Buckling modes and failure of test specimens from fiber-reinforced composites with a [0∘]_s layup under axial compression. Theory and experiment

The analytical solutions for the problems of macroscale flexural-shear and purely transverse-shear buckling modes of test specimens made of fiber-reinforced composites with a [0∘]_s layup (s denoting the number of laminas) were analyzed, as well as the problems of mesoscale transverse-shear buckling modes of their peripheral layers under axial compression. Composite materials characterized by a physically nonlinear relationship only between transverse tangential stresses and the corresponding shear strains were examined. The solutions were obtained using three variants of linearized equations of the equilibrium in a perturbed state: based on the simplest refined S.P. Timoshenko’s model; from a linear approximation of the deflection and a cubic polynomial approximation of the axial displacements in the transverse coordinate with the preliminary satisfaction of the boundary conditions for tangential forces (the first refined version of the theory; Reddy–Nemirovsky model type); and without the preliminary satisfaction of such conditions (the second refined version of the theory). The physical nonlinearity of the material was incorporated in the linearized equations following the Shanley concept by introducing the tangential shear modulus. The theoretical data were compared with the experimental results.

1. Jumahat A., Soutis C., Jones F.R., Hodzic A. Fracture mechanisms and failure analysis of carbon fibre/toughened epoxy composites subjected to compressive loading. Compos. Struct., 2010, vol. 92, no. 2, pp. 295–305. https://doi.org/10.1016/j.compstruct.2009.08.010.

2. Hapke J., Gehrig F., Huber N., Schulte K., Lilleodden E.T. Compressive failure of UD-CFRP containing void defects: In situ SEM microanalysis. Compos. Sci. Technol., 2011, vol. 71, no. 9, pp. 1242–1249. https://doi.org/10.1016/j.compscitech.2011.04.009.

3. Niu K., Talreja R. Modeling of compressive failure in fiber reinforced composites. Int. J. Solids Struct., 2000, vol. 37, no. 17, pp. 2405–2428. https://doi.org/10.1016/S0020-7683(99)00010-4.

4. Naik N.K., Kumar R.S. Compressive strength of unidirectional composites: Evaluation and comparison of prediction models. Compos. Struct., 1999, vol. 46, no. 3, pp. 299–308. https://doi.org/10.1016/S0263-8223(99)00098-7.

5. Davidson P., Waas A.M. Mechanics of kinking in fiber-reinforced composites under compressive loading. Math. Mech. of Solids, 2016, vol. 21, no. 6, pp. 667–684. https://doi.org/10.1177/1081286514535422.

6. Prabhakar P., Waas A.M. Interaction between kinking and splitting in the compressive failure of unidirectional fiber reinforced laminated composites. Compos. Struct., 2013, vol. 98, pp. 85–92. https://doi.org/10.1016/j.compstruct.2012.11.005.

7. Pimenta S., Gutkin R., Pinho S.T., Robinson P. A micromechanical model for kink-band formation: Part I — experimental study and numerical modelling. Compos. Sci. Technol., 2009, vol. 69, nos. 7–8, pp. 948–955. https://doi.org/10.1016/j.compscitech.2009.02.010.

8. Lee S.H., Yerramalli C.S., Waas A.M. Compressive splitting response of glass reinforced unidirectional composites. Compos. Sci. Technol., 2000, vol. 60, no. 16, pp. 2957–2966. https://doi.org/10.1016/S0266-3538(00)00159-7.

9. Allix O., Feld N., Baranger E., Guimard J.-M., Ha-Minh C. The compressive behaviour of composites including fiber kinking: Modelling across the scales. Meccanica, 2014, vol. 49, no. 11, pp. 2571–2586. https://doi.org/10.1007/s11012-013-9872-y.

10. Polilov A.N. Etyudy po mekhanike kompozitov [Studies on the Mechanics of Composites]. Moscow, Fizmatlit, 2015. 320 p. (In Russian)

11. Guz’ A.N. Ustoichivost’ uprugikh tel pri konechnykh deformatsiyakh [Stability of Elastic Bodies under Finite Deformations]. Kyiv, Naukova Dumka, 1973. 270 p. (In Russian)

12. Bolotin V.V., Novichkov Yu.N. Mekhanika mnogosloinykh konstruktsii [Mechanics of Multilayer Structures]. Moscow, Mashinostroenie, 1980. 375 p. (In Russian)

13. Lubin G. (Ed.) Spravochnik po kompozitsionnym materialam [Handbook of Composites]. Book 2. Geller A.B. (Trans.), Geller B.E. (Ed.). Moscow, Mashinostroenie, 1988. 584 p. (In Russian)

14. Suarez J.A., Whiteside J.B., Hadcock R.N. The influence of local failure modes on the compressive strength of boron/epoxy composites. Composite Materials: Testing and Design (Second Conf.). Corten H. (Ed.). ASTM Special Technical Publication 497. Philadelphia, PA, ASTM Int., 1972, pp. 237–257. https://doi.org/10.1520/STP27750S.

15. Budiansky B., Fleck N.A. Compressive failure of fibre composites. J. Mech. Phys. Solids, 1993, vol. 41, no. 1, pp. 183–211. https://doi.org/10.1016/0022-5096(93)90068-Q.

16. Xu Y.L., Reifsnider K.L. Micromechanical modeling of composite compressive strength. J. Compos. Mater., 1993, vol. 27, no. 6, pp. 572–588. https://doi.org/10.1177/002199839302700602.

17. Zhang G., Latour R.A., Jr. FRP composite compressive strength and its dependence upon interfacial bond strength, fiber misalignment, and matrix nonlinearity. J. Thermoplast. Compos. Mater., 1993, vol. 6, no. 4, pp. 298–311. https://doi.org/10.1177/089270579300600403.

18. Zhang G., Latour R.A., Jr. An analytical and numerical study of fiber microbuckling. Compos. Sci. Technol., 1994, vol. 51, no. 1, pp. 95–109. https://doi.org/10.1016/0266-3538(94)90160-0.

19. Grigolyuk E.I., Kulikov G.M. General direction of development of the theory of multilayered shells. Mech. Compos. Mater., 1988, vol. 24, no. 2, pp. 231–241. https://doi.org/10.1007/BF00608158.

20. Noor A.K., Burton W.S. Assessment of computational models for multilayered composite shells. Appl. Mech. Rev., 1990, vol. 43, no. 4, pp. 67–97. https://doi.org/10.1115/1.3119162.

21. Piskunov V.G., Rasskazov A.O. Development of the theory of layered plates and shells. Prikl. Mekh., 2002, vol. 38, no. 2, pp. 22–57. (In Russian)

22. Paimushin V.N. Refined models for an analysis of internal and external buckling modes of a monolayer in a layered composite. Mech. Compos. Mater., 2017, vol. 53, no. 5, pp. 613–630. https://doi.org/10.1007/s11029-017-9691-7.

23. Paimushin V.N., Kholmogorov S.A., Gazizullin R.K. Mechanics of unidirectional fiber-reinforced composites: Buckling modes and failure under compression along fibers. Mech. Compos. Mater., 2018, vol. 53, no. 6, pp. 737–752. https://doi.org/10.1007/s11029-018-9699-7.

24. Paimushin V.N., Kholmogorov S.A., Makarov M.V., Tarlakovskii D.V., Lukaszewicz A. Mechanics of fiber composites: Forms of loss of stability and fracture of test specimens resulting from three- point bending tests. Z. Angew. Math. Mech., 2019, vol. 99, no. 1, art. e201800063. https://doi.org/10.1002/zamm.201800063.

25. Kayumov R.A., Lukankin S.A., Paimushin V.N., Kholmogorov S.A. Identification of mechanical properties of fiber-reinforced composites. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2015, vol. 157, no. 4, pp. 112–132. (In Russian)

26. Paimushin V.N., Kholmogorov S.A. Physical-mechanical properties of a fiber-reinforced composite based on an ELUR-P carbon tape and XT-118 binder. Mech. Compos. Mater., 2018, vol. 54, no. 1, pp. 2–12. https://doi.org/10.1007/s11029-018-9712-1.

27. Paimushin V.N., Kayumov R.A., Tarlakovskii D.V., Kholmogorov S.A. Deformation model of [±45∘]𝑎s cross-ply fiber reinforced plastics under tension. Proc. 2nd Int. Conf. on Theoretical, Applied and Experimental Mechanics (ICTAEM 2019). Gdoutos E. (Ed.). Ser.: Structural Integrity. Vol. 8. Cham, Spriger, 2019, pp. 29–35. https://doi.org/10.1007/978-3-030-21894-2_6.

28. Paimushin V.N., Kayumov R.A., Kholmogorov S.A. Deformation features and models of [±45∘]2𝑎s cross-ply fiber-reinforced plastics in tension. Mech. Compos. Mater., 2019, vol. 55, no. 2, pp. 141–154. https://doi.org/10.1007/s11029-019-09800-5.

29. Paimushin V.N., Gazizullin R.K., Shishov M.A. Flat internal buckling modes of fibrous composite elements under tension and compression at the mini- and microscale. J. Appl. Mech. Tech. Phys., 2019, vol. 60, no. 3, pp. 548–559. https://doi.org/10.1134/S0021894419030180.

30. Paimushin V.N., Polykova N.V., Kholmogorov S.A., Shishov M.A. Buckling modes of structural elements of off-axis fiber-reinforced plastics. Mech. Compos. Mater., 2018, vol. 54, no. 2, pp. 133–144. https://doi.org/10.1007/s11029-018-9726-8.

31. Paimushin V.N., Gazizullin R.K., Shishov M.A. Spatial buckling modes of a fiber (fiber bundle) of composites with a [±45∘]2𝑎s stacking sequence under tension and compression on test specimens. Mech. Compos. Mater., 2020, vol. 55, no. 6, pp. 743–760. https://doi.org/10.1007/s11029-020-09855-9.

32. Rikards R.B., Teters G.A. Ustoychivost’ obolochek iz kompozitnykh materialov [The Stability of Shells Made of Composite Materials]. Riga, Zinatne, 1974. 310 p. (In Russian)

33. Vasil’ev V.V. Mekhanika konstruktsii iz kompozitsionnykh materialov [Mechanics of Composite Structures]. Moscow, Mashinostroenie, 1988. 272 p. (In Russian)

34. Paimushin V.N., Makarov M.V., Kholmogorov S.A., Polyakova N.V. Shear buckling mode and failure of flat fiber-reinforced specimens under axial compression 1. Refined nonlinear mathematical deformation model. Mech. Compos. Mater., 2023, vol. 59, no. 5, pp. 885–900. https://doi.org/10.1007/s11029-023-10140-8.

35. Paimushin V.N., Makarov M.V., Kholmogorov S.A., Polyakova N.V. Shear buckling mode and failure of flat fiber-reinforced specimens in the axial compression 2. Numerical method, experimental and numerical investigations of the specimens with a [0]𝑎s layup. Mech. Compos. Mater., 2024, vol. 59, no. 6, pp. 1065–1082. https://doi.org/10.1007/s11029-023-10157-z.

36. Paimushin V.N., Makarov M.V., Polyakova N.V., Shishov M.A., Kamalutdinov A.M., Panin S.V. Refined nonlinear deformation models of semi-infinite plates made of fiber reinforced plastics. 1. Reddy–Nemirovsky type model. Lobachevskii J. Math., 2022, vol. 43, no. 8, pp. 2257–2266. https://doi.org/10.1134/S1995080222110245.