A machine learning-based multiscale modeling for analyzing gadolinia-doped ceria fracture behavior under mechano-electrochemical coupling fields

The fracture behavior of gadolinia-doped ceria (GDC) electrolytes under complex mechano-electrochemical conditions is significantly affected by various factors, especially when microcracks are present within the material. This paper develops an atom-to-continuum (AtC) multiscale method that integrates molecular dynamics (MD) simulations with the finite element method (FEM), utilizing a machine learning force field (MLFF), to examine the fracture behavior of CeO₂ and GDC containing a central crack under varying temperatures and low oxygen partial pressures. First, leveraging the accuracy of first-principles calculations and the efficiency of MD simulations, an MLFF for partially reduced Ce⁴⁺ in GDC is developed and its accuracy is validated. Subsequently, building on fracture mechanics theory, the macroscopic structure of GDC is converted into a microscopic nanometer-scale intermediate transition model. Finally, this approach is employed to investigate the fracture toughness of CeO₂ and GDC macroscopic structure under mechano-electrochemical coupling fields at varying temperatures and low oxygen partial pressures. The results reveal that the fracture toughness of CeO₂ and 10GDC under mechano-electrochemical coupling fields is significantly affected by temperature, oxygen partial pressure, and the magnitude of external load. Specifically, the fracture toughness of CeO₂ decreased by 34.44% at 1000°C, with an external load of 0.5 MPa and logP(O₂) = − 14. For 10GDC, the fracture toughness decreased by 40.04% at 900°C, with an external load of 0.5 MPa and logP(O₂) = − 18. These findings are essential for accurately predicting the fracture behavior of CeO₂ and GDC electrolyte in complex operational environments.