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Strength of Materials

, Volume 51, Issue 2, pp 183–192 | Cite as

Determination of Effective Characteristics of the Fibrous Viscoelastic Composite with Transversal and Isotropic Components

  • A. F. Bulat
  • V. I. DyrdaEmail author
  • S. N. Grebenyuk
  • M. I. Klimenko
Article
  • 12 Downloads

The method of determining the parameters of the integral operator of the effective longitudinal elastic modulus of the first-kind composite material is proposed. The viscoelastic transversal and isotropic composite with a periodic structure is used as an object of study. The elements of its cell are the transversal and isotropic viscoelastic matrix and the elastic fiber, which are approximated by hollow and solid cylinders, respectively. The rheological matrix characteristics are described according to the Boltzmann–Volterra hereditary theory. The axisymmetric longitudinal tension of the cell is considered. It is assumed that the radial displacements and stresses on the border between the matrix and the fiber are continuous, the lateral surface of the cell is free from stresses, and axial deformations of the matrix and the fiber coincide. The Laplace transform is applied to solve the obtained boundary value problem. The similar problem in image space is solved for the homogeneous transversely isotropic viscoelastic composite. The effective instantaneous longitudinal elastic modulus and the relaxation kernel are determined via the relation between deformation of the composite and its components, namely the equality of their axial deformations. The proposed method allows one to determine the viscoelastic composite characteristics via the corresponding characteristics of its elements and the volume fractions of the matrix and the fiber in the composite material.

Keywords

composite material matrix fiber longitudinal tension viscoelasticity effective characteristics instantaneous elastic modulus relaxation kernel 

References

  1. 1.
    É. Z. Plume, “Comparative analysis of creep of unidirectional composites reinforced with fibers of various types,” Mekh. Kompoz. Mater., No. 4, 557–566 (1992).Google Scholar
  2. 2.
    V. A. Kochetkov, “Prediction of thermal deformation of laminated hybrid composites with account for thermoviscoelastic properties of binder and fibers,” Mekh. Kompoz. Mater., No. 3, 317–323 (1993).Google Scholar
  3. 3.
    V. I. Zelin and Yu. O. Yanson, “Determination of creep kernels on the basis of shortterm tests,” Mekh. Polimer., No. 6, 972–975 (1977).Google Scholar
  4. 4.
    I. A. Trufanov and O. Yu Smetannikov, “Approximate definition of transversal viscoelastic properties of organofibre as a part of unidirectional organoplastic,”in: Numerical Modeling of Static and Dynamic Deformation of Structures [in Russian], Ural Branch of the Academy of Sciences of the USSR, Sverdlovsk (1990), pp. 114–118.Google Scholar
  5. 5.
    E. V. Kuimova and I. A. Trufanov, “Numerical prediction of effective thermoviscoelastic characteristics of unidirectional fiber composite with viscoelastic components,” Vestn. Samar. Gos. Univ., No. 4, 129–148 (2009).Google Scholar
  6. 6.
    A. A. Kaminskii and M. F. Selivanov, “On a method for determining the characteristics of viscoelastic deformation of composites,” Prikl. Mekh., 41, No. 5, 9–21 (2005).Google Scholar
  7. 7.
    B. E. Pobedrya, Mechanics of Composite Materials [in Russian], Izd. Mosk. Univ., Moscow (1984).Google Scholar
  8. 8.
    O. O. Gorbatko, “Effective characteristics of viscoelastic composite material with interphase crack,” Visn. Chernigiv Derzh. Tekhnol. Univ., No. 4, 144–150 (2012).Google Scholar
  9. 9.
    M. Gosz, B. Moran, and J. D. Achenbach, “Effect of a viscoelastic interface on the transverse behavior of fiber-reinforced composites,” Int. J. Solids Struct., 27, No. 14, 1757–1771 (1991).CrossRefGoogle Scholar
  10. 10.
    L. A. Fyl’shtyns’kyi and P. I. Zagryazhs’ka, “Modeling of composite material with viscoelastic components,” Visn. Zaporizh. Nats. Univ., No. 2, 141–144 (2010).Google Scholar
  11. 11.
    S. Grebenyuk, M. Klymenko, O. Titova, and A. Boguslavska, “Effective longitudinal elastic modulus of the composite with viscoelastic matrix and transtropic fiber,” in: Proc. of the 20th Int. Sci. Conf. Mechanika 2015 (University of Technology, Kaunas) (2015), pp. 96–100.Google Scholar
  12. 12.
    A. R. Rzhanitsin, Theory of Creep [in Russian], Stroiizdat, Moscow (1967).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • A. F. Bulat
    • 1
  • V. I. Dyrda
    • 1
    Email author
  • S. N. Grebenyuk
    • 2
  • M. I. Klimenko
    • 2
  1. 1.Institute of Geotechnical MechanicsNational Academy of Sciences of UkraineDneprUkraine
  2. 2.Zaporozhye National UniversityZaporozhyeUkraine

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