Deformation Model of [±45]S Cross-Ply Fiber Reinforced Plastics Under Tension

  • V. N. PaimushinEmail author
  • R. A. Kayumov
  • D. V. Tarlakovskii
  • S. A. Kholmogorov
Conference paper
Part of the Structural Integrity book series (STIN, volume 8)


A series of experiments on tensile testing of specimens from cross-ply reinforced plastics made from unidirectional tape ELUR-P and cold-curing binder XT-118 and stacking sequence [±45°] were carried out. Tests were carried out on different specimens at three maximum stress values. It was established that the total axial strain can be represented as a sum of four components, including: reversible strain, residual (irreversible) strain, irreversible creep deformation and reversible creep strain due to the viscoelastic properties of the epoxy. The questions of the choice of relations for the description of the components of the strains and the identification of their mechanical characteristics are considered. The conclusion is formulated that for a hereditarily elastic model, one can use the Abel creep kernel and determine its parameters from an experiment for long holding times. To determine the parameters included in the irreversible creep relations, we use the results obtained immediately after the start of exposure at maximum stresses, and a method for their determination is proposed. After this is the initial modulus of elasticity. At the last stage, after determining the rheological characteristics and the initial modulus of elasticity, the nonlinear elastic reversible part of the strain can be singled out.


Unidirectional CFRP Specimen Residual strain Creep strain Secant modulus of elasticity Identification Creep kernel 



The research results were obtained in the framework of the fulfilment of the state task of the Ministry Science and High Education of Russia No. 9.5762.2017/VU (project No. 9.1395.2017/PCh) and supported by Russian Science Foundation (project No. 19-19-00059).


  1. 1.
    Rabotnov, U.N.: Creep of Structural Elements. Nauka, Moscow (1966)zbMATHGoogle Scholar
  2. 2.
    Rzanicun, R.A.: Creep Theory. Gosstroyizdat, Moscow (1968)Google Scholar
  3. 3.
    Kachanov, L.M.: Creep Theory. Gos.izd.fiz.-mat.lit, Moscow (1960)Google Scholar
  4. 4.
    Udin, V.E., Volodin, V.P., Gubanova, G.N.: Features of the viscoelastic behavior of carbon plastics on the basis of the polymer matrix: a model study and calculation. Mech. Compos. Mater. 5, 656–669 (1997)Google Scholar
  5. 5.
    Kayumov, R.A., Teregulov, I.G.: Structure of defining relations for hereditary-elastic materials reinforced with hard fibers. J. Appl. Mech. Tech. Phys. 3, 120–128 (2005)zbMATHGoogle Scholar
  6. 6.
    Giannadakis, K., Mannberg, P., Joffe, R., Varna, J.: The sources of inelastic behavior of Glass Fibre/Vinylester non-crimp fabric [±45]s laminates. J. Reinf. Plast. Compos. 30(12), 1015–1028 (2011)CrossRefGoogle Scholar
  7. 7.
    Paimushin, V.N., Kholmogorov, S.A., Kayumov, R.A.: Experimental investigation of residual strain formation mechanisms in composite laminates under cycling loading. UCHENYE ZAPISKI KAZANSKOGO UNIVERSITETA-SERIYA FIZIKO-MATEMATICHESKIE NAUKI 159(4), 473–492 (2017)Google Scholar
  8. 8.
    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. 54(1), 2–12 (2018)CrossRefGoogle Scholar
  9. 9.
    Van Paepegem, W., De Baere, I., Degrieck, J.: Modelling the nonlinear shear stress–strain response of glass fibre-reinforced composites. Part I: experimental results. Compos. Sci. Technol. 66, 1455–1464 (2006)Google Scholar
  10. 10.
    Kayumov, R.A.: The extended task of identifying the mechanical characteristics of materials according to the results of structural tests. Mech. Solids 2, 94–105 (2004)Google Scholar
  11. 11.
    Kachanov, L.M.: About failure time in creep conditions. Izv. AN USSR. Otd.tehn.nauk 8, 26–31 (1958)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • V. N. Paimushin
    • 1
    • 2
    Email author
  • R. A. Kayumov
    • 1
    • 3
  • D. V. Tarlakovskii
    • 4
    • 5
  • S. A. Kholmogorov
    • 1
  1. 1.Kazan National Research Technical University Named After A.N. TupolevKazanRussia
  2. 2.Kazan Federal UniversityKazanRussia
  3. 3.Kazan State University of Architecture and Building ConstructionKazanRussia
  4. 4.Lomonosov Moscow State UniversityMoscowRussia
  5. 5.Moscow Aviation Institute (National Research University)MoscowRussia

Personalised recommendations