Equations of viscoelasticity for an incompletely cured epoxy binder under small strains

V. M. Pestrenin ; I. V. Pestrenina ; L. V. Landik ; T. N. Pomortseva ; A. F. Merzlyakov

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 89 (2024), pp. 119-134

Résumé

In this paper, the mechanical state of an epoxy binder during incomplete curing is studied. The degree of curing is described by a three-parameter kinetic equation of conversion with the material parameters and their temperature dependence determined using mathematical optimization methods based on isothermal conversion data. Mechanical properties of the incompletely cured polymer are obtained with the use of experimental data on uniaxial loading of reference samples according to a program assuming stretching to a specified strain at a given rate and holding at a fixed strain during a specified period of time. The physical equations for the polymer under study are assumed to be linear viscoelastic Volterra equations under the condition that the volumetric deformation is elastic. A method for determining the material parameters of the equations, i.e., instantaneous elastic constants and relaxation kernels, is proposed. Curing of the epoxy binder in vacuum is accompanied by foaming due to the presence of air bubbles in the binder. This phenomenon is shown to be prevented by pre-curing up to the “barrier” level in atmospheric conditions. The research results can be used when calculating the technological processes of manufacturing structures made of composites.

Détail

Keywords: epoxy binder, incomplete curing, kinetic equation, viscoelasticity equation, foaming.

Bibliographie

[1] Sakhabutdinova L.R., Smetannikov O.Yu., Ilinykh G.V., “Chislennoe modelirovanie protsessa izgotovleniya krupnogabaritnogo kompozitnogo kokona s uchetom termovyazkouprugosti”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, 2022, no. 76, 165–181

[2] Natsik V.D., Fomenko L.S., Lubenets S.V., “Issledovanie polzuchesti i steklovaniya elastomerov metodom mikroindentirovaniya: epoksidnaya smola i nanokompozity na ee osnove”, Fizika tverdogo tela, 55:5 (2013), 940–952

[3] Sadikova M.M., Khamraeva M.K., “Epoksidnye kompozitsionnye materialy i ikh vliyanie na fiziko-mekhanicheskie svoistva polimerov”, Universum: tekhnicheskie nauki: elektronnyi nauchnyi zhurnal, 2020, no. 6 (75) (data obrascheniya: 03.06.2023) http://7universum.com/ru/tech/archive/item/9796

[4] Molokov M.V., Nizin D.R., Nizina T.A., Startsev O.V., “Rezultaty eksperimentalnykh issledovanii polimernykh kompozitsionnykh materialov na osnove nizkovyazkikh epoksidnykh svyazuyuschikh”, Ogarev-online, 2014, no. S2 (40) (data obrascheniya: 03.06.2023) https://cyberleninka.ru/article/n/rezultaty-eksperimentalnyh-issledovaniy-polimernyh-kompozitsionnyh-materialov-na-osnove-nizkovyazkih-epoksidnyh-svyazuyuschih

[5] Manickam R., Lakshmi Narasimhan R., Nagarajan S., Damodaran V.K., Devarajan B., “Influence of filler material on properties of fiber-reinforced polymer composites: a review”, E-Polymers, 22:1 (2022), 898–916

[6] Poloz A.Yu., Ebich Yu.R., Dolinskaya R.M., Mozgalev V.V., “Vyazkouprugie svoistva iznoso stoikikh epoksidnykh kompozitov”, Voprosy khimii i khimicheskoi tekhnologii, 2013, no. 5, 72–77

[7] Bockenhoff P., Gundlach C., Kastner M., “Experimental characterization and modeling of the material behavior of an epoxy system”, SN Appl. Sci., 2:1702 (2020), 1–13

[8] Rocha I.B.C.M., van der Meer F.P., Raijmaekers S., Lahuerta F., Nijssen R.P.L., Sluys L.J., “Numerical/experimental study of the monotonic and cyclic viscoelastic/viscoplastic/fracture behavior of an epoxy resin”, International Journal of Solids and Structures, 168 (2019), 153–165

[9] Lascano D., Quiles-Carrillo L., Torres-Giner S., Boronat T., Montanes N., “Optimization of the Curing and Post-Curing Conditions for the Manufacturing of Partially Bio-Based Epoxy Resins with Improved Toughness”, Polymers, 11:1354 (2019)

[10] Karkanas P.I., Partridge I.K., “Cure modeling and monitoring of epoxy/amine resin systems. I. Cure kinetics modeling”, J. Appl Polym Sci., 77:7 (2000), 1419–1431

[11] Pater J.T.M., Weicker G., van Swaaij W.P.M., “Polymerization of liquid propylene with a fourth generation Ziegler-Natta catalyst: Influence of temperature, hydrogen, monomer concentration, and prepolymerization method on polymerization kinetics”, J. Appl. Polym. Sci., 87 (2003), 1421–1435

[12] Zakharova V.G., Kavardina V.A., “Kineticheskoe uravnenie elementarnoi reaktsii”, Pokolenie buduschego: vzglyad molodykh uchenykh, sb. st. 10-i Mezhdunar. molodezhnoi nauch. konf., v. 4, Yugo-Zap. gos. un-t, Kursk, 2021, 35–38

[13] Khozin V.G., Zykova E.S., “Modifitsirovanie epoksidnykh svyazuyushdkh nanochastitsami dlya polimerkompozitnoi armatury”, Vestnik Kazanskogo tekhnologicheskogo universiteta, 2013, no. 18 (data obrascheniya: 03.06.2023) https://cyberleninka.ru/article/n/modifitsirovanie-epoksidnyh-svyazuyuschih-nanochastitsami-dlya-polimerkompozitnoy-armatury

[14] Bornosuz N.V., Gorbunova I.Yu., Petrakova V.V., Onuchin D.V., Sirotin I.S., “Isothermal kinetics of epoxyphosphazene cure”, Polimers, 13:2 (2021), 297, 1–16

[15] Kovaleva E.G., Savotchenko S.E., “Kinetic features of polymerization of epoxy resin modified by silicon-containing additives and mineral fillers”, Polymer Engineering Science, 62:1 (2022), 75–82

[16] Abhijit S., Mahanwar P.A., Bambole V.A., “Effect of polypyrrole on the properties of conventional epoxy coatings”, Pigment Resin Technology, 42:5 (2013), 317–325

[17] Kondyurin A.V., Komar L.A., Svistkov A.L., “Modelirovanie kinetiki reaktsii otverzhdeniya kompozitsionnogo materiala na osnove epoksidnogo svyazuyuschego”, Mekhanika kompozitsionnykh materialov i konstruktsii, 16:4 (2010), 597–611

[18] Svistkov A.L., Komar L.A., Kondyurin A.V., Maltsev M.S., Terpugov V.N., “Isparenie molekul otverditelya v reaktsii polimerizatsii epoksidnoi smoly”, Materialy XI Mezhdunar. konf. po neravnovesnym protsessam v soplakh i struyakh, NPNJ2016, Mosk. aviatsionnyi in-t, M., 2016, 385–387

[19] Jingkuan Duan, Jun Zhang, Pingkai Jiang, “Effect of external electric field on morphologies and properties of the cured epoxy and epoxy/acrylate systems”, Journal of Applied Polymer Science, 125:2 (2012), 902–914

[20] Kupriyanova E.V., Osipchik V.S., Kravchenko T.P., Pachina A.N., Morozova T.V., “Optimization of Properties of Epoxy Binders during Their Modification”, Polymer Science. Series D, 14:4 (2021), 483–488

[21] Arinina M.P., Kostenko V.A., Gorbunova I.Y., Il'in S.O., Malkin A.Y., “Kinetics of Curing of Epoxy Oligomer by Diaminodiphenyl Sulfone: Rheology and Calorimetry”, Polymer Science. Series A, 60:5 (2018), 683–690

[22] Roschin D.E., Patlazhan S.A., Berlin A.A., “Modelirovanie svobodno-radikalnoi polimerizatsii pri periodicheskom fotoinitsiirovanii”, Vysokomolekulyarnye soedineniya B, 64:1 (2022), 71–80

[23] Bondaletova L.I., Bondaletov V.G., Polimernye kompozitsionnye materialy, ucheb. posobie, v. 1, Izd-vo Tom. politekhn. un-ta, Tomsk, 2013, 118 pp.

[24] Kim W.G., Lee J.Y., “Cure Properties of Methacrylate-Type Prepolymer That Include Cyclohexane Moiety”, Journal of Applied Polymer Science, 92:1 (2004), 43–52

[25] Malkin A.Ya., Begishev V.P., Khimicheskoe formovanie polimerov, Khimiya, M., 1991, 240 pp.

[26] Kondyurin A., Design and Fabrication of Large Polymer Constructions in Space, Elsevier, 2022, 630 pp.

[27] Morozov I.A., Svistkov A.L., “Strukturno-fenomenologicheskaya model mekhanicheskogo povedeniya reziny”, Mekhanika kompozitsionnykh materialov i konstruktsii, 14:4 (2008), 583–596

[28] Kachanov L.M., Teoriya polzuchesti, Fizmatgiz, M., 1960, 455 pp.

[29] Odkvist F., “Tekhnicheskie teorii polzuchesti”, Mekhanika: sb. perevodov i obzorov, 1959, no. 2, 101–111

[30] Ilyushin A.A., Pobedrya B.E., Osnovy matematicheskoi teorii termovyazkouprugosti, Nauka, M., 1970, 280 pp.

[31] Khimmelblau D., Prikladnoe nelineinoe programmirovanie, Mir, M., 1975, 536 pp.