Acta Mechanica Sinica

, Volume 21, Issue 2, pp 103–111 | Cite as

The dynamical complexity of work-hardening: a large-scale molecular dynamics simulation

  • Markus J. Buehler
  • Alexander Hartmaier
  • Huajian GaoEmail author
  • Mark A. Duchaineau
  • Farid F. Abraham


We analyze a large-scale molecular dynamics simulation of work hardening in a model system of a ductile solid. With tensile loading, we observe emission of thousands of dislocations from two sharp cracks. The dislocations interact in a complex way, revealing three fundamental mechanisms of work-hardening in this ductile material. These are (1) dislocation cutting processes, jog formation and generation of trails of point defects; (2) activation of secondary slip systems by Frank-Read and cross-slip mechanisms; and (3) formation of sessile dislocations such as Lomer-Cottrell locks. We report the discovery of a new class of point defects referred to as trail of partial point defects, which could play an important role in situations when partial dislocations dominate plasticity. Another important result of the present work is the rediscovery of the Fleischer-mechanism of cross-slip of partial dislocations that was theoretically proposed more than 50 years ago, and is now, for the first time, confirmed by atomistic simulation. On the typical time scale of molecular dynamics simulations, the dislocations self-organize into a complex sessile defect topology. Our analysis illustrates numerous mechanisms formerly only conjectured in textbooks and observed indirectly in experiments. It is the first time that such a rich set of fundamental phenomena have been revealed in a single computer simulation, and its dynamical evolution has been studied. The present study exemplifies the simulation and analysis of the complex nonlinear dynamics of a many-particle system during failure using ultra-large scale computing.


Work-hardening Large-scale atomistic simulation Dislocation junction Cross-slip 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Hirth, J.P., Lothe, J. : Theory of Dislocations. Wiley-Interscience, 1982Google Scholar
  2. 2.
    Hull, D., Bacon, D.J.: Introduction to Dislocations. Butterworth Heinemann, 2002Google Scholar
  3. 3.
    Courtney, T.H.: Mechanical behavior of materials. McGraw-Hill, 1990Google Scholar
  4. 4.
    Allen, M.P., Tildesley, D.J.: Computer Simulation of Liquids. Oxford University Press, 1989Google Scholar
  5. 5.
    Abraham, F.F., Walkup, R., Gao, H. 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, 99(9): 5783–5787 (2002)Google Scholar
  6. 6.
    Gumbsch, P., Gao, H.: Dislocations faster than the speed of sound. Science, 283: 965–968 (1999)Google Scholar
  7. 7.
    Buehler, M.J., Abraham, F.F., Gao, H.: Hyperelasticity governs dynamic fracture at a critical length scale. Nature, 426: 141–146 (2003)Google Scholar
  8. 8.
    Wolf, D., Yamakov, V., Phillpot, S.R. et al.: Deformation mechanism and inverse Hall-Petch behavior in nanocrystalline materials. Z. Metallk., 94: 1052–1061 (2003)Google Scholar
  9. 9.
    Yamakov, V., Wolf, D., Phillpot, S.R., Mukherjee, A.K. et al.: Dislocation processes in the deformation of nanocrystalline aluminium by MD simulation. Nature Materials, 1: 1–4 (2002)Google Scholar
  10. 10.
    van Swygenhoven, H., Derlet, P.M., Hasnaoui, A.: Atomic mechanism for dislocation emission from nanosized grain boundaries. Phys. Rev. B, 66: 024101 (2002)Google Scholar
  11. 11.
    Farkas, D., van Swygenhoven, H., Derlet, P.: Intergranular fracture in nanocrystalline metals. Phys. Rev. B, 66: 060101 (2002)Google Scholar
  12. 12.
    Derlet, P.M., Hasnaoui, A., van Swygenhoven, H.: Atomistic simulations as guidance to experiments. Scripta Mater., 49: 629–635 (2003)Google Scholar
  13. 13.
    Schiotz, J., Leffers, T., Singh, B.N.: Dislocation nucleation and vacancy formation during high-speed deformation of fcc metals. Phil. Mag. Lett., 81: 301–309 (2001)Google Scholar
  14. 14.
    Jacobsen, K.W., Schiotz, J.: Computational materials science - nanoscale plasticity. Nature Materials, 1: 15–16 (2002)Google Scholar
  15. 15.
    Rhee, M., Zbib, H.M., Hirth, J.P. et al.: Models for long-/short-range interactions and cross slip in 3D dislocation simulation of bcc single crystals. Modeling Simul. Mater. Sci. Eng., 6(4): 467–492 (1998)Google Scholar
  16. 16.
    Wen, M., Lin, D.L.: Atomistic process of dislocation cross-slip in Ni3Al. Scripta Mater., 36: 265–268 (1997)Google Scholar
  17. 17.
    Zhou, S.J., Preston, D.L., Louchet, F.: Investigation of vacancy formation by a jogged dissociated dislocation with large-scale molecular dynamics and dislocation energetics. Acta Mater., 47: 2695–2703 (1999)Google Scholar
  18. 18.
    Li, M., Zhou, S.J.: Investigation of jog motion in gamma-TiAl via molecular dynamics. Phil. Mag. Lett., 79: 773–784 (1999)Google Scholar
  19. 19.
    Li, M., Chu, W.Y., Qian, C.F. et al.: Molecular dynamics simulation of dislocation intersections in aluminum. Mat. Sci. Eng. A, 363: 234–241 ( 2003)Google Scholar
  20. 20.
    Zhou, S.J., Preston, D.L., Lomdahl, P.S. et al.: Large-scale molecular-dynamics simulations of dislocation interactions in copper. Science, 279: 1525–1527 (1998)Google Scholar
  21. 21.
    Bulatov, V., Abraham, F.F., Kubin, L. et al.: Connecting atomistic and mesoscale simulations of crystal plasticity. Nature, 391: 669–672 (1998)Google Scholar
  22. 22.
    Schiotz, J., Jacobsen, K.W.: A maximum in the strength of nanocrystalline copper. Science, 301: 1357–1359 (2003)Google Scholar
  23. 23.
    Yamakov, V., Wolf, D., Phillpot, S.R. et al.: Dislocation-dislocation and dislocation-twin reactions in nanocrystalline Al by molecular dynamics simulation. Acta Mat., 51: 4135–4147 (2003)Google Scholar
  24. 24.
    Yamakov, V., Wolf, D., Phillpot, S.R. et al.: Deformation-mechanism map for nanocrystalline metals by molecular dynamics simulation. Nature Materials, 3: 43–47 (2004)Google Scholar
  25. 25.
    Kelchner, C., Plimpton, S.J., Hamilton, J.C.: Dislocation nucleation and defect structure during surface-indentation. Phys. Rev. B, 58: 11085–11088 (1998)Google Scholar
  26. 26.
    Mott, N.F.: The work hardening of metals. Trans. Met. Soc. AIME, 218: 962 (1960)Google Scholar
  27. 27.
    Krause-Rehberg, R., Brohl, M., Leipner, H. et al.: Defects in plastically deformed semiconductors studied by positron annihilation: Silicon and germanium. Phys. Rev. B, 47: 13266–13276 (1993)Google Scholar
  28. 28.
    Rempel, A.A., Nazarova, S.Z., Gusev, A.I.: Intrinsic defects in palladium after severe plastic deformation. Phys. Stat. Sol., 181: R16 (2000)Google Scholar
  29. 29.
    Marian, J., Cai, W., Bulatov, V.V.: Dynamic transitions from smooth to rough to twinning in dislocation motion. Nature Materials, 3: 158–163 (2004)Google Scholar
  30. 30.
    Fleischer, R.L.: Cross slip of extended dislocations. Acta Metall., 7: 134–135 (1959)Google Scholar
  31. 31.
    Qi, Y., Strachan, A., Cagin, T., Goddard, W.A.: Large-scale atomistic simulations of screw dislocation structure, annihilation and cross-slip in FCC Ni. Mat. Sci. Eng.A, 309–310, 156–159 (2001)Google Scholar
  32. 32.
    Vegge, T., Jacobsen, W.: Atomistic simulations of jog migration on extended screw dislocations. Mat. Sci. Eng. A, 319–321 , 119–123 (2001)Google Scholar
  33. 33.
    Vegge, T., Jacobsen, W.: Atomistic simulations of dislocation processes in copper. J. Phys. Condens. Matt., 14: 2929–2956 (2002)Google Scholar
  34. 34.
    Shenoy, V.B., Kukta, R.V., Phillips, R.: Quasicontinuum models of interfacial structure and deformation. Phys. Rev. Lett., 84: 1491–1494 (2000)Google Scholar
  35. 35.
    Hirsch, P.B., Warrington, D.H.: The flow stress of aluminium and copper at high temperatures. Phil. Mag., 6: 735 (1961)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Markus J. Buehler
    • 1
    • 2
  • Alexander Hartmaier
    • 2
  • Huajian Gao
    • 2
    Email author
  • Mark A. Duchaineau
    • 3
  • Farid F. Abraham
    • 4
  1. 1.California Institute of TechnologyPasadenaUSA
  2. 2.Max Planck Institute for Metals ResearchStuttgartGermany
  3. 3.Lawrence Livermore National LaboratoryLivermoreUSA
  4. 4.IBM Almaden Research CenterSan JoseUSA

Personalised recommendations