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In Situ AFM Investigations and Fracture Mechanics Modeling of Slow Fracture Propagation in Oxide and Polymer Glasses

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Abstract

Fracture propagation is inherently a multiscale problem, involving the coupling of many length scales from sample dimension to molecular level. Fracture mechanics provides a valuable link between the macroscopic scale of the structural loading of the samples and the scale of the process zone for brittle materials. Modeling the toughness of materials requires yet an investigation at scales smaller than this process zone, which is nanometric in oxide glasses and micrometric in polymer glasses. We present here the important insights that have been obtained through an in situ experimental investigation of the strain fields in the micrometric neighborhood of a propagating crack. We show the richness of atomic force microscopy combined with digital image correlation although it limits the observations to the external surface of the sample and to very slow crack propagation (below nm/s). For oxide glasses, this novel technique provided enlightening information on the nanoscale mechanisms of stress corrosion during subcritical crack propagation (Ciccotti, J Phys D Appl Phys 42:214006, 2009; Pallares et al., Corros Rev 33(6):501–514, 2015), including the relevance of crack tip plasticity (Han et al., EPL 89:66003, 2010), stress-induced ion exchange processes (Célarié et al., J Non-Cryst Solids 353:51–68, 2007), and capillary condensation in the crack tip cavity (Grimaldi et al., Phys Rev Lett 100:165505, 2008; Pallares et al., J Am Ceram Soc 94:2613–2618, 2011). An extension of this technique has recently been developed for glassy polymers (George et al., J Mech Phys Solids 112:109–125, 2018), leading to novel insights on the transition between crazing and shear yielding mechanisms and to promising new ways to link the toughness properties to the time-dependent large strain material properties of these nominally brittle materials.

Notes

Acknowledgments

This work has been supported by the French ANR through grants CORCOSIL ANR-07-BLAN-0261-02 and PROMORPH ANR-2011-RMNP-006. We thank C. Marlière, F. Célarié, J.M. Fromental, G. Prevot, and B. Bresson for important developments of the in situ AFM technique. We thank S.M. Wiederhorn, J.P. Guin, T. Fett, S. Roux, E. Charlaix, E. Bouchaud, L. Ponson, C. Fretigny, J.W. Hutchinson, J. Rice, and C.H. Hui for fruitful discussions. A special thanks to PhD and post-doc students involved in past investigations: L. Wondraczec, A. Grimaldi, G. Pallares, F. Lechenault, K. Han, Y. Nziakou, and G. Fischer.

References

  1. Bazant ZP, Estenssoro LF (1979) Surface singularity and crack propagation. Int J Solids Struct 15:405–426CrossRefMathSciNetzbMATHGoogle Scholar
  2. Benthem JP (1977) State of stress at the vertex of a quarter-infinite crack in a half-space. Int J Solids Struct 13:479–492CrossRefzbMATHGoogle Scholar
  3. Bonamy D, Ponson L, Prades S, Bouchaud E, Guillot C (2006) Scaling exponents for fracture surfaces in homogeneous glass and glassy ceramics. Phys Rev Lett 97:135504CrossRefADSGoogle Scholar
  4. Bowden FP, Tabor D (1950) Friction and lubrication in solids. Clarendon Press, Oxford, U.KGoogle Scholar
  5. Brown HR (1991) A molecular interpretation of the toughness of glassy polymers. Macromolecules 24:2752–2756CrossRefADSGoogle Scholar
  6. Bunker BC (1994) Molecular mechanisms for corrosion of silica and silicate glasses. J Non-Cryst Solids 179:300–308CrossRefADSGoogle Scholar
  7. Célarié F, Prades S, Bonamy D, Ferrero L, Bouchaud E, Guillot C, Marliére C (2003) Glass breaks like metal, but at the nanometer scale. Phys Rev Lett 90:075504CrossRefADSGoogle Scholar
  8. Célarié F (2004) Dynamique de fissuration a basse vitesse des matériaux vitreux. PhD thesis, Université Montpellier 2Google Scholar
  9. Célarié F, Ciccotti M, Marlière C (2007) Stress-enhanced ion diffusion at the vicinity of a crack tip as evidenced by atomic force microscopy in silicate glasses. J Non-Cryst Solids 353:51–68CrossRefADSGoogle Scholar
  10. Charlaix E, Ciccotti M (2010) Capillary condensation in confined media. In: Sattler K (ed) Handbook of nanophysics: principles and methods. CRC Press, Boca Raton, p 12–1Google Scholar
  11. Ciccotti M (2009) Stress-corrosion mechanisms in silicate glasses. J Phys D Appl Phys 42:214006CrossRefADSGoogle Scholar
  12. Cleveland JP, Anczykowski B, Schmid AE, Elings VB (1998) Energy dissipation in tapping-mode atomic force microscopy. Appl Phys Lett 72:2613–2615CrossRefADSGoogle Scholar
  13. Crichton SN, Tomozawa M, Hayden JS, Suratwala TI, Campbell JH (1999) Subcritical crack growth in a phosphate laser glass. J Am Ceram Soc 82:3097–104CrossRefGoogle Scholar
  14. Dimitrov A, Buchholz FG, Schnack E (2006) 3D-corner effects in crack propagation. Comput Model Eng Sci 12:1–25Google Scholar
  15. Doll W (1983) Optical interference measurements and fracture mechanics analysis of crack tip craze zones. Adv Polym Sci 52/53:105–168CrossRefGoogle Scholar
  16. Donald AM, Kramer EJ (1982) The competition between shear deformation and crazing in glassy polymers. J Mater Sci 17:1871–1879CrossRefADSGoogle Scholar
  17. Du J, Cormack AN (2005) Molecular dynamics simulation of the structure and hydroxylation of silica glass surfaces. J Am Ceram Soc 88:2532–2539CrossRefGoogle Scholar
  18. Dugdale DS (1960) Yielding of steel sheets containing slits. J Mech Phys Solids 8:100–104CrossRefADSGoogle Scholar
  19. Fett T, Guin JP, Wiederhorn SM (2005) Interpretation of effects at the static fatigue limit of soda-lime-silicate glass. Eng Fract Mech 72:2774–2791CrossRefGoogle Scholar
  20. Fineberg J, Marder M (1999) Instability in dynamic fracture. Elsevier, Phys Rep 313:1–108CrossRefADSMathSciNetGoogle Scholar
  21. Freund LB (1990) Dynamic fracture mechanics. Cambridge University, Cambridge; Rate J Mat Sci 14:583–591Google Scholar
  22. Gehrke E, Ullner C, Mahnert M (1991) Fatigue limit and crack arrest in alkali containing silicate glasses. J Mater Sci 26:5445–5455CrossRefADSGoogle Scholar
  23. George M, Nziakou Y, Goerke S, Genix AC, Bresson B, Roux S, Delacroix H, Halary JL, Ciccotti M (2018) In situ AFM investigation of slow crack propagation mechanisms in a glassy polymer. J Mech Phys Solids 112:109–125CrossRefADSGoogle Scholar
  24. Griffith AA (1920) The phenomena of rupture and flow in solids. Phil Trans R Soc Lond A 221:163–198ADSGoogle Scholar
  25. Grimaldi A, George M, Pallares G, Marlière C, Ciccotti M (2008) The crack tip: a nanolab for studying confined liquids. Phys Rev Lett 100:165505CrossRefADSGoogle Scholar
  26. G’Sell C, Jonas JJ (1979) Determination of the plastic behaviour of solid polymers at constant true strain. J Mater Sci 14:583–591CrossRefADSGoogle Scholar
  27. Guilloteau E, Charrue H, Creuzet F (1996) The direct observation of the core region of a propagating fracture crack in glass. Europhys Lett 34:549–553CrossRefADSGoogle Scholar
  28. Guin JP, Wiederhorn SM (2004) Fracture of silicate glasses: ductile or brittle? Phys Rev Lett 92:215502CrossRefADSGoogle Scholar
  29. Han K, Ciccotti M, Roux S (2010) Measuring nanoscale stress intensity factors with an atomic force microscope. EPL 89:66003CrossRefADSGoogle Scholar
  30. Halary JL, Lauprétre F, Monnerie L (2011) Polymer materials. Wiley, HabokenGoogle Scholar
  31. Hattali ML, Barés, Ponson L, Bonamy D (2012) Low velocity surface fracture patterns in brittle material: a newly evidenced mechanical instability. Math Sci Forum 706–709:920–924CrossRefGoogle Scholar
  32. He MY, Turner MR, Evans AG (1995) Analysis of the double cleavage drilled compression specimen for interface fracture energy measurements over a wide range of mode mixities. Acta Metall Mater 43:3453–3458CrossRefGoogle Scholar
  33. Hutter K (2013) Deformation and failure in metallic materials. Springer, BerlinGoogle Scholar
  34. Irwin GR (1957) Analysis of stresses and strains near the end of a crack traversing a plate. J Appl Mech 24:361–364Google Scholar
  35. Janssen C (1974) Specimen for fracture mechanics studies on glass. In: Proceedings of the 10th International Congress on Glass, Kyoto, pp 10.23–10.30Google Scholar
  36. Jones RM (2015) Mechanics Of composite materials, 2nd edn. CRC Press, PhiladelphiaGoogle Scholar
  37. Kermode JR, Albaret T, Sherman D, Bernstein N, Gumbsch P, Payne MC, Csanyi G, De Vita A (2008) Low-speed fracture instabilities in a brittle crystal. Nature 455:1224–1228CrossRefADSGoogle Scholar
  38. Kinloch AJ, Williams JG (1980) Crack blunting mechanisms in polymers. J Mat Sci 15: 897–996Google Scholar
  39. Kramer EJ (1983) Microscopic and molecular fundamentals of crazing. Adv Polym Sci 52/53:1–56Google Scholar
  40. Lawn BR (1993) Fracture of brittle solids, 2nd edn. Cambridge University, CambridgeCrossRefGoogle Scholar
  41. Lechenault F, Pallares G, George M, Rountree C, Bouchaud E, Ciccotti M (2010) Effects of finite probe size on self-affine roughness measurements. Phys Rev Lett 104:025502CrossRefADSGoogle Scholar
  42. Marsh DM (1964) Plastic flow and fracture of glass. Proc R Soc London A 282:33–43CrossRefADSGoogle Scholar
  43. Maugis D (1985) Review: subcritical crack growth, surface energy, fracture toughness, stick-slip and embrittlement. J Mater Sci 20:3041–3073CrossRefADSGoogle Scholar
  44. McClintock FA, Irwin GR (1964) Plasticity aspects of fracture mechanics. In: Fracture toughness testing and its applications. ASTM STP 381; Philadelphia, pp 84–113Google Scholar
  45. Michalske TA, Freiman SW (1983) A molecular mechanism for stress corrosion in vitreous silica. J Am Ceram Soc 66:284–288CrossRefGoogle Scholar
  46. Michalske TA, Bunker BC (1984) Slow fracture mode based on strained silicate structures. J Appl Phys 56:2686–2693CrossRefADSGoogle Scholar
  47. Mischler C, Horbach J, Kob W, Binder K (2005) Water adsorption on amorphous silica surfaces: a Car-Parrinello simulation study. J Phys Cond Matt 17:4005–4013CrossRefADSGoogle Scholar
  48. Nziakou Y (2015) Analyse multi-échelle des mécanismes d’endommagement des matériaux composites à morphologie complexe destinés à l’aéronautique. PhD Thesis, Université Pierre et Marie CurieGoogle Scholar
  49. Nziakou Y, George M, Fisher G, Bresson B, Roux S, Halary JL, Ciccotti M (2019) Bridging steady-state and stick-slip fracture propagation in glassy polymers. preprint Soft Matter (submitted)Google Scholar
  50. Orowan E (1955) Energy criteria of fracture. Weld J Res Suppl 34:S157–S160Google Scholar
  51. Pallares G, Ponson L, Grimaldi A, George M, Prevot G, Ciccotti M (2009) Crack opening profile in DCDC specimen. Int J Fract 156:11–20CrossRefGoogle Scholar
  52. Pallares G, Grimaldi A, George M, Ponson L, Ciccotti M (2011) Quantitative analysis of crack closure driven by Laplace pressure in silica glass. J Am Ceram Soc 94:2613–2618CrossRefGoogle Scholar
  53. Pallares G, George M, Ponson L, Chapuliot S, Roux S, Ciccotti M (2015) Multiscale investigation of stress-corrosion crack propagation mechanisms in oxide glasses. Corros Rev 33(6):501–514. Freund Publishing House Ltd.Google Scholar
  54. Pallares G, Lechenault F, George M, Bouchaud E, Ottina C, Rountree CL, Ciccotti M (2017) Roughness of oxide glass subcritical fracture surfaces J Am Ceram Soc 101:1279–1288CrossRefGoogle Scholar
  55. Phillips DC, Scott JM, Jones M (1978) Crack propagation in an amine-cured epoxide resin. J Mat Sci 13:311–322CrossRefADSGoogle Scholar
  56. Réthoré J, Estevez R (2013) Identification of a cohesive zone model from digital images at the micron-scale. J Mech Phys Solids 61:1407–1420CrossRefADSMathSciNetGoogle Scholar
  57. Roduit C, AFM figures 2010, Creative Commons AttributionGoogle Scholar
  58. Roux S, Hild F (2006) Stress intensity factor measurements from digital image correlation: post-processing and integrated approaches. Int J Fract 140:141–157CrossRefzbMATHGoogle Scholar
  59. Taylor EW (1949) Plastic Deformation of Optical Glass. Nature 163:323CrossRefADSGoogle Scholar
  60. Takahashi K, Arakawa K (1984) Dependence of crack acceleration on the dynamic stress-intensity factor in polymers. Exp Mech 27:195–199CrossRefGoogle Scholar
  61. Thomson W (1871) On the equilibrium of vapour at a curved surface of liquid. Philos Mag 42:448–452CrossRefGoogle Scholar
  62. Tomozawa M (1984) Effect of stress on water diffusion in silica glass. J Am Ceram Soc 67: 151–154CrossRefGoogle Scholar
  63. Tomozawa M (1996) Fracture of glasses. Ann Rev Mater Sci 26:43–74CrossRefADSGoogle Scholar
  64. Wiederhorn SM (1967) Influence of water vapor on crack propagation in soda-lime glass. J Am Ceram Soc 50:407–414CrossRefGoogle Scholar
  65. Wiederhorn SM (1969) Fracture surface energy of glass. J Am Ceram Soc 52:99–105CrossRefGoogle Scholar
  66. Wiederhorn SM, Bolz LH (1970) Stress-corrosion and static fatigue of glass. J Am Ceram Soc 53:543–548CrossRefGoogle Scholar
  67. Wiederhorn SM, Lopez-Cepero J, Wallace J, Guin JP, Fett T (2007) Roughness of glass surfaces formed by sub-critical crack growth. J Non-Cryst Solids 353:1582CrossRefADSGoogle Scholar
  68. Wiederhorn SM, Fett T, Rizzi G, Fünfschilling S, Hoffmann MJ, Guin JP (2011) Effect of water penetration on the strength and toughness of silica glass. J Am Ceram Soc 94:S196–S203CrossRefGoogle Scholar
  69. Wiederhorn SM, Fett T, Guin JP, Ciccotti M (2013) Griffith cracks at the nanoscale. Int J Appl Glass Science 4:76–86CrossRefGoogle Scholar
  70. Williams JG (1984) Fracture Mechanics of Polymers. Ellis Horwood, ChichesterGoogle Scholar
  71. Williams ML (1957) On the stress distribution at the base of a stationary crack. ASME J Appl Mech 24:109–114MathSciNetzbMATHGoogle Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Laboratoire Sciences et Ingénierie de la Matière Molle (SIMM)ESPCI Paris, PSL University, Sorbonne Université, CNRSParisFrance
  2. 2.Laboratoire Charles Coulomb (L2C)Université de Montpellier, CNRSMontpellierFrance

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