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| Phase Field Model of Graded Materials with Residual Stress Under Thermomechanical Load |
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Abstract This study develops a phase-field fracture model to investigate the cracking behavior of a novel YTaO4/8YSZ functionally graded thermal barrier coating (TBC) under extreme thermomechanical loading. The performance of such coatings is often limited by fracture driven by thermal mismatch and residual stresses, yet predictive models capturing the coupled effects of temperature-dependent properties and intrinsic stress states are lacking. To address this, we propose a coupled thermomechanical framework with three key innovations. First, a temperature-dependent damage criterion, based on a mechanical-thermal energy density equivalence principle, is introduced to modify the critical energy release rate and other material parameters. Second, the Voigt homogenization scheme is employed to model the continuous gradation of material properties. Third, the eigenstrain method is integrated to incorporate the initial residual stress field from fabrication. The model is implemented numerically on the COMSOL Multiphysics platform. Its validity is first established by accurately simulating crack propagation patterns in alumina plates during water quenching. The model is then applied to analyze thermal shock-induced fracture in the YTaO4/8YSZ graded structure. The simulation results reveal that the temperature-dependent criterion significantly improves the prediction accuracy of crack initiation time and propagation paths compared to models using constant parameters. Furthermore, the initial residual compressive stress plays a beneficial dual role by effectively delaying crack nucleation and subsequently inhibiting crack growth into the coating. The coupling of damage-dependent thermal conductivity is also shown to influence local heat flux and crack branching behavior. This work provides a reliable and advanced numerical tool for probing the complex fracture mechanisms in graded TBCs, offering valuable insights for optimizing their design to enhance durability in high-temperature applications such as gas turbines and aero-engines.
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Received: 23 January 2026
Published: 28 June 2026
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2026, Vol. 47 
