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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


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.


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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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