Keywords: resin transfer molding, dual porosity media, unsaturated flows, relative permeability, macroscopic capillary pressure, homogenization methods.

RTM (Resin Transfer Molding) is a widely used process to manufacture advanced composites with continuous fiber reinforcements. The process consists of four stages: an arrangement of fiber preforms in a mold cavity, followed by injection of a thermoset resin into the mold cavity. In the next stage the liquid resin cure and solidifies before it is demolded in the final stage. From manufacturing viewpoint, one would like to fill the spaces between the fibres before it starts curing, because the viscosity of the resin increases rapidly with degree of cure and high viscosity might aggravate or even stop resin flow leaving voids and dry spots, which are detrimental for the mechanical resistance of the final part. Infiltration of the low viscosity resin into empty spaces between fibers is driven by the hydrodynamic pressure gradient originated by the higher inlet pressure, however, in certain regions this gradient can be so low, that the wicking gradient will exceed it and the driving mechanism of the flow will change. This situation occurs more often when preforms built from fiber tows (containing few thousands of fiber strands) are used. In such preforms, the spacing between the tows can be nearly an order of magnitude higher than the spacing of pores inside the tows, forming in this way dual porosity media.

Main objectives in the numerical simulation of the filling phase are to determine progression of the resin front, evolution of the pressure distribution, prediction of dry spots and voids formation and an optimization of injection gates and air vents locations that will accomplish successful impregnation without any voids. Due to the thousands of fibers and very low ratio of their characteristic cross- sectional size to the size of the mold, numerical simulation of the filling phase, accounting for all the fiber geometry details, is a formidable task and not necessary. Homogenization techniques are often used in order to reformulate the original problem in terms of the microlevel (local) and the macrolevel (global, effective) analyses. Flow of commonly used resins can be viewed as low Reynolds number flow of an incompressible Newtonian liquid. The macrolevel problem is described using Darcy's equation for flow through porous media and standard approaches are used to solve for the pressure and explicit schemes are adopted to model the movement of the resin into the fiber preform on a macroscopic scale. The resistance of the fiber preforms to the flow is lumped into a permeability tensor, which is required as one of the input data. One could either obtain this experimentally or predict it by analytic or numerical methods by considering flow in a unit cell to represent the repetitive fiber architecture.

Seldom one observes a sharp flow front during the mold filling stage. In most cases, during infiltration a transition (partially filled) region along the macroscopic resin front is clearly visible, which the standard approaches cannot capture. In order to describe this transition region, first of all, it is necessary to modify the macroscopic governing equations by introduction of relative permeability and macroscopic capillary pressure as functions of saturation, defined as the ratio of the filled pore space to the total pore space in a basic cell. Relative permeability and macroscopic capillary pressure must enter the governing equations as known functions. Unlike absolute permeability, no simple procedure is available to determine relative permeability or macroscopic capillary pressure at least numerically. Their determination should be based on transient microlevel analysis. This was our motivation to create a Free boundary program. The program uses the general-purpose finite element code Ansys and it is written in the Ansys Parametric Design Language and Fortran. Its initial form without the inclusion of the surface tension influence was presented in [1], with surface tension influence and contact angle formation in [2]. Filling is simplified as quasi steady-state process, explicit form of the free boundary condition is used for the front progression and moving mesh scheme is adopted. Based on filling results obtained by the Free boundary program, semi-analytical approach allows us to determine the relative permeability and the macroscopic capillary pressure for flow across cylindrical fibers with periodic geometry. ([2] and [3]).

1

Z. Dimitrovová, L. Faria, "Finite element modeling of the RTM process", Proceedings of the 5th International Conference on Flow Processes in Composite Materials, Plymouth, UK, July 1999, 125-135.

2

Z. Dimitrovová, S.G. Advani, "A Semi-Analytical Approach to the Relative Permeability Determination in LCM Processes", Proceedings of the 8th International Conference on Composites Engineering, Tenerife, Canary Islands, Spain, August 2001, 191-192.

3

Z. Dimitrovová, S.G. Advani, "Analysis and Characterization of Relative Permeability and Capillary Pressure for Free Surface Flow of a Viscous Fluid across an Array of Aligned Cylindrical Fibers", Journal of Colloid and Interface Science, 245, 325-337, 2002. doi:10.1006/jcis.2001.8003

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