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Experimental Analysis of Fast Crack Growth in Elastomers

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Degradation of Elastomers in Practice, Experiments and Modeling

Part of the book series: Advances in Polymer Science ((POLYMER,volume 289))

Abstract

Crack growth often leads to catastrophic failure of rubber products. Understanding the crack growth mechanism is important for toughening elastomers. This article described in summarized form our recent experimental investigations on fast crack growth in elastomers. The crack-tip features, including the crack-tip profiles and the local crack-tip strain fields, are revealed for a quasi-stationary crack and fast-moving cracks ranging from subsonic to super-shear (intersonic) cracks. The velocity and crack-tip features of fast-moving cracks are discussed in relation to the nonlinear elasticity and viscoelasticity of bulk elastomers. The effects of anisotropic stress softening (anisotropic Mullins effect), which is pronounced in filler-reinforced elastomers, on the crack-tip properties are elucidated. We also describe the characterization of quasi-stationary cracks in elastomers subjected to various types of biaxial loading, providing a basis for the fracture mechanics of elastomers under multiaxial deformation.

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References

  1. Rodgers B, Waddell W (2013) Tire engineering. In: Mark JE, Erman B, Roland M (eds) The science and technology of rubber4th edn. Elsevier, Waltham, pp 653–695

    Chapter  Google Scholar 

  2. Freund LB (1990) Dynamic fracture mechanics. Cambridge University Press, Cambridge

    Book  Google Scholar 

  3. Ravi-Chandar K (2004) Dynamic fracture. Elsevier

    Google Scholar 

  4. Anderson TL (2017) Fracture mechanics. CRC Press

    Book  Google Scholar 

  5. Persson BNJ, Albohr O, Heinrich G, Ueba H (2005) Crack propagation in rubber-like materials. J Phys Condens Matter 17. https://doi.org/10.1088/0953-8984/17/44/R01

  6. Long R, Hui C-Y (2015) Crack tip fields in soft elastic solids subjected to large quasi-static deformation – a review. Extrem Mech Lett 4:131–155. https://doi.org/10.1016/j.eml.2015.06.002

    Article  Google Scholar 

  7. Creton C, Ciccotti M (2016) Fracture and adhesion of soft materials: a review. Rep Prog Phys 79:046601. https://doi.org/10.1088/0034-4885/79/4/046601

    Article  CAS  Google Scholar 

  8. Kadir A, Thomas AG (1981) Tear behavior of rubbers over a wide range of rates. Rubber Chem Technol 54:15–23. https://doi.org/10.5254/1.3535791

    Article  Google Scholar 

  9. Horst T, Heinrich G (2008) Crack propagation behavior in rubber materials. Polym Sci Ser A 50:583–590. https://doi.org/10.1134/S0965545X08050131

    Article  Google Scholar 

  10. Tsunoda K, Busfield JJC, Davies CKL, Thomas AG (2000) Effect of materials variables on the tear behaviour of a non-crystallizing elastomer. J Mater Sci 35:5187–5198. https://doi.org/10.1023/A:1004860522186

    Article  CAS  Google Scholar 

  11. Greensmith HW, Thomas AG (1955) Rupture of rubber. III. Determination of tear properties. J Polym Sci 18:189–200. https://doi.org/10.1002/pol.1955.120188803

    Article  CAS  Google Scholar 

  12. Greensmith HW (1956) Rupture of rubber. IV. Tear properties of vulcanizates containing carbon black. J Polym Sci 21:175–187. https://doi.org/10.1002/pol.1956.120219802

    Article  Google Scholar 

  13. Persson BNJ, Brener EA (2005) Crack propagation in viscoelastic solids. Phys Rev E Stat Nonlinear Soft Matter Phys 71:1–8. https://doi.org/10.1103/PhysRevE.71.036123

    Article  CAS  Google Scholar 

  14. Morishita Y, Tsunoda K, Urayama K (2016) Velocity transition in the crack growth dynamics of filled elastomers: contributions of nonlinear viscoelasticity. Phys Rev E 93:043001. https://doi.org/10.1103/PhysRevE.93.043001

    Article  CAS  Google Scholar 

  15. Morishita Y, Tsunoda K, Urayama K (2017) Crack-tip shape in the crack-growth rate transition of filled elastomers. Polymer 108:230–241. https://doi.org/10.1016/j.polymer.2016.11.041

    Article  CAS  Google Scholar 

  16. Morishita Y, Tsunoda K, Urayama K (2019) Universal relation between crack-growth dynamics and viscoelasticity in glass-rubber transition for filled elastomers. Polymer 179:121651. https://doi.org/10.1016/j.polymer.2019.121651

    Article  CAS  Google Scholar 

  17. Heinrich G, Klüppel M, Vilgis TA (2002) Reinforcement of elastomers. Curr Opin Solid State Mater Sci 6:195–203. https://doi.org/10.1016/S1359-0286(02)00030-X

    Article  CAS  Google Scholar 

  18. Donnet J-B, Custodero E (2013) Reinforcement of elastomers by particulate fillers. In: Mark JE, Erman B, Roland M (eds) The science and technology of rubber4th edn. Elsevier, Waltham, pp 367–400

    Google Scholar 

  19. Mullins L, Tobin NR (1957) Theoretical model for the elastic behavior of filler-reinforced vulcanized rubbers. Rubber Chem Technol 30:555–571. https://doi.org/10.5254/1.3542705

    Article  Google Scholar 

  20. Mullins L (1969) Softening of rubber by deformation. Rubber Chem Technol 42:339–362. https://doi.org/10.5254/1.3539210

    Article  CAS  Google Scholar 

  21. Diani J, Fayolle B, Gilormini P (2009) A review on the Mullins effect. Eur Polym J 45:601–612. https://doi.org/10.1016/j.eurpolymj.2008.11.017

    Article  CAS  Google Scholar 

  22. Mai T-T, Morishita Y, Urayama K (2017) Novel features of the Mullins effect in filled elastomers revealed by stretching measurements in various geometries. Soft Matter 13:1966–1977. https://doi.org/10.1039/C6SM02833K

    Article  CAS  Google Scholar 

  23. MacHado G, Chagnon G, Favier D (2012) Induced anisotropy by the Mullins effect in filled silicone rubber. Mech Mater 50:70–80

    Article  Google Scholar 

  24. Mai T-T, Morishita Y, Urayama K (2017) Induced anisotropy by Mullins effect in filled elastomers subjected to stretching with various geometries. Polymer 126:29–39. https://doi.org/10.1016/j.polymer.2017.08.012

    Article  CAS  Google Scholar 

  25. Mai T-T, Matsuda T, Nakajima T et al (2019) Damage cross-effect and anisotropy in tough double network hydrogels revealed by biaxial stretching. Soft Matter 15:3719–3732. https://doi.org/10.1039/C9SM00409B

    Article  CAS  Google Scholar 

  26. Mai T-T, Okuno K, Tsunoda K, Urayama K (2021) Anisotropic stress-softening effect on fast dynamic crack in filler-reinforced elastomers. Mech Mater 155:103786. https://doi.org/10.1016/j.mechmat.2021.103786

    Article  Google Scholar 

  27. Marder M (2006) Supersonic rupture of rubber. J Mech Phys Solids 54:491–532. https://doi.org/10.1016/j.jmps.2005.10.002

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  29. Petersan P, Deegan R, Marder M, Swinney H (2004) Cracks in rubber under tension exceed the shear wave speed. Phys Rev Lett 93:015504. https://doi.org/10.1103/PhysRevLett.93.015504

    Article  CAS  Google Scholar 

  30. Chen CH, Zhang HP, Niemczura J et al (2011) Scaling of crack propagation in rubber sheets. EPL 96. https://doi.org/10.1209/0295-5075/96/36009

  31. Rosakis AJ (1999) Cracks faster than the shear wave speed. Science 284:1337–1340. https://doi.org/10.1126/science.284.5418.1337

    Article  CAS  Google Scholar 

  32. Marder M (2005) Shock-wave theory for rupture of rubber. Phys Rev Lett 94:1–4. https://doi.org/10.1103/PhysRevLett.94.048001

    Article  CAS  Google Scholar 

  33. Guozden TM, Jagla EA, Marder M (2010) Supersonic cracks in lattice models. Int J Fract 162:107–125. https://doi.org/10.1007/s10704-009-9426-4

    Article  Google Scholar 

  34. Kroon M (2011) Steady-state crack growth in rubber-like solids. Int J Fract 169:49–60. https://doi.org/10.1007/s10704-010-9583-5

    Article  Google Scholar 

  35. Kroon M (2014) Energy release rates in rubber during dynamic crack propagation. Int J Solids Struct 51:4419–4426. https://doi.org/10.1016/j.ijsolstr.2014.09.010

    Article  Google Scholar 

  36. Mai T, Okuno K, Tsunoda K, Urayama K (2020) Crack-tip strain field in Supershear crack of elastomers. ACS Macro Lett 9:762–768. https://doi.org/10.1021/acsmacrolett.0c00213

    Article  CAS  Google Scholar 

  37. Urayama K (2006) An experimentalist’s view of the physics of rubber elasticity. J Polym Sci B Polym Phys 44:3440–3444. https://doi.org/10.1002/polb.21010

    Article  CAS  Google Scholar 

  38. Adams NJI (1973) Some comments on the effect of biaxial stress on fatigue crack growth and fracture. Eng Fract Mech 5:983–991. https://doi.org/10.1016/0013-7944(73)90063-5

    Article  Google Scholar 

  39. Liebowitz H, Lee JD, Eftis J (1978) Biaxial load effects in fracture mechanics. Eng Fract Mech 10:315–335. https://doi.org/10.1016/0013-7944(78)90015-2

    Article  Google Scholar 

  40. Eftis J, Jones DL, Liebowitz H (1990) Load biaxiality and fracture: synthesis and summary. Eng Fract Mech 36:537–574. https://doi.org/10.1016/0013-7944(90)90112-T

    Article  Google Scholar 

  41. Marano C, Calabrò R, Rink M (2010) Effect of molecular orientation on the fracture behavior of carbon black-filled natural rubber compounds. J Polym Sci B 48:1509–1515. https://doi.org/10.1002/polb.22054

    Article  CAS  Google Scholar 

  42. Caimmi F, Calabrò R, Briatico-Vangosa F et al (2015) Toughness of natural rubber compounds under biaxial loading. Eng Fract Mech 149:250–261. https://doi.org/10.1016/j.engfracmech.2015.08.003

    Article  Google Scholar 

  43. Schneider K, Calabrò R, Lombardi R et al (2017) Grellmann W, Langer B (eds) Characterisation of the deformation and fracture behaviour of elastomers under biaxial deformation. Springer, Cham, pp 335–349

    Google Scholar 

  44. Ahmad D, Sahu SK, Patra K (2019) Fracture toughness, hysteresis and stretchability of dielectric elastomers under equibiaxial and biaxial loading. Polym Test 79:106038. https://doi.org/10.1016/j.polymertesting.2019.106038

    Article  CAS  Google Scholar 

  45. Dedova S, Schneider K, Stommel M, Heinrich G (2021) Dissipative heating, fatigue and fracture behaviour of rubber under multiaxial loading. Adv Polym Sci 286:421–443. https://doi.org/10.1007/12_2020_75

    Article  CAS  Google Scholar 

  46. Mai T, Urayama K (2021) Biaxial loading effects on strain energy release rate and crack-tip strain field in elastic hydrogels. Macromolecules. https://doi.org/10.1021/acs.macromol.1c00445

  47. Rivlin RS, Thomas AG (1953) Rupture of rubber. I. Characteristic energy for tearing. J Polym Sci 10:291–318. https://doi.org/10.1002/pol.1953.120100303

    Article  CAS  Google Scholar 

  48. Livne A, Bouchbinder E, Svetlizky I, Fineberg J (2010) The near-tip fields of fast cracks. Science 327:1359–1363. https://doi.org/10.1126/science.1180476

    Article  CAS  Google Scholar 

  49. Livne A, Bouchbinder E, Fineberg J (2008) Breakdown of linear elastic fracture mechanics near the tip of a rapid crack. Phys Rev Lett 101:1–4. https://doi.org/10.1103/PhysRevLett.101.264301

    Article  CAS  Google Scholar 

  50. Bouchbinder E, Livne A, Fineberg J (2010) Weakly nonlinear fracture mechanics: experiments and theory. Int J Fract 162:3–20. https://doi.org/10.1007/s10704-009-9427-3

    Article  Google Scholar 

  51. Bouchbinder E, Livne A, Fineberg J (2008) Weakly nonlinear theory of dynamic fracture. Phys Rev Lett 101:2–5. https://doi.org/10.1103/PhysRevLett.101.264302

    Article  CAS  Google Scholar 

  52. Treloar LRG (1975) The physics of rubber elasticity.3rd edn. Oxford University Press Inc., New York

    Google Scholar 

  53. Williams ML, Landel RF, Ferry JD (1955) The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids. J Am Chem Soc 77:3701–3707. https://doi.org/10.1021/ja01619a008

    Article  CAS  Google Scholar 

  54. Gent AN, Lai S-M, Nah C, Wang C (1994) Viscoelastic effects in cutting and tearing rubber. Rubber Chem Technol 67:610–618. https://doi.org/10.5254/1.3538696

    Article  CAS  Google Scholar 

  55. Carbone G, Persson BNJ (2005) Crack motion in viscoelastic solids: the role of the flash temperature. Eur Phys J E 17:261–281. https://doi.org/10.1140/epje/i2005-10013-y

    Article  CAS  Google Scholar 

  56. Carbone G, Persson BNJ (2005) Hot cracks in rubber: origin of the giant toughness of rubberlike materials. Phys Rev Lett 95:9–12. https://doi.org/10.1103/PhysRevLett.95.114301

    Article  CAS  Google Scholar 

  57. Carbone G, Persson BNJ (2005) Hot cracks in rubber: origin of the Giant toughness of rubberlike materials. Phys Rev Lett 95:114301. https://doi.org/10.1103/PhysRevLett.95.114301

    Article  CAS  Google Scholar 

  58. D’Amico F, Carbone G, Foglia MM, Galietti U (2013) Moving cracks in viscoelastic materials: temperature and energy-release-rate measurements. Eng Fract Mech 98:315–325. https://doi.org/10.1016/j.engfracmech.2012.10.026

    Article  Google Scholar 

  59. Knauss WG (2015) A review of fracture in viscoelastic materials. Int J Fract 196:99–146. https://doi.org/10.1007/s10704-015-0058-6

    Article  Google Scholar 

  60. Kubo A, Sakumichi N, Morishita Y et al (2021) Dynamic glass transition dramatically accelerates crack propagation in rubberlike solids. Phys Rev Mater 5:073608. https://doi.org/10.1103/PhysRevMaterials.5.073608

    Article  CAS  Google Scholar 

  61. Kubo A, Umeno Y (2017) Velocity mode transition of dynamic crack propagation in hyperviscoelastic materials: a continuum model study. Sci Rep 7:4–6. https://doi.org/10.1038/srep42305

    Article  CAS  Google Scholar 

  62. Sakumichi N, Okumura K (2017) Exactly solvable model for a velocity jump observed in crack propagation in viscoelastic solids. Sci Rep 7:1–11. https://doi.org/10.1038/s41598-017-07214-8

    Article  CAS  Google Scholar 

  63. Zhang T, Lin S, Yuk H, Zhao X (2015) Predicting fracture energies and crack-tip fields of soft tough materials. Extrem Mech Lett 4:1–8. https://doi.org/10.1016/j.eml.2015.07.007

    Article  Google Scholar 

  64. Diani J, Brieu M, Batzler K, Zerlauth P (2015) Effect of the Mullins softening on mode I fracture of carbon-black filled rubbers. Int J Fract 194:11–18. https://doi.org/10.1007/s10704-015-0030-5

    Article  CAS  Google Scholar 

  65. El Yaagoubi M, Juhre D, Meier J et al (2018) Tearing energy and path-dependent J-integral evaluation considering stress softening for carbon black reinforced elastomers. Eng Fract Mech 190:259–272. https://doi.org/10.1016/j.engfracmech.2017.12.029

    Article  Google Scholar 

  66. Mzabi S, Berghezan D, Roux S et al (2011) A critical local energy release rate criterion for fatigue fracture of elastomers. J Polym Sci B 49:1518–1524. https://doi.org/10.1002/polb.22338

    Article  CAS  Google Scholar 

  67. Diaz R, Diani J, Gilormini P (2014) Physical interpretation of the Mullins softening in a carbon-black filled SBR. Polymer 55:4942–4947. https://doi.org/10.1016/j.polymer.2014.08.020

    Article  CAS  Google Scholar 

  68. Schreier H, Orteu J-J, Sutton MA (2009) Image correlation for shape, motion and deformation measurements. Springer, Boston

    Book  Google Scholar 

  69. Zhang H, Scholz AK, De Crevoisier J et al (2015) Nanocavitation around a crack tip in a soft nanocomposite: a scanning microbeam small angle X-ray scattering study. J Polym Sci B 53:422–429. https://doi.org/10.1002/polb.23651

    Article  CAS  Google Scholar 

  70. Slootman J, Waltz V, Yeh CJ et al (2020) Quantifying rate- and temperature-dependent molecular damage in elastomer fracture. Phys Rev X 10:041045. https://doi.org/10.1103/PhysRevX.10.041045

    Article  CAS  Google Scholar 

  71. Mihai LA, Goriely A (2017) How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity. Proc R Soc A Math Phys Eng Sci 473:20170607. https://doi.org/10.1098/rspa.2017.0607

    Article  Google Scholar 

  72. Huang Y, Gao H (2001) Intersonic crack propagation-part I: the fundamental solution. J Appl Mech Trans ASME 68:169–175. https://doi.org/10.1115/1.1357871

    Article  Google Scholar 

  73. Bouchbinder E, Fineberg J, Marder M (2010) Dynamics of simple cracks. Annu Rev Condens Matter Phys 1:371–395. https://doi.org/10.1146/annurev-conmatphys-070909-104019

    Article  Google Scholar 

  74. Thomas AG (1960) Rupture of rubber. VI. Further experiments on the tear criterion. J Appl Polym Sci 3:168–174. https://doi.org/10.1002/app.1960.070030805

    Article  CAS  Google Scholar 

  75. Long R, Hui C-Y (2010) Effects of triaxiality on the growth of crack-like cavities in soft incompressible elastic solids. Soft Matter 6:1238. https://doi.org/10.1039/b917148g

    Article  CAS  Google Scholar 

  76. Trabelsi S, Albouy PA, Rault J (2002) Stress-induced crystallization around a crack tip in natural rubber. Macromolecules 35:10054–10061. https://doi.org/10.1021/ma021106c

    Article  CAS  Google Scholar 

  77. Saintier N, Cailletaud G, Piques R (2011) Cyclic loadings and crystallization of natural rubber: an explanation of fatigue crack propagation reinforcement under a positive loading ratio. Mater Sci Eng A 528:1078–1086. https://doi.org/10.1016/j.msea.2010.09.079

    Article  CAS  Google Scholar 

  78. Brüning K, Schneider K, Roth SV, Heinrich G (2012) Kinetics of strain-induced crystallization in natural rubber studied by WAXD: dynamic and impact tensile experiments. Macromolecules 45:7914–7919. https://doi.org/10.1021/ma3011476

    Article  CAS  Google Scholar 

  79. Brüning K, Schneider K, Heinrich G (2012) Deformation and orientation in filled rubbers on the nano- and microscale studied by X-ray scattering. J Polym Sci B 50:1728–1732. https://doi.org/10.1002/polb.23148

    Article  CAS  Google Scholar 

  80. Brüning K, Schneider K, Heinrich G (2013) Grellmann W, Heinrich G, Kaliske M et al (eds) In-situ structural characterization of rubber during deformation and fracture. Springer, Berlin, pp 43–80

    Google Scholar 

  81. Brüning K, Schneider K, Roth SV, Heinrich G (2013) Strain-induced crystallization around a crack tip in natural rubber under dynamic load. Polymer 54:6200–6205. https://doi.org/10.1016/j.polymer.2013.08.045

    Article  CAS  Google Scholar 

  82. Brüning K, Schneider K, Roth SV, Heinrich G (2015) Kinetics of strain-induced crystallization in natural rubber: a diffusion-controlled rate law. Polymer 72:52–58. https://doi.org/10.1016/j.polymer.2015.07.011

    Article  CAS  Google Scholar 

  83. Samaca Martinez JR, Balandraud X, Toussaint E et al (2014) Thermomechanical analysis of the crack tip zone in stretched crystallizable natural rubber by using infrared thermography and digital image correlation. Polymer 55:6345–6353. https://doi.org/10.1016/j.polymer.2014.10.010

    Article  CAS  Google Scholar 

  84. Rublon P, Huneau B, Verron E et al (2014) Multiaxial deformation and strain-induced crystallization around a fatigue crack in natural rubber. Eng Fract Mech 123:59–69. https://doi.org/10.1016/j.engfracmech.2014.04.003

    Article  Google Scholar 

  85. Xiang F, Schneider K, Heinrich G (2020) New observations regarding fatigue crack paths and their fracture surfaces in natural rubber: influences of R-ratio and pre-load. Int J Fatigue 135:105508. https://doi.org/10.1016/j.ijfatigue.2020.105508

    Article  Google Scholar 

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Acknowledgments

This work was supported by JST, CREST grant number JPMJCR2091, Japan, and the ImPACT Program of the Council for Science, Technology and Innovation (Cabinet Office, Government of Japan).

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Authors and Affiliations

  1. Department of Macromolecular Science and Engineering, Kyoto Institute of Technology, Kyoto, Japan

    Thanh-Tam Mai & Kenji Urayama

  2. Advanced Materials Division, Bridgestone Corporation, Tokyo, Japan

    Yoshihiro Morishita & Katsuhiko Tsunoda

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  1. Thanh-Tam Mai
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  2. Yoshihiro Morishita
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  3. Katsuhiko Tsunoda
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Correspondence to Kenji Urayama .

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  1. Technische Universitðt Dresden, Dresden, Germany

    Gert Heinrich

  2. Coesfeld GmbH and Co. KG, Dortmund, Germany

    Reinhold Kipscholl

  3. PRL Polymer Research Lab s.r.o., ZlÚn, Czech Republic

    Radek Stoček

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Mai, TT., Morishita, Y., Tsunoda, K., Urayama, K. (2021). Experimental Analysis of Fast Crack Growth in Elastomers. In: Heinrich, G., Kipscholl, R., Stoček, R. (eds) Degradation of Elastomers in Practice, Experiments and Modeling. Advances in Polymer Science, vol 289. Springer, Cham. https://doi.org/10.1007/12_2021_109

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