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.

  • Letter
  • Published:

Topological defects govern crack front motion and facet formation on broken surfaces

Nature Materials volume 17, pages 140–144 (2018)Cite this article

Subjects

Abstract

Cracks develop intricate patterns on the surfaces that they create. As faceted1,2 fracture surfaces are commonly formed by slow tensile cracks in both crystalline and amorphous materials3,4,5, facet formation and structure cannot reflect microscopic order. Although fracture mechanics predict that slow crack fronts should be straight and form mirror-like surfaces6,7,8,9, facet-forming fronts propagate simultaneously within different planes separated by steps. Here we show that these steps are topological defects of crack fronts and that crack front separation into disconnected overlapping segments provides the condition for step stability. Real-time imaging of propagating crack fronts combined with surface measurements shows that crack dynamics are governed by localized steps that drift at a constant angle to the local front propagation direction while their increased dissipation couples to long-ranged elasticity to determine front shapes. We study how three-dimensional topology couples to two-dimensional fracture dynamics to provide a fundamental picture of how patterned surfaces are generated.

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: Fracture surface patterns in brittle polyacrylamide gels.
Figure 2: Image sequences of facet-forming crack fronts and the resulting surface patterns.
Figure 3: Step-lines propagate at a constant angle to the local front normal in the crack frame.
Figure 4: Local dissipation at a step determines the long-range shape of the front.

Similar content being viewed by others

References

  1. Lawn, B. R. Fracture of Brittle Solids 2nd edn (Cambridge Univ. Press, 1993).

    Book  Google Scholar 

  2. Kermode, J. R. et al. Low-speed fracture instabilities in a brittle crystal. Nature 455, U1224–U1241 (2008).

    Article  Google Scholar 

  3. Gent, A. N. & Pulford, C. T. R. Micromechanics of fracture in elastomers. J. Mater. Sci. 19, 3612–3619 (1984).

    Article  CAS  Google Scholar 

  4. Tanaka, Y., Fukao, K., Miyamoto, Y. & Sekimoto, K. Discontinuous crack fronts of three-dimensional fractures. Europhys. Lett. 43, 664–670 (1998).

    Article  CAS  Google Scholar 

  5. Baumberger, T., Caroli, C., Martina, D. & Ronsin, O. Magic angles and cross-hatching instability in hydrogel fracture. Phys. Rev. Lett. 100, 178303 (2008).

    Article  CAS  Google Scholar 

  6. Katzav, E., Adda-Bedia, M. & Derrida, B. Fracture surfaces of heterogeneous materials: a 2D solvable model. Europhys. Lett. 78, 46006 (2007).

    Article  Google Scholar 

  7. Larralde, H. & Ball, R. C. The shape of slowly growing cracks. Europhys. Lett. 30, 87–92 (1995).

    Article  CAS  Google Scholar 

  8. Ramanathan, S., Ertas, D. & Fisher, D. S. Quasistatic crack propagation in heterogeneous media. Phys. Rev. Lett. 79, 873–876 (1997).

    Article  CAS  Google Scholar 

  9. Gao, H. J. & Rice, J. R. A first-order perturbation analysis of crack trapping by arrays of obstacles. J. Appl. Mech. Trans. ASME 56, 828–836 (1989).

    Article  Google Scholar 

  10. Freund, L. B. Dynamic Fracture Mechanics (Cambridge Univ. Press, 1998).

    Google Scholar 

  11. Goldman, T., Livne, A. & Fineberg, J. Acquisition of inertia by a moving crack. Phys. Rev. Lett. 104, 114301 (2010).

    Article  Google Scholar 

  12. Ponson, L., Bonamy, D. & Bouchaud, E. Two-dimensional scaling properties of experimental fracture surfaces. Phys. Rev. Lett. 96, 035506 (2006).

    Article  CAS  Google Scholar 

  13. Pons, A. J. & Karma, A. Helical crack-front instability in mixed-mode fracture. Nature 464, 85–89 (2010).

    Article  CAS  Google Scholar 

  14. Ronsin, O., Caroli, C. & Baumberger, T. Crack front echelon instability in mixed mode fracture of a strongly nonlinear elastic solid. Europhys. Lett. 105, 34001 (2014).

    Article  Google Scholar 

  15. Pham, K. H. & Ravi-Chandar, K. On the growth of cracks under mixed-mode I plus III loading. Int. J. Fract. 199, 105–134 (2016).

    Article  CAS  Google Scholar 

  16. Chen, C. H. et al. Crack front segmentation and facet coarsening in mixed-mode fracture. Phys. Rev. Lett. 115, 265503 (2015).

    Article  Google Scholar 

  17. Leblond, J.-B. & Ponson, L. Out-of-plane deviation of a mode I + III crack encountering a tougher obstacle. C. R. Méc. 344, 521–531 (2016).

    Article  Google Scholar 

  18. Livne, A., Cohen, G. & Fineberg, J. Universality and hysteretic dynamics in rapid fracture. Phys. Rev. Lett. 94, 224301 (2005).

    Article  CAS  Google Scholar 

  19. Boue, T. G., Cohen, G. & Fineberg, J. Origin of the microbranching instability in rapid cracks. Phys. Rev. Lett. 114, 054301 (2015).

    Article  Google Scholar 

  20. Ramanathan, S. & Fisher, D. Dynamics and instabilities of planar tensile cracks in heterogeneous media. Phys. Rev. Lett. 79, 877–880 (1997).

    Article  CAS  Google Scholar 

  21. Rice, J. R. 1st-order variation in elastic fields due to variation in location of a planar crack front. J. Appl. Mech. Trans. ASME 52, 571–579 (1985).

    Article  Google Scholar 

  22. Kolvin, I., Cohen, G. & Fineberg, J. Crack front dynamics: the interplay of singular geometry and crack instabilities. Phys. Rev. Lett. 114, 175501 (2015).

    Article  Google Scholar 

  23. Dalmas, D., Barthel, E. & Vandembroucq, D. Crack front pinning by design in planar heterogeneous interfaces. J. Mech. Phys. Solids 57, 446–457 (2009).

    Article  CAS  Google Scholar 

  24. Chopin, J., Prevost, A., Boudaoud, A. & Adda-Bedia, M. Crack front dynamics across a single heterogeneity. Phys. Rev. Lett. 107, 144301 (2011).

    Article  CAS  Google Scholar 

  25. Vasoya, M., Unni, A. B., Leblond, J. B., Lazarus, V. & Ponson, L. Finite size and geometrical non-linear effects during crack pinning by heterogeneities: an analytical and experimental study. J. Mech. Phys. Solids 89, 211–230 (2016).

    Article  Google Scholar 

  26. Adda-Bedia, M., Arias, R. E., Bouchbinder, E. & Katzav, E. Dynamic stability of crack fronts: out-of-plane corrugations. Phys. Rev. Lett. 110, 014302 (2013).

    Article  Google Scholar 

  27. Leblond, J. B., Karma, A. & Lazarus, V. Theoretical analysis of crack front instability in mode I + III. J. Mech. Phys. Solids 59, 1872–1887 (2011).

    Article  Google Scholar 

  28. Adda-Bedia, M. Path prediction of kinked and branched cracks in plane situations. Phys. Rev. Lett. 93, 185502 (2004).

    Article  CAS  Google Scholar 

  29. Bouchbinder, E., Mathiesen, J. & Procaccia, I. Branching instabilities in rapid fracture: dynamics and geometry. Phys. Rev. E 71, 056118 (2005).

    Article  Google Scholar 

  30. Bouchbinder, E., Livne, A. & Fineberg, J. Weakly nonlinear theory of dynamic fracture. Phys. Rev. Lett. 101, 264302 (2008).

    Article  Google Scholar 

Download references

Acknowledgements

J.F. and I.K. acknowledge the support of the Israel Science Foundation (grant no.1523/15), as well as the US-Israel Bi-national Science Foundation (grant no. 2016950). I.K. thanks I. Svetlizky and E. Katzav for fruitful discussions about step stability. I.K. is grateful to P. M. Chaikin for an enlightening conversation on the complexity of fracture surfaces.

Author information

Authors and Affiliations

  1. The Racah Institute of Physics, the Hebrew University of Jerusalem, Jerusalem 9190401, Israel

    Itamar Kolvin, Gil Cohen & Jay Fineberg

Authors
  1. Itamar Kolvin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gil Cohen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jay Fineberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

I.K. and G.C. designed the gel preparation method and fracture experiments. I.K. synthesized the gel samples, performed the fracture experiments and surface profilometry, and analysed data. J.F. conceived the 3D crack front imaging, and initiated and supervised the research. The manuscript was written by all authors.

Corresponding author

Correspondence to Jay Fineberg.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 512 kb)

Supplementary Information

Supplementary movie 1 (AVI 2367 kb)

Supplementary Information

Supplementary movie 2 (AVI 2514 kb)

Supplementary Information

Supplementary movie 3 (AVI 1536 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kolvin, I., Cohen, G. & Fineberg, J. Topological defects govern crack front motion and facet formation on broken surfaces. Nat. Mater. 17, 140–144 (2018). https://doi.org/10.1038/nmat5008

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nmat5008

This article is cited by

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