## 4 Results and Discussion
### In-Plane Stiffness of QNCF Lamina  
According to the inter-structure of QNCF lamina, three kinds of unit cells have been established. Certainly, the predicted results with any of the three unit cells cannot represent the actual values. As the method of taking data average is commonly used in the data processing of composite stiffness test, the averaged value of the predicted results employing the three unit cells is taken as stiffness properties of the QNCF lamina. The displacement load is applied on the surface of the three kinds of representative volume elements, and the deformation and stress distribution of the three unit cells are shown in Figure 7.  
The estimated in-plane effective engineering constants \(E_{1}^{1}\), \(E_{2}^{1}\), \(v_{12}^{1}\), and \(G_{12}^{1}\) are listed in Table 6. The averaged stiffness of the three unit cells and the numerical homogenization results obtained by micromechanical model for UD composite tows are also presented in Table 6 as a reference. Figure 7: Deformed shape and contour plot of stress in different displacement loads. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & \(V_{\text{f}}^{\text{t}}\) & \(X_{\text{T}}^{\text{t}}\) & \(X_{\text{C}}^{\text{t}}\) & \(Y_{\text{T}}^{\text{t}}\) & \(Y_{\text{C}}^{\text{t}}\) & \(S_{\text{12}}^{\text{t}}\) \\ \hline Ref-RM & 42.1\% & 2095.2 & 1677.3 & - & - & - \\ Ref-FEM & 42.1\% & 1792.3 & 1224 & 72.3 & 148.0 & 72.5 \\ In Cell A & 48.1\% & 2247 & 1871 & 81.0 & 160.8 & 73.6 \\ In Cell B & 43\% & 1906 & 1460 & 75.0 & 154.7 & 72.3 \\ In Cell C & 47.3\% & 2234 & 1850 & 80.2 & 156.7 & 73.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Strength of composite tows obtained using micromechanical model/MPa. The averaged stiffness obtained with the three unit cells are in a good agreement with experimental results. The elastic data of UD laminate test in Reference [13] are used in this comparison. The average value of \(E_{1}^{1}\) and \(v_{12}^{1}\) are 0.9% and 6.3% higher than the corresponding experiment results, respectively, and the average value of \(G_{12}^{1}\) is 5.3% lower than the test value. Considering that, the procedures for predicting the stiffness is done in the linear elastic range of the material, and the stiffness of the constituent materials attributed to the numerical calculation are experimental data, and reasonable boundary conditions are used in the numerical homogenization method, which make it possible to get a relatively accurate results. When we compare the average value with the reference value (Ref-FEM), as shown in Table 6, \(E_{1}^{1}\) is reduced by 3.34%, but this difference is not significant. The maximum difference of \(E_{1}^{1}\) is about 4.8% among the three unit cells. To consider the same averaged fiber volume fraction, this difference in the elastic properties could be caused by fiber distortion. This result is consistent with the view of Reference [13], which concluded that absence of a significant difference in stiffness between experimental results and classical laminate theory predictions. We confirm this conclusion by multiscale analysis. Stitch yarn induces the localized crack in the fibrous ply. If the width of the localized crack is seen as the amplitude of fiber waviness, the amplitude of a single crack (for large crack, \(b=0.48\) mm) accounts for 9.5% of the unit cell width (\(A=5.07\) mm). With a constant fiber volume fraction, these localized in-plane cracks are such small amplitude and waviness angle that effect on stiffness might be not obvious. Stitching has minor effect on the in-plane stiffness of continuousplies, which is different from traditional conclusions. It is generally considered that the stitching can reduce the in-plane stiffness by 10%-20% [15; 27], these contrary conclusions may only be applicable for stiffness of the open structure NCF composite.