Experimental investigation of residual strain formation mechanisms in composite laminates under cycling loading
V.N. Paimushina,b*, S.A. Kholmogorova**, R.A. Kayumovc**
a Tupolev Kazan National Research Technical University, Kazan, 420111 Russia
b Kazan Federal University, Kazan, 420008 Russia
c Kazan State University of Architecture and Engineering, Kazan, 420043 Russia
E-mail: * vpajmushin@mail.ru, ** hkazan@yandex.ru, *** kayumov@rambler.ru
Received September 12, 2017
Abstract
Cycling tension tests of the specimens from symmetric angle-ply laminate based on ELUR-P unidirectional carbon fiber and XT-118 cold-hardening epoxy have been carried out. Using the obtained experimental results, the process of residual strains formation has been investigated and qualitatively analyzed. It has been shown that there is such a level of ultimate stress in cycling loading conditions for the composite under investigation in the principal material axes, below which stabilization of the strain increment parameter at each loading cycle occurs. A method has been developed for determining the residual strains at each loading cycle by introducing the secant moduli of elasticity in the loading and unloading paths and their determination from the stress-strain curve. For several loading rates, which differ significantly from each other, the experimental dependencies of secant moduli formed in the loading and unloading paths on the cycle number have been obtained. A method has been proposed, which allows to isolate a viscoelastic component from the total strain accumulated during the cycling loading. This is specified by the epoxy creeping in the shear conditions. It has been found that the total strain for the fiber reinforced plastics under consideration can be represented as a sum of the viscoelastic part, which is recoverable over time, and the residual strain, which is probably associated with unrecoverable structural changes in the composite.
Keywords: unidirectional carbon fiber reinforced plastic, angle-ply laminate, specimen, cycling tension, unloading, secant modulus of elasticity, residual strain, creep strain, adaptability, unconvertible component of strain, viscoelastic convertible component of strain
Acknowledgments. The study was performed within the framework of the state task of the Ministry of Education of the Russian Federation (project no. 9.1395.2017/PCh, no. 9.5762.2017/VU).
Figure Captions
Fig. 1. The stress-strain diagrams σ+x = σ+x (ε+x)and the dependencies of residual strain increments on the number of cycles (8-month-long ageing of specimens after manufacturing): a), d) σmaxx = 65 MPa; b), e) σmaxx = 55 MPa; c), f) σmaxx = 45 MPa.
Fig. 2. The stress-strain diagram σ+x = σ+x (ε+x) for σmaxx = 65 MPa (two weeks ageing of specimens after manufacturing).
Fig. 3. The scheme for determination of residual strain according to the diagram σ+x = σ+x (ε+x).
Fig. 4. The secant moduli of elasticity under tension and compression with the rate of 0.5 mm/min.
Fig. 5. The stress-strain diagram under compression (σmaxx = -80 MPa, two weeks ageing of specimens after manufacturing).
Fig. 6. Dependencies of the secant moduli of elasticity on the cycle number for different loading rates (σmaxx = 45 MPa).
Fig. 7. Dependence of the residual strain on loading time.
Fig. 8. The dependencies G(i)12 = G(i)12 (γ(i)12)of the shear moduli on shear strain (round markers – under tension, triangular markers – under compression).
Fig. 9. The dependence εx = εx(t) of the axial strain on time.
Fig. 10. The dependence σx = σx(t) stress on time.
Fig. 11. Loading curve.
Fig. 12. The scheme for creep determination.
Fig. 13. The scheme for creep strain determination.
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For citation: Paimushin V.N., Kholmogorov S.A., Kaymov R.A. Experimental investigation of residual strain formation mechanisms in composite laminates under cycling loading. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2017, vol. 159, no. 4, pp. 473–492. (In Russian)
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