13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- 3. Strength of Graphene Stress of a graphene sheet (σ) is obtained from the gradient of the strain energy (U) - strain (ε) curve as, σ= 1 V ∂U ∂ε (1) where, V is the volume of graphene sheet and the thickness of graphene is taken as 0.34 nm. The stress-strain curves of sheets for different crack lengths at 300 K are shown in Fig. 3. The results reveal that a single vacancy (one missing atom) reduces σult in armchair sheets by 15.7% and in zigzag sheets by 23.3%, which indicates that graphene is very sensitive to vacancy defects. It can also be noticed in Fig. 3 that Young’s modulus does not change with crack length. (a) (b) Figure 3. Stress - strain curve of graphene with crack length; (a) armchair and (b) zigzag at 300 K. Figure 4. Effect of temperature on strength of graphene for various crack lengths. Figure 5 shows a plot of 1/√a vs. σult, and it clearly shows proportionality at 1 K. This indicates a formal similarity with continuum fracture mechanics. The stress intensity factor of graphene (KI g ) can therefore be approximated as Kg I = σf −c ( ) 2πa, (2) where c is a constant (c is zero for a continuum) and a is the crack length. The values of KI g and c are given in Table 1 based on MD simulations. KI g decreases as temperature increases from 1 K to 300 K, which reflects the reduction of σult as shown in Fig. 4. The reduction of KI g in zigzag sheets is greater than that of armchair. The general agreement of MD simulation results with continuum
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