Numerical modelling of compression cure high-filled polimer material

Konstantin A. Chekhonin ; Victor D. Vlasenko

Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 6, pp. 805-814.

Résumé

The article presents phenomenological constitutive relations for modeling the compression curing of a highly filled polymer medium, obtained in the framework of the mechanics of an almost incompressible viscoelastic solid using the modified Herrmann variational principle. The relations are based on the representation of the medium as a composition of a fluid and solidified material, taking into account the history of continuous nucleation and deformation of a new phase in the temperature range of phase transformations. During the manufacturing process, different mechanisms lead to process-induced deformations and stresses. These mechanisms depend on thermal expansion, shrinkage, nonlinear viscoelastic properties of the material, and variation in local temperatures. In critical cases, these residual stresses can lead to initial degradation and up to failure of the material. A stable numerical algorithm for the problem’s solution has been developed on the base of finite element method. Numerical investigation of the stress and deformation in system during the polymerization process has been carried out. The evolution of curing stresses in a singular zone of domain has been investigated.

Détail

Keywords: polymerization, high-filled polymer, finite element method, curing stress, viscoelasticity, variational theorem Herrmann.

Bibliographie

[1] A. AY.Malkin, V.P Begishev, Chemical forming of polymers, Chemistry, M., 1991 (in Russian)

[2] V.V. Bolotin, A.N Vorontsov, V.B. Antokhov, “The theory compression forming of products from composite of materials”, Mechanics of Composite Materials, 6 (1982), 1034–1042 (in Russian)

[3] B.W. Shaffe, M. Lewitsky, “Termoelastic constitutive equation for chemically hardering materials”, Journal of Appl. Mech., 41 (1974), 652–657 | DOI | Zbl

[4] D.A. Frank-Kamenecki, Diffusion and heat transfer in chemical kinetics, Science, M., 1967 (in Russian)

[5] N.M. Chechilo, N.S. Enikolopayn, “About structure of front polymerization of a wave and mechanism of distribution of reaction polymerization”, Dokl. Acad. Sci. USSR, 214:5 (1974), 1131–1133 (in Russian)

[6] N.H. Arutynayn, A.D. Drozdov, “Phase transitions in elastic and viscoelastic bodies”, Mechanics of Composite Materials, 1 (1986), 94–102 (in Russian)

[7] L.V. Klichnikov, E.E Alaynova, B.A. Rozenberg, “Method of equivalent definition of internal voltage in elastic models frontal polymerization”, Mechanics of Composite Materials, 31 (1995), 3–9 (in Russian)

[8] V.V. Moskvitin, Resistance viscoelastic of materials, Science, M., 1972 (in Russian)

[9] K.A. Chekhonin, A.N. Baklanov, The decision of primary tasks of the theory of elasticity at polymerization of incompressible environments, Science, Vladivostok, 1998 (in Russian)

[10] A.M. Lipanov, M.Y. Al'es, O.I. Evstefiev, “Numerical modeling to an intense - deformated status polymerization of polymeric systems”, J. High-molecular of connection, 33:1 (1991), 52–59 (in Russian)

[11] L.A. Golotina, V.P. Matveenko, I.N. Shardakov, “Analysis of deformation process characteristics in amorphous-crystalline polymers”, Mechanics of Solids, 47 (2012), 634–640 | DOI

[12] K.A. Chekhonin, R.N. Pilipchuk, Modeling polymerization press-forms with the account incompressibility or near-incompressibility of the fuel, Science, Vladivostok, 1998 (in Russian)

[13] A.N. Baklanov, Mathematical modeling volumetric solidification higt-filled of a com-posite in the press-forms, Ph. D. Tesis, The Khabarovsk State Technical University, Khabarovsk, 2000 (in Russian)

[14] R.N. Pilipchuk, Mathematical modeling compression polymerization incompressible or nearly incompressible composite of materials, Ph. D. Tesis, The Khabarovsk State Technical University, Khabarovsk, 2000 (in Russian)

[15] V.K. Bulgakov, K.A. Chekhonin, I.I. Potapov, A.N. Baklanov, “The analysis of the three-dimensional FCM press-form at a stage solidification”, J. Mathematical modeling, 3 (1997), 181–192 (in Russian)

[16] K.A. Chekhonin, A.N. Baklanov, “Modeling of the stressedly-deformed conditions incompressible solidification of a polymeric material in conditions of contact with moment by the thin-walled shell of rotation”, J. Mathematical modeling, 4 (1998), 40–66 (in Russian)

[17] V.K. Bulgakov, K.A. Chekhonin, “Modeling of a 3D Problem of compression forming system “Composite shell - low compressible consolidating filler””, J. Mathematical Modeling, 4 (2002), 121–131 (in Russian)

[18] I.N. Shardakov, V.P. Matveyenko, N.V. Pistsov, V.P. Beghishev, “Simulation of thermomechanical processen in crystallising polymer”, Polym. Eng. and Sci., 37:8 (1997), 1270–1279 | DOI

[19] K.A. Chekhonin, “The Essential priciples for theory curing process solid propellant grain”, Vestnik ITPS, 12:1 (2016), 131–145 (in Russian)

[20] L.R. Herrmann, “Elasticity equations for incompressible and nearly incompressible materials by a variational theorem”, AIAA J., 3 (1965), 1896–1900 | DOI

[21] N. Kikuchi, J.T. Oden, Contact problem in elasticity study of variational inequalities and finite element methods, SIAM, Philadelphia, 1988

[22] V.V. Novogilov, The theory of thin shells, Sudpromgis, M., 1951 (in Russian)

[23] V. Girault, P-A. Raviart, Finite element methods for Navier-Stokes equations, Springer-Verlag, Berlin, 1986 | Zbl

[24] E.G. Diaykonov, Minimization of computing work. Asymptotically optimum algorithms for elliptic tasks, Science, M., 1989 (in Russian)

[25] F. Brezzi, M. Fortin, Mixed and hybrid finite element method, Springer, New York, 1991

[26] K.A. Chekhonin, A.N. Baklanov, About some finite element approximations of the mixed type for incompressible or near-incompressible environments in $R^{3} $, Science, Vladivostok, 1998 (in Russian)

[27] R. Glowinski, O. Pironneau, “Finite element method for Navier-Stokes equations”, Annu. Rev. Fluid Mech., 24 (1992), 167–204 | DOI | Zbl

[28] V.K. Bulgakov, K.A. Chekhonin, The Biseline theory mixed finite element method, Khabarovsk State Technical University, Khabarovsk, 1999 (in Russian)

[29] Y. Saad, Iterative methods for sparse linear systems, PWS Publishing Company, 1996 | Zbl

[30] K.A. Chekhonin, P.A. Sukhinin, “Numerical modeling of filling axisymetric of the channel nonlinear viscoplastic by a liquid in view of wall-boundary-effect”, Engineering Phys. J., 72:5 (1999), 881–885 (in Russian)