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  • Letter
  • Open Access

Dynamics of three-dimensional stepped cracks, bistability, and their transition to simple cracks

Meng Wang1, Mokhtar Adda-Bedia2, and Jay Fineberg1,*

  • 1The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
  • 2Université de Lyon, Ecole Normale Supérieure de Lyon, CNRS, Laboratoire de Physique, Lyon F-69342, France

  • *jay@mail.huji.ac.il
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Phys. Rev. Research 5, L012001 – Published 9 January, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L012001

Abstract

Slow cracks may be simple, with no internal structure. The leading edge of a simple crack, the crack front, forms a single fracture plane in its wake. Slow cracks may also develop segmented crack fronts, each segment propagating along a separate fracture plane. These planes merge at locations that form steps along fracture surfaces. Steps are not stationary, but instead propagate within a crack front. Real-time measurements of crack front structure and energy flux reveal that step dynamics significantly increase energy dissipation and drastically alter crack dynamics. Simple and stepped cracks are each stable. By extending the use of energy balance to include 3D crack front structure, we find that, while energy balance is obeyed, it is insufficient to select the energetically favorable crack growth mode. Transitions from stepped cracks to simple cracks occur only when their in-plane front lengths become equal and a perturbation momentarily changes step topology. Such 3D crack dynamics challenge our traditional understanding of fracture.

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References (33)

  1. L. B. Freund, Dynamic Fracture Mechanics (Cambridge University Press, Cambridge, England, 1998).
  2. J. Fineberg and M. Marder, Instability in dynamic fracture, Phys. Rep. 313, 1 (1999).
  3. E. Bouchbinder, J. Fineberg, and M. Marder, Dynamics of simple cracks, Annu. Rev. Condens. Matter Phys. 1, 371 (2010).
  4. I. Kolvin, G. Cohen, and J. Fineberg, Crack Front Dynamics: The Interplay of Singular Geometry and Crack Instabilities, Phys. Rev. Lett. 114, 175501 (2015).
  5. T. Goldman, A. Livne, and J. Fineberg, Acquisition of Inertia by a Moving Crack, Phys. Rev. Lett. 104, 114301 (2010).
  6. E. Bouchbinder, T. Goldman, and J. Fineberg, The dynamics of rapid fracture: instabilities, nonlinearities and length scales, Rep. Prog. Phys. 77, 046501 (2014).
  7. K. Ravi-Chandar and W. Knauss, An experimental investigation into dynamic fracture: Ii. microstructural aspects, Int. J. Fract. 26, 65 (1984).
  8. J. Fineberg, S. P. Gross, M. Marder, and H. L. Swinney, Instability in dynamic fracture, Phys. Rev. Lett. 67, 457 (1991).
  9. K. Ravi-Chandar, Dynamic Fracture (Elsevier, Amsterdam, 2004).
  10. M. Wang, M. Fourmeau, L. Zhao, F. Legrand, and D. Nélias, Self-emitted surface corrugations in dynamic fracture of silicon single crystal, Proc. Natl. Acad. Sci. USA 117, 16872 (2020).
  11. O. Ronsin, C. Caroli, and T. Baumberger, Crack front echelon instability in mixed mode fracture of a strongly nonlinear elastic solid, Europhys. Lett. 105, 34001 (2014).
  12. K. Pham and K. Ravi-Chandar, On the growth of cracks under mixed-mode i+ iii loading, Int. J. Fract. 199, 105 (2016).
  13. A. J. Pons and A. Karma, Helical crack-front instability in mixed-mode fracture, Nature (London) 464, 85 (2010).
  14. C.-H. Chen, T. Cambonie, V. Lazarus, M. Nicoli, A. J. Pons, and A. Karma, Crack Front Segmentation and Facet Coarsening in Mixed-Mode Fracture, Phys. Rev. Lett. 115, 265503 (2015).
  15. E. Sommer, Formation of fracture lances in glass, Eng. Fract. Mech. 1, 539 (1969).
  16. Y. Tanaka, K. Fukao, Y. Miyamoto, and K. Sekimoto, Discontinuous crack fronts of three-dimensional fractures, Europhys. Lett. 43, 664 (1998).
  17. T. Baumberger, C. Caroli, D. Martina, and O. Ronsin, Magic Angles and Cross-Hatching Instability in Hydrogel Fracture, Phys. Rev. Lett. 100, 178303 (2008).
  18. I. Kolvin, G. Cohen, and J. Fineberg, Topological defects govern crack front motion and facet formation on broken surfaces, Nat. Mater. 17, 140 (2018).
  19. M. Wang, M. Adda-Bedia, J. M. Kolinski, and J. Fineberg, How hidden 3d structure within crack fronts reveals energy balance, J. Mech. Phys. Solids 161, 104795 (2022).
  20. T. G. Boué, R. Harpaz, J. Fineberg, and E. Bouchbinder, Failing softly: a fracture theory of highly-deformable materials, Soft Matter 11, 3812 (2015).
  21. A. Livne, G. Cohen, and J. Fineberg, Universality and Hysteretic Dynamics in Rapid Fracture, Phys. Rev. Lett. 94, 224301 (2005).
  22. Y. Hu and Z. Suo, Viscoelasticity and poroelasticity in elastomeric gels, Acta Mechanica Solida Sinica 25, 441 (2012).
  23. C. Li, Z. Wang, Y. Wang, Q. He, R. Long, and S. Cai, Effects of network structures on the fracture of hydrogel, Extreme Mech. Lett. 49, 101495 (2021).
  24. S. Hassan, J. Kim et al., Polyacrylamide hydrogels. iv. near-perfect elasticity and rate-dependent toughness, J. Mech. Phys. Solids 158, 104675 (2022).
  25. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.5.L012001 for details of fracture experiments surrounded by water, simple crack front shapes, evolution of in-plane crack front length of stepped crack fronts during the multiple step reflections, and how the internal structures within the stepped crack front lead to the crack arrest. The material includes Refs. [11, 24].
  26. G. Noselli, A. Lucantonio, R. M. McMeeking, and A. DeSimone, Poroelastic toughening in polymer gels: A theoretical and numerical study, J. Mech. Phys. Solids 94, 33 (2016).
  27. Y. Yu, C. M. Landis, and R. Huang, Steady-state crack growth in polymer gels: A linear poroelastic analysis, J. Mech. Phys. Solids 118, 15 (2018).
  28. R. Long and C.-Y. Hui, Fracture toughness of hydrogels: measurement and interpretation, Soft Matter 12, 8069 (2016).
  29. A. Livne, E. Bouchbinder, I. Svetlizky, and J. Fineberg, The near-tip fields of fast cracks, Science 327, 1359 (2010).
  30. T. G. Boué, G. Cohen, and J. Fineberg, Origin of the Microbranching Instability in Rapid Cracks, Phys. Rev. Lett. 114, 054301 (2015).
  31. P. S. Theocaris, Local yielding around a crack tip in plexiglas, J. Appl. Mech. 37, 409 (1970).
  32. Y. Morishita, K. Tsunoda, and K. Urayama, Velocity transition in the crack growth dynamics of filled elastomers: Contributions of nonlinear viscoelasticity, Phys. Rev. E 93, 043001 (2016).
  33. Y. Tanaka, K. Fukao, and Y. Miyamoto, Fracture energy of gels, Eur. Phys. J. E 3, 395 (2000).

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Phys. Rev. Research 5, L012001– Published 9 January, 2023
  • Received 1 February 2022
  • Revised 10 May 2022
  • Accepted 7 November 2022
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