On the Problem of Composite Beam Degradation under Longitudinal Bending and the Solution Method for Large Displacements
https://doi.org/10.26907/2541-7746.2024.3.364-376
Abstract
Constitutive relations and a method for analyzing the behavior of fiberglass during longitudinal bending under the combined influence of force factors and an alkaline medium were proposed. Both natural and numerical experimental designs were outlined. A new approach to solving the problem of longitudinal bending of a fiberglass beam with initial failure was introduced, without involving geometrically nonlinear relations. This approach proved to be applicable when the resulting beam configuration is a flat curve. The results of numerical calculations were presented. In the first case, the beam with initial failure was studied using the new approach along with the finite element method (FEM). In the second case, for verification, the problem was solved in a geometrically nonlinear formulation. The results obtained showed a strong agreement.
Keywords
About the Authors
R. A. KayumovRussian Federation
Kazan, 420043
I. Z. Mukhamedova
Russian Federation
Kazan, 420043, 420008
L. I. Khaidarov
Russian Federation
Kazan, 420043
B. F. Tazyukov
Russian Federation
Kazan, 420008
References
1. Vasil’ev V.V., Dudchenko A.A., Elpat’evskii A.N. Analysis of the tensile deformation of glass-reinforced plastics. Polym. Mech., 1970, vol. 6, no. 1, pp. 127–130. https://doi.org/10.1007/BF00860460.
2. Alfutov N.A., Zinov’ev P.A., Popov B.G. Raschet mnogosloinykh plastin i obolochek iz kompozitsionnykh materialov [Design of Multilayered Plates and Shells Made of Composite Materials]. Moscow, Mashinostroenie, 1984. 263 p. (In Russian)
3. Astaf ’ev V.I., Radaev Yu.N., Stepanova L.V. Nelineinaya mekhanika razrusheniya [Nonlinear Fracture Mechanics]. Samara, Samar. Univ., 2001. 631 p. (In Russian)
4. Rabotnov Yu.N. Polzuchest’ elementov konstruktsii [Creep of Structural Elements]. Moscow, Nauka, 1966. 752 p. (In Russian)
5. Cocks A.C.F., Ashby M.F. The growth of dominant crack in a creeping material. Scr. Metall., 1982, vol. 16, no. 1, pp. 109–114. https://doi.org/10.1016/0036-9748(82)90413-6.
6. Akhundov M.B. Damage and deformation of nonlinear hereditary media in a complex stress state. Mech. Compos. Mater., 1991, vol. 27, no. 2, pp. 155–158. https://doi.org/10.1007/BF00614731.
7. Suvorova Yu.V. Strength criterion based on defectiveness buildup and its application to composite materials. Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, 1979, no. 4, pp. 107–111. (In Russian)
8. Dumanskii A.M., Finogenov G.N. Methodology for assessing the damage in polymer fiber composites during prolonged static loading. Zavod. Lab., 1993, no. 4, pp. 60–62. (In Russian)
9. Moskvitin V.V. Some problems of the long-term strength of viscoelastic media. Probl. Prochn., 1972, no. 2, pp. 55–58. (In Russian)
10. Luat D. C., Lurie S. A., Dudchenko A. A. Modeling the degradation of composite properties due to cracking and delamination under static and cyclic loadings. Mekh. Kompoz. Mater. Konstr., 2008, vol. 14, no. 4, pp. 623–637. (In Russian)
11. Bokhoeva L.A. Osobennosti rascheta na prochnost’ elementov konstruktsii iz izotropnykh i kompozitsionnykh materialov s dopustimymi defektami [Strength Calculation for Structural Elements Made of Isotropic and Composite Materials with Minor Defects]. Ulan-Ude, VSGTU, 2007. 192 p. (In Russian)
12. Bryanskii A.A., Bashkov O.V., Protsenko A.E., Malysheva D.P. A study of damage accumulation kinetics in fiberglass during buckling and stretching tests. Mater. IV Vseros. nats. nauchn. konf. stud., aspir. i molod. uchen. [Proc. IV All-Russ. Natl. Sci. Conf. of Students, Graduate Students, and Young Researchers]. 2021, pp. 12–15. (In Russian)
13. Lokoshchenko A.M., Agakhi K.A., Fomin L.V. Beam bending under creep conditions considering material failure and varying resistance. Mashinostr. Inzh. Obraz., 2012, no. 3, pp. 29–35. (In Russian)
14. Bolotin V.V. Defects of the delamination type in composite structures. Mech. Compos. Mater., 1984, vol. 20, no. 2, pp. 173–188. https://doi.org/10.1007/BF00610358.
15. Bottega W.J., Maewal A. Delamination buckling and growth in laminates. J. Appl. Mech., 1983, vol. 50, no. 1, pp. 184–189. https://doi.org/10.1115/1.3166988.
16. Chai H., Babcock C.D., Knauss W.G. One dimensional modeling of failure in laminated plates by delamination buckling. Int. J. Solids Struct., 1981, vol. 27, no. 11, pp. 1069–1083. https://doi.org/10.1016/0020-7683(81)90014-7.
17. Muc A., Stawiarski A. Identification of damages in composite multilayered cylindrical panels with delaminations. Compos. Struct., 2012, vol. 94, no. 5, pp. 1871–1879. https://doi.org/10.1016/j.compstruct.2011.11.026.
18. Paimushin V.N., Kayumov R.A., Kholmogorov S.A. Degradation of the mechanical properties of fiber reinforced plastic under cyclic loading. Mech. Compos. Mater., 2023, vol. 59, no. 2, pp. 371–380. https://doi.org/10.1007/s11029-023-10101-1.
19. Kayumov R.A. Extended problem of the identification of mechanical characteristics of materials on the basis of testing of structures. Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, 2004, no. 2, pp. 94–103. (In Russian)
20. Teregulov I.G., Butenko Yu.I., Kayumov R.A., Safiullin D.Kh., Alekseev K.P. On determining the mechanical properties of nonlinear-elastic composite materials. J. Appl. Mech. Tech. Phys., 1996, vol. 37, no. 6, pp. 917–925. https://doi.org/10.1007/BF02369273.
21. Teregulov I.G., Kayumov R.A., Butenko Yu.I., Safiullin D.Kh. Determination of the mechanical indices of composite materials by testing multilayered samples. Mech. Compos. Mater., 1996, vol. 31, no. 5, pp. 446–452. https://doi.org/10.1007/BF00617127.
22. Vorontsov G.V., Plyushchev B.I., Reznichenko A.I. Determining the reduced elastic characteristics of reinforced composite materials using the methods of inverse tensometric problems. Mech. Kompoz. Mater., 1990, no. 4, pp. 733–747. (In Russian)
23. Suvorova Yu.V., Dobrynin V.S., Statnikov I.N. Determining the properties of a composite in a structure by the parametric-identification method. Mech. Compos. Mater., 1989, vol. 25, no. 1, pp. 130–136. https://doi.org/10.1007/BF00608463.
24. Alfutov N.A., Tairova L.P. Possibilities for determining the properties of a composite monolayer. In: Metody i sredstva diagnostiki nesushchei sposobnosti izdelii iz kompozitov [Methods and Tools for Determining the Load-Bearing Capacity of Composite Products]. Riga, Zinatne, 1986, pp. 212–215. (In Russian)
25. Alfutov N.A., Zinov’ev P.A., Tairova L.P. Identification of elastic characteristics of unidirectional materials by testing multilayer composites. In: Raschety na prochnost’ [Strength Calculations].Vol. 30. Moscow, Mashinostroenie, 1989, pp. 16–31. (In Russian)
26. Rikards R., Chate A. Identification of mechanical properties of composites based on design of experiments. Mech. Compos. Mater., 1998, vol. 34, no. 1, pp. 1–11. https://doi.org/10.1007/BF02256137.
27. Frederiksen P.S. Experimental procedure and results for the identification of elastic constants of thick orthotropic plates. J. Compos. Mater., 1997, vol. 31, no. 4, pp. 360–382. https://doi.org/10.1177/002199839703100403.
28. Kayumov R.A. Identification of mechanical characteristics of materials and design of structures made of these materials. Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, 1999, no. 6, pp. 118–127. (In Russian)
29. Teregulov I.G., Kayumov R.A., Fakhrutdinov I.H. Identification of the mechanical characteristics of composite materials from experimental data of shells of revolution. Mech. Compos. Mater., 1998, vol. 34, no. 6, pp. 545–548. https://doi.org/10.1007/BF02254663.
30. Morozov V.A. Metody regulyarizatsii neustoichivykh zadach [Regular Methods for Solving Ill-Posed Problems]. Moscow, MGU, 1987. 216 p. (In Russian)
31. Tikhonov A.N., Arsenin V.Ya. Metody resheniya nekorrektnykh zadach [Methods for Solving Ill-Posed Problems]. Moscow, Nauka, 1979. 285 p. (In Russian)
32. Kayumov R.A., Mukhamedova I.Z., Tazyukov B.F. Modeling of fiberglass degradation process under stresses and alkaline environment. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2022, vol. 164, nos. 2–3, pp. 194–205. https://doi.org/10.26907/2541-7746.2022.2-3.194-205. (In Russian)
33. Kayumov R.A., Suleymanov A.M., Muhamedova I.Z. Estimation of the durability of polymer composites on a fabric basis, taking into account the influence of non-force factors. IOP Conf. Ser.: Mater. Sci. Eng., 2020, vol. 934, no. 1, art. 012041. https://doi.org/10.1088/1757-899X/934/1/012041.
34. Kayumov R.A., Strakhov D.E., Mukhamedova I.Z., Tazyukov B.F. Mathematical models of inelastic behavior of flat fiberglass samples under three-point bending. Lobachevskii J. Math., 2023, vol. 44, no. 10, pp. 4448–4456. https://doi.org/10.1134/S1995080223100207.
35. Rabotnov Yu.N. Mekhanika deformiruemogo tverdogo tela [Mechanics of Deformable Solids]. Moscow, Nauka, 1979. 744 p. (In Russian)
36. Kachanov L.M. Osnovy mekhaniki razrusheniya [Principles of Fracture Mechanics]. Moscow, Nauka, 1974. 312 p. (In Russian)
37. Malinin N.N. Prikladnaya teoriya plastichnosti i polzuchesti [Applied Theory of Plasticity and Creep]. Moscow, Mashinostroenie, 1975. 400 p. (In Russian)
38. Kayumov R.A., Nezhdanov R.O., Tazyukov B.F. Opredelenie kharakteristik voloknistykh kompozitnykh materialov metodami identifikatsii [Determining Fiber Composite Material Characteristics by the Identification Methods]. Kazan, Izd. KGU. 2005. 258 p. (In Russian)
Review
For citations:
Kayumov R.A., Mukhamedova I.Z., Khaidarov L.I., Tazyukov B.F. On the Problem of Composite Beam Degradation under Longitudinal Bending and the Solution Method for Large Displacements. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki. 2024;166(3):364-376. (In Russ.) https://doi.org/10.26907/2541-7746.2024.3.364-376