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A model to describe the cyclic anisotropic mechanical behavior of short fiber-reinforced thermoplastics

  • Libor Navrátil
  • Louis Leveuf
  • Vincent Le Saux
  • Yann Marco
  • Jérôme Olhagaray
  • Sylvain Leclercq
  • Sylvain Moyne
  • Matthieu Le SauxEmail author
Article
  • 22 Downloads

Abstract

Due to the injection molding process, short fiber-reinforced thermoplastic composites show a complex fiber orientation distribution and, as a consequence, an overall anisotropic mechanical behavior. The monotonic and cyclic mechanical behavior of PolyEtherEtherKetone thermoplastic reinforced with 30 wt.% of short carbon fibers was characterized through a series of tests generating various complex loading histories (loading–unloading with creep or recovery steps, cyclic loading with various stress amplitudes) performed at room temperature on samples with various homogeneous and heterogeneous fiber orientation distributions. A three-dimensional model relying on a thermodynamic framework was then developed to represent the anisotropic mechanical behavior of the material, including elastic, viscoelastic, and plastic phenomena. Relevant constitutive laws were defined to describe the phenomena within wide ranges of loading rates and levels, with a limited number of parameters. Elastic anisotropy and plastic anisotropy were naturally described by using a two-step homogenization method and a Hill-like equivalent stress taking into account the fiber orientation distribution. The model was implemented into a finite element code to be able to simulate the response of complex parts with a heterogeneous fiber orientation distribution subjected to a heterogeneous loading. Model parameters were identified by applying a robust and original approach relying on a limited number of relevant experiments. The prediction capability of the model was demonstrated by simulating several types of tests not used for the identification, covering a wide range of monotonic and cyclic, homogeneous and heterogeneous, loading conditions, for various simple and complex fiber orientation distributions. In particular, the model is shown to be able to predict the energy dissipated in the material when subjected to cyclic loading.

Keywords

Short fiber-reinforced thermoplastic Anisotropic nonlinear mechanical behavior Model Fiber orientation 

Notes

References

  1. Advani, S., Tucker, C.: The use of tensors to describe and predict fiber orientation in short fiber composite. Polym. Compos. 31, 751 (1987) Google Scholar
  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, Solids 29, 1065–1077 (2010) CrossRefGoogle Scholar
  3. Armstrong, J., Frederick, C.: A mathematical representation of the multiaxial Bauschinger effect. Mater. High Temp. 24(1), 1–26 (2007) CrossRefGoogle Scholar
  4. Benveniste, Y.: A new approach to the application of Mori–Tanaka’s theory in composite materials. Compos. Sci. Technol. 6, 147–157 (1987) Google Scholar
  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. Camacho, C., Tucker, C., Yalvaç, S., McGee, R.: Stiffness and thermal expansion predictions for hybrid short fiber composites. Polym. Compos. 11, 229–239 (1990) CrossRefGoogle Scholar
  7. 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
  8. Chen, C., Cheng, C.: Effective elastic moduli of misoriented shortfiber composites. Int. J. Solids Struct. 33, 2519–2539 (1996) CrossRefGoogle Scholar
  9. Cintra, J., Tucker, C.: Orthotropic closure approximations for flow-induced fiber orientation. J. Rheol. 39, 1095–1122 (1995) CrossRefGoogle Scholar
  10. Colak, O.: Modeling deformation behavior of polymers with viscoplasticity theory based on overstress. Int. J. Plast. 21, 145–160 (2005) CrossRefGoogle Scholar
  11. 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
  12. de Waele, A.: Description and modeling of fiber orientation in injection molding of fiber reinforced thermoplastics. J. Oil Colour Chem. Assoc. 6, 33–69 (1923) Google Scholar
  13. Drozdov, A., Dusunceli, N.: Cyclic deformations of polypropylene with a strain-controlled program. Polym. Eng. Sci. 52, 2316–2326 (2012) CrossRefGoogle Scholar
  14. Drozdov, A., Al-Mulla, A., Gupta, R.: The viscoelastic and viscoplastic behavior of polymer composites: polycarbonate reinforced with short fibers. Comput. Mater. Sci. 28, 16–30 (2003) CrossRefGoogle Scholar
  15. Halphen, B., Nguyen, Q.: Sur les matériaux standards généralisés. J. Méc. 14, 39–63 (1975) zbMATHGoogle Scholar
  16. Hill, R.: The Mathematical Theory of Plasticity. Clarendon Press, Oxford (1950) zbMATHGoogle Scholar
  17. 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
  18. 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
  19. 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
  20. Launay, A.: Thermoplastiques renforcés en fibres de verre courtes: Comportement cyclique, fatigue et durée de vie. Ph.D. thesis, Ecole Polytechnique, France (2011) Google Scholar
  21. 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
  22. Launay, A., Maitournam, M., Marco, Y., Raoult, I.: Multiaxial fatigue models for short glass fiber reinforced polyamide. Part I: nonlinear anisotropic constitutive behavior for cyclic response. Int. J. Fatigue 47, 382–389 (2013a) CrossRefGoogle Scholar
  23. 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 (2013b) CrossRefGoogle Scholar
  24. 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) CrossRefGoogle Scholar
  25. Lemaitre, J., Chaboche, J.: Mechanics of Solid Materials. Cambridge University Press, Cambridge (1990) CrossRefGoogle Scholar
  26. Leveuf, L., Marco, Y., Le Saux, V., Navrátil, L., Leclercq, S., Olhagaray, J.: Fast screening of the fatigue properties of thermoplastics reinforced with short carbon fibers based on thermal measurements. Polym. Test. 68, 19–26 (2018a) CrossRefGoogle Scholar
  27. Leveuf, L., Navrátil, L., Le Saux, V., Marco, Y., Olhagaray, J., Leclercq, S.: Constitutive equations for the cyclic behaviour of short carbon fibre-reinforced thermoplastics and identification on a uniaxial database. Contin. Mech. Thermodyn., 1–18 (2018b) Google Scholar
  28. Lielens, G., Pirotte, P., Couniot, A., Dupret, F., Keunings, R.: Prediction of thermomechanical properties for compression moulded composites. Composites, Part A, Appl. Sci. Manuf. 29, 63–70 (1998) CrossRefGoogle Scholar
  29. 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
  30. Meneghetti, G., Quaresimin, M.: Fatigue strength assessment of a short fiber composite based on the specific heat dissipation. Composites, Part B, Eng. 42, 217–225 (2011) CrossRefGoogle Scholar
  31. Mlekusch, B.: Thermoelastic properties of short-fibre-reinforced thermoplastics. Compos. Sci. Technol. 59, 911–923 (1999) CrossRefGoogle Scholar
  32. Mori, T., Tanaka, K.: Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. 21, 571–574 (1973) CrossRefGoogle Scholar
  33. 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
  34. Nouri, H., Meraghni, F., Lory, P.: Fatigue damage model for injection-molded short glass fibre reinforced thermoplastics. Int. J. Fatigue 31, 934–942 (2009) CrossRefGoogle Scholar
  35. Ostwald, W.: Ueber die Geschwindigkeitsfunktion der Viskosität disperser Systeme. I. Kolloid-Z. 36, 99–117 (1925) CrossRefGoogle Scholar
  36. 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
  37. Régnier, G., Dray, D., Gilormini, P.: Assessment of the thermoelastic properties of an injection molded short-fiber composite: experimental and modelling. Int. J. Mater. Forming 1, 787–790 (2008) CrossRefGoogle Scholar
  38. Rémond, Y.: Constitutive modelling of viscoelastic unloading of short glass fibre-reinforced polyethylene. Compos. Sci. Technol. 65, 421–428 (2005) CrossRefGoogle Scholar
  39. Santharam, P., Parenteau, T., Charrier, P., Taveau, D., Le Saux, V., Marco, Y.: Complex fibers orientation distribution evaluation in short glass fiber-reinforced thermoplastic (PA66 GF50). MATEC Web Conf. 165, 22026 (2018) CrossRefGoogle Scholar
  40. Serrano, L., Marco, Y., Le Saux, V., Robert, G., Charrier, P.: Fast prediction of the fatigue behavior of short fiber reinforced thermoplastics from heat build-up measurements. Proc. Eng. 66, 737–745 (2013) CrossRefGoogle Scholar
  41. 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) MathSciNetCrossRefGoogle Scholar
  42. Tandon, S., Weng, G.: The effect of aspect ratio of inclusions on the elastic properties of unidirectionally aligned composites. Polym. Compos. 5(4), 327–333 (1984) CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2020

Authors and Affiliations

  1. 1.ENSTA Bretagne, UMR CNRS 6027IRDLBrestFrance
  2. 2.Safran CompositesIttevilleFrance
  3. 3.Safran Landing systemsVélizyFrance

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