*3.3. Out-Of-PlanePermeability Measurements by Ultrasonic Wave Propagation*

Unsaturated K<sup>3</sup> permeability has been measured using a single ultrasonic transducer working in pulse-echo mode, i.e., working either as emitter either as receiver. A dedicated software is able to visualize and save the echoes and to record the time delay between them (time of flight). The principle underlying the measurement is based on the reflection of the ultrasonic wave at the interface between two materials of different density and elastic properties [59]. Since ultrasounds are almost completely reflected at the interface between a solid or a liquid and air, and strongly attenuated by scattering in porous media, the reflected ultrasonic signal (echo) from a dry preform is nearly negligible while that one from a wetted preform is clearly detectable.

As sketched in Figure 5a, when the infusion has not yet begun and the carbon fiber (CF) preform is still dry, the ultrasonic wave is almost completely reflected at the glass/preform interface because ultrasound is very scarcely transmitted in air. Therefore, in Figure 5a, only one ultrasonic wave path is sketched by green arrows. The corresponding echogram (Figure 5b) reports the signals relative to the multiple reflections back and forth from the upper glass plate. No echo relative to reflections from the preform is observed. *Materials* **2020**, *13*, x FOR PEER REVIEW 9 of 17 the multiple reflections back and forth from the upper glass plate. No echo relative to reflections from the preform is observed.

**Figure 5.** Ultrasonic wave path and corresponding echograms at different stages of the impregnation process: (**a**,**b**) no impregnation; (**c**,**d**) partial impregnation;(**e**,**f**) complete impregnation. **Figure 5.** Ultrasonic wave path and corresponding echograms at different stages of the impregnation process: (**a**,**b**) no impregnation; (**c**,**d**) partial impregnation;(**e**,**f**) complete impregnation.

As sketched in Figure 5c, after the beginning of infusion, when the preform is partially impregnated, a fraction of the ultrasonic wave is transmitted at the glass/wet preform interface and travels through the wet preform but it is totally reflected (red arrows) at the flow front, i.e., at the interface between the wet preform and the dry preform. The signals relative to the reflections at the glass/wet preform interface (echo No.1) and at the wet/dry preform interface (echo No.2) are shown in Figure 5d. The time difference, t, between the two peak times relative to the echo from the partial impregnated preform (No.2) and the echo from the glass plate (No.1) is called time of flight (TOF)and corresponds to the time the ultrasonic waves take to travel twice between the glass plate and the As sketched in Figure 5c, after the beginning of infusion, when the preform is partially impregnated, a fraction of the ultrasonic wave is transmitted at the glass/wet preform interface and travels through the wet preform but it is totally reflected (red arrows) at the flow front, i.e., at the interface between the wet preform and the dry preform. The signals relative to the reflections at the glass/wet preform interface (echo No.1) and at the wet/dry preform interface (echo No.2) are shown in Figure 5d. The time difference, ∆t, between the two peak times relative to the echo from the partial impregnated preform (No.2) and the echo from the glass plate (No.1) is called time of flight (TOF)and corresponds to the time the ultrasonic waves take to travel twice between the glass plate and the impregnation front.

impregnation front When the preform is filled, the path of ultrasonic wave is represented by the red arrows in Figure When the preform is filled, the path of ultrasonic wave is represented by the red arrows in Figure 5e. Consequently, the echo No.2 in Figure 5f is right shifted while the position of the two echoes

5e. Consequently, the echo No.2 in Figure 5f is right shifted while the position of the two echoes No.1

of the flow front from the transducer increases. As observable from Figure 5d-f, the TOF of partial impregnated preform t1 is lower than that of completely impregnated preform t2. The echo No.2 can be therefore used to monitor the flow front position through the thickness of the preform.

ultrasonic wave [46].

injection pressure:

No.1 and No.3 relative to multiple reflections at the top glass plate-preform interface remains constant. Therefore, the recorded time of flight of the wave reflected from preform increases since the distance of the flow front from the transducer increases. As observable from Figure 5d–f, the TOF of partial impregnated preform ∆t<sup>1</sup> is lower than that of completely impregnated preform ∆t2. The echo No.2 can be therefore used to monitor the flow front position through the thickness of the preform. *Materials* **2020**, *13*, x FOR PEER REVIEW 10 of 17

A custom-made software has been used to record the TOF during the infusion of the carbon fiber preform. The time of flight measured during an infusion experiment is reported as a function of the infusion time in Figure 6a. TOF increases when the infusion starts, then it reaches a plateau value when the preform is fully impregnated. At this point, it can be deduced that the impregnation of the preform is complete. A custom-made software has been used to record the TOF during the infusion of the carbon fiber preform. The time of flight measured during an infusion experiment is reported as a function of the infusion time in Figure 6a. TOF increases when the infusion starts, then it reaches a plateau value when the preform is fully impregnated. At this point, it can be deduced that the impregnation of the preform is complete.

**Figure 6.** Preform C at fiber volume fraction of 0.628: (**a**) measured ultrasonic time of flight during the infusion; (**b**) calculated flow front position from ultrasonic data. **Figure 6.** Preform C at fiber volume fraction of 0.628: (**a**) measured ultrasonic time of flight during the infusion; (**b**) calculated flow front position from ultrasonic data.

The TOF value can be used to determine the distance xf of the flow front from the glass plate, which in the pulse echo mode is given by: The TOF value can be used to determine the distance x<sup>f</sup> of the flow front from the glass plate, which in the pulse echo mode is given by:

$$\mathbf{x}\_{\mathbf{f}} = \frac{\mathbf{A}\mathbf{f}\mathbf{c}}{2} \tag{5}$$

where t is the TOF value and c the longitudinal wave velocity in the wet preform. This latter has been determined for each analyzed preform at each fiber volume content, by applying the inverse rule of mixture for a composite material with carbon fibers and PEG400 matrix: 1 where ∆t is the TOF value and c the longitudinal wave velocity in the wet preform. This latter has been determined for each analyzed preform at each fiber volume content, by applying the inverse rule of mixture for a composite material with carbon fibers and PEG400 matrix:

$$\mathbf{c} = \frac{1}{\frac{\mathbf{V\_f}}{\mathbf{c\_f}} + \frac{\mathbf{V\_m}}{\mathbf{c\_m}}} \tag{6}$$

where Vf and Vm are the volume fraction of carbon fiber and PEG matrix, respectively, while cf and cm are the sound velocity of carbon fiber and PEG matrix, respectively. The sound velocity of PEG 400 has been measured and it is equal to 1507 m/s. The sound velocity of carbon fiber has been estimated from the elastic modulus and density of the different fibers used for the three preforms according to the following equation: where V<sup>f</sup> and V<sup>m</sup> are the volume fraction of carbon fiber and PEG matrix, respectively, while c<sup>f</sup> and c<sup>m</sup> are the sound velocity of carbon fiber and PEG matrix, respectively. The sound velocity of PEG 400 has been measured and it is equal to 1507 m/s. The sound velocity of carbon fiber has been estimated from the elastic modulus and density of the different fibers used for the three preforms according to the following equation:

$$\mathbf{c}\_{\mathbf{f}} = \sqrt{\frac{\mathbf{E}}{\rho}} \tag{7}$$

where is the density, equal to 1.78 g/cm<sup>3</sup> for all the fibers, while the elastic modulus E is equal to 231 GPa for the carbon fibers of preform A and 290 GPa for those of preform B and C (see Table 1). A sound speed of 11,392 m/s for carbon fibers of preform A and 12,764 m/s for carbon fibers of preform B and C has been obtained from Equation (7). The ultrasonic velocity value c, calculated according to where ρ is the density, equal to 1.78 g/cm<sup>3</sup> for all the fibers, while the elastic modulus E is equal to 231 GPa for the carbon fibers of preform A and 290 GPa for those of preform B and C (see Table 1). A sound speed of 11,392 m/s for carbon fibers of preform A and 12,764 m/s for carbon fibers of preform B and C has been obtained from Equation (7). The ultrasonic velocity value c, calculated according

The xf values as a function of square root of time, reported in Figure 6b, present an initial linear behavior which can be used for the determination of unsaturated out-of-plane permeability K3-unsat of the preform using the Darcy's equation, valid in the case of one-dimensional flow and constant to Equation (6), is considered constant during the experiment. The eventual presence of microscopic air bubbles during the flow does not affect ultrasonic velocity but can decreases the amplitude of the ultrasonic wave [46].

The x<sup>f</sup> values as a function of square root of time, reported in Figure 6b, present an initial linear behavior which can be used for the determination of unsaturated out-of-plane permeability K3-unsat of the preform using the Darcy's equation, valid in the case of one-dimensional flow and constant injection pressure:

$$\mathbf{x}\_{\text{f}} = \sqrt{\frac{2\mathbf{K}\_{\text{3-unsat}}\Delta\mathbf{P}}{\eta}} \sqrt{\mathbf{t}\_{\text{f}}} \tag{8}$$

where ∆P is the pressure difference and η the viscosity of the fluid, determined according to Equation (2), accounting for the test temperature.

The slope obtained from the linear fit of the data can be used for the determination of K3-unsat, according to the following equation:

$$\mathbf{K}\_{\text{3-unsat}} = \frac{(\text{slope})^2 \eta}{2\Delta\mathbf{P}} \tag{9}$$

The values of saturated and unsaturated permeabilities of all the investigated preforms are reported in Table 2. The values are the average of at least three measurements. For each preform, as the fiber volume fraction increases, the permeability values decrease, due to the increased fiber compaction that leads to a reduced flow rate under the same pressure gradient. Moreover, at the same fiber volume fraction and for the same preform, the saturated out-of-plane permeability is higher than the unsaturated out-of-plane permeability. The discrepancy between saturated and unsaturated permeabilities, which has been observed also for in-plane permeability, has been explained by many authors by the void formation during the unsaturated flow. During the filling process, the liquid flow advancement is not uniform and air is entrapped at the flow front, creating partially impregnated zone leading to a change of the hydraulic conductivity [25].

The effect of fiber volume fraction on the unsaturated out-of-plane permeability of all the investigated preforms is reported in Figure 7. Preform A is characterized by higher permeability at similar V<sup>f</sup> , between 0.585 and 0.605, probably as a consequence of the different architecture of each ply. The weft tows in preform A, not only limit its compressibility leading to a lower V<sup>f</sup> at the same compaction level but are also responsible of the presence of lower resistance pathways to fluid advancement. On the other hand, lower permeability of preforms B and C at the same V<sup>f</sup> , can be attributed to the absence of low resistance pathways. The slightly higher permeability of preform B compared to C is probably due to the stitching yarns used in preform B to stabilize the UD arrangement (Figure 1). The impregnation experiments made for the measurement of in-plane permeabilities K<sup>1</sup> and K<sup>2</sup> (not reported), indicated that these yarns are more easily wetted by the fluid which find a low resistance pathways inside them [60]. On the other hand, the carbon fiber tows of preform C, obtained using tapes stabilized by a binder also acting as tackifying agent during the lay up, are better compacted, even if the control of temperature and pressure applied during AFP is less accurate than in vacuum bagging.

A comparison with literature data is very difficult since the reported permeability data are characterized by a strong scattering depending on the measurement method, the fiber preform, the test fluid and the fluid injection parameters. As also observed also by Konstantopoulos et al. [53], the literature data can be used only as a reference to confirm that the results of this study lie in the correct order of magnitude: the unsaturated data obtained by Agougue et al. [30], on TX100 preform at Vf=58% are very close to the results obtained in this work. Despite the different preform architecture (quasi-isotropic for [30] and unidirectional in this study) and the different measurement method, the same order of magnitude of 100 µm<sup>2</sup> is obtained by correcting the value reported by Agogue et al. [30] by the (1-V<sup>f</sup> ) coefficient.

accurate than in vacuum bagging.

*Materials* **2020**, *13*, x FOR PEER REVIEW 11 of 17

3 unsat f f 2K P x t

The slope obtained from the linear fit of the data can be used for the determination of K3-unsat,

The values of saturated and unsaturated permeabilities of all the investigated preforms are reported in Table 2. The values are the average of at least three measurements. For each preform, as the fiber volume fraction increases, the permeability values decrease, due to the increased fiber compaction that leads to a reduced flow rate under the same pressure gradient. Moreover, at the same fiber volume fraction and for the same preform, the saturated out-of-plane permeability is higher than the unsaturated out-of-plane permeability. The discrepancy between saturated and unsaturated permeabilities, which has been observed also for in-plane permeability, has been explained by many authors by the void formation during the unsaturated flow. During the filling process, the liquid flow advancement is not uniform and air is entrapped at the flow front, creating

The effect of fiber volume fraction on the unsaturated out-of-plane permeability of all the investigated preforms is reported in Figure 7. Preform A is characterized by higher permeability at similar Vf, between 0.585 and 0.605, probably as a consequence of the different architecture of each ply. The weft tows in preform A, not only limit its compressibility leading to a lower Vf at the same compaction level but are also responsible of the presence of lower resistance pathways to fluid advancement. On the other hand, lower permeability of preforms B and C at the same Vf, can be attributed to the absence of low resistance pathways. The slightly higher permeability of preform B compared to C is probably due to the stitching yarns used in preform B to stabilize the UD arrangement (Figure 1). The impregnation experiments made for the measurement of in-plane permeabilities K1 and K2 (not reported), indicated that these yarns are more easily wetted by the fluid which find a low resistance pathways inside them [60]. On the other hand, the carbon fiber tows of preform C, obtained using tapes stabilized by a binder also acting as tackifying agent during the lay

2

where P is the pressure difference and the viscosity of the fluid, determined according to Equation

(slope) <sup>K</sup> 2 P

(8)

(9)

3 unsat

partially impregnated zone leading to a change of the hydraulic conductivity [25].

(2), accounting for the test temperature.

according to the following equation:

**Figure 7. Figure 7.** Unsaturated out-of-plane permeability as a function of fiber volume fraction. Unsaturated out-of-plane permeability as a function of fiber volume fraction.
