Experimental characterization by fluorescence of capillary flows in dual-scale engineering fabrics

Abstract

Liquid composite molding (LCM) is an increasingly used family of processes to manufacture composite parts. In LCM, the fibrous reinforcement is first laid in a mold cavity. After closure of the mold or covering of the reinforcement with a plastic bag, a liquid polymer resin is injected or infused under vacuum through the fiber bed. A key issue and novel feature of this investigation lies in the dual-scale architecture of engineering fabrics: microscopic pores exist between the filaments of the fiber tows, while macroscopic pores are created between the tows as a result of the stitching/weaving process. On a microscopic scale, capillary flows in fiber tows and gaps between tows play a major role on the quality of impregnation of the fiber bed by the liquid resin. In order to better understand the mechanisms that govern the impregnation of fibrous reinforcements in LCM, an experimental study of wicking behavior was carried out based on capillary rise experiments. A new monitoring technique based on fluorescent dye penetration inspection (DPI) and digital imaging was implemented in this investigation to track the capillary flow front. Visual monitoring of the capillary front is coupled with Wilhelmy’s approach based on real-time fluid mass acquisition with a high resolution balance. Experimental observations of the height of the capillary front and the uptake fluid mass absorbed by the fabric were analyzed by two different imbibition models.

Keywords

Liquid composite molding porosity wicking dual-scale fibrous reinforcement Lucas–Washburn model

One key issue in composite manufacturing by resin injection, or liquid composite molding (LCM), is related to the impregnation of the fibrous reinforcement by the liquid reactive resin. In processes such as resin transfer molding (RTM), compression resin transfer molding (CRTM) and vacuum-assisted resin infusion (VARI), a reactive liquid resin is injected or infused inside a mold cavity containing a dry fibrous reinforcement. In order to produce a high-performance composite, fibers must be completely saturated prior to resin gelation.^1,2 Indeed, impregnation defects have a detrimental impact on the mechanical properties of composite parts such as the maximum compression, flexural and shear inter-laminar strengths.^3–6 It has also a substantial effect on crack initiation and fatigue life, as well as on moisture absorption and surface finish.^7,8 Hence, developing practical strategies to produce composite parts of high impregnation quality becomes a critical industrial goal.^9,10

During impregnation of the fibrous reinforcements under pressure, two competitive forces take place: viscous and capillary forces. Viscous forces make the fluid flow through the open gaps between fiber tows resulting in the formation of microscopic voids inside the fiber tows (last point to be filled). Capillary forces act pulling the fluid inside the fiber tows and may result in the formation of macroscopic voids between the fiber tows. These two competitive phenomena have to be studied in order to better understand the formation of voids during impregnation of a dual-scale porous media.¹¹ This work focuses on the study of the capillary-driven flows and the subsequent formation of macroscopic voids between fiber tows.

In order to better understand fabric impregnation mechanisms during part manufacturing by LCM, a comprehensive, repeatable and less time-consuming wicking characterization for dual-scale fibrous reinforcements can be of great help to identify optimal processing conditions. Such characterization must take into account a key feature of engineering fabrics, namely their dual-scale porosity. As a matter of fact, microscopic pores exist inside the fiber bundles, whereas macroscopic pores are created between the bundles as a result of the stitching/weaving process.

Among the experimental procedures presented in the literature to characterize wicking in fibrous reinforcements, the capillary rise method seems adequate. Over the last decades, this approach has been used to characterize the permeability, the architecture of porous media and the capillary pressure at equilibrium in different soils, of polymer wicks, of paper-like porous media and of engineering textiles. Researchers such as Amico and Lekakou,^12,13 Batch et al.,¹⁴ Sénécot¹⁵ as well as Mhetre and Parachuru¹⁶ have also studied by this method the microscopic and macroscopic properties of industrial fabrics used as fibrous reinforcements in high-performance composites. However, for composite materials, this characterization technique suffered from a lack of precision, repeatability and robustness. These problems arise from different technical difficulties, among which three major ones have been identified: (1) textile alterations may occur during capillary rise tests; (2) significant changes in the properties of the infiltration fluids may happen as a result of solvent evaporation and (3) the progression of the capillary front cannot be followed accurately during long wicking tests because of front fading in time, even when dyes are used.^15,17–20

To circumvent these limitations, a new monitoring technique based on fluorescent dye penetration inspection (DPI) and charge-coupled device (CCD) image acquisition has been implemented in this investigation. The fluorescent DPI approach has been previously used in non-destructive testing and defect detection in welding.²¹ This visual monitoring of the capillary front by fluorescence was coupled with real-time acquisition of the fluid mass absorbed by capillarity with a high resolution balance. This coupled approach allows gathering automatically and simultaneously the capillary front position and the uptake fluid mass in time with a high degree of resolution and repeatability. The consistency of the experimental procedure is discussed and demonstrated on a single ply laminate configuration cut from an E-glass non-crimp fabric. The results obtained along the warp and weft directions are compared with those of other standard characterization methods such as microscopic analysis and wicking characterization in individual fiber tows.

This new capillary setup allowed investigating the impact of sizing and of fiber volume content on the wicking behavior in fibrous reinforcements. The fabric wicking behavior was characterized for a significant sample size (representative elementary volume (REV)) in the final stacking configuration of the laminate, which depends on upstream manufacturing steps such as stitching, weaving, draping and preforming (compaction). In this work, two imbibition models are introduced that consider the evolutions of the capillary height and of the uptake fluid mass without gravity. The Lucas–Washburn models were selected to complete the wicking characterization for several laminate configurations. After presentation of the capillary rise setup based on fluorescence visualization, this new approach is validated by comparison with other standard characterization methods. The wicking experiments are carried out along the warp and weft directions for a single ply configuration of a non-crimp fabric. This characterization provides also an evaluation of the impact of sizing and fiber volume content on wicking.

Bibliography

Over the last decades, several experimental studies have been carried out on capillary flows in fiber tows based on the capillary rise method. Indeed, this characterization setup was used to investigate wicking phenomena along and across the fiber tows of engineering fabrics used in polymer composite manufacturing.^19,22,23 However, few experimental investigations focused on capillary flows in dual-scale fabrics and none addressed the impact of fiber volume content on the wicking flow behavior in fibrous reinforcements of dual-scale porosity. In order to track capillary flows in engineering fabrics, visual monitoring of the visual tracking of the capillary front and monitoring of the uptake fluid mass have long been used by researchers. In this regard, Sénécot¹⁵ and Kissa²⁴ developed experimental setups to monitor visually with cameras, but without edge detection algorithms or other numerical tools, the vertical and horizontal progressions of the capillary flow in engineering fabrics. Other researchers such as Tagaya et al.²⁵ have used a method based on electrical capacitance to monitor the front position during the capillary rise of liquid electrolytes in fabrics. However, according to Law,²⁶ these electrical methods exhibit some drawbacks: the liquid impurity and the uneven distribution of chemicals on the surface of the textile may affect the electrical capacitance and resistance of the porous medium, which in turn reduces the accuracy.

Sénécot¹⁵ has focused his wicking study on short and medium terms capillary rise experiments in various glass fibrous reinforcements. This author carried out capillary rise tests with several dyed liquids such as bromonaphtalene, silicone oil and alkanes. Significant deviations of the wicking flow behavior from the linear Lucas–Washburn model have been observed with highly volatile alkanes in unsaturated and uncontrolled atmospheres. New approaches have been considered to circumvent this limitation. First, the evaporation phenomenon can be explicitly taken into account in the fabric wicking model. Another alternative consists of avoiding or limiting the fluid evaporation during the capillary rise tests by using nonvolatile alkanes and/or a closed transparent cavity. These technical improvements allowed following visually the wicking front and recovering the typical Lucas–Washburn flow trend from the experimental data. Besides, Sénécot¹⁵ carried out two sets of experiments in order to investigate the impact of the fabric tension and the fibrous strip width on the wicking behavior of a single fabric ply. No significant impact of these two factors has been noticed. However, a significant coupling has been observed between the faster inter-bundle flow and the slower intra-bundle flow in dual-scale fabrics. This flow coupling has been also noticed visually by Bico and Quéré,²⁷ Zhuang et al.²⁸ and Miller.²⁹ Sénécot¹⁵ found that significant fluid transfer was taking place at each fiber tow crossover. This fluid transfer results in a slowdown of the leading wicking front inside longitudinal fiber tows and in the development of a lagging wicking front along transversal fiber bundles.

Pezron et al.³⁰ and Hsieh¹⁸ and Yu³¹ were among the first researchers to study the vertical imbibition of liquids based on the uptake fluid mass analysis inside complete textile fabrics of various materials such as cotton and polyethylene terephthalate. They have chosen an electronic tensiometer or a microbalance to monitor the wicking mass evolution over time in short fabric samples, i.e. for sample lengths between 0.25 and 3 cm. Pezron et al.³⁰ carried out their capillary rise experiments on one inch wide fabric strips with nonvolatile fluids such as silicone oil, decane, dodecane, hexadecane and decanol in order to prevent evaporation, thus unwanted losses of liquid mass. According to these authors, with hexadecane the deviation of the imbibition behavior from single linearity could be explained by the occurrence of two coupled capillary flows: a microscopic intra-bundle flow and a macroscopic flow in the superficial fabric alveolus. In this regard, Pezron et al.³⁰ succeeded in separating and isolating the contributions from both capillary flows by blocking the superficial wicking with a coating. These authors highlighted that the isolated intra-bundle flow was following closely the linear model of Lucas–Washburn and the fast wicking flow in the superficial alveolus was exchanging fluid with the intra-bundle flow. Note also that no measurable effect of the dye on the absorption process in textile fabrics was noticed.³⁰ On the other hand, Hsieh and Yu³¹ carried out their capillary rise experiments with distilled and deionized water, as well as hexadecane, on 6.35 mm wide fabric strips of 100% cotton cut with a die cutter. They used a fabric approach velocity of 1 µm/s with respect to the liquid reservoir in order to detect properly the initial contact force and minimize the immersion depth of the fabric-liquid interface. This experimental strategy has been reused here to carry out the fabric imbibition. According to the work of Hsieh and Yu,³¹ the wetting characteristics of their cotton fabric were independent of the fabric length, of the liquid-fabric immersion depth and of the fabric orientation with respect to the liquid surface. Thus, wetting characteristics depend on the wettability of the fabrics and are not affected by their configuration.

Modeling of capillary rise through dual-scale fabrics

The Lucas–Washburn imbibition models are based on the modified Jurin’s law and the global force balance for creeping flows.^32–35 These models are recalled in this section in order to study capillary flows inside dual-scale fibrous reinforcements. These mathematical models of capillary flows have already allowed characterizing the wicking phenomenon inside individual fiber tows and dual-scale fibrous reinforcements.^16,22 The current characterization is based on capillary rise experiments with a perfectly wetting probe fluid, i.e. pure hexadecane. The Lucas–Washburn imbibition models selected here consider the evolution of the capillary height and of the uptake fluid mass without gravity. In order to introduce these two models, the main concepts related to the porous structure of dual-scale fibrous reinforcements must be presented: the microscopic and macroscopic pore distributions, the equivalent hydraulic diameter of the capillary channels, the pore surface area per unit mass and the tortuosity of the fiber bundles.

Modified Jurin’s law for dual-scale fabrics

Microscopic pores in fiber tows

Woven fibrous reinforcements are porous media composed of oriented fiber tows that contain microscopic pores inside the fiber bundles and macroscopic pores between the fiber tows created as a result of the stitching/weaving fabrication process (see Figure 1(a)). Such materials can be modeled as a statistical bimodal set of parallel and tortuous capillary tubes of circular section (see Figure 1(b)).¹⁵ The equivalent hydraulic diameter $d_{h}^{m}$ of the parallel capillary tubes inside the fiber bundles is defined as the ratio between the cross-sectional area of the flow canals and their wetted perimeters. If $V_{f}^{tow}$ denotes the fiber volume content of the fiber bundle, φ_tow is the porosity of the fiber tow and d_f is the average filament diameter, the theory of porous media gives the following expression of the equivalent hydraulic diameter $d_{h}^{m}$ ²²

d_{h}^{m} = \frac{d_{f} (1 - V_{f}^{tow})}{V_{f}^{tow}} = \frac{d_{f} φ_{tow}}{(1 - φ_{tow})}

(1)

Figure 1.

Origin of the tortuosity of fiber bundles and filaments in fibrous reinforcements: (a) woven pattern of a 2D reinforcement; (b) tortuous capillary tube.

It was previously observed that flows inside vertical capillary tubes stopped at a given equilibrium height when gravitational force are balanced by capillary force.³⁵ As reported by de Gennes et al.,³⁶ this equilibrium height in capillary pores can be evaluated a priori by the standard Jurin’s law derived from the Young-Laplace equation. From this standard Jurin’s law and the definition of the hydraulic diameter $d_{h}^{m}$ of microscopic pores inside fiber tows of equation (1), a modified expression of Jurin’s law can also be proposed in fiber tows as follows^13,35,37

z_{Jurin}^{m} = f_{geo} \cdot (\frac{4}{d_{h}^{m}}) \cdot (\frac{γ_{lv} \cos θ}{ρ g}) = f_{geo} \cdot S_{pv} \cdot (\frac{γ_{lv} \cos θ}{ρ g})

(2)

where

f_{geo}

, S_pv,

γ_{lv}

, ρ , θ , and g are respectively a geometrical constant, the specific surface area of the fiber bundles per unit pore volume, the surface tension and mass density of the wicking liquid, the contact angle between the liquid-vapor interface and the fibers and the gravity acceleration. The geometrical constant

f_{geo}

0 \leq f_{geo} \leq 1

, depends only on the pore size distribution and on the flow direction with respect to the fiber tows.³⁸ On the other hand, the theoretical specific surface area S_pv of the fiber bundle per unit pore volume can be estimated in a first approximation by assuming that the fibers are smooth parallel cylinders in a regular array.^39,40 This latter property of the fiber bundles can be calculated from the fiber volume content and the specific surface area S_m per unit mass of the fiber tow. S_m in a porous medium represents the ratio of the total surface of the pores to the solid volume. It can be characterized experimentally by Brunauer-Emmett-Teller (BET) analysis, a technique based on the multilayer adsorption of gas molecules on solid surfaces.^41,42 S_m can be also estimated from the filament diameter and the glass mass density

ρ_{glass}

by assuming that the filaments are smooth cylinders packed in a regular array in the following form

S_{m} = \frac{s_{f}}{m_{f}} = \frac{s_{f}}{ρ_{glass} v_{f}} = \frac{S_{f}}{ρ_{glass}} = \frac{N_{f} π d_{f} L}{ρ_{glass} (N_{f} π d_{f}^{2} L / 4)} = \frac{4}{ρ_{glass} d_{f}}

(3)

where s_f , m_f , v_f and L denote respectively the surface, mass, volume and length of a fiber tow, N_f is the number of filaments per fiber tow and S_f is the specific surface area per unit fiber volume of a tow defined by

S_{f} = \frac{s_{f}}{v_{f}}

(4)

Regarding S_pv, it can be estimated from the filament diameter and the tow fiber volume content as follows

S_{pv} = \frac{s_{f}}{v_{pore}} = S_{f} \cdot \frac{V_{f}}{(1 - V_{f})} = ρ_{glass} \cdot S_{m} \cdot \frac{V_{f}}{(1 - V_{f})} = \frac{4}{d_{f}} \cdot \frac{V_{f}}{(1 - V_{f})} = \frac{4}{d_{h}^{m}}

(5)

In the above equation, the pore volume v_pore in a fiber tow is defined by the following standard relationship in porous media

v_{pore} = \frac{v_{f} (1 - V_{f})}{V_{f}}

(6)

The value of the geometrical constant $f_{geo}$ in equation (2) depends on the global curvature of the liquid meniscus. Default values for $f_{geo}$ are respectively 1 and 0.5 for capillary-driven flows parallel and perpendicular to the fiber tows.^12,38,43 However, capillary flows in fiber tows are rather complex and tridimensional interactions may occur between the axial and perpendicular flows. Thus, these geometrical factors $f_{geo}$ have been generalized in tensorial form by Ahn et al.³⁸ A value of the geometrical parameter $f_{geo}$ between 0.5 and 1 is usually obtained by nonlinear fitting of the capillary height evolution in time for long wicking tests in fiber tows.⁴³ Furthermore, following Bear,³⁹ the concept of tortuosity needs to be introduced to take into account the non-rectilinear path of the fiber bundles and the filaments in woven fabrics (see Figure 1). Tortuosity represents the ratio between the distance L_e(t) covered by the fluid during imbibition and the equivalent distance L(t) along a straight line

τ_{tow} = L_{e} (t) / L_{e} (t) L (t) L (t)

(7)

Macroscopic pores between fiber tows

The hydraulic diameter of the macroscopic pores $d_{h}^{M}$ is usually one or two orders of magnitude larger than the hydraulic diameter of the microscopic pores $d_{h}^{m}$ inside the fiber bundles and it can be estimated as follows

d_{h}^{M} = \frac{4 A_{gap}}{P_{gap}}

(8)

where the cross-sectional area A_gap and the wetted perimeter P_gap of these rectangular gap channels between fiber tows were calculated using the gap width values and the thicknesses h_tow of the warp and weft tows

A_{gap} = h_{tow} \cdot w_{gap}

(9)

P_{gap} = 2 (h_{tow} + w_{gap})

(10)

Accordingly, the equilibrium capillary height $z_{Jurin}^{m}$ in the microscopic pores is about one or two orders of magnitude larger than in the macroscopic pores. In this regard, the standard expression of Jurin’s law allowed estimating the equilibrium height $z_{Jurin}^{M}$ in macroscopic pores between fiber tows as follows

z_{Jurin}^{M} = (\frac{4}{d_{h}^{M}}) \cdot (\frac{γ_{lv} \cos θ}{ρ g})

(11)

Thus, the capillary flow contribution of the macroscopic pores in the porous medium to the medium and long-term imbibition behavior in dual-scale fabrics can be neglected compared to the wicking contribution inside fiber tows.^16,44 However, as a result of their larger hydraulic diameter, the capillary flows in macroscopic pores can be significant in the initial wicking behavior of a dual-scale fabric.^15,27 In summary, the fiber tows and the macroscopic pores between the tows in a woven fabric can be modeled by a bimodal (dual-scale) system of parallel capillary channels with a microscopic hydraulic diameter $d_{h}^{m}$ and tortuosity τ_tow of the fiber tows and a macroscopic hydraulic diameter $d_{h}^{M}$ and tortuosity τ_gap for the macroscopic pores.¹⁵ In this regard, the dual-scale nature of fibrous reinforcements must be taken into account in order to interpret properly experimental data from capillary rise experiments.

Lucas–Washburn imbibition models

Usually, during isothermal capillary rise experiments in immobile and unstretchable fibrous reinforcements, the infiltration fluid is considered incompressible and Newtonian. Figure 2 shows a typical capillary rise through a porous medium. The progression of the capillary front tends asymptotically towards an equilibrium height $z_{eq}$ , for which the capillary and gravitational forces balance each other in static equilibrium. The equilibrium capillary height $z_{eq}$ can be estimated by the modified Jurin’s law, equation (2), using the fiber tow properties. Figure 2 highlights also the linear Lucas–Washburn flow regime, for which the gravity contribution can be neglected with respect to viscous and capillary forces at the beginning of the capillary rise, i.e. for short imbibition distances ( $z (t) << z_{Jurin}$ ). At this point, capillary forces are balanced only by viscous forces.

Figure 2.

Schematic view of the flow front evolution during a typical capillary rise through a porous medium.

Furthermore, the inertia and the transient wettability terms can be considered as relevant only during the first microseconds of the imbibition phenomena through the largest pores ( $d_{h} >> 100 μ m$ ) and for low viscosity liquids such as low molecular weight alkanes.^45,46 By neglecting the inertia term, the capillary flows through the macroscopic and microscopic pores of tortuosity τ are governed in dual-scale fabrics by the Hagen-Poiseuille equation for Reynolds numbers that do not exceed a value between 1 and 10.³⁹ Note that this latter validity range of Reynolds numbers has been proposed in order to cover five different definitions of the characteristic length dimension of the porous medium, the dimension which is indeed taken into account in the computation of the Reynolds number.³⁹ From the balance between capillary, viscous and gravitational forces, the following form of the Hagen-Poiseuille equation for the flow in a capillary tube is obtained

\underset{inertia}{\underset{︸}{_{_{_{_{_{_{_{_{}}}}}}}} 0}} = \underset{capillarity}{\underset{︸}{π \frac{d_{h}^{2}}{4} ρ_{} g z_{Jurin}}} - \underset{viscous drag}{\underset{︸}{8 π μ τ^{2} z \frac{dz}{dt}}} - \underset{gravity}{\underset{︸}{π \frac{d_{h}^{2}}{4} ρ g z_{\binom{}{}}}}

(12)

The medium and long-term imbibition behaviors in dual-scale fabrics are dominated by the capillary flow contribution of the microscopic pores inside the fiber bundles.^16,44 However, the capillary flow contribution of the macroscopic pores can be significant during the short-term imbibition of dual-scale fabrics. This contribution can even outperform the initial wicking contribution of fiber tows alone as a result of the high permeability of the macroscopic pores (lower viscous forces) compared to the lower axial permeability of fiber tows.^15,27 Therefore, a synergy between the macroscopic and the microscopic pores is taking place during the initial wicking stage of a dual-scale fibrous reinforcement.²⁷ This results in a flow regime with a higher wicking performance than in fiber tows alone.¹⁶ Accordingly, imbibition models already implemented for wicking in individual fiber tows are still valid for wicking in dual-scale fabrics, but only for short imbibition distances, i.e. as long as $z (t) < 1 < z_{Jurin}$ . (see equation (2) for the introduction of the term z_Jurin.)

Imbibition model I

By rearranging and simplifying equation (12), an ordinary differential equation (ODE) describing the progression in time of the flow height in a capillary tube is obtained

\frac{dz}{dt} = β_{h} (\frac{z_{Jurin}}{z} - 1)

(13)

where

β_{h} = d_{h}^{2} ρ g / d_{h}^{2} ρ g 32 μ τ^{2} 32 μ τ^{2}

(14)

As a result, a first imbibition model (model I) arises from the space-time integration of equation (13) as follows

- \frac{β_{h} t}{z_{Jurin}} = \ln (1 - \frac{z}{z_{Jurin}}) + \frac{z}{z_{Jurin}}

(15)

Imbibition model II

Neglecting the gravity contribution, i.e. for short imbibition distances ( $z (t) << z_{Jurin}$ ), the velocity of the capillary front during the Lucas–Washburn flow regime results in the following equation derived from the Jurin’s law, equation (11), or the modified Jurin’s law, equation (2)

\frac{dz}{dt} = β_{h} (\frac{z_{Jurin}}{z})

(16)

where

β_{h} = \frac{(d_{h}^{M})^{2}}{16 k_{o} τ_{gap}^{2}} \cdot \frac{ρ g}{μ}

(17)

β_{h} = \frac{(d_{h}^{m})^{2}}{16 k_{o} τ_{tow}^{2}} \cdot \frac{ρ g}{μ} = \frac{1}{k_{o} τ_{tow}^{2} S_{pv}^{2}} \cdot \frac{ρ g}{μ}

(18)

where k_o is the Kozeny geometrical constant of Blake-Kozeny-Carman model.²² Integrating the equation (16) results in the imbibition model II, namely the classical Lucas–Washburn law of capillary height evolution³²

z^{2} = B_{h} t

(19)

where

B_{h} = 2 β_{h} z_{Jurin}

(20)

Parameter B_h represents the Lucas–Washburn slope of the square of the capillary height evolution during the linear Lucas–Washburn flow regime (see Figure 2). It has also been referred to as a diffusion coefficient (m²/s) or capillary rate coefficient by Hamdaoui et al.⁴⁷ The parameter B_h can be obtained by linear regression on the evolution of the square height of the capillary front in time. For fiber tows, this parameter B_h can be estimated analytically using the properties of fiber tows and of the infiltration fluid as follows

B_{h}^{theo} = \frac{f_{geo}}{2 k_{o}} \cdot \frac{d_{f} φ_{tow}}{τ_{m}^{2} (1 - φ_{tow})} \cdot \frac{γ_{lv} \cos θ}{μ}

(21)

Imbibition model III

The initial evolution of the capillary uptake fluid mass m(t) can be considered homogeneous through all pores, namely the macroscopic and microscopic pores of a dual-scale fabric. This saturated imbibition flow in a bidirectional fabric is observed before the end of the capillary rise in the axial gaps between axial fiber tows as a result of the static force balance between gravity and capillarity effects in these macroscopic pores (for an equilibrium height z_Jurin). This initial capillary uptake behavior on a fabric strip of width w_fabric and thickness h_fabric can be modeled as follows

m (t) = ρ w_{fabric} h_{fabric} (1 - V_{f}^{fabric}) s z (t)

(22)

where

V_{f}^{fabric}

and s denote respectively the fiber volume content of the fabric and its saturation level. For a saturated flow, s is considered equal to one. The following equation can thus be obtained for the capillary height

z (t) = \frac{m (t)}{ρ w_{fabric} h_{fabric} (1 - V_{f}^{fabric})}

(23)

By substituting equation (23) into the second imbibition model, equation (16), if gravity can be neglected, the uptake wicking mass can be modeled by the following ODE

\frac{dm}{dt} = β_{m} (\frac{z_{Jurin}}{m})

(24)

where

β_{m} = ρ^{2} {\underset{c_{v}}{\underset{︸}{[w_{fabric} h_{fabric} (1 - V_{f}^{fabric})]}}}^{2} β_{h} = (ρ c_{v})^{2} β_{h}

(25)

Parameter c_v in the above equation is referred to as the volumetric fluid-holding capacity per unit length (m³/m) of the fabric. It depends only on the architecture of the fiber bundles and the gaps between fiber tows. The integration of this ODE results in the new imbibition model III, which describes the evolution in time of the uptake fluid mass for short imbibition distances (without gravity)

m^{2} = B_{m} t

(26)

where

B_{m} = (ρ c_{v})^{2} B_{h}

(27)

Parameter B_m is the Lucas–Washburn slope for the square of the capillary mass evolution during the linear Lucas–Washburn flow regime. It can be obtained by linear regression on the evolution of the square uptake wicking mass in time for short imbibition distances.

On the other hand, when the capillary flow stops in the macroscopic pores, wicking still continues its rise only through axial fiber bundles in dual-scale fibrous reinforcements. Wicking will also sustain fluid transfer from axial to transversal fiber tows.¹⁶ This typical medium and long-term imbibition of the fabric will leave behind all the macroscopic pores empty. Thus, the real fluid volume V_real(t) and the apparent fluid volume V_app(t) contained in a rigid mold cavity of given cross-sectional area can be used to evaluate the saturation level of the fabric in time s(t), $0 \leq s \leq 1$ , as follows

s (t) = \frac{V_{real} (t)}{V_{app} (t)}

(28)

where

V_{real} (t) = \frac{m (t)}{ρ}

(29)

and

V_{app} (t) = w_{fabric} h_{fabric} (1 - V_{f}^{fabric}) z (t)

(30)

where $V_{f}^{fabric}$ is the fiber volume content of the fabric. This experimental approach was already used by researchers to estimate the evolution of unsaturated volume in time during impregnation of fibrous reinforcements.⁴⁸

Capillary rise measurement

When fabrics are dipped into a liquid, interfacial forces develop at the meniscus contact line along the wetted perimeter P_w of the fiber tows. According to the balance or the imbalance of interfacial forces along the contact line, the dipped fiber bundles can be pulled or pushed off by the liquid. Moreover, along the submerged part of the dipped bundles, buoyancy forces F_buoyancy may develop. The mass offset from these two forces must be taken into account as follows in order to get the net uptake fluid mass²³

m (t) = m_{total} (t) - m_{meniscus} + m_{buoyancy}

(31)

where m_meniscus and m_buoyancy represent respectively the meniscus and buoyancy force contributions in the total measured mass. The buoyancy force can be cancelled by limiting the dipping depth of the fabric under the wicking liquid surface.

Fabric anisotropy and pore volume ratio

The total effective cross-sectional area of the pores in the fabric plays an important role in the establishment of the capillary flow in both the microscopic and macroscopic pores. This parameter can be derived from the results of the capillary rise experiments. Indeed, an approximation of the total cross-sectional area of the pores A_φ normal to the flow direction can be evaluated from the slopes B_h and B_m of the height and mass evolutions respectively obtained by Lucas–Washburn laws, equations (19) and (26). In this regard, dividing B_m given by equation (27) by B_h given by equation (20) and substituting the corresponding expression of c_v introduced in equation (25) gives the following expression of A_φ

A_{φ} = w_{fabric} h_{fabric} (1 - V_{f}^{fabric}) = \frac{1}{ρ τ} \sqrt{\frac{B_{m}}{B_{h}}}

(32)

This parameter can also be evaluated by 2D microscopic image analysis or derived from the final uptake fluid mass as follows

A_{φ} = [n_{tows} A_{tow} φ_{tow} τ_{m} + n_{gaps} A_{gap} τ_{M}]_{axial} + [h_{tow} φ_{tow} τ_{m}]_{trans}

(33)

where A_tow, A_gap, n_tows and n_gaps are respectively the cross-sectional area of the axial fiber tows, the cross-sectional area of the axial gaps between fiber bundles, the number of axial fiber tows per centimeter as well as the number of axial gaps between fiber tows per centimeter along the fabric width. On the other hand, h_tow is the thickness of the transversal fiber tow with respect to the capillary flow direction. Finally, the tortuosities of fiber tows τ_m and gaps τ_M of a typical non-crimp fabric such as the one studied here are the same, i.e. τ, and equal to one. The approximation of the total cross-sectional area of the pores A_φ in both flow directions can be used to estimate the warp/weft anisotropy ratio

R_{a}^{φ}

of the pore areas (with the same fabric width and the same stitching/weaving pattern, thus the same tortuosity)

R_{a}^{φ} = \frac{\sqrt{B_{m} / B_{h}} |_{warp}}{\sqrt{B_{m} / B_{h}} |_{weft}} \approx \frac{(n_{tows}^{warp} A_{tow}^{warp} φ_{tow}^{warp} + n_{gaps}^{warp} A_{gap}^{warp} + h_{tow}^{weft} φ_{tow}^{weft})}{(n_{tows}^{weft} A_{tow}^{weft} φ_{tow}^{weft} + n_{gaps}^{weft} A_{gap}^{weft} + h_{tow}^{warp} φ_{tow}^{warp})} \to 1

(34)

Again, this anisotropy ratio $R_{a}^{φ}$ can be evaluated from the results of microscopic image analysis or by capillary rise experiments. It must be equal to one for saturated flows along both fabric directions. From the properties of the fiber tows and of the fibrous reinforcement in its natural configuration, the ratio $R_{REV}^{m}$ of the microscopic pore volume to the total pore volume available in a REV can be estimated as follows

R_{REV}^{m} = \frac{V_{micropores}}{V_{REV}} = \frac{[n_{tows}^{warp} \cdot A_{tow}^{warp} \cdot φ_{tow}^{warp} + n_{tows}^{weft} \cdot A_{tow}^{weft} \cdot φ_{tow}^{weft}]}{h_{fabric} \cdot (1 - V_{f}^{fabric})}

(35)

where

V_{micropores}

and

V_{REV}

are respectively the total volume of microscopic pores in the REV and the total pore volume of the REV. This ratio represents the volumetric contribution of the microscopic pores to the overall porosity of the fibrous reinforcement. For higher compaction levels, this ratio changes as a result of gap pore reduction, nesting/slippage effects, tow bending and bundle deformation.⁴⁹ The ratio

R_{REV}^{m}

of the microscopic pore volume to the total pore volume was also introduced by Pillai and Advani⁵⁰ as a key parameter connected to the saturation of dual-scale porous media.

Material characterization

Fabric characterization

The bidirectional glass non-crimp fabric (NCF) of JB Martin® (TG15N60A/#3028) tested in this investigation (see Figure 3(a)) is a glass fabric made by Vetrotex™ warp (735 tex) and weft (275 tex) tows stitched together by polyester binder filaments (17 tex). The polyester filaments hold the untwisted glass strands together as shown in Figure 3(b). This unbalanced fabric has 45% of its glass filament volume along the warp and 55% along the weft. Each fabric ply consists of two weft and one warp layers. The characterization results for the fiber tows are summarized in Table 1 and they were carried out by LeBel et al.⁵¹ The characterization of the filament average diameter d_f, of the total cross-sectional area of fiber tows A_tow and of the fiber tow porosity φ_tow were firstly evaluated by microscopic image analysis along the warp and weft directions. On the other hand, the equivalent hydraulic diameter $d_{h}^{m}$ of fiber tows along the warp and weft directions was evaluated by capillary flow porometry. Note that the values of φ_tow and A_tow derived from the analysis of the final uptake fluid mass in fiber tows and the information provided by the fabric supplier are given in parentheses in Table 1. These properties of fiber tows were used to estimate their Lucas–Washburn slopes with hexadecane using equation (21).

Figure 3.

Pictures of the TG15N60A E-glass NCF from JB Martin®: (a) the unit cell and the REV definitions; (b) binocular microscopic image of the fabric along the weft showing a polyester binding filament.

Table 1.

Properties of fiber tows in JB Martin TG15N60A NCF.⁵¹

Properties^a	Values from standard characterization methods^b	Values from capillary rise method or supplier^c	Units
Warp direction
Filament diameter d_f	14.9 ± 0.1	(15)	µm
Total cross-section area A_tow	0.54 ± 0.03 2.20 ± 0.02× 0.32 ± 0.01	0.52 ± 0.02	mm²
Microscopic porosity φ ^warp	49 ± 8	45 ± 2	%
Hydraulic diameter $d_{h}^{m}$ (equation (1))	12 ± 2; 8.76 to 16.04	12 ± 1	µm
Lucas–Washburn slope with hexadecane $B_{h}^{theo}$ (equation (21))	4 ± 1	2.7 ± 0.2	×10⁻⁵ m²/s
Weft direction
Filament diameter d_f	13.1 ± 0.2	(13)	µm
Total cross-section area A_tow	0.178 ± 0.009 1.347 ± 0.007× 0.168 ± 0.007	0.186 ± 0.009	mm²
Microscopic porosity φ ^weft	50 ± 10	44 ± 4	%
Hydraulic diameter $d_{h}^{m}$ (equation (1))	12 ± 2; 8.76 to 16.04	10 ± 2	µm
Lucas–Washburn slope with hexadecane $B_{h}^{theo}$ (equation (21))	3 ± 1	2.3 ± 0.3	× 10⁻⁵ m²/s

Characterizations were carried out at room temperature (22.5 ± 2.5℃) for a relative humidity of 22 ± 5%.

Standard methods are microscopy, porometry by liquid expulsion, BET analysis and gravimetry.

Information provided by the fabric supplier is given in parentheses.

Fabric thickness

The fabric thickness h_fabric was measured 50 times at rest following the ASTM D1777-96 (2007) standard. The experimental device consisted of a calibrated gage and presser foots used to apply a uniform pressure on the fibrous reinforcement placed on a marble table. The thickness measurements were carried out at 22.5 ± 2.5℃ with a relative humidity (RH) of 22 ± 5%. According to option 1 of the ASTM D1777-96 (2007) standard, a compaction pressure of 4.14 kPa has to be applied on woven fabrics by the gage in order to measure the fabric thickness. This compaction pressure resulted in a fabric thickness of 0.614 mm. However, in the case of glass fiber mats (option 4 of the standard), a compaction pressure of 18.9 kPa must be applied to measure the fabric thickness. Under this condition, the measured fabric thickness was 0.543 mm.

Microscopic image analysis

Procedures based on microscopic image analysis were devised to evaluate the morphological and topological properties of the fibrous reinforcement along the warp and weft directions. In order to prepare fabric plies for 2D microscopic analysis, laminates were made by capillary impregnation with D.E.R. 383 epoxy resin mixed with 30 PHR of amine hardener in order to cure at room temperature with low shrinkage. After the resin is fully cured, samples were cut out with a diamond saw, cast in epoxy and polished with sanding papers (60, 120, 240, 400 - 15 µm grains) as well as polishing pastes (9 µm and 1 µm grains). Cured-glass epoxy samples were analyzed with a JEOL JSM840 scanning electron microscope (SEM), an optical microscope from Nikon Japan LU1176C-Clemex and an Olympus SZ61 binocular microscope. The fiber tow centers were measured by ellipse fitting and centroid determination algorithms from Matlab functions.

The mean distances L_c between the centers of fiber tows along the warp and weft directions were about 1.94 mm and 3.26 mm respectively. The measured fiber tow counts per centimeter n_tow in the warp and weft directions were 3.07 tows/cm and 10.31 tows/cm respectively, which is consistent with the specifications of the fabric manufacturer. The width of the gaps between the fiber tows along the warp

w_{gap}^{warp}

and weft

w_{gap}^{weft}

directions were found to be about 1.08 mm and 0.61 mm respectively. The cross-sectional area A_gap and the wetted perimeter P_gap of the rectangular gap channels were calculated in the warp and weft directions using the gap width values and the thicknesses h_tow of the warp and weft tows (respectively 0.32 mm and 0.168 mm in Table 1). The equivalent hydraulic diameters of the macroscopic pores in the warp and weft directions were found to be respectively 490 µm and 260 µm using equation (8). All the data obtained by image analysis are reported in Table 2.

Table 2.

Properties of JB Martin TG15N60A NCF

Properties	Values	Units
Global fabric
Fabric mass density ρ_fabric	2.54 ± 0.01	g/cm³
Polyester mass fraction R_polyester	1.72 ± 0.03	%
Polyester degradation temperature T_polyester	385	℃
Thickness h_fabric	0.543 ± 0.004^a 0.614 ± 0.003^b	mm
Superficial density ρ_s	517 ± 6 (518)^c	g/m²
Fiber volume content $V_{f}^{fabric}$	37.7 ± 0.7^a 33.1 ± 0.6^b	%
Ratio of total volume of microscopic pores to REV volume $R_{REV}^{m}$ (equation (35))	46 ± 7^a 38 ± 6^b	%
Anisotropy ratio of total pore area $R_{a}^{φ}$ (equation (34))	1.0 ± 0.3 (1.0 ± 0.1)	−
Warp direction
Tow count n_tows	3.07 (3.1)	tows/cm
Center-to-center tow distance L_c	1.94 (1.92)	mm
Width of gap between fiber tows w_gap	1.08 ± 0.03	mm
Hydraulic diameter of macropores $d_{h}^{M}$ (equation (8))	490 ± 30	µm
Total effective pore area A_φ (equation (32))	9 ± 2 (8.4 ± 0.8)	mm²
Weft direction
Tow count n_tows	10.31 (10.4)	tows/cm
Center-to-center tow distance L_c	3.26 (3.23)	mm
Width of gap between fiber tows w_gap	0.61 ± 0.02	mm
Hydraulic diameter of macropores $d_{h}^{M}$ (equation (8))	260 ± 30	µm
Total effective pore area A_φ (equation (32))	9 ± 2 (8.5 ± 0.8)	mm²

ASTM D1777-96 standard (option 4; applied pressure of 18.9 ± 0.7 kPa); compacted.

ASTM D1777-96 standard (option 1; applied pressure of 4.14 ± 0.21 kPa); uncompacted.

Values derived from final uptake fluid mass and information provided by the fabric supplier are given in parentheses.

Thermogravimetric analysis

The degradation temperatures of the polyester filaments T_polyester and of the fabric sizing T_sizing as well as the polyester mass fraction R_polyester in the fibrous reinforcement were evaluated by thermogravimetric analysis. The results are also presented in Table 2. The degradation of the polyester filaments was observed around 385℃ with a Q500 thermogravimetric analyzer (TGA) from TA Instruments®. The same apparatus was also used to measure the degradation temperature of the fabric sizing which was around 245℃. A pyrolytic oven was used to evaluate the polyester mass fraction of the fabric samples because their size was too large for the TGA. Knowing the initial mass of the sample and the remaining mass above 385℃, the polyester mass fraction was measured for several samples cut out from the fibrous reinforcement. The bottom curve in Figure 4 shows the polyester mass fraction for several sample sizes. The polyester mass fraction in the fabric starts to converge for a sample area larger than 225 mm². The average polyester mass fraction of the fibrous reinforcement turned out to be around 1.72%.

Figure 4.

Porosity of the fibrous reinforcement and polyester mass fraction plotted as a function of the area of fabric samples.

Fiber volume content and mass density

The macroscopic properties of the fibrous reinforcement such as the superficial density ρ_s, the porosity φ_fabric, the fiber volume content $V_{f}^{fabric}$ and the mass density ρ_fabric of the fabric were evaluated by scanner imagery and buoyancy principle from 25 disk-shaped samples larger than the REV of the fabric. The characterization results are reported in Table 2.

A CanoScan 4400F scanner from Canon® coupled with an edge detection algorithm in Matlab were used to measure the surface area of the fibrous reinforcement samples. The procedure was calibrated with high precision shims of known dimensions, thus known surface areas.

The mass of fabric samples and polyester binder were measured in air with a CP225D Sartorius microbalance of 10 µg resolution. The volume of the fibers was evaluated by buoyancy. A superficial density of 517 g/m² was derived for the fibrous reinforcement from the weight of the samples.

The porosity φ_fabric, the fiber volume content $V_{f}^{fabric}$ and the mass density ρ_fabric were computed from the thickness, mass and fiber volume of the fabric samples. The mass density of the fibrous reinforcement was 2.54 g/cm³. The fiber volume content varied between 33.1% (option 1) and 37.7% (option 4) depending on the thickness measurement option (see Table 2). Accordingly, the fabric porosity in its natural configuration turned out to vary from 62.3% (option 4) to 66.9% (option 1). The mass density of the polyester binder was found to be around 1.61 g/cm³.

Analysis of the REV

The size of the fabric REV was evaluated by plotting in Figure 4 the fabric porosity and the polyester mass fraction for fabric samples of different areas. These results show that the REV area was about 225 mm². The 95% confidence intervals for the average values of the polyester mass fraction and the porosity are also shown in Figure 4. As illustrated in Figure 3(a), the area of the REV was significantly larger than that of the unit cell, because the former must take into account the intrinsic variability of the fabric structure.

Evaluation of the microscopic pore volume to REV volume ratio and the anisotropy ratio

The fiber tow properties of Table 1 obtained by wicking characterization and the experimental data of Table 2 for the uncompacted fabric allow estimating the ratio $R_{REV}^{m}$ of the microscopic pore volume with respect to the total pore volume of the REV. This ratio $R_{REV}^{m}$ was calculated by equation (35) for the two different compaction levels considered

R_{REV}^{m} |_{V_{f}^{fabric} = 37.7 %} = 46 \pm 4 %

(36)

R_{REV}^{m} |_{V_{f}^{fabric} = 33.1 %} = 38 \pm 3 %

(37)

The values of this ratio show that the microscopic pore volume represents a significant contribution to the overall porosity of the fibrous reinforcement.

The anisotropy ratio $R_{a}^{φ}$ of the total pore area between the two fabric directions was evaluated by equation (34) using two different approaches: a) by image analysis and b) by capillary rise. The results of both approaches stand as follows

R_{a}^{φ} |_{capillary rise} = 1.0 \pm 0.1

(38)

R_{a}^{φ} |_{image analysis} = 1.0 \pm 0.3

(39)

Note that the anisotropy ratio of the total pore area is not significantly different from unity, which means that the fibrous reinforcement has a nearly isotropic structure in terms of porosity.

Fabric variability

Fabric variability depends on two factors: (1) variability of the fiber bundles and (2) variability of the fabric architecture. Figure 4 shows the fabric porosity and polyester mass fraction as a function of sample size for the confidence interval. Variations in porosity of about 3% were observed, while the variability of the polyester mass fraction remains less than 1%. Similar variabilities can be observed in Table 2. Due to the intrinsic variability of fibers, characterization of fabric properties such as Lucas–Washburn slopes for capillary height evolution, equation (20), and uptake fluid mass, equation (27), has to be carried out in a REV. Indeed, it was already noticed that even for the same porosity, two experiments can show different rates of impregnation if they have different pore size distributions.^19,20 For all these reasons, the mold and the fabric should be at least 15 mm wide to minimize the variability effect and thus allow a comprehensive and robust wicking characterization of dual-scale fibrous reinforcements.

Fluid characterization

A 99% pure hexadecane from Sigma-Aldrich® was chosen as infiltration fluid because of its totally wetting behavior, its low volatility (low vapor pressure) and its non-hygroscopic behavior. This liquid was mixed with a fluorescent tracer (0.1 g/liter) to improve the impregnation traceability. This increased the contrast between the capillary front and the glass fibers and prevented the fading of the flow front in time. The UV-excited Pyrromethene 567A from Exciton® was chosen for its high solubility in hexadecane. This visual monitoring approach is based on a non-destructive testing method called DPI.

All the properties were characterized at room temperature (22.5 ± 2.5℃) at a RH of 22 ± 5%. The mass density was measured with a 25 ml pycnometer from Fisher Scientific® and a CP225D balance from Sartorius®. The dynamic viscosity was measured with a double Couette geometry, at a constant shear rate of 10 s⁻¹, by a MCR-501 rheometer from Anton-Paar®. The surface tension was evaluated with a K14 force tensiometer from Krüss® and a platinum-iridium Wilhelmy’s plate of known wetted perimeter. The same tensiometer allowed measuring the dynamic contact angle and the wetted perimeter on glass filaments. For this purpose, the measurement speed was set to 3 mm/min in order to minimize the viscous and inertial effects and remain close to the range of capillary flow velocity. Moreover, segments only 3 to 4 mm long were used to ensure the rigidity of the filaments during the measurement. Tensiometry was preferred over optical goniometric measurements, because the curved surface of the filaments makes it more difficult to evaluate the contact angle by an optical method. The dynamic contact angle of hexadecane on glass filaments was estimated to be zero degree, thus exhibiting totally wetting behavior for a typical range of spontaneous imbibition velocity.

Tensiometric measurements were also used to evaluate the apparent contact angle between the fiber bundles of the fibrous reinforcement and the probe fluid. Indeed, the contact angle was evaluated from the mass jump during the initial contact between the fibers and pure hexadecane. Warp tows were chosen for their significantly larger wetted perimeter than weft tows, thus the corresponding mass jump reading was higher, which improves the relative resolution of the microbalance measurement. The characterization setup was first used in conjunction with a reference fluid of known properties such as a 99% pure hexane to evaluate the average wetted perimeter of warp tows, and then with the infiltrating hexadecane to measure the contact angle with warp tows. Finally, for comparison purpose, a static contact angle analysis between a reference surface of clean glass and the hexadecane probe fluid was also conducted with a NRL-100 optical goniometer from Ramé-Hart®. The measured physical properties are reported in Table 3. Both measurements of the apparent static contact angle between hexadecane and fiber tows or a clean glass surface gave a zero degree angle, thus confirming the totally wetting behavior of the probe fluid. The results of this comprehensive characterization are summarized in Table 3.

Table 3.

Characterization results of hexadecane fluid

	Fluid properties			Interfacial properties
	Density (kg/m³)	Dynamic viscosity (mPa·s)	Surface tension (mN/m)	Advancing dynamic contact angle (degree)	Static contact angle (degree)
Sigma-Aldrich® 99% pure hexadecane	767.1948 ± 0.0004	3.51 ± 0.01	27.50 ± 0.03	∼0	∼0

Experimental setup

Capillary rise setup

An experimental setup was developed in this study to monitor simultaneously the flow front position and the total uptake mass by spontaneous imbibition during 24 hours. As shown in Figure 5, it is composed of a motorized platform, a transparent glass mold, a data acquisition unit, a 14.7 megapixels Powershot G10 digital camera from Canon® and a high resolution balance from Sartorius® (CP225D). The liquid containers used here were standard rheometer capsules of 63.0 mm in diameter by 9.6 mm depth. This high surface area of the liquid containers with respect to the total fluid uptake volume allows minimizing buoyancy force variations during wicking tests that result from a decrease of the liquid level.

Figure 5.

Schematic representation of the capillary rise setup for fibrous reinforcements.

To properly control the initial contact of the fabric and hexadecane, a motorized platform from Newport® (UTM100CC) moved the mold that contained the fibrous reinforcement. The UTM100CC motorized platform has a minimal velocity of 0.1 µm/s (order of magnitude of commercial tensiometers), which was appropriate to position the mold with respect to the liquid container. The UTM100CC was controlled via a LabView program that allows the users to set the velocity and mass thresholds for resin/fabric contact detection. When this mass threshold is reached, a signal is sent to stop the motor and trigger the charge-coupled (CCD) digital camera as well as the CP225D balance for data acquisition.

Two rectangular molds made of glass were used to encapsulate the fabric in order to follow visually the capillary rise of the fluid inside the fibrous reinforcement while keeping the fabric straight and controlling the fiber volume content during imbibition. These molds were supported in the vertical position by specimen bottle forceps. These molds were also held inside the Sartorius CP225D glass chamber that can be closed as required in order to minimize air convection interference. A mold thickness of 3.18 mm was used for multiple ply laminate analysis, while a mold thickness of 0.56 mm was reserved for single ply analysis. Glass was the only material that could offer simultaneously the required specific rigidity and transparency as well as the necessary chemical and thermal resistance. The molds were equipped with self-adhesive rulers to provide a visual reference during the capillary impregnation. A level board was used to ensure that the mold remains vertical and perfectly perpendicular to the liquid container.

The 3.18 mm thick mold was loaded with several plies of fabric strips, i.e. four, five, six or seven plies. The thickness of this mold was significantly larger than the hydraulic diameters $d_{h}^{m}$ and $d_{h}^{M}$ of the microscopic and macroscopic pores of the fibrous reinforcement (see Table 1 and Table 2). The 0.56 mm thick mold was used with a single fabric ply. Capillary flow as a result of the mold cavity alone was limited to less than 5 mm. Both mold cavities were 25.4 mm wide by 305 mm long, sealed on the side with vacuum grease and closed with miniature clamps. Both molds possessed vents on their top edges. Each border of the mat strips was first held in place with an adhesive tape to facilitate their handling. Then they were cut roughly with an electrical chisel and finished off with a steel cutting die and hydraulic press to get a reproducible and straight, clean cut without using tape on the fabric edges. At the end of each imbibition test, the length of the fibrous reinforcement was measured by image analysis on the last pictures recorded. Two 15 W UV black lights were used to follow the progression of the hexadecane blended with the fluorescent dye. The complete setup (see Figure 5) was installed in a darkroom to facilitate the visualization of the capillary rise.

Image post-treatment

An automated tracking of the capillary front was developed in Matlab. This tracking of the fluid front was found to be robust and efficient despite the variable brightness of the recorded images. Two factors contributed to this variable brightness: (1) the variable shutter speeds of the semi-automatic camera and (2) the global increase in brightness resulting from the use of a fluorescent dye. Figure 6 illustrates the tracking of the capillary front. Figure 6(a) shows a typical image recorded with the CCD camera. Figure 6(b) shows the successive capillary fronts evaluated by Otsu’s thresholding and edge filtering algorithms.⁵² The average flow front position and standard deviations were computed at each time step from these pixel images. This approach gives an average position of the wicking front through the thickness of the laminate.

Figure 6.

Capillary flow front tracking inside a fabric ply with Otsu’s algorithm: (a) raw picture of capillary flow; (b) successive flow front positions along the fabric ply plotted with Matlab.

Experimental results

Verification of basic assumptions

In order to validate the experimental setup and verify the basic underlying assumptions, the capillary rise experiments were conducted at room temperature and atmospheric pressure, i.e. 22.5 ± 2.5℃, for a RH of 22 ± 5% and an atmospheric pressure of 95 ± 6 kPa, on single ply fabrics in the warp and weft directions. The validity of Young-Laplace’s equation and, thus of the modified Jurin’s law introduced in equation (2), was established when the deformation of the spherical-shaped meniscus as a result of gravity is neglected. This hypothesis can be verified by comparing the hydraulic diameter $d_{h}^{m}$ of the fiber tows (see Table 1) and the hydraulic diameter $d_{h}^{M}$ of the macroscopic pores (see Table 2) with a characteristic capillary length $l_{cap}$ defined as follows⁵³

l_{cap} = 2 \sqrt{\frac{γ_{lv}}{ρ g}}

(40)

The above equation allows estimating

l_{cap}

from the properties of hexadecane listed in Table 3. The negligible impact of gravity on the meniscus shape and, thus the validity of Young-Laplace’s equation and the modified Jurin’s law, can be confirmed for capillary canal sizes of equivalent hydraulic diameter

d_{h} < l_{cap}

. A characteristic capillary length of the order of 4 mm was found (see Table 4), which is significantly larger than the hydraulic diameter

d_{h}^{m}

of the warp and weft tows (12 µm and 10 µm respectively). This capillary length is also larger than the hydraulic diameter

d_{h}^{M}

of the macroscopic pores in the warp and weft directions estimated to 490 µm and 260 µm respectively (see Table 2). Moreover, an additional dimensionless criterion can also be introduced to check the validity of the Young-Laplace’s equation and, thus of the modified Jurin’s law. When capillary effects dominate, the liquid column in the capillary tubes exhibits a low Bond dimensionless number defined as follows:

Bo = \frac{Δ ρ g d_{h}^{2}}{16 γ_{lv}}

(41)

Table 4.

Dimensionless numbers for single ply imbibition with hexadecane along the warp and weft directions

Properties	Gap between tows		Fiber tow		Unit
Properties	Warp	Weft	Warp	weft	Unit
Capillary length l_cap (equation (40))	3.823 ± 0.002				mm
Bond number $Bo$ (equation (41))	4100 ± 300	1200 ± 100	2.2 ± 0.2	2.3 ± 0.2	× 10⁻⁶
Range of Reynolds numbers $Re$	[0.05–5.82]	[0.04–5.12]	[0.001–0.14]	[0.001–0.20]	× 10⁻¹
Range of capillary numbers $Ca$ (equation (43))	[0.003–0.69]	[0.002–1.15]	[0.003–0.69]	[0.002–1.15]	× 10⁻³

Values of the Bond number were calculated for the fiber tows and for the gaps between the fiber bundles (see Table 4). Low Bond numbers were obtained, i.e. lower than 10⁻², confirming the negligible impact of gravity on the meniscus shape, and thus the validity of the modified Jurin’s law.

Reynolds number Re of the capillary flow inside fiber tows and in the macroscopic pores can be calculated to validate the hypothesis of creeping flow modeled by Darcy’s law. Re was first evaluated for a length scale equal to the hydraulic diameter of the gaps between fiber tows $d_{h}^{M}$ . Then, it was also evaluated for a length scale equal to the hydraulic diameter of capillary channels inside fibers tows $d_{h}^{m}$ . The characteristic velocity v was obtained by the differentiation of the Lucas–Washburn model of capillary front of equation (19) as follows

v = B_{h} / B_{h} 2 z 2 z, z \in [l_{cap}, l_{total}]

(42)

As reported in Table 4, Re for capillary flows inside the fiber tows as well as in the gaps between fiber bundles remain below 10, which validate the use of the Darcy’s law.³⁹

On the other hand, the capillary number is defined as follows

Ca = \frac{μ v}{γ_{lv}}

(43)

where the characteristic velocity v is given by equation (42). Table 4 gives the range of capillary numbers covered in this investigation. Ca varies in two orders of magnitude from 10⁻³ down to 10⁻⁵, which is close to the equilibrium state where inertia effects are neglected and the dynamic wettability term disappears in the balance of forces that governs imbibition in a porous medium.^38,40,53,54

Finally, the capillary rise in fiber tows (microscopic pores) and in the gaps between fiber tows (macroscopic pores) was estimated a priori using the imbibition model I developed in equation (15) for closed capillary tubes. The capillary rise in both kinds of pores was first considered separately using their respective hydraulic diameters reported in Table 1 and in Table 2 and the hexadecane properties of Table 3. These analytical estimations of the imbibition behavior are presented in Figure 7. Figure 7 shows that the initial imbibition behavior of the fabric was driven by the macroscopic pores, but on a limited distance. Indeed, the equilibrium capillary heights z_Jurin in the gaps between fiber tows along the warp and weft directions were reached after a few minutes. These z_Jurin heights for the macroscopic pores along the warp and the weft direction were below two centimeters. Thereafter, there was a crossing point where the capillary flow progression in the microscopic pores of the fiber tows took over the imbibition in the fabric. Before this crossing point, the interactions between the capillary flows in the fiber tows and in the gaps between fiber tows are considered significant.²⁷ However, the analytical imbibition model I for closed capillary tubes did not consider any synergy or transversal flow between the microscopic and the macroscopic pores of the fabric. Accordingly, one must remember that a dual-scale fabric is not an assembly of closed capillary pores but rather a complex porous medium with open and interconnected pores.¹⁶

Figure 7.

Capillary rise modeling in closed capillary tubes of diameters equal to the hydraulic diameters of fiber tows and of the gaps between fiber tows.

These analytical predictions of the imbibition behavior of a dual-scale fabric have been qualitatively confirmed by a capillary rise experiment in a single fabric ply with two supplies of hexadecane of different colors. The first infiltration fluid was hexadecane with a yellow fluorescent dye, whereas the second one was hexadecane with a blue fluorescent dye. This qualitative experiment, presented in Figure 8, highlights the contribution of the macroscopic pores during the initial imbibition of the fabric and the contribution of the microscopic pores during the medium and long-term imbibitions. Indeed, Figure 8 shows that the gaps between fiber tows were filled with the blue fluorescent hexadecane whereas axial and transversal fiber tows were filled with the yellow fluorescent hexadecane. Furthermore, the capillary rise in the gaps between fiber tows stopped above a height of two centimeters, leaving all the macroscopic pores empty above this equilibrium height (see Figure 8). This observation confirms the analytical predictions on the imbibition of a dual-scale fabric carried out previously with the imbibition model I developed in equation (15) and presented in Figure 7.

Figure 8.

Qualitative imbibition test in a single fabric ply along the weft direction with two successive alkanes of different colors (yellow and blue fluorescent dyes): (a) during imbibition; (b) after imbibition.

Wicking in single ply with sizing

Quantitative analysis of the uptake fluid mass and capillary height evolution

The first tests were conducted on a single ply fabric with fiber sizing. The results are presented in Figure 9, where the square of the capillary height along the warp and weft directions respectively is plotted with respect to imbibition time. The error bars on the imbibition heights were computed from the standard deviations of the flow front positions at each time step. In both experiments, Lucas–Washburn mass evolutions exhibited nonlinear behaviors after five seconds. This phenomenon can be first explained by the heterogeneous imbibition progression (fingering in fiber tows) across the fabric ply as a result of the capillary rise stop in the macroscopic pores. It can be also explained by the mass transfer coming from transversal wicking at the tow/stitch cross-overs.^15,17,30 For imbibitions in a single ply, this transversal wicking flow can be tracked visually by fluorescence via the saturation of transversal tows (see Figure 6(a)). The initial Lucas–Washburn weight slopes B_m for single ply imbibitions were 1.9 × 10⁻⁹ kg²/s and 3.9 × 10⁻⁹ kg²/s in the warp and weft directions respectively.

Figure 9.

Comparison of the Lucas–Washburn fits on the square height evolutions in time of hexadecane imbibitions of a single fabric ply in the warp and weft directions for initial and medium-term wicking behaviors.

The values of parameter B_h for the initial wicking behavior of a single ply are larger than those obtained in single fiber tows (see Table 5).⁵¹ Indeed, the height Lucas–Washburn slopes B_h for single plies were 4.2 × 10⁻⁵ m²/s and 7 × 10⁻⁵ m²/s in the warp and weft directions respectively. This represents a relative increase in B_h of 100% and 260% with respect to single fiber tow imbibition along the warp and the weft directions respectively (see Table 5). This upward shift in the imbibition behavior can be mainly attributed to the synergetic interaction between capillary flows in microscopic and macroscopic pores.^16,27 As a matter of fact, because of the dual-scale pore structure of the fabric, the gaps between the fiber tows play a major role during the initial wicking stage of the fibrous reinforcement.^15,55 Figure 9 showed also that the slopes B_h of the medium-term imbibition of a single ply in the warp and weft directions converged to the previous wicking slopes B_h for single fiber tows after a transition period. Indeed, as reported in Table 5, the slope B_h for medium-term imbibition of single plies was about 2.02 × 10⁻⁵ m²/s in both fabric directions, a value consistent with the tow wicking slopes B_h of 2.14 × 10⁻⁵ m²/s and 1.95 × 10⁻⁵ m²/s in the warp and weft directions respectively. Besides, the slopes B_h of the Lucas–Washburn square height reported in Table 6 for the initial imbibition of single plies in the warp and weft directions were significantly different. This demonstrates the distinct wicking behavior in the warp and weft directions that arise from the distribution of macroscopic pores. This is consistent with the microscopic image analysis that gave different values of the hydraulic diameter

d_{h}^{M}

in both directions.

Table 5.

Results of warp and weft fiber tow imbibitions with hexadecane.⁵¹

Properties	With sizing		Without sizing (LOI)		Units
Properties	Warp	Weft	Warp	Weft	Units
Microscopic porosity	43 ± 1	47 ± 1	51.2 ± 0.4	51 ± 1	%
Height Lucas–Washburn slope B_h (equation (20))	2.14 ± 0.05	1.95 ± 0.07	3.4 ± 0.1	2.24 ± 0.03	× 10⁻⁵ m²/s
Weight Lucas-Washborn slope B_m (equation (27))	24.66 ± 0.08	2.20 ± 0.03	76 ± 1	3.08 ± 0.07	× 10⁻¹⁴ kg²/s
Jurin’s height $z_{Jurin}$ (equation (2))	1.28 ± 0.05	1.26 ± 0.05	0.93 ± 0.02	1.07 ± 0.04	m

LOI: Fabric sizing removed by carbonization.

Table 6.

Results of single ply imbibitions with hexadecane

Properties	Warp direction	Weft direction	Units
Initial Weight Lucas–Washburn slope B_m (equation (27))	1.9 ± 0.3	3.9 ± 0.8	× 10⁻⁹ kg²/s
Initial Height Lucas–Washburn slope B_h (equation (20))	4.2 ± 0.6	7 ± 1	× 10⁻⁵ m²/s
Relative Increase in B_h with respect to Single Fiber Tow Imbibition	100 ± 30	260 ± 60	%
Medium-term Height Lucas–Washburn slope B_h (equation (20))	2.02 ± 0.09	2.02 ± 0.09	× 10⁻⁵ m²/s

Quantitative analysis of the fabric saturation

From the acquisition of the capillary flow height and uptake fluid mass, the evolution of the saturation of the fabric ply along the warp and the weft directions could be estimated by equation (28). The evolution of the saturation of the fabric in both directions was plotted with respect to the imbibition height as reported in Figure 10. The saturation of the fabric converges to 42% in both fabric directions. This value is consistent with the ratio $R_{REV}^{m}$ estimated by equation (35) and obtained for a fabric ply thickness h_fabric of 0.56 mm and a fabric fiber volume content $V_{f}^{fabric}$ of 36.3%. Indeed, this ratio $R_{REV}^{m}$ was equal to 44 ± 4%. This confirms that the capillary flow was only progressing through axial and transversal fiber tows, thus leaving behind all the macroscopic pores empty, during the medium and the long-term imbibition behaviors of the dual-scale fabric. Furthermore, the total void content %V_void(t) was estimated as follows from the saturation of the fabric s(t)

% V_{void} (t) = (1 - V_{f}^{fabric}) (1 - s (t))

(44)

Figure 10.

Saturation evolution along the warp and weft directions in single ply fabrics with respect to imbibition height.

The evolution of the total void content in the single ply fabrics along the warp and the weft directions was plotted in Figure 11 with respect to the capillary number defined in equation (43). This showed that the total void content in both fabric directions converges to an asymptotic value of 38% when the capillary rise slowed down. Indeed, this value of the total void content corresponds to a situation in which all the macroscopic pores are empty as observed for flow progression around the equilibrium state below Ca = 10⁻⁵. This asymptotic behavior of the total void content in dual-scale fabrics with respect to capillary number is consistent with previous results published in the scientific literature.⁵⁶

Figure 11.

Total void content evolution along the warp and the weft directions in single ply fabrics with respect to the capillary number.

For the fabric structure studied here, the tortuosity of fiber tows in both directions is assumed to be equal to unity for this NCF. From the ply imbibition data in Table 6, the total effective cross-sectional area of the pores A_φ in the fabric was estimated by equation (32) using B_m and B_h values. The values of A_φ along the warp and the weft directions were respectively 8.8 ± 0.2 mm² and 10 ± 1 mm². These values were consistent with the ones reported in Table 2 and obtained by microscopic image analysis or by analysis of the final uptake fluid mass. These values were also consistent with the A_φ value of 9.1 ± 0.1 mm² evaluated by equation (32) based on current fabric properties, namely $V_{f}^{fabric}$ , h_fabric and w_fabric. This confirms that the capillary rise was a homogeneous saturated flow through all the pores, namely the macroscopic and microscopic pores, during the initial imbibition of the current dual-scale fabric. Furthermore, the warp to weft anisotropy ratio $R_{a}^{φ}$ of the total pore area A_φ (equation (34)) was equal to 0.9 ± 0.2. This ratio was consistent with the values of 1.0 evaluated from microscopic image analysis or from the analysis of the final uptake fluid mass as reported in Table 2.

Wicking in single ply fabric without sizing

In order to study the impact of sizing on imbibition behavior, the fabric sizing was removed by carbonization (LOI) at 245℃ for three hours. Afterwards, plies were kept under vacuum at −85 kPa for 15 minutes to remove residual ashes. The uptake fluid masses over time with and without sizing are compared in Figure 12. The capillary front positions over time with and without sizing are compared in Figure 13. The fabric without sizing sucks spontaneously a significantly larger fluid mass than the one with sizing. Moreover, this fluid mass is rising faster in the fabric without sizing than with sizing. The removal of the sizing seems to increase significantly the tow microscopic porosity, thus the average hydraulic diameters of the capillary channels in the fiber bundles. The alteration of the fabric is more of a geometrical nature than a chemical one and originates from a loss of bundle integrity due to the degradation of the film forming agent.⁵⁷

Figure 12.

Comparison of weight evolutions of hexadecane for weft imbibition in a single ply fabric with and without sizing.

Figure 13.

Comparison of height evolutions of hexadecane for weft imbibition in a single ply fabric with and without sizing.

Wicking in multiple ply laminates

As mentioned previously, single and multiple ply imbibition behaviors are complex and more difficult to predict than tow imbibitions for several reasons: (1) transversal flows are created at the fiber/stitch intersections; (2) part of the fluid mass is absorbed in the macroscopic pores and (3) complex flow interactions exist between the microscopic and macroscopic pores. Moreover, during fabric compaction, phenomena such as pore reorganization, nesting/slippage, tow bending and bundle deformation affect the pore structure and distribution. Because these phenomena have an influence on the microscopic and macroscopic wicking flows inside fiber tows and in the gaps between the fiber bundles, wicking analysis can bring useful information to characterize the dual-scale porosity structure of engineering fabrics and better understand the evolution of porosity after compaction as a function of fiber volume content. The glass mold was used to investigate multiple ply fibrous reinforcements for fiber volume contents between 25% and 45%.

Qualitative analysis of the uptake fluid mass evolution

The uptake fluid mass was monitored for several multiple ply laminates. As presented in Figure 14, laminates of higher fiber volume contents with several plies contain more fiber tows and hence more microscopic pores, and should therefore exhibit a superior fluid uptake capacity in medium-term imbibitions. However, by zooming in on the first minute of the wicking tests, the evolution of the uptake fluid mass was nonlinear. Furthermore, there was an inversion of the uptake fluid mass evolution in Figure 14. Indeed, a laminate with less plies exhibits the fastest initial uptake wicking flow in macroscopic pores but possesses a lower total fluid uptake capacity. This can be explained by the existence of larger channels between the ply layers. As shown previously for fabrics without sizing, the reinforcements with larger macroscopic channels and with fiber tows of higher porosity exhibit a higher permeability. This facilitates the initial uptake fluid mass by wicking. However, this behavior holds on a short-term basis only. Such inversions between short and medium-term imbibition evolutions have already been noticed in porous media.¹⁵

Figure 14.

Impact of fiber volume content on the square weight evolutions of hexadecane in multiple ply fabrics (weft).

Quantitative analysis of capillary height evolution

By monitoring the wicking height in laminates, interesting features appear as illustrated in Figure 15. For both laminates at negligible compaction levels (four and five plies), i.e. for fiber volume contents less than 35%, the medium-term wicking height evolutions are approximately similar. Indeed, in Figure 15, the curves of square height evolution for four and five plies are superposed. From the previous analysis on medium-term imbibitions, it turns out that the fiber tows of both laminates have similar microscopic architectural properties. In addition, their macroscopic channels were too large to sustain long-term wicking. Neither fiber tow deformations nor gap restructuring could be observed before and during the wicking tests.

Figure 15.

Impact of fiber volume content on the evolutions of square imbibition height of hexadecane in multiple ply fabrics (weft).

However, for the six ply laminate, the medium-term wicking behavior is significantly different from the two previous ones. In this configuration, it seems that inter-layer slippage and gap/pore reduction generated channels of high permeability between the fiber bundles of each single ply. These macroscopic capillary channels seem to interact with tow wicking and thus promote the medium-term imbibition in contrast with the four and five ply laminates. In that respect, the wicking height evolutions for the single ply and the six ply laminates are very close, which is consistent with the small difference in fiber volume content (around 2%) between the two samples.

A wicking test has also been conducted on a seven ply laminate. As shown in Figure 15, the medium-term wicking capacity remains below that of the six ply laminate. This lower wicking result for the seven ply laminate could be explained by two factors: (1) smaller channels appear because of increased inter-layer slippage and macroscopic gap reduction and (2) the size of the microscopic pores is also reduced as a result of fiber tow compaction and filament packing reorganization. These wicking height results and their interpretations are consistent with previous observations of the uptake fluid mass. Furthermore, several studies on the impact of fabric compaction on the microscopic architecture of fabrics and the morphological reorganization of non-crimp fibrous reinforcements confirm this analysis.^58-60 This complex behavior could be further investigated as a function of fabric compaction by in situ measurements of tribological effects and pore size distribution analysis by capillary flow porometry or the liquid expulsion technique.

Discussion

The multiple ply imbibition Lucas–Washburn results are summarized in Table 7. For the four and seven ply laminate configurations, the Lucas–Washburn slopes of capillary height evolution for initial wicking behavior were both approximately 5 × 10⁻⁵ m²/s. On the other hand, for the five and six ply configurations, the Lucas–Washburn slopes of capillary height evolution for the initial wicking behavior were both approximately 6 × 10⁻⁵ m²/s. Note that for multiple ply laminates, the wicking front positions were harder to pinpoint with accuracy through the laminate thickness, because the imbibitions takes place simultaneously in several layers. Concurrent wicking in multiple layers results in an uneven and blurred three-dimensional capillary front. Therefore, technological enhancements are required to improve the observation and understanding of these complex phenomena.

Table 7.

Results of the initial wicking behavior of fabric multiple ply imbibition tests with hexadecane in the weft direction

Laminate properties	4 ply	5 ply	6 ply	7 ply	Units
Initial Height LW slope B_h (equation (19))	5 ± 1	6 ± 1	6.2 ± 0.8	4.9 ± 0.9	× 10⁻⁵ m²/s

From the acquisition of capillary flow height and uptake fluid mass progression, the evolution of the saturation of multiple ply laminates along the weft direction was estimated by equation (28). The evolution of saturation was plotted with respect to the imbibition height in Figure 16. Saturation levels in the laminates converged to different asymptotic values according to the fiber volume content of the laminate. Indeed, when the fiber volume content increased, a higher saturation was obtained at the end of the capillary rise experiment. The saturation levels estimated were 27%, 35% and 44% for laminates of four, five and six plies respectively. These asymptotic values of the saturation were consistent with the ratios $R_{REV}^{m}$ estimated by equation (35) for each multiple ply laminate. Indeed, these ratios $R_{REV}^{m}$ were equal to 27 ± 2%, 36 ± 3% and 48 ± 3% for laminates of four, five and six plies respectively. This confirms again that the capillary flow was only progressing through axial and transversal fiber tows, thus leaving behind all the macroscopic pores empty during the medium and the long-term imbibition behaviors of the laminates.

Figure 16.

Impact of fiber volume content on the saturation of multiple ply fabrics along the weft direction.

As shown by the wicking results of Table 6 and Table 7, the imbibition behavior of a single ply configuration can be extended to low and medium compaction levels as long as the tow architecture and tortuosity remain undisturbed. However, for higher compaction levels, this is no longer true, because significant tow deformation and slippage can take place. Note that upstream manufacturing steps such as stitching, weaving, draping and preforming have also an impact on the fabric architecture, thus on the microscopic flow progression. Accordingly, it is justified to characterize the reinforcement wicking properties in their final stacking configurations and for a REV.

Microstructural reconfiguration after compaction of woven and non-crimp fabrics have recently been studied by optical/SEM and x-ray micro-CT tools.^59,60 According to these authors, the permanent and elastic deformations during fabric compaction are mainly related to changes in the bundle cross-sectional shape and size. It was also suggested that time-dependent deformations are related to the evolution of bundle tortuosity over time that result from tow nesting and slippage. However, for low compaction levels, the non-crimp fabric showed low or even no nesting. As compaction increased, the layers of reinforcement adjust together by slippage as a result of the non-crimp fabric architecture, so the tortuosity of the fiber tows remains low, i.e. close to one. Compaction ensured that no rich resin areas were created and that the pore volume was reduced to a minimum, leaving few small pores for the resin flow. The reason why the pore volume does not decrease further is related to the residual pores that remain between the fiber tows in a single ply. These residual pores are difficult to reduce further as bundle layers are stitched together, thus inhibiting the relative motion of the fiber tows.

The laminate wicking analysis carried out clearly shows that fabric wicking properties such as height Lucas–Washburn slopes depend on the tow morphology and on the initial reinforcement stitching/weaving pattern at low and medium fabric compaction levels. However, for higher compaction levels of the fibrous reinforcement, this behavior no longer holds. Tow deformation, nesting and slippage must also be taken into account in order to obtain representative wicking characterizations.

Conclusion

The new capillary rise setup proposed in this investigation was used for tracking the capillary flow progression in a bidirectional glass fabric. Visualization based on fluorescence coupled with monitoring of the uptake fluid mass ensured a representative and a reproducible characterization of the wicking behavior of the fibrous reinforcement. For these tests, an initial evaluation of the REV was carried out: a representative area of 250 mm² is required for proper wicking characterization of the fabric. The molds used for the capillary rise setup were conceived in glass and took into account this fabric REV size.

Dimensionless numbers, namely the Reynolds, capillary and Bond numbers, were calculated for each experiment condition in order to validate the flow hypotheses. Reynolds numbers below 10 and capillary numbers between 2 × 10⁻⁶ and 1 × 10⁻³ were obtained for fiber tows and gaps between fiber tows along the warp and weft directions. Imbibition tests were first carried out on a single ply fabric with the proposed capillary setup. Results along warp and weft directions show a nonlinearity of the squared imbibition weights with respect to time. This is due to a heterogeneous imbibition (fingering along the fiber tows) across the fabric ply as a result of the capillary rise stop in the macroscopic pores and to the contribution of transversal wicking flows at the tow/stitch cross-overs. The capillary front position measured with the CCD camera during these imbibition tests was used to estimate the apparent fluid volume over time contained inside the fabric ply. This estimated apparent fluid volume was compared to the real fluid mass sucked in by the fabric and measured by the microbalance. From the comparison between the real and apparent imbibition volumes, the saturation levels in the single ply fabric were found to converge to 42% for the warp and weft directions. This value is consistent with the ratio $R_{REV}^{m}$ of the microscopic pore volume to the total pore volume available in a REV that was equal to 44 ± 4%. This confirms that the capillary flow progressed only through axial and transversal fiber tows, thus leaving behind all the macroscopic pores empty during the medium and the long-term imbibitions. However, significant flow contributions from the gaps between fiber tows were also noticed during the initial imbibition behavior of this fabric. Indeed, this generated a synergy between the macroscopic and the microscopic pores, thus increasing the imbibition performance of the fabric compared to the fiber tow alone.

Finally, capillary rise experiments were carried out on several fabric plies to study the impact of fiber volume content on fabric imbibition. It was concluded from these imbibition tests that when the fiber volume content of the laminate was increased, higher saturation of the laminate was obtained at the end of the capillary rise experiment. The saturation levels of 27%, 35% and 44% were measured for laminates of four, five and six plies respectively. These asymptotic values of saturation were consistent with the ratios $R_{REV}^{m}$ for each multiple ply laminate as follows: ratios $R_{REV}^{m}$ were 27 ± 2%, 36 ± 3% and 48 ± 3% respectively. This confirms that the capillary flow was only progressing through the axial and transversal fiber tows, thus leaving behind all the macroscopic pores empty during the medium and the long-term imbibition behaviors in the laminates.

This study on fibrous laminate wicking confirmed the results of other investigations reported in the scientific literature on the compaction and microscopic architecture of fabrics and on their reorganization under compaction in the case of non-crimp reinforcements. This complex behavior of fibrous reinforcements could be further investigated by carrying out in situ measurements of tribological effects and pore size distributions by capillary flow porometry.

Footnotes

Acknowledgements

The authors would like to express their deep appreciation to Suzie Poulin, Yves Bédard, Régina Zamojska and Catherine Billotte for their support in the characterization work. Finally, the contributions of Christian-Charles Martel, Alex Bourgeois, Antonin Leclair-Maréchal, Michael Cantin, Nadir Nchit, Mickëal Leduc, Simon Dulong, Frédérick Marcil St-Onge, Francisco Doyon, Matthieu Sola, Farida Bensadoun, Julian Gutierrez, Philippe Causse and Vincent Achim are also gratefully acknowledged.

Funding

The authors are grateful to the National Science and Engineering Research Council of Canada (NSERC) and the Canada Research Chair (CRC) for their financial support. The authors would also like to thank the Fonds Québécois de Recherche sur la Nature et la Technologie (FQRNT), the Chair on Composites of High Performance (CCHP) of École Polytechnique de Montréal and the Center for applied research on polymer and composites (CREPEC) for providing the research infrastructure and equipment. They are also very grateful to JB Martin for donating the fiber reinforcement used in the experiments.

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