Published July 5, 2022 | Version v1
Journal article Open

New approach for filling simulations of dual-scale preforms used in the manufacturing of composites materials.

Authors/Creators

  • 1. Institución Universitaria Pascual Bravo

Contributors

  • 1. Universidad de Antioquia

Description

Some fibrous reinforcements used in the manufacturing of parts by Liquid Composite Molding (LCM) have a dual-scale nature, which supposes flow imbalances between the tows and channels at mesoscopic scale, which in turn, cause uncontrolled defects (voids, dry points, among others) and could considerably affect the global flow behavior during the filling of cavities at macroscopic scale. In the present work, a new approach to conduct filling simulations of dual-scale fibrous reinforcements at mesoscopic scale is proposed. This consists of prescribing a pressure gradient along the Representative Unitary Cell, and imposing Stokes-Darcy matching conditions between the tows and the channel sub-domains to determine the filling of the former ones. Contrarily to the traditional approach, where a uniform pressure is assumed for the channels and only the porous media fluid is modeled, the present one allows considering the fluid pressure gradient at channels (fluid motion), air compressibility and dissolution, flow-direction dependent capillary pressure, and vacuum pressure, as well as capturing several phenomena involved in the dynamic evolution of intra-tow voids, namely, compression, mobilization at constant volume and migration from tows towards channel. The velocity vectors and streamlines in the tows and channel subdomains, when these phenomena take place, are analyzed as well.

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References

  • H. Jinlian, L. Yi, and S. Xueming, "Study on void formation in multi-layer woven fabrics," Composites Part A: Applied Science and Manufacturing, vol. 35, no. 5, May., 2004. [Online]. Available: https://doi.org/10.1016/j.compositesa.2003.11.007
  • D. H. Lee, W. I. Lee, and M. K. Kang, "Analysis and minimization of void formation during resin transfer molding process," Composites Science and Technology, vol. 66, no. 16, Dec. 18, 2006. [Online]. Available: https://doi.org/10.1016/j.compscitech.2005.07.008
  • B. Gourichon, C. Binetruy, and P. Krawczak, "A new numerical procedure to predict dynamic void content in liquid composite molding," Composites Part A: Applied Science and Manufacturing, vol. 37, no. 11, Nov., 2006. [Online]. Available: https://doi.org/10. 1016/j.compositesa.2005.12.017
  • K. M. Pillai, "Governing equations for unsaturated flow through woven fiber mats. part 1. isothermal flows," Composites Part A: Applied Science and Manufacturing, vol. 33, no. 7, Jul. 1, 2002. [Online]. Available: https://doi.org/10.1016/S1359-835X(02)00034-9
  • K. M. Pillai and M. S. Munagavalasa, "Governing equations for unsaturated flow through woven fiber mats. part 2. non-isothermal reactive flows," Composites Part A: Applied Science and Manufacturing, vol. 35, no. 4, Apr. 2004. [Online]. Available: https://doi.org/10.1016/j.compositesa.2004.01.001
  • H. Tan and K. M. Pillai, "Multiscale modeling of unsaturated flow of dual-scale fiber preform in liquid composite molding ii: Non-isothermal flows," Composites Part A: Applied Science and Manufacturing, vol. 43, no. 1, Jan. 2012. [Online]. Available: https://doi.org/10.1016/j.compositesa.2011.06.012
  • M. S. Munagavalasa and K. M. Pillai, "An estimation of effective thermal conductivity of a fibrous dual-scale porous medium during unsaturated flow," International Journal of Heat and Mass Transfer, vol. 49, no. 1-2, Jan. 2006. [Online]. Available: https://doi.org/10.1016/j.ijheatmasstransfer.2005.06.020
  • M. S. Munagavalasa, "Theoretical modeling of unsaturated flow in fibrous dual-scale porous media using the volume averaging method," PhD. thesis, Dissertation, College Of Engineering and Applied Science, University of Wisconsin Milwaukee, USA, 2006
  • J. M. Lawrence, V. Neacsu, and S. G. Advani, "Modeling the impact of capillary pressure and air entrapment on fiber tow saturation during resin infusion in LCM," Composites Part A: Applied Science and Manufacturing, vol. 40, no. 8, Aug. 2009. [Online]. Available: https://doi.org/10.1016/j.compositesa.2009.04.013
  • H. Tan, "Simulation of flow in dual-scale porous media," PhD. thesis, Dissertation, College Of Engineering and Applied Science, University of Wisconsin Milwaukee, USA, 2011.
  • P. Simacek and S. G. Advani, "A numerical model to predict fiber tow saturation during liquid composite molding," Composites Science and Technology, vol. 63, no. 12, Sep. 2003. [Online]. Available: https://doi.org/10.1016/S0266-3538(03)00155-6
  • H. Tan and K. M. Pillai, "Multiscale modeling of unsaturated flow in dual-scale fiber preforms of liquid composite molding i: Isothermal flows," Composites Part A: Applied Science and Manufacturing, vol. 43, no. 1, Jan. 2012. [Online]. Available: https://doi.org/10.1016/j.compositesa.2010.12.013
  • P. Simacek and S. G. Advani, "Modeling resin flow and fiber tow saturation induced by distribution media collapse in vartm," Composites Science and Technology, vol. 67, no. 13, Oct. 2007. [Online]. Available: https://doi.org/10.1016/j.compscitech.2007.02.008
  • Y. Wang and S. M. Grove, "Modelling microscopic flow in woven fabric reinforcements and its application in dual-scale resin infusion modelling," Composites Part A: Applied Science and Manufacturing, vol. 39, no. 5, May. 2008. [Online]. Available: https://doi.org/10.1016/j.compositesa.2008.01.014
  • H. Tan and K. M. Pillai, "Modeling Unsaturated Flow in Dual-Scale Fiber Mats of Liquid Composite Molding: Some Recent Developments," in 10th International Conference on Flow Processes in Composite Materials (FPCM10), Monte Verità, 2010.
  • F. Zhou, N. Kuentzer, P. Simacek, S. G. Advani, and S. Walsh, "Analytic characterization of the permeability of dual-scale fibrous porous media," Composites Science and Technology, vol. 66, no. 15, Dec. 1, 2006. [Online]. Available: https://doi.org/10.1016/j.compscitech.2006.02.025
  • J. A. F. Zhou and S. G. Advani, "A closed form solution for flow in dual scale fibrous porous media under constant injection pressure conditions," Composites Science and Technology, vol. 68, no. 3-4, Mar. 2018. [Online]. Available: https://doi.org/10.1016/j.compscitech.2007.09.010
  • L. He, S. Yan, Y. Li, P. Wen, X. Xie, and et al., "Simulation of stochastic flow considering mesoscale permeability variability during the resin transfer molding process," Polym. Compos, vol. 41, no. 5, May. 2020. [Online]. Available: https://doi.org/10.1002/pc.25490
  • P. Carlone, F. Rubino, V. Paradiso, and F. Tucci, "Multi-scale modeling and online monitoring of resin flow through dual-scale textiles in liquid composite molding processes," The International Journal of Advanced Manufacturing Technology, vol. 96, no. 5, Feb. 21, 2018. [Online]. Available: https://doi.org/10.1007/s00170-018-1703-9
  • M. Imbert, S. Comas-cardona, E. Abisset-chavanne, and D. Prono, "Introduction of intra-tow release/storage mechanisms in reactive dual-scale flow numerical simulations," Journal of Composite Materials, vol. 53, no. 1, 2019. [Online]. Available: https://doi.org/10.1177/0021998318780498
  • I. D. P. Arcila, H. Power, C. N. Londoño, and W. F. F. Escobar, "Boundary element simulation of void formation in fibrous reinforcements based on the stokes–darcy formulation," Computer Methods in Applied Mechanics and Engineering, vol. 401, Jun. 1, 2016. [Online]. Available: https://doi.org/10.1016/j.cma.2016.02.010
  • B. R. Gebart, "Permeability of unidirectional reinforcements for rtm," Journal of Composite Materials, vol. 26, no. 8, Aug. 1, 1992. [Online]. Available: https://doi.org/10.1177/002199839202600802
  • A. Mikelic, W. Jäger, and W. J. Ager, "On the interface boundary condition of beavers, joseph, and saffman," SIAM Journal on Applied Mathematics, vol. 60, no. 4, 2000. [Online]. Available: https://doi.org/10.1137/S003613999833678X
  • M. L. Bars and M. G. Worster, "Interfacial conditions between a pure fluid and a porous medium: implications for binary alloy solidification," Journal of Fluid Mechanics, vol. 550, Mar. 10, 2006. [Online]. Available: https://doi.org/10.1017/S0022112005007998
  • Y. Cao, M. Gunzburger, F. Hua, and X. Wang, "Coupled stokes-darcy model with beavers-joseph interface boundary condition," COMMUN. MATH. SCI., vol. 8, no. 1, 2010. [Online]. Available: https://bit.ly/3KbTfW1
  • G. S. Beavers, E. M. Sparrow, and R. A. Magnuson, "Experiments on coupled parallel flows in a channel and a bounding porous medium," Journal of Basic Engineering, vol. 92, no. 4, Dec. 15, 1970. [Online]. Available: https://doi.org/10.1115/1.3425155
  • L.-H. Huang, I.-L. Chiang, and C.-H. Song, "A re-investigation of laminar channel flow passing over porous bed," Journal of the Chinese Institute of Engineers, vol. 20, no. 4, Mar. 10, 1997. [Online]. Available: https://doi.org/10.1080/02533839.1997.9741848
  • I. D. Patiño, H. Power, C. Nieto-Londoño, and W. F. Flórez, "Stokes–Brinkman formulation for prediction of void formation in dual-scale fibrous reinforcements: a BEM/DR-BEM simulation," Computational Mechanics, vol. 59, no. 4, Feb. 16, 2017. [Online]. Available: https://doi.org/10.1007/s00466-016-1360-5
  • R. Masoodi and K. M. Pillai, "A general formula for capillary suction-pressure in porous media," Journal of Porous Media, vol. 15, no. 8, 2012. [Online]. Available: https://doi.org/10.1615/JPorMedia.v15.i8.60
  • T. Chandrupatla and T. Osler, "The perimeter of an ellipse," Mathematical Scientist, vol. 35, no. 2, Dec. 2010. [Online]. Available: https://bit.ly/3k6LoOL
  • V. Neacsu, A. A. Obaid, and S. G. Advani, "Spontaneous radial capillary impregnation across a bank of aligned micro-cylinders – part i: Theory and model development," International Journal of Multiphase Flow, vol. 32, no. 6, Jun. 2006. [Online]. Available: https://doi.org/10.1016/j.ijmultiphaseflow.2006.02.006
  • O. A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow. New York: Gordon and Breach, 1963.
  • R. Gantois, A. Cantarel, G. Dusserre, J. N. Félices, and F. Schmidt, "Mold Filling Simulation of Resin Transfer Molding Combining BEM and Level Set Method," Applied Mechanics and Materials, vol. 62, Jun. 2011. [Online]. Available: https://doi.org/10.4028/www.scientific.net/AMM.62.57
  • C. Posrikidis, A Practical Guide to Boundary Element Methods with the Software Library BEMLIB. London: CRC Press, 2002.
  • D. L. Clements, Boundary value problems governed by second order elliptic systems. Boston: Pitman Advanced Pub. Program, 1981.
  • H. Power and L. C. Wrobel, Boundary integral methods in fluid mechanics. Southampton, UK ; Boston: Computational Mechanics Publications, 1995.
  • J. F. Telles, "A self-adaptive co-ordinate transformation for efficient numerical evaluation of general boundary element integrals," International Journal for Numerical Methods in Engineering, vol. 24, no. 5, May. 1987. [Online]. Available: https://doi.org/10.1002/nme.1620240509
  • A. Neumaier, "Solving ill-conditioned and singular linear systems: A tutorial on regularization," SIAM Review, vol. 40, no. 3, 1998. [Online]. Available: https://doi.org/10.1137/S0036144597321909
  • A. Rap, L. Elliott, D. B. Ingham, D. Lesnic, and X. Wen, "DRBEM for Cauchy convection-diffusion problems with variable coefficients," Engineering Analysis with Boundary Elements, vol. 28, no. 11, Nov. 2004. [Online]. Available: https://doi.org/10.1016/j.enganabound.2004.06.003
  • I. Patiño, H. Power, C. Nieto, and W. Flórez, "Boundary element method for the dynamic evolution of intra-tow voids in dual-scale fibrous reinforcements using a stokes–darcy formulation," Engineering Analysis with Boundary Elements, vol. 87, Feb. 2018. [Online]. Available: https://doi.org/10.1016/j.enganabound.2017.11.014