# Numerical Analysis of Fatigue Life of Wind Turbine Blades Reinforced with Graphene Platelets
## 3 Fatigue Life Assessment for Wind Turbine Blades
### Fatigue Damage Assessment  
To assess the fatigue life of a structure under combined load conditions, a method to precisely evaluate cumulative fatigue damage based on the number of cycles to failure and the number of load cycles corresponding to each stress amplitude is required. This study evaluated cumulative fatigue damage by applying the most widely used Palmgren-Miner rule. Cumulative fatigue damage \(D\) is defined as Equation (10). Based on this, fatigue life can be calculated through Equation (11). Table 7 is an example of the fatigue life assessment results of this study. It shows the results of the fiberglass-based wind turbine blade presented in Section 4.1 at location 5. Here, 'peak' and the corresponding 'cycle' are obtained from the frequency-domain stress spectrum, as shown in Figure 5. The maximum stress \(\sigma_{\text{max}}\) and minimum stress \(\sigma_{\text{min}}\) are calculated based on the time-domain stress spectra, divided by the number of fatigue cycles. The equivalent stress \(\sigma_{\text{e}}\) can be determined using the mean stress \(\sigma_{\text{m}}\) and amplitude stress \(\sigma_{\text{a}}\), as expressed in Equation (8). \[D=\sum_{i=1}^{n}\frac{n_{i}}{N_{i}} \tag{10}\]  
with \(n_{i}\) and \(N_{i}\) being the numbers of the load cycles and cycles to failure, respectively. Here, \(n_{i}\) is set to 1, since the concept of fatigue cycles is employed in this study, as indicated in Table 7.  
\[\text{Fatigue life (years)}=\frac{1}{\sum D\times 24\times 365} \tag{11}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Material Properties** & **GFRP** & **CFRP** & **GPLRC (\(V_{GPL}\) = 2.7\%)** \\ \hline \(\sigma_{u}\) (MPa) & 700 & 1546 & 200 \\ \(b\) & 10 & 14 & 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Material properties for fatigue life assessment. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Peak** & **Cycle** & \(\sigma_{\text{max}}\) & \(\sigma_{\text{min}}\) & \(\sigma_{\text{m}}\) & \(\sigma_{\text{a}}\) & \(\sigma_{\text{e}}\) & **N** & **D** \\  & **(MPa)** & **(MPa)** & **(MPa)** & **(MPa)** & **(MPa)** & **(MPa)** & **(Cycle)** & **D** \\ \hline
1 & 3 & 197.33 & 14.59 & 105.96 & 91.37 & 107.67 & \(5.39\times 10^{6}\) & \(1.86\times 10^{-7}\) \\  & & 199.31 & 10.48 & 104.90 & 94.42 & 111.06 & \(3.95\times 10^{6}\) & \(2.53\times 10^{-7}\) \\  & & 185.96 & 24.53 & 105.25 & 80.71 & 95.00 & \(1.88\times 10^{7}\) & \(5.31\times 10^{-8}\) \\
2 & 7 & 197.33 & 19.73 & 108.53 & 88.80 & 105.09 & \(6.86\times 10^{6}\) & \(1.46\times 10^{-7}\) \\  & & 181.65 & 35.26 & 108.45 & 73.19 & 86.61 & \(4.75\times 10^{7}\) & \(2.11\times 10^{-8}\) \\  & & 199.31 & 14.59 & 106.95 & 92.36 & 109.02 & \(4.75\times 10^{6}\) & \(2.10\times 10^{-7}\) \\  & & 119.65 & 10.48 & 65.06 & 54.59 & 60.18 & \(1.81\times 10^{9}\) & \(5.53\times 10^{-10}\) \\  & & 190.16 & 38.82 & 114.49 & 75.67 & 90.46 & \(3.07\times 10^{7}\) & \(3.26\times 10^{-8}\) \\  & & 181.90 & 27.95 & 104.92 & 76.98 & 90.55 & \(3.04\times 10^{7}\) & \(3.29\times 10^{-8}\) \\  & & 185.92 & 24.53 & 105.22 & 80.69 & 94.97 & \(1.89\times 10^{7}\) & \(5.29\times 10^{-8}\) \\
3 & 9 & 197.33 & 19.73 & 108.53 & 88.80 & 105.09 & \(6.86\times 10^{6}\) & \(1.46\times 10^{-7}\) \\  & & 155.41 & 35.26 & 95.33 & 60.08 & 69.55 & \(4.26\times 10^{8}\) & \(2.35\times 10^{-9}\) \\  & & 181.65 & 14.59 & 98.12 & 83.53 & 97.15 & \(1.51\times 10^{7}\) & \(6.64\times 10^{-8}\) \\  & & 199.31 & 56.31 & 127.81 & 71.50 & 87.47 & \(4.30\times 10^{7}\) & \(2.33\times 10^{-8}\) \\  & & 119.65 & 10.48 & 65.06 & 54.59 & 60.18 & \(1.81\times 10^{9}\) & \(5.53\times 10^{-10}\) \\  & & 190.16 & 38.82 & 114.49 & 75.67 & 90.46 & \(3.07\times 10^{7}\) & \(3.26\times 10^{-8}\) \\  & & 185.96 & 27.95 & 106.95 & 79.01 & 93.25 & \(2.27\times 10^{7}\) & \(4.41\times 10^{-8}\) \\  & & 181.90 & 50.25 & 116.08 & 65.82 & 78.91 & \(1.21\times 10^{8}\) & \(8.30\times 10^{-9}\) \\  & & 185.92 & 24.53 & 105.22 & 80.69 & 94.97 & \(1.89\times 10^{7}\) & \(5.29\times 10^{-8}\) \\ \hline \hline \end{tabular}
\end{table}