## 4 Discussion
### Effect of Stitched Density  
In order to analyze the effect of stitched density on the failure and residual strengths of the laminates after impact, laminates with three stitched densities, namely 2 mm \(\times\) 2 mm, 5 mm \(\times\) 5 mm, and 10 mm \(\times\) 10 mm (2 \(\times\) 2, 5 \(\times\) 5 and 10 \(\times\) 10 laminates), and the stitching thread thickness of 1500d, were investigated after the impact of 10 J. Figure 10 shows the full-processes of low-velocity impact damage and residual strength for stitched composite laminates with different stitched densities. In the simulation process of low-velocity impact damage, four kinds of damage modes, i.e., FTF, MTF, FCF, and DF, were found. The rules of the damage expansion are similar, e.g., the DF occurs firstly, then the FCF occurs and the FTF occurs at last. The impact time of the stitched (2 \(\times\) 2, 5 \(\times\) 5 and 10 \(\times\) 10) composite laminates are 1.3 ms, 1.4 ms and 1.4 ms, respectively. This change of the impact time is mainly caused by the difference of stiffness between laminates that are associated with the different stitched densities. The initial impact damage of 2 \(\times\) 2 laminate is slightly larger than others, which means that there is no obvious association between the initial impact damage and the final impact damage. Compared with the 10 \(\times\) 10 laminate, the final impact damage areas for the 5 \(\times\) 5 and 2 \(\times\) 2 laminates are reduced by about 10% and 28.1%,  
Figure 9: Progressive damage process of the laminate after the impact of 16.8 J. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Impact Energy (J)** & **Experiment [18] (MPa)** & **Simulation (MPa)** & **Error (\%)** \\ \hline
11.0 & 311 & 330 & 6.1 \\
16.8 & 301 & 315 & 4.65 \\
23.4 & 280 & 255 & \(-\)8.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison between the experiment and simulation for residual strength. respectively. However, no matter how large the stitched density is, the shapes of the final damaged areas are always the spindle-shaped. In the simulation processes of residual strength, stitched density has a significant effect on the damage mode. The stitched composites with different stitched densities have different failure modes. For example, the FMSF and MCF are found in the 10 \(\times\) 10 laminate, whereas the 2 \(\times\) 2 and 5 \(\times\) 5 laminates extend the damage with the FTF and FTF+FCF, respectively. Moreover, the greater the stitched density of the stitched composites, the less the damage mode and the smaller the damaged area are found in final damage, as shown in Figure 10. When compared with the 10 \(\times\) 10 laminate, the final damage area of the 2 \(\times\) 2 laminate is smaller, and only the FTF mode is found on its boundary, whereas the damage modes of the FTF, FCF, MTF, and FMSF are found on the boundary of the 10 \(\times\) 10 laminate. As shown in Figure 11, the damage area of the DF is the largest and the area of the FTF is the smallest. With the increase of the number of layers, the damage area of the MTF decreases firstly and then increases; and, the FCF occurs in the first four layers and the area of damage shows a tendency to decrease; the FTF only occurs in the 7 th and 8 th layers and is not found in the stitched (2 \(\times\) 2) composites; the DF occurs in all layers and the damage area increases significantly. It also can be seen that, the greater the stitched density of the stitched composites, the less the damage mode, the smaller the damaged area, and the fewer the damaged layers after impact. Figure 12 shows the predicted residual strengths of the laminates with three stitched densities. It is observed that stitched density has a significant effect on residual strength after impact. When compared with the 10 \(\times\) 10 laminate, the residual strengths for the 5 \(\times\) 5 and 2 \(\times\) 2 laminates are increased by 20% and 30.9%, respectively. This means that the greater the stitched density of the stitched composites, the greater the residual strength.