# A Combined High and Low Cycle Fatigue Life Prediction Model for Wind Turbine Blades
## 1 Introduction  
The fatigue life of wind turbine blades is a critical aspect of turbine performance and reliability research. With the advancement of wind turbine technology, fatigue load analysis, particularly under combined high and low cycle fatigue (CCF) conditions, has become a key factor in optimizing blade design and enhancing turbine stability [1, 2, 3]. In the fatigue analysis of wind turbine blades, CCF loading plays a crucial role. Compared to traditional low cycle fatigue (LCF) and high cycle fatigue (HCF), CCF loading involves more complex load interactions that significantly impact the fatigue life of the blades [4, 5]. The fatigue analysis, vibration suppression, and condition monitoring of wind turbine blades under CCF loading conditions are key areas for improving turbine performance and extending service life [6, 7, 8, 9]. However, most of the existing research on wind turbine blade damage mechanisms typically treats HCF and LCF damage theories separately, leading to significant discrepancies between the predicted and experimental fatigue life [10, 11, 12, 13]. Therefore, developing a damage accumulation model that considers the impact of CCF failure on blade fatigue is essential for ensuring blade safety. The fatigue damage accumulation hypothesis is currently the most widely adopted method for predicting CCF life [14, 15, 16, 17]. To evaluate the fatigue life under CCF loading, several researchers have looked into different fatigue prediction models [18, 19]. Most of these cumulative damage models, particularly the early ones, were developed under loading conditions limited to either pure HCF or LCF. The complexity of CCF loading often leads to highly discrete life forecast errors, making it difficult to achieve the desiredaccuracy. Moreover, neither pure HCF nor LCF adequately models blade fatigue strength damage mechanisms or accurately represents real operational conditions when compared to CCF damage. [PERSON]'s rule [20], one of the most traditional approaches, has been widely applied due to its simplicity and practicality. However, it fails to account for the interaction between LCF and HCF loading, leading to non-conservative predictions. To address this limitation, [PERSON] and [PERSON] (M-H) [21] proposed the damage curve method to model interaction effects. Similarly, [PERSON] and [PERSON] (T-K) [22] established a damage curve approach to improve CCF fatigue life predictions. These two models demonstrated better prediction accuracy compared to [PERSON]'s rule. In recent years, [PERSON] et al. [23; 24] introduced a pioneering nonlinear damage accumulation model that incorporates current HCF damage and threshold damage factors for a specific material type, achieving improved prediction outcomes. Building on this, [PERSON] [25] developed a life prediction model designed for turbine blades under CCF loading, yielding better results. Additionally, a dual threshold model was created by [PERSON] [26] to evaluate the turbine blade's CCF fatigue life. [PERSON] [27] et al. provided valuable insights into advanced damage mechanics for ductile materials, which were discussed to highlight the comparative novelty of our proposed model in terms of incorporating load interactions and coupled damage effects. [PERSON] [28] et al. focused on quasi-brittle materials and presented advanced damage simulation techniques, offering a relevant benchmark for positioning our model. However, rather than predicting the accumulation of fatigue damage in composite materials under CCF loading, the models presented above are mostly used to predict the CCF fatigue life of metallic materials. As a result, few models are able to predict the CCF fatigue life of composite materials with any degree of accuracy. The purpose of this paper is to develop a comprehensive and accurate CCF fatigue life prediction model for wind turbine blades.