The relations between the heredity kernels of isotropic nonlinear viscoelastic materials in combined and one-dimensional stress states are derived. The constitutive equations are presented in a form corresponding to the proportional deviator hypothesis. The nonlinearity of viscoelastic properties is described by Rabotnov’s type models. The creep strains and stress relaxation in thin-walled tubular elements subject to a combination of tension and torsion are determined and tested experimentally.
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References
I. I. Bugakov, Creep of Polymeric Materials. Theory and Application [in Russian], Nauka, Moscow (1973).
I. I. Gol’denblat., V. L. Bazhanov, and V. A. Kopnov, Long-Term Strength in Mechanical Engineering [in Russian], Mashinostroenie, Moscow (1977).
A. A. Koltunov, “Method of determining the volume and shear characteristics of elastico-viscous hereditary media from uniaxial-tension (compression) experiments,” Mech. Polym., 5, No. 4, 667–671 (1969).
M. A. Koltunov, Creep and Relaxation [in Russian], Vysshaya Shkola, Moscow (1976).
A. F. Kregers and M. R. Kilevits, “Detailed examination of high-density polyethylene in the conditions of nonlinear creep and stress relaxation,” Mech. Comp. Mater., 21, No. 2, 117–123 (1985).
M. N. Stepnov, Statistical Processing of Mechanical Test Data [in Russian], Mashinostroenie, Moscow (1972).
G. M. Fichtenholz, A Course in Differential and Integral Calculus [in Russian], Vol. 2, Nauka, Moscow (1960).
R. M. Christensen, Theory of Viscoelasticity. An Introduction, Academic Press Inc., New-York (1971).
J. D. Ferry, Viscoelastic Properties of Polymers. 2nd ed., John Willey and Sons, New-York (1971).
W. N. Findley, J. S. Lai, and K. Onaran, Creep and Relaxation of Nonlinear Viscoelastic Materials, North-Holland Publishing Company, Amsterdam (1976).
V. P. Golub, “Application of fractional exponential hereditary kernels in the nonlinear theory of viscoelasticity,” Int. Appl. Mech., 47, No. 6, 727–734 (2011).
V. P. Golub, P. V. Fernati, and Ya. G. Lyashenko, “Determining the parameters of the fractional exponential hereditary kernels of linear viscoelastic materials,” Int. Appl. Mech., 44, No. 9, 963–974 (2008).
V. P. Golub, Yu. M. Kobzar’, and V. S. Ragulina, “A method for determining the parameters of the hereditary kernels in the nonlinear theory of viscoelasticity,” Int. Appl. Mech., 47, No. 3, 290–301 (2011).
V. P. Golub, Ya. V. Pavlyuk, and P. V. Fernati, “Determining parameters of fractional-exponential heredity kernels of nonlinear viscoelastic materials,” Int. Appl. Mech., 53, No. 4, 419–433 (2017).
V. P. Golub, A. D. Pogrebnyak, and I. B. Romanenko, “Application of smoothing spline approximations in problems on identifications of creep parameters,” Int. Appl. Mech., 33, No. 6, 477–484 (1997).
Y. M. Kobzar’, “Models of long-term brittle fracture of rods in tension and compression under creep conditions,” Int. Appl. Mech., 53, No. 4, 444–453 (2017).
J. S. Y. Lai and W. N. Findley, “Behavior of nonlinear viscoelastic material under simultaneous stress relaxation in tension and creep in torsion,” ASME J. Appl. Mech., No. 36, 22–37 (1969).
H. Leaderman, Elastic and Creep Properties of Filaments Materials and Other High Polymers, Textile Foundation, Washington (1943).
B. P. Maslov, “Combined numerical and analytical determination of Poisson’s ratio for viscoelastic isotropic materials,” Int. Appl. Mech., 54, No. 2, 220–230 (2018).
B. Persoz, “Le principle de superposition de Boltzman,” Cahier Groupe Frans, Ĕtudes Rhĕol, 2, No. 1, 237–245 (1957).
Y. N. Rabotnov, Creep Problems in Structural Members, North-Holland Publishing Company, Amsterdam (1969).
R. O. Stafford, “On mathematical forms for the material functions in nonlinear viscoelasticity,” J. Mech. and Phys. Solids, 17, No. 5, 339–354 (1969).
I. M. Ward, Mechanical Properties of Solid Polymers, Willey and Sons, New York (1971).
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* This study was sponsored by the budget program “Support for Priority Areas of Scientific Research” (KPKVK 6541230).
Translated from Prikladnaya Mekhanika, Vol. 55, No. 6, pp. 25–45, November–December 2019.
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Golub, V.P., Kobzar’, Y.M. & Fernati, P.V. Determining the Parameters of the Hereditary Kernels of Isotropic Nonlinear Viscoelastic Materials in Combined Stress State*. Int Appl Mech 55, 601–619 (2019). https://doi.org/10.1007/s10778-019-00982-y
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DOI: https://doi.org/10.1007/s10778-019-00982-y