# Out-Of-Plane Permeability Evaluation of Carbon Fiber Preforms by Ultrasonic Wave Propagation

^{*}

## Abstract

**:**

## 1. Introduction

_{1}, where in-plane refers to the reinforcement ply; (ii) transversal in-plane permeability K

_{2}, oriented perpendicular to K

_{1}and lower than K

_{1}; (iii) out-of-plane permeability K

_{3}, oriented perpendicular to K

_{1}and K

_{2}, lower than K

_{1}and of the same order of K

_{2}[21].

## 2. Materials and Methods

#### 2.1. Materials

^{2}, the same weight distribution in warp and weft directions and filled with an epoxy binder. The binder content was 4% of the weight of the carbon fiber [15]. Preforms A were obtained in laboratory by vacuum bagging of [0]

_{22}stacks of G0926 5H satin fabric in an oven during the following thermal cycle: heating up to 100 °C at 3 °C/min, isotherm for 75 min at 110 °C and cooling to room temperature at 1.5 °C/min. This cycle was able to dissolve the epoxy powders used as binder and to give stiffness to the preforms.

#### 2.2. Experimental Set-Up for Permeability Measurements by Ultrasonic Wave Propagation

#### 2.3. Experimental Set-Up for Measurement of Saturatedpermeability

^{−4}g.

## 3. Results

#### 3.1. Rheological Analysis of the Model Fluid

_{g}[57]:

_{0}is a pre-exponential factor, T the absolute temperature, R the universal gas constant and E

_{a}the activation energy. The nonlinear fitting of PEG 400 viscosity with Equation (2) (see Figure 3b) provides an E

_{a}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.

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

_{3-sat}is thus obtained by plotting the fluid weight as a function of time, t, according to the following equation:

_{f}is the fiber density and S

_{0}the areal weight of a single ply.

_{3}decreases. The same reinforcement can be characterized by a different permeability depending on the fiber content, related to the cavity height. The different K

_{3}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.

_{3-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

^{2}and 0.0185 µm

^{2}on preforms with a band width of 6.35 mm and 12.7 mm, respectively. The experimental value of 0.702 µm

^{2}obtained in this study on Preform C (produced by automated fiber placement with a band width of 8 mm) at V

_{f}= 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.

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

_{3}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.

_{1}is lower than that of completely impregnated preform Δt

_{2}. The echo No.2 can be therefore used to monitor the flow front position through the thickness of the preform.

_{f}of the flow front from the glass plate, which in the pulse echo mode is given by:

_{f}and V

_{m}are the volume fraction of carbon fiber and PEG matrix, respectively, while c

_{f}and c

_{m}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:

^{3}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 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].

_{f}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 K

_{3-unsat}of the preform using the Darcy’s equation, valid in the case of one-dimensional flow and constant injection pressure:

_{3-unsat}, according to the following equation:

_{f}, 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

_{f}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

_{f}, 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

_{1}and K

_{2}(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.

_{f}=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

^{2}is obtained by correcting the value reported by Agogue et al. [30] by the (1-V

_{f}) coefficient.

#### 3.4. Mathematical Modeling

_{f}is the fiber volume fraction, r

_{f}the fiber radius and the constants C

_{1}and V

_{fmax}depend on the fiber packing arrangement according to the values reported in Table 3.

_{f}is the fiber volume fraction and V

_{a}is equal to 0.9069 and 0.7854 in case of hexagonal or quadratic fiber arrangement, respectively.

_{3}values as a function of fiber volume fraction has been performed using Equations (10) and (11), in order to obtain the fiber radius r

_{f}, whose values are reported in Table 4. The quadratic fiber arrangement is not able to properly model the experimental values, as inferred by the high differences reported in Table 4, since the obtained fiber radius is higher than the nominal value, which is equal to 3.35 μm for Preform A and 2.5 μm for Preforms B and C. Therefore, the fit obtained with the quadratic fiber arrangement with both the models are not reported in Figure 8 for the sake of clarity.

_{3}of preform A, with all models, leads always to fiber radii much larger than the nominal ones. From Figure 8 it can be observed good agreement among the unsaturated K

_{3}values calculated by ultrasonic measurement and the model prediction. This can be considered a further validation of the proposed measurement method, based on ultrasonic wave propagation.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Preforms for permeability measurements: (

**a**,

**d**) balanced, (

**b**,

**e**) unidirectional (UD) stitched and (

**c**,

**f**) unidirectional (UD) consolidated by AFP.

**Figure 2.**Experimental set-up for out-of-plane permeability measurements by ultrasonic wave propagation: (

**a**) general sketch not in scale; (

**b**) particular of the ultrasonic measurement device.

**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 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 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 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 8.**Mathematical modeling of unsaturated (

**a**–

**c**) and saturated permeability (

**d**–

**f**) values: (

**a**,

**d**) preform A; (

**b**,

**e**) preform B; (

**c**,

**f**) preform C.

A Balanced Preform | B Stitched Preform | C AFP Preform | |
---|---|---|---|

Carbon fiber type | G0926 HS06K (Hexcel) | BNCF-24KIMS-(0)-196-600 (Cytec) | TX 1100 IMS65 24k(Cytec) |

Fiber diameter (μm) | 6.9 | 5.0 | 5.0 |

Fiber elastic modulus (GPa) | 231 | 290 | 290 |

Fiber areal weight (g/m^{2}) | 375 | 196 | 200 |

Number of layers | 22 | 40 | 40 |

Nominal preform size (mm^{3}) | 80 × 50 × 8 | 80 × 50 × 8 | 80 × 50 × 8 |

Preform manufacturing process | vacuum bagging | vacuum bagging | automated fiber placement |

Material | V_{f} (%) | Out-Of-Plane Saturated Permeability (µm^{2}) | Out-Of-Plane Unsaturated Permeability (µm^{2}) |
---|---|---|---|

Preform A | 51.6 | 0.688 ± 0.0290 | 0.306 ± 0.032 |

55.9 | 0.407 ± 0.0052 | 0.143 ± 0.039 | |

60.5 | 0.266 ± 0.0027 | 0.107 ±0.029 | |

Preform B | 58.8 | 0.087 ± 0.005 | 0.057 ± 0.009 |

62.6 | 0.034 ± 0.006 | 0.035 ± 0.009 | |

64.4 | 0.017 ± 0.005 | 0.018 ± 0.009 | |

Preform C | 58.9 | 0.070 ± 0.010 | 0.051 ± 0.003 |

60.1 | 0.050 ± 0.007 | 0.040 ± 0.006 | |

62.8 | 0.021 ± 0.005 | 0.029 ± 0.004 |

Fiber Arrangement | C_{1} | V_{fmax} |
---|---|---|

Quadratic | $\frac{16}{9\pi \times \sqrt{2}}$ | $\frac{\pi}{4}$ |

Hexagonal | $\frac{16}{9\pi \times \sqrt{6}}$ | $\frac{\pi}{2\times \sqrt{3}}$ |

**Table 4.**Unsaturated out-of-plane fiber radius obtained from the mathematical modeling of the experimental K

_{3}values and percentage difference from the nominal fiber radius.

Material | Out-Of-Plane Permeability | Model | Fiber Radius from Model Best Fit, r_{f} (µm) | Nominal Fiber Radius r_{fn} (µm) | Difference [(r _{fn} − r_{f})/r_{f}] × 100 (%) |
---|---|---|---|---|---|

Preform A | Unsaturated | Gebart-hexagonal | 4.57 | 3.45 | +32 |

Gebart-quadratic | 5.45 | 3.45 | +58 | ||

Berdichevsky-hexagonal | 3.23 | 3.45 | −6.8 | ||

Berdichevsky-quadratic | 4.80 | 3.45 | +39 | ||

Saturated | Gebart-hexagonal | 7.09 | 3.45 | +105 | |

Gebart-quadratic | 8.41 | 3.45 | +144 | ||

Berdichevsky-hexagonal | 4.99 | 3.45 | +45 | ||

Berdichevsky-quadratic | 7.39 | 3.45 | +114 | ||

Preform B | Unsaturated | Gebart-hexagonal | 2.89 | 2.5 | +16 |

Gebart-quadratic | 4.04 | 2.5 | +62 | ||

Berdichevsky-hexagonal | 2.20 | 2.5 | −12 | ||

Berdichevsky-quadratic | 3.73 | 2.5 | +49 | ||

Saturated | Gebart-hexagonal | 3.32 | 2.5 | +33 | |

Gebart-quadratic | 4.69 | 2.5 | +88 | ||

Berdichevsky-hexagonal | 2.53 | 2.5 | +1.2 | ||

Berdichevsky-quadratic | 4.43 | 2.5 | +77 | ||

Preform C | Unsaturated | Gebart-hexagonal | 2.81 | 2.5 | +12 |

Gebart-quadratic | 3.87 | 2.5 | +55 | ||

Berdichevsky-hexagonal | 2.13 | 2.5 | −15 | ||

Berdichevsky-quadratic | 3.65 | 2.5 | +46 | ||

Saturated | Gebart-hexagonal | 3.09 | 2.5 | +24 | |

Gebart-quadratic | 4.29 | 2.5 | +72 | ||

Berdichevsky-hexagonal | 2.35 | 2.5 | −6 | ||

Berdichevsky-quadratic | 4.05 | 2.5 | +62 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Lionetto, F.; Montagna, F.; Maffezzoli, A. Out-Of-Plane Permeability Evaluation of Carbon Fiber Preforms by Ultrasonic Wave Propagation. *Materials* **2020**, *13*, 2684.
https://doi.org/10.3390/ma13122684

**AMA Style**

Lionetto F, Montagna F, Maffezzoli A. Out-Of-Plane Permeability Evaluation of Carbon Fiber Preforms by Ultrasonic Wave Propagation. *Materials*. 2020; 13(12):2684.
https://doi.org/10.3390/ma13122684

**Chicago/Turabian Style**

Lionetto, Francesca, Francesco Montagna, and Alfonso Maffezzoli. 2020. "Out-Of-Plane Permeability Evaluation of Carbon Fiber Preforms by Ultrasonic Wave Propagation" *Materials* 13, no. 12: 2684.
https://doi.org/10.3390/ma13122684