Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Hyperelasticity governs dynamic fracture at a critical length scale

Nature volume 426, pages 141–146 (2003)Cite this article

Abstract

The elasticity of a solid can vary depending on its state of deformation. For example, metals will soften and polymers may stiffen as they are deformed to levels approaching failure. It is only when the deformation is infinitesimally small that elastic moduli can be considered constant, and hence the elasticity linear. Yet, many existing theories model fracture using linear elasticity, despite the fact that materials will experience extreme deformations at crack tips. Here we show by large-scale atomistic simulations that the elastic behaviour observed at large strains—hyperelasticity—can play a governing role in the dynamics of fracture, and that linear theory is incapable of fully capturing all fracture phenomena. We introduce the concept of a characteristic length scale for the energy flux near the crack tip, and demonstrate that the local hyperelastic wave speed governs the crack speed when the hyperelastic zone approaches this energy length scale.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: The simulation geometry with the lattice orientation and the weak layer.
Figure 2: Hyperelastic zone and the associated change in energy flow near the crack tip.
Figure 3: Change of crack speed with the onset strain of hyperelasticity.
Figure 4: Intersonic mode I crack motion and supersonic mode II crack motion.
Figure 5: Scaling law for the characteristic length associated with energy transport near the crack tip.

Similar content being viewed by others

References

  1. Freund, L. B. Dynamic Fracture Mechanics 2nd edn (Cambridge Univ. Press, Cambridge, UK, 1998)

    MATH  Google Scholar 

  2. Broberg, B. Cracks and Fracture (Academic, San Diego, 1999)

    Google Scholar 

  3. Slepyan, L. I. Models and Phenomena in Fracture Mechanics (Springer, Berlin, 2002)

    Book  MATH  Google Scholar 

  4. Fineberg, J., Gross, S. P., Marder, M. & Swinney, H. L. Instability in dynamic fracture. Phys. Rev. Lett. 67, 141–144 (1991)

    Article  Google Scholar 

  5. Ravi-Chandar, K. Dynamic fracture of nominally brittle materials. Int. J. Fract. 90, 83–102 (1998)

    Article  CAS  Google Scholar 

  6. Abraham, F. F., Brodbeck, D., Rudge, W. E. & Xu, X. Instability of fracture—a computer-simulation investigation. Phys. Rev. Lett. 73, 272–275 (1994)

    Article  ADS  CAS  PubMed  Google Scholar 

  7. Abraham, F. F., Brodbeck, D. & Rudge, W. E. A molecular-dynamics investigation of rapid fracture mechanics. J. Mech. Phys. Solids 45, 1595–1619 (1997)

    Article  ADS  CAS  MATH  Google Scholar 

  8. Falk, M. L., Needleman, A. & Rice, J. R. A critical evaluation of cohesive zone models of dynamic fracture. J. Phys. IV France 11, 43–50 (2001)

    Article  Google Scholar 

  9. Washabaugh, P. D. & Knauss, W. G. A reconcilation of dynamic crack velocity and Rayleigh-wave speed in isotropic brittle solids. Int. J. Fract. 65, 97–114 (1994)

    Google Scholar 

  10. Sharon, E. & Fineberg, J. Confirming the continuum theory of dynamic brittle fracture for fast cracks. Nature 397, 333 (1999)

    Article  ADS  CAS  Google Scholar 

  11. Field, J. E. Brittle fracture—its study and application. Contemp. Phys. 12, 1–31 (1971)

    Article  ADS  Google Scholar 

  12. Cramer, T., Wanner, A. & Gumbsch, P. Energy dissipation and path instabilities in dynamic fracture of silicon single crystals. Phys. Rev. Lett. 85, 788–791 (2000)

    Article  ADS  CAS  PubMed  Google Scholar 

  13. Hauch, J. A. & Marder, M. P. Energy balance in dynamic fracture, investigated by a potential drop technique. Int. J. Fract. 90 (1–2), 133–151 (1998)

    Article  CAS  Google Scholar 

  14. Hauch, J. A., Holland, D., Marder, M. P. & Swinney, H. L. Dynamic fracture in single crystal silicon. Phys. Rev. Lett. 82, 3823–3826 (1999)

    Article  ADS  CAS  Google Scholar 

  15. Hull, D. & Beardmore, P. Velocity of propagation of cleavage cracks in Tungsten. Int. J. Fract. Mech. 2, 468–488 (1966)

    Article  CAS  Google Scholar 

  16. Gao, H. A theory of local limiting speed in dynamic fracture. J. Mech. Phys. Solids 44, 1453–1474 (1996)

    Article  ADS  CAS  Google Scholar 

  17. Gao, H. Elastic eaves in a hyperelastic solid near its plane-strain equibiaxial cohesive limit. Phil. Mag. Lett. 76, 307–314 (1997)

    Article  ADS  CAS  Google Scholar 

  18. Abraham, F. F. Dynamics of brittle fracture with variable elasticity. Phys. Rev. Lett. 77, 272–275 (1996)

    Google Scholar 

  19. Abraham, F. F.. et al. Instability dynamics in three-dimensional fracture: An atomistic simulation. J. Mech. Phys. Solids 45, 1461–1471 (1997)

    Article  ADS  CAS  MATH  Google Scholar 

  20. Rountree, C. L. et al. Atomistic aspects of crack propagation in brittle materials: Multimillion atom molecular-dynamics simulations. Annu. Rev. Mater. Res. 32, 377–400 (2002)

    Article  CAS  Google Scholar 

  21. Zhou, S. J., Lomdahl, P. S., Thomson, R. & Holian, B. L. Dynamic crack processes via molecular-dynamics. Phys. Rev. Lett. 76, 2318–2321 (1996)

    Article  ADS  CAS  PubMed  Google Scholar 

  22. Heizler, S. I., Kessler, D. A. & Levine, H. Mode I fracture in a nonlinear lattice with viscoelastic forces. Phys. Rev. E 66, 016126 (2002)

    Article  ADS  Google Scholar 

  23. Abraham, F. F et al. Simulating materials failure by using up to one billion atoms and the world's fastest computer: Brittle fracture. Proc. Natl Acad. Sci. USA 99, 5777–5782 (2002)

    Article  ADS  CAS  PubMed  Google Scholar 

  24. Swadener, J. G., Baskes, M. I. & Nastasi, M. Molecular dynamics simulation of brittle fracture in silicon. Phys. Rev. Lett. 89, 085503 (2002)

    Article  ADS  CAS  PubMed  Google Scholar 

  25. Abraham, F. F. The atomic dynamics of fracture. J. Mech. Phys. Solids 49, 2095–2111 (2001)

    Article  ADS  MATH  Google Scholar 

  26. Fratini, S., Pla, O., Gonzalez, P., Guinea, F. & Louis, E. Energy radiation of moving cracks. Phys. Rev. B 66, 104104 (2002)

    Article  ADS  Google Scholar 

  27. Abraham, F. F. & Gao, H. How fast can cracks propagate? Phys. Rev. Lett. 84, 3113–3116 (2000)

    Article  ADS  CAS  PubMed  Google Scholar 

  28. Rosakis, A. J. Intersonic shear cracks and fault ruptures. Adv. Phys. 51, 1189–1257 (2002)

    Article  ADS  Google Scholar 

  29. Broberg, K. B. Dynamic crack propagation in a layer. Int. J. Sol. Struct. 32 (6–7), 883–896 (1995)

    Article  MATH  Google Scholar 

  30. Allen, M. & Tildesley, D. Computer Simulation of Liquids (Oxford Univ. Press, 1989)

    MATH  Google Scholar 

  31. Knauss, W. G. Stresses in an infinite strip containing a semi-infinite crack. J. Appl. Mech. 33, 356–362 (1966)

    Article  ADS  Google Scholar 

  32. Zimmermann, J. Continuum and Atomistic Modeling of Dislocation Nucleation at Crystal Surface Ledges PhD thesis, Stanford Univ. (1999)

    Google Scholar 

Download references

Acknowledgements

F.F.A. acknowledges the generous support provided by the Humboldt Research Award for Senior US Scientists.

Author information

Author notes

  1. Markus J. Buehler, Farid F. Abraham and Huajian Gao: These authors contributed equally to this work

Authors and Affiliations

  1. Max Planck Institute for Metals Research, Heisenbergstrasse 3, Stuttgart, 70569, Germany

    Markus J. Buehler & Huajian Gao

  2. IBM Research Division, Almaden Research Center, 650 Harry Road, San Jose, California, 95120, USA

    Farid F. Abraham

Authors
  1. Markus J. Buehler
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Farid F. Abraham
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Huajian Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Huajian Gao.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Buehler, M., Abraham, F. & Gao, H. Hyperelasticity governs dynamic fracture at a critical length scale. Nature 426, 141–146 (2003). https://doi.org/10.1038/nature02096

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature02096

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing