## 3 Results
### Analysis of the Fracture Mechanisms  
The appearance of ripples during tension determines the course of the stress-strain curves at this deformation regime. In Figure 5a, the comparison between stress-strain curves (a) for tension at 0 K along armchair direction for graphene, graphene with SW and DD\({}_{2}\) is presented in comparison with the average amplitude of ripples (b) and bond length (c) as the function of strain. Only results for graphene with DD\({}_{2}\) under tension at 0 K are presented since the overall behavior of graphene with DD is the same. However, some differences will be discussed further in the text. Average amplitude of ripples is calculated as \(\overline{A}=0.5(|A_{max}|+|A_{min}|)\), where \(A_{max}\) is the maximal amplitude and \(A_{min}\) is the minimal amplitude of the ripples. Obtained amplitudes are in good agreement with the literature [30; 32]. Amplitude as the function of strain for one more defect is presented by green dots and dashed green approximation to show that graphene with any DD\({}_{n}\) has almost the same behavior. As it was mentioned, a linear regime is a regime without ripples, when graphene is still planar. Small amplitude of the downward bubble around each dislocation as well as very small-amplitude ripples is neglected. Figure 4: (**a**,**b**) Stress-strain curves for graphene and graphene with DD\({}_{2}\) under tension along armchair (**a**) and zigzag (**b**) direction at 0 and 300 K. (**c**) Snapshots of graphene after a fracture. Snapshots of the structure during tension along armchair and zigzag direction are presented for critical points on stress-strain curves in Figure 6. Let us consider tension in armchair direction first. As it can be seen, there are four different loading regimes: (i) after the elastic regime is over and before point A, (ii) between A and B (B' for graphene with SW and DD\({}_{2}\)), (iii) from B (B') to C, and (iv) from C to D (D' for graphene with SW and DD\({}_{2}\)). Almost the same deformation behavior at critical strains is observed for all structures. Point C can be considered as the pre-critical state. Figure 5: (**a**) Stress-strain curves for graphene, graphene with SW, and DD\({}_{2}\) under tension along armchair direction at \(T\) = 0 K. (**b**) Average amplitude \(\overline{A}\) of ripples for defect-free graphene, graphene with SW, and DD\({}_{2}\) as the function of strain under tension along armchair direction at \(T\) = 0 K. Numerical data are shown by dots, while approximations are shown by solid lines. One more structure with the dipole (DD\({}_{6}\)) is added for comparison with the approximation shown by a thick dashed line. The thin black dashed lines show different deformation regimes. (**c**) The bond length in graphene and graphene with DD\({}_{2}\) as the function of applied tensile strain. Before point A, the amplitude of the ripples constantly increases for all structures. It should be mentioned that the size of the structure along \(x\) (armchair) direction is enough to obtain two ripples with the same parameters. Previously, in [32] it was shown that the amplitude and wavelength of ripples depend on the size of the graphene nanoribbon, which is also valid for graphene. The amplitude value achieves the maximum at point B for graphene and at about \(\epsilon_{xx}^{a}\) = 0.3--for graphene with SW and DD. In fact, the deformation is determined by two factors: changes in the lattice constant and the de-wrinkling of graphene. Different bonds in the structure are analyzed during tension for graphene, graphene with SW, and DD. In Figure 5c, changes of the bonds in graphene and graphene with DD\({}_{2}\) have presented: two main bonds in graphene (\(a\) along armchair and \(b\) along zigzag) and three characteristic bonds near the dislocation--1, 2 and 3. Other different bonds in graphene are changing in a similar way to these three.