banner MD simulation of crack propagation in brittle crystals

118094 - Introduction to Computational Physics - Fall 2012/13
Liron Ben-Bashat Bergman
Overview Theory Setup Results Manual
 

 

Results

Crack propagation under three different intial strain conditions (mode 1) was simulated (5%, 5.5% and 6% strain). The average kinetic energy per atom vs. time is shown figure 5. The kinetic energy of the system behaves as expected and matches the results from the IMD simulations (see setup ). At low strains ( <4.8%) the crack doesn't propagate because the energy isn't sufficient to break Si-Si bonds. At high strains the crack becomes unstable due to shock waves and there is a need to create incremental loading in order to achieve stable crack propagation.



EkTime

Fig. 5 Green, blue and red curves represent  6%, 5.5% and 5% strains respectively.

 The strain energy release rate (G0)  of the system was calculated using eq. 12 :

 G(5%)= 6.2 J/m2 , G(5.5%)= 7.5 J/m2 , G(6%) = 9 J/m2.

while the height of the specimen equals 256.101 Angstrom, E=169, Poisson ratio = 0.36 and E*=194.16GPa [8].

Fig. 6 shows snapshots of the crack at different timesteps (26,800 , 36,800 ,46,800, 56,800). It can be seen from the red curve that the crack is propagating at a constant speed.


ConstVel

Fig. 6 Snapshots of crack propagation showing constant crack propagation.

pe 

Fig. 7 A snapshot of the specimen. Only atoms with potential energy above a certain threshold are visible. It is observed that the crack free surfaces (green) have high surface energy and that the energy distribution surrounding the crack tip behaves similarly to Irwin's theory. Strain 5%, timestep 26,800.


Dynamic crack propagation along the {110} plane in the [110] direction is presented in the following movie for 5% strain:

References:
[8] What is the Young's Modulus of silicon? W. D. Nix et al. J. Micro/ Sys. Vol 19 No.2 2010