# A Combined High and Low Cycle Fatigue Life Prediction Model for Wind Turbine Blades
## 5 Wind Turbine Blade Life Prediction  
The wind turbine blade used in the analysis is modeled based on the 5 MW reference turbine blade geometry. Table 2 [10] provides detailed data for each segment of the wind turbine blades studied. A fatigue life prediction model was developed by combining load interactions, improving the damage curve, and applying the model to predict blade life [41]. The FEA steps and CCF life prediction steps under this model are shown in Figure 8.  
Since the overall fatigue life of a blade is determined by the root of the blade, which is the first to fail, the local stresses in the root were chosen to assess the fatigue condition of the \begin{table}
\begin{tabular}{c c c c c} \hline
**Span (m)** & **Relem (\% Span)** & **Twist (Deg)** & **Chord (m)** & **Chord (\% Span)** \\ \hline  
& 0 & 1 & 0.024 \\ \hline \end{tabular}
\end{table} 
Table 2: Turbine blade geometry. Figure 7: Box plot of prediction error. blade. The loaded fatigue damage depends not only on the applied stress but also on the number of cycles over 20 years [42]. The number of cycles at each wind speed is calculated based on the Weibull wind speed distribution, and the expression is shown in Equation (26):  
\[h_{i}=8760\ F(v)\ \big{|}_{v_{i}+\Delta v}^{v_{i}-\Delta v}=8760\int_{v_{i}+1}^{v_{ i}-1}f(v)\mathrm{d}v \tag{26}\]  
where \(h_{i}\) denotes the number of hours per year, \(v_{i}\) denotes the wind speed, \(\Delta v\) denotes the wind speed increment, and \(f(v)\) and \(F(v)\) denote the corresponding probability density and distribution function, respectively. The time expression for the distribution of effective wind speed over the year is shown in Equation (27):  
\[H=\Sigma h_{i} \tag{27}\]  
When \(\Delta v=2\ \mathrm{m/s}\), the number of hours per year at each wind speed is calculated according to Equation (27), and the results are shown in Table 3. The effective wind speed distribution time in a year is estimated according to Equation (27) \(H=8610\ \mathrm{h}\). The Weibull wind speed distribution curve is shown below in Figure 9.  
Figure 8: _Cont._ \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Number**} & **Wind Speed** & **Annual** & **Stress \(\sigma_{i}\)** & **Fatigue Life \(N_{\beta}/10^{3}\)** \\  & **(m/s)** & **Hours (h)** & **(MPa)** & **(Cycles)** \\ \hline
1 & 3 & 797 & 28.86 & - \\
2 & 4 & 1380 & 29.31 & - \\
3 & 6 & 1629 & 39.37 & 6933 \\
4 & 8 & 1554 & 45.56 & - \\
5 & 10 & 1262 & 50.66 & - \\
6 & 12 & 894 & 48.72 & - \\
7 & 14 & 559 & 42.20 & 2125 \\
8 & 16 & 311 & 41.22 & 3337.8 \\
9 & 18 & 155 & 35.46 & 32,754 \\
10 & 20 & 69 & 31.25 & 202,600 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Stress distribution table at each wind speed. Figure 8: CCF analysis process. (**a**) CCF FEA model of wind turbine blades; (**b**) CCF life prediction analysis process. The tested blade is made of composite material, and its fatigue limit is \(\sigma_{e}=30.2\) MPa. The stress distribution at each wind speed is shown in Table 3. Stresses lower than the fatigue limit have no effect on fatigue performance and can be neglected. Stresses above the fatigue limit will be predicted based on Equation (21) for fatigue life. According to Table 3, the \(N_{L}=7.2981\times 10^{5}\) cycles and the \(S\)-\(N\) curves of HCF [43] are shown in Figure 10. Figure 10 shows the relationship between the stress amplitude \(\sigma_{H}\) and the number of cycles \(N_{H}\) for HCF loading. The data are represented by a fitted curve, described by Equation (28):  
\[y=102.09\times x^{-0.0596} \tag{28}\]  
where \(y\) represents the stress amplitude \(\sigma_{H}\), and \(x\) represents the number of cycles \(N_{H}\). The equation suggests a weak inverse relationship between stress and the number of cycles that as the number of cycles increases, the stress amplitude decreases, which is characteristic of fatigue behavior in materials subjected to HCF loading.