Characterization and Modeling of the Time- and Temperature-Dependent Behavior of a Closed-Cell Polymer Structural Foam under Compression
Source abstract
Abstract
Abstract The thermo-viscoelastic behavior of a closed-cell polyethylene terephthalate (PET) structural foam is investigated in order to accurately capture foam core deformations during manufacturing of composite sandwich structures, e.g. in Liquid Composite Molding (LCM), and their influence on the structural performance of the final components. The foam exhibits a transversely isotropic material behavior due to its manufacturing in the strand foam extrusion process. Compression tests are carried out in Dynamic Mechanical Analysis (DMA), where the heterogenous foam structure poses some difficulties in finding a valid measuring range and adequate parameter sets compared to a homogenous material. Therefore, close care is taken to select the right load range and sample size. In this way, the time- and temperature-dependency of the homogenized macroscopic material behavior of the structural foam is received. From the measured data, master curves are constructed using the time-temperature superposition principle and a temperature- and time-dependent prony series is fitted to the data. A non-isothermal modeling approach is proposed to capture the stiffness changes due to heating during the manufacturing process. The model is integrated into an open-source finite element framework and the underlying behavior is verified against a commercially available finite element model. The results show that the proposed model is able to accurately capture the thermoviscoelastic behavior of the foam under non-isothermal conditions.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Polymer Foaming and Composites · Cellular and Composite Structures · Polymer crystallization and properties
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (49)
Show source-provided references
1. Taghavian, S.H., Ghasemi, A.R.: The effect of manufacturing methods on the interface debonding and flexural behavior of sandwich structures: Thermography approach and three-point-bending Experiments. Polym. Compos. 43(9), 6332–6343 (2022). https://doi.org/10.1002/pc.2694210.1002/pc.26942 ↗
2. Ahmadi, R., Wirawan, R., Judawisasastra, H.: Evaluation of facings and sandwich properties of carbon fiber/epoxy-PVC foam sandwich composites: Comparison of VARI co-cure and precure manufacturing methods. J. Sandwich Struct. Mater. 10996362241312871 (2025). https://doi.org/10.1177/1099636224131287110.1177/10996362241312871 ↗
3. Fischer Kerche, E., Silveira Caldas, B.G., Carvalho, R.F., Amico, S.C.: Mechanical response of sisal/glass fabrics reinforced polyester – polyethylene terephthalate foam core sandwich panels. J. Sandwich Struct. Mater. 24(6), 1993–2009 (2022). https://doi.org/10.1177/1099636222111505710.1177/10996362221115057 ↗
4. Al-Hamdan, A., Rudd, C.D., Long, A.C.: Dynamic core movements during liquid moulding of sandwich structures. Compos. A Appl. Sci. Manuf. 29(3), 273–282 (1998). https://doi.org/10.1016/S1359-835X(97)00082-110.1016/S1359-835X(97)00082-1 ↗
5. Nedanov, P., Advani, S.G.: Mold filling simulation of sandwich composite structures manufactured by liquid molding: A parametric study. J. Sandwich Struct. Mater. 2(2), 117–130 (2000). https://doi.org/10.1177/10996362000020020210.1177/109963620000200202 ↗
6. Dietrich, S., Seuffert, J., Kärger, L.: Numerical investigation of the mold filling behavior of sandwich parts in resin transfer molding. In: Proceedings of the 23rd International Conference on Composite Materials (ICCM 2023) (2023). https://zenodo.org/records/15316800/files/ICCM23_Full_Paper_170.pdf
7. Seuffert, J.: Mold-filling simulation of resin transfer molding with fluid-structure interaction, Doctoral Thesis, Karlsruher Institut für Technologie (KIT). Karlsruhe (2022) https://doi.org/10.5445/IR/100014439310.5445/IR/1000144393 ↗
8. Viot, P.: Hydrostatic compression on polypropylene foam. Int. J. Impact Eng 36(7), 975–989 (2009). https://doi.org/10.1016/j.ijimpeng.2008.11.01010.1016/j.ijimpeng.2008.11.010 ↗
9. Fathi, A.: Mechanical properties of strand PET foams at different length scales, Universität Bayreuth (2018). https://doi.org/10.15495/EPub_UBT_0000428610.15495/EPub_UBT_00004286 ↗
10. Rezaei, M., Karatzas, V., Berggreen, C., Carlsson, L.A.: The effect of elevated temperature on the mechanical properties and failure modes of GFRP face sheets and PET foam cored sandwich beams. J. Sandwich Struct. Mater. 22(4), 1235–1255 (2020). https://doi.org/10.1177/109963621878199510.1177/1099636218781995 ↗
11. Garrido, M., Correia, J.R., Keller, T.: Effects of elevated temperature on the shear response of PET and PUR foams used in composite sandwich panels. Constr. Build. Mater. 76, 150–157 (2015). https://doi.org/10.1016/j.conbuildmat.2014.11.05310.1016/j.conbuildmat.2014.11.053 ↗
12. Mazzuca, P., Firmo, J.P., Correia, J.R., Castilho, E.: Mechanical behaviour in shear and compression at elevated temperature of Polyethylene Terephthalate (PET) foam. J. Build. Eng. 42, 102526 (2021). https://doi.org/10.1016/j.jobe.2021.10252610.1016/j.jobe.2021.102526 ↗
13. Jebur, Q.H., Harrison, P., Guo, Z., Schubert, G., Ju, X., Navez, V.: Characterisation and modelling of a transversely isotropic melt-extruded low-density polyethylene closed cell foam under uniaxial compression. Proceed. Institut. Mechan. Eng., Part C 226(9), 2168–2177 (2012). https://doi.org/10.1177/095440621143152810.1177/0954406211431528 ↗
14. Salloum, J., Léger, R., Chebbo, H., Daridon, L., Ienny, P.: A New methodology for the mechanical behavior analysis of polyvinyl chloride and recycled polyethylene terephthalate foams: finite element model updating using mechanical field measurements. J. Sandw. Struct. Mater. 26(1), 73–93 (2024). https://doi.org/10.1177/1099636223120320710.1177/10996362231203207 ↗
15. Henriques, I.R., Rouleau, L., Castello, D.A., Borges, L.A., Deü, J.-F.: Viscoelastic behavior of polymeric foams: Experiments and modeling. Mech. Mater. 148, 103506 (2020). https://doi.org/10.1016/j.mechmat.2020.10350610.1016/j.mechmat.2020.103506 ↗
16. Daniel, I.M., Cho, J.-M.: Characterization of anisotropic polymeric foam under static and dynamic loading. Exp. Mech. 51(8), 1395–1403 (2011). https://doi.org/10.1007/s11340-011-9466-310.1007/s11340-011-9466-3 ↗
17. Briody, C., Duignan, B., Jerrams, S., Tiernan, J.: The implementation of a visco-hyperelastic numerical material model for simulating the behaviour of polymer foam materials. Comput. Mater. Sci. 64, 47–51 (2012). https://doi.org/10.1016/j.commatsci.2012.04.01210.1016/j.commatsci.2012.04.012 ↗
18. Santo, L., Bellisario, D., Quadrini, F.: Shape Memory Behavior of PET Foams. Polymers 10(2), 115 (2018). https://doi.org/10.3390/polym1002011510.3390/polym10020115 ↗
19. Dietrich, S., Dohmen, C., Frölich, F., Jackstadt, A., Wittemann, F., Kärger, L.: Investigation of the thermoviscoelastic behavior of a closed‑cell polymer structural foam under pressure for processing in hybrid LCM processes. In: Binetruy C. (Eds) Proceedings of the 21st European Conference on Composite Materials, Vol. 2 Material Science, pp. 548 (2024). https://doi.org/10.5445/IR/1000173753/pub10.5445/IR/1000173753/pub ↗
20. Denay, A.-G., Castagnet, S., Roy, A., Alise, G.: Creep compression behaviour of a polyurethane foam from cryogenic temperatures: Size effect and long-term prediction. EPJ Web Conf 6, 25006 (2010). https://doi.org/10.1051/epjconf/2010062500610.1051/epjconf/20100625006 ↗
21. Boltzmann, L.: Zur Theorie Der Elastischen Nachwirkung. In: Sitzungsberichte Kaiserliche Akademie Wissenschaft Wien Mathematisch-Naturwissenschaftliche Klasse, vol. 70, pp. 275–306 (1874)
22. Klempner, D., Aseeva, R.M., Sendijarevic, V.: Handbook of Polymeric Foams and Foam Technology, 2nd edn. Hanser, Munich (2004). ISBN 978-3-446-21831-4
23. Ramsteiner, F., Fell, N., Forster, S.: Testing the deformation behaviour of polymer foams. Polym. Test. 20(6), 661–670 (2001). https://doi.org/10.1016/S0142-9418(00)00090-810.1016/S0142-9418(00)00090-8 ↗
24. Lakes, R.S.: Viscoelastic Solids (1998), 1st ed., CRC Press Revivals, CRC Press, Boca Raton, FL (2017). https://doi.org/10.1201/978131512136910.1201/9781315121369 ↗
25. Bertram, A. (collab. Glüge, R.).: Solid mechanics: Theory, modeling, and problems. Springer, Cham (2015. https://doi.org/10.1007/978-3-319-19566-7. ISBN 978‑3‑319‑19565‑010.1007/978-3-319-19566-7 ↗
26. Ferry, J.D.: Viscoelastic Properties of Polymers, 3rd edn. John Wiley & Sons, New York (1980). ISBN 0-471-04894-1
27. Schwarzl, F.: Polymermechanik: Struktur Und Mechanisches Verhalten von Polymeren. Springer, Berlin (1990)10.1007/978-3-642-61506-1 ↗
28. Menard, K.P., Menard, N.R.: Dynamic Mechanical Analysis, 3rd ed., CRC Press, Boca Raton (2020). https://doi.org/10.1201/9780429190308. ISBN 978-0-429-19030-810.1201/9780429190308 ↗
29. Ehrenstein, G.W., Riedel, G., Trawiel, P.: Praxis Der Thermischen Analyse von Kunststoffen. Hanser, München (2003). ISBN 3-446-22340-1
30. Rajput, M.S., Burman, M., Köll, J., Hallström, S.: Compression of structural foam materials - experimental and numerical assessment of test procedure and specimen size effects. J. Sandwich Struct. Mater. 21(1), 260–288 (2019). https://doi.org/10.1177/109963621769050010.1177/1099636217690500 ↗
31. 3A Composites Core Materials: AIREX® T92 - Easy Processing Structural Foam: Data Sheet (2020). https://www.3accorematerials.com/uploads/documents/TDS-AIREX-T92-E-01.2020.pdf
32. Boltzmann, L.: Zur Theorie Der Elastischen Nachwirkung. Ann. Phys. 241(11), 430–432 (1878). https://doi.org/10.1002/andp.1878241110710.1002/andp.18782411107 ↗
33. Cole, K.S., Cole, R.H.: Dispersion and absorption in dielectrics I. Alternating current characteristics. J. Chem. Phys. 9(4), 341–351 (1941). https://doi.org/10.1063/1.175090610.1063/1.1750906 ↗
34. Cho, K.S.: Viscoelasticity of polymers: Theory and numerical algorithms. Springer Science+Business Media, Dordrecht (2016). ISBN 978-94-017-7564-9
35. Williams, M.L., Landel, R.F., Ferry, J.D.: The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids. J. Am. Chem. Soc. 77(14), 3701–3707 (1955). https://doi.org/10.1021/ja01619a00810.1021/ja01619a008 ↗
36. Kaliske, M., Rothert, H.: Formulation and implementation of three-dimensional viscoelasticity at small and finite strains. Comput. Mech. 19(3), 228–239 (1997). https://doi.org/10.1007/s00466005017110.1007/s004660050171 ↗
37. Pacheco, J.E.L., Bavastri, C.A., Pereira, J.T.: Viscoelastic relaxation modulus characterization using prony series. Latin Am J Solids Struct 12(2), 420–445 (2015). https://doi.org/10.1590/1679-7825141210.1590/1679-78251412 ↗
38. Barrientos, E., Fernández, F., Noriega, Á., Lamela, M.J., Fernández-Canteli, A., Tanaka, E.: Optimal discrete-time prony series fitting method for viscoelastic materials. Mechan. Time-Depend. Mater. 23(2), 193–206 (2019). https://doi.org/10.1007/s11043-018-9394-z10.1007/s11043-018-9394-z ↗
39. Tobolsky, A.V.: Properties and Structure of Polymers. Wiley, New York (1960)10.1149/1.2427514 ↗
40. Huberth, H., Schirber, H., Schlör, N.: Kunststoffkunde: Aufbau. Eigenschaften, Verarbeitung, Anwendungen Der Thermoplaste, Duroplaste Und Elastomere, Vogel Business Media, Würzburg (2016). ISBN 3-8343-3366-2
41. Broyden, C.G.: The convergence of a class of double-rank minimization algorithms 1. Gen. Consider. IMA J. Appl. Math. 6(1), 76–90 (1970). https://doi.org/10.1093/imamat/6.1.7610.1093/imamat/6.1.76 ↗
42. Goldfarb, D.: A family of variable-metric methods derived by variational means. Math. Comput. 24(109), 23–26 (1970). https://doi.org/10.1090/S0025-5718-1970-0258249-610.1090/S0025-5718-1970-0258249-6 ↗
43. Fletcher, R.: A new approach to variable metric algorithms. Comput. J. 13(3), 317–322 (1970). https://doi.org/10.1093/comjnl/13.3.31710.1093/comjnl/13.3.317 ↗
44. Shanno, D.F.: Conditioning of quasi-Newton methods for function minimization. Math. Comput. 24(111), 647–656 (1970). https://doi.org/10.1090/S0025-5718-1970-0274029-X10.1090/S0025-5718-1970-0274029-X ↗
45. Baumgaertel, M., Winter, H.H.: Determination of discrete relaxation and retardation time spectra from dynamic mechanical data. Rheol. Acta 28, 511–519 (1989)10.1007/BF01332922 ↗
46. Kehrer, L., Keursten, J., Hirschberg, V., Böllke, T.: Dynamic mechanical analysis of PA 6 under hydrothermal influences and viscoelastic material modeling. J. Thermoplast. Compos. Mater. 36(11), 4630–4664 (2023). https://doi.org/10.1177/0892705723115586410.1177/08927057231155864 ↗
47. Flügge, W.: Viscoelasticity, 2nd rev. ed., Springer, Berlin (1975). ISBN 978‑3‑540‑07344‑410.1007/978-3-662-02276-4_2 ↗
48. Kiasat, M.S.: Curing shrinkage and residual stresses in viscoelastic thermosetting resins and composites, Ph.D. thesis, Technische Universiteit Delft, Delft (2000)
49. Dhondt, G.: The finite element method for three-dimensional thermomechanical applications. Wiley, Chichester (2004). ISBN 0-470-85752-810.1002/0470021217 ↗