Stresses in Composite Building Reinforcement due to Differences in Poisson's Ratios

The aim of the work is the calculation assessment of stresses in the elements of composite building reinforcement caused by differences in the Poisson’s ratios of reinforcing fibers and polymer binders. The research methodology is based on the development of a micromechanical model of the interphase interaction of the reinforcing fiber and a polymer matrix in an elementary cell, which is a hollow polymer micro-cylinder in which a fibrous reinforcing filler is located in the form of a connection with a deformation tension changing under load. The transformation of the Lame problem to the calculation assessment of the effect of differences in the values of the Poisson’s ratios of the reinforcing fibers and the polymer matrix, as well as nominal tensile stresses and the volumetric content of fibers in the composite reinforcement on changes  in local stresses in the reinforcing fibers and polymer matrix is made. Analytical dependencies are obtained linking the parameters of the local stress-strain state of the walls of an elementary cylinder in the vicinity of a fibrous filler with a set of indices of the physical and mechanical properties of  polymer matrix materials and fibrous filler (moduli of elasticity and Poisson's ratios), as well as the volume content of the filler. As an example, these parameters are calculated for a wide range of degrees of filling with glass and basalt fiber for a number of polymer matrices (epoxy and polyester). It is shown that in the range of the volumetric filler content of 0.5–0.7, contact pressures at the interface of the reinforcing fibers with the polymer matrix are from 2 to 6 % of the nominal tensile stresses in the polymer matrix, depending on the combination of  Poisson ratios of the fibers and the matrix. In this case, the circumferential tensile stresses in the polymer matrix at the interface with the fiber are from 11.6 to 19.2 % of the nominal axial tensile stresses in the polymer matrix for fiberglass and from 10.6 to 17.1 % for basalt-plastic reinforcement. The research results can be used in scientific research and educational activities.

1. ACI 440.1R–06. Guide for the Design and Construction of Structural Concrete Reinforced with FRP Bars. Detroit: American Concrete Institute (ACI), 2006. 44.

2. CAN/CSA-S806–02 (R2007). Design and Construction of Building Components with Fibre-Reinforced Polymers. Canadian Standards Association, 2012. 206.

3. Japan Society of Civil Engineers (JSCE) (1997). Recommendation for Design and Construction of Concrete Structures Using Continuous Fiber Reinforcing Materials. Concrete Engineering, Series 23. Tokyo, JSCE. 199.

4. Jarek B., Kubik A. (2015) Zastosowanie Prętόw Zbrojeniowych z Włόkna Szklanego (GFRP) w Budownictwie. Przegląd Budowlany, (012), 21–26.

5. Cui Y., Cheung M. M. S., Noruziaan B., Lee S., Tao J. (2008) Development of Ductile Composite Reinforcement Bars for Concrete Structures. Materials and Structures, 41 (9), 1509–1518. https://doi.org/10.1617/s11527-007-9344-8.

6. CNR-DT 203/2006. Guide for the Design and Construction of Concrete Structures Reinforced with Fiber-Reinforced Polymer Bars. Rome, Italian National Research Council (CNR), 2006. 35.

7. Koryagin S. I. (1996) Load-Bearing Capacity of Composite Materials. Kaliningrad, Kaliningrad University. 301 (in Russian).

8. Ashchepkau M. Yu., Shil’ko S. V., Drobysh T. V., Choe H. (2020) Tensile Fracture Specificity of Unidirectional Metal-Polymer Glass-Fiber Composites With Cord Wire. Mechanics of Machines, Mechanisms and Materials, 3 (52), 55–62. https://doi.org/10.46864/1995-0470-2020-3-52-55-62.

9. Barsukov V. G., Volik A. R., Sazon S. A. (2020) Structural and Mechanical Aspect of Composite Reinforcement Strength. E3S Web Conf., 212, 02002. https://doi.org/10. 1051/e3sconf/202021202002.

10. Sadin E. Ya. (2016) Anchoring of Fiberglass Reinforcement in Concrete Produced in the Republic of Belarus. Arkhitektura i Stroitelstvo [Architecture and Construction], (3), 68–71 (in Russian).

11. Gizdatullin G. A., Khozin V. G., Kuklin A. N., Khusnutdinov A. M. (2014) Specifics of Testing and Fracture Behavior of Fibre-Reinforced Polymer Bars. Magazine of Civil Engineering, 47 (3), 40–47. https://doi.org/10.5862/ mce.47.4(in Russian).

12. Castro P. F., Carino N. J. (1998) Tensile and Nondestructive Testing of FRP Bars. Journal of Composites for Construction, 2 (1), 17–27. https://doi.org/10.1061/(asce)1090-0268(1998)2:1(17).

13. Vasilevich Yu. V. (2016) The Influence of Chemical Shrinkage of the Binder during Curing Process on the Formation of Residual Stresses in Cylindrical Composite Shells. Teoreticheskaya i prikladnaya mekhanika: mezhdunar. nauch.-tekhn. sb. [Theoretical and Applied Mechanics: International Scientific and Technical Collection]. Minsk, BNTU, Iss. 31, 67–72 (in Russian).

14. Skudra A. M., Bulavs F. Ya. (1982) Strength of Reinforced Plastics. Moscow, Khimiya Publ. 213 (in Russian).

15. Barsukov V. G. Shishkin A. E., Krupich B., Barsukov V. V. (2013) Model Concepts of the Mechanics of Interphase Microcontact Interaction in Cast Irons with Vermicular Graphite. Aktual'nye voprosy mashinovedeniya: sb. nauch. tr. [Actual Issues of Mechanical Engineering: Collection of Scientific Papers]. Minsk, Prompechat Publ., Iss. 2, 382–387 (in Russian).

16. Dems K., Radaszewska E., Turant J. (2012) Modeling of Fiber-Reinforced Composite Material Subjected to Thermal Load. Journal of Thermal Stresses, 35 (7), 579–595. https://doi.org/10.1080/01495739.2012.674786.

17. Barsukov V. G., Grakholskaya E. V. (2020) Parameters of Elementary Cells for Analytical Determination of Thermoelastic Shrinkage Stresses in Filled Thermoplastics. Vesnik Hrodzenskaha Dziarzhaunaha Universiteta Imia Ianki Kupaly. Seryia 6. Tekhnika = Vesnik of Yanka Kupala State University of Grodno. Series 6. Engineering Science, 10 (2), 32–40 (in Russian).

18. Pisarenko G. S., Yakovlev A. P., Matveev V. V. (1988) Handbook of Strength of Materials. 2nd ed. Kiev, Naukova Dumka Publ. 736 (in Russian).

19. Skoibeda A. T., Miklashevich A. A., Levkovskii E. N. [et al.] (1997) Applied Mechanics. Minsk, Vysshaya Shkola Publ. 522 (in Russian).

20. Matthews F., Rawlings R. (1999) Composite Materials: Engineering and Science. Woodhead Publishing. https:// doi.org/10.1016/C2013-0-17714-8.

21. Vasil'ev V. V., Protasov V. D., Bolotin V. V. [et al.] (1990) Composite Materials: Handbook. Moscow, Mashinostroenie Publ. 512 (in Russian).

22. Minenkov B. V., Stasenko I. V. (1977) Strength of Plastic Parts. Moscow, Mashinostroenie Publ. 264 (in Russian).

23. International Federation for Structural Concrete (fib) (2007) FRP Reinforcement in RC Structures: Technical Report. Bulletin 40. 147. Available at: https://www.alientechnologies.ru/docs/40%20-%20FRP%20reinforcement%20in%20RC%20structures.pdf.