The brief review and analysis devoted to the problem of the degradation processes of materials, including fiber reinforced plastics, is carried out. As a specific object, a unidirectional carbon fiber reinforced plastic with [±45]2s lay-up under cyclic loading was selected. In the theoretical description of this process, it was assumed that the strain includes the elastic, viscoelastic, and viscoplastic components and the strain, formed as a result of the microdamages accumulation in the material. Modeling the degradation process is based on a phenomenological approach; moreover, the kinetic equation for the degradation parameter contains as the arguments both physical time and number of cycles transformed into a continuous variable. When determining the parameters from the experimental results, that are included in the constitutive relations for the strain components, the hypothesis is used, that with a small number of cycles, the strain caused by degradation is much less the strain caused by the rheological properties of the material. In addition, a number of hypotheses were introduced (a generalization of the Kachanov hypothesis, as well as the assumption that the rates of various inelastic strain cannot always be of the same order at all times of loading). It makes possible to simplify the problem of mechanical characteristics identification, as well as to reduce the variety and amount of experiments. The results of experiments and the problems solved for determining the parameters included in the physical relationships proposed were presented, and their good agreement was obtained.
Similar content being viewed by others
References
Yu. N. Rabotnov, Creep of Structural Elements [In Russian], Nauka, Moscow (1966).
L. M. Kachanov, “On the time of failure under creep conditions,” [In Russian], Izv. AN SSSR, No.8, 26-31 (1958).
V. V. Vasiliev, A. A. Dudchenko, and A. N. Elpatyevsky, “On the features of deformation of orthotropic fiberglass under tension” [In Russian], Mech. Polymers, No.1, 144-146 (1970).
N. A. Alfutov, P. A. Zinoviev, and B. G. Popov, Calculation of Multilayer Plates and Shells Made of Composite Materials [In Russian], Mashinostroenie, Moscow (1984).
V. I. Astafiev, Yu. N. Radaev, and L. V. Stepanova, Nonlinear fracture mechanics [In Russian], Izd-vo “Samarskii Universitet”, Samara (2001).
V. V. Bolotin., “To the theory of delayed fracture,” [In Russian], Mechanica tverdogo tela, No.1, 137-146 (1981).
S. Murakami and Yu. N. Radaev, “Mathematical model of a three-dimensional anisotropic state of damage,” [In Russian], Mech. Solids, No.4, 98-110 (1966).
S. A. Nazarov, “Tensor and damage measures. 1. Asymptotic analysis of an anisotropic medium with defects,” [In Russian], Mech. Solids, No. 3, 113-124 (2000).
I. G. Teregulov, “Strength criterion of an orthotropic body and its relationship with the process of microdamages accumulation,” [In Russian], Applied Problems of Strength and Plasticity. Interuniversity. Mezhvuzovskiy sbornik “Analiz i Optimizatsiya Konstruktsiy”. Izd-vo NNGU, No. 51, 32-39 (1994).
A. A. Ilyushin and B. E. Pobedrya, Thermoviscoelasticity Based on Mathematical Theory [In Russian], Nauka, Moscow (1970).
A. C. F. Cocks and M. F. Ashby, “The growth of dominant crack in a creeping material,” Scr. Metall, 16, 109-114 (1982).
M. B. Akhundov, “Damage and deformation of nonlinear hereditary media in a complex stressed state,” Mech. Compos. Mater., No. 2, 155-158 (1991).
Yu. V. Suvorova, “On the criterion of strength based on the damage accumulation and its applications to composite,” [In Russian], Mech. Solids, No. 4, 107-111 (1979).
A. M. Dumansky and G. N. Finogenov, “Methods for assessing the damage of polymer fiber composites under prolonged static loading,” [In Russian], Industrial Laboratory, No. 4, 60-62 (1993).
V. V. Moskvitin, “Some questions of long-term strength of viscoelastic bodies,” [In Russian], Strength Problems, No. 2, 55-58 (1972).
A. R. Harutyunyan and R. A. Harutyunyan, “Fatigue strength criterion of composite materials based on the damage concept,” Russian Congress on Fundamental Problems of Theoretical and Applied Mechanics: Proc. in 4 Volumes. D23 V. 3: Mechanics of Rigid Bodies, Ufa, Russia (2019), 556-558.
R. A. Harutyunyan, “High-temperature embrittlement and long-term strength of metallic materials,” [In Russian], Mech. Solids, 50, No. 2, 191-197 (2015).
W. Van Paepegem and J. Degrieck, “A new coupled approach of residual stiffness and strength for fatigue of fibre-reinforced composites,” Int. J. Fatigue, 24, No. 7, 747-762 (2002)
J. Bogdanoff and F. Kozin, Probabilistic Models of Damage Accumulation [In Russian], Mir, Moscow (1989).
O. G. Rybakina, “About the works of V. V. Novozhilov in the field of phenomenological description of the first stage of fracture (damage accumulation),” [In Russian], Proc. of the Central Research Institute. Acad. A. N. Krylov, No. 53-1 (337-1), 127-134 (2010).
N. N. Golovin and G. N. Kuvyrkin, “Mathematical models of deformation of carbon-carbon composites,” [In Russian], Mech. Solids, No. 5, 111-123 (2016).
Non-Destructive Testing: Handbook: In 8 volumes [In Russian], Under total. ed. V. V. Klyuev, 1-8 (2006).
J. Varna and L. Asp, “Microdamage in composite laminates: experiments and observation,” Appl. Mech. Mater., 518, 84-89 (2014).
Yu. G. Matvienko, I. E. Vasiliev, A. V. Pankov, and M. A. Trusevich, “Early diagnosis of damage and fracture zones of composite materials using brittle strain gauges and acoustic emission,” [In Russian], Industrial Laboratory. Diagnostics of Materials, No. 1, 45-56 (2016).
V. E. Wildemann, E. V. Spaskova, A. I. Shilova, “Composite materials based on acoustic emission monitoring and method of digital image correlation problems of deformation and fracture in materials and structures,” Solid State Phenomena, 243, 163-170 (2016).
D. L. Bykov, A. V. Kazakov, D. N. Konovalov, V. P. Melnikov, Yu. M. Milekhin, V. A. Peleshko, and D. N. Sadovnichy, “On the law of damage accumulation and fracture criteria in highly filled polymeric materials,” Mech. Solids, No. 5, 76-97 (2014).
A. Yu. Izyumova, A. N. Vshivkov, A. E. Prokhorov, O. A.Plekhov, and B. Venkatraman, “Study of heat source evolution during elastic-plastic deformation of titanium alloy Ti-0.8AL-0.8MN based on contact and non-contact measurements,” PNRPU Mechanics Bulletin, No. 1, 68-81 (2016).
S. A. Kapustin, Yu. A. Churilov, and V. A. Gorokhov, Modeling of Nonlinear Deformation and Failure of Structures under Conditions of Multifactor Effects Based on FEM [In Russian], Izdatelstvo Nizegorodskogo gos. un-ta. named by N. I. Lobachevskij, Nizhny Novgorod (2015).
I. A. Volkov and Yu. G. Korotkikh, Equations of State for Damaged Viscoelastoplastic Media [In Russian], Fizmatlit, Moscow (2008).
I. A. Volkov, L .A. Igumnov, D. A. Kazakov, D. N. Shishulin, I. S. Tarasov, and I. V. Smetanin, “Constitutive relations of the mechanics of a damaged medium for evaluating the long-term strength structural alloys,” J. Appl. Mech.Tech. Physics, No. 1, 181-194 (2019).
M. S. Loukil and J. Varna, “Effective shear modulus of a damaged ply in laminate stiffness analysis: Determination and validation”, J. Compos. Mater., 54, No. 9, 1-16 (2019).
R. Talreja and C. V. Singh, Damage and Failure of Composite Materials, Cambridge University Press, New York (2012).
R. A. Kayumo and R. O. Nezhdanov, “Long-term strength criterion for fiber composite” [In Russian], Izv. TulGU. Seria “Matematika. Mekhanika. Informatika,” 10, No. 2, 111-123 (2004).
W. Van Paepegem, “Fatigue damage modelling of composite materials with the phenomenological residual stiffness approach,” Fatigue Life Pred. Compos. Compos. Struct., 1, 102-138 (2010).
A. V. Berezin and A. I. Kozinkina, “Features of damage diagnosis and assessment of the strength of composites” [In Russian], Mech. Compos. Mater. Struct, 5, No. 1, 99-122 (1999).
P. A. Belov, A. A. Dudchenko, S. A. Lurie, A. M. Semernin, and H. Khadarman, “About one algorithm for accounting for damage in material mechanics,” [In Russian], Mech. Compos. Mater. Struct, 12, No. 4, 566-578 (2006).
V. N. Paimushin, R. A. Kayumov, and S. A. Kholmogorov, “Deformation features and models of [+/-45]2s cross-ply fiber-reinforced plastics in tension”, Mech. Compos. Mater., 55, No. 2, 141-154 (2019).
R. A. Kayumov, “Extended problem of identification of mechanical characteristics of materials based on the results of tests of structures,” Mech. Solids, No. 2, 94-105 (2004).
Ospina Cadavid M., Al-Khudairi O., Hadavinia H., Goodwin D., and Liaghat G.H., “Experimental studies of stiffness degradation and dissipated energy in glass fibre reinforced polymer composite under fatigue loading,” Polymers and Polymer Compos., 25, No. 6, 435-446 (2017).
Acknowledgments
The work was funded by Russian Science Foundation (project No. 19-79-10018 (Section "Introduction", "Experimental Results and Their Theoretical Explanation")) and by the Kazan Federal University Strategic Academic Leadership Program (“PRIORITY-2030”).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Paimushin, V.N., Kayumov, R.A. & Kholmogorov, S.A. Degradation of the Mechanical Properties of Fiber Reinforced Plastic under Cyclic Loading. Mech Compos Mater 59, 371–380 (2023). https://doi.org/10.1007/s11029-023-10101-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11029-023-10101-1