Force-induced breakdown of flexible polymerized membrane

Details Force-induced breakdown of flexible polymerized membrane Force-induced breakdown of flexible polymerized membrane

2011-11-29

arxiv.org/abs/1111.6719v3

Phys. Rev. E 85, 021805 (2012)

Physics

Condensed Matter

Soft Condensed Matter

12 pages, 10 figures, LaTeX, misprints corrected

Scientific paper

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 $<\tau_r> \propto N^{-\phi(f)}$. 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 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 $f$.

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