Ferroelastic toughening of single crystalline yttria-stabilized t′ zirconia: A phase field study

Yttria stabilized zirconia with the tetragonal prime phase (t'-YSZ) is most widely used in thermal barrier coatings. In this paper, a concise 2D phase field (PF) model is proposed to simulate domain switching in single crystalline t'-YSZ, where the energy barrier for domain switching is explicitly considered. The coercive stress for domain switching can be easily tuned by adjusting the energy barrier for domain switching. After that, a coupled PF model is developed by combing the new PF model for domain switching and the existing PF model for fracture. The coupled PF model can simulate the domain switching and crack propagation simultaneously without any adhoc criteria. The propagation of an edge crack in single crystalline t'-YSZ under different types of loadings are then studied with PF simulations. The influences of crystalline orientation and loading types on crack propagation and domain switching are systematically discussed. The distribution of the domain switching zone is validated by analyzing the stress field around the crack tip. When the c-axis of the initial t' phase is in parallel with or perpendicular to the crack surface, the crack propagates in mode I due to the symmetry of the model. In order to assess the ferroelastic toughening quantitatively, the energy release rate (ERR) along with the crack growth is calculated, where a stepwise displacement load is applied to the numerical model. At each load step, the crack can reach the equilibrium state, where the energy release rate equals the crack growth resistance. By computing the energy release rate at each load step, the ferroelastic toughening effect of domain switching is revealed and quantitatively characterized. It is shown that the domain switching of the t' phase can produce obvious toughening effect on crack propagation. Besides crystal orientation, loading types can also have distinct influences on domain switching and the toughening effect. For crystal orientations asymmetric to the crack surface, the crack may deflect due to the asymmetric distribution of the domain switching zone. The coupled PF model developed in this paper can act as an effective numerical tool to characterize the fracture behavior and ferroelastic toughening effect of single crystalline t' zirconia.