*3.1. Rheological Analysis of the Model Fluid*

As shown in Figure 3a, PEG400 presents a Newtonian behavior, indicating that its viscosity is not dependent on the shear rate. The temperature dependence of the viscosity has been modeled by an Arrhenius like equation, a common approach for oligomers and polymers at a temperature much higher than their T<sup>g</sup> [57]:

$$
\eta = \eta\_0 \exp\left(\frac{\mathcal{E}\_\mathbf{a}}{\mathcal{R}\mathcal{T}}\right) \tag{2}
$$

where η<sup>0</sup> is a pre-exponential factor, T the absolute temperature, R the universal gas constant and E<sup>a</sup> the activation energy. The nonlinear fitting of PEG 400 viscosity with Equation (2) (see Figure 3b) provides an E<sup>a</sup> value of 36.9 kJ/mol. Depending on the temperature of the infusion, Equation (2) has been used to determine the value of viscosity needed for permeability calculation from Darcy's law.

*Materials* **2020**, *13*, x FOR PEER REVIEW 7 of 17

*Materials* **2020**, *13*, x FOR PEER REVIEW 7 of 17

**Figure 3.** (**a**) Effect of the shear rate on the viscosity of the test fluid at different temperatures; (**b**) temperature dependence of the viscosity of the test fluid. **Figure 3.** (**a**) Effect of the shear rate on the viscosity of the test fluid at different temperatures; (**b**) temperature dependence of the viscosity of the test fluid. **Figure 3.** (**a**) Effect of the shear rate on the viscosity of the test fluid at different temperatures; (**b**)

#### *3.2. Saturated Out-Of-PlanePermeability Measurements by VARI Process 3.2. Saturated Out-Of-PlanePermeability Measurements by VARI Process*

temperature dependence of the viscosity of the test fluid.

Saturated out-of-plane permeability has been determined from gravimetric measurements at constant flow rate during a Vacuum Assisted Resin Infusion (VARI) process [20]. When steady state conditions are achieved, the quantity of the fluid that enters the preform is equal to the quantity that comes out per time unit. The decrease in weight of the fluid is then monitored as a function of the time. The out-of-plane saturated permeability K3-sat is thus obtained by plotting the fluid weight as a function of time, t, according to the following equation: Saturated out-of-plane permeability has been determined from gravimetric measurements at constant flow rate during a Vacuum Assisted Resin Infusion (VARI) process [20]. When steady state conditions are achieved, the quantity of the fluid that enters the preform is equal to the quantity that comes out per time unit. The decrease in weight of the fluid is then monitored as a function of the time. The out-of-plane saturated permeability K3-sat is thus obtained by plotting the fluid weight as a function of time, t, according to the following equation: *3.2. Saturated Out-Of-PlanePermeability Measurements by VARI Process*  Saturated out-of-plane permeability has been determined from gravimetric measurements at constant flow rate during a Vacuum Assisted Resin Infusion (VARI) process [20]. When steady state conditions are achieved, the quantity of the fluid that enters the preform is equal to the quantity that comes out per time unit. The decrease in weight of the fluid is then monitored as a function of the time. The out-of-plane saturated permeability K3-sat is thus obtained by plotting the fluid weight as a

$$\text{QAt} = \text{Weight} = \frac{\rho \frac{\text{Q}}{\text{S} - \text{sal}} \text{ A}}{\text{\(\frac{\text{P}}{\text{L}}\)} \text{\(\frac{\text{A}}{\text{L}}\)}} \frac{\text{\(\frac{\text{P}}{\text{L}}\)}}{\text{\(\frac{\text{A}}{\text{L}}\)}} \tag{3}$$

(3)

(4)

(4)

where Q is the flow rate, A is the flow channel cross-sectional area, ρis the fluid density, P is the pressure difference(the pressure drop in the pipes was neglected, as well as the effect of gravity), L is the specimen thickness, respectively. The fluid viscosity has been determined according to Equation (2), accounting for the test temperature. A typical plot of the weight loss as a function of time is reported in Figure 4a for Preform A. where Q is the flow rate, A is the flow channel cross-sectional area, ρ is the fluid density, ∆P is the pressure difference (the pressure drop in the pipes was neglected, as well as the effect of gravity), L is the specimen thickness, respectively. The fluid viscosity η has been determined according to Equation (2), accounting for the test temperature. A typical plot of the weight loss as a function of time is reported in Figure 4a for Preform A. L where Q is the flow rate, A is the flow channel cross-sectional area, ρis the fluid density, P is the pressure difference(the pressure drop in the pipes was neglected, as well as the effect of gravity), L is the specimen thickness, respectively. The fluid viscosity has been determined according to Equation (2), accounting for the test temperature. A typical plot of the weight loss as a function of time is reported in Figure 4a for Preform A.

**Figure 4.** (**a**) Weight loss as a function of time for preform A; (**b**) saturated out-of-plane permeability as a function of fiber volume fraction. **Figure 4.** (**a**) Weight loss as a function of time for preform A; (**b**) saturated out-of-plane permeability as a function of fiber volume fraction. **Figure 4.** (**a**) Weight loss as a function of time for preform A; (**b**) saturated out-of-plane permeability as a function of fiber volume fraction.

Considering that the preform is placed between two glass plates at a cavity height h, the fiber

Considering that the preform is placed between two glass plates at a cavity height h, the fiber

0

h

f

h

f

0

nS <sup>V</sup>

 

volume fraction of the preform can be obtained according to following equation:

volume fraction of the preform can be obtained according to following equation:

Considering that the preform is placed between two glass plates at a cavity height h, the fiber volume fraction of the preform can be obtained according to following equation:

$$\mathbf{V\_{f}} = \frac{\mathbf{n}\mathbf{S\_{0}}}{\rho\_{\rm f}\mathbf{h}} \tag{4}$$

where n is the number of plies, ρ<sup>f</sup> is the fiber density and S<sup>0</sup> the areal weight of a single ply.

The effect of fiber volume fraction on the saturated out-of-plane permeability of all the investigated preforms is reported in Figure 4b. The values are the average of at least three measurements. As expected, by increasing the fiber volume fraction, K<sup>3</sup> decreases. The same reinforcement can be characterized by a different permeability depending on the fiber content, related to the cavity height. The different K<sup>3</sup> values among the different preform typologies can be attributed to the different structure of the materials. Preform A is a woven UD fabric with stabilizing weft tows, while the Preform B and C are unidirectional, the former stabilized by stitches, the latter, used in AFP, is a true UD tape. Comparing preforms A and B, both obtained by vacuum bagging, the same pressure produced a higher compaction of fibers for preform B than for preform A, thus leading to a higher fiber volume fraction. The dependence of permeability on fiber volume fraction is different for preform A since it is more compressible than the other two as a consequence of the presence of a woven fabric in it.

The measured saturated out-of-plane permeabilities are also reported in Table 2. To the best of author knowledge, a comparison with literature data can be only made between the values of unidirectional Preform C and the work of Aziz et al. [58] who measured K3-sat by a saturated unidirectional flow device on TX 1100 quasi-isotropic preforms produced by automated fiber placement with different band widths. In particular, at a fiber content of 58%, the obtained saturated permeability was 0.0831 µm<sup>2</sup> and 0.0185 µm<sup>2</sup> on preforms with a band width of 6.35 mm and 12.7 mm, respectively. The experimental value of 0.702 µm<sup>2</sup> obtained in this study on Preform C (produced by automated fiber placement with a band width of 8 mm) at V<sup>f</sup> = 58.8% is in the range measured by Aziz et al. [58], at the same preform material and fiber content, even if the preform architecture is different.


**Table 2.** Out-of-plane saturated and unsaturated permeabilities for the investigated preforms.
