# Material Characterization for Reliable Resin Transfer Molding Process Simulation
## 2 Materials and Methods
### Methods Used for Material Properties Characterization  
Resin viscosity was measured by using a Thermo Scientific Brookfield Haake 7 plus viscosimeter. Four values of the rotational speed were used for testing, i.e., 20, 30, 50, and 100 rpm, considering both room and production temperature. The viscosity of the oil employed for the permeability tests was also measured by using the same apparatus.  
The textile permeability was assessed by means of unsaturated linear flow tests. Assuming that the textile reinforcement in an RTM component is a porous medium through which the fluid flows, the resin flow can be estimated by [PERSON]'s law:  
\[V=-\frac{K}{\mu}\
abla P, \tag{1}\]  
where \(V\) is the velocity of the flowing resin, \(\
abla P\) is the applied pressure gradient, \(\mu\) is the dynamic viscosity of the resin, and \(K\) is the permeability tensor. Using a coordinate system aligned to the  
\begin{table}
\begin{tabular}{c c c} \hline
**Propriety** & **Testing Standard** & **Value** \\ \hline Absolute density at 25 \({}^{\circ}\)C & ISO 1675/75 & 1.06 g/mL \\ Brookfield Viscosity at 25 \({}^{\circ}\)C & MA 041 LCP & 300 \(\pm\) 50 cPs \\ Gel time at 25 \({}^{\circ}\)C & MA 120-LR & 6\({}^{\prime}\)00\({}^{\prime\prime}\)\(\pm\) 1\({}^{\prime}\)30\({}^{\prime\prime}\) \\ Exothermic peak & MA 120-LR & 178 \(\pm\) 2 \({}^{\circ}\)C \\ \hline \end{tabular}
\end{table}
Table 1: Resin properties.  
principal directions of the fiber reinforcement, the permeability tensor can be expressed in the following diagonal form:  
\[K=\left[\begin{array}{ccc}K_{1}&0&0\\ 0&K_{2}&0\\ 0&0&K_{3}\end{array}\right]. \tag{2}\]  
Thus, measurements of only three distinct scalar coefficients is required, which can be done according to existing procedures reported in the literature [13; 14; 15; 16; 17; 18; 19; 20; 21]. A further simplification is possible: as the thickness of the reinforcement is small compared to its length and width, the problem can be assumed to be 2D. This leaves only the two planar components of permeability, i.e., \(K_{1}\) and \(K_{2}\), to be determined. The principal directions of the reinforcement, with respect to which the components of permeability are found, are also found from the experimental tests.  
By applying a given pressure gradient, an unsaturated fluid flow is obtained. In the case of a mono-dimensional, i.e., linear, unsaturated flow, [PERSON]'s equation can be expressed as  
\[\frac{dx}{dt}=\frac{K_{xx}\Delta P}{\mu\varepsilon x(t)}, \tag{3}\]  
where \(x(t)\) is the position of the flow front at time \(t\), \(\Delta P\) is the pressure difference between the inlet and outlet, \(\varepsilon=1-V_{f}\) is the void ratio (portion of volume not occupied by the fibres), and \(K_{xx}\) is the component of the permeability matrix along the direction of the flow. With the initial conditions \(x(t=0)~{}=0\), the solution of Equation (3) reads:  
\[\frac{x_{i}^{2}}{2}=\frac{K_{xx}\Delta Pt_{i}}{\mu\varepsilon}, \tag{4}\]  
which allows one to measure the permeability \(K_{xx}\), provided the position of the flow front is tracked throughout the test.  
In order to identify the principal directions and the corresponding components of the permeability matrix using linear injection experiments, tests in three planar directions were performed, i.e., 0, 45, and 90\({}^{\circ}\) orientations. The principal directions were then found by [22; 23]  
\[K_{1}=K_{\text{exp}}^{0}\frac{\alpha_{1}-\alpha_{2}}{\alpha_{1}-\frac{\alpha_{ 2}}{\cos(2\beta)}}, \tag{5}\]  
\[K_{2}=K_{\text{exp}}^{90}\frac{\alpha_{1}+\alpha_{2}}{\alpha_{1}+\frac{\alpha_ {2}}{\cos(2\beta)}}, \tag{6}\]  
\[\beta=0.5\tan^{-1}\left(\frac{\alpha_{1}}{\alpha_{2}}-\frac{\alpha_{1}^{2}- \alpha_{2}^{2}}{\alpha_{2}K_{\text{exp}}^{45}}\right) \tag{7}\]  
where the parameters \(\alpha_{1}\) and \(\alpha_{2}\) are defined as  
\[\alpha_{1}=\frac{K_{\text{exp}}^{0}+K_{\text{exp}}^{90}}{2}, \tag{8}\]  
\[\alpha_{2}=\frac{K_{\text{exp}}^{0}-K_{\text{exp}}^{90}}{2}. \tag{9}\]