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Moisture transport in PA6 and its influence on the mechanical properties

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Abstract

Various studies have reported the changes in the mechanical properties and the modification in morphology of polyamide due to the absorption of water. However, the relation between the local water content and the alteration in the properties has not been consolidated in a coupled model yet. In the current work, a simulation model is proposed that can capture the diffusion of water as well as simulate the effect of the local moisture content on the stiffness of polyamide (PA6). To this end, a finite element model was developed by coupling of a nonlinear diffusion model and a viscoelastic material model. The Galerkin finite element method was used to formulate the weak form of the equations for the two physical processes. The coupled nonlinear equations were solved with the help of the Newton method. The diffusion process was studied experimentally with the help of gravimetric measurements. Relaxation tests were conducted on the polyamide specimens that were saturated under different moisture levels. Based on these experimental results, the dependency of the material parameters on the local moisture content was identified and an efficient and stable numerical simulation model has been developed.

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References

  1. Abacha, N., Kubouchi, M., Sakai, T.: Diffusion behavior of water in polyamide 6 organoclay nanocomposites. Express Polym. Lett. 3(4), 245–255 (2009)

    Article  Google Scholar 

  2. Alfrey, T., Gurnee, E.F., Lloyd, W.G.: Diffusion in glassy polymers. J. Polym. Sci. Polym. Symp. 12, 249–261 (1966)

    Article  Google Scholar 

  3. Arhant, M., Gac, P.L., Gall, M.L., Burtin, C., Briançon, C., Davies, P.: Modelling the non fickian water absorption in polyamide 6. Polym. Degrad. Stabil. 133, 404–412 (2016)

    Article  Google Scholar 

  4. Arndt, D., Bangerth, W., Davydov, D., Heister, T., Heltai, L., Kronbichler, M., Maier, M., Pelteret, J.P., Turcksin, B., Wells, D.: The deal. ii library, version 8.5. J. Numer. Math. 25(3), 137–145 (2017)

    Article  MathSciNet  Google Scholar 

  5. Bailakanavar, M., Fish, J., Aitharaju, V., Rodgers, W.: Computational coupling of moisture diffusion and mechanical deformation in polymer matrix composites. Int. J. Numer. Methods Eng. 98(12), 859–880 (2014)

    Article  MathSciNet  Google Scholar 

  6. Bangerth, W., Hartmann, R., Kanschat, G.: deal.II—a general purpose object oriented finite element library. ACM Trans. Math. Softw. 33(4), 24–27 (2007)

    Article  MathSciNet  Google Scholar 

  7. Becker, F.: Entwicklung einer beschreibungsmethodik für das mechanische verhalten unverstärkter thermoplaste bei hohen deformationsgeschwindigkeiten. Ph.D. thesis (2009)

  8. Boukal, I.: Effect of water on the mechanism of deformation of nylon 6. J. Appl. Polym. Sci. 11(8), 1483–1494 (1967)

    Article  Google Scholar 

  9. Buchdahl, R., Zaukelies, D.A.: Deformationsprozesse und die struktur von kristallinen polymeren. Angewandte Chemie 74(15), 569–573 (1962)

    Article  Google Scholar 

  10. Carrascal, I., Casado, J.A., Polanco, J.A., Gutiérrez-Solana, F.: Absorption and diffusion of humidity in fiberglass-reinforced polyamide. Polym. Compos. 26(5), 580–586 (2005)

    Article  Google Scholar 

  11. Crank, J.: The Mathematics of Diffusion. Oxford University Press, Oxford (1979)

    MATH  Google Scholar 

  12. Crank, J., Nicolson, P.: A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. In: Mathematical Proceedings of the Cambridge Philosophical Society, vol. 43, pp. 50–67. Cambridge University Press (1947)

  13. Diebels, S., Scheffer, T., Schuster, T., Wewior, A.: Identifying elastic and viscoelastic material parameters by means of a tikhonov regularization. Math. Problems Eng. (2018). https://doi.org/10.1155/2018/1895208

  14. Dunwoody, N.T.: A thermomechanical theory of diffusion in solid–fluid mixtures. Arch. Ration. Mech. Anal. 38(5), 348–371 (1970)

    Article  MathSciNet  Google Scholar 

  15. Engelhard, M., Lion, A.: Modelling the hydrothermomechanical properties of polymers close to glass transition. ZAMM J. Appl. Math. Mech. 93(2–3), 102–112 (2013)

    Article  MathSciNet  Google Scholar 

  16. Engl, H.W., Hanke, M., Neubauer, A.: Regularization of Inverse Problems, vol. 375. Springer, Berlin (1996)

    Book  Google Scholar 

  17. Flory, P.J.: Thermodynamics of high polymer solutions. J. Chem. Phys. 10(1), 51–61 (1942)

    Article  ADS  Google Scholar 

  18. Goldschmidt, F., Diebels, S.: Modelling and numerical investigations of the mechanical behavior of polyurethane under the influence of moisture. Arch. Appl. Mech. 85(8), 1035–1042 (2015)

    Article  ADS  Google Scholar 

  19. Hedenqvist, M., Gedde, U.: Parameters affecting the determination of transport kinetics data in highly swelling polymers above Tg. Polymer 40(9), 2381–2393 (1999). https://doi.org/10.1016/S0032-3861(98)00453-4

    Article  Google Scholar 

  20. Hong, W., Zhao, X., Zhou, J., Suo, Z.: A theory of coupled diffusion and large deformation in polymeric gels. J. Mech. Phys. Solids 56(5), 1779–1793 (2008)

    Article  ADS  Google Scholar 

  21. Huggins, M.L.: Solutions of long chain compounds. J. Chem. Phys. 9(5), 440–440 (1941)

    Article  ADS  Google Scholar 

  22. Joannès, S., Mazé, L., Bunsell, A.R.: A concentration-dependent diffusion coefficient model for water sorption in composite. Compos. Struct. 108, 111–118 (2014)

    Article  Google Scholar 

  23. Joannès, S., Mazé, L., Bunsell, A.R.: A simple method for modeling the concentration-dependent water sorption in reinforced polymeric materials. Compos. Part B Eng. 57, 219–227 (2014)

    Article  Google Scholar 

  24. Johlitz, M., Lion, A.: Chemo-thermomechanical ageing of elastomers based on multiphase continuum mechanics. Contin. Mech. Thermodyn. 25(5), 605–624 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  25. Khanna, Y.P., Kuhn, W.P., Sichina, W.J.: Reliable measurements of the nylon 6 glass transition made possible by the new dynamic dsc. Macromolecules 28(8), 2644–2646 (1995)

    Article  ADS  Google Scholar 

  26. Klepach, D., Zohdi, T.I.: Strain assisted diffusion: modeling and simulation of deformation-dependent diffusion in composite media. Compos. Part B Eng. 56, 413–423 (2014)

    Article  Google Scholar 

  27. Launay, A., Maitournam, M.H., Marco, Y., Raoult, I., Szmytka, F.: Cyclic behaviour of short glass fibre reinforced polyamide: experimental study and constitutive equations. Int. J. Plast. 27(8), 1267–1293 (2011)

    Article  Google Scholar 

  28. Monson, L., Braunwarth, M., Extrand, C.W.: Moisture absorption by various polyamides and their associated dimensional changes. J. Appl. Polym. Sci. 107(1), 355–363 (2008)

    Article  Google Scholar 

  29. Müller, I.: A thermodynamic theory of mixtures of fluids. Arch. Ration. Mech. Anal. 28(1), 1–39 (1968)

    Article  MathSciNet  Google Scholar 

  30. Nagamatsu, K.: On the viscoelastic properties of crystalline high polymers. Kolloid-Zeitschrift 172(2), 141 (1960)

    Article  Google Scholar 

  31. Nelder, J.A., Mead, R.: A simplex method for function minimization. Comput. J. 7(4), 308–313 (1965)

    Article  MathSciNet  Google Scholar 

  32. Picard, E., Gérard, J.F., Espuche, E.: Water transport properties of polyamide 6 based nanocomposites prepared by melt blending: on the importance of the clay dispersion state on the water transport properties at high water activity. J. Membr. Sci. 313(1–2), 284–295 (2008)

    Article  Google Scholar 

  33. Preda, F., Alegría, A., Bocahut, A., Fillot, L., Long, D., Sotta, P.: Investigation of water diffusion mechanisms in relation to polymer relaxations in polyamides. Macromolecules 48(16), 5730–5741 (2015)

    Article  ADS  Google Scholar 

  34. Puffr, R., Šebenda, J.: On the structure and properties of polyamides. xxvii. The mechanism of water sorption in polyamides. J. Polym. Sci. Polym. Symp. 16, 79–93 (1967)

    Article  Google Scholar 

  35. Reimschuessel, H.K.: Relationships on the effect of water on glass transition temperature and young’s modulus of nylon 6. J. Polym. Sci. Part A Polym. Chem. 16(6), 1229–1236 (1978)

    Article  ADS  Google Scholar 

  36. Scheffer, T., Seibert, H., Diebels, S.: Optimisation of a pretreatment method to reach the basic elasticity of filled rubber materials. Arch. Appl. Mech. 83(11), 1659–1678 (2013)

    Article  ADS  Google Scholar 

  37. Steinbrecher, G., Cohen, B., Altus, E.: Hygromechanical coupling in laminate composites and its effect on interlaminar failure. Compos. Part A Appl. Sci. Manuf. 84, 123–133 (2016)

    Article  Google Scholar 

  38. Starkweather Jr., H.W.: Some aspects of water clusters in polymers. Macromolecules 8(4), 476–479 (1975)

    Article  ADS  Google Scholar 

  39. Stommel, M., Naumann, T.: Simulation of the long term behaviour of plastics components. Macromol. Symp. 311, 92–97 (2012)

    Article  Google Scholar 

  40. Taktak, R., Guermazi, N., Derbeli, J., Haddar, N.: Effect of hygrothermal aging on the mechanical properties and ductile fracture of polyamide 6: experimental and numerical approaches. Eng. Fract. Mech. 148, 122–133 (2015)

    Article  Google Scholar 

  41. Tikhonov, A., Goncharsky, A., Stepanov, V., Yagola, A.: Numerical Methods for the Solution of Ill-Posed Problems, vol. 328. Springer, Berlin (2013)

    MATH  Google Scholar 

  42. Truesdell, C., Toupin, R.: The classical field theories. In: Flügge, S. (ed.) Principles of Classical Mechanics and Field Theory, vol. 2, pp. 226–858. Springer, Berlin (1960)

    Google Scholar 

  43. Wilmers, J., Bargmann, S.: A continuum mechanical model for the description of solvent induced swelling in polymeric glasses: thermomechanics coupled with diffusion. Eur. J. Mech. A Solids 53, 10–18 (2015)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors are grateful for the financial support provided by the German Science Foundation (DFG) under Project numbers Di 430/29-01, He 7079/5-01 and Sto 910/10-01.

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Correspondence to P. Sharma.

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Communicated by Michael Johlitz, Lucien Laiarinandrasana,Yann Marco.

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Sharma, P., Sambale, A., Stommel, M. et al. Moisture transport in PA6 and its influence on the mechanical properties. Continuum Mech. Thermodyn. 32, 307–325 (2020). https://doi.org/10.1007/s00161-019-00815-w

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