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Licensed Unlicensed Requires Authentication Published by De Gruyter September 15, 2021

Model Approach for Displaying Dynamic Filament Displacement during Impregnation of Continuous Fibres Based on the Theory of Similarity – Theory and Modelling

  • F. Schulte-Hubbert , D. Drummer and L. Hoffmann

Abstract

The underlying process for the production of textile reinforced thermoplastics is the impregnation of dry textile reinforcements with a thermoplastic matrix. The process parameters such as temperature, time and pressure of the impregnation are mainly determined by the permeability of the reinforcement. This results from a complex interaction of hydrodynamic compaction and relaxation behavior caused by textile and process parameters. The foundation for the description and optimization of impregnation progresses is therefore the determination of the pressure-dependent permeability of fibre textiles. Previous experimental investigations have shown that the dynamic compaction behavior during the impregnation of fibre reinforcements with thermoplastics or thermosets can be successfully characterized. However, for most cases, an analytical representation has not been possible due to the complexity of the process. Although it may be possible to reproduce this behavior by numerical calculations, the results need to be confirmed by experiments. This paper lays the analytical foundation for building a scaled model system, based on the theory of similarity, to observe, measure, and evaluate the dynamic compaction behavior of textile reinforcements under controlled process conditions.

References

Ahn, S. H., Lee, Woo, I. and Springer, G. S., "Measurement of the Three-Dimensional Permeability of Fiber Preforms Using Embedded Fiber Optic Sensors", J. Compos. Mater., 29, 714–733 (1995), DOI:10.1177/00219983950290060210.1177/002199839502900602Search in Google Scholar

AVK Industrievereinigung Verstärkte Kunststoffe e. V. (Ed.): Handbuch Faserverbundkunststoffe/Composites. Grundlagen, Verarbeitung, Anwendung, Springer, Berlin, Heidelberg (2014)Search in Google Scholar

Ballata, W. O., Walsh, S. M. and Advani, S., "Determination of the Transverse Permeability of a Fiber Preform", J. Reinf. Plast. Compos., 18, 1450–1464 (1999), DOI:10.1177/07316844990180160110.1177/073168449901801601Search in Google Scholar

Bear, J.: Dynamics of Fluids in Porous Media, American Elsevier, New York (1972)Search in Google Scholar

Becker, D., "Transversales Imprägnierverhalten textiler Verstärkungsstrukturen für Faser-Kunststoff-Verbunde", PhD Thesis, Institut für Verbundwerkstoffe GmbH, TU Kaiserslautern, Kaiserslautern (2015)Search in Google Scholar

Bühler, V. A., "Gradual Impregnation during the Production of Thermoplastic Composites", PhD Thesis, Lehrstuhl für Carbon Composites Technische Universität München, Munich (2017)Search in Google Scholar

Chen, B., Cheng, A. H.-D. and Chou, T.-W., "A Nonlinear Compaction Model for Fibrous Preforms", Composites Part A, 32, 701–707 (2001), DOI:10.1016/S1359-835X(00)00148-210.1016/S1359-835X(00)00148-2Search in Google Scholar

Christmann, M., "Optimierung der Organoblechherstellung durch 2D-Imprägnierung", PhD Thesis, Institut für Verbundwerkstoffe GmbH, TU Kaiserslautern, Kaiserslautern (2014)Search in Google Scholar

Darcy, H.: Les Fontaines Publiques de la Ville de Dijon: Exposition et Application des Principes à Suivre et des Formules à Employer dans les Questions de Distribution d’Eau. . ., Henry Darcy. Paris (1856)Search in Google Scholar

Dullien, F. A. L., "Single Phase Flow through Porous Media and Pore Structure", Chem. Eng. J., 10, 1–34 (1975), DOI:10.1016/0300-9467(75)88013-010.1016/0300-9467(75)88013-0Search in Google Scholar

Gibson, A. G., Månson, J.-A., "Impregnation Technology for Thermoplastic Matrix Composites", Compos. Manuf., 3, 223–233 (1992), DOI:10.1016/0956-7143(92)90110-G10.1016/0956-7143(92)90110-GSearch in Google Scholar

Grieser, T., Mitschang, P., "Investigation of the Compaction Behavior of Carbon Fiber NCF for Continuous Preforming Processes", Polym. Compos., 38, 2609–2625 (2017), DOI:10.1002/pc.2385410.1002/pc.23854Search in Google Scholar

Grote, K.-H., Feldhusen, J., "Chapter 7 Ähnlichkeitsmechanik", in Dubbel – Taschenbuch für den Maschinenbau, 23rd Edition, Springer, Berlin Heidelberg, B65-B68 (2011), DOI:10.1007/978-3-642-17306-610.1007/978-3-642-17306-6Search in Google Scholar

Gutowski, T. G., Cai, Z., Bauer, S., Boucher, D., Kingery, J. and Wineman, S., "Consolidation Experiments for Laminate Composites", J. Compos. Mater., 21, 650–669 (1987), DOI:10.1177/00219983870210070510.1177/002199838702100705Search in Google Scholar

Jespersen, S. T., Wakeman, M. D., Michaud, V., Cramer, D. and Månson, J.-A. E., "Film Stacking Impregnation Model for a Novel Net Shape Thermoplastic Composite Preforming Process", Compos. Sci. Technol., 68, 1822–1830 (2008), 10.1016/j.compscitech.2008.01.019Search in Google Scholar

Karaki, M., Hallal, A., Younes, R., Trochu, F., Lafon, P. and Hayek, A., Kobeissy, A. and Fayad, A., "A Comparative Analytical, Numerical and Experimental Analysis of the Micoscopic Permeability of Fiber Bundles in Composite Materials", Int. J. Compos. Mater. (V3–7), 82–102 (2017), DOI:10.5923/j.cmaterials.20170703.0210.5923/j.cmaterials.20170703.02Search in Google Scholar

Karaki, M., Younes, R., Trochu, F. and Lafon, P., "Progress in Experimental and Theoretical Evaluation Methods for Textile Permeability", J. Compos. Sci., 3, 73 (2019), DOI:10.3390/jcs303007310.3390/jcs3030073Search in Google Scholar

Kögl, B., Moser, F., "Chapter 5 Ähnlichkeitstheorie", in Grundlagen der Verfahrenstechnik, Springer, Vienna, p. 120–178 (1981), DOI:10.1007/978-3-7091-2270-9_510.1007/978-3-7091-2270-9_5Search in Google Scholar

Loendersloot, R., Grouve, W. J. B., Akkerman, R. and van den Berg, S., "Permeability Prediction Using a Multigrid Method", 9th International Conference on Flow Processes in Composite Materials, Montreal, Canada (2008)Search in Google Scholar

Loendersloot, R., Grouve, W. J. B., Lamers, E. A. D. and Wijskamp, S., "Textile Impregnation with Thermoplastic Resin – Models and Application", 11th International Conference on Flow Processes in Composite Materials, Auckland, New Zealand, p. 344–351 (2012)Search in Google Scholar

Mayer, C., "Prozessanalyse und Modellbildung zur Herstellung gewebeverstärkter, thermoplastischer Halbzeuge", PhD Thesis, Institut für Verbundwerkstoffe GmbH, Maschinenbau und Verfahrenstechnik, TU Kaiserslautern, Kaiserslautern (2000)Search in Google Scholar

Meier, R., Walbran, A., Hahn, C., Zaremba, S. and Drechsler, K., "Methoden zur Bestimmung der Permeabilität von Verstärkungstextilien", Kunststofftechnik, 4, 90–116 (2014)Search in Google Scholar

Michaud, V., Månson, J.-A. E., "Impregnation of Compressible Fiber Mats with a Thermoplastic Resin. Part I: Theory", J. Compos. Mater., 35, 1150–1173 (2001), DOI:10.1106/8108-1VMC-B4FG-FXPU10.1106/8108-1VMC-B4FG-FXPUSearch in Google Scholar

Neitzel, M.: Handbuch Verbundwerkstoffe. Werkstoffe, Verarbeitung, Anwendung, 2nd Edition, Hanser, Munich (2014), DOI:10.3139/9783446436978.fm10.3139/9783446436978.fmSearch in Google Scholar

Rieber, G., "Einfluss von textilen Parametern auf die Permeabilität von Multifilamentgeweben für Faserverbundkunststoffe", PhD Thesis, Institut für Verbundwerkstoffe GmbH, TU Kaiserslautern, Kaiserslautern (2014)Search in Google Scholar

Sandmaier, H.: Skalierung der physikalischen Gesetze und mathematischen Modellierung, Springer, Berlin, Heidelberg (2019), DOI:10.1007/978-3-662-59673-910.1007/978-3-662-59673-9Search in Google Scholar

Shojaei, A., Trochu, F., Ghaffarian, S. R., Karimian, S. M. H. and Lessard, L., "An Experimental Study of Saturated and Unsaturated Permeabilities in Resin Transfer Molding Based on Unidirectional Flow Measurements", J. Reinf. Plast. Compos., 23, 1515–1536 (2004), DOI:10.1177/073168440403978710.1177/0731684404039787Search in Google Scholar

Stadtfeld, H. C., "Entwicklung einer Messzelle zur Bestimmung von Kompaktierungs- und Permeabilitätskennwerten bei flächigen Faserhalbzeugen", PhD Thesis, Institut für Verbundwerkstoffe GmbH, TU Kaiserslautern, Kaiserslautern (2006)Search in Google Scholar

Stöven, T., Weyrauch, F., Mitschang, P. and Neitzel, M., "Continuous Monitoring of Three-Dimensional Resin Flow through a Fibre Preform", Composites Part A, 34, 475–480 (2003), DOI:10.1016/S1359-835X(03)00059-910.1016/S1359-835X(03)00059-9Search in Google Scholar

Terzaghi, K., Peck, R. B.: Soil Mechanics in Engineering Practice, Read Books, Alcester, UK (2010)Search in Google Scholar

Toll, S., "Packing Mechanics of Fiber Reinforcements", Polym. Eng. Sci., 38, 1337–1350 (1998), DOI:10.1002/pen.1030410.1002/pen.10304Search in Google Scholar

Appendix

Equations commonly used in the literature to calculate the permeability of fibre textiles:

(18)  Kozeny  Carman: KKozeny=r24kΦ3(1Φ)2,

with k: Kozeny-Konstante (empirically determine), U: porosity.

(19)  Gutowski:  K Gutowski  = r f 2 4 k V f m a x , G u t o w s k i v f 1 3 v fmax  , G u t o w s k i v f + 1 ,

with λ0: constant (0,2), vfmax : 0,76 • • • 0,82.

(20)  Gebart KGebart =C1(Vmaxvf1)52r2,

with Vfmax=π4 and C1=169π2, for square fibre arrangement, Vfmax=π23 und C1=169π6, for hexagonal fibre arrange-Berdichevsky and Chai

(21) K=0,229r2(1,814va1)((1vfva)vfva)2,5,

with va = 0, 7854, for square fibre arrangement,

va = 0, 9069, for hexagonal fibre arrangement.

(22)  Kuwabara K=r28Vf(ln1VfVf21Vf2+1),

for random fibre arrangements.

(23)  Lee and Yang K=4r2(1Vf)3(0,7854Vf)31Vf1,3,

considered a non-Darcy flow through a porous medium.

Received: 2020-08-12
Accepted: 2021-02-16
Published Online: 2021-09-15
Published in Print: 2021-09-27

© 2021 Walter de Gruyter GmbH, Berlin/Boston, Germany

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