# A Simulation Model for the Infusion Process

Tariq Ouahbi, Abdelghani Saouab, Pierre Ouagne, Joël Bréard, Sylvain Chatel

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Tariq Ouahbi, Abdelghani Saouab, Pierre Ouagne, Joël Bréard, Sylvain Chatel. A Simulation Model for the Infusion Process. The 9 th International ESAFORM Conference on Material Forming, 2006, Glasgow, United Kingdom. hal-05410525

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# A Simulation Model for the Infusion Process

T. Ouahbi¹, A. Saouab¹, P. Ouagne¹, J. Bréard¹, S. Chatel²

¹Laboratoire de Mécanique, Physique et Géosciences, Université du Havre,
25 rue Philippe Lebon, BP 540, 76058, Le Havre, France

URL: www.univ-lehavre.fr

e-mail: tariq.ouahbi@univ-lehavre.fr

abdelghani.saouab@univ-lehavre.fr

²European Aeronautic Defence and Space – Corporate Research Center
12 rue Pasteur, BP 76, 92150 SURESNES

URL: www.eads.net

e-mail: sylvain.chatel@eads.net

ABSTRACT: In the infusion process, it is important to predict resin infusion time and final thickness of the part according to the process conditions such as compaction pressure and resin temperature. Hence, the objective of this work was to develop and verify a comprehensive numerical model to simulate the infusion process and to predict the final thickness and the resin infusion time.

An experimental device with hydro-mechanical coupling HMz was used to obtain the permeability and the compressibility of preform. A numerical validation of the proposed model was made with an inverse method. The numerical code developed in the present study was found to be useful to predict the resin infusion time which plays an important role in the total process cycle time, and the final thickness which determines the final fibre volume fraction of the part.

Key words: Infusion Process, Hydro-Mechanical Coupling, Infusion Height, Resin Infusion time.

## 1 INTRODUCTION

The request for composite parts is ever increasing particularly in the aeronautic industry. The infusion process has been developed to be a cost-effective technique for the fabrication of large and complex composite structures [1]. Thus, this process has been identified as an alternative to the RTM (Resin Transfer Moulding) as well as the conventional autoclave prepreg technique [2].

Several investigators have studied and proposed models for the RFI (Resin Film Infusion) process used in composites manufacturing. Resin flow through the dry fibres is conventionally modelled as an unsaturated flow through porous media, where Darcy's law is employed. The determination of the exact location of the flow front is an important issue in the analysis. When high pressure gradients are applied, it is necessary to treat the fibre layers as deformable. A study on this fluids-structure interaction problem has been performed by Ambrosi and Preziosi [3]. Another important issue is the elimination of trapped air since the presence of voids can significantly degenerates the quality of the composites. A mathematical model of void formation during the RFI process has been developed by Sevostianov et al [4]. In a paper of

Blest et al. [5], the modelling and simulation of resin flow, heat transfer and the curing of a multilayer thermoset composites by the resin film infusion process has been treated. Loos and MacRae [6] have developed an analytical model for two-dimensional resin film infusion process, which can be used to simulate non-isothermal infiltration of a hot-melt resin into a textile preform of complex shape. A non-isothermal RFI process for stitched stiffened panels was numerically modelled by Han et al [7]. The performance of the stitched stiffened panels under compressive loading has been compared with that of the unstitched stiffened panels.

In the infusion process, it is important to predict resin infusion time and final thickness of the part according to the process conditions such as compaction pressure and resin temperature. Hence, the objective of this work was to develop and verify a comprehensive numerical model to simulate the infusion processes, and to predict the final thickness and the resin infusion time.

## 2 DESCRIPTION OF INFUSION PROCESSES

The LCM (Liquid Composites Moulding) processes [8] are used to manufacture high quality and complex-shaped fibre reinforced polymeric
composite parts particularly in the aeronautic industry.

We can classify them into two groups: the injection by resin transfer (RTM & derivatives) and the infusion by resin infiltration (Infusion & derivatives). This work focused on the simulation and the modelling of the infusion process.

In infusion process, Dry textile preforms are infiltrated by semi-cured resin (fig. 1) and the resin is consolidated and cured in a single step, eliminating the labour to lay-up of prepreg tape.

<figure><img src="image_2.png" /><figcaption>Fig. 1. Resin infusion process setup.</figcaption></figure>

# 3 ANALYSIS OF INFUSION PROCESSES

The hydro-mechanical coupling (HM) of fibrous reinforcements and the compression with the resin flow in the reinforcement are essential to model the infusion processes, such as the RFI, because the compression of the reinforcements and the impregnation of the resin in the fibrous medium occur at the same time.

## 3.1 Governing equations

We can define the relations representing the physics of LCM processes, by a description based on the concept of continuous medium [9, 10, 11].

As presented in table 1, we represented the whole formulations corresponding to the modelling of HMz couplings applied to the infusion process.

<table><caption>**Table1.** Equations for the HMz coupling analysis</caption><thead><tr><th></th><th>Equations</th><th>Dependent variables</th></tr></thead><tbody><tr><td>Mass balance (1)</td><td>∇·q = <sup>1</sup>&frasl;<sub>V<sub>f</sub></sub> (∂V<sub>f</sub>/∂t + u<sub>si</sub>∇V<sub>f</sub>)</td><td>q, V<sub>f</sub></td></tr><tr><td>Darcy's law (2)</td><td>∇p = -<sup>μ</sup>&frasl;<sub>K<sub>Z</sub>(V<sub>f</sub>)</sub> q</td><td>p</td></tr><tr><td>Force balance (3)</td><td>∇·σ'<sub>z</sub> - ∇p = 0</td><td>σ'<sub>z</sub></td></tr><tr><td>Constraint-Fibre volume fraction relation (4)</td><td>σ'<sub>z</sub> = C<sub>Z</sub>(V<sub>f</sub>)</td><td>None</td></tr><tr><td>total :</td><td>4 equations</td><td>4 variables (scalsars)</td></tr></tbody></table>

## 3.2 Experimental device for HMz coupling analysis

In infusion processes, the fibre volume fraction can change dynamically as the applied pressure is re-distributed between the resin and the preform. Hence, it is important to model the compaction of the fabric and its relation with the fibre volume fraction as a function of the applied pressure. In addition, the permeability of fabric depends on the fibre volume fraction. Hence, it is also of significance to model the relationship between the permeability and fibre volume fraction.

An experimental device (fig. 2) with hydro-mechanical coupling HMz was used to obtain the permeability and the compressibility of preform.

<figure><img src="image_3.png" /><figcaption>Fig. 2. Experimental device for Kz measurement and HMz coupling analysis.</figcaption></figure>

## 3.3 Numerical formulation

The numerical algorithm used in this study is based on a one dimensional discretization of the governing equation by the finite difference method with a moving boundary flow front. The pressure and the saturation values are calculated at the nodes. The fibre volume fraction and the permeability are computed and assigned to each element. The combination of equations (1) and (2), gives the following governing equation, expressed in the 1D form:

$$ \frac{\partial}{\partial z} \left( -\frac{K}{\mu} \frac{\partial P}{\partial z} \right) = \frac{1}{V_f} \frac{\partial V_f}{\partial t} + \frac{1}{V_f} \frac{\partial V_f}{\partial z} v_k^f \quad (5) $$

where $v_k^f$ is solid velocity (fibres velocity) in transverse direction.

The term $(\frac{1}{V_f} \frac{\partial V_f}{\partial z} v_k^f)$ in RHS of the equation (5)

represented the relaxation or the compression of the wet fibres. To deal with it, the initial grid of the field is deformed in such a manner to take into account
the relieving or the compression of the porous environment [12, 13] during the calculation.

This assumption simplifies the governing equation (5) to:

$$ \frac{\partial}{\partial z} \left( -\frac{K}{\mu} \frac{\partial P}{\partial z} \right) = \frac{1}{V_f} \frac{\partial V_f}{\partial t} \qquad (6) $$

# 4 NUMERICAL SIMULATION (VALIDATION & RESULTS)

## 4.1 Validation of numerical infusion model

An experimental validation of the infusion model was made in Saouab et al [14]. In this paper we present a numerical validation of the infusion model by an inverse method. This method consists of computing the compaction pressure by imposed displacement code, and using the obtained pressure as the input data of imposed compaction pressure code to compute the displacement. The displacements for each calculation were compared (fig. 3), and a good agreement was observed.

<figure><img src="image_4.png" /><figcaption>Fig. 3. Numerical validation of the infusion model with an inverse method.</figcaption></figure>

## 4.2 Numerical results and parametric study

The numerical prediction for resin infusion process was performed for an initial fibre volume fraction of 40%. The resin temperature was 90°C. Five different compaction pressures of 1, 2, 3, 4 and 5 (10⁵ Pa) were considered. As can be seen in fig. 4, the infusion height, as expressed in percentage, increased in the course of time.

<figure><img src="image_5.png" /><figcaption>Fig. 4. The time-dependent evolution of the infusion height percentage for different pressure compaction.</figcaption></figure>

For an initial fibre volume fraction of 40% and a fixed compaction pressure of 200 kPa, four different resin temperatures of 80, 90, 100 and 110 °C were considered (fig. 5). As can be expected, higher temperature leaded to a faster infusion at the beginning of mould filling. However, it also resulted in a faster curing of resin and the total infusion height was not reached. Lower resin temperature resulted in longer infusion time, but the resin cure reaction was also delayed. As a result, the total infusion height was attained.

<figure><img src="image_6.png" /><figcaption>Fig. 5. The time-dependent evolution of the infusion height percentage for different temperature.</figcaption></figure>

The ratio between the initial and the final height of the part in function of compaction pressure was presented in fig. 6. We also illustrated the relation of the final fibre volume fraction versus compaction pressure.
<figure><img src="image_7.png" /><figcaption>Fig. 6. Representation of the final fibre volume fraction in function of the compaction pressure.</figcaption></figure>

The final volume fraction of the part increased with the increase in compaction pressure.

In fig. 7, a representation of the infusion time in function of the compaction pressure was provided. The infusion time is the time necessary for the resin to completely infuse the part, and it does not include the cure time.

<figure><img src="image_8.png" /><figcaption>Fig. 7. Representation of the time infusion in function of the compaction pressure.</figcaption></figure>

As seen in fig.7, the infusion time decreases according to the increase in compaction pressure. Hence, this information can be used to determine the compaction pressure necessary for a total process cycle time to be achieved.

## 5 CONCLUSIONS

A numerical modelling of infusion processes was made. A numerical simulation of the governing equation by the finite different method with an iterative decoupling method was performed. A numerical validation of the resin infusion model by an inverse method was made. The infusion height

was investigated for different compaction pressures and resin temperatures. The simulation can also be used to predict the resin infusion time and the final fibre volume fraction.

## ACKNOWLEDGEMENTS

The authors would like to acknowledge the financial supports by the ‘Haute Normandie’ Region and by the European Aeronautic Defence and Space Company (Corporate Research Center France) ‘EADS-CCR’.

## REFERENCES

1. Park J, Kang MK. A numerical simulation of the resin film infusion process. Composite Structures 60 (2003) 431-437.

2. Antonucci V, Giordano M, Nicolais L, Calabrò A, Cusano A, Culoto A, Inserra S. Resin flow monitoring in the resin film infusion process. Materials Processing Technology 143-144(2003) 687-692.

3. D. Ambrosi and L. Preziosi. Modelling matrix injection through elasticporous performs. Composites Part A 29A (1998) 5-18.

4. Sevotianov I, Verijenko VE, Klemperer CJ. Mathematical model of cavitation during resin film infusion process. Composite Structure 2000; 48:197-203.

5. Blest DC, McKee S, Zulkifle AK, Marshall P. Curing simulation by autoclave resin infusion. Compos Sci Technol 1999; 59:2297-2313.

6. Loos AC, MacRae JD. A process simulation model for the manufacture of a blade-stiffened panel by the resin infusion process. Compos Sci Technol 1996; 56:273-288.

7. Han NL, Suh SS, Yang JM, Hahn HT. Resin film infusion of stitched stiffened composite panels. Composites Part A: Appl Sci Manuf 2003; 34:227-236.

8. Bréard J, Saouab A, “Numerical Simulation of Liquid Composite Moulding Processes”. Revue européenne des éléments finis. Volume 14 – N° 6-7/2005, p. 841-865.

9. Bear J., 1990. "Continuum Approach and Contaminant Transport in Ground Water Flows", Modelling and Applications of Transport Phenomena in Porous Media, Von Karman Institute for Fluid Dynamics, Lecture Series 1990-01.

10. Bréard J., Henzel Y., Trochu F., Gauvin R., 2003. "Analysis of dynamic flows through porous media. Part I: Comparison between saturated and unsaturated flows in fibrous reinforcements", Polymer Composites, vol. 24, n°3, pp. 391-408.

11. Tucker C., 1996. "Heat Transfer and reaction issues in Liquid Composite Moulding", Polymer Composites, vol. 7, n°1, pp. 60-72.

12. Danis M., Del Borrello C., Lacoste E., Mantaux O., "Infiltration of fibrous preform by a liquid metal: modelization of the preform deformation", Proc. Of ICCM12, 1999, Paris, paper n°877.

13. Lacoste E, Mantaux O, Danis M. Numerical simulation of metal matrix composites and polymer matrix composites processing by infiltration : a review. Composites: Part A 33 (2002) 1605-1614.

14. Saouab A., Ouahbi T., Ouagne P., Breard J. and Chatel S. Modélisation des procédés d'infusion et analyse expérimentale des couplages hydromécaniques. Revue des Composites et des Matériaux Avancés (sous presse).