Molecular Dynamics Simulation of Brittle Fracture in Silicon

Brittle fracture in silicon is simulated with molecular dynamics utilizing a modified embedded atom method potential. The simulations produce propagating crack speeds that are in agreement with previous experimental results over a large range of fracture energy. The dynamic fracture toughness is found to be equal to the energy consumed by creating surfaces and lattice defects in agreement with theoretical predictions. The dynamic fracture toughness is approximately of the static strain energy release rate, which results in a limiting crack speed of of the Rayleigh wave speed.

Figure 1

Molecular dynamics model oriented with crystallographic axes as shown. Crack propagates in the $[2\overline{11}]$ direction.

Figure 2

Variation of $C_{33}$ (for ${ϵ}_{xx}={ϵ}_{yy}=0$) (dashed line) and the mean value of $E^{*}$ (for ${ϵ}_{xx}={ϵ}_{yy}=-0.25{ϵ}_{zz}$) (solid line) with strain for the silicon MEAM potential [8] with the $z$ direction aligned with the [111] crystallographic direction.

Figure 3

(a) Variation of Rayleigh wave speed ($c_R$) with static energy release rate ($J_s$) in the $H=147\AA$ model. (b) Normalized crack speed ($v/c_R$) as a function of $J_s$ and model heights $H=239\AA$ (open circle), $H=147\AA$ (full circle), and $H=112\AA$ (full triangle), compared with the experimental results (open square) of Hauch et al. [1]. Solid line is continuum prediction for $J_d=2{\gamma }_0$.

Figure 4

Detail of a crack propagating in the $H=147\AA$ silicon model for $J_s=13.1\mathrm{J}/{\mathrm{m}}^2$.

Figure 5

Normalized crack speed ($v/c_R$) as a function of $J_d/J_s$ for dynamic fracture in the $H=147\AA$ silicon model. Solid line is the prediction from Eq. (1).