We consider the fracture of a free-standing two-dimensional (2D) elastic-brittle network to be used as protective coating subject to constant tensile stress applied on its rim. Using a Molecular Dynamics simulation with Langevin thermostat, we investigate the scission and recombination of bonds, and the formation of cracks in the 2D graphene-like hexagonal sheet for different pulling force $f$ and temperature $T$. We find that bond rupture occurs almost always at the sheet periphery and the First Mean Breakage Time $<tau>$ of bonds decays with membrane size as $<tau> propto N^{-beta}$ where $beta approx 0.50pm 0.03$ and $N$ denotes the number of atoms in the membrane. The probability distribution of bond scission times $t$ is given by a Poisson function $W(t) propto t^{1/3} exp (-t / <tau>)$. The mean failure time $<tau_r>$ that takes to rip-off the sheet declines with growing size $N$ as a power law $<tau_r> propto N^{-phi(f)}$. We also find $<tau_r> propto exp(Delta U_0/k_BT)$ where the nucleation barrier for crack formation $Delta U_0 propto f^{-2}$, in agreement with Griffiths theory. $<tau_r>$ displays an Arrhenian dependence of $<tau_r>$ on temperature $T$. Our results indicate a rapid increase in crack spreading velocity with growing external tension $f$.
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