Mechanical properties of polycrystalline graphene based on a realistic atomistic model

Graphene can at present be grown at large quantities only by the chemical vapor deposition method, which produces polycrystalline samples. Here, we describe a method for constructing realistic polycrystalline graphene samples for atomistic simulations, and apply it for studying their mechanical properties. We show that cracks initiate at points where grain boundaries meet and then propagate through grains predominantly in zigzag or armchair directions, in agreement with recent experimental work. Contrary to earlier theoretical predictions, we observe normally distributed intrinsic strength ($\sim 50$% of that of the monocrystalline graphene) and failure strain which do not depend on the misorientation angles between the grains. Extrapolating for grain sizes above 15 nm results in a failure strain of $\sim 0.09$ and a Young's modulus of $\sim 600$ GPa. The decreased strength can be adequately explained with a conventional continuum model when the grain boundary meeting points are identified as Griffith cracks.

Figure 1

Model structures for polycrystalline graphene. (a) Top and (b) side view of a periodic 20 nm $\times$ 20 nm graphene sheet with four grains, as marked by the numbered shaded areas. The lines indicate orientations of the graphene lattice within each grain. Note that all the presented mechanical studies have been carried out for bicrystalline samples. (c) Distribution of misorientation angles for the bicrystalline sample structures used in this study. (d) Relative probabilities for nonhexagonal carbon rings in the same structures.

Figure 2

Stress-strain curves for polycrystalline graphene samples as plotted for grain sizes of (a) $d\approx 12$ nm, (b) $d\approx 6$ nm, and (c) $d\approx 3$ nm. The size of the grains is determined as an average diameter for a grain assumed to be circular as indicated in panel (d).

Figure 3

Mechanical properties of the sample structures as a function of the misorientation between the two grains $\theta$ and the grain size $d$ (or system size). (a) Failure strain, (b) intrinsic strength, and (c) Young's modulus as a function of $\theta$ for $d\approx 12$ nm grains. (d) Failure strain as a function of $d$. (e) Distribution of the intrinsic strengths for all $d$. (f) Young's modulus as a function of $d$.

Figure 4

An example case of crack formation and propagation. (a) The structure with no strain with different grains (1 and 2) marked with different colors. The lines indicate the orientations of the grains. The square shows the area where the grain boundaries meet and the crack will appear. (b-e) Snapshots of the area immediately around the crack during straining showing how the crack penetrates along the zigzag axis of the bulk of the grain. (f) The structure after the crack has penetrated through the grains.