## 4 Results and Discussion
### In-Plane Strength of QNCF Lamina  
The in-plane strength is predicted by meso-scale failure model. The progress failure model is introduced in Section 3.3.3 that used to predict the failure of composite tows. The von Mises criterion and the Drucker-Prager yield criterion are introduced to predict the failure of the resin pocket under different loads. Failure analysis is performed by the Abaqus commercial FE code combined with the user subroutine UMAT, axial displacement load and in-plane shear load are applied on the surface of the unit cells, and then the predictions of in-plane strength are listed in Table 7.  
The strength data of non-crimp UD laminate that tested in Reference [13] are used in this section as a comparison. Each of these three unit cells represents a QNCF lamina, and the predicted strength \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Description** & \(\mathbf{V_{\mathrm{f}}^{\mathrm{A}}}\) & \(\mathbf{V_{\mathrm{f}}^{\mathrm{A}}}\) & \(\mathbf{E_{1}^{1}}\) & \(\mathbf{E_{2}^{1}}\) & \(\mathbf{v_{12}^{1}}\) & \(\mathbf{G_{12}^{1}}\) \\ \hline Cell A & 42.1\% & 48.1\% & 93.45 & 6.07 & 0.349 & 2.301 \\ Cell B & 42.1\% & 43\% & 93.85 & 6.11 & 0.347 & 2.322 \\ Cell C & 42.1\% & 47.3\% & 98.16 & 6.1 & 0.324 & 2.2 \\ Average & 42.1\% & - & 95.15 & 6.09 & 0.34 & 2.274 \\ Ref-FEM & 42.1\% & - & 98.44 & 6.196 & 0.323 & 2.303 \\ Experiment [13] & 42.8\% \(\pm\) 0.8\% & - & 94.3 \(\pm\) 8.2 & - & 0.32 \(\pm\) 0.04 & 2.4 \(\pm\) 0.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: In-plane stiffness of the NCF (non-crimp fabric) lamina obtained with mesomechanical analysis procedure (GPa). of each unit cell represents possible values of the QNCF lamina. For these reasons, the individual prediction of each unit cell and average value are both compared with experimental results. Similar to that described above, the averaged value of the predicted results is taken as strength properties of the QNCF lamina. Compared with the experimental results in reference [13], the average value of \(X_{\text{T}}^{\text{l}}\) obtained using the above three unit cells is 11.4% higher than the experimental results. Figure 8 shows the fiber tension failure modes in the unit cells and Figure 9 presents the stress-strain response of the unit cells subjected to uni-axial tension parallel to fiber. As shown in Figure 9, the numerically determined curves agree well with the experiment, although a slight overestimate of the tensile strength is observed. Although fiber reinforced composite materials are often considered as brittle materials, a certain non-linear behavior is observed in Figure 9. This non-linear behavior is caused by material stiffness degradation after local failures within the composite tow. In fact, the test data in Reference [13] also have a stiffness reduction. For non-crimp UD laminate in the test, the initial [PERSON]'s modulus is 94.3 GPa, and [PERSON]'s modulus is 82.8 GPa in the end of the test. It can be concluded that stiffness of the laminate is reduced by 12.2% at the ultimate failure. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Description** & \(\mathbf{V_{\text{f}}^{\text{d}}}\) & \(\mathbf{V_{\text{f}}^{\text{d}}}\) & \(\mathbf{X_{\text{T}}^{\text{l}}}\) & \(\mathbf{X_{\text{C}}^{\text{l}}}\) & \(\mathbf{Y_{\text{T}}^{\text{l}}}\) & \(\mathbf{Y_{\text{C}}^{\text{l}}}\) & \(\mathbf{S_{\text{12}}^{\text{l}}}\) \\ \hline Cell A & 42.1\% & 48.1\% & 1314.4 & 1055.1 & 66.7 & 148.1 & 69.4 \\ Cell B & 42.1\% & 43\% & 1247.6 & 965.2 & 69.5 & 150.2 & 70.3 \\ Cell C & 42.1\% & 47.3\% & 1557.5 & 1340.4 & 70.1 & 153.0 & 72.8 \\ Average & 42.1\% & - & 1373.2 & 1120.2 & 68.8 & 150.4 & 70.8 \\ Ref-FEM & 42.1\% & - & 1792.3 & 1224 & 72.3 & 148.0 & 71.5 \\ Experiment [13] & 42.8\% \(\pm\) 0.8\% & - & 1233 & - & 59.6 & - & 71.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: In-plane strength of the non-crimp fabric (NCF) lamina evaluated with mesomechanical failure analysis procedure/MPa. Figure 8: The fiber fracture (FF) failure modes in the unit cells under longitudinal tensile.