Unsaturated flow characteristics in dual-scale fibre fabrics at one-dimensional constant flow rate

1 Introduction

Liquid composite moulding (LCM) is a general term used for the moulding process of resin matrix composites [1]. The fundamental principle of LCM is as follows: First, place the fibre reinforcement material, such as glass fibre or carbon fibre fabrics, into the cavity, inject the pre-catalytic resin with the liquid state and then wait for the cure. Finally, the product will be obtained after knockout. With its high efficiency, simple setup and low moulding pressure, LCM is gradually becoming the most competitive manufacturing technology for producing large composite parts with complex geometry but with high quality and low cost [2]. These parts include those for airplanes, wind turbine blades and automobile components [1], [3]. By studying the flow characteristics of a resin in porous media, we determined that LCM has an important role in determining the forming pressure, filling time and injection port. Fibre preforms for LCM usually consist of several fibre tows, which are woven, stitched or randomly arranged. This geometric structure is recognised as porous media. Figure 1 shows the corresponding images.

Figure 1:

Different types of fibre preforms used in LCM.

In theory, the pores in fibre preforms behind the moving flow front are completely saturated with resin, and the liquid resin flow impregnating the dry fibre preforms presumably and strictly obey Darcy’s law [1], [4], [5], which can be expressed as

where v is the volume-averaged flow velocity (Darcy velocity), K is the permeability tensor for the fibre preforms, p is the fluid pressure, and μ is the resin viscosity. Theoretically, the region behind the flow front is completely saturated, whilst an evident interface is observed tracking the flow front [5], [6], [7], [8], [9]. However, researchers have recently found that resin flow behaviour does not completely obey Darcy’s law [10], [11], [12]. An unsaturated region exists in the woven or stitched fabrics, which have dual-scale pores [13], [14], [15]. The first pore is a macropore found between fibre tows at the millimetre level, whilst the second pore is a micropore found inside fibre tows at the micron-size level. The inter-tow channels are previously filled with resin, and then the tows are gradually impregnated because of the dual-scale fibre mats [11]. The delayed impregnation of the tows leads to the occurrence of a partially saturated region behind the macroscopic flow front [16]. Figure 2 shows the typical unsaturated flow pattern within the dual-scale fibre preformation [17]. The figure shows that Area A is a completely saturated region, which corresponds to the absence of voids through the fibre preforms. Area B is a partially saturated region. In this region, the fibre tow is not completely impregnated by the resin. Last, Area C is an unsaturated region that could still be filled.

Figure 2:

Schematic representation of unsaturated flow.

To explain this phenomenon, a theory of sink model has been presented by several researchers [17], [18], [19], [20], [21]. This theory assumes that the delayed impregnation of tows acts as sinks for liquids in the macroscopic flow field. In the mass conservation equation, a new general form of the continuity equation can be shown as

where S is the sink term representing the resin disappearance as well as a function of pressure and saturation. This statement is based on the basic logic rules and agrees with the results of current studies. Through this model, Pillai et al. [20] successfully simulated for the first time the inlet pressure profile, which is typically observed in 1D flow experiments with constant injection rates in dual-scale fibre mats [22]. This modified model was applied to a 2D mould filling simulation to simulate the flow [10]. Furthermore, Wang and Pillai developed a three-dimensional finite to track the fluid front during the mould-filling process by using two distinctly different permeabilities in tows and gaps. The study reveals that infiltration of an idealized dual-scale preform is marked by irregular flow fronts and an unsaturated region behind the front due to the formation of gas pockets inside fibre tows [17]. Recently, Zhou et al. used a 3D unit attached to a 1D unit to study the micropermeability characteristics [23]. Their study is a preliminary investigation of seepage theory in dual-scale fibres. However, the characteristics of unsaturated flow, such as the variation of inlet pressure or length of unsaturated region, are still going to be researched. Thus, the present study focussed on experiments involving the unsaturated flow in dual-scale fibre preformation.

2 Materials and methods

2.1 Experimental setup

In the present study, a visualisation experimental device was developed. The system mainly consisted of a mould, constant flow pump, pressure sensor, data and acquisition terminal. The length-width ratio of the mode cavity was higher than 100. To assure that the flow is along the 1D dimension, a buffer between the inlet area and the fibre fabrics was utilised. This buffer could also reduce the edge effect. The whole filling process could be considered as a 1D flow in the lengthwise direction. Based on the above principle, the cavity was designed with 4-mm thickness, 90-mm width, 1000-mm length. It used 7075-T651 aluminium alloy with excellent performance for the mould. To enable observation of the flow process, the upper mould had a 1000 mm×150 mm×10 mm transparent organic glass (PMMA) attached to the aluminium alloy frame. To avoid race tracking, we have reduced the porosity as possible in reasonable range, and chosen double sealing design on experiment: rubber seal ring and vacuum sealant. The vacuum sealant was laid on the edge of the cavity. With the pressure of the upper panel, it would expand and fill both sides of the cavity. This can be viewed in Figure 7, the yellow region. A piston constant flow pump purchased from Shanghai Hooyo Instrument and Equipment Corporation (Shanghai, China) was utilised for constant injection. The fluid was injected into the mould through the injection port once gas was expelled from the piston cylinder. This equipment was connected to a computer using an RS-232 interface, and the inlet flow rate could be controlled by the EZChrom software (developed by Agilent Technologies Inc., Santa Clara, CA, USA). Pressure data were collected through the pressure sensor until the fluid fully impregnated the fabric and the vent. Each sample has been tested three times, and an average was applied. Figure 3 shows a simple schematic of the above process.

Figure 3:

Schematic of experiment.

2.2 Experimental scheme

In this study, triaxially stitched and biaxially woven glass fibre fabrics were selected as fibre preforms. Vegetable oil and low-viscosity resin were used as the experimental fluid. Their viscosities were previously measured before each experiment. First, the fabrics were cut to a 12 mm×75 mm dimension. Afterwards, the fabrics were placed into the cavity with a fixed number of layers and then fitted on the PMMA panel and aluminium alloy frame. The data line was then connected to a computer (Figure 3). The valves were opened, and the whole experiment was recorded using a digital camera. An image of the 1D controlled flow system is shown in Figure 4.

Figure 4:

Schematic of 1D controlled flow system.

The ideal flow of porous media should follow Darcy’s law. If the relative parameters are known, the filling time for the saturated flow can be predicted and expressed as

(3)tp=Vc-Vfv

where v is the velocity of the fluid, V_c is the volume of the cavity and V_f is the volume of the fabrics. Porosity can be obtained through the expression

(4)ϕ=1-nξtσf

where n is the number of fabric layers, ξ is the fabric surface density, σ_f is the glass fibre density and t is the cavity thickness. Table 1 presents the parameters described above. Samples 1–4 were injected with oil, and Sample 5 was injected with low-density resin.

Table 1

Experimental samples and parameters.

Sample	Material	Ply	Flow rate (ml/min)	Porosity	Viscosity (mpa·s)
1	Triaxially stitched	5	120	0.40	59
2	Triaxially stitched	5	150	0.41	59
3	Biaxially woven	4	150	0.39	59
4	Biaxially woven	4	120	0.39	59
5	Biaxially woven	4	120	0.41	88

3 Results and discussion

Table 2 presents the time usage for the flow front at the edges of the fibre fabrics. Predicted time refers to the ideal saturated flow, and actual time corresponds to the experimental data. Table 2 shows that the filling time for the unsaturated flow was faster than that for the saturated flow, and the lead time could be obtained for the unsaturated flow. Samples 1 and 2 are both triaxially stitched fibre fabrics but with different injection flow rates. The lead time for sample 1 was 6.1 s and that for sample 2 was 5.7 s. Samples 2 and 3 were both injected with 150 ml/min of oil but have different geometric structures. The lead time for sample 3 was 2.8 s. Samples 3 and 4 are both biaxially woven fibre fabrics injected with oil at 120 ml/min. The lead time for sample 4 was 2.5 s. The varying lead times show that geometric structure is an essential factor that affects unsaturated flow. Sample 5 was injected with resin, and its lead time was 9.8 s. Based on the results of sample 4, we found that viscosity would promote the formation of an unsaturated area, considering that the surface tension of the fibre tows is not changed. The higher the viscosity, the bigger is the capillary number. This would hinder the flow impregnating to the tows. Viscosity may be another essential factor that affects unsaturated flow. These results elucidate the unsaturated flow behaviour of dual-scale fabrics.

According to Darcy’s law, a 1D flowing can be expressed as

However, inlet flow has a constant flow rate,

From Equations (5) and (6), we obtain

After integrating Equation (7), we obtain

Based on the constant flow rate, we obtain

where v^t is the actual velocity of the flow front. From Equations (8) and (9), we obtain

where P₀ is the inlet pressure. We found that P₀ against time shows linear relation. When the unsaturated flow front arrived at the edge of the fibre fabrics, we continued injecting oil until the fibre fabric was completely infiltrated. Therefore, a final pressure was obtained through our sensor, and the value of this pressure was equal to the ideal saturated flow under the same experimental conditions. The ideal filling time for different samples was also identified. Hence, the diagram of pressure for ideal saturated flow could be illustrated. The inlet pressure data for real experiment were collected by the sensor, and then, the experimental and ideal saturated data were collected. Figure 5 shows the plot of the inlet pressure against time for the different experimental samples. Diagrams a to e represent samples 1–5 in Table 1. The triangular line segment represents the saturated flow, and the curve with squares corresponds to the data collected in the experiment. These figures show two significant characteristics. First is that the unsaturated flowing front is faster than the saturated flow when it reaches the fabric edge. Second is that the inlet pressure of the unsaturated flow is always higher than the saturated flow until they both maximally increase.

Figure 5:

Plot of inlet pressure against time for different cases.

To verify the mechanism of this unsaturated flow, the filling process was divided into three parts according to their pressure characteristics. The unsaturated area was rapidly generated in the first stage (Section A). The resistance of the inside tows was higher than that of the macropore between tows because the scale of the macropore was significantly higher than that of the micropore. The fluid only filled the macropore, and only macro flow was observed. Thus, the true porosity was smaller than the theoretical porosity listed in Table 1. This finding is the main factor causing the inlet pressure to be higher than the theoretical value. In the present section, the unsaturated flow and length of the unsaturated area rapidly increased in a short period. The inlet pressure plotted in Figure 5C and D against time exhibited linear relation. This result was caused by the geometric structure of the fibre fabrics. Samples 3 and 4 were biaxially woven; their gaps were homogeneously distributed, and both have high densities. In addition, sample 5 was biaxially woven, but the pressure nonlinearly increased because the injection medium was resin, which is more viscous. Comparing samples 1 and 2, triaxially stitched fabrics have low densities and evident large gaps between the fabrics. These gaps appear disordered. Therefore, Figure 5A and B shows a nonlinear increase.

As the fluid continued to fill the cavity, it gradually impregnated the fibre tows in Section B. True porosity was lower than that in the initial phases of Section A, but still higher than theoretical porosity. Therefore, the inlet pressure was still higher than the theoretical value. In the present section, the flow front velocity gradually decreased. This event can be reviewed in the video. The inlet pressure slowly increased, and the length of the unsaturated flow was shorter, as presented in Figure 5. This section shows nonlinear relation.

The unsaturated area was stable in Section C. In this section, the formation rate of the new unsaturated area was equal to the disappearance of the previous unsaturated area, which was observed to be filled by fluid. In this stage, the length of the unsaturated area maintained the balance, as shown in Figure 6. This balance represented the position of the unsaturated flow front against time. The figure shows that the last stage exhibited linear relation, indicating that the unsaturated flow was balanced and had no changes. In this section, the pressure maximally increased until the unsaturated front reached the fabric edges. When the unsaturated front reached the fabric edges, the inlet pressure no longer increased until the fibre fabrics were fully infiltrated. This phenomenon is consistent with the observations of Kuentzer et al. [16], [23]. The pressure was equal to the final theoretical pressure. The inlet pressure with a constant flow rate increased from start to end. Therefore, the pressure in Section C was higher than the theoretical value.

Figure 6:

Position of unsaturated flow front against time.

One of the conclusions in this study is that the inlet pressure of the unsaturated flow for dual-scale fibre fabrics is always higher than the saturated flow, but this finding is different from the results of previous studies [24], [25]. These studies indicated that the inlet pressure of the unsaturated flow is lower than the saturated flow. Based on our results and discussion, we concluded that the pressure exceeds the saturated flow. This divergence is important for the mould design and industrial production. Otherwise, the unsaturated flow front will be faster than the saturated flow front.

We modified the injection rate for similar samples, and the results show that a higher velocity leads to a more rapid unsaturated flow front (Figure 7). The screenshot corresponds to samples 1 and 2 with the flow front at the same place and with the length of 500 mm for the mould. The flow rate for A was 120 ml/min and that for B was 150 ml/min. In these images, an evident unsaturated area was observed. However, the zone length for A was smaller than that for B, and the time usage for B was 37 s while that for A was 47 s. A high injection flow rate also promoted the unsaturated flow.

Figure 7:

Flow fronts at the same location.

Figure 8 shows the scheme of the pressure with different fabric structures (samples 1 and 4) but with the same injection rate of 120 ml/min. The triangular line segment represents the triaxially stitched fabrics, and the square line segment represents the biaxially woven fabrics. These segments reached the fabric edge almost at the same time. Moreover, the inlet pressure of the biaxially woven fabrics was significantly higher than that of the triaxially stitched fabrics. After observing the structure of two fabrics, the gap of the fibre tow in the biaxial woven fabrics was evidently more compact than that in the triaxially stitched fabrics.

Figure 8:

Schematic of pressure for different structure fabrics.

4 Conclusions

1. The formation of unsaturated regions is related to the geometric structure of the preforms.

2. The inlet pressure with unsaturated flow is higher than that with ideal saturated flow under constant flow rate injection.

3. The flow behaviour of unsaturated flow under 1D constant injection can be divided into three stages. First, the inlet pressure increases with amplitude, and the fibre tows are not impregnated. After some time, flows will have infiltrated the fibre tows, and unsaturated flow can be observed. Finally, the inlet pressure slowly and linearly increases, and the pressure reaches maximum when the unsaturated flow front reaches the preform edges.

4. An increase in flow rate will result in a more visible region of the unsaturated flow. Porosity will also determine the speed of the unsaturated flow when injected at the same flow rate. As the porosity decreases, the resin flows more rapidly.