing the simulated lifetime with existing literature data during uniaxial as well as thermal cycling. The results demonstrated that the modelling framework can predict damage accumulation and the lifetime of TBC system under realistic and design-based loading scenarios.