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.
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É. Z. Plume, “Comparative analysis of creep of unidirectional composites reinforced with fibers of various types,” Mekh. Kompoz. Mater., No. 4, 557–566 (1992).
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).
V. I. Zelin and Yu. O. Yanson, “Determination of creep kernels on the basis of shortterm tests,” Mekh. Polimer., No. 6, 972–975 (1977).
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.
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).
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).
B. E. Pobedrya, Mechanics of Composite Materials [in Russian], Izd. Mosk. Univ., Moscow (1984).
O. O. Gorbatko, “Effective characteristics of viscoelastic composite material with interphase crack,” Visn. Chernigiv Derzh. Tekhnol. Univ., No. 4, 144–150 (2012).
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).
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).
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.
A. R. Rzhanitsin, Theory of Creep [in Russian], Stroiizdat, Moscow (1967).
Translated from Problemy Prochnosti, No. 2, pp. 15 – 25, March – April, 2019.
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Bulat, A.F., Dyrda, V.I., Grebenyuk, S.N. et al. Determination of Effective Characteristics of the Fibrous Viscoelastic Composite with Transversal and Isotropic Components. Strength Mater 51, 183–192 (2019). https://doi.org/10.1007/s11223-019-00064-x
- composite material
- longitudinal tension
- effective characteristics
- instantaneous elastic modulus
- relaxation kernel