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Deformation Features and Models of [±45]2s Cross-Ply Fiber-Reinforced Plastics in Tension

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Mechanics of Composite Materials Aims and scope

Series of experiments on [±45]2s cross-ply carbon-fiber-reinforced plastic specimens were carried out in tension with various loading programs. In analyzing stress–strains relations, the material was considered homogeneous. The total axial strain is presented as the sum of instantaneous residual (irreversible), nonlinear reversible, irreversible creep, and reversible creep strains. To separate the last two components, the hypothesis that their rates at different instants of time are different is used. Together with a generalized Kachanov hypothesis, this allowed us first to obtain equations for increments of only the viscoelastic strain. Further, equations in which only the viscoplastic strain is unknown are written, and only then the secant elastic modulus is determined. Questions of the choice of relations for describing strain components and the problem on identification of parameters of the relations are considered. Experimental data and results of their processing are presented, and they testify to the acceptability of the assumptions used and the efficiency of the approaches proposed.

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References

  1. Yu. N. Rabotnov, Creep of Structural Members [in Russian], M., Nauka, (1966).

  2. Yu. N. Rabotnov, Elements of Hereditary Mechanics of Solid Bodies [in Russian], M., Nauka, (1977).

  3. R. A. Rzhanitsyn, Theory of Creep[in Russian], M., Gosstrojizdat (1968).

  4. M. A. Koltunov, Creep and Relaxation [in Russian], M., Vysshaya Shkola (1976).

  5. Yu. S. Urzhumtsev and R. D. Maximov, Prediction of Deformation of Polymer Materials [in Russian], Riga, Zinatne, (1975).

  6. Mechanics of Composite Materials. Composite Materials, Vol. 2, ed. by G. P. Sendeckyj, Academic Press, N. Y, London (1974).

  7. N. N. Malinin, Applied Theory of Plasticity and Creep, Studies, Textbook for University students [in Russian], 2nd ed., M., Mashinostroenie (1975).

  8. L. M. Kachanov, Theory of Creep [in Russian], M., Gosizdat (1960).

  9. A. A. Adamov and V. P. Matvienko, Methods of Applied Viscoelasticity [in Russian], M., Mashinostroenie (2003).

  10. A. Ya. Malkin, Rheology: Concepts, Methods, Applications [in Russian], St. Petersburg (2007).

  11. V. E. Yudin, V. P. Volodin, and G. N. Gubanova, “Features of the viscoelastic behavior of carbon plastics on the basis of the polymer matrix: a model study and calculation,” Mekh. Kompoz. Mater., 33, No. 5, 656-669 (1997).

    Google Scholar 

  12. R. A. Kayumov and I. G. Teregulov, “Structure of governing relations for hereditary-elastic materials reinforced with rigid fibers,” Prikl.. Mekh. Tekchn. Fiz., 3, 120-128 (2005).

    Google Scholar 

  13. K. Giannadakis and J. Varna, “Analysis of nonlinear shear stress-strain response of unidirectional GF/EP composite,” Composites: Part A, 62, 67-76 (2014).

    Article  Google Scholar 

  14. K. Giannadakis, P. Mannberg, R. Joffe, and J. Varna, “The sources of inelastic behavior of glass fibre/vinylester non-crimp fabric [±45] s laminates,” J. Reinf. Plast. Compos., 30, No. 12, 1015-1028. (2011).

    Article  Google Scholar 

  15. L.-O. Nordin and J. Varna, “Methodology for parameter identification in nonlinear viscoelastic material model,” 9, No. (4), 259-280 (2005).

  16. S. Ogihara and H. Nakatani, “Modeling of mechanical response in CFPR angle-ply laminates,” Proc. of the 19th Int. Conf. on Composite Materials (ICCM19), Montreal, Canada, 7268-7276 (2013).

  17. A. M. Dumansky and L. P. Tairova, “The prediction of viscoelastic properties of layered composites on example of cross-ply carbon reinforced plastic,” World Congr. on Eng., 2-4 July, 2007. Vol. II, London, UK, 1346-1351 (2007).

  18. J. Berthe, M. Brieu, and E. Deletombe, “Thermo-viscoelastic modeling of organic matrix composite behavior – Application to T700GC/M21,” Mech. Mater., 81, 18-24(2015).

    Article  Google Scholar 

  19. M. Mondali, V. Monfared, and A. Abedian, “Nonlinear creep modeling of short-fiber composites using Hermite polynomials, hyperbolic trigonometric functions and power series,” Comptes Rendus Mecanique, 341, 592-604 (2013).

    Article  Google Scholar 

  20. V. P. Golub, Ya. V. Pavlyuk, and P. V. Fernati, “Determining parameters of fractional-exponential heredity kernels of nonlinear viscoelastic materials,” Int. Appl. Mech., 53, No. 4, 419-433 (2017).

    Article  Google Scholar 

  21. V. N. Paimushin, S. A. Kholmogorov, and I. B. Badriev, “Theoretical and experimental investigations of the formation mechanisms of residual deformations of fibrous layered structure composites,” MATEC Web of Conf., 2017. Vol. 129, 02042 (Int. Conf. on Modern Trends in Manufacturing Technologies and Equipment, ICMTMTE 2017, Sevastopol, Russian Federation; 11-17 Sept., (2017).

  22. V. N. Paimushin and S.A. Kholmogorov, “Residual strains in obliquely reinforced fibrous composites: experiments on cyclic tension,” Proc. X All Russian Conf. On Mechanics of Deformable Solid Body (18-22 Sept., 2017, Samara, Russia). Vol. 2. Samara Sam. GTU, 136-140 (2017).

  23. V. N. Paimushin, S. A. Kholmogorov, and R. A. Kayumov, “Experimental studies of the mechanisms of formation of residual strains of fibrous composites of a layered structure under cyclic loading,” Uch. Zap. Kazan. Univ. Ser. Fiz.-Mat. Nauki, 159, No. 40, 395-428 (2017).

    Google Scholar 

  24. V. N. Paimushin and S. A. Kholmogorov, “Physical-mechanical properties of a fiber-reinforced composite based on an ELUR-P carbon tape and XT-118 binder,” Mech. Compos. Mater., 54, No. 1, 2-12 (2018).

    Article  Google Scholar 

  25. K. B. Pettersson, J. M. Neumeister, K. E. Gamstedt, and H. Öberg, “Stiffness reduction, creep, and irreversible strains in fiber composites tested in repeated interlaminar shear,” Compos. Struct., 76, Nos. 1-2, 151-161 (2006).

    Article  Google Scholar 

  26. W. Van Paepegem, I. De Baere, and J. Degrieck, “Modelling the nonlinear shear stress-strain response of glass fibre-reinforced composites. Part I: Experimental results,” Compos. Sci. Technol., 66, 1455-1464 (2006).

    Article  Google Scholar 

  27. V. V. Vasil’jev, A. A. Dudchenko, and A. N. Elpatyevskii, “On the deformation features of orthotropic fiberglass in tension,” Polym. Mekh., 1, 144-146 (1970).

    Google Scholar 

  28. I. F. Obraztsov, V. V. Vasil’jev, and V. A. Bunakov, Optimal Reinforcement of Shells of Rotation from Composite Materials [in Russian], M., Mashinostroenie (1977).

  29. N. A. Alfutov, P. A. Zinovjev, and B. G. Popov Calculation of Multilayered Plates and Shells from Composite Materials [in Russian], M., Mashinostoenie (1984).

  30. V. N. Paimushin, N. V. Polyakova, S. A. Kholmogorov, and M. A. Shishov, “Multi-scale modes of buckling of reinforcing elements in fibrous composites,” Izv. Vuz. Matematika, 9, 89-95 (2017).

    Google Scholar 

  31. V. N. Paimushin, N. V. Polyakova, S. A. Kholmogorov, and M. A. Shishov, “Buckling modes of structural elements of off-axis fiber-reinforced plastics,” Mech. Compos. Mater., 54, No. 2, 133-144 (2018).

    Article  Google Scholar 

  32. I. F. Obraztsov and V. V. Vasiliev, “Nonlinear phenomenological models of deformation of fibrous composite materials,” Mekh. Kompoz. Mater., 3, 390-393 (1982).

    Google Scholar 

  33. R. A. Kayumov, “Structure of nonlinear elastic relationships for the highly anisotropic layer of a nonthin shell,” Mech. Compos. Mater., 35, No. 5, 409-419 (1999).

    Article  Google Scholar 

  34. N. Ch. Arutyunyan, “On the theory of creep in heterogeneous hereditary aging media,” Dokl. AN SSSR, 229, No. 3, 569-571 (1976).

    Google Scholar 

  35. O. L. Kravchenko and V. E. Vilderman, “Modeling the inelastic deformation of angle-ply reinforced laminates,” Matem. Model. Syst. Proc., 5, 49-55 (1997).

    Google Scholar 

  36. R. M. Christensen, Mechanics of Composite Materials, New York–Chichester–Brisbane–Toronto, John Wiley & Sons (1979).

    Google Scholar 

  37. G. C. Papanicolaou, S. P. Zaoutsos, and E. A. Kontou, “Fiber orientation dependence of continuous carbon/epoxy composites nonlinear viscoelastic behavior,” Compos. Sci. Technol., 64, No.16, 2535-2545 (2004).

    Article  Google Scholar 

  38. E. Kontou and A. Kallimanis, “Formulation of the viscoplastic behavior of epoxy-glass fiber composites,” J. Compos. Mater., 39, No.8, 711-721 (2005).

    Article  Google Scholar 

  39. R. A. Kayumov, “Extended problem of identifying the mechanical characteristics of materials according to results of structure testing,” Izv. RAN Mekh. Tverd. Tela, No. 2, 94-105 (2004).

  40. D. Grop, Identification Methods of Systems [Russsian translation], M., Mir (1979).

  41. L. M. Kachanov, “About the time of creep rupture,” Izv. AN SSSR, Otd. Tekhn. Nauk, 8, 26-31 (1958).

    Google Scholar 

  42. A. N. Polilov, Etudes on Mechanics of Composites [in Russian], M., Fizmatlit (2015).

Download references

Acknowledgements

The research results were obtained within the framework of fulfillment of the state task of the Ministry of Education and Science of Russia No. 9.5762.2017/VU (Project No. 9.1395.2017/PCh), (Introduction, Section 1) and supported by Russian Science Foundation (project No. 19-19-00059), (Section 2)).

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Correspondence to V. N. Paimushin.

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Translated from Mekhanika Kompozitnykh Materialov, Vol. 55, No. 2, pp. 205-224, March-April, 2019.

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Paimushin, V.N., Kayumov, R.A. & Kholmogorov, S.A. Deformation Features and Models of [±45]2s Cross-Ply Fiber-Reinforced Plastics in Tension. Mech Compos Mater 55, 141–154 (2019). https://doi.org/10.1007/s11029-019-09800-5

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