Year: 2012
Type: article
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 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 $\ensuremath{\langle}\ensuremath{\tau}\ensuremath{\rangle}$ of bonds decays with membrane size as $\ensuremath{\langle}\ensuremath{\tau}\ensuremath{\rangle}\ensuremath{\propto}{N}^{\ensuremath{-}\ensuremath{\beta}}$, where $\ensuremath{\beta}\ensuremath{\approx}0.50\ifmmode\pm\else\textpm\fi{}0.03$ and $N$ denotes the number of atoms in the membrane. The probability distribution of bond scission times $t$ is given by a Poisson function $W(t)\ensuremath{\propto}{t}^{1/3}\mathrm{exp}(\ensuremath{-}t/\ensuremath{\langle}\ensuremath{\tau}\ensuremath{\rangle})$. The mean failure time $\ensuremath{\langle}{\ensuremath{\tau}}_{r}\ensuremath{\rangle}$ necessary to rip off the sheet declines with growing size $N$ as a power law $\ensuremath{\langle}{\ensuremath{\tau}}_{r}\ensuremath{\rangle}\ensuremath{\propto}{N}^{\ensuremath{-}\ensuremath{\varphi}(f)}$. We also find $\ensuremath{\langle}{\ensuremath{\tau}}_{r}\ensuremath{\rangle}\ensuremath{\propto}\mathrm{exp}(\ensuremath{\Delta}{U}_{0}/{k}_{B}T)$, where the nucleation barrier for crack formation $\ensuremath{\Delta}{U}_{0}\ensuremath{\propto}{f}^{\ensuremath{-}2}$, in agreement with Griffith's theory. $\ensuremath{\langle}{\ensuremath{\tau}}_{r}\ensuremath{\rangle}$ displays an Arrhenian dependence of $\ensuremath{\langle}{\ensuremath{\tau}}_{r}\ensuremath{\rangle}$ on temperature $T$. Our results indicate a rapid increase in crack spreading velocity with growing external tension $f$.
Source: Physical Review E
Authors: J. Paturej, H. Popova, A. Milchev, T. A. Vilgis
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2040899111