International Journal of Fracture

, Volume 182, Issue 2, pp 209–237 | Cite as

Fracture path in brittle thin sheets: a unifying review on tearing

  • Benoît RomanEmail author
Review Article


We review several studies of crack path in brittle thin sheets where large out of plane bending is involved. Fracture path are observed to be very reproducible. We present a unifying framework based on an energetic point of view. A simplified description, where the sheet is considered to behave as an inextensible fabric, captures important features of experiments: the fact that fracture path seems to obey geometry. We quantify the possible effects of additional bending and stretching terms, and estimate the validity of the model.


Plate mechanics Crack path  Thin sheets 



I thank K. Ravichandar for his suggestions and comments. I also thank José Bico and Basile Audoly for invaluable help.


  1. Adda-Bedia M, Amar M (1996) Stability of quasi-equilibrium cracks under uniaxial loading. Phys Rev Lett 76(1996):1497–1500Google Scholar
  2. Amestoy M, Leblond JB (1992) Crack paths in plane situationii, detailed form of the expansion of the stress intensity factors. Int J Solids Struct 29(4):465501CrossRefGoogle Scholar
  3. Argon A (1959) Surface cracks on glass. Proc R Soc A 250:472CrossRefGoogle Scholar
  4. Atkins A (1995) Opposite paths in the tearing of sheet materials. Endeavour 19(1):2–10CrossRefGoogle Scholar
  5. Atkins A (2007) Wiggly crack paths in the tearing of thin films. Eng Fract Mech 74:1018–1025. doi: 10.1016/j.engfracmech.2006.12.006 CrossRefGoogle Scholar
  6. Audoly B, Pomeau Y (2010) Elasticity and geometry: from hair curls to the non-linear response of shells. OUP, OxfordGoogle Scholar
  7. Audoly B, Reis PM, Roman B (2005) Cracks in thin sheets: when geometry rules the fracture path. Phys Rev Lett 95(025):502 doi: 10.1103/PhysRevLett.95.025502 Google Scholar
  8. Bayart E, Boudaoud A, Adda-Bedia M (2010) On the tearing of thin sheets. Eng Fract Mech 77:18491856. doi: 10.1016/j.engfracmech.2010.03.006 CrossRefGoogle Scholar
  9. Bayart E, Boudaoud A, Adda-Bedia M (2011) Finite-distance singularities in the tearing of thin sheets. Phys Rev Lett 106(194):301. doi: 10.1103/PhysRevLett.106.194301 Google Scholar
  10. Ben-Amar M, Pomeau Y (1997) Crumpled paper. Proc Math 453:729–755Google Scholar
  11. Bico J, Roman B, Moulin L, Boudaoud A (2004) Elastocapillary coalescence in wet hair. Nature 432(7018):690–690. doi: 10.1038/432690a Google Scholar
  12. Bourdin B, Francfort G, Marigo JJ (2008) The variational approach to fracture. J Elast 91:5–148. doi: 10.1007/s10659-007-9107-3 CrossRefGoogle Scholar
  13. Bui H (1978) Mécanique de la rupture fragile. Masson, ParisGoogle Scholar
  14. Cerda E, Hamm L, Roman B, Romero V (2012) Film mince d’emballage amorce de dchirure. INPI (2953499)Google Scholar
  15. Cerup-Simonsen B, Tornqvist R, Lutzen M (2009) A simplified grounding damage prediction method and its application in modern damage stability requirements. Marine Struct 22: 62–83Google Scholar
  16. Chambolle A, Francfort G, Marigo JJ (2009) When and how do cracks propagate? J Mech Phys Solids 57:16141622CrossRefGoogle Scholar
  17. Cohen Y, Procaccia I (2010) Dynamics of cracks in torn thin sheets. Phys Rev E 81:066103. doi: 10.1103/PhysRevE.81.066103
  18. Cotterell B, Rice J (1980) Slightly curved or kinked cracks. Int J Fract 16(2):155169CrossRefGoogle Scholar
  19. Davidovitch B, Schroll RD, Vella D, Adda-Bedia M, Cerda EA (2011) Prototypical model for tensional wrinkling in thin sheets. Proc Natl Acad Sci USA 108(45):18227–18232. doi: 10.1073/pnas.1108553108 CrossRefGoogle Scholar
  20. Dillard D, Hinkley J, Johnson W, St. Clair T (1994) Spiral tunneling cracks induced by environmental stress cracking in larc-tpi. J Adhesion 44: 1–2, 51–67. doi: 10.1080/00218469408026616
  21. Duplaix S (2008) Jacques Villéglé, la comdie urbaine. Centre Georges Pompidou Service CommercialGoogle Scholar
  22. Eiffel G (1900) La Tour de Trois Cent Metres. Société des Imprimeries Le Mercier, ParisGoogle Scholar
  23. Ghatak A, Mahadevan L (2003) Crack street: the cycloidal wake of a cylinder tearing through a thin sheet. Phys Rev Lett 91:215507Google Scholar
  24. Gladden J, Belmonte A (2007) Motion of a viscoelastic micellar fluid around a cylinder: flow and fracture. Phys Rev Lett 98(223):501. doi: 10.1103/PhysRevLett.98.224501 Google Scholar
  25. Goldstein R, Salganik R (1974) Brittle fracture of solids with arbitrary cracks. Int J Fract 10(2):507523Google Scholar
  26. Hakim V, Karma A (2009) Laws of crack motion and phase-field models of fracture. J Mech Phys Sol 57(235501):342368Google Scholar
  27. Hamm E, Reis P, Leblanc M, Roman B, Cerda E (2008) Tearing as a test for mechanical characterization of thin adhesive films. Nat Mater 7:386–390. doi: 10.1038/nmat2161 Google Scholar
  28. Hui C-Y, Zehnder AT, Potdar YK (1998) Williams meets von Karman: Mode coupling and nonlinearity in the fracture of thin plates International Journal of Fracture 93:409–429Google Scholar
  29. Kendall K (1971) The adhesion and surface energy of elastic solids. J Phys D Appl Phys 4:1186–1195CrossRefGoogle Scholar
  30. Kendall K (1975) Thin-film peeling- the elastic term. J Phys D Appl Phys 8:115CrossRefGoogle Scholar
  31. Kruglova O, Brau F, Villers D, Damman P (2011) How geometry controls the tearing of adhesive thin films on curved surfaces. Phys Rev Lett 107(164):303. doi: 10.1103/PhysRevLett.107.164303 Google Scholar
  32. Landau L, Lifshitz E (1967) Theory of elasticity. MirGoogle Scholar
  33. Lawn B (1993) Fracture of brittle solids. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  34. Lebental M (2007) Chaos quantique et micro-lasers organiques. Ph.D. Thesis, Univ Paris XI.
  35. Leblond J (2003) Mécanique de la rupture fragile et ductile. Hermes Science PublicationsGoogle Scholar
  36. Leung KT, Jozsa L, Ravasz M, Nda Z (2001) Spiral cracks without twisting. Nature 410(6825):166. doi: 10.1038/35065517 Google Scholar
  37. Lobkovsky AE, Gentges S, Li H, Morse D, Witten TA (1995) Scaling properties of stretching ridges in a crumpled elastic sheet. Science 270:1482–1485CrossRefGoogle Scholar
  38. Love A (1944) Treatise on the mathematical theory of elasticity. Dover, New YorkGoogle Scholar
  39. Mansfield EH (1989) The bending and stretching of plates. Cambridge university press, CambridgeCrossRefGoogle Scholar
  40. Marigo JJ, Meunier N (2006) Hierarchy of one-dimensional models in nonlinear elasticity. J Elast 83:1–28. doi: 10.1007/s10659-005-9036-y CrossRefGoogle Scholar
  41. Meyer DC, Leisegang T, Levin A, Paufler P, Volinsky A (2004) Tensile crack patterns in mo/si multilayers on si substrates under high-temperature bending. Appl Phys A 78:303–305. doi: 10.1007/s00339-003-2340-0 Google Scholar
  42. Monsalve A, Gutierrez I (2000) Application of a modified rigid plastic model to the out-plane fracture of ‘easy open end cans’. Int J Fract 102:323–339. doi: 10.1023/A:1007625512996 CrossRefGoogle Scholar
  43. Néda Z, t Leung K, Józsa L, Ravasz M (2002) Spiral cracks in drying precipitates. Phys Rev Lett 88(9):095502. doi: 10.1103/PhysRevLett.88.095502 Google Scholar
  44. O’keefe R (1994) Modeling the tearing of paper. Am J Phys 62(4):299–305. doi: 10.1119/1.17570 Google Scholar
  45. Pogorelov A (1988) Bendings of surfaces and stability of shells. American Mathematical Society, ProvidenceGoogle Scholar
  46. Reis P, Kumar A, Shattuck MD, Roman B (2008) Unzip instabilities: straight to oscillatory transitions in the cutting of thin polymer sheets. Eur Phys Lett 82(64):002. doi: 10.1209/0295-5075/82/64002 Google Scholar
  47. Roman B, Bico J (2010) Elasto-capillarity: deforming an elastic structure with a liquid droplet. J Phys-Condens Mater 22(49). doi: 10.1088/0953-8984/22/49/493101
  48. Roman B, Gay C, Clanet C (2013) Pendulum, drops and rods: a physical analogy. Am J Phys (submitted)Google Scholar
  49. Roman B, Reis PM, Audoly B, De Villiers S, Vigui V, Vallet D (2003) Oscillatory fracture paths in thin elastic sheets/oscillatory fracture paths in thin elastic sheets. C R Mecanique 331:811–816. doi: 10.1016/j.crme.2003.10.002 Google Scholar
  50. Romero V (2010) Spiraling cracks in thin sheets. Ph.D. Thesis, UPMC/USACH.
  51. Romero V, Hamm E, Cerda E (2013) Spiral tearing of thin films. Soft Matter (in press). doi: 10.1039/c3sm50564b
  52. Ronsin O, Heslot F, Perrin B (1995) Experimental study of quasistatic brittle crack propagation. Phys Rev Lett 75(12):2352–2355. doi: 10.1103/PhysRevLett.75.2352 Google Scholar
  53. Sendova M, Willis K (2003) Spiral and curved periodic crack patterns in sol-gel films. Appl Phys A Mater Sci Process 76:957–959. doi: 10.1007/s00339-002-1757-1
  54. Stein M, Hedgepeth J (1961) Analysis of partly wrinkled membranes. Tech. rep, NASA, Langley research center, Langley Field, VAGoogle Scholar
  55. Struik D (1988) Lectures on classical differential geometry. Dover, New YorkGoogle Scholar
  56. Takei A, Roman B, Bico J, Hamm E, Melo F (2013) Forbidden directions for the fracture of thin anisotropic sheets: an analogy with the wulff plot. Phys Rev Lett 110(144):301. doi: 10.1103/PhysRevLett.110.144301 Google Scholar
  57. Tallinen T, Mahadevan L (2011) Forced tearing of ductile and brittle thin sheets. Phys Rev Lett 107(245):502. doi: 10.1103/PhysRevLett.107.245502 Google Scholar
  58. Timoshenko S, Woinowski-Krieger S (1959) Theory of plates and shells. McGraw-Hill, New YorkGoogle Scholar
  59. Vella D, Wettlaufer JS (2007) Finger rafting: a generic instability of floating elastic sheets. Phys Rev Lett. doi: 10.1103/PhysRevLett.98.088303
  60. Vermorel R (2010) Elasticité et fragmentation solide. Ph.D. Thesis, Univ. Provence Aix-Marseille. PRL 104:175502. doi: 10.1103/PhysRevLett.104.175502
  61. Vermorel R, Vandenberghe N, Villermaux E (2009) Impacts on thin elastic sheets. Proc R Soc Lond A 465:823842Google Scholar
  62. Vermorel R, Vandenberghe N, Villermaux E (2010) Radial cracks in perforated thin sheets. Phys Rev Lett 104Google Scholar
  63. Villermaux E, Vandenberghe N (2013) Geometry and fragmentation of soft brittle impacted bodies. Soft Matter (in press). doi: 10.1039/C3SM50789K
  64. Wan N, Xu J, Lin T, Xu L, Chen K (2009) Observation and model of highly ordered wavy cracks due to coupling of in-plane stress and interface debonding in silica thin films. Phys Rev B. doi: 10.1103/PhysRevB.80.014121
  65. Wierzbicki T, Trauth KA, Atkins AG (1998) On diverging concertina tearing. J Appl Mech 65:990CrossRefGoogle Scholar
  66. Williams M (1961) The bending stress distribution at the base of a stationary crack. J Appl Mech 28:7882CrossRefGoogle Scholar
  67. Witten TA (2007) Stress focusing in elastic sheets. Rev Mod Phys 79(2):643–675. doi: 10.1103/RevModPhys.79.643 Google Scholar
  68. Xiaa C, Hutchinson JW (2000) Crack patterns in thin films. J Mech Phys Solids 48:1107–1131CrossRefGoogle Scholar
  69. Yang B, Ravi-Chandar K (2001) Crack path instabilities in a quenched glass plate. J Mech Phys Solids 49(2001):91–130Google Scholar
  70. Yuse A, Sano M (1993) Transition between crack patterns in quenched glass plates. Nature 362:329 Google Scholar
  71. Zehnder AT, Viz MJ (2005) Fracture mechanics of thin plates and shells under combined membrane, bending, and twisting loads. Appl Mech Rev 58(1):37CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.PMMH UMR 7636 CNRS/ESPCI/UPMC/Paris DiderotESPCIParisFrance

Personalised recommendations