# Modeling of the influence of fibrous medium deformation on fiber tow saturation and void formation during the vacuum assisted process (VAP)

Mouna Zaidani, Tariq Ouahbi, Chung Hae Park, Abdelghani Saouab, Joël Bréard

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Mouna Zaidani, Tariq Ouahbi, Chung Hae Park, Abdelghani Saouab, Joël Bréard. Modeling of the influence of fibrous medium deformation on fiber tow saturation and void formation during the vacuum assisted process (VAP). ICSAAM 2011, 2011, Bucarest, Romania. hal-05410535

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# Modeling of the influence of fibrous medium deformation on fiber tow saturation and void formation during the vacuum assisted process (VAP).

Mouna Zaidani, Tariq Ouahbi*, Chung-Hae Park, Abdelghani Saouab & Joël Bréard

Laboratoire Ondes et Milieux Complexes. (LOMC, FRE 3102 CNRS)
University of Le Havre - BP 540 - 76058 Le Havre CEDEX

* e-mail : ouahbit@univ-lehavre.fr

## Abstract

Liquid composite molding (LCM) processes consist of injecting a liquid resin through a fibrous reinforcement. In the resin transfer molding (RTM) process, liquid thermosetting resin is injected under pressure into a rigid mold filled with fiber performance. In resin infusion processes (such as the vacuum assisted process), however, the preform stack is covered by an air/gas permeable, but liquid impermeable, microporous membrane which leads to a uniform vacuum distribution over the whole part. Unlike in the RTM process, a strong hydro-mechanical coupling between the resin flow and the reinforcement deformation takes place in resin infusion processes. A numerical model to simulate the hydro-mechanical coupling in resin film infusion processes was developed to compute the maximum height infused by the resin, the final height of the part and the resin infusion time in the previous work. In the simulation code, a void formation model is integrated considering two different flows in the macropore and the micropore, i.e., the viscous flow and the capillary wicking, respectively.

To meet aeronautic requirements, the content of entrapped air in the final part should be as low as possible. In this work, we propose modeling and simulation of the void formation and the tow saturation in the vacuum assisted process. We will show that the creation, compression and elimination of microvoids and macrovoids could be numerically predicted. Finally, a parametric study will be presented to show the advantage of vacuum application at air vents to reduce the void content and the influence of fibrous medium deformation on fiber tow saturation and void formation during vacuum assisted process.

## 1 Introduction

Resin infusion process (such as vacuum assisted process) is one of LCM processes. The LCM processes are the closed mould processes in which a liquid polymeric resin is impregnated through a fibrous reinforcement. Vacuum Assisted Process (VAP) is a low-pressure infiltration process for manufacturing fiber-reinforced parts by means of vacuum technology. The fiber preform that is to be infiltrated is covered by a semi permeable membrane, under a vacuum condition, during the entire process. Over the whole membrane surface, the small molecules of trapped air can be readily removed, while the large-molecules of resin stays stable in the mould (Figure 1). In this way the amount of trapped air is reduced and a uniform vacuum distribution over the whole part is maintained during infiltration and curing.

In the RTM process, the accurate control of the laminate thickness and of the fiber volume fraction can be achieved by the use of rigid mould tools. In the infusion process (such as VAP), however, as the vacuum bag
is employed during the process, the compaction of the fibrous reinforcement is governed by the pressure difference between the inside of the cavity and the external atmospheric pressure. The preform thickness will vary with the resin pressure inside the cavity [3,4]. Hence, it is important to take into account the reinforcement deformation as well as the resin flow. Moreover, a strong coupling takes place between these two phenomena.

<figure><img src="image_2.png" /><figcaption>Fig.1. Schematic of a Vacuum Assisted Process setup.</figcaption></figure>

In most case studies found in the literature related to resin infiltration modeling in composite manufacturing, the assumption is greatly simplified by considering saturated infiltration of a rigid preform [5,6]. The porous medium is then characterized by its permeability tensor K, which remains constant throughout the process. Alternatively, some researchers have concentrated on the problem of resin flow in compressible porous media. Again, most of these studies are based on soil mechanics, dating from the first work of Dave [7] to more recent work predicting local change in fiber volume fraction in the preform during infiltration [8,9]. In this work, we are based on a numerical model for the hydro-mechanical coupling in resin film infusion process. This model based on material behavior obtained from experimental measurements, was validated through the comparison with experimental results [1,21,22,23]. In addition, the fiber reinforcement was considered as deformable in the thickness direction, and the resin infiltration occurs through the thickness of the preform, too. Particularly, the variation of fiber volume fraction and fiber compaction stress in the thickness direction, were investigated.

The presence of trapped air can significantly alter the quality of the composites. To meet aeronautic requirements, the content of void should be as low as possible. Voids result mainly from heterogeneous micro-structure of fiber preform. Such inhomogeneity leads to non-uniform permeability of the fiber preform, which in turn causes the resin velocity variation from point to point at a micro scale. In the micro-structure of the fiber preform, we can find two kinds of pores, micropore (inside tow), and macropore in the channel (between tows). Viscous flow is dominant in the macropore, while capillary wicking is more important in the micropore since capillary pressure is inversely proportional to the pore size. Hence, it is assumed that the void formation mechanism is a competition between the viscous flow in the macropore and the capillary wicking in the micropore as represented by the modified capillary number (Ca*) [10-12], which is the ratio between viscous effect and surface tension :

$$Ca^* = \frac{\mu\nu}{\gamma \cos\theta}$$

Where $\mu$ is the resin viscosity, $\nu$ is the global resin velocity, $\gamma$ is the surface tension of resin and $\theta$ is the contact angle.

The formation of microvoids or macrovoids depends on the local resin flow velocity. In the case of a high resin velocity (i.e. high capillary number), voids will form within tows because the flow in the channel is
faster than that inside the fiber tow due to the higher permeability of the channel (Figure 1.a). For a lower resin velocity (i.e. low capillary number), the capillary flow will dominate within the tows and hence the voids will form in the channels between tows (Figure 1.b).

In this work, we therefore present a tool for simulating the multiphase flow in a compressible porous preform, considering to void formation and compression, the resin flow through dry fibers is modeled as an unsaturated flow through porous media, where Darcy's law and mass conservation equations of resin and fiber are used. Once air bubbles are created, at the flow front, their size and position change with time as a function of fibrous medium deformation. By a parametric study, we will present the advantage of vacuum application at air vents to reduce the void content and the influence of fibrous medium deformation on fiber tow saturation and void formation during vacuum assisted process.

<figure><img src="image_3.png" /><figcaption>Figure 1.a: Voids within tows (high capillary number)</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Figure 1.b: Voids between tows (low capillary number)</figcaption></figure>

<figure><img src="image_5.png" /></figure>

# 2 Hydro-mechanical coupling modeling

The case study of two phase flow in deformable porous medium requires an analyse of the pore-scale phenomena and an up-scaling method on a Representative Elementary Volume (REV). A usual volume averaging method consists in an integration of the local mass conservation equations on a non-deformable REV. Whether the medium is deformable or not, the results of this integration are averaged mass conservation equations. We considered a unidirectional transverse infiltration and assumed that the temperature remained constant during infiltration. A set of governing equations were modified to consider preform deformation and resin infiltration.

## 2.1 Governing equations

The resin flow in LCM processes has been conventionally treated as a single-phase flow, considering liquid resin as the only phase, and the void formation and compression cannot be modeled using this approach. The resin flow in a partially saturated region can be characterized as two phase flow through a porous medium. In this case, the governing equations are based on the two phase flow description, by similarity with soil mechanics. We also define the degree of saturation in fluid phase $S$ as (1), when the preform is empty, the saturation $S$ is equal to 0, and when it is fully filled with fluid $S$ equals 1.

$$S = \frac{v_l}{(1 - v_f)} \qquad (1)$$
If the governing equations are written over a representative element volume (REV), the following mass conservation equations of resin and fiber can be derived respectively:

$$ \frac{\partial \phi S}{\partial t} + \nabla \cdot (\phi S u^l) = 0 \qquad (2) $$

$$ \frac{\partial (1-\phi)}{\partial t} + \nabla \cdot ((1-\phi)u^s) = 0 \qquad (3) $$

Where $\phi$ represents the porosity of the medium, $u^l$ the fluid velocity and $u^s$ the reinforcement velocity. The combination of these two equations, leads to the following mass conservation equation.

$$ \nabla \cdot \mathbf{q} = - \frac{S}{1-\phi} \left( \frac{\partial \phi}{\partial t} + \nabla \phi \cdot u^s \right) - \phi \left( \frac{\partial S}{\partial t} + \nabla S \cdot u^s \right) \qquad (4) $$

Where $\mathbf{q}$ is the relative velocity of the fluid, $S$ is the degree of saturation and $u^s$ is the solid velocity.

The resin flow through the fiber reinforcement is a typical example of a flow through a porous medium, which, on the macroscopic scale, is well described by Darcy's law relating linearly the fluid velocity to the negative pressure gradient by the resin viscosity and the permeability of porous medium [13].

$$ q_i = \frac{-k_{ij}(S)}{\mu} \nabla P \qquad (5) $$

Where $\mu$ is the fluid viscosity, $P$ is the fluid pressure, subscripts i and j are the direction indices and $k_{ij}$ describes the permeability tensor.

The combination of mass and Darcy's law Eqs. (4) and (5), gives the following governing equation:

$$ \nabla \left( \frac{-k_{ij}}{\mu} \nabla P \right) = - \frac{S}{1-\phi} \left( \frac{\partial \phi}{\partial t} + \nabla \phi \cdot u^s \right) - \phi \left( \frac{\partial S}{\partial t} + \nabla S \cdot u^s \right) \qquad (6) $$

In the resin infusion processes, the fibrous medium is subjected to two types of pressures: (i) the pressure due to the infiltration of the resin through the preform and (ii) the action of the total stress applied on the flexible membrane. By analogy with soil mechanics [14] in composites manufacturing [15], the relation with definite mechanical balance between these forces is formulated by Terzaghi's law (7):

$$ \langle \sigma_{tot} \rangle = \langle \sigma' \rangle + PSI \qquad (7) $$

This law states that the total stress $\sigma_{tot}$ is broken up into an effective stress $\sigma'$ which acts on the solid and a hydrostatic pressure $P$ of the liquid phase and $S$ is the saturation level.

In the case of the infusion process, the analysis of the process physics clearly shows the existence of a hydromechanical coupling. The reinforcement compressibility and the resin flow occur simultaneously and there is thus a mutual influence between the two 'solid and liquid' phases. Consequently, it is important that the modeling takes into account the coupling of these two phenomena.

An experimental device developed at the University of Le Havre is placed on a universal testing machine. It enables us to analyze the hydro-mechanical coupling in the transverse direction and to determine the evolution of the compressibility and permeability as the reinforcements are compressed [16].
## 3 Void modeling

The main source of void formation at the flow front is a non-uniform flow caused by a competition between the viscous flow in the macropore and the capillary suction in the micropore. A void formation model considering two different flows in the macropore and the micropore was proposed by Kang et al [17]. In their approach, both the voids between and within fiber tows were successfully modeled and the modeling result showed a good agreement in a qualitative way with an experimental correlation of void content with capillary number. Assuming that the global resin pressure gradient is identical both in the macropore (between fiber tows) and in the micropore (within fiber tows), time scales for the resin to traverse a single tow height are computed between tows and through a tow at the flow front [2], where $h_c(t)$ and $h_T(t)$ are the resin flow front positions in the channel and inside the tow, respectively (Figure 2).

<figure><img src="image_6.png" /><figcaption>Figure 2: Two different flows in the macropore and the micropore.</figcaption></figure>

### 2.1 Void formation

Between fiber tows, the resin flow is a viscous flow. In this zone, the resin velocity is obtained using Darcy's law. The resin velocity in the channel, $u_c$, can be approximated as:

$$u_c = \frac{dh_c}{dt} = - \frac{k_{unsat}}{\mu} \frac{\partial P}{\partial z} \qquad (8)$$

Within fiber tows, the capillary pressure should be considered to compute the resin advancing velocity through the tow (see the red solid line in Fig. 2). The resin velocity within the tow is given by:

$$u_T = \frac{dh_T}{dt} = - \frac{1}{1-V_{f,T}} \frac{k_T}{\mu} \left( \frac{\partial P}{\partial z} - \frac{P_{cap}}{h_T} \right) \qquad (9)$$

Where $V_{f,T}$ is the fiber volume fraction of tow, $K_T$ is the permeability of tow and $P_{cap}$ is the capillary pressure. The tow permeability in the transverse directions is obtained by Gebart's model [15]. Capillary pressure is obtained as the following relation [18].

$$P_{cap} = \left( \frac{F}{D_f} \right) \frac{V_{f,T}}{1-V_{f,T}} \gamma \cdot \cos \theta \qquad (10)$$

Here, $\gamma$ is the surface tension of the resin, $D_f$ is the fiber diameter, $\theta$ is the contact angle and $F$ is the shape factor (two for the transverse direction).

The time required for the flow front within the channel $\Delta t_c$ and within a tow $\Delta t_T$ to traverse the tow height $h_T$ is then computed. If the time scale inside tows $\Delta t_T$ is greater than the time scale in the channel between tows $\Delta t_c$, an air bubble is created in the micropore (Figure 3.a), and vice versa (Figure 3.b).
<figure><img src="image_7.png" /><figcaption>Figure 3.a: Air bubble created inside the tow. ($\Delta t_T \Delta t_C$: void in the micropore)</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Figure 3.b: Air bubble created in the channel. ($\Delta t_T \Delta t_C$: void in the macropore)</figcaption></figure>

The time ratio between $\Delta t_T$ and $\Delta t_C$ describes the competition between the intra-tow and inter-tow flow fronts. If time scale within tow is greater than in the channel zone ($\Delta t_T \Delta t_C$), the void content in tows is obtained as (11) and (12) for the void content in the channel:

$$ \Phi_T = h_v \cdot \left( 1 - \frac{\Delta t_C}{\Delta t_T} \right) \qquad (11) $$

$$ \Phi_C = h_v \cdot \left( 1 - \frac{\Delta t_T}{\Delta t_C} \right) \qquad (12) $$

Where $h_v$ is the shape factor of bubble which depends on the microarchitecture of fabric.

## 2.1 Void compression and tow saturation

In the channel, once air bubbles are formed, at the flow front, their sizes can change as the resin pressure surrounding them vary with time. Assuming that the resin temperature is constant, by the ideal gas law, we obtain the new void fraction in the channel region at each instant as a function of resin pressure and the old void fraction [2]:

$$ \Phi_{C, new} (t + \Delta t, z) = \frac{P_{old} (t, z)}{P_{new} (t + \Delta t, z)} \cdot \Phi_{C, old} (t, z) \qquad (13) $$

To simplify tow saturation modeling, in several modeling approaches, the tow geometry is simplified as a rectangular or a cylindrical shape [19]. We assume that the fiber tow has a rectangular shape, where 'H' is the half height of the tow and 'h(t)' is the average half height of air bubble inside the tows and the fiber cross-section is a long rectangle with dimensions (b(t), l(t)) as shown in figure (Fig.4.a). This matches the shape in well-compacted preforms.

The resin flow inside the tow is driven by the overall effect of resin pressure, the air pressure inside the bubble and the capillary pressure at the flow front (Figure 4.a). If we assume that the entrapped air inside the tow, cannot escape from the bundle and cannot dissolve into the matrix, the void pressure increases within the reinforcement, as the bundle is impregnated and the air bubble is then compressed [2,20]. The void pressure $P_{void}$ at each instant can be estimated using the ideal gas law:

$$ P_{void} (t + \Delta t, z) = \frac{\Phi_T (t, z)}{\Phi_T (t + \Delta t, z)} \cdot P_{void} (t, z) \qquad (14) $$

Under the pressure difference between the resin and the air inside the tow, micro impregnation in the fiber bundle is estimated by Darcy's law.

$$ q_T = \frac{K_T P_{resin} - P_{void} + P_{cap}}{\mu H - h(t)} \qquad (15) $$

During the saturation of fiber tow, at each instant, the filled portion by the resin flow into the fiber tow $\Delta\Phi$ is computed (see the red portion in Figure 4.b).
$$ \Delta\Phi_T = \frac{q_T \cdot A \cdot \Delta t}{(1 - V_f) \cdot Volume_{total}} \qquad (16) $$

Where A and Volume$_{total}$ are the area of the saturated fiber tow portion and the total volume of the fiber tow, respectively. In most modeling approaches, it is assumed that the resin will infiltrate the tows from the upper and top sides only [20]. We propose that fiber tow is saturated by resin flow from all sides, we introduce an impregnation factor $\alpha$, which takes a value between 0 and 1.

As illustrated in (Figure 4.b), the new dimensions of unsaturated portion inside the tow are approximated as a function of the updated microvoid content $\Phi_T(t)$ and impregnation factor $\alpha$, they are as follows:

$$ \begin{cases} 2h = 2H \cdot \Phi^{\alpha} \\ bl = BL \cdot \Phi^{1-\alpha} \end{cases} \qquad 0 < \alpha < 1 \qquad (17) $$

Integrating Eq. (17) into Eq. (16), at each instant, the new microvoid content during fiber tow saturation is updated as:

$$ \Phi_T(t + \Delta t) = \Phi_T(t) - \frac{K_T \Delta t}{\mu (1 - V_f) H^2} \frac{1}{\Phi^{(2\alpha - 1)}} \qquad (18) $$

<figure><img src="image_9.png" /><figcaption>Figure 4.a: Assumed fiber tow (blue) and unsaturated region (gray) dimensions.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Figure 4.b: Schematic of fiber tow during saturation.</figcaption></figure>

# 4 Numerical simulation: results and discussion

Resin infusion time, final thickness and final void content in the part are significant information in the manufacturing of composite parts with resin infusion process. These parameters determine the manufacturing cost and the mechanical properties of the final part. Hence, in the present study, we integrated the void formation and compression models into the hydro-mechanical coupling model for resin infusion process previously proposed, and developed a simulation tool to investigate the influence of fibrous medium deformation on fiber tow saturation and void formation. The resin infusion time, the final fiber volume fraction and the resin pressure gradient during infusion are calculated. Eventually, the air bubbles content in the final part is directly predicted.

## 4.1 Numerical results

Vacuum assisted process is a low-pressure infiltration process, the injection pressure is the atmospheric pressure (10⁵Pa), the air vent pressure is maintained as a constant value of (5.10³Pa). The resin infusion is performed for an initial fiber volume fraction of 60%. The fibrous preform used is a non crimped fabric (NCF). The resin properties and the fabric micro-structure parameters are indicated in Table 1. The numerical simulations were performed to obtain the air bubble contents inside tows and in the channel zones as a function of fiber preform final thickness. The air void content expressed in percentage was also presented as a function of modified capillary number $Ca^*$. Simulation results of void formation and bubble compression/tow saturation were presented (Figure 5.a). In resin infusion processes, the resin flows through the thickness to infuse the part. When the resin starts to infiltrate the fiber preform, the progression of flow front is great.
Hence, the viscous flow between tows is more important than the capillary wicking inside tows. Consequently, this leads to an air bubble entrapment within tows. Thus, there is a formation of microvoids. As the resin flows through the preform, further, the progression of flow front is weaker and the capillary suction inside tows becomes more important than the viscous flow. Subsequently, air bubbles are formed between tows. On the other hand, the air bubble compression (between tows) is less important near the vacuum vent (Figure 5.a), since the air bubble is formed where the resin pressure is very low. Consequently, near the vacuum vent, the macovoid content is great. The void formation can be minimized by optimizing the resin velocity at the flow front. It has been observed that there exists an optimal capillary number that minimizes the void formation based on many experimental results obtained by in situ monitoring of void formation [12]. This optimal capillary number corresponds to a minimal void content (Figure 5.b), is about of an order of 10⁻³ [2, 12].

<table><caption>Table 1: Resin properties and Fabric micro-structure parameters.</caption><thead><tr><td>Parameter</td><td>Symbol</td><td>Value</td></tr></thead><tbody><tr><td>Viscosity</td><td>μ</td><td>0.15 Pa.s</td></tr><tr><td>Surface tension</td><td>γ</td><td>0.0317 N/m</td></tr><tr><td>Contact angle</td><td>θ</td><td>30°</td></tr><tr><td>Fiber volume fraction of fabric</td><td>V<sub>f</sub></td><td>0.6</td></tr><tr><td>Fiber volume fraction of fiber tow</td><td>V<sub>f,t</sub></td><td>0.65</td></tr><tr><td>Shape factor of bubble</td><td>h<sub>v</sub></td><td>0.6</td></tr><tr><td>Fiber diameter</td><td>D<sub>f</sub></td><td>7 μm</td></tr><tr><td>Fiber tow height</td><td>2H</td><td>0.8 mm</td></tr></tbody></table>

<figure><img src="image_11.png" /><figcaption>Figure 5.a: Void content vs. position (with void formation, compression/tow saturation).</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Figure 5.b: Void content vs. modified capillary number (without compression/tow saturation).</figcaption></figure>

It is of a great importance to study the influence of fibrous medium deformation on void formation, air bubble compression and tow saturation (Figure.6). Therefore, a comparison of void content within tows (Figure.6.a) and in the channel (Figure.6.b) for a rigid medium and deformable medium was performed. For this comparison, the initial part height was reduced from 10 to 8.5 cm. In rigid medium, the void content were more important, since the bubble compression/tow saturation was greater in deformable medium.
<figure><img src="image_13.png" /><figcaption>Figure 6.a: Microvoid content vs. position</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Figure 6.b: Macrovoid content vs. position</figcaption></figure>

<caption>Figure 6: Void content for rigid and deformable media vs. thickness position.</caption>

## 4.2 Parametric study

Total void content and final fiber volume fraction in the part are two key parameters to the product quality, since, these two parameters decide the mechanical properties of the finished part. Hence, in this present parametric study, the fiber volume fraction and the total void content were presented as a function of different air vent pressures (Figure 7). As the air vent pressure was lower, the void content was reduced and the fiber volume fraction was slightly increased. If the air vent pressure is reduced by a vacuum application, the initial air pressure at the moment of void formation is also low. Hence, this favors the bubble compression and tow saturation. It was observed that when air vent pressure of 1 bar was applied, total void content was a value of 4%. It was also observed that when a lower pressure, such as 100 mbar, was applied, this void content decreased to 0.5%. This shows an advantage of vacuum application in order to decrease the void content in real processes.

<figure><img src="image_15.png" /><figcaption>Figure 7: Simulation results of total void content and the final fiber volume fraction vs. air vent pressure.</figcaption></figure>
## 4 Conclusion

This paper presented a numerical tool to model the unsaturated flow into a compressible preform of dual-scale porosity, considering a void formation and compression/tow saturation models. The total void content in the final part as a function of position was presented. A parametric study was presented to show the advantage of vacuum application to reduce the void content and the influence of fibrous medium deformation on fiber tow saturation and void formation. The future work will cover the accurate description of the material and processing parameters used in the model. Sensitivity analyses to these parameters and careful validation with model experiments will be performed.

## References

[1] T. Ouahbi, A. Saouab, J. Bréard, P. Ouagne, S. Chatel. Comp Part A 38 (2007) 1646.

[2] C. H. Park, A. Lebel, J. Bréard, A. Saouab, W. I. Lee. Comp Part A 42 (2011) 658.

[3] N.C. Correia, F. Robitaille, A. C. Long, C. D. Rudd, P. Simacek, P. S. G. Advani. Comp Part A 36(2005) 1645.

[4] C. Williams, J. Summerscales, S. Grove. Comp Part A 27(1996) 517.

[5] R. Parnas R. Liquid composite molding. Munich: Hanser Publisher; (2000) 170.

[6] S. G. Advani. Flow and rheology in polymer composite manufacturing. 10 (1994) 10.

[7] R. Dave, J. L. Kardos, M. P. Dudukovic. Polym Compos 8(1987) 29.

[8] V. Michaud, J. AE. Manson. J Compos Mater 35 (2001) 1150.

[9] A. Farina, L. Preziosi. Torino: Politecnico di Torino (1999) 1.

[10] E. Ruiz, V. Achim, S. Soukane, F. Trochu, J. Bréard. Comp Sci Tech 66 (2006) 475.

[11] N. Patel, V. Rohatgi, L. J. Lee. Polym Compos 17(1996) 104.

[12] N. Patel, V. Rohatgi, L. J. Lee. Polym Eng Sci 35(1995) 837.

[13] V. Antonucci, M. Giordano, L. Nicolais, A. Calabro, A. Cusano, et al. J Mat Pro Tech 143 (2003) 687.

[14] M. A. Biot. J Appl Phys 12 (1946) 155.

[15] B. R. Gebart. J Comp Mater 26 (1992) 1101.

[16] P. Ouagne, J. Bréard, T. Ouahbi, C.H. Park, A. Saouab. Int J Mat Forming. 3 (2010) 1287.

[17] M. K. Kang, W. I. Lee, H. T. Hahn. Comp Sci Tech 60 (2000) 2427.

[18] K. J. Ahn, J. C. Seferis, J. C. Berg. Polym Compos 12 (1991) 146.

[19] P. Simacek, S. G. Advani. Comp Sci Tech 63 (2003) 1725.

[20] J. Wolfrath, V. Michaud, A. Modaressi and J.-A.E. Manson. Comp Part A 37 (2006) 881.

[21] Ouahbi T., Ouagne P., Park C.H., Bréard J., Simultaneous identification of preform permeability and compressibility, Proceedings of 18th International Conference on Composite Materials, Jeju Island, South Korea, August 2011.

[22] P. Ouagne, J. Breard, T. Ouahbi, C.H. Park, A. Saouab, S. Chatel, "Hydromechanical loading and compressibility of fibrous reinforcements", International Journal of Material Forming, 1, pp. 933-936, 2008.

[23] P. Ouagne, J. Breard, T. Ouahbi, C. H. Park, A. Saouab, S. Chatel, "Hydromechanical loading and compressibility of fibrous media for resin infusion processes", International Journal of Material Forming, 3, pp. 1287-1294, 2010.