Abstract
The thermo-viscoelastic constitutive equation of unidirectional carbon fiber reinforced plastic (CFRP) is evaluated using a numerical approach based on the finite element method (FEM) and homogenization theory. The constitutive equation of the CFRP is considered in the Laplace-transformed domain, and it is discussed on the basis of the correspondence principle, which is satisfied by each of the Laplace-transformed elastic moduli. Homogenization theory is employed to estimate the ‘homogenized elastic moduli’ of the composite composed of matrix resin and carbon fibers. Using the approximation of a generalized Maxwell model, the relaxation moduli of CFRP are obtained by numerical computation using the FEM. From the relaxation modulus of epoxy resin and elastic moduli of carbon fiber, thermo-viscoelastic properties of CFRP laminates at several temperatures can be estimated using the FEM with homogenization theory. The effectiveness of the present study is verified by comparing the experimental results and numerical calculations for the relaxation moduli of the CFRP laminates.
Similar content being viewed by others
References
Papanicolaou G.C., Zaqoutsos S.P, Kontou E.A.: Fiber orientation dependence of continuous carbon/epoxy composites nonlinear viscoelastic behavior. Compos. Sci. Technol. 64, 2535–2545 (2004)
Al-Haik M.S., Hussaini M.Y., Garmestani H.Y.: Prediction of nonlinear viscoelastic behavior of polymeric composites using an artificial neural network. Int. J. Plast. 22, 1367–1392 (2006)
Matsuda T., Ohno N., Tanaka H., Shimizu T.: Homogenized in-plane elastic-viscoelastic behavior of long fiber-reinforced laminates. JSME Int. J. Ser. A 45, 538–544 (2002)
Matsuda T., Ohno N., Tanaka H., Shimizu T.: Effects of fiber distribution on elastic-viscoplastic behavior of long fiber-reinforced laminates. Int. J. Mech. Sci. 45, 1583–1598 (2003)
Mori T., Tanaka K.: Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica 21, 571–574 (1973)
Wu X., Ohno N.: A homogenization theory for time-dependent nonlinear composites with periodic internal structures. Int. J. Solids Struct. 36, 4991–5012 (1999)
Bensoussan A., Lions J.L., Papanicolaou G.: Asymptotic Analysis for Periodic Structures. North-Holland Publishing Company Amsterdam, The Netherlands (1978)
Sanchez-Palencia E.: Non-Homogeneous Media and Vibration Theory, Lecture Notes in Physics, No. 127. Springer, Berlin (1980)
Arai M., Sumida T., Shimizu M.: Effect of residual stress on interlaminar fracture toughness of CFRP laminates. J. Therm. Stress. 30, 1099–1116 (2007)
Ohno N., Wu X., Matsuda T.: Homogenized properties of elastic-viscoplastic composites with periodic internal structures. Int. J. Mech. Sci. 42, 1519–01536 (2000)
Ward, I.M., Sweeney, J.: An Introduction to the Mechanical Properties of Solid Polymers. pp. 79–107. 2nd edn. Wiley (2004)
Ferry, J.D.: Viscoelastic Properties of Polymers, Second Editon. pp. 59–87. 2nd edn. Wiley (1970)
Morland L.W., Lee E.H.: Stress analysis for linear viscoelastic materials with temperature variation. Trans. Soc. Rheol. 4, 233–263 (1960)
Hosono T.: Numerical Laplace transform. J. Inst. Elect. Eng. Jpn. A 99, 494–500 (1979) in Japanese
Arai M., Adachi T., Matsumoto H.: Boundary element analysis for unsteady elastodynamic problems based on the Laplace transform. JSME Int. J. Ser. A 42, 507–514 (1999)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kaku, Kh., Arai, M., Fukuoka, T. et al. Evaluation of thermo-viscoelastic property of CFRP laminate based on a homogenization theory. Acta Mech 214, 111–121 (2010). https://doi.org/10.1007/s00707-010-0319-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-010-0319-4