# A Combined High and Low Cycle Fatigue Life Prediction Model for Wind Turbine Blades
## 2 Miner's Rule and Fatigue Damage Accumulation Under Variable Amplitude Cyclic Load
### Fatigue Damage Accumulation Under Variable Amplitude Cyclic Loading  
As [PERSON]'s rule predicts fatigue life inaccurately under variable amplitude loading, a nonlinear fatigue damage model was proposed to address its limitation in handling different stress levels independently.  
Throughout the damage cycle, internal material fractures emerge as the damage rate increases under sustained stress. Interfacial debonding initiates fractures, and the damage rate gradually stabilizes as fissures expand to saturation. Subsequent fractures and damage coupling within the material result in large-scale cracking and accelerated degradation, ultimately leading to fatigue failure. Consequently, the progression of material damage exhibits significant nonlinearity [30].  
In the two-stage fatigue test, the specimen is subjected to repeated second-level loading \(\sigma_{2}\) until fatigue failure occurs, following \(n_{1}\) cycles of first-level loading \(\sigma_{1}\). The number of loading cycles is recorded as \(n_{2}\). Considering the impact of load sequence, H-L represents the sequence of two-level loading, meaning that H-L stands for high load followed by low load, and L-H stands for low load followed by high load. Figure 2 illustrates the cumulative damage mode under the H-L sequence. Likewise, Figure 3 displays the cumulative damage mode under the L-H sequence.  
Figure 3: Accumulated damage mode under L-H load sequence.  
Figure 2: Accumulated damage patterns under H-L load sequences.  
The equivalent damage hypothesis, which states that fatigue damage may be converted equivalently under various loadings, is used to forecast fatigue life under varying cyclic loading. Under the equivalent damage theory, during two-stage cyclic loading, loading occurs \(n_{1}\) times under load \(\sigma_{1}\) and is converted to \(n^{\prime}\) times under load \(\sigma_{2}\). This means that the load cycle ratio at \(\sigma_{1}\) matches the equivalent conversion cycle ratio at \(\sigma_{2}\). Equation (4) displays the corresponding damage expression at \(\sigma_{1}\) under two-level cyclic loading [31].  
\[D\bigg{(}\frac{n_{1}}{N_{1}}\bigg{)}=D\bigg{(}\frac{n^{\prime}}{N_{2}}\bigg{)} \tag{4}\]  
where \(n^{\prime}\) represents the equivalent number of cycles after converting the first-level load \(\sigma_{1}\) to the second-level load \(\sigma_{2}\).  
The fatigue damage under primary load \(\sigma_{1}\) is converted to fatigue damage under secondary load \(\sigma_{2}\) by introducing the equivalent damage theory. The equivalent damage under secondary load \(\sigma_{2}\) is shown in Equation (5):  
\[D\bigg{(}\frac{n_{2}}{N_{2}}\bigg{)}=D\bigg{(}1-\frac{n^{\prime}}{N_{2}}\bigg{)} \tag{5}\]  
The microstructure within the material undergoes transformation caused by varying applied loads, leading to distinct damage patterns like cracking and fracture. Under equal amplitude cyclic loading, high loading accelerates crack formation, whereas low loading enhances fatigue and yield strengths, thereby extending fatigue life. Under CCF loading, fatigue damage from the current cycle is influenced by the loading sequence and the magnitude of the preceding load. The previous loading level affects material damage evolution and the subsequent loading level. Fatigue life predictions may deviate from expectations if load sequences and interactions are ignored [31].