## 3 Results and Discussion
### Failure Mechanism  
The evolution of the atomic structures at the \(\text{c-ZrO}_{2}(001)/\alpha\text{-Al}_{2}\text{O}_{3}(1\overline{1}02)\) interface during the shearing process is shown in Figure 4. The atom indices Zr1 and Zr2 denote the first Zr layer atom and second Zr layer in the \(\text{c-ZrO}_{2}\) block from the interface, respectively. The same procedure is applied to Al1 and Al2. The capital letters of the markers in Figure 4 correspond to those in Figure 2. The failure process of the interfaces is investigated by combining Figures 2 and 4.  
From Figure 2, it can be seen that the shear stresses exhibit an obvious rebound phenomenon in region I. The shear stress increases gradually until it reaches the first peak value (point B), drops slightly to point C, and then continues to increase to the maximum value (point D). This rebound is mainly due to the shifting of Zr atoms, which represents the process of breaking and rebonding of the specific Zr-O and Zr-Al bonds near the interface. For the O-\(<\)11\(\overline{1}\)01\(>\) model, Figure 2a shows the breaking of the Zr1-O2 and Zr2-Al2 bonds; it also shows the rebonding of the Zr1-O1 and Zr1-Al2 bonds. For the O-\(<\)11\(\overline{2}\)0\(>\) model shown in Figure 2b, the Zr1-O1 and Zr1-O3 bonds break; in addition, the Zr1-Al2, Zr1-O2, and Zr2-O4 bonds rebond. For the 2O-model, the Zr1-O3 and Al1-O2 bonds break; the Zr1-O1, Zr1-O4, Zr1-Al1, and Al2-O2 bonds rebond along the \(<\)11\(\overline{1}\)01\(>\) direction, as shown in Figure 2c; the Zr1-O3, Zr1-O4, and Zr1-O5 bonds break; and the Zr-O1 and Zr1-Al1 bonds rebond along the \(<\)11\(\overline{2}\)0\(>\) direction (Figure 2d). For the Zr-model, the Zr2-O3 bond breaks, the Zr2-O2 bond rebonds, and the Zr2-Al2 bond rebonds along the \(<\)11\(\overline{1}\)01\(>\) direction (Figure 2e); the Zr2-O1 bond breaks and the Zr2-Al2 bond rebonds along the \(<\)11\(\overline{2}\)0\(>\) direction, as shown in Figure 2f.  
The ZrO\({}_{2}\) atomic layers slide along the shear direction, accompanied by the shifting of Zr atoms, until the shear stresses reach the maximum value; this is shown in Figure 4 from A to D. The ZrO\({}_{2}\) atom layers undergo reconstruction from D to E, as shown in Figure 4. It is apparent that the models failed within the ZrO\({}_{2}\) atomic layer. The shear stresses  
Figure 4: The evolution of the atomic structures at the c-ZrO\({}_{2}\)(001)/\(\alpha\)-Al\({}_{2}\)O\({}_{3}\)(1\(\overline{1}\)02) interfaces during the shearing process: (**a**) O\(<\)1\(\overline{1}\)01\(>\), (**b**) O\(<\)1\(\overline{1}\)0\(>\), (**c**) 2O\(<\)1\(\overline{1}\)01\(>\), (**d**) 2O\(<\)1\(\overline{1}\)0\(>\), (**e**) Zr\(<\)1\(\overline{1}\)01\(>\), and (**f**) Zr\(<\)1\(\overline{1}\)0\(>\). The red, grey, and green spheres represent O, Al, and Zr atoms, respectively.  
decrease rapidly after point D in Figure 2, mainly because the ZrO\({}_{2}\) atom layers reconstruct intensively in the direction opposite to that of the shear accompanying the shifting of the Al atoms. Furthermore, the interfacial atomic configuration is transformed near both stress peaks; this indicates that the reconstruction of the interface structure has a significant influence on the mechanical strength of the interface region to resist sliding deformation. This phenomenon is consistent with the conclusions of [PERSON] [33]. Thus, it is concluded that in the process of the ZrO\({}_{2}\)/Al\({}_{2}\)O\({}_{3}\) interfacial shear deformation, the sliding of the ZrO\({}_{2}\) atomic layers, accompanied by the shifting of Zr and Al atoms near the interface, will play a dominant role. According to the comparison results of the maximum shear stress in regions I and II, it can also be concluded that the mechanical strength of the reconstructed interfaces is lower than that of the initial interfaces. Therefore, the reconstructed interfaces are more unstable and prone to slip than the initial interface.