Journal Journal of Mechanical Engineering
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol 21, No 2, 2018 (June)
Pages 25–31



Sh. G. Hasanov, Azerbaijan Technical University, Baku, Azerbaijan, e-mail:



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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  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.
  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. Eng. Fracture Mech. Vol. 108. pp. 170–182.
  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.
  4. Hasanov F. F. (2014). Razrushenie kompozita, armirovannogo odnonapravlennymi voloknami. Mekhanika kompozit. materialov [Fracture of a Composite Reinforced by Unidirectional Fibers]. Mech. Composite Materials. Vol. 50. pp. 593–602 (in Russian).
  5. Mirsalimov V. M., Hasanov F. F. (2014). Vzaimodeystvie periodicheskoy sistemy inorodnykh uprugikh vklyucheniy, poverkhnost kotorykh ravnomerno pokryta odnorodnoy tsilindricheskoy plenkoy, i dvukh sistem pryamolineynykh treshchin s kontsevymi zonami. Problemy mashinostroeniya i nadezhnosti mashin [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]. J Machinery Manufacture and Reliability. Vol. 43. pp. 408–415 (in Russian).
  6. Hao W., Yao X., Ma Y., Yuan Y. (2015). Experimental Study on Interaction Between Matrix Crack and Fiber Bundles Using Optical Caustic Method. Eng. Fracture Mech. Vol. 134. pp. 354–367.
  7. Hasanov F. F. (2014). Modelirovanie zarozhdeniya treshchiny sdviga v volokne kompozita, armirovannogo odnonapravlennymi voloknami. Problemy. mashinostroeniya. [Modelling of Crack Nucleation in the Fibre of Composite Reinforced with Unidirectional Fibres Under Shear]. J. Mech.Eng. Vol. 17 (2). pp. 17–25 (in Russian).
  8. Hasanov F. F. (2014). Zarozhdenie treshchiny v kompozite, armirovannom odnonapravlennymi ortotropnymi voloknami pri prodolnom sdvige. Mekhanika mashin, mekhanizmov i materialov [Nucleation of the Crack in a Composite with Reinforced Unidirectional Orthotropous Fbers at Longitudinal Shear]. Mech. 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. Uch. zap. Kazan. un-ta. Ser. Fiz.-mat. nauki [Identification of Mechanical Properties of Fiber-Reinforced Composites]. 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. Stroit. mekhanika inzh. konstruktsiy i sooruzheniy [Interaction of Periodic System Heterogeneous Inclusions and Cohesive Cracks Under Longitudinal Shear]. Structural Mech. Eng. Constructions and Buildings. Vol. (2). pp. 18–28 (in Russian).
  11. Polilov A. N. (2014). Mekhanizmy umensheniya kontsentratsii napryazheniy v voloknistykh kompozitakh. Prikl. mekhanika i tekhn. fizika [Mechanisms of Stress Concentration Reduction in Fiber Composites]. J Appl. Mech. and Techn. Physics. Vol. 55. pp. 154–163 (in Russian).
  12. Mirsalimov V. M., Askarov V. A. (2016). Minimizatsiya parametrov razrusheniya v kompozite pri izgibe. Mekhanika kompozit. materialov [Minimization of Fracture Parameters of a Composite at Bending]. Mech. Composite Materials. Vol. 51. pp. 737–744 (in Russian).
  13. Mokhtari A., Ouali M. O., Tala-Ighil N. (2015). Damage Modelling in Thermoplastic Composites Reinforced with Natural Fibres Under Compressive Loading. Int J Damage Mech. Vol. 24. pp. 1239–1260.
  14. Mirsalimov V. M, Askarov V. A. (2016). Minimizatsiya koeffitsientov intensivnosti napryazheniy dlya kompozita, armirovannogo odnonapravlennymi voloknami pri izgibe. Vestn. Chuvash. ped. un-ta im. I. Ya. Yakovleva. Ser.: Mekhanika predelnogo sostoyaniya. [Minimization of Stress Intensity Factors for Composite Reinforced by Unidirectional Fibers at Bending]. Vestnik I. Yakovlev Chuvach State Pedagogical University. Series: Mechanics of a 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. pp. 385–395.
  16. Kruminsh Ya., Zesers A. (2015). Eksperimentalnoe issledovanie razrusheniya betona, armirovannogo gibridnymi voloknami. Mekhanika kompozit. materialov [Experimental Investigation of the Fracture of Hybrid-Fiber-Reinforced Concrete]. Mech. Composite Materials. Vol. 51(1). pp. 25–32 (in Russian).
  17. Tang C. (2015). A Study of Crack-Fiber Interaction in Fiber-Reinforced Composites Using Optical Caustic Method. Polymer Eng. and Sci. Vol. 55. pp. 852–857.
  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 Sci. and Technology. Vol. 146. pp. 26–33.
  19. Ju J. W., Wu Y. (2016). Stochastic Micromechanical Damage Modeling of Progressive Fiber Breakage for Longitudinal Fiber-Reinforced Composites. Int J. Damage Mech. Vol. 25. pp. 203–227.
  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 Eng. Materials & Structures. Vol. 40 (3). pp. 375–390.
  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.;
  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 Eng. Materials & Structures. Vol. 40. pp. 2183–2193.
  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]. Kiev: Naukova Dumka (in Russian).
  25. Rusinko A., Rusinko K. (2011). Plasticity and Creep of Metals. Berlin; Springer.
  26. Muskhelishvili N. I. (1977). Nekotorye osnovnye zadachi matematicheskoy teorii uprugosti [Some Basic Problem of Mathematical Theory of Elasticity]. Amsterdam: Kluwer Academic (in Russian).
  27. Panasyuk V. V., Savruk M. P. and Datsyshyn A. P. (1976). Raspredelenie napryazheniy okolo treshchin v plastinakh i obolochkakh [The Stress Distribution Around Cracks in Plates and Shells]. Kiev: 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]. Kiev: Naukova Dumka (in Russian).


Received: 11 March 2018