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 $<\tau >$ of bonds decays with membrane size as $<\tau >\propto N^{-\beta }$ 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 $W(t)\propto t^{1/3}\exp (-t/<\tau >)$. The mean failure time $<{\tau }_r>$ that takes to rip-off the sheet declines with growing size $N$ as a power law $<{\tau }_r>\propto N^{-\varphi (f)}$. We also find $<{\tau }_r>\propto \exp (\Delta U_0/k_{B}T)$ where the nucleation barrier for crack formation $\Delta U_0\propto f^{-2}$, in agreement with Griffith's theory. $<{\tau }_r>$ displays an Arrhenian dependence of $<{\tau }_r>$ on temperature $T$. Our results indicate a rapid increase in crack spreading velocity with growing external tension $f$.

12 pages, 10 figures, LaTeX, misprints corrected

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Cited by in corpus (1)

• Thermal decomposition of a honeycomb-network sheet - A Molecular Dynamics simulation study