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Mechanical Properties of Glass

  • Jean-Pierre GuinEmail author
  • Yann Gueguen
Chapter
Part of the Springer Handbooks book series (SHB)

Abstract

This chapter focuses on the mechanical properties and behavior of glasses below their glass transition temperature. In this temperature range, they are usually seen as perfectly brittle materials: materials that deform only elastically, until they break. This chapter explores the behavior of glasses from the domain from elasticity to fracture. We first review the most widely used methods for measuring the elastic moduli of glasses, and the state of the art regarding knowledge of the relationship between elastic moduli and short- to medium-range order in glasses. We then discuss nonlinear elasticity in glasses, and how temperature and pressure impact on elastic moduli. But glasses can also deform plastically under high levels of compressive stress, particularly under sharp contact (indentation), because of high pressure and shear stress. This plastic deformation is highly dependent on glass composition; it results from densification and shear flow, two mechanisms that are affected by the loading path, temperature and strain rate. We examine how plasticity occurs under sharp contact (e. g., indentation, scratch), until damage appears (cracks). Finally, we examine the practical strength of glasses, which is highly dependent on resistance to surface damage as well as to crack propagation (fracture toughness). The important role of moisture is also discussed, as it is responsible for subcritical crack propagation, and thus lower durability of glass parts.

References

  1. R. Hooke: Lectures de Potentia Restitutiva (John Martyn, London 1931)Google Scholar
  2. P.M. Morse: Diatomic molecules according to the wave mechanics. II. Vibrational levels, Phys. Rev. 34(1), 57 (1929)CrossRefGoogle Scholar
  3. P.K. Gupta, C.R. Kurkjian: Intrinsic failure and non-linear elastic behavior of glasses, J. Non-Cryst. Solids 351(27–29), 2324–2328 (2005)CrossRefGoogle Scholar
  4. F.P. Mallinder, B.A. Proctor: Elastic constants of fused silica as a function of large tensile strain, Phys. Chem. Glasses 5(4), 91–103 (1964)Google Scholar
  5. L.H. Donnell: A new theory for the buckling of thin cylinders under axial compression and bending, Trans. ASME 56(11), 795–806 (1934)Google Scholar
  6. J.K. Banerjee: Barreling of solid cylinders under axial compression, J. Eng. Mater. Technol. 107(2), 138–144 (1985)CrossRefGoogle Scholar
  7. V. Chean, E. Robin, R. El Abdi, J.C. Sangleboeuf, P. Houizot: Use of the mark-tracking method for optical fiber characterization, Opt. Laser Technol. 43(7), 1172–1178 (2011)CrossRefGoogle Scholar
  8. R.J. Angel, J.M. Jackson, H.J. Reichmann, S. Speziale: Elasticity measurements on minerals: A review, Eur. J. Mineral. 21(3), 525–550 (2009)CrossRefGoogle Scholar
  9. S. Timoshenko: History of Strength of Materials: With a Brief Account of the History of Theory of Elasticity and Theory of Structures (Courier Corporation, Chelmsford 1953)Google Scholar
  10. H.J. McSkimin: Measurement of elastic constants at low temperatures by means of ultrasonic waves—data for silicon and germanium single crystals, and for fused silica, J. Appl. Phys. 24(8), 988–997 (1953)CrossRefGoogle Scholar
  11. H.J. McSkimin: Notes and references for the measurement of elastic moduli by means of ultrasonic waves, J. Acoust. Soc. Am. 33(5), 606–615 (1961)CrossRefGoogle Scholar
  12. V. Keryvin, T. Rouxel, M. Huger, L. Charleux: Elastic moduli of a ZrCuAlNi bulk metallic glass from room temperature to complete crystallisation by in situ pulse-echo ultrasonic echography, J. Ceram. Soc. 116(1356), 851–854 (2008)CrossRefGoogle Scholar
  13. M.J. Bamber, K.E. Cooke, A.B. Mann, B. Derby: Accurate determination of Young's modulus and Poisson's ratio of thin films by a combination of acoustic microscopy and nanoindentation, Thin Solid Films 398, 299–305 (2001)CrossRefGoogle Scholar
  14. X. Xiao, N. Hata, K. Yamada, T. Kikkawa: Mechanical properties of periodic porous silica low-k films determined by the twin-transducer surface acoustic wave technique, Rev. Sci. Instrum. 74(10), 4539–4541 (2003)CrossRefGoogle Scholar
  15. ASTM E1875-13: Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio by Sonic Resonance (ASTM, West Conshohocken 1875)Google Scholar
  16. G. Roebben, B. Bollen, A. Brebels, J. Van Humbeeck, O. der Biest: Impulse excitation apparatus to measure resonant frequencies, elastic moduli, and internal friction at room and high temperature, Rev. Sci. Instrum. 68(12), 4511–4515 (1997)CrossRefGoogle Scholar
  17. G. Roebben, B. Basu, J. Vleugels, J. Van Humbeeck, O. der Biest: The innovative impulse excitation technique for high-temperature mechanical spectroscopy, J. Alloys Compd. 310(1/2), 284–287 (2000)CrossRefGoogle Scholar
  18. L. Brillouin: Diffusion de la lumière et des rayons X par un corps transparent homogène. Influence de l'agitation thermique, Ann. Phys. 9(17), 88–122 (1922)CrossRefGoogle Scholar
  19. E. Gross: Change of wave-length of light due to elastic heat waves at scattering in liquids, Nature 126(3171), 201 (1930)CrossRefGoogle Scholar
  20. W. Hayes, R. Loudon: Scattering of Light by Crystals (Courier Corporation, Chelmsford 2012)Google Scholar
  21. S. Speziale, H. Marquardt, T.S. Duffy: Brillouin scattering and its application in geosciences, Rev. Mineral. Geochem. 78(1), 543–603 (2014)CrossRefGoogle Scholar
  22. G. Hernández: Fabry–Perot Interferometers (Cambridge Univ. Press, Cambridge 1988)Google Scholar
  23. S.M. Shapiro, R.W. Gammon, H.Z. Cummins: Brillouin scattering spectra of crystalline quartz, fused quartz and glass, Appl. Phys. Lett. 9(4), 157–159 (1966)CrossRefGoogle Scholar
  24. E.S. Zouboulis, M. Grimsditch, A.K. Ramdas, S. Rodriguez: Temperature dependence of the elastic moduli of diamond: A Brillouin-scattering study, Phys. Rev. B 57(5), 2889 (1998)CrossRefGoogle Scholar
  25. S.V. Sinogeikin, J.M. Jackson, B. O'Neill, J.W. Palko, J.D. Bass: Compact high-temperature cell for Brillouin scattering measurements, Rev. Sci. Instrum. 71(1), 201–206 (2000)CrossRefGoogle Scholar
  26. J.A. Bucaro, H.D. Dardy: High-temperature Brillouin-scattering in fused quartz, J. Appl. Phys. 45(12), 5324–5329 (1974)CrossRefGoogle Scholar
  27. C.H. Whitfield, E.M. Brody, W.A. Bassett: Elastic moduli of NaCl by Brillouin scattering at high pressure in a diamond anvil cell, Rev. Sci. Instrum. 47(8), 942–947 (1976)CrossRefGoogle Scholar
  28. C. Zha, R.J. Hemley, H. Mao, T.S. Duffy, C. Meade: Acoustic velocities and refractive index of SiO2 glass to 57.5 GPa by Brillouin scattering, Phys. Rev. B 50(18), 13105–13112 (1994)CrossRefGoogle Scholar
  29. H. Shimizu, E.M. Brody, H.K. Mao, P.M. Bell: Brillouin Measurements of Solid n-H2 and n-D2 to 200 kbar at room temperature, Phys. Rev. Lett. 47(2), 128 (1981)CrossRefGoogle Scholar
  30. C. Sonneville, D. De Ligny, A. Mermet, B. Champagnon, C. Martinet, G.H. Henderson, T. Deschamps, J. Margveritat, E. Barthel: In situ Brillouin study of sodium alumino silicate glasses under pressure, J. Chem. Phys. 139(7), 074501 (2013)CrossRefGoogle Scholar
  31. W.C. Oliver, G.M. Pharr: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, J. Mater. Res. 7(06), 1564–1583 (1992)CrossRefGoogle Scholar
  32. A.N. Sreeram, A.K. Varshneya, D.R. Swiler: Molar volume and elastic properties of multicomponent chalcogenide glasses, J. Non-Cryst. Solids 128(3), 294–309 (1991)CrossRefGoogle Scholar
  33. W.H. Wang, C. Dong, C.H. Shek: Bulk metallic glasses, Mater. Sci. Eng. R Rep. 44(2/3), 45–89 (2004)Google Scholar
  34. T. Rouxel: Elastic properties and short-to medium-range order in glasses, J. Am. Ceram. Soc. 90(10), 3019–3039 (2007)CrossRefGoogle Scholar
  35. L.C.E. Struik: Integration of polymer science and technology? In: Integration of Fundamental Polymer Science and Technology 3, ed. by P.J. Lemstra, L.A. Kleintjens (Springer, Dordrecht 1989) pp. 3–16CrossRefGoogle Scholar
  36. C. Zwikker, R. Smoluchowski: Physical properties of solid materials, Phys. Today 8, 17 (1955)CrossRefGoogle Scholar
  37. A. Makishima, J.D. Mackenzie: Calculation of bulk modulus, shear modulus and Poisson's ratio of glass, J. Non-Cryst. Solids 17(2), 147–157 (1975)CrossRefGoogle Scholar
  38. A.K. Bandyopadhyay, L.C. Ming: Pressure-induced phase transformations in amorphous selenium by x-ray diffraction and Raman spectroscopy, Phys. Rev. B 54(17), 12049 (1996)CrossRefGoogle Scholar
  39. M.E. Fine: Elasticity and thermal expansion of germanium between $$-195$$ and 275 °C, J. Appl. Phys. 24(3), 338–340 (1953)CrossRefGoogle Scholar
  40. G. Yang, B. Bureau, T. Rouxel, Y. Gueguen, O. Gulbiten, C. Roiland, E. Soignord, J.L. Yarger, J. Troles, J.-C. Sangleboeuf, P. Lucas: Correlation between structure and physical properties of chalcogenide glasses in the AsxSe1-x system, Phys. Rev. B 82(19), 195206 (2010)CrossRefGoogle Scholar
  41. G. Yang, Y. Gueguen, J.-C. Sangleboeuf, T. Rouxel, C. Boussard-Plédel, J. Troles, P. Lucas, B. Bureau: Physical properties of the GexSe1-x glasses in the $$0<x<0.42$$ range in correlation with their structure, J. Non-Cryst. Solids 377, 54–59 (2013)CrossRefGoogle Scholar
  42. A. Makishima, J.D. Mackenzie: Direct calculation of Young's modulus of glass, J. Non-Cryst. Solids 12(1), 35–45 (1973)CrossRefGoogle Scholar
  43. J. Rocherulle's, C. Ecolivet, M. Poulain, P. Verdier, Y. Laurent: Elastic moduli of oxynitride glasses: Extension of Makishima and Mackenzie Theory, J. Non-Cryst. Solids 108(2), 187–193 (1989)CrossRefGoogle Scholar
  44. A. Pönitzsch, M. Nofz, L. Wondraczek, J. Deubener: Bulk elastic properties, hardness and fatigue of calcium aluminosilicate glasses in the intermediate-silica range, J. Non-Cryst. Solids 434, 1–12 (2016)CrossRefGoogle Scholar
  45. G.N. Greaves, A.L. Greer, R.S. Lakes, T. Rouxel: Poisson's ratio and modern materials, Nat. Mater. 10(11), 823–837 (2011)CrossRefGoogle Scholar
  46. J.C. Phillips: Topology of covalent non-crystalline solids I: Short-range order in chalcogenide alloys, J. Non-Cryst. Solids 34(2), 153–181 (1979)CrossRefGoogle Scholar
  47. M.F. Thorpe: Continuous deformations in random networks, J. Non-Cryst. Solids 57(3), 355–370 (1983)CrossRefGoogle Scholar
  48. P.K. Gupta, J.C. Mauro: Composition dependence of glass transition temperature and fragility. I. A topological model incorporating temperature-dependent constraints, J. Chem. Phys. 130(9), 094503 (2009)CrossRefGoogle Scholar
  49. M.M. Smedskjaer, J.C. Mauro, Y. Yue: Prediction of glass hardness using temperature-dependent constraint theory, Phys. Rev. Lett. 105(11), 115503 (2010)CrossRefGoogle Scholar
  50. H. He, M.F. Thorpe: Elastic properties of glasses, Phys. Rev. Lett. 54(19), 2107 (1985)CrossRefGoogle Scholar
  51. S.S. Yun, H. Li, R.L. Cappelletti, R.N. Enzweiler, P. Boolchand: Onset of rigidity in Se1-xGex glasses: Ultrasonic elastic moduli, Phys. Rev. B 39(12), 8702 (1989)CrossRefGoogle Scholar
  52. C.A. Angell: Formation of glasses from liquids and biopolymers, Science 267(5206), 1924–1935 (1995)CrossRefGoogle Scholar
  53. R.E. Youngman, J. Kieffer, J.D. Bass, L. Duffrene: Extended structural integrity in network glasses and liquids, J. Non-Cryst. Solids 222, 190–198 (1997)CrossRefGoogle Scholar
  54. Y. Gueguen, T. Rouxel, P. Gadaud, C. Bernard, V. Keryvin, J.-C. Sangleboeuf: High-temperature elasticity and viscosity of GexSe1-x glasses in the transition range, Phys. Rev. B 84(6), 064201 (2011)CrossRefGoogle Scholar
  55. J.C. Dyre, N.B. Olsen, T. Christensen: Local elastic expansion model for viscous-flow activation energies of glass-forming molecular liquids, Phys. Rev. B 53(5), 2171–2174 (1996)CrossRefGoogle Scholar
  56. L. Huang, J. Kieffer: Amorphous-amorphous transitions in silica glass. I. Reversible transitions and thermomechanical anomalies, Phys. Rev. B 69(22), 224203 (2004)CrossRefGoogle Scholar
  57. Q. Zhao, M. Guerette, G. Scannell, L. Huang: In-situ high temperature Raman and Brillouin light scattering studies of sodium silicate glasses, J. Non-Cryst. Solids 358(24), 3418–3426 (2012)CrossRefGoogle Scholar
  58. A.N. Clark, C.E. Lesher, S.D. Jacobsen, S. Sen: Mechanisms of anomalous compressibility of vitreous silica, Phys. Rev. B 90(17), 174110 (2014)CrossRefGoogle Scholar
  59. R. Ota, T. Yamate, N. Soga, M. Kunugi: Elastic properties of Ge-Se glass under pressure, J. Non-Cryst. Solids 29(1), 67–76 (1978)CrossRefGoogle Scholar
  60. H.S. Chen: The influence of structural relaxation on the density and Young's modulus of metallic glasses, J. Appl. Phys. 49(6), 3289–3291 (1978)CrossRefGoogle Scholar
  61. A. Kursumovic, M.G. Scott: The use of Young's modulus to monitor relaxation in metallic glasses, Appl. Phys. Lett. 37(7), 620–622 (1980)CrossRefGoogle Scholar
  62. P.C. Anderson, U. Senapati, A.K. Varshneya: Sub-Tg relaxation in Ge5Se95 and As5Se95 glasses, J. Non-Cryst. Solids 176(1), 51–57 (1994)CrossRefGoogle Scholar
  63. D.L. Anderson: Theory of the Earth (Blackwell Scientific, Oxford 1989)Google Scholar
  64. D.N. Nichols, D.S. Rimai, R.J. Sladek: Effect of hydrostatic pressure on the elastic moduli of As2S3 and As2Se3 glasses at 195 and 296 K, J. Non-Cryst. Solids 34(3), 297–305 (1979)CrossRefGoogle Scholar
  65. R. Ota, N. Soga: Elastic properties of fluoride glasses under pressure and temperature, J. Non-Cryst. Solids 56(1–3), 105–110 (1983)CrossRefGoogle Scholar
  66. J.C. Thompson, K.E. Bailey: Survey of elastic properties of some semiconducting glasses under pressure, J. Non-Cryst. Solids 27(2), 161–172 (1978)CrossRefGoogle Scholar
  67. M.H. Manghnani: Pressure and temperature dependence of the elastic moduli of Na2O-TiO2-SiO2 glasses, J. Am. Ceram. Soc. 55(7), 360–365 (1972)CrossRefGoogle Scholar
  68. R. Ota, H. Yamanaka, M. Kunugi: Pressure dependence of elastic properties for B2O3-Na2O glasses and equations of state for glass. In: High-Pressure Science and Technology, ed. by K.D. Timmerhaus, M.S. Barber (Springer, Boston 1979) pp. 1241–1247CrossRefGoogle Scholar
  69. E. Gamberg, D.R. Uhlmann, D.H. Chung: Pressure dependence of the elastic moduli of glasses in the K2O-SiO2 system, J. Non-Cryst. Solids 13(3), 399–408 (1974)CrossRefGoogle Scholar
  70. L. Huang, J. Kieffer: Thermomechanical anomalies and polyamorphism in B2O3 glass: A molecular dynamics simulation study, Phys. Rev. B 74(22), 224107 (2006)CrossRefGoogle Scholar
  71. R. Hill: The Mathematical Theory of Plasticity (Clarendon, Oxford 1950)Google Scholar
  72. A.E.H. Love: A Treatise on the Mathematical Theory of Elasticity (Cambridge Univ. Press, Cambridge 1892)Google Scholar
  73. J.W. French: Some notes on glass grinding and polishing, Trans. Opt. Soc. 17(2), 24–71 (1916)CrossRefGoogle Scholar
  74. G.T. Beilby: Researches on polished surfaces, Trans. Opt. Soc. 9(1), 22–71 (1907)CrossRefGoogle Scholar
  75. G.I. Finch, A.G. Quarrell, J.S. Roebuck: The Beilby layer, Proc. R. Soc. A 145(855), 676–681 (1934)CrossRefGoogle Scholar
  76. T. Suratwala, W. Steele, L. Wong, M.D. Feit, P.E. Miller, R. Dylla-Spears, N. Shen, R. Desjardin: Chemistry and formation of the Beilby layer during polishing of fused silica glass, J. Am. Ceram. Soc. 98(8), 2395–2402 (2015)CrossRefGoogle Scholar
  77. E.W. Taylor: A hardness table for some well-known types of optical glass, J. Sci. Instrum. 26(9), 314 (1949)CrossRefGoogle Scholar
  78. J.F.H. Custers: Plastic deformation of glass during scratching, Nature 164(4171), 627–627 (1949)CrossRefGoogle Scholar
  79. P.W. Bridgman, I. Simon: Effects of very high pressures on glass, J. Appl. Phys. 24(4), 405–413 (1953)CrossRefGoogle Scholar
  80. T. Rouxel, H. Ji, T. Hammouda, A. Moréac: Poisson's ratio and the densification of glass under high pressure, Phys. Rev. Lett. 100(22), 225501 (2008)CrossRefGoogle Scholar
  81. C. Meade, R.J. Hemley, H.K. Mao: High-pressure x-ray diffraction of SiO2 glass, Phys. Rev. Lett. 69(9), 1387–1390 (1992)CrossRefGoogle Scholar
  82. T. Deschamps, A. Kassir-Bodon, C. Sonneville, J. Margveritat, C. Martinet, D. de Ligny, A. Mermet, B. Champagnon: Permanent densification of compressed silica glass: A Raman-density calibration curve, J. Phys. Condens. Matter 25(2), 025402 (2013)CrossRefGoogle Scholar
  83. B. Hehlen: Inter-tetrahedra bond angle of permanently densified silicas extracted from their Raman spectra, J. Phys. Condens. Matter 22(2), 25401 (2010)CrossRefGoogle Scholar
  84. V. Keryvin, J.-X. Meng, S. Gicquel, J.-P. Guin, L. Charleux, J.-C. Sangleboeuf, P. Pilvin, T. Rouxel, G. Le Quilliec: Constitutive modeling of the densification process in silica glass under hydrostatic compression, Acta Mater. 62, 250–257 (2014)CrossRefGoogle Scholar
  85. D. Wakabayashi, N. Funamori, T. Sato, T. Taniguchi: Compression behavior of densified SiO2 glass, Phys. Rev. B 84(14), 144103 (2011)CrossRefGoogle Scholar
  86. Y. Satoshi, J.-C. Sangleboeuf, T. Rouxel: Quantitative evaluation of indentation-induced densification in glass, J. Mater. Res. 20(12), 3404–3412 (2005)CrossRefGoogle Scholar
  87. M.I. Eremets: High Pressure Experimental Methods (Oxford Univ. Press, Oxford 1996)Google Scholar
  88. H.M. Cohen, R. Roy: Effects of ultra high pressures on glass, J. Am. Ceram. Soc. 44(10), 523 (1961)CrossRefGoogle Scholar
  89. E.B. Christiansen, S.S. Kistler, W.B. Gogarty: Irreversible compressibility of silica glass as a means of determining the distribution of force in high-pressure cells, J. Am. Ceram. Soc. 45(4), 172–177 (1962)CrossRefGoogle Scholar
  90. J.D. Mackenzie: High-pressure effects on oxide glasses: I, densification in rigid state, J. Am. Ceram. Soc. 46(10), 461 (1963)CrossRefGoogle Scholar
  91. C. Martinet, A. Kassir-Bodon, T. Deschamps, A. Cornet, S. Le Floch, V. Martinez, B. Champagnon: Permanently densified SiO2 glasses: A structural approach, J. Phys. Condens. Matter 27(32), 325401 (2015)CrossRefGoogle Scholar
  92. A. Cornet, V. Martinez, D. de Ligny, B. Champagnon, C. Martinet: Relaxation processes of densified silica glass, J. Chem. Phys. 146(9), 94504 (2017)CrossRefGoogle Scholar
  93. J. Arndt: Shock-wave densification of silica glass, Phys. Chem. Glasses 12, 1–7 (1971)Google Scholar
  94. M. Okuno, B. Reynard, Y. Shimada, Y. Syono, C. Willaime: A Raman spectroscopic study of shock-wave densification of vitreous silica, Phys. Chem. Miner. 26(4), 304–311 (1999)CrossRefGoogle Scholar
  95. R. Renou, L. Soulard, E. Lescoute, C. Dereure, D. Loison, J.-P. Guin: Silica glass structural properties under elastic shock compression: Experiments and molecular simulations, J. Phys. Chem. C 121(24), 13324–13334 (2017)CrossRefGoogle Scholar
  96. R. Renou, L. Soulard, E. Lescoute, C. Dereure, D. Loison, J.P. Guin: Understanding shock induced glass densification using molecular dynamics simulation, Phys. Chem. Phys.Google Scholar
  97. P. Klapetek, D. Nečas, C. Anderson: Gwyddion, http://www.gwyddion.net/ (2004)
  98. W.C. Oliver, G.M. Pharr: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, J. Mater. Res. 7(6), 1564–1583 (1992)CrossRefGoogle Scholar
  99. A.C. Fischer-Cripps: Introduction to Contact Mechanics, Vol. 101 (Springer, New York 2007)CrossRefGoogle Scholar
  100. D. Tabor: The physical meaning of indentation and scratch hardness, Br. J. Appl. Phys. 7(5), 159 (1956)CrossRefGoogle Scholar
  101. M.M. Smedskjaer, J.C. Mauro, S. Sen, Y. Yue: Quantitative design of glassy materials using temperature-dependent constraint theory, Chem. Mater. 22(18), 5358–5365 (2010)CrossRefGoogle Scholar
  102. A. Kassir-Bodon, T. Deschamps, C. Martinet, B. Champagnon, J. Teisseire, G. Kermouche: Raman mapping of the indentation-induced densification of a soda-lime-silicate glass, Int. J. Appl. Glasses Sci. 3(1), 29–35 (2012)CrossRefGoogle Scholar
  103. A. Perriot, D. Vandembroucq, E. Barthel, V. Martinez, L. Grosvalet, C. Martinet, B. Champagnon: Raman microspectroscopic characterization of amorphous silica plastic behavior, J. Am. Ceram. Soc. 89(2), 596–601 (2006)CrossRefGoogle Scholar
  104. H. Tran, S. Clement, R. Vialla, D. Vandembroucq, B. Ruffle: Micro-Brillouin spectroscopy mapping of the residual density field induced by Vickers indentation in a soda-lime-silicate glass, Appl. Phys. Lett. 100(23), 231901–2319014 (2012)CrossRefGoogle Scholar
  105. G. Kermouche, E. Barthel, D. Vandembroucq, P. Dubujet: Mechanical modelling of indentation-induced densification in amorphous silica, Acta Mater. 56(13), 3222 (2008)CrossRefGoogle Scholar
  106. Y. Niu, K. Han, J. Guin: Locally enhanced dissolution rate as a probe for nanocontact-induced densification in oxide glasses, Langmuir 28, 10733–10740 (2012)CrossRefGoogle Scholar
  107. R. Lacroix, V. Chomienne, G. Kermouche, J. Teisseire, E. Barthel, S. Queste: Micropillar testing of amorphous silica, Int. J. Appl. Glass Sci. 3(1), 36–43 (2012)CrossRefGoogle Scholar
  108. G. Kermouche, G. Guillonneau, J. Michler, J. Teisseire, E. Barthel: Perfectly plastic flow in silica glass, Acta Mater. 114, 146–153 (2016)CrossRefGoogle Scholar
  109. M. Mačković, F. Niekiel, L. Wondraczek, E. Spiecker: Direct observation of electron-beam-induced densification and hardening of silica nanoballs by in situ transmission electron microscopy and finite element method simulations, Acta Mater. 79, 363–373 (2014)CrossRefGoogle Scholar
  110. M. Mačković, F. Niekiel, L. Wondraczek, E. Bitzek, E. Spiecker: In situ mechanical quenching of nanoscale silica spheres in the transmission electron microscope, Scr. Mater. 121, 70–74 (2016)CrossRefGoogle Scholar
  111. S. Romeis, J. Paul, P. Herre, D. de Ligny, J. Schmidt, W. Peukert: Local densification of a single micron sized silica sphere by uniaxial compression, Scr. Mater. 108, 84–87 (2015)CrossRefGoogle Scholar
  112. V. Keryvin, L. Charleux, R. Hin, J.-P. Guin, J.-C. Sangleboeuf: Mechanical behaviour of fully densified silica glass under vickers indentation, Acta Mater. 129, 492–499 (2017)CrossRefGoogle Scholar
  113. B. Mantisi, G. Kermouche, E. Barthel, A. Tanguy: Impact of pressure on plastic yield in amorphous solids with open structure, Phys. Rev. E 93(3), 33001 (2016)CrossRefGoogle Scholar
  114. G. Molnár, G. Kermouche, E. Barthel: Plastic response of amorphous silicates, from atomistic simulations to experiments—A general constitutive relation, Mech. Mater. 114, 1–8 (2017)CrossRefGoogle Scholar
  115. H. Hertz: On the contact of elastic solids, Z. reine angew. Math. 92, 156–171 (1881)Google Scholar
  116. B.R. Lawn: Indentation of ceramics with spheres: A century after Hertz, J. Am. Ceram. Soc. 81(8), 1977–1994 (1998)CrossRefGoogle Scholar
  117. B.R. Lawn, M.V. Swain: Microfracture beneath point indentations in brittle solids, J. Mater. Sci. 10(1), 113–122 (1974)CrossRefGoogle Scholar
  118. R.F. Cook, G.M. Pharr: Direct observation and analysis of indentation cracking in glasses and ceramics, J. Am. Ceram. Soc. 73(4), 787–817 (1990)CrossRefGoogle Scholar
  119. J.T. Hagan: Cone cracks around Vickers indentations in fused silica glass, J. Mater. Sci. 14(2), 462 (1979)CrossRefGoogle Scholar
  120. A. Arora, D.B. Marshall, B.R. Lawn, M.V. Swain: Indentation deformation/fracture of normal and anomalous glasses, J. Non-Cryst. Solids 31(3), 415–428 (1979)CrossRefGoogle Scholar
  121. R. Limbach, A. Winterstein-Beckmann, J. Dellith, D. Möncke, L. Wondraczek: Plasticity, crack initiation and defect resistance in alkali-borosilicate glasses: From normal to anomalous behavior, J. Non-Cryst. Solids 417/418, 15–27 (2015)CrossRefGoogle Scholar
  122. T.M. Gross: Deformation and cracking behavior of glasses indented with diamond tips of various sharpness, J. Non-Cryst. Solids 358(24), 3445–3452 (2012)CrossRefGoogle Scholar
  123. J.-P. Guin, T. Rouxel, J.-C. Sanglebœuf, I. Melscoët, J. Lucas: Hardness, toughness, and scratchability of germanium-selenium chalcogenide glasses, J. Am. Ceram. Soc. 85(6), 1545–1552 (2002)CrossRefGoogle Scholar
  124. Y. Ahna, T.N. Farris, S. Chandrasekar: Sliding microindentation fracture of brittle materials: Role of elastic stress fields, Mech. Mater. 29(3), 143–152 (1998)CrossRefGoogle Scholar
  125. V. Le Houérou, J.-C. Sangleboeuf, S. Dériano, T. Rouxel, G. Duisit: Surface damage of soda-lime-silica glasses: Indentation scratch behavior, J. Non-Cryst. Solids 316(1), 54–63 (2003)CrossRefGoogle Scholar
  126. J.D.B. Veldkamp, N. Hattu: Deformation and cracking during high-temperature scratching of a glass, J. Mater. Sci. 16(5), 1273–1284 (1981)CrossRefGoogle Scholar
  127. J. Sehgal, S. Ito: A new low-brittleness glass in the soda-lime-silica glass family, J. Am. Ceram. Soc. 81(9), 2485–2488 (1998)CrossRefGoogle Scholar
  128. G.R. Anstis, P. Chantikul, B.R. Lawn, D.B. Marshall: A critical evaluation of indentation techniques for measuring fracture toughness: I, direct crack measurements, J. Am. Ceram. Soc. 64(9), 533–538 (1981)CrossRefGoogle Scholar
  129. G. Quinn, R. Bradt: On the Vickers indentation fracture toughness test, J. Am. Ceram. Soc. 90(3), 673–680 (2007)CrossRefGoogle Scholar
  130. S. Dériano, A. Jarry, T. Rouxel, J.-C. Sangleboeuf, S. Hampshire: The indentation fracture toughness (\(K\)c) and its parameters: The case of silica-rich glasses, J. Non-Cryst. Solids 344(1), 44–50 (2004)CrossRefGoogle Scholar
  131. B.R. Lawn, D.B. Marshall: Hardness, toughness, and brittleness: An indentation analysis, J. Am. Ceram. Soc. 62(7/8), 347–350 (1979)CrossRefGoogle Scholar
  132. J. Sehgal, Y. Nakao, H. Takahashi, S. Ito: Brittleness of glasses by indentation, J. Mater. Sci. Lett. 14(3), 167–169 (1995)CrossRefGoogle Scholar
  133. S. Yoshida, A. Hidaka, J. Matsuoka: Crack initiation behavior of sodium aluminosilicate glasses, J. Non-Cryst. Solids 344(1/2), 37–43 (2004)CrossRefGoogle Scholar
  134. P. Sellappan, T. Rouxel, F. Celarie, E. Becker, P. Houizot, R. Conradt: Composition dependence of indentation deformation and indentation cracking in glass, Acta Mater. 61(16), 5949–5965 (2013)CrossRefGoogle Scholar
  135. T. Rouxel: Driving force for indentation cracking in glass: Composition, pressure and temperature dependence, Philos. Trans. R. Soc. A 373(2038), 20140140 (2015)CrossRefGoogle Scholar
  136. T. Rouxel, P. Sellappan, F. Celarie, P. Houizot, J.-C. Sangleboeuf: Toward glasses with better indentation cracking resistance, Comptes Rendus Mécanique 342(1), 46–51 (2014)CrossRefGoogle Scholar
  137. E.H. Yoffe: Elastic stress fields caused by indenting brittle materials, Philos. Mag. A 46(4), 617–628 (1982)CrossRefGoogle Scholar
  138. J. Boussinesq: Application des potentiels à l’étude de l’équilibre det des mouvements des solides élastiques (Gauthier-Villars, Paris 1885)Google Scholar
  139. K. Januchta, R.E. Youngman, A. Goel, M. Bauchy, S.L. Logunov, S.J. Rzoska, M. Bockowski, L.R. Jensen, M.M. Smedskjaer: Discovery of ultra-crack-resistant oxide glasses with adaptive networks, Chem. Mater. 29(14), 5865–5876 (2017)CrossRefGoogle Scholar
  140. S. Bista, J.F. Stebbins, J. Wu, T.M. Gross: Structural changes in calcium aluminoborosilicate glasses recovered from pressures of 1.5 to 3 GPa: Interactions of two network species with coordination number increases, J. Non-Cryst. Solids 478, 50–57 (2017)CrossRefGoogle Scholar
  141. M.S. Pambianchi, M. Dejneka, T. Gross, A. Ellisol, S. Goinez, J. Price, Y. Fang, P. Tandon, D. Bookbinder, M.-J. Li: Corning incorporated: Designing a new future with glass and optics. In: Materials Research for Manufacturing: An Industrial Perspective of Turning Materials into New Products, ed. by L.D. Madsen, E.B. Svedberg (Springer, Cham 2016) pp. 1–38Google Scholar
  142. C. Janssen: Specimen for fracture mechanics studies on glass. In: Proc. 10th Int. Congr. Glass Ceram. Soc., Tokyo (1974)Google Scholar
  143. A. Shyam, E. Lara-Curzio: The double-torsion testing technique for determination of fracture toughness and slow crack growth behavior of materials: A review, J. Mater. Sci. 41(13), 4093–4104 (2006)CrossRefGoogle Scholar
  144. M. Sakai, R.C. Bradt: Fracture toughness testing of brittle materials, Int. Mater. Rev. 38(2), 53–78 (1993)CrossRefGoogle Scholar
  145. S. Freiman, J.J. Mecholsky Jr.: The Fracture of Brittle Materials: Testing and Analysis (Wiley, Hoboken 2012)CrossRefGoogle Scholar
  146. ASTM C1421-18: Standard Test Methods for Determination of Fracture Toughness of Advanced Ceramics at Ambient Temperature (ASTM, West Conshohocken 2010)Google Scholar
  147. M. Sakai, K. Urashima, M. Inagaki: Energy principle of elastic-plastic fracture and its application to the fracture mechanics of a polycrystalline graphite, J. Am. Ceram. Soc. 66(12), 868–874 (1983)CrossRefGoogle Scholar
  148. J. Glucklich: On crack stability in some fracture tests, Eng. Fract. Mech. 3(3), 333–344 (1971)CrossRefGoogle Scholar
  149. D. Munz, R.T. Bubsey, J.L. Shannon: Fracture toughness determination of Al2O3 using four-point-bend specimens with straight-through and chevron notches, J. Am. Ceram. Soc. 63(5/6), 300–305 (1980)CrossRefGoogle Scholar
  150. J.I. Bluhm: Stability considerations in the generalized three dimensional ‘work of fracture’ specimen. In: Analysis and Mechanics, ed. by D.M.R. Taplin (Elsevier 1978) pp. 409–417Google Scholar
  151. National Institute of Standards and Technology (NIST): https://srdata.nist.gov/CeramicDataPortal/fracture
  152. E. Orowan: Fracture and strength of solids, Rep. Prog. Phys. XII, 185–232 (1949)CrossRefGoogle Scholar
  153. S.M. Wiederhorn: Fracture surface energy of glass, J. Am. Ceram. Soc. 52(2), 99 (1969)CrossRefGoogle Scholar
  154. I. Naray-Szabo, J. Ladik: Strength of silica glass, Nature 188(4746), 226 (1960)CrossRefGoogle Scholar
  155. T.F. Soules: Models of glass strength and relaxation phenomena suggested by molecular dynamic simulations, J. Non-Cryst. Solids 73(1–3), 315–330 (1985)CrossRefGoogle Scholar
  156. R. Ochoa, T.P. Swiler, J.H. Simmons: Molecular dynamics studies of brittle failure in silica: Effect of thermal vibrations, J. Non-Cryst. Solids 128(1), 57–68 (1991)CrossRefGoogle Scholar
  157. K. Muralidharan: Molecular dynamics studies of brittle fracture in vitreous silica: Review and recent progress, J. Non-Cryst. Solids 351, 1532–1542 (2005)CrossRefGoogle Scholar
  158. B.A. Proctor, I. Whitney, J.W. Johnson: The strength of fused silica, Proc. R. Soc. A 297(1451), 534–557 (1967)CrossRefGoogle Scholar
  159. G. Brambilla, D.N. Payne: The ultimate strength of glass silica nanowires, Nano Lett. 9(2), 831–835 (2009)CrossRefGoogle Scholar
  160. B. Varughese, Y.-K. Lee, M. Tomozawa: Effect of fictive temperature on mechanical strength of soda-lime glasses, J. Non-Cryst. Solids 241(2/3), 134–139 (1998)CrossRefGoogle Scholar
  161. H. Li, A. Agarwal, M. Tomozawa: Effect of fictive temperature on dynamic fatigue behavior of silica and soda-lime glasses, J. Am. Ceram. Soc. 78(5), 1393–1396 (1995)CrossRefGoogle Scholar
  162. C.E. Inglis: Stresses in a plate due to the presence of cracks and sharp corners, Trans. Inst. Nav. Archit. 55(219–241), 193–198 (1913)Google Scholar
  163. A.A. Griffith: The phenomena of rupture and flow in solids, Philos. Trans. R. Soc. A 221(582–593), 163–198 (1921)CrossRefGoogle Scholar
  164. G.R. Irwin: Crack-extension force for a part-through crack in a plate, J. Appl. Mech. 29(4), 651–654 (1962)CrossRefGoogle Scholar
  165. H.M. Westergaard: Bearing pressures and cracks, J. Appl. Mech. 6, 49 (1939)Google Scholar
  166. M.L. Williams: On the stress distribution at the base of a stationary crack, J. Appl. Mech. 24, 109–114 (1957)Google Scholar
  167. H. Tada, P.C. Paris, G.R. Irwin: The Stress Analysis of Cracks Handbook, 3rd edn. (American Society of Mechanical Engineers, New York 2000)CrossRefGoogle Scholar
  168. M.J. Matthewson, C.R. Kurkjian, S.T. Gulati: Strength measurement of optical fibers by bending, J. Am. Ceram. Soc. 69(11), 815–821 (1986)CrossRefGoogle Scholar
  169. J.B. Murgatroyd: The strength of glass fibers, J. Soc. Glass Technol. 28, 388–405 (1944)Google Scholar
  170. P.W. France, M.J. Paradine, M.H. Reeve, G.R. Newns: Liquid nitrogen strengths of coated optical glass fibres, J. Mater. Sci. 15(4), 825–830 (1980)CrossRefGoogle Scholar
  171. ASTM C158-02: Standard Test Methods for Strength of Glass by Flexure (Determination of Modulus of Rupture) (ASTM, West Conshohocken 2017)Google Scholar
  172. W. Weibull: A Statistical Theory of the Strength of Materials (Generalstabens litografiska anstalt, Stockholm 1939)Google Scholar
  173. F.W. Zok: On weakest link theory and Weibull statistics, J. Am. Ceram. Soc. 100(4), 1265–1268 (2017)CrossRefGoogle Scholar
  174. J.T. Littleton Jr.: A new method for measuring the tensile strength of glass, Phys. Rev. 22(5), 510 (1923)CrossRefGoogle Scholar
  175. M. Grenet: Recherches sur la résistance mécanique du verre, Bull. Soc. Encourag. Ind. Natl. 5(4), 838–848 (1899)Google Scholar
  176. D.G. Holloway: The fracture of glass, Phys. Educ. 3(6), 317 (1968)CrossRefGoogle Scholar
  177. R.E. Mould, R.D. Southwick: Strength and static fatigue of abraded glass under controlled ambient conditions: I, general concepts and apparatus, J. Am. Ceram. Soc. 42(11), 542–547 (1959)CrossRefGoogle Scholar
  178. R.E. Mould: Strength and static fatigue of abraded glass under controlled ambient conditions: IV, effect of surrounding medium, J. Am. Ceram. Soc. 44(10), 481–491 (1961)CrossRefGoogle Scholar
  179. F.W. Preston: The mechanical properties of glass, J. Appl. Phys. 13(10), 623–634 (1942)CrossRefGoogle Scholar
  180. R.J. Charles: Static fatigue of glass. I, J. Appl. Phys. 29(11), 1549–1553 (1958)CrossRefGoogle Scholar
  181. R.J. Charles: Static fatigue of glass. II, J. Appl. Phys. 29(11), 1554–1560 (1958)CrossRefGoogle Scholar
  182. R.J. Charles, W.B. Hilling: Surfaces, stress-dependent reactions and strength. In: High-Strength Materials, ed. by V.F. Zackay (Wiley, Hoboken 1965) pp. 682–705Google Scholar
  183. W.B. Hillig: Model of effect of environmental attack on flaw growth kinetics of glass, Int. J. Fract. 143(3), 219–230 (2007)CrossRefGoogle Scholar
  184. J.T. Dickinson, S.C. Langford, L.C. Jensen, G.L. McVay, J.F. Kelso, C.G. Pantano: Fractoemission from fused silica and sodium silicate glasses, J. Vac. Sci. Technol. A 6(3), 1084–1089 (1988)CrossRefGoogle Scholar
  185. S.N. Crichton, M. Tomozawa, J.S. Hayden, T.I. Suratwala, J.H. Campbell: Subcritical crack growth in a phosphate laser glass, J. Am. Ceram. Soc. 82(11), 3097–3104 (1999)CrossRefGoogle Scholar
  186. C.L. Rountree: Recent progress to understand stress corrosion cracking in sodium borosilicate glasses: Linking the chemical composition to structural, physical and fracture properties, J. Phys. D 50(34), 343002 (2017)CrossRefGoogle Scholar
  187. S. Yoshida, J. Matsuoka, N. Soga: Sub-critical crack growth in sodium germanate glasses, J. Non-Cryst. Solids 316(1), 28–34 (2003)CrossRefGoogle Scholar
  188. T.A. Michalske, B.C. Bunker: Slow fracture model based on strained silicate structures, J. Appl. Phys. 56(10), 2686–2693 (1984)CrossRefGoogle Scholar
  189. E. Silva, J. Li, D. Liao, S. Subramanian, T. Zhu, S. Yip: Atomic scale chemo-mechanics of silica: Nano-rod deformation and water reaction, J. Computer-Aided Mater. Des. 13(25), 135–159 (2006)CrossRefGoogle Scholar
  190. T. Zhu, J. Li, X. Lin, S. Yip: Stress-dependent molecular pathways of silica–water reaction, J. Mech. Phys. Solids 53, 1597–1623 (2005)CrossRefGoogle Scholar
  191. S.M. Wiederhorn: Influence of water vapor on crack propagation in soda-lime glass, J. Am. Ceram. Soc. 50(8), 407–414 (1967)CrossRefGoogle Scholar
  192. S.M. Wiederhorn, L.H. Bolz: Stress corrosion and static fatigue of glass, J. Am. Ceram. Soc. 53(10), 543 (1970)CrossRefGoogle Scholar
  193. F. Célarié, S. Prades, D. Bonamy, L. Ferrero, E. Bouchard, C. Guillot, C. Marlière: Glass breaks like metal, but at the nanometer scale, Phys. Rev. Lett. 90(7), 75504 (2003)CrossRefGoogle Scholar
  194. C. Kocer, R.E. Collins: Measurement of very slow crack growth in glass, J. Am. Ceram. Soc. 84(11), 2585–2593 (2001)CrossRefGoogle Scholar
  195. T. Cramer, A. Wanner, P. Gumbsch: Crack velocities during dynamic fracture of glass and single crystalline silicon, Phys. Status Solidi (a) 164(1), R5/R6 (1997)CrossRefGoogle Scholar
  196. S.M. Wiederhorn: Effect of deuterium oxide on crack growth in soda-lime-silica glass, J. Am. Ceram. Soc. 65(12), C-202/C-203 (1982)CrossRefGoogle Scholar
  197. S.W. Freiman: Effect of alcohols on crack propagation in glass, J. Am. Ceram. Soc. 57(8), 350–353 (1974)CrossRefGoogle Scholar
  198. S.M. Wiederhorn, S.W. Freiman, E.R. Fuller, C.J. Simmons: Effects of water and other dielectrics on crack-growth, J. Mater. Sci. 17(12), 3460–3478 (1982)CrossRefGoogle Scholar
  199. B.R. Lawn: Diffusion-controlled subcritical crack growth in the presence of a dilute gas environment, Mater. Sci. Eng. 13(3), 277–283 (1974)CrossRefGoogle Scholar
  200. R.G. Horn, K.T. Wan, S. Courmont, B.R. Lawn: Diffusion of water along “closed” mica interfaces, J. Colloid Interface Sci. 159(2), 509–511 (1993)CrossRefGoogle Scholar
  201. T.A. Michalske, B.C. Bunker: A chemical kinetics model for glass fracture, J. Am. Ceram. Soc. 76(10), 2613–2618 (1993)CrossRefGoogle Scholar
  202. P. Paris, F. Erdogan: A critical analysis of crack propagation laws, J. Basic Eng. 85(4), 528–533 (1963)CrossRefGoogle Scholar
  203. E. Gehrke, C. Ullner, M. Hähnert: Fatigue limit and crack arrest in alkali-containing silicate glasses, J. Mater. Sci. 26(20), 5445–5455 (1991)CrossRefGoogle Scholar
  204. T.A. Michalske: The stress corrosion limit: Its measurement and implications. In: Fracture Mechanics of Ceramics, Vol. 5 (Plenum, New York 1977) p. 277Google Scholar
  205. J.-P. Guin, S.M. Wiederhorn: Crack growth threshold in soda lime silicate glass: Role of hold-time, J. Non-Cryst. Solids 316(1), 12–20 (2003)CrossRefGoogle Scholar
  206. J.H. Seaman, P.J. Lezzi, T.A. Blanchet, M. Tomozawa: Modeling slow crack growth behavior of glass strengthened by a subcritical tensile stress using surface stress relaxation, J. Am. Ceram. Soc. 98(10), 3075–3086 (2015)CrossRefGoogle Scholar
  207. J.H. Seaman, T.A. Blanchet, M. Tomozawa: Origin of the static fatigue limit in oxide glasses, J. Am. Ceram. Soc. 99(11), 3600–3609 (2016)CrossRefGoogle Scholar
  208. T. Fett, J.-P. Guin, S.M. Wiederhorn: Stresses in ion-exchange layers of soda-lime-silicate glass, Fatigue Fract. Eng. Mater. Struct. 28(6), 507–514 (2005)CrossRefGoogle Scholar
  209. T. Fett, J.P. Guin, S.M. Wiederhorn: Interpretation of effects at the static fatigue limit of soda-lime-silicate glass, Eng. Fract. Mech. 72(18), 2774–2791 (2005)CrossRefGoogle Scholar
  210. S. Ito, M. Tomozawa: Crack blunting of high-silica glass, J. Am. Ceram. Soc. 65(8), 368–371 (1982)CrossRefGoogle Scholar
  211. Y. Bando, S. Ito, M. Tomozawa: Direct observation of crack tip geometry of SiO2 glass by high-resolution electron microscopy, J. Am. Ceram. Soc. 67(3), C-36–C-37 (1984)Google Scholar
  212. W.-T. Han, M. Tomozawa: Mechanism of mechanical strength increase of soda-lime glass by aging, J. Am. Ceram. Soc. 72(10), 1837–1843 (1989)CrossRefGoogle Scholar
  213. B.R. Lawn, D.B. Marshall, A.H. Heuer: Comment on direct observation of crack-tip geometry of SiO2 glass by high-resolution electron microscopy, J. Am. Ceram. Soc. 67(11), c253 (1984)CrossRefGoogle Scholar
  214. M. Tomozawa, Y. Bando, S. Ito: Reply, J. Am. Ceram. Soc. 67(11), c254 (1984)CrossRefGoogle Scholar
  215. P.J. Lezzi, M. Tomozawa, R.W. Hepburn: Confirmation of thin surface residual compressive stress in silica glass fiber by FTIR reflection spectroscopy, J. Non-Cryst. Solids 390, 13–18 (2014)CrossRefGoogle Scholar
  216. R.M. McMeeking, A.G. Evans: Mechanics of transformation-toughening in brittle materials, J. Am. Ceram. Soc. 65(5), 242–246 (1982)CrossRefGoogle Scholar
  217. A.Q. Tool: Relation between inelastic deformability and thermal expansion of glass in its annealing range, J. Am. Ceram. Soc. 29(9), 240–253 (1946)CrossRefGoogle Scholar
  218. M. Muraoka, H. Abé: Subcritical crack growth in silica optical fibers in wide range of crack velocities, J. Am. Ceram. Soc. 79(1), 51–57 (1996)CrossRefGoogle Scholar
  219. M. Tomozawa: Fracture of glasses, Annu. Rev. Mater. Sci. 26(1), 43–74 (1996)CrossRefGoogle Scholar
  220. S. Hénaux, F. Creuzet: Kinetic fracture of glass at the nanometer scale, J. Mater. Sci. Lett. 16(12), 1008–1011 (1997)CrossRefGoogle Scholar
  221. S. Hénaux, F. Creuzet: Crack tip morphology of slowly growing cracks in glass, J. Am. Ceram. Soc. 83(2), 415–417 (2000)CrossRefGoogle Scholar
  222. M. Ciccotti, M. George, V. Ranieri, L. Wondraczek, C. Marlière: Dynamic condensation of water at crack tips in fused silica glass, J. Non-Cryst. Solids 354(2–9), 564–568 (2008)CrossRefGoogle Scholar
  223. K. Han, M. Ciccotti, S. Roux: Measuring nanoscale stress intensity factors with an atomic force microscope, Europhys. Lett. 6, 66003 (2010)CrossRefGoogle Scholar
  224. S.M. Wiederhorn, T. Fett, J.-P. Guin, M. Ciccotti: Griffith cracks at the nanoscale, Int. J. Appl. Glass Sci. 4(2), 76–86 (2013)CrossRefGoogle Scholar
  225. G. Pezzotti, A. Leto, A.A. Porporati: Visualization of microscopic stress fields in silica glass in the scanning electron microscope, J. Ceram. Soc. 116(1356), 869–874 (2008)CrossRefGoogle Scholar
  226. J.-F. Poggemann, A. Gofl, G. Heide, E. Rädlein, G.H. Frischat: Direct view of the structure of a silica glass fracture surface, J. Non-Cryst. Solids 281(1–3), 221–226 (2001)CrossRefGoogle Scholar
  227. J.-F. Poggemann, G. Heide, G.H. Frischat: Direct view of the structure of different glass fracture surfaces by atomic force microscopy, J. Non-Cryst. Solids 326/327, 15–20 (2003)CrossRefGoogle Scholar
  228. G.H. Frischat, J.F. Poggemann, G. Heide: Nanostructure and atomic structure of glass seen by atomic force microscopy, J. Non-Cryst. Solids 345, 197–202 (2004)CrossRefGoogle Scholar
  229. S.M. Wiederhorn, J.-P. Guin, T. Fett: The use of atomic force microscopy to study crack tips in glass, Metall. Mater. Trans. A 42(2), 267–278 (2011)CrossRefGoogle Scholar
  230. S.M. Wiederhorn, J.M. López-Cepero, J. Wallace, J.-P. Guin, T. Fett: Roughness of glass surfaces formed by sub-critical crack growth, J. Non-Cryst. Solids 353(16/17), 1582–1591 (2007)CrossRefGoogle Scholar
  231. J.-P. Guin, S.M. Wiederhorn: Fracture of silicate glasses: Ductile or brittle?, Phys. Rev. Lett. 92(21), 215502 (2004)CrossRefGoogle Scholar
  232. J.-P. Guin, S.M. Wiederhorn: Investigation of the subcritical crack growth process in glass by atomic force microscopy. In: Fractography of Glasses and Ceramics V: Ceramic Transactions, Vol. 199, ed. by J.R. Varner, G.D. Quinn, M. Wightman (Wiley, Hoboken 2007) pp. 13–23Google Scholar
  233. G. Wang, D.Q. Zhao, H.Y. Bai, M.X. Pan, A.L. Xia, B.S. Han, X.K. Xi, Y. Wu, W.H. Wang: Nanoscale periodic morphologies on the fracture surface of brittle metallic glasses, Phys. Rev. Lett. 98(23), 235501 (2007)CrossRefGoogle Scholar
  234. F. Celarie, M. Ciccotti, C. Marlière: 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(1), 51–68 (2007)CrossRefGoogle Scholar
  235. C.R. Kurkjian, P.K. Gupta, R.K. Brow, N. Lower: The intrinsic strength and fatigue of oxide glasses, J. Non-Cryst. Solids 316(1), 114–124 (2003)CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Institute of Physics – Rennes (IPR), UMR CNRS 6251University of Rennes 1RennesFrance

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