  Graphene and some graphene like two dimensional materials; hexagonal boron
nitride (hBN) and silicene have unique mechanical properties which severely
limit the suitability of conventional theories used for common brittle and
ductile materials to predict the fracture response of these materials. This
study revealed the fracture response of graphene, hBN and silicene nanosheets
under different tiny crack lengths by molecular dynamics (MD) simulations using
LAMMPS. The useful strength of these large area two dimensional materials are
determined by their fracture toughness. Our study shows a comparative analysis
of mechanical properties among the elemental analogues of graphene and
suggested that hBN can be a good substitute for graphene in terms of mechanical
properties. We have also found that the pre-cracked sheets fail in brittle
manner and their failure is governed by the strength of the atomic bonds at the
crack tip. The MD prediction of fracture toughness shows significant difference
with the fracture toughness determined by Griffth's theory of brittle failure
which restricts the applicability of Griffith's criterion for these materials
in case of nano-cracks. Moreover, the strengths measured in armchair and zigzag
directions of nanosheets of these materials implied that the bonds in armchair
direction has the stronger capability to resist crack propagation compared to
zigzag direction.
