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Stress and energy flow field near a rapidly propagating mode I crack

  • Markus J. Buehler
  • Farid F. Abraham
  • Huajian Gao
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 39)

Summary

Crack branching and instability phenomena are believed to be closely related to the circumferential or hoop stress in the vicinity of the crack tip. In this paper we show that the hoop stress around a mode I crack in a harmonic solid becomes bimodal at a critical speed of about 73 percent of the Rayleigh speed, in agreement with the continuum mechanics theory. Additionally, we compare the energy flow field predicted by continuum theory with the solution of molecular-dynamics simulations and show that the two approaches yield comparable results for the dynamic Poynting vector field. This study exemplifies joint atomistic and continuum modelling of nanoscale dynamic systems and yields insight into coupling of the atomistic scale with continuum mechanics concepts.

Keywords

Hoop Stress Continuum Mechanic Theory Rayleigh Velocity Rayleigh Speed 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [ABRR94]
    F.F. Abraham, D. Brodbeck, R.A. Rafey, and W.E. Rudge. Instability dynamics of fracture: A computer simulation investigation. Phys. Rev. Lett.73(2):272–2751994.CrossRefGoogle Scholar
  2. [ABRX97]
    F.F. Abraham, D. Brodbeck, W.E. Rudge, and X. Xu. A molecular dynamics investigation of rapid fracture mechanics. J. Mech. Phys. Solids45(9):1595–16191997.CrossRefzbMATHGoogle Scholar
  3. [AT89]
    M.P. Allen and D.J. Tildesley. Computer Simulation of Liquids. Oxford University Press, 1989.Google Scholar
  4. [AW G+02a]_F.F. Abraham, R. Walkup, H. Gao, M. Duchaineau, T.D. de la Rubia, and M. Seager. Simulating materials failure by using up to one billion atoms and the world’s fastest computer: Brittle fracture. PNAS99(9):5788–57922002.CrossRefGoogle Scholar
  5. [AW G+02b]_F.F. Abraham, R. Walkup, H. Gao, M. Duchaineau, T.D. de la Rubia, and M. Seager. Simulating materials failure by using up to one billion atoms and the world’s fastest computer: Work-hardening. PNAS99(9):5783–57872002.CrossRefGoogle Scholar
  6. [BAG03]
    M.J. Buehler, F.F. Abraham, and H. Gao. Hyperelasticity governs dynamic fracture at a critical length scale. Nature426:141–1462003.CrossRefGoogle Scholar
  7. [Bak62]
    B.R. Baker. Dynamic stresses created by a moving crack. Journal of Applied Mechanics29:567–5781962.Google Scholar
  8. [BC00]
    A. Boresi and K. P. Chong. Elasticity in Engineering Mechanics. Wiley-Interscience, New York2nd edition2000.Google Scholar
  9. [BGH03a]
    M.J. Buehler, H. Gao, and Y. Huang. Continuum and atomistic studies of a suddenly stopping supersonic crack. Computational Materials Science28(3-4):385–4082003.CrossRefGoogle Scholar
  10. [BGH03b]
    M.J. Buehler, H. Gao, and Y. Huang. Continuum and atomistic studies of the near-crack field of a rapidly propagating crack in a harmonic lattice. Theor. Appl. Fract. Mech., in press, 2003.Google Scholar
  11. [BH56]
    M. Born and K. Huang. Dynamical Theories of Crystal Lattices. Clarendon, Oxford1956.Google Scholar
  12. [BHG03]
    M.J. Buehler, A. Hartmeier, and H. Gao. Atomistic and continuum studies of crack-like diffusion wedges and dislocations in submicron thin films. J. Mech. Phys. Solids51:2105–21252003.CrossRefzbMATHGoogle Scholar
  13. [BV81]
    V.K. Kinra B.Q. Vu. Britle fracture of plates in tension — static field radiated by a suddenly stopping crack. Engrg. Fracture Mechanics15(1-2):107–1141981.CrossRefGoogle Scholar
  14. [CY93]
    K.S. Cheung and S. Yip. A molecular-dynamics simulation of crack tip extension: the brittle-to-ductile transition. Modelling Simul. Mater. Eng.2:865–8921993.CrossRefGoogle Scholar
  15. [dAY83]
    B. deCelis, A.S. Argon, and S. Yip. Molecular-dynamics simulation of crack tip processes in alpha-iron and copper. J. Appl. Phys.54(9):4864–48781983.CrossRefGoogle Scholar
  16. [FGMS91]
    J. Fineberg, S.P. Gross, M. Marder, and H.L. Swinney. Instability in dynamic fracture. Phys. Rev. Lett.67:141–1441991.CrossRefGoogle Scholar
  17. [FPG+02]_S. Fratini, O. Pla, P. Gonzalez, F. Guinea, and E. Louis. Energy radiation of moving cracks. Phys. Rev. B66(10):1041042002.CrossRefGoogle Scholar
  18. [Fre90]
    L.B. Freund. Dynamic Fracture Mechanics. Cambridge University Press, 1990.Google Scholar
  19. [GHA01]
    H. Gao, Y. Huang, and F. F. Abraham. Continuum and atomistic studies of intersonic crack propagation. J. Mech. Phys. Solids49:2113–21322001.CrossRefzbMATHGoogle Scholar
  20. [GK01]
    H. Gao and P. Klein. Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds. J. Mech. Phys. Solids46(2):187–2182001.CrossRefzbMATHGoogle Scholar
  21. [Hua02]
    K. Huang. On the atomic theory of elasticity. Proc. R. Soc. London203:178–1942002.Google Scholar
  22. [KG98]
    P. Klein and H. Gao. Crack nucleation and growth as strain localization in a virtual-bond continuum. Engineering Fracture Mechanics61:21–481998.CrossRefGoogle Scholar
  23. [Mar99]
    M. Marder. Molecular dynamics of cracks. Computing in Science and Engineering1(5):48–551999.CrossRefGoogle Scholar
  24. [MG95]
    M. Marder and S. Gross. Origin of crack tip instabilities. J. Mech. Phys. Solids43(1):1–481995.Google Scholar
  25. [RKL+02]_C.L. Rountree, R.K. Kalia, E. Lidorikis, A. Nakano, L. van Brutzel, and P. Vashishta. Atomistic aspects of crack propagation in brittle materials: Multimillion atom molecular dynamics simulations. Annual Rev. of Materials Research32:377–4002002.CrossRefGoogle Scholar
  26. [Tsa79]
    D.H. Tsai. Virial theorem and stress calculation in molecular-dynamics. J. of Chemical Physics70(3):1375–13821979.CrossRefGoogle Scholar
  27. [We i83]
    J.J. Weiner. Hellmann-feynmann theorem, elastic moduli, and the cauchy relation. Phys. Rev. B24:845–8481983.MathSciNetCrossRefGoogle Scholar
  28. [YDPG02]
    V. Yamakov, D. Wolf D, S.R. Phillpot, and H. Gleiter. Grain-boundary diffusion creep in nanocrystalline palladium by molecular-dynamics simulation. Acta mater.50:61–732002.CrossRefGoogle Scholar
  29. [Yof51]
    E.H. Yoffe. The moving griffith crack. Philosophical Magazine42:739–7501951.MathSciNetzbMATHGoogle Scholar
  30. [Zim99]
    J. Zimmermann. Continuum and atomistic modelling of dislocation nucleation at crystal surface ledges. PhD thesis, Stanford University, 1999.Google Scholar
  31. [ZKHG98]
    P. Zhang, P. Klein, Y. Huang, and H. Gao. Numerical simulation of cohesive fracture by the virtual-internal-bond model. CMES-Computer Modeling in Engineering and Sciences3(2):263–2771998.Google Scholar
  32. [ZM02]
    M. Zhou and D.L. McDowell. Equivalent continuum for dynamically deforming atomistic particle systems. Phil. Mag. A82(13):2547–25742002.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Markus J. Buehler
    • 1
  • Farid F. Abraham
    • 2
  • Huajian Gao
    • 1
  1. 1.Max Planck Institute for Metals ResearchStuttgartGermany
  2. 2.IBM Almaden Research CenterUSA

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