# Numerical Analysis of Fatigue Life of Wind Turbine Blades Reinforced with Graphene Platelets
## 4 Results and Discussion
### Fatigue Life of Wind Turbine Blades with Conventional Fiberglass Composites Reinforced with GPLs  
The fatigue life of wind turbine blades with GPLRC was nearly zero at location 5, as presented in Section 4.2. To address this issue, this section investigates the potential improvements in fatigue performance by reinforcing conventional fiberglass composites with GPLs rather than completely replacing the matrix with GPLRC, as previously explored in Section 4.2. Table 10 summarizes the material properties of fiberglass composites reinforced with a 0.2% weight fraction of GPLs, which aligns with the reference data used for subsequent S-N curve analysis. The Halpin-Tsai model was applied to determine the elastic and shear moduli of uni-axial (UA) fiberglass composite, similar to the material modeling approach used for GPLRC. For double-bias (DB) fiberglass composites, which are laminated with plies oriented at various angles, the laminate theory was applied to determine the corresponding moduli. To represent the overall material properties of GFRP, an average value of the UA and DB composites was calculated, as described by [PERSON] and [PERSON] [44]. Finally, the material properties of GPL-reinforced fiberglass composites were derived by replacing the original epoxy matrix with GPLRC, incorporating a 0.2% weight fraction of GPLs.  
In this study, the S-N curve for GPL-reinforced GFRP was developed by incorporating the increased stress levels corresponding to the number of cycles to failure reported in  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Material** & \(\mathbf{E_{11}}\) (GPa) & \(\mathbf{E_{22}}\) (GPa) & \(\mathbf{G_{12}}\) (GPa) & \(\mathbf{\
u_{12}}\) & \(\mathbf{\rho}\) (kg/m3) \\ \hline UA fiberglass composite & 42.69 & 16.40 & 5.02 & 0.28 & 1921 \\ DB fiberglass composite & 18.97 & 18.97 & 14.06 & 0.49 & 2010 \\ GFRP with 0.2\% wt. GPL & 30.83 & 17.69 & 9.55 & 0.39 & 1966 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Material properties of fiberglass composites reinforced with 0.2% weight fraction of GPLs.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Characteristics**} & \multicolumn{2}{c}{**Blade Materials**} \\ \cline{2-3}  & **Conventional Materials** & **GPLRC (\(\mathbf{V_{GPL}}\) = 2.7\%)** \\ \hline Total material cost (USD) & 137,972 & 146,170 \\ Total weight (kg) & 16,829 & 13,209 \\ Natural frequency—mode 1 (Hz) & 0.8415 & 0.9412 \\ Minimum fatigue life (years) & 68 & Less than 1 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Comprehensive comparison of wind turbine blades made with conventional materials and GPLRC [15,16].  
[PERSON] et al. [45], as the weight fraction of GPLs increased. Figure 9 compares the S-N curves of GFRP with and without GPL reinforcement, demonstrating a significant improvement in fatigue performance with the addition of GPLs. Furthermore, Table 11 compares the fatigue life of wind turbine blades made of GFRP with and without GPL reinforcement. The results indicate that the fatigue life of the GPL-reinforced wind turbine blade was at least 30 times greater than that of its non-reinforced counterpart. These results underscore the significant potential of GPL reinforcement in enhancing the fatigue life of wind turbine blades. However, further studies are recommended to explore its practical application to full-scale turbine blades.