Force-induced breakdown of flexible polymerized membrane

Abstract

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 $<τ>$ of bonds decays with membrane size as $<τ> \propto N^{-β}$ where $β\approx 0.50\pm 0.03$ and $N$ denotes the number of atoms in the membrane. The probability distribution of bond scission times $t$ is given by a Poisson function $W(t) \propto t^{1/3} \exp (-t / <τ>)$. The mean failure time $<τ_r>$ that takes to rip-off the sheet declines with growing size $N$ as a power law $<τ_r> \propto N^{-ϕ(f)}$. We also find $<τ_r> \propto \exp(ΔU_0/k_BT)$ where the nucleation barrier for crack formation $ΔU_0 \propto f^{-2}$, in agreement with Griffith's theory. $<τ_r>$ displays an Arrhenian dependence of $<τ_r>$ on temperature $T$. Our results indicate a rapid increase in crack spreading velocity with growing external tension $f$.