## 3 Calculation Results and Discussion
### Influence Mechanism Analysis
#### 3.4.1 Temperature Effect  
In order to analyze the mechanism of the influence of temperature on the interface, the pull-out model was taken as an example. Figure 18a-d shows the interface topography of the pull-out process at different temperatures. It can be seen from the figure that at a low temperature (100-300 K), the separation of copper matrix and graphene lamellar is almost rigid, the atomic arrangement of the copper matrix is regular, and the fold of graphene lamellar is small. The vacancy will be formed in the copper matrix (Figure 18a,b). As the temperature increases (700-1100 K), the lattice distortion in the copper matrix becomes  
Figure 16: Cohesion–displacement curves at different graphene contents.  
Figure 17: Maximum cohesion/normal strength–graphene content relationship curves.  
more severe, and the atomic arrangement becomes more irregular. With the removal of the graphene lamella, the copper atoms will gradually fill the vacancy formed by the removal of the graphene lamella. At 1100 K, after the removal of the graphene lamella, all the copper atoms will fill the vacancy simultaneously. The tendency of copper atoms to be removed by adhesion increases.  
It can be concluded from the above analysis that temperature will directly affect the atomic thermal motion of the pull-out system, thus leading to changes in the energy of the system. Figure 19 shows the curve of the energy of the system with temperature under different temperatures. The trend of the energy of a representative copper atom changing with temperature during the pull-out process is shown in the red diagonal line. The total energy of the system increases with the increase in the energy of a single atom. Meanwhile, the energy oscillation trend of the system becomes more obvious with the increase in temperature, indicating that the thermal motion of atoms is intensified [35]. The increase in energy and the intensification of atomic thermal motion will reduce the stability of the system and lead to a decrease in interface strength.  
On the other hand, the melting point of copper is about 1300 K, while the melting point of graphene is above 3000 K. Therefore, when the temperature reaches 1100 K, the physical properties of the copper matrix have been greatly changed, but graphene is almost unaffected (Figure 18d). At this time, when the graphene is pulled out, some of the softened copper will fill into the graphene vacancy. The softening of the copper matrix will seriously affect the properties of the interface, resulting in the inability to form a suitable interface and significantly reduced strength.  
For cohesion and pull-out mechanical behavior, the energy of the system also increases with the increase in temperature (Figure 20). As can be seen from the figure, in pull-out simulation, the energy of the system increases with the increase in temperature, while the energy fluctuates more violently, indicating that the stability of the system decreases with the increase in temperature, which explains the phenomenon that the normal strength decreases with the increase in temperature. In cohesion simulation, the curve fluctuation was significantly less affected by temperature than that in pull-out and pull-out simulation.  
Figure 19: Energy curves of the system and individual copper atoms.  
Figure 18: Morphology of pull-out interface at different temperatures: (**a**) 100 K pull-out model; (**b**) 300 K pull-out model; (**c**) 700 K pull-out model; (**d**) 1100 K pull-out model.  
The analysis showed that only copper atoms existed at the bottom of the graphene sheet in the cohesion model, while the separation of the graphene sheet from the bottom copper matrix in the simulation had little impact on the copper matrix itself, so the energy fluctuation was small. However, the total energy of the system increases with the increase in temperature, and the stability of the system decreases significantly, resulting in a decrease in cohesion strength.