1111.6719 (J. Paturej et al.)

Force-induced breakdown of flexible polymerized membrane    [PDF]

J. Paturej, H. Popova, A. Milchev, T. A. Vilgis

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 $f$.

View original: http://arxiv.org/abs/1111.6719