# Fatigue Characteristics Analysis of Carbon Fiber Laminates with Multiple Initial Cracks
## 3 Experimental Tests
### Fatigue Test  
The fatigue testing parameters for carbon fiber laminates containing multiple cracks are detailed in Table 3, where the variables include edge crack lengths L\({}_{1}\) and internal crack lengths L\({}_{2}\), the internal crack angle \(\theta\), and the distance S between internal and edge cracks. The specific configurations of these parameters, along with the results of the experimental evaluations, are delineated in Table 4. It can be observed that the fatigue life of the specimen \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Serial Number**} & \multirow{2}{*}{\begin{tabular}{c} **S Inter-Crack** \\ **Distance** \\ **(mm)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **\(\Theta\) Crack Angle** \\ **(\({}^{\circ}\))** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **\(\mathbf{L_{1}\) Crack** \\ **Length** \\ **(mm)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **\(\mathbf{L_{2}\) Crack** \\ **Length** \\ **(mm)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Maximum Load** \\ **(KN)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Average** \\ **Value** \\ **(KN)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **CV** \\ **(\%)** \\ \end{tabular} } \\ \hline A1-1-1 & 0 & 30 & 4 & 6 & 148, 13.93, 16.18, 14.75, 14.15 & 14.762 & 5.94 \\ A1-2-1 & 0 & 60 & 4 & 6 & 13.63, 13.12, 13.98, 13.43, 14.32 & 13.696 & 3.42 \\ A1-3-1 & 0 & 90 & 4 & 6 & 13.17, 13.04, 13.16, 13.17, 13.86 & 13.388 & 2.76 \\ B1-1 & 0 & 90 & 4 & 4 & 14.28, 13.55, 14.77, 13.95, 15.21 & 14.312 & 5.03 \\ B1-2-1 & 0 & 90 & 4 & 8 & 11.47, 11.5, 10.86, 11.33, 11.2 & 11.272 & 2.30 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Sample parameters and results of static tests. Figure 8: Static test displacement curve and load capacity. (**a**) Maximum failure force-displacement curves of carbon fiber plates with different angles of internal cracks; (**b**) Maximum failure force and coefficient of variation of static tensile force of carbon fiber plates with different angles of internal cracks; (**c**) Maximum failure force-displacement curves of carbon fiber plates with different lengths of internal cracks; (**d**) Maximum failure force and coefficient of variation of static tensile force of carbon fiber plates with different lengths of internal cracks. can reach up to 52,032 cycles. This phenomenon can be attributed to the impact of changes in the internal crack angle on the stress field distribution. When the internal crack angle is tilted from 30\({}^{\circ}\) to 90\({}^{\circ}\), the overlap of the cracks causes the stress field to redistribute. This redistribution alters the path and rate of crack propagation, thereby affecting the fatigue life. Specifically, a 30\({}^{\circ}\) crack angle may reduce the stress concentration at individual crack tips because the stress is more dispersed at the crack tips. In contrast, when the internal crack angle is 90\({}^{\circ}\), the overlap of the cracks leads to more direct and continuous stress concentration. This concentrated stress accelerates the propagation of the crack, thereby reducing the fatigue life. In this case, the path of crack propagation is more direct, and the stress concentration at the crack tips is more severe, leading to a reduction in fatigue life. Additionally, the A2-1-1 (F) specimen has the shortest inner and outer crack lengths among the samples, which is also one of the reasons for it exhibiting the highest fatigue life. A shorter crack length means that more cycles are required for the crack to propagate to a critical size, thus extending the fatigue life under the same load conditions. Figure 9 illustrates that the fatigue life of carbon fiber laminates diminishes progressively with increasing crack length. There is a notable 21.57% reduction in fatigue life as the internal crack L\({}_{2}\) extends from 4 mm to 6 mm and a more substantial 40.45% decrease as it extends further from 6 mm to 8 mm.