JEC COMPOSITES MAGAZINE - Issue #39 - March/April 2008 - 58

FEATURE “Process” 1-D injection simulation Simulation g…/… Flow simulation of particle-filled resins The resin-particles-fibres system can be considered as the overlaying of two distinct sub-assemblies (Figure 2): the filter (stationary) and the suspension (in motion with respect to the filter). The initial permeability of the filter (K) is equal to the permeability of the fibrous preform (KF). Similarly, the initial porosity of the filter is identical to that of the preform, ε0. Furthermore, the suspension (resin/filler mix) is characterized by its initial concentration (C0) and its initial viscosity (η0), the latter in turn depending on the nature of the fluid and of the particles and on C0. During flow, the particles are trapped in the preform. The retention that takes place is then considered as the transfer of some of the particles from the suspension to the filter. These particles, which were in motion with the suspension, then become stationary. In its intermediate state, the filter sub-assembly now consists of the fibres of the preform and the trapped particles. Since the volume of the filter is increased by the volume of the retained particles, its porosity is reduced along with its permeability (K). Similarly, the suspension “loses” some of its particles. In the intermediate state, the suspension is therefore characterized by a concentration (C) that is different from the initial concentration (C0) and, consequently, by a viscosity (η) that is also different from η0 . Thanks to the development of a system of equations based on the conservation of mass and retention kinetics, a finite element analysis allows the total quantity of filler particles present at each point of the part and at each instant to be modelled. The simulation of particle-filled resin flow through a fibrous preform requires the simultaneous resolution of two interlinked problems: the flow problem (modelled with the Darcy equation) and the filtration problem (Figure 3). The Darcy equation relates the injection pressure to the fluid velocity, the fluid viscosity and the permeability of the fibrous reinforcements. On the basis of the system’s input data (material properties, injection parameters), the simulation is run using an iteration loop carrying out a series of calculations for each element of the mesh. The total injection time and the filler profile in the finished part can thus be estimated. The study is complemented by the development of an experimental methodology enabling the filler concentration in the part to be measured and the model input parameters to be identified. Fig.3: Flow-filtration coupling (U = fluid velocity) Conclusions and outlook The study presented in this article offers real advances in the understanding of the physical phenomena involved in the flow of a particle-filled resin through a fibrous reinforcement. This has led to the development of an injection simulation tool for composite parts, combining analysis and measurements, which for the time being is limited to unidirectional flows. This study has also opened up various paths for development, offering a number of possibilities for process enhancement. In particular, from an industrial perspective, this tool can be used for: - selecting fillers (particle size) - selecting and/or optimizing the architecture of the fibrous reinforcement - defining the best injection strategy. Contact: comas-cardona@ensm-douai.fr lefevre@ensm-douai.fr JEC Composites Magazine / No39 March - April 2008

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JEC COMPOSITES MAGAZINE - Issue #39 - March/April 2008

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