This paper reveals the existence of a critical separation distance (dc) beyond which the elastic interactions between a pair of monovacancies in graphene or hexagonal boron nitride become inconsequential for the strength and toughness of the defective lattice. This distance is independent of the chirality of the lattice. For any inter-defect distance higher than dc, the lattice behaves mechanically as if there is a single defect. For a distance less than dc, the defect–defect elastic interactions produce distinctive mechanical behavior depending on the orientation (θ) of the defect pair relative to the loading direction. Both strength and toughness of the lattice containing a pair of “interacting monovacancies (iMVs)” are either higher or smaller than that of the lattice containing a pair of “non-interacting monovacancies (nMVs),” suggesting the existence of a critical orientation angle θc. For θ<θc, the smaller the distance between the iMVs, the higher the toughness and strength compared to the lattice containing nMVs, whereas, for θ≥θc, the smaller the separation distance between the iMVs, the smaller the toughness and strength compared to the lattice containing nMVs. The transitional behavior has a negligible dependence on the chirality of the lattice, which indicates that the crystallographic anisotropy has a much weaker influence on toughness and strength compared to the anisotropy induced by the orientation angle itself. These observations underline an important point that the elastic fields emanating from vacancy defects are highly localized and fully contained within a small region of around 1.5 nm radius.
Applying classical molecular dynamics simulations, we report the effects of length (λ) and orientation (θ) of a line-defect on strength and toughness in defective 2D hexagonal boron nitride. Results reveal the existence of a “transition angle,” θt=2.47°, at which both toughness and strength are insensitive to the finite length of the defect in an infinite domain. For θ<θt, both toughness and strength increase with an increase in defect-length; whereas, for θ>θt, they show the opposite behavior. Examination of the stress-fields shows that θ-dependent variation in stress-localization at the edges of the line-defect and symmetry-breaking of the stress-fields with respect to the defect-axis govern the disparate θ-dependent behavior. For θ<θt, the intensity of elastic fields at the edges of the line-defect is substantially weakened by the elastic interactions originating from the atoms on the sides of the line-defect. For θ>θt, the stress-intensity at the edges is strongly localized at the opposite sides of the line-defect. The stress-intensity increases asymptotically with the increasing defect-length and reduces the strength and toughness of the defective lattice. The stress-localization, however, saturates at a “saturation angle” of around 60° for strength and 30° for toughness. Additionally, there exists a critical defect-length λc=60 Å, below which there is a strong θ-dependent variation in elastic interactions between the edges, affecting strength and toughness substantially. For λ>λc, the elastic interactions saturate and make both strength and toughness insensitive to the change in the length of the defect.
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