# Two Deformation Behaviors in Resin-Impregnated Glass Fibers under Different Flow Rates
## 4 Results and Discussion
### Observation of Tow Behaviors with Different Flow Rates  
#### 4.2.1 Tow Thickness (Minor Axis of Tow)  
The fibers in glass fiber-reinforced polymers can be influenced by the hydrodynamic forces induced by the fluid flow of resin during LCM. It was found that the hydrodynamic force was related to the flow rate. For the double-scale porous media, each tow consists of many single fiber filaments, as shown in Figure 4. The fiber behavior under the hydrodynamic fluid force affects the tow with the fiber filaments. Therefore, the tow behaviors of the double-scale porous media with respect to the flow rate were investigated. To examine the structural changes in the porous media, the tow behaviors were observed under different flow rates with 97 cP (0.097 Pa-s) of viscosity using cross-sections of the deformed tow and the two representative indices of the minor and major axes, noted previously, as shown in Figure 2. These two indices as functions of the hydrodynamic pressure were measured at the different positions from inlet, with an average of 20 points. In the present study, fiber bundle was assumed to no shearing.  
Figure 3: Permeability behavior with different flow rate under different viscosities: (**a**) 97 cP, (**b**) 340 cP.  
ow thickness, or the minor axis of the tow, was observed for the flow rates of 50 and 200 mm\({}^{3}\)/s at the different positions from inlet, as shown in Figure 5. The most important observation was that the tow thickness decreased by 2-5% on average with increasing flow rate. In addition, the thickness of the tow decreased along the flow position. Generally, larger tow deformations are expected with increasing flow rates. However, the change in tow thickness was not prominent near the inlet. The main reason for this is the hydrodynamic entry length, which is determined by the flow rate [30; 31; 32]. At different flow rates, flows in different amounts of fully developed regions could be observed. For this reason, at a higher flow rate of 200 mm\({}^{3}\)/s, the most decreased tow shape was observed at a relatively large distance of 300 mm from the inlet, compared with the distance of 180 mm for the flow rate of 50 mm\({}^{3}\)/s. Furthermore, the thickness decreased more with higher flow rates because of the different hydrodynamic forces exerted by the fluid flow, as shown by the shapes of the compressed rows. Compressed relaxation behavior, in which the compressed rows returned to their original shapes, was observed as the hydrodynamic fluid force decreased. The further away from the inlet, the smaller the local fluid pressure, therefore the smaller the effect on the fiber bundle shape with fluid flow.  
Figure 5: Tow thickness (minor axis of the tow) for the flow rates of 50 mm\({}^{3}\)/s (**a**) and 200 mm\({}^{3}\)/s (**b**) at the different positions (all dimensions are in mm).  
Figure 6: Major axis of the tow for the flow rates of 50 mm\({}^{3}\)/s (**a**) and 200 mm\({}^{3}\)/s (**b**) at the different positions (all dimensions are in mm).  
It can be concluded that the minor axis tended to show a decreasing trend, where it showed its minimum values at different positions because of different hydrodynamic entry lengths. The major axis showed an increasing trend, with the phase showing a decreasing trend of the minor axis at the same time. This tendency was more prominent in the high-flow-rate case. The different hydrodynamic forces exerted by the different flow rates resulted in the deformed shape of the tow as described by the major and minor axes.