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 a Langevin thermostat, we investigate the scission and recombination of bonds, and the formation of cracks in the 2D graphenelike 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 $\langle \tau \rangle$ of bonds decays with membrane size as $\langle \tau \rangle \propto N^{-\beta }$, where $\beta \approx 0.50\pm 0.03$ and $N$ denotes the number of atoms in the membrane. The probability distribution of bond scission times $t$ is given by a Poisson function $W\left(t\right)\propto t^{1/3}\exp (-t/\langle \tau \rangle )$. The mean failure time $\langle {\tau }_r\rangle$ necessary to rip off the sheet declines with growing size $N$ as a power law $\langle {\tau }_r\rangle \propto N^{-\phi \left(f\right)}$. We also find $\langle {\tau }_r\rangle \propto \exp (\Delta U_0/k_{B}T)$, where the nucleation barrier for crack formation $\Delta U_0\propto f^{-2}$, in agreement with Griffith's theory. $\langle {\tau }_r\rangle$ displays an Arrhenian dependence of $\langle {\tau }_r\rangle$ on temperature $T$. Our results indicate a rapid increase in crack spreading velocity with growing external tension $f$.

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