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TECHNICAL PAPERS

A Closed Form Solution for Flow During the Vacuum Assisted Resin Transfer Molding Process

[+] Author and Article Information
K-T. Hsiao, R. Mathur, S. G. Advani

Department of Mechanical Engineering, Center for Composite Materials, University of Delaware, Newark, DE 19716

J. W. Gillespie

Department of Materials Science and Engineering, Department of Civil and Environmental Engineering, Center for Composite Materials, University of Delaware, Newark, DE 19716

B. K. Fink

Army Research Laboratory, Aberdeen Proving Grounds, MD 21005

J. Manuf. Sci. Eng 122(3), 463-475 (Sep 01, 1999) (13 pages) doi:10.1115/1.1285907 History: Received December 01, 1998; Revised September 01, 1999
Copyright © 2000 by ASME
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References

Seeman II, W., 1990, “Plastic Transfer Molding Techniques for the Production of Fiber Reinforced Plastic Structures,” United States Patent 4,902,215, February.
Bruschke,  M. V., and Advani,  S. G., 1990, “A Finite Element/Control Volume Approach to Mold Filling in Anisotropic Porous Media,” Polym. Compos., 11, pp. 398–405.
Bruschke,  M. V., and Advani,  S. G., 1991, “A Numerical Approach to Model Non-Isothermal, Viscous Flow with Free Surfaces Through Fibrous Media,” Int. J. Numer. Methods Fluids, 19, pp. 575–603.
Liu,  D., Bickerton,  S., and Advani,  S. G., 1996, “Modeling and Simulation of RTM: Gate Control, Venting and Dry Spot Prediction,” Composites Part A, 27A, pp. 135–141.
Mohan,  R. V., Ngo,  N. D., Tamma,  K. K., and Fickie,  K. D., 1999, “On a Pure Finite Element Based Methodology for Resin Transfer Mold Filling Simulations,” Polym. Eng. Sci., 39, No. 1, pp. 26–43.
Bruschke,  M. V., and Advani,  S. G., 1991, “RTM: Filling Simulation of Complex Three-Dimensional Shell-Like Structures,” SAMPE Q., 23, No. 1, pp. 2–11.
Trochu,  F., Gauvin,  R., Gao,  D. M., and Boudreault,  J.-F., 1994, “RTMFLOT—An Integrated Software Environment for the Computer Simulation of the Resin Transfer Molding Process,” J. Reinf. Plast. Compos., 13, No. 3, pp. 262–270.
Lee,  L. J., Young,  W. B., and Lin,  R. J., 1994, “Mold Filling and Cure Modeling of RTM and SRIM Processes,” Compos. Struct., 27, Nos. 1–2.
De Parseval,  Y., Pillai,  K. M., and Advani,  S. G., 1997, “A Simple Model for the Variation of Permeability Due to Partial Saturation in Dual Scale Porous Media,” Transp. Porous Media, 27, pp. 243–264.
Bickerton,  S., and Advani,  S. G., 1997, “Experimental Investigation and Flow Visualization of Resin Transfer Molding Process in a Non-Planar Geometry,” Compos. Sci. Technol., 57, pp. 23–33.
Simacek,  P., Sozer,  E. M., and Advani,  S. G., 1998, User manual for DRAPE 1.1 and LIMS 4.0. Technical Report, Center for Composite Materials.
Gallez, X. E., and Advani, S. G., 1996, “Numerical Simulations for Impregnation of Fiber Preforms in Composites Manufacturing,” in Proceedings of the Fourth International Conference on Flow Processes in Composite Materials, University of Wales, 1996.
Scheidegger, Adrian E., 1974, The Physics of Flow Through Porous Media, University of Toronto Press.
Bear, J., Flow Through Porous Media, American Elsevier, 1972.
Adler, Pierre M., Porous Media: Geometry and Transports, Butterworth-Heinemann, 1992.
Woerdeman,  D. L., Phelan,  F. R., and Parnas,  R. S., 1996, “Interpretation of 3-D Permeability Measurements for RTM Modeling,” Polym. Compos., 16, pp. 470–480.
Tari,  M. J., Imbert,  J. P., Lin,  M. Y., Lavine,  A. S., and Hahn,  H. T., 1998, “Analysis of Resin Transfer Molding with High Permeability Layers,” J. Manuf. Sci. Eng., 120, pp. 609–616.
Pillai,  K. M., and Advani,  S. G., 1998, “Numerical Simulation of Unsaturated Flow in Woven or Stitched Fiber Mats in Resin Transfer Molding,” Polym. Compos., 19, No. 1, pp. 71–80.
Murphy, G. M., Ordinary Differential Equations and Their Solutions, Van Nostrand, 1960.
Pillai,  K. M., and Advani,  S. G., 1998, “A Model for Unsaturated Flow in Woven or Stitched Fiber Mats in Resin Transfer Molding,” J. Compos. Mater., 32, No. 19, pp. 1753–1783.
Sun,  X., Li,  S., and Lee,  J. L., 1998, “Mold Filling Analysis in Vacuum-Assisted Resin Transfer Molding. Part I: Scrimp Based on a High-Permeable Medium,” Polym. Compos., 19, No. 6, pp. 807–817.

Figures

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Applications of VARTM technology to the manufacture of large-scale composite parts for defense and civilian applications
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Lay-up of materials in the SCRIMP/VARTM process
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Two-layer model of resin flow in the VARTM process
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Schematic of resin flow in the flow front region, in the two-layer model for VARTM
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Variation of the ratio of flow rates into the flow front region in the x and y directions, Qx/Qy with the nondimensional flow parameter ε=K2xxh22/K2yyd2
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Plot of the pressure gradient in the flow front region, ∂P/∂y(x), and the cumulative flow rate Cq(x)=∫0x−(K2yy/μ)(∂P/∂y)dx, from numerical simulation, when the flow front is at D=40cm . The values of the process parameters are: K2xx=8.8×10−7cm2,K2yy=4.4×10−7cm21=0.99,Φ2=0.5,h1=0.01cm , h2=1.0cm , P0=106Pa .
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Illustration for resin mass balance in the flow front region in the two-layer model
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Two mathematical roots of hf*(x*)=0. Note that only the smaller root is physically possible.
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Example of a full-scale numerical simulation: (a) flow front history (time contours in seconds) (b) pressure distribution at the final time step (pressure contours in Pa)
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Comparison of the analytical model with numerical simulations: percentage errors in estimating the flow front length (d) and the time to fill a length of 40 cm are plotted against the flow parameter, ε
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Flow front velocity and fill time as a function of length of the saturated region: effect of thickness ratios
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Flow front velocity and fill time as a function of length of the saturated region: effect of permeability of distribution medium
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Flow front velocity and fill time as a function of length of the saturated region: effect of in-plane permeability of fiber preform
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Flow front velocity and fill time as a function of length of the saturated region: effect of through transverse permeability of fiber preform
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Flow front velocity and fill time as a function of length of the saturated region: effect of porosity of distribution medium
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Flow front velocity and fill time as a function of length of the saturated region: effect of porosity of fiber preform

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