MODELING CRACK INITIATION IN A COMPOSITE UNDER BENDING

Author

Sh. G. Hasanov, Azerbaijan Technical University (25, H. Cavid ave., Baku, AZ 1073, Azerbaijan), e-mail: hssh3883@gmail.com

Abstract

It is known that multi-component structures are more reliable and durable than homogeneous ones. At the design stage of new structures from composite materials, it is necessary to take into account the cases when cracks may appear in the material. The purpose of this paper is to construct a computational model for a binder-inclusion composite body, which makes it possible to calculate the limiting external bending loads at which cracking occurs in a composite. A thin plate of elastic isotropic medium (matrix) and inclusions (fibers) from other elastic material, distributed in the plate under bending, is considered. A mathematical description of a crack initiation model in a binder composite under bending is carried out. The theory of analytic functions and the method of power series are used. The determination of the unknown parameters characterizing an initial crack reduces to solving a singular integral equation. A closed system of nonlinear algebraic equations is constructed, whose solution helps to predict cracks in a composite under bending, depending on the geometric and mechanical characteristics of both the binder and the inclusions. The criterion of crack initiation in a composite under the influence of bending loads is formulated. The size of the limiting minimum pre-fraction zone, at which crack initiation occurs is recommended to be considered as a design characteristic of a binder material.

Keywords: binder, inclusion, composite plate, bending, pre-fracture zone, crack formation

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References

1. Greco, F., Leonetti, L., & Lonetti, P. A. (2013). Two-Scale Failure Analysis of Composite Materials in Presence of Fiber/Matrix Crack Initiation and Propagation. Composite Structures, vol. 95, pp. 582–597. https://doi.org/10.1016/j.compstruct.2012.08.035
2. Brighenti, R., Carpinteri, A., Spagnoli, A., & Scorza, D. (2013). Continuous and Lattice Models to Describe Crack Paths in Brittle-Matrix Composites with Random and Unidirectional Fibres. Engineering Fracture Mechanics, vol. 108, pp. 170–182. https://doi.org/10.1016/j.engfracmech.2013.05.006
3. Mirsalimov, V. M. & Hasanov, F. F. (2014). Interaction between Periodic System of Rigid Inclusions and Rectilinear Cohesive Cracks in an Isotropic Medium under Transverse Shear. Acta Polytechnica Hungarica, vol. 11 (5), pp. 161–176. https://doi.org/10.12700/APH.11.05.2014.05.10
4. Hasanov, F. F. (2014). Fracture of a Composite Reinforced by Unidirectional Fibers. Mechanics of Composite Materials, vol. 50, iss. 5, pp. 593–602. https://doi.org/10.1007/s11029-014-9447-6
5. Mirsalimov, V. M. & Hasanov, F. F. (2014). Interaction of a Periodic System of Foreign Elastic Inclusions Whose Surface is Uniformly Covered with a Homogeneous Cylindrical Film and Two Systems of Straight Line Cracks with End Zones. Journal of Machinery Manufacture and Reliability, vol. 43, iss. 5, pp. 408–415. https://doi.org/10.3103/S1052618814050124
6. Hao, W., Yao, X., Ma, Y., & Yuan, Y. (2015). Experimental Study on Interaction between Matrix Crack and Fiber Bundles Using Optical Caustic Method. Engineering Fracture Mechanics, vol. 134, pp. 354–367. https://doi.org/10.1016/j.engfracmech.2014.12.004
7. Hasanov, F. F. (2014). Modelirovanie zarozhdeniya treshchiny sdviga v volokne kompozita, armirovannogo odnonapravlennymi voloknami [Modelling of Crack Nucleation in the Fibre of Composite Reinforced with Unidirectional Fibres under Shear]. Problemy mashinostroeniya – Journal of Mechanical Engineering, vol. 17 (2), pp. 17–25 (in Russian).
8. Hasanov, F. F. (2014). Zarozhdenie treshchiny v kompozite, armirovannom odnonapravlennymi ortotropnymi voloknami pri prodolnom sdvige [Nucleation of the Crack in a Composite, Reinforced Unidirectional Orthotropous Fibres at Longitudial Shear]. Mekhanika mashin, mekhanizmov i materialov – Mechanics of Machines, Mechanisms and Materials, vol. 2, pp. 45–50 (in Russian).
9. Kayumov, R. A., Lukankin, S. A., Paymushin, V. N., & Kholmogorov, S. A. (2015). Identifikatsiya mekhanicheskikh kharakteristik armirovannykh voloknami kompozitov [Identification of Mechanical Properties of Fiber-Reinforced Composites]. Uch. zap. Kazan. un-ta. Ser. fiz.-mat. nauki – Proc. Kazan University. Physics and Mathematics Series, vol. 157 (4), pp. 112–132 (in Russian).
10. Mirsalimov, V. M. & Hasanov, F. F. (2015). Vzaimodeystvie periodicheskoy sistemy inorodnykh vklyucheniy i kogezionnykh treshchin pri prodolnom sdvige [Interaction of Periodic System Heterogeneous Inclusions and Cohesive Cracks under Longitudinal Shear]. Stroit. mekhanika inzh. konstruktsiy i sooruzheniy – Structural Mech. Eng. Constructions and Buildings, vol. (2), pp. 18–28 (in Russian).
11. Polilov, A. N. (2014). Mechanisms of Stress Concentration Reduction in Fiber Composites. Journal of Applied Mechanics and Technical Physics, vol. 55, iss. 1, pp. 154–163. https://doi.org/10.1134/S0021894414010180
12. Mirsalimov, V. M. & Askarov, V. A. (2016). Minimization of Fracture Parameters of a Composite at Bending. Mechanics of Composite Materials, vol. 51, iss.6, pp. 737–744. https://doi.org/10.1007/s11029-016-9544-9
13. Mokhtari, A., Ouali, M. O., & Tala-Ighil, N. (2015). Damage Modelling in Thermoplastic Composites Reinforced with Natural Fibres Under Compressive Loading. International Journal of Damage Mechanics, vol. 24, iss. 8, pp. 1239–1260. https://doi.org/10.1177/1056789515573900
14. Mirsalimov, V. M. & Askarov, V. A. (2016). Minimizatsiya koeffitsientov intensivnosti napryazheniy dlya kompozita, armirovannogo odnonapravlennymi voloknami pri izgibe [Minimization of Stress Intensity Factors for Composite Reinforced by Unidirectional Fibers at Bending]. Vestn. Chuvash. ped. un-ta im. I. Ya. Yakovleva. Ser.: Mekhanika predelnogo sostoyaniya – Bulletin of the Yakovlev Chuvash State Pedagogical University. Series: Mechanics of Limit State, vol. 3, pp. 105–116 (in Russian).
15. Mirsalimov, V. M. & Hasanov, F. F. (2015). Nucleation of Cracks in an Isotropic Medium with Periodic System of Rigid Inclusions under Transverse Shear. Acta Mechanica, vol. 226, iss. 2, pp. 385–395. https://doi.org/10.1007/s00707-014-1187-0
16. Kruminsh, Ya. & Zesers, A. (2015). Experimental Investigation of the Fracture of Hybrid-Fiber-Reinforced Concrete. Mechanics of Composite Materials, vol. 51, iss. 1, pp. 25–32. https://doi.org/10.1007/s11029-015-9473-z
17. Tang, C. (2015). A Study of Crack-Fiber Interaction in Fiber-Reinforced Composites Using Optical Caustic Method. Polymer Engineering and Science, vol. 55, pp. 852–857. https://doi.org/10.1002/pen.23951
18. Takeda, T. & Narita, F. (2017). Fracture Behavior and Crack Sensing Capability of Bonded Carbon Fiber Composite Joints with Carbon Nanotube-Based Polymer Adhesive Layer Under Mode I Loading. Composites Science and Technology, vol. 146, pp. 26–33. https://doi.org/10.1016/j.compscitech.2017.04.014
19. Ju, J. W. & Wu, Y. (2016). Stochastic Micromechanical Damage Modeling of Progressive Fiber Breakage for Longitudinal Fiber-Reinforced Composites. International Journal of Damage Mechanics, vol. 25, iss. 2, pp. 203–227. https://doi.org/10.1177/1056789515576863
20. Babaei, R. & Farrokhabadi, A. A. (2017). Computational Continuum Damage Mechanics Model for Predicting Transverse Cracking and Splitting Evolution in Open Hole Cross-Ply Composite Laminates. Fatigue & Fracture Engineering Materials & Structures, vol. 40, iss. 3, pp. 375–390. https://doi.org/10.1111/ffe.12502
21. Bakhshan, H., Afrouzian, A., Ahmadi, H., & Taghavimehr, M. (2017). Progressive Failure Analysis of Fiber-Reinforced Laminated Composites Containing a Hole. Int. J. Damage Mech., vol. 27, iss. 7, pp. 963-978. https://doi.org/10.1177/1056789517715088
22. Cameselle-Molares, A., Sarfaraz, R., Shahverdi M., Keller T., Vassilopoulos A. P. (2017). Fracture Mechanics-Based Progressive Damage Modelling of Adhesively Bonded Fibre-Reinforced Polymer Joints. Fatigue & Fracture Engineering Materials & Structures, vol. 40, iss. 12, pp. 2183–2193. https://doi.org/10.1111/ffe.12647
23. Mirsalimov, V. M. (1987). Neodnomernye uprugoplasticheskie zadachi [Non-One-Dimensional Elastoplastic Problems]. Moscow: Nauka (in Russian).
24. Panasyuk, V. V. (1991). Mekhanika kvazikhrupkogo razrusheniya materialov [Mechanics of Quasibrittle Fracture of Materials]. Kiyev: Naukova Dumka (in Russian).
25. Rusinko, A. & Rusinko, K. (2011). Plasticity and Creep of Metals. Berlin: Springer. https://doi.org/10.1007/978-3-642-21213-0
26. Muskhelishvili, N. I. (1977). Some Basic Problem of Mathematical Theory of Elasticity. Amsterdam: Kluwer Academic. https://doi.org/10.1007/978-94-017-3034-1
27. Panasyuk, V. V., Savruk, M. P., & Datsyshyn, A. P. (1976). Raspredelenie napryazheniy okolo treshchin v plastinakh i obolochkakh [The Stress Distribution around Cracks in Plates and Shells]. Kiyev: Naukova Dumka (in Russian).
28. Savruk, M. P. (1981). Dvumernye zadachi uprugosti dlya tel s treshchinami [Two-Dimensional Problem of Elasticity for Bodies with Cracks]. Kiyev: Naukova Dumka (in Russian). 

Received 11 March 2018

Published 30 June 2018