## 3 Results
### Fracture Strength of Graphene with Defects
Moreover, for graphene, fracture strength for tension along zigzag is higher than for tension along armchair. Here, it can be seen that \(\varepsilon_{F}^{z}>\varepsilon_{F}^{a}\), which would be further described from the changes of the structural state of graphene under such tension technique. Elastic modulus can be defined from the slope of the stress-strain curves in the elastic regime. Here, in the presence of ripples, the elastic regime is considered only before the first ripples with an amplitude higher than 0.5 A appeared. Stress-strain curves for graphene and graphene with SW are closely matched before the fracture point. The same behavior was shown previously for a single SW defect in graphene [46; 47]. The initial slope is significantly higher, indicating an increased elastic modulus of \(E^{a}\) = 16.4 GPa and \(E^{z}\) = 13.9 GPa. At the same time, the presence of any type of defect results in a considerable decrease of \(\varepsilon_{F}^{a}\), which should be discussed in accordance with the structural transformations. Figure 3: Variations of the ultimate strength \(\sigma_{UITS}\), fracture strain \(\varepsilon_{F}\) and elastic modulus for defective graphene under tensile tests along the armchair/zigzag direction as the function of the dipole arm \(l\). Open circles show these values for defect-free graphene. Temperature also plays a very important role in the degradation of the graphene strength with or without defects [48; 49; 50]. Thermal fluctuations drive the generation of atomic vacancies or dislocations since temperature increases the possibility of an atomic movement in the structure. For graphene, strength is considerably decreased by thermal fluctuations. Ultimate tensile strength and fracture strain of graphene under tension along armchair direction at room temperature is more than two times lower than at 0 K, while the further increase of temperature does not lead to a significant decrease of strength (see Figure 3a,b). Very similar results can be seen for graphene with SW. Elastic modulus \(E\) is almost not affected by the temperature increase, which is in line with the previous studies [51]. For tension along zigzag, the effect of temperature is not so significant. As can be seen, the increase of temperature considerably lower the \(\sigma_{UTS}^{a}\) of graphene and graphene with SW, while almost not affecting these values for graphene with DD. The extremely similar slopes of the stress-strain curves for all of the structures with the DD\({}_{n}\) in Figure 2 imply that the distance between dislocations in the dipole does not noticeably affect the elastic modulus of graphene. The fitted elastic modulus is in the range of 3.76 to 4.14 GPa for tension along armchair and from 3.00 to 3.52 GPa for tension along zigzag. Hence, it can be concluded that the presence of DD does not have a significant effect on the elastic properties of graphene. Experimental and numerical observations showed the same results for grain boundaries [7; 52]: elastic properties are not affected by the type of grain boundary. Despite, the value of fracture strength, the arm of dislocation dipole is not meaningful, but this issue is still important. The interesting point is that the dipole arm will affect the dislocation dynamics and, also, the wrinkling process. As a result, there is a correlation between wrinkling and fracture strain and stress. In Figure 4 another critical issue is presented--simulation of graphene tension with another interatomic potential for comparison: stress-strain curves during tension at 0 and 300 K for graphene and graphene with DD\({}_{2}\) and snapshots of graphene after a fracture. Two interatomic potentials are compared--AIREBO and Tersoff. Tersoff interatomic potential is well-known for the simulation of physical and mechanical properties of graphene and other carbon structures [53]. As it is known, interatomic potential can considerably affect the simulation results [54].