## 4 Results and Discussion
### In-Plane Strength of QNCF Lamina
Figure 9: Typical stress-strain curve of micromechanical non-crimp fabric (NCF) unit cells computations: (a) longitudinal tensile loads in 1-direction; and (b) shear in 1–2 plane. As shown in Figure 9a, the curves of Cell A and Cell B have more obvious stiffness reduction compared with that of Cell C. This result can be explained by the rhomboidal cracks in the laminas which are more likely to cause stress concentration compared with the channels in the 0\({}^{\circ}\) lamina. The QNCF layer discussed in this work is composited with four laminas, and three laminas are provided with the cracks, so the lamina with the cracks is more representative of the actual stress state. Compared with Cell C, Cell A and Cell B are unit cells with cracks, thus the numerical predictions employing these two kinds of unit cells are closer to the experiment values. From Table 7, \(Y_{\text{T}}^{\text{I}}\) is 15.3% higher than test value, and the average shear strength is close to test value. For composite tows under shear loading, the nonlinear behavior of material should be considered in failure analysis. Generally, this nonlinear behavior is caused by micro crack and plasticity of matrix. According to the failure model above, the internal state variables of material degradation are used to analyze the combined influence of the two factors. The engineering analysis method is also used in Reference [21] to predict matrix shear cracking. Based on this method, the stress-strain response of the unit cells subjected to simple shear load are shown in Figure 9b. The stiffness decreased about \(\varepsilon=1.8\%\) due to local damage in matrix according to Figure 9b. After elastic range, the nonlinear curves are obtained. With the progressive damage method, reasonable shear behaviors are obtained. However, since mechanical properties of the fiber/matrix interface are modeled perfectly in a conventional mesh, a high transverse strength value is predicted. Considering the dispersion parameters of strength of composites and the reference experiment is only for one type of non-crimped UD specimen, therefore, the three unit cells given here can predict in-plane strength of the QNCF lamina with sufficient engineering accuracy. As can be seen in Table 7, in the fiber direction, the longitudinal tensile strength \(X_{\text{T}}^{\text{I}}\) obtained by employing Cell B with fiber waviness is 19.8% lower than Cell C, and the average value of \(X_{\text{T}}^{\text{I}}\) is 23.4% lower than the reference value (Ref-FEM). For longitudinal compressive strength \(X_{\text{C}}^{\text{I}}\), the maximum difference among the three unit cells reaches to 28.0%. Generally, the differences between mechanical properties obtained using the cells with fiber waviness and the cell with no waviness are quite obvious. The average value can still be reduced by approximately 20% relative to the reference value. Considering the same volume friction of the three unit cells, this difference could be caused by the local stress concentration, which is a result of fiber waviness induced by the stitch yarn in this material. This difference between the three unit cells or difference between the average value and the reference value is obvious. Moreover, this may explain the results of [PERSON] [14] who found that the tensile strength of NCF composite is 34.7% lower than the UD composites and the compress strength is 40% lower than the UD, which is caused by the effect of the stitching in the materials. The difference of \(Y_{\text{T}}^{\text{I}}\) or \(Y_{\text{C}}^{\text{I}}\) between the three unit cells and the corresponding reference value (Ref-FEM) is not obvious, \(S_{12}\) is also a similar trendy. This indicates that fiber disturbance has no significant effect on the strength in the direction transverse to the fibers. According to the failure mechanism, the transverse strength and shear strength are also matrix-dominated, and it has little relation with the strength of the fiber itself.