Advertisement

Continuum Mechanics and Thermodynamics

, Volume 32, Issue 2, pp 403–420 | Cite as

Constitutive equations for the cyclic behaviour of short carbon fibre-reinforced thermoplastics and identification on a uniaxial database

  • Louis Leveuf
  • Libor Navrátil
  • Vincent Le SauxEmail author
  • Yann Marco
  • Jérôme Olhagaray
  • Sylvain Leclercq
Original Article

Abstract

A constitutive model for the cyclic behaviour of short carbon fibre-reinforced thermoplastics for aeronautical applications is proposed. First, an extended experimental database is generated in order to highlight the specificities of the studied material. This database is composed of complex tests and is used to design a relevant constitutive model able to capture the cyclic behaviour of the material. A general 3D formulation of the model is then proposed, and an identification strategy is defined to identify its parameters. Finally, a validation of the identification is performed by challenging the prediction of the model to the tests that were not used for the identification. An excellent agreement between the numerical results and the experimental data is observed revealing the capabilities of the model.

Keywords

Short fibre-reinforced thermoplastic Cyclic loading Constitutive equations Complex experimental database Thermodynamics of irreversible processes 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

The authors would like to thank C. Doudard, S. Calloch and S. Moyne from ENSTA Bretagne, R. Billardon from Safran Landing Systems and N. Carrère from Safran Composites for stimulating discussions and F. Montel from ENSTA Bretagne for the development of the LabView software. One of the authors (L. Leveuf) would like to thank Safran Composites for the funding of this study.

References

  1. 1.
    Advani, S., Tucker, C.: A numerical simulation of short fiber orientation in compression molding. Polym. Compos. 11(3), 164–173 (1990)CrossRefGoogle Scholar
  2. 2.
    Andriyana, A., Billon, N., Silva, L.: Mechanical response of a short fiber-reinforced thermoplastic: experimental investigation and continuum mechanical loading. Eur. J. Mech. A 29, 1065–1077 (2010)CrossRefGoogle Scholar
  3. 3.
    Benoit, A., Maitournam, M., Rémy, L., Oger, F.: Cyclic behaviour of structures under thermomechanical loadings: application to exhaust manifolds. Int. J. Fatigue 38, 65–74 (2012)CrossRefGoogle Scholar
  4. 4.
    Bernasconi, A., Cosmi, F., Hine, P.: Analysis of fibre orientation distribution in short fibre reinforced polymers: a comparison between optical and tomographic methods. Compos. Sci. Technol. 72, 2002–2008 (2012)CrossRefGoogle Scholar
  5. 5.
    Blaber, J., Adair, B., Antoniou, A.: Ncorr: open-source 2D digital image correlation matlab software. Exp. Mech. 55, 1105–1122 (2015)CrossRefGoogle Scholar
  6. 6.
    Chaboche, J.: Thermodynamic formulation of constitutive equations and application to the viscoplasticity and viscoelasticity of metals and polymers. Int. J. Solids Struct. 34, 2239–2254 (1997)CrossRefGoogle Scholar
  7. 7.
    Colak, O.: Modeling deformation behavior of polymers with viscoplasticity theory based on overstress. Int. J. Plast. 21, 145–160 (2005)CrossRefGoogle Scholar
  8. 8.
    Constantinescu, A., Van Dang, K., Maitournam, M.: A unified approach for high and low cycle fatigue based on shakedown concepts. Fatigue Fract. Eng. Mater. Struct. 26, 561–568 (2003)CrossRefGoogle Scholar
  9. 9.
    Dray Bensahkoun, D.: Pédiction des propriétés thermo-élastiques d’un composite injecté et chargé de fibres courtes. Ph.D. Thesis, ENSAM Paris (2006)Google Scholar
  10. 10.
    Drozdov, A., Dusunceli, N.: Cyclic deformations of polypropylene with a strain-controlled program. Polym. Eng. Sci. 52, 2316–2326 (2012)CrossRefGoogle Scholar
  11. 11.
    Halphen, B., Nguyen, Q.: Sur les matériaux standards généralisés. J. Mec. 14, 39–63 (1975)zbMATHGoogle Scholar
  12. 12.
    Jégou, L., Marco, Y., Le Saux, V., Calloch, S.: Fast prediction of the wöhler curve from heat build-up measurements on short fiber reinforced thermoplastics. Int. J. Fatigue 47, 259–267 (2012)CrossRefGoogle Scholar
  13. 13.
    Kichenin, J.: Comportement thermomécanique du polyéthylène. Application aux structures gazières. Ph.D. Thesis, Ecole Polytechnique (1992)Google Scholar
  14. 14.
    Klimkeit, B., Nadot, Y., Castagnet, S., Nadot-Martin, C., Dumas, C., Bergamo, S., Sonsino, C., Buter, A.: Multiaxial fatigue life assessment for reinforced polymers. Int. J. Fatigue 33, 766–780 (2011)CrossRefGoogle Scholar
  15. 15.
    Krairi, A., Doghri, I.: A thermodynamically-based constitutive model for thermoplastic polymers coupling viscoelasticity, viscoplasticity and ductile damage. Int. J. Plast. 60, 163–181 (2014)CrossRefGoogle Scholar
  16. 16.
    Krairi, A., Doghri, I., Robert, G.: Multiscale high cycle fatigue models for neat and short fiber reinforced thermoplastic polymers. Int. J. Fatigue 92, 179–192 (2016)CrossRefGoogle Scholar
  17. 17.
    Krairi, A.: Multiscale modeling of the damage and failure of homogeneous and short-fiber reinforced thermoplastics under monotonic and fatigue loadings. Ph.D. Thesis, Université Catholique de Louvain (2015)Google Scholar
  18. 18.
    Launay, A., Maitournam, M., Marco, Y., Raoult, I.: Multiaxial fatigue models for short glass fiber reinforced polyamide. Part II: fatigue life estimation. Int. J. Fatigue 47, 390–406 (2013)CrossRefGoogle Scholar
  19. 19.
    Launay, A., Maitournam, M., Marco, Y., Raoult, I., Szmytka, F.: Cyclic behaviour of short glass fibre reinforced polyamide: experimental study and constitutive equations. Int. J. Plast. 27, 1267–1293 (2011)CrossRefGoogle Scholar
  20. 20.
    Launay, A., Marco, Y., Maitournam, M., Raoult, I.: Modelling the influence of temperature and relative humidity on the time-dependent mechanical behaviour of a short glass fibre reinforced polyamide. Mech. Mater. 56, 1–10 (2013)CrossRefGoogle Scholar
  21. 21.
    Le Saux, V., Doudard, C.: Proposition of a compensated pixelwise calibration for photonic infrared cameras and comparison to classic calibration procedures: case of thermoelastic stress analysis. Infrared Phys. Technol. 80, 83–92 (2017)ADSCrossRefGoogle Scholar
  22. 22.
    Lemaitre, J., Chaboche, J.: Mechanics of Solid Materials. Cambridge University Press, Cambridge (1990)CrossRefGoogle Scholar
  23. 23.
    Leveuf, L., Marco, Y., Le Saux, V., Navrátil, L., Leclercq, S.: Fast screening of the fatigue properties of thermoplastics reinforced with short carbon fibers based on thermal measurements. Polym. Test. (2017) (submitted)Google Scholar
  24. 24.
    Marco, Y., Le Saux, V., Jégou, L., Launay, A., Serrano, L., Raoult, I., Calloch, S.: Dissipation analysis in SFRP structural samples: thermomechanical analysis and comparison to numerical simulations. Int. J. Fatigue 67, 142–150 (2014)CrossRefGoogle Scholar
  25. 25.
    Marco, Y.: Caractérisation multi-axiale du comportement et de la micro-structure d’un semi-cristallin: application au cas du P.E.T. Ph.D. Thesis, Ecole Normale Supérieure de Cachan (2003)Google Scholar
  26. 26.
    Masquelier, I., Marco, Y., Le Saux, V., Calloch, S., Charrier, P.: Determination of dissipated energy fields from temperature mappings on a rubber-like structural sample: experiments and comparison to numerical simulations. Mech. Mater. 80, 113–123 (2015)CrossRefGoogle Scholar
  27. 27.
    Mortazavian, S., Fatemi, A.: Fatigue of short fiber thermoplastic composites: a review of recent experimental results and analysis. Int. J. Fatigue 102, 171–183 (2017)CrossRefGoogle Scholar
  28. 28.
    Ostwald, W.: Ueber die rechnerische darstellung des strukturgebietes der viskosität. Kolloid Z. 47, 176–187 (1929)CrossRefGoogle Scholar
  29. 29.
    Praud, F., Chatzigeorgiou, G., Bikard, J., Meraghni, F.: Phenomenological multi-mechanisms constitutive modelling for thermoplastic polymers, implicit implementation and experimental validation. Mech. Mater. 114, 9–29 (2017)CrossRefGoogle Scholar
  30. 30.
    Rémond, Y.: Constitutive modelling of viscoelastic unloading of short glass fibre-reinforced polyethylene. Compos. Sci. Technol. 65, 421–428 (2005)CrossRefGoogle Scholar
  31. 31.
    Selmi, A., Doghri, I., Adam, L.: Micromechanical simulations of biaxial yield, hardening and plastic flow in short glass fiber reinforced polyamide. Int. J. Mech. Sci. 53, 696–706 (2011)CrossRefGoogle Scholar
  32. 32.
    Serrano, L., Marco, Y., Le Saux, V., Robert, G., Charrier, P.: Fast prediction of the fatigue behavior of short-fiber-reinforced thermoplastics based on heat build-up measurements: application to heterogeneous cases. Contin. Mech. Thermodyn. 29, 1113–1133 (2017)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    Vincent, M., Giroud, T., Clarker, A.: Eberhardt: description and modeling of fiber orientation in injection molding of fiber reinforced thermoplastics. Polymer 46, 6719–6725 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.ENSTA BretagneInstitut de Recherche Dupuy de Lôme (iRDL), FRE CNRS 3744BrestFrance
  2. 2.Safran CompositesIttevilleFrance
  3. 3.Safran Landing SystemsVélizyFrance

Personalised recommendations