On the effect of stress on the nonequilibrium viscosity of glasses

U. P. Karaseva ; A. B. Freidin

Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 165 (2023) no. 3, pp. 219-235

Résumé

Two processes related to the relaxation of a glassy material’s structure were discussed. One entails stress relaxation, while the other involves the relaxation of the structure to its equilibrium state following the stress relief and is described by the change of fictive temperature. Both processes affect the viscosity coefficient. The nonequilibrium viscosity model was analyzed with account of these relaxation processes. The importance of considering stresses when modeling the viscoelastic behavior of glassy materials was showcased by solving the problem of stress relaxation in a plate under thermal stresses.

Détail

Keywords: stress relaxation, viscosity models, fictive temperature, nonequilibrium structure, thermal stresses.

Bibliographie

[1] D. B. Kao, J. P. McVittie, W. D. Nix, K. C. Saraswat, “Two-dimensional thermal oxidation of silicon. II. Modeling stress effects in wet oxides”, IEEE Trans. Electron Devices, 35:1 (1988), 25–37 | DOI

[2] M. T. McDowell, S. W. Lee, W. D. Nix, Y. Cui, “25th anniversary article: Understanding the lithiation of silicon and other alloying anodes for lithium-ion batteries”, Adv. Mater, 25:36 (2004), 4966–4984 | DOI

[3] M. Poluektov, A. B. Freidin, L. Figiel, “Modelling stress-affected chemical reactions in non linear viscoelastic solids with application to lithiation reaction in spherical Si particles”, Int. J. Eng. Sci, 128 (2018), 44–62 | DOI | MR | Zbl

[4] O. V. Mazurin, S. M. Rekhson, Yu. K. Startsev, “O roli vyazkosti pri raschete relaksatsii svoistv stekla v intervale steklovaniya”, Fiz. khim. stekla, 1:5 (1975), 438–442

[5] O. S. Narayanaswamy, “A model of structural relaxation in glass”, J. Am. Ceram. Soc, 54:10 (1971), 491–498 | DOI

[6] O. V. Mazurin, V. P. Kluyev, S. V. Stolyar, “Temperature dependences of structural relaxation times at constant fictive temperatures in oxide glasses”, Glastech. Ber, 56:2 (1983), 1148–1153

[7] J. C. Mauro, D. C. Allan, M. Potuzak, “Nonequilibrium viscosity of glass”, Phys. Rev. B, 80:9 (2009), 094204 | DOI

[8] Yu. K. Startsev, “Nekotorye oblasti primeneniya stekol, ozhidayuschie issledovatelei (po materialam otkrytykh publikatsii)”, Steklo: nauka i praktika, GLASSP 2021, Sb. tez. Tretei Ros. konf. s mezhdunar. uchast., In-t khimii silikatov im. I.V. Grebenschikova RAN, 2021, 40–41

[9] A. J. Ellison, I. A. Cornejo, “Glass substrates for liquid crystal displays”, Int. J. Appl. Glass Sci, 1:1 (2010), 87–103 | DOI | MR

[10] Yu. K. Startsev, Stekla v displeyakh. Trebovaniya, osobennosti tekhnologii, modelirovanie svoistv, SPbGTI (TU), SPb, 2008, 134 pp.

[11] Q. Zheng, J. C. Mauro, “Variability in the relaxation behavior of glass: Impact of thermal history fluctuations and fragility”, J. Chem. Phys., 146:7 (2017), 074504 | DOI

[12] A. M. Butaev, Prochnost stekla. Ionoobmennoe uprochnenie, Makhachkala, 1997, 249 pp.

[13] A. K. Varshneya, “Chemical strengthening of glass: Lessons learned and yet to be learned”, Int. J. Appl. Glass Sci, 1:2 (2010), 131–142 | DOI

[14] Yu. K. Startsev, V. A. Bakhanov, M. Vostrikova, “S Issledovanie osobennostei relaksatsionnykh protsessov v ionoobmenennykh sloyakh promyshlennykh stekol”, Tez. dokl. III Chekhoslovatsko-Sovetsk. simp. po stroeniyu i svoistvam silikatnykh i oksidnykh sistem (Bratislava, 1986), 102–104

[15] O. V. Mazurin, Yu. K. Startsev, V. P. Klyuev, “O strukturnoi relaksatsii v ionoobmenennykh steklakh”, Tez. dokl. Vses. simp. «Relaksatsionnye yavleniya v neorga nicheskikh steklakh» (Tbilisi, 1984), 25–26

[16] Yu. K. Startsev, “Influence of structural relaxation on changes in properties of ion exchanged glasses” (New Delhi, 1986), XIVth Int. Congr. Glass., 363–369

[17] A. I. Fu, J. C. Mauro, “Mutual diffusivity, network dilation, and salt bath poisoning effects in ion-exchanged glass”, J. Non-Cryst. Solids, 363 (2013), 199–204 | DOI

[18] S. A. Chizhik, A. A. Sidel'nikov, “Kinetics of solid state reactions with a positive feedback between the reaction and fracture. 2. The kinetics of ion exchange in an alkaline-silicate glass”, Russ. Chem. Bull, 47:4 (1998), 610–614 | DOI

[19] S. A. Chizhik, A. A. Sidel'nikov, “Kinetics of the Na+ Li+ ion exchange in alkali silicate glass”, Glass Phys. Chem, 26:3 (2000), 280–286 | DOI

[20] S. A. Chizhik, A. A. Sidel'nikov, “The kinetics of solid state reactions accompanied by fracture: I. Reaction of ion exchange in lime-soda glass”, Solid State Ionics, 178:23-24 (2007), 1344–1352 | DOI | MR

[21] J. C. Mauro, A. J. Ellison, L. D. Pye, “Glass: The nanotechnology connection”, Int. J. Appl. Glass Sci, 4:2 (2013), 64–75 | DOI

[22] J. C. Mauro, A. Tandia, K. D. Vargheese, Y. Z. Mauro, M. M. Smedskjaer, “Accelerating the design of functional glasses through modeling”, Chem. Mater, 28:12 (2016), 4267–4277 | DOI

[23] J. C. Mauro, “Decoding the glass genome”, Curr. Opin. Solid State Mater. Sci, 22:2 (2018), 58–64 | DOI

[24] K. Tsujikawa, K. Tajima, J. Zhou, “Intrinsic loss of optical fibers”, Opt. Fiber Technol, 11:4 (2005), 319–331 | DOI

[25] J. C. Mauro, S. Soyer Uzun, W. Bras, S. Sen, “Nonmonotonic evolution of density fluctuations during glass relaxation”, Phys. Rev. Lett., 102 (2009), 155506 | DOI

[26] J. C. Mauro, “Effect of fragility on relaxation of density fluctuations in glass”, J. Non Cryst. Solids, 357:19-20 (2011), 3520–3543 | DOI

[27] M. Reiner, Reologiya, Nauka, M, 1965, 224 pp.

[28] O. V. Mazurin, Steklovanie, Nauka, L., 1986, 158 pp.

[29] D. K. Tagantsev, Stekloobraznye materialy, uchebnoe posobie, Izd-vo Poli tekhn. un-ta, SPb., 2010, 204 pp.

[30] A. Q. Tool, “Relation between inelastic deformability and thermal expansion of glass in its annealing range”, J. Am. Ceram. Soc, 29:9 (1946), 240–253 | DOI

[31] J. C. Mauro, Y. Yue, A. J. Ellison, P. K. Gupta, D. C. Allan, “Viscosity of glass-forming liquids”, Proc. Natl. Acad. Sci. U. S. A, 106:47 (2009), 19780–19784 | DOI

[32] H. N. Ritland, “Limitations of the fictive temperature concept”, J. Am. Ceram. Soc., 39:12 (1956), 403–406 | DOI

[33] J. C. Mauro, Y. Z. Mauro, “On the Prony series representation of stretched exponential relaxation”, Phys. A: Stat. Mech. Appl, 506 (2018), 75–87 | DOI | MR

[34] J. C. Phillips, “Kohlrausch explained: The solution to a problem that is 150 years old”, J. Stat. Phys, 77:3-4 (1994), 945–947 | DOI

[35] J. C. Phillips, “Stretched exponential relaxation in molecular and electronic glasses”, Rep. Prog. Phys, 59 (1996), 1133–1207 | DOI

[36] U. Fotheringham, R. Muller, K. Erb, A. Baltes, F. Siebers, E. Weiß, R. Dudek, “Evaluation of the calorimetric glass transition of glasses and glass ceramics with respect to structural relaxation and dimensional stability”, Thermochim. Acta, 461:1-2 (2007), 72–81 | DOI