Determining the effective characteristics of a composite with hollow fiber at longitudinal elongation

Authors

DOI:

https://doi.org/10.15587/1729-4061.2018.143406

Keywords:

unidirectional fibrous composite, longitudinal elongation, hollow fiber, effective elastic constants

Abstract

When solving problems on the mechanics of composites, it is convenient to use a composite model in the form of a continuous homogeneous medium with effective constants, which adequately reflect its most essential characteristics. Modern engineering and construction commonly use the composites, reinforced with hollow fibers. Unknown for today are the analytical dependences for the effective elastic constants of such composite materials with transtropic components. The task on constructing such dependences is resolved in this paper.

We have derived analytical dependences for the effective longitudinal modulus of elasticity and the Poisson’s coefficient in the unidirectional fiber composite, consisting of a transtropic matrix and hollow fiber. The composite is simulated by a solid uniform transtropic material. The conditions for a perfect connection are satisfied at the interphase surfaces. In order to obtain the analytical dependences, we have solved two boundary problems: on the longitudinal elongation of a composite cylinder, whose components are the transtropic matrix and hollow fiber, and a solid homogeneous cylinder that models the transtropic composite. The application of conditions for displacements alignment and stresses, found by solving these problems, provided an opportunity to derive formulae for the effective longitudinal modulus of elasticity and Poisson’s coefficient. These formulae reflect the dependences of effective characteristics of a composite on elastic characteristics of the matrix, fibers, and volumetric shares of the fiber and the cavity inside it.

We have compared results of calculations using the formulae derived with the calculation results based on previously known ratios for the isotropic ratios. This comparison has shown that their relative deviation does not exceed one percent. Application of the obtained dependences makes it possible to design structures with elements made from the composite materials

Author Biographies

Serhii Homeniuk, Zaporizhzhia National University Zhukovskoho str., 66, Zaporizhzhia, Ukraine, 69600

Doctor of Technical Sciences, Professor

Department of Software Engineering

Sergii Grebenyuk, Zaporizhzhia National University Zhukovskoho str., 66, Zaporizhzhia, Ukraine, 69600

Doctor of Technical Sciences, Associate Professor, Head of Department

Department of Fundamental Mathematics

Mykhailo Klimenko, Zaporizhzhia National University Zhukovskoho str., 66, Zaporizhzhia, Ukraine, 69600

PhD, Associate Professor

Department of Fundamental Mathematics

Anastasia Stoliarova, Zaporizhzhia National University Zhukovskoho str., 66, Zaporizhzhia, Ukraine, 69600

Postgraduate student

Department of Fundamental Mathematics

References

  1. Klastorny, M., Konderla, P., Piekarskiy, R. (2009). An exact stiffness theory of unidirectional xFRP composites. Mekhanika kompozitnyh materialov, 45 (1), 109–144.
  2. Grebenyuk, S. N. (2011). Elastic characteristics of composite material with transversaly isotropic matrix and fiber. Methods of solving applied problems of mechanics of a deformable solid, 12, 62–68.
  3. Tang, T., Yu, W. (2007). A variational asymptotic micromechanics model for predicting conductivities of composite materials. Journal of Mechanics of Materials and Structures, 2 (9), 1813–1830. doi: https://doi.org/10.2140/jomms.2007.2.1813
  4. Tang, T. (2008). Variational Asymptotic Micromechanics Modeling of Composite Materials. Logan: Utah State University, 280.
  5. Bol'shakov, V. I., Andrianov, I. V., Danishevskiy, V. V. (2008). Asimptoticheskie metody rascheta kompozitnyh materialov s uchetom vnutrenney struktury. Dnepropetrovsk: «Porogi», 196.
  6. Dimitrienko, Yu. I., Gubareva, E. A., Sborshchikov, S. V. (2014). Finite element modulation of effective viscoelastic properties of unilateral composite materials. Matematicheskoe modelirovanie i chislennye metody, 2, 28–48. Available at: http://www.mathnet.ru/links/4986a9de2f7714798765784534f1cd23/mmcm12.pdf
  7. Kuimova, E. V., Trufanov, N. A. (2009). The numerical prediction of effective thermoviscoelastic properties of unidirectional fiber composite with the viscoelastic components. Vestnik Samarskogo gosudarstvennogo universiteta, 4 (70), 129–148. Available at: https://cyberleninka.ru/article/v/chislennoe-prognozirovanie-effektivnyh-termovyazkouprugih-harakteristik-odnonapravlennogo-voloknistogo-kompozita-s-vyazkouprugimi
  8. Kaminskii, A. A., Selivanov, M. F. (2005). A Method for Determining the Viscoelastic Characteristics of Composites. International Applied Mechanics, 41 (5), 469–480. doi: https://doi.org/10.1007/s10778-005-0112-6
  9. Srivastava, V., Gabbert, U., Berger, H., Singh, S. (2011). Analysis of particles loaded fiber composites for the evaluation of effective material properties with the variation of shape and size. International Journal of Engineering, Science and Technology, 3 (1), 52–68. doi: https://doi.org/10.4314/ijest.v3i1.67638
  10. Klusemann, B., Svendsen, В. (2010). Homogenization methods for multi-phase elastic composites: Comparisons and benchmarks. Technische mechanic, 30 (4), 374–386. Available at: http://www.ovgu.de/ifme/zeitschrift_tm/2010_Heft4/07_Klusemann.pdf
  11. Yao, Y., Chen, S., Chen, P. (2013). The effect of a graded interphase on the mechanism of stress transfer in a fiber-reinforced composite. Mechanics of Materials, 58, 35–54. doi: https://doi.org/10.1016/j.mechmat.2012.11.008
  12. Yao, Y., Chen, S. (2012). The effects of fiber’s surface roughness on the mechanical properties of fiber-reinforced polymer composites. Journal of Composite Materials, 47 (23), 2909–2923. doi: https://doi.org/10.1177/0021998312459871
  13. Kling, S., Czigany, T. (2013). A comparative analysis of hollow and solid glass fibers. Textile Research Journal, 83 (16), 1764–1772. doi: https://doi.org/10.1177/0040517513478455
  14. Francevich, I. N., Karpinos, D. M. (Eds.) (1970). Kompozicionnye materialy voloknistogo stroeniya. Kyiv, 403.
  15. Van Fo Fy, G. A., Klyavlin, V. V. (1972). Ob effektivnosti ispol'zovaniya kompozicionnyh materialov, orientirovanno armirovannyh polymi voloknami. Problemy prochnosti, 4, 10–13.
  16. Vanin, G. A. (1985). Mikromekhanika kompozicionnyh materialov. Kyiv: Naukova dumka, 304.
  17. Zaitsev, A. V., Sokolkin, Yu. V., Fukalov, A. A. (2011). Effective bulk moduli under plain strain to two-phase unidirectional composites reinforced by anisotropic hollow and solid fibers. Vestnik Permskogo nacional'nogo issledovatel'skogo politekhnicheskogo universiteta, 37–48. Available at: https://cyberleninka.ru/article/n/effektivnye-moduli-obemnogo-szhatiya-pri-ploskoy-deformatsii-dvuhfaznyh-odnonapravlenno-armirovannyh-kompozitov-s-anizotropnymi
  18. Nasr-Isfahani, M., Tehran, M. A., Latifi, M., Halvaei, M., Warnet, L. (2017). Experimental and theoretical investigation of hollow polyester fibers effect on impact behavior of composites. Journal of Industrial Textiles, 47 (7), 1528–1542. doi: https://doi.org/10.1177/1528083717699367
  19. Nasr-Isfahani, M., Latifi, M., Amani-Tehran, M. (2013). Improvement of impact damage resistance of epoxy-matrix composites using ductile hollow fibers. Journal of engineered fibers and fabrics, 8 (1), 69–74. Available at: https://www.jeffjournal.org/papers/Volume8/JEFF8-01-08.M.Latifi.pdf
  20. Balaji, R., Sasikumar, M., Jeyanthi, S. (2016). Characterisation of Hollow Glass Fibre Reinforced Vinyl-Ester Composites. Indian Journal of Science and Technology, 9 (48). Available at: http://www.indjst.org/index.php/indjst/article/viewFile/107921/76821
  21. Grebenyuk, S. M. (2012). Determination of the elastic constants of composite with transtropic matrix and fiber based on the kinematic consistency condition. Visnyk Zaporizkoho natsionalnoho universytetu, 1, 62–76.
  22. Vasil'ev, V. V., Tarnopol'skiy, Yu. M. (Eds.) (1990). Kompozicionnye materialy. Moscow: Mashinostroenie, 512.

Downloads

Published

2018-10-03

How to Cite

Homeniuk, S., Grebenyuk, S., Klimenko, M., & Stoliarova, A. (2018). Determining the effective characteristics of a composite with hollow fiber at longitudinal elongation. Eastern-European Journal of Enterprise Technologies, 6(7 (96), 6–12. https://doi.org/10.15587/1729-4061.2018.143406

Issue

Vol. 6 No. 7 (96) (2018): Applied mechanics

Section

Applied mechanics

License

Copyright (c) 2018 Serhii Homeniuk, Sergii Grebenyuk, Mykhailo Klimenko, Anastasia Stoliarova

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.