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

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

Serhii Homeniuk, Sergii Grebenyuk, Mykhailo Klimenko, Anastasia Stoliarova

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.


Keywords


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

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References


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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.

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

Tang, T. (2008). Variational Asymptotic Micromechanics Modeling of Composite Materials. Logan: Utah State University, 280.

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Van Fo Fy, G. A., Klyavlin, V. V. (1972). Ob effektivnosti ispol'zovaniya kompozicionnyh materialov, orientirovanno armirovannyh polymi voloknami. Problemy prochnosti, 4, 10–13.

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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

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

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

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.

Vasil'ev, V. V., Tarnopol'skiy, Yu. M. (Eds.) (1990). Kompozicionnye materialy. Moscow: Mashinostroenie, 512.


GOST Style Citations


Klastorny M., Konderla P., Piekarskiy R. An exact stiffness theory of unidirectional xFRP composites // Mekhanika kompozitnyh materialov. 2009. Vol. 45, Issue 1. P. 109–144.

Grebenyuk S. N. Elastic characteristics of composite material with transversaly isotropic matrix and fiber // Methods of solving applied problems of mechanics of a deformable solid. 2011. Issue 12. P. 62–68.

Tang T., Yu W. A variational asymptotic micromechanics model for predicting conductivities of composite materials // Journal of mechanics of materials and structures. 2007. Vol. 2, Issue 9. P. 1813–1830. doi: https://doi.org/10.2140/jomms.2007.2.1813 

Tang T. Variational Asymptotic Micromechanics Modeling of Composite Materials. Logan: Utah State University, 2008. 280 p.

Bol'shakov V. I., Andrianov I. V., Danishevskiy V. V. Asimptoticheskie metody rascheta kompozitnyh materialov s uchetom vnutrenney struktury: monografiya. Dnepropetrovsk: «Porogi», 2008. 196 p.

Dimitrienko Yu. I., Gubareva E. A., Sborshchikov S. V. Finite element modulation of effective viscoelastic properties of unilateral composite materials // Matematicheskoe modelirovanie i chislennye metody. 2014. Issue 2. P. 28–48. URL: http://www.mathnet.ru/links/4986a9de2f7714798765784534f1cd23/mmcm12.pdf

Kuimova E. V., Trufanov N. A. The numerical prediction of effective thermoviscoelastic properties of unidirectional fiber composite with the viscoelastic components // Vestnik Samarskogo gosudarstvennogo universiteta. 2009. Issue 4 (70). P. 129–148. URL: https://cyberleninka.ru/article/v/chislennoe-prognozirovanie-effektivnyh-termovyazkouprugih-harakteristik-odnonapravlennogo-voloknistogo-kompozita-s-vyazkouprugimi

Kaminskii A. A., Selivanov M. F. A Method for Determining the Viscoelastic Characteristics of Composites // International Applied Mechanics. 2005. Vol. 41, Issue 5. P. 469–480. doi: https://doi.org/10.1007/s10778-005-0112-6 

Analysis of particles loaded fiber composites for the evaluation of effective material properties with the variation of shape and size / Srivastava V. K., Gabbert U., Berger H., Singh S. // International Journal of Engineering, Science and Technology. 2011. Vol. 3, Issue 1. P. 52–68. doi: https://doi.org/10.4314/ijest.v3i1.67638 

Klusemann B., Svendsen В. Homogenization methods for multi-phase elastic composites: Comparisons and benchmarks // Technische mechanic. 2010. Vol. 30, Issue 4. P. 374–386. URL: http://www.ovgu.de/ifme/zeitschrift_tm/2010_Heft4/07_Klusemann.pdf

Yao Y., Chen S., Chen P. The effect of a graded interphase on the mechanism of stress transfer in a fiber-reinforced composite // Mechanics of Materials. 2013. Vol. 58. P. 35–54. doi: https://doi.org/10.1016/j.mechmat.2012.11.008 

Yao Y., Chen S. The effects of fiber’s surface roughness on the mechanical properties of fiber-reinforced polymer composites // Journal of Composite Materials. 2012. Vol. 47 (23). P. 2909–2923. doi: https://doi.org/10.1177/0021998312459871 

Kling S., Czigany T. A comparative analysis of hollow and solid glass fibers // Textile Research Journal. 2013. Vol. 83, Issue 16. P. 1764–1772. doi: https://doi.org/10.1177/0040517513478455 

Kompozicionnye materialy voloknistogo stroeniya / I. N. Francevich, D. M. Karpinos (Eds.). Kyiv, 1970. 403 p.

Van Fo Fy G. A., Klyavlin V. V. Ob effektivnosti ispol'zovaniya kompozicionnyh materialov, orientirovanno armirovannyh polymi voloknami // Problemy prochnosti. 1972. Issue 4. P. 10–13.

Vanin G. A. Mikromekhanika kompozicionnyh materialov: monografiya. Kyiv: Naukova dumka, 1985. 304 p.

Zaitsev A. V., Sokolkin Yu. V., Fukalov A. A. 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. 2011. P. 37–48. URL: https://cyberleninka.ru/article/n/effektivnye-moduli-obemnogo-szhatiya-pri-ploskoy-deformatsii-dvuhfaznyh-odnonapravlenno-armirovannyh-kompozitov-s-anizotropnymi

Experimental and theoretical investigation of hollow polyester fibers effect on impact behavior of composites / Nasr-Isfahani M., Tehran M. A., Latifi M., Halvaei M., Warnet L. // Journal of Industrial Textiles. 2017. Vol. 47, Issue 7. P. 1528–1542. doi: https://doi.org/10.1177/1528083717699367 

Nasr-Isfahani M., Latifi M., Amani-Tehran M. Improvement of impact damage resistance of epoxy-matrix composites using ductile hollow fibers // Journal of engineered fibers and fabrics. 2013. Vol. 8, Issue 1. P. 69–74. URL: https://www.jeffjournal.org/papers/Volume8/JEFF8-01-08.M.Latifi.pdf

Balaji R., Sasikumar M., Jeyanthi S. Characterisation of Hollow Glass Fibre Reinforced Vinyl-Ester Composites // Indian Journal of Science and Technology. 2016. Vol. 9, Issue 48. URL: http://www.indjst.org/index.php/indjst/article/viewFile/107921/76821

Grebenyuk S. M. Determination of the elastic constants of composite with transtropic matrix and fiber based on the kinematic consistency condition // Visnyk Zaporizkoho natsionalnoho universytetu. 2012. Issue 1. P. 62–76.

Kompozicionnye materialy: spravochnik / V. V. Vasil'ev, Yu. M. Tarnopol'skiy (Eds.). Moscow: Mashinostroenie, 1990. 512 p.







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ISSN (print) 1729-3774, ISSN (on-line) 1729-4061