## 3 Experiments and Simulation  
### Experimental Method  
In this study, composite carbon-fiber material (T800H-6K/803A) with dimensions of 230 mm \(\times\) 25 mm \(\times\) 1.5 mm was selected as the experimental specimen, in accordance with GB/T 3354-2014. The dispersion of carbon fibers within the matrix can significantly impact the material's mechanical properties [38; 39]. To minimize the influence of fiber dispersion on the experimental results, the preparation process for all samples was kept consistent, with the process parameters being strictly controlled to ensure uniform fiber dispersion. The structure and dimensions are shown in Figure 4. The properties of the unidirectionalply provided for the study are listed in Table 1. The specimens were laminated in a \([0/90]_{4}\) lay-up sequence. \begin{table}
\begin{tabular}{c c} \hline \hline
**Material Properties** & **Value** \\ \hline [PERSON]’s modulus & \(E_{11}=105.5\) GPa; \(E_{22}=E_{33}=7.2\) GPa \\ Poisson’s ratio & \(v_{12}=v_{13}=0.34\); \(v_{23}=0.378\) \\ Shear modulus & \(G_{12}=G_{13}=3.4\) GPa; \(G_{23}=2.520\) GPa \\ Strength & \(X_{T}=1060\) MPa; \(X_{C}=657\) MPa; \(Y_{T}=694\) MPa; \(Y_{C}=651\) MPa; \\ Fracture energy & \(S_{12}=108\) MPa; \(S_{13}=S_{23}=81.1\) MPa \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material Properties for T800H-6K/803A Composite Laminates. Figure 4: Geometry of the Specimen. Figure 5 illustrates part of the experimental process for the cracked carbon-fiber structure. Initially, a static tensile test was conducted until the carbon-fiber structure completely fractured, obtaining the maximum stress value that the specimen could withstand. Subsequently, 60% of the maximum stress value from the static tensile test was used for the fatigue test. The loading method was a constant amplitude sinusoidal load with a frequency of 30 Hz and a stress ratio of 0.1. Under a constant load P, the fatigue life and its dispersion for different crack lengths L of the carbon-fiber structure are shown in Table 2, and the trend of the fatigue life variations for different crack lengths L is depicted in Figure 6.  
Table 2 and Figure 6 illustrate the trend of the fatigue life changes as the crack length increases. It is clearly observed that, as the crack length L increases, the fatigue life significantly decreases and the rate of decrease gradually increases. This indicates that crack growth has a substantial negative impact on the fatigue life of the material. The coefficients of variation are all within 10%, indicating that the fatigue life of the carbon-fiber structure exhibits a certain degree of dispersion due to the uncertainty in the carbon-fiber material parameters. This dispersion reflects the influence of the internal structure of the material and external load uncertainty on the fatigue life. Additionally, as the crack length L increases, the standard deviation (SD) shows a decreasing trend. This suggests that the larger the crack length, the more significant the impact of the crack on the fatigue life, resulting in reduced dispersion of the fatigue life. Further analysis suggests that, when the crack length is relatively small, the random effects of factors such as the microstructure of \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{L/mm} & \multirow{2}{*}{P/KN} & \multicolumn{6}{c}{**Experimental Result/10\({}^{5}\)**} & \multirow{2}{*}{**Mean Value/10\({}^{5}\)**} & \multirow{2}{*}{**SD/10\({}^{5}\)**} & \multirow{2}{*}{**CV**} \\ \cline{3-3} \cline{5-10}  & & **1** & **2** & **3** & **4** & **5** & & \\ \hline
4 & & 5.84 & 6.21 & 6.41 & 6.02 & 6.11 & 6.11684 & 0.21 & 0.04 \\
5 & & 3.85 & 3.93 & 4.37 & 4.11 & 4.21 & 4.09344 & 0.21 & 0.05 \\
6 & 9.5 & 3.74 & 3.35 & 3.83 & 3.71 & 3.85 & 3.69575 & 0.18 & 0.03 \\
7 & & 2.71 & 3.06 & 2.86 & 2.92 & 2.97 & 2.90287 & 0.13 & 0.05 \\
8 & & 0.54 & 0.48 & 0.47 & 0.32 & 0.38 & 0.43478 & 0.09 & 0.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Fatigue Test Results for Different Initial Crack Lengths. Figure 5: Experimental Procedure.