## 3 Calculation Results and Discussion
### Mechanical Behavior Analysis of Interface Pulling Out  
The pull-out simulation of the model in Figure 1b was carried out to obtain the relationship curves of side pull-out output-displacement at different temperatures, as shown in Figure 9.  
As can be seen from the figure, the pull-out output curves at different temperatures all showed a trend of first increasing, then continuously fluctuating, and finally decreasing to 0, corresponding to the unpull-out stage, partial pull-out stage, and complete pull-out stage, respectively. In the non-pull-out stage, the interaction between the interfaces is similar to the static friction form, and the pull-out displacement is nearly 0, while the pull-out force continues to increase. When the pulling force exceeds the \"static friction force\", the graphene and copper matrix slide relatively, and the interaction is similar to the form of dynamic friction, and with the change of graphene and copper atoms' relative position, the pulling force shows a vibration pattern. When the graphene layer is completely pulled out, the distance between graphene and copper atoms continues to increase, and the interaction force decreases until it reaches 0. With the increase in temperature, the average pull-out force in some pull-out stages showed a downward trend and showed a significant decline between 900 K and 1100 K, which was analyzed to be due to the fact that 1100 K was close to the melting point of copper, at which time the crystal structure of copper would change greatly, and the pull-out force showed a significant downward trend. In general, the interface shear strength is defined as the ratio of the maximum tangential pulling force to the contact area [34]. However, considering the strong fluctuation of the pulling force during the pulling process, large errors may be generated if calculated by this method. In addition, since the system energy increment in the pull-out process is the  
Figure 8: Maximum pull-up force/normal strength–graphene content relationship curves. Figure 9: Pull-out force–displacement curves of tangential pull-out at different temperatures. work performed by the pull-out force, the interfacial shear strength can be obtained by the following formula:  
\[ \begin{array}{c}E_{pull-out}=\Delta E=E_{2}-E_{1}\\ E_{pull-out}=\int_{x=0}^{x=l}\Lambda\tau_{\mathrm{d}}\mathrm{dx}=\int_{x=0}^{x= l}2\mathrm{S}\tau_{\mathrm{d}}\mathrm{dx}=w\tau_{l}l^{2}\\ \tau_{pull-out}=\frac{E_{pull-out}}{wl^{2}}\end{array}  \tag{5}\]  
where \(E_{pull-out}\) is the work performed by the pull-out force, J; \(E_{1}\) is the system energy at the initial pull-out state, J; \(E_{2}\) is the system energy at the end of the pull-out state, J; \(\tau_{pull-out}\) is the interfacial shear strength, Pa; \(w\) and \(l\) are the width and length of the contact surface between graphene and copper, m.  
According to Formula (5), the interfacial shear strength at different temperatures can be obtained, and then the relationship between average pull-out force, interfacial shear strength, and temperature in the partial pull-out stage can be obtained, as shown in Figure 10. As can be seen from the figure, the average pulling force and interface shear strength are negatively correlated with temperature. The shear strength and pulling force at 1100 K are 71.8 MPa and 1.58 eV/A, respectively, only 67.1% and 66.9% of those at 100 K. In the range of 100-700 K, the average pull-out force and interfacial shear strength decreased by 11.4% and 11.65%, respectively, while in the range of 700-1100 K, the average pull-out force and interfacial shear strength decreased by 24.22% and 24.29%, respectively. By changing the graphene content in the composite material and conducting the pull-out simulation at 300 K, the pull-out output-displacement relationship curves under different graphene content can be obtained, as shown in Figure 11.  
As can be seen from the figure, graphene content has little effect on the overall trend of the pull-out outdoor-displacement curve and the maximum pull-out output.