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Simulation of curing-induced viscoplastic deformation: a new approach considering chemo-thermomechanical coupling

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Abstract

A modelling and simulation approach for plastic deformation effects in curing resins is presented. For this purpose known rheological models of viscoelasticity and viscoplasticity are combined and a thermochemical element is added to account for chemical shrinkage and thermal expansion. The degree of cure of the resin has a major influence on the behaviour of the curing material, and therefore, the material model is formulated depending on the degree of cure. It affects the viscoelastic behaviour as well as the chemical shrinkage and the yield function of the viscoplastic part of the model. For the yield function a von Mises approach with isotropic hardening is chosen, where the initial yield stress as well as the yield surface depends on the degree of cure and the temperature.

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References

  1. Adolf D.B., Martin J.E.: Time-cure superposition during crosslinking. Macromolecules 23, 3700–3704 (1990)

    Article  Google Scholar 

  2. Adolf D.B., Martin J.E.: Calculating of stresses in crosslinking polymers. J. Compos. Mater. 30(1), 13–34 (1996)

    Article  Google Scholar 

  3. Adolf D.B., Chambers R.S.: A thermodynamically consistent, nonlinear viscoelastic approach for modelling thermosets during cure. J. Rheol. 51, 23–50 (2007)

    Article  Google Scholar 

  4. Blumenstock, T.: Analyse der Eigenspannungen während der Aushärtung von Epoxidharzmassen. Dissertation, University of Stuttgart (2003)

  5. Boey F.Y.C., Qiang B.: Experimental modeling of the cure kinetics of an epoxy-hexaanhydro-4-methylphtalicanhydride (MHHPA) system. Polymer 41, 2081–2094 (2000)

    Article  Google Scholar 

  6. Ehlers W., Ellsiepen P.: PANDAS: Ein FE-System zur Simulation von Sonderproblemen der Bodenmechanik. In: Wriggers, P., Meißner, U., Stein, E., Wunderlich, W. (eds) Finite Elemente in der Baupraxis: Modellierung, pp. 391–400. Berechnung und Konstruktion, Ernst & Sohn (1998)

    Google Scholar 

  7. Ellsiepen P.: PANDAS user manual. Institut für Mechanik. Lehrstuhl II—Prof. Dr.-Ing. W. Ehlers . Universität Stuttgart, Stuttgart (2001)

    Google Scholar 

  8. Enns J.B., Gillham J.K.: Time-temperature-transformation cure diagram: modeling the cure behavior of thermosets. J. Appl. Polym. Sci. 28, 2567–2591 (1983)

    Article  Google Scholar 

  9. Flügge W.: Viscoelasticity. Springer, Berlin (1975)

    MATH  Google Scholar 

  10. Fournier J., Williams G., Duch C., Aldridge G.A.: Changes in molecular dynamics during bulk polymerization of an epoxide-amine system as studied by dielectric relaxation spectroscopy. Macromolecules 29, 7097–7107 (1996)

    Article  Google Scholar 

  11. Hahn, O., Jendrny, J., Figge, V.: Einfluss des Fertigungsprozesses auf die Verbindungseigenschaften geklebter Hybridstrukturen. Tagungsband des 1. Berichtskolloquiums der DFG-Forschergruppe “Hochleistungsfügetechnik für Hybridstrukturen”, Hannover, pp. 64–73

  12. Halley P.J., Mackay E.: Chemorheology of thermosets—an overview. Polym. Eng. Sci. 36(5), 593–609 (1996)

    Article  Google Scholar 

  13. Harsch, M.: Methoden und Ansätze zur spannungsarmen Vernetzung von Epoxidharzen. In: IVW-Schriftenreihe, vol. 76, pp. 150 (2008)

  14. Haupt P.: Continuum Mechanics and Theory of Materials. Springer, Berlin (1999)

    Google Scholar 

  15. Hossain M., Possart G., Steinmann P.: A small-strain model to simulate the curing of thermosets. Comput. Mech. 43, 769–779 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Hossain M., Possart G., Steinmann P.: A finite strain framework for the simulation of polymer curing. Part I:. Elasticity. Comput. Mech. 44, 621–630 (2009)

    MathSciNet  MATH  Google Scholar 

  17. Hossain M., Possart G., Steinmann P.: A finite strain framework for the simulation of polymer curing. Part II: Viscoelasticity and shrinkage. Comput. Mech. 46, 363–375 (2010)

    Article  MATH  Google Scholar 

  18. Jendrny, J.: Entwicklung von Berechnungsmodellen zur Abschätzung der Verformung geklebter dünnwandiger Stahlbauteile in Leichtbaukonstruktionen während der Warmaushärtung. Schriftenreihe P513 der Forschungsvereinigung Stahlanwendung e.V., Düsseldorf (2004)

  19. Kamal M.R.: Thermoset characterization for moldability analysis. Polym. Eng. Sci. 14, 231–239 (1974)

    Article  Google Scholar 

  20. Kiasat, M.S.: Curing shrinkage and residual stress in viscoelastic thermosetting resins and composites. Dissertation, Delft University of Technology (2000)

  21. Kolmeder S., Lion A.: On the thermomechanical-chemically coupled behavior of acrylic bone cements: Experimental characterization of material behavior and modeling approach. Tech. Mech. 30(1–3), 195–202 (2010)

    Google Scholar 

  22. Lion A., Höfer P.: On the phenomenological representation of curing phenomena in continuum mechanics. Arch. Mech. 59, 59–89 (2007)

    MATH  Google Scholar 

  23. Lührs, G.: Randwertaufgaben der Viskoplastizität—Modellierung, Simulation und Vergleich mit experimentellen Daten aus zyklischen Prozessen und Umformvorgängen. Dissertation, University of Kassel (1997)

  24. Mahnken R., Schlimmer M.: Simulation of strength difference in elasto-plasticity for adhesive materials. Int. J. Numer. Methods Eng. 63, 1461–1477 (2005)

    Article  MATH  Google Scholar 

  25. MatLab User Manual. Online documentation http://www.mathworks.com/help/ (2011)

  26. Matzenmiller, A., Schlimmer, M., Mahnken, R., Hahn, O., Dilger, K., Gumbsch, P., Thoma, K., Hennemann, O.-D.: Methodenentwicklung zur Berechnung von höherfestigen Stahlklebverbindungen des Fahrzeugbaus unter Crashbelastung. Abschlussbericht zum AiF/FOSTA ZUTECH-Forschungsprojekt P676, Forschungsvereinigung Stahlanwendung e.V., Düsseldorf (2008)

  27. Retka, J., Höfer, P.: Numerische Simulation aushärtender Klebstoffe. Tech. Rep., Universität der Bundeswehr München (2007)

  28. Schlimmer, M., Hahn, O., Hennemann, O.-D.: Methodenentwicklung zur Berechnung und Auslegung geklebter Stahlbauteile für den Fahrzeugbau. Abschlussbericht zum AiF/FOSTA ZUTECH-Forschungsprojekt 76 ZN, Forschungsvereinigung Stahlanwendung e.V., Düsseldorf (2004)

  29. Schwarzl F.R.: Polymermechanik—Struktur und mechanisches Verhalten von Polymeren. Springer, Berlin (1990)

    Google Scholar 

  30. Sourour S., Kamal M.R.: Differential scanning calorimetry of epoxy cure: isothermal cure kinetics. Thermochim. Acta 14, 41–59 (1976)

    Article  Google Scholar 

  31. Tobolsky A.: Mechanische Eigenschaften und Struktur von Polymeren. Berliner Union, Stuttgart (1967)

    Google Scholar 

  32. White S.R., Hahn H.T.: Process modelling of composite materials: residual stress development during cure. J. Compos. Mater. 26, 2402–2453 (1992)

    Article  Google Scholar 

  33. Yagimli B., Lion A.: Modelling and simulation of curing processes of epoxy resin. PAMM 9, 325–326 (2010)

    Article  Google Scholar 

  34. Yagimli B., Lion A.: Experimental investigations and material modelling of curing processes under small deformations. ZAMM 91, 342–359 (2011)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Faculty for Aerospace Engineering, Institute of Mechanics, Universität der Bundeswehr München, Munich, Germany

    Christoph Liebl, Michael Johlitz, Bülent Yagimli & Alexander Lion

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  1. Christoph Liebl
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  2. Michael Johlitz
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  3. Bülent Yagimli
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  4. Alexander Lion
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Correspondence to Christoph Liebl.

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Liebl, C., Johlitz, M., Yagimli, B. et al. Simulation of curing-induced viscoplastic deformation: a new approach considering chemo-thermomechanical coupling. Arch Appl Mech 82, 1133–1144 (2012). https://doi.org/10.1007/s00419-012-0639-z

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  • DOI: https://doi.org/10.1007/s00419-012-0639-z

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