Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-25T15:33:17.610Z Has data issue: false hasContentIssue false
  • English
  • Français

Threshold crack speed in dynamic fracture of silicon

Published online by Cambridge University Press:  26 February 2011

Markus J. Buehler ,
Harvey Tang ,
Adri C.T. van Duin  and
William A. Goddard
Markus J. Buehler
Affiliation:
[email protected], MIT, Civil and Environmental Engrg, 77 Mass Ave, Cambridge, MA, 02139, United States, 626 628 4087
Harvey Tang
Affiliation:
[email protected], Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 77 Mass Ave, Cambridge, MA, 02139, United States
Adri C.T. van Duin
Affiliation:
[email protected], California Institute of Technology, Chemistry, 1200 E. Calif. Blvd., Pasadena, CA, 91125, United States
William A. Goddard
Affiliation:
[email protected], California Institute of Technology, Chemistry, 1200 E. Calif. Blvd., Pasadena, CA, 91125, United States
Get access

Abstract

We report a study of dynamic cracking of a silicon single crystal in which the ReaxFF reactive force field is used for about 3,000 atoms near the crack tip while the other 100,000 atoms of the model system are described with a simple nonreactive force field. The ReaxFF is completely derived from quantum mechanical calculations of simple silicon systems without any empirical parameters. This model has been successfully used to study crack dynamics in silicon, capable of reproducing key experimental results such as orientation dependence of crack dynamics (Buehler et al., Phys. Rev. Lett., 2006). Here we focus on crack speeds as a function of loading and crack propagation mechanisms. We find that the steady state crack speed does not increase continuously with applied load, but instead jumps to a finite value immediately after the critical load, followed by a regime of slow increase. Our results quantitatively reproduce experimental observations of crack speeds during fracture in silicon along the (111) planes, confirming the existence of lattice trapping effects. We find that the underlying reason for this behavior is formation of a 5-7-double ring defect at the tip of the crack, effectively hindering nucleation of the crack at the Griffith load. We develop a simple continuum model that explains the qualitative behavior of the fracture dynamics.

Keywords

Sifracturesimulation
Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 978: Symposium GG – Multiscale Modeling of Materials , 2006 , 0978-GG02-03
Copyright
Copyright © Materials Research Society 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Deegan, R.D. et al. , Wavy and rough cracks in silicon. Phys. Rev. E, 2003. 67(6): p. 066209.Google Scholar
2. Cramer, T., Wanner, A., and Gumbsch, P., Energy dissipation and path instabilities in dynamic fracture of silicon single crystals. Phys. Rev. Lett., 2000. 85: p. 788–791.Google Scholar
3. Cramer, T., Wanner, A., and Gumbsch, P., Crack Velocities during Dynamic Fracture of Glass and Single Crystalline Silicon. Phys. Status Solidi A, 1997. 164: p. R5.Google Scholar
4. Hauch, J.A. et al. , Dynamic fracture in Single Crystal Silicon. Phys. Rev. Lett., 1999. 82: p. 3823–2826.Google Scholar
5. Holland, D. and Marder, M., Ideal brittle fracture of silicon studied with molecular dynamics. Phys. Rev. Lett., 1998. 80(4): p. 746.Google Scholar
6. Abraham, F.F. et al. , Spanning the length scales in dynamic simulation. Computers in Physics, 1998. 12(6): p. 538–546.10.1063/1.168756Google Scholar
7. Bailey, N.P. and Sethna, J.P., Macroscopic measure of the cohesive length scale: Fracture of notched single-crystal silicon. Phys. Rev. B, 2003. 68(20): p. 205204.Google Scholar
8. Bazant, M.Z., Kaxiras, E., and Justo, J.F., Environment-Dependent Interatomic Potential for bulk silicon. Physical Review B-Condensed Matter, 1997. 56: p. 8542.Google Scholar
9. Swadener, J.G., Baskes, M.I., and Nastasi, M., Molecular Dynamics Simulation of Brittle Fracture in Silicon. Phys. Rev. Lett., 2002. 89(8): p. 085503.10.1103/PhysRevLett.89.085503Google Scholar
10. Tersoff, J., Empirical interatomic potentials for carbon, with applications to amorphous carbon. Phys. Rev. Lett., 1988. 61(25): p. 2879–2883.Google Scholar
11. Stillinger, F. and Weber, T.A., Computer-simulation of local order in condensed phases of silicon. Phys. Rev. B, 1985. 31(8): p. 5262–5271.10.1103/PhysRevB.31.5262Google Scholar
12. Duin, A.C.T.v. et al. , ReaxFF: A Reactive Force Field for Hydrocarbons. J. Phys. Chem. A, 2001. 105: p. 9396–9409.Google Scholar
13. Duin, A.C.T.v. et al. , ReaxFF SiO: Reactive Force Field for Silicon and Silicon Oxide Systems. J. Phys. Chem. A, 2003. 107: p. 3803–3811.10.1021/jp0276303Google Scholar
14. Buehler, M.J., Duin, A.C.T.v., and Goddard, W.A., Multi-paradigm modeling of dynamical crack propagation in silicon using the ReaxFF reactive force field. Phys. Rev. Lett., 2006. 96(9): p. 095505.Google Scholar
15. Bernstein, N. and Hess, D.W., Lattice trapping barriers to brittle fracture. Physical Review Letters, 2003. 91(2).10.1103/PhysRevLett.91.025501Google Scholar
16. Parker, S.G., Johnson, C.R., and Beazley, D., Computational steering software systems and strategies. IEEE Computational Science and Engineering, 1997. 4(4): p. 50–599.Google Scholar
17. Abraham, F.F. et al. , Simulating materials failure by using up to one billion atoms and the world's fastest computer: Work-hardening. P. Natl. Acad. Sci. USA, 2002. 99(9): p. 5783–5787.Google Scholar
18. Freund, L.B., Dynamic Fracture Mechanics. 1990: Cambridge University Press, ISBN 0–521-30330–3.Google Scholar
19. Anderson, T.L., Fracture mechanics: Fundamentals and applications. 1991: CRC Press.Google Scholar