NFX|风力发电机叶片疲劳分析
Abstract:
The rapid growth of wind energy has necessitated the development of advanced materials to address the increasing structural demands of wind turbine blades. Graphene platelets (GPLs) have garnered attention as a promising reinforcement material due to 4 their outstanding mechanical properties, such as high strength and low density. This study investigates the fatigue life of wind turbine blades reinforced with GPLs, benchmarking their performance against conventional fiberglass blades. A finite element model of a 5MW wind turbine blade was developed to evaluate stresses within the blade structure. The traditional fiberglass blade was modeled based on the SNL 61.5 m design by Sandia National Laboratories, while the GPL-reinforced composite (GPLRC) blade was designed by substituting fiberglass with GPLRCs. Material properties of the GPLRCs were determined using the rule of mixtures and the Halpin–Tsai micromechanics model. Wind speed data were randomly sampled following the probability distribution observed at European wind farms,and corresponding aerodynamic loads were computed using blade element momentum theory. Finite element analyses were performed to derive stress time histories, and fatigue life was predicted using the S-N curve approach, incorporating the Goodman diagram and the Palmgren–Miner rule. The results reveal that while GPLRC-reinforced blades exhibit some limitations in fatigue performance compared to traditional fiberglass blades, potential solutions for improving their durability are proposed, highlighting avenues for further research and optimization in the application of GPLRCs to wind turbine blades
Keywords:
wind turbine blades; graphene platelets (GPLs); fatigue damage; fatigue life assessment; finite element structural analysis; blade element momentum theory (BEMT)
1. Introduction
Since the industrial revolution in the 18th century, the rapid growth of science, technology,and industry has accelerated the development of human civilization. However,we now face serious energy crises and climate change owing to rapidly increasing energy demands and the greenhouse gas emissions caused by fossil fuel consumption. Renewable energy has attracted attention as a key alternative to address these problems. Specifically,wind energy has been established as a major axis of the renewable energy industry along with solar energy based on its low carbon emission characteristics and large-scale power generation potential. With a recent sharp increase in demand for wind energy, various strategies have been adopted to increase economic feasibility and efficiency. Among them,large wind turbines have been evaluated as a representative approach to increasing power generation efficiency. Large wind turbines, however, increase operational loads and the weight of the structure, presenting new engineering challenges in design and manufacturing processes.
To address these problems, academia and industry have explored various methods.One of them is to ensure structural safety and economic feasibility by applying cuttingedge new materials with ultralight and high-strength properties to wind turbine blades.Wind turbine blades represent 10 to 15% of the total manufacturing cost and 8% of the total weight [1]. Given that they are key structures that have the largest impact on the power generation efficiency of wind turbines, various studies have been conducted by applying cutting-edge new materials to them. For example, Mengal et al. [2] examined the applicability of basalt fibers to wind turbine blades by comparing them with conventional glass and carbon fibers. Chikhradze et al. [3] analyzed the structural performance of the wind turbine blades reinforced with nanopowder and hybrid fibers composed of glass,carbon, and basalt. Paquette et al. [4] experimentally verified that the structural integrity of wind turbine blades is effectively improved via carbon fiber reinforcement. Muhammed et al. [5] analyzed the bending behavior of the wind turbine blades reinforced with SiO2 and Al2O3. Holmes et al. [6,7] and Shen-xue et al. [8] conducted research on the application of bamboo epoxy composite laminates to wind turbine blades and verified that they are applicable as alternative materials by providing sufficient strength and stiffness when compared to conventional fiberglass composites.
Recently, a number of studies have been conducted on the application of carbon-based nanomaterials to wind turbine blades. As a representative case, Ma and Zhang [9] analyzed the applicability of carbon nanotube (CNT)/polymer composites to wind turbine blades,considering structural and functional requirements. Buyuknalcaci et al. [10] suggested that the application of CNT-based composites to wind turbine blades can improve the mechanical performance and fatigue resistance of the blades. Boncel et al. [11] comprehensively analyzed various potentials, such as mechanical performance, excellent fatigue resistance, and environmental resistance, when CNT-based composites are applied to wind turbine blades based on the experimental results and theoretical modeling reported in the existing literature. Furthermore, there are research cases in the literature where graphene platelets (GPLs), which attract attention as carbon-based, cutting-edge nanomaterials along with CNTs, are applied to wind turbine blades. For example, Bahaadini and Saidi [12] parametrically investigated the vibration characteristics of blades based on functionally graded GPL-reinforced composites (FG-GPLRCs) according to the GPL distribution pattern,weight fraction, and geometry. Song et al. [13] systematically analyzed the nonlinear coupled resonance characteristics of GPL-reinforced rotating blades according to various variables. There are cases in which GPLRC-reinforced blades were mainly analyzed as simplified beam models, as in the studies introduced above; however, only a few studies have actually applied them to detailed blade models. With this background, the authors of this paper have conducted a detailed analysis of the application of graphene platelets(GPLs) to wind turbine blade models, examining their bending, vibration, deflection, and stress concentration characteristics due to fatigue cracks, weight reduction, and economic feasibility[14–17].
Wind turbine blades are constantly exposed to repeated wind loads and irregular environmental conditions, and such environments act as major factors that threaten the structural safety of blades. Specifically, fatigue damage due to cyclic loads initiates with the occurrence of microcracks in the early stage and leads to the fracture of the structure through crack propagation, as shown in Figure 1.
Therefore, fatigue life assessment is a very important factor in structural design, along with yielding and buckling. Given this importance, various studies have been conducted on fatigue life assessment for wind turbine blades. For example, Kong et al. [18] analyzed the fatigue load spectrum using the S-N curve and Spera's empirical formula to assess the fatigue life of wind turbine blades and examined whether a design life of 20 years was met. Loza et al. [19] assessed the fatigue life of wind turbine blades under stall and pitch regulation conditions and analyzed the difference in fatigue damage between the two methods. Hu et al. [20] presented a method to more precisely assess fatigue life considering varying wind loads and multi-axial complex stress. Zhang et al. [21] introduced a method to assess the fatigue life of wind turbine blades by applying the modified blade element momentum theory (BEMT). Many other studies contributed to improving the fatigue performance of wind turbine blades, but further research is required when cutting-edge new materials are applied to meet the requirements of large wind turbines. For example, Zheng et al. [22] assessed fatigue performance by applying basalt fiber-reinforced composites to offshore wind turbine blades, and they confirmed that fatigue life was significantly improved when compared to conventional fiberglass blades. Dai and Mishnaevsky [23] analyzed the fatigue performance of CNT-reinforced composites using a multiscale finite element model, and they confirmed that the fatigue performance of the composites was significantly improved by CNT reinforcement.This indicated that CNT reinforcement can be effective when large blades, such as offshore wind turbine blades, are used. When new materials are used, it is required to closely examine the fatigue performance of wind turbine blades.
It is difficult, however, to find cases in which the fatigue performance of GPLreinforced wind turbine blades was evaluated using detailed finite element models. Hence,this study aims to assess the fatigue life of GPL-reinforced wind turbine blades by introducing an effective and reliable numerical evaluation method and comparing it with that of conventional fiberglass blades as a follow-up study to previous studies [14–17] conducted by the authors. In Section 2, the wind turbine blade model and material modeling method used for fatigue load analysis are described in detail, and the validity of the finite element model constructed based on them is verified. In Section 3, the stepwise procedure for fatigue life assessment and applied method are addressed in-depth. The results derived through the same procedure are closely analyzed in Section 4. Finally, based upon the numerical results, future research directions are presented by discussing potential alternatives to overcome the limitations of GPL-reinforced blades in terms of fatigue strength and to improve performance.
2. Finite Element Model of a 5 MW Wind Turbine Blade
2.1. Blade Layup
In this study, the geometry and material properties of the SNL 61.5-m model, representing a 5 MW wind turbine blade, were modeled based on the report by Resor [26].Table 1 presents the material properties of laminates used in the blade model. The geometry of the blade was created considering the airfoil type according to the blade span direction,chord length, torsion angle, and the location of the aerodynamic center. The cross-section of the blade comprises seven parts: the leading edge (LE), LE panel, spar cap, trailing edge(TE), TE reinforcement, TE panel, and shear web (SW).
Table 1. Material properties of laminates [26].
As listed in Table 2, the material and stacking sequence were modeled differently depending on each part and the location in the blade span direction.
Table 2. Stacking sequence in each panel of the blade model along the span [26].
2.2. Material Modeling of GPLRC
The GPL-reinforced wind turbine blade of this study was implemented by replacing the conventional fiberglass composite with GPLRCs. The thickness of GPLRCs was the same as that of the conventional fiberglass composite. For material modeling of GPLRCs,effective material properties were calculated in terms of the base material properties of GPL,a reinforcing material, and epoxy and their volume fractions. Equations (1) and (2) show the effective material properties calculated based on the linear rule of mixtures. Specifically,V denotes the volume fraction of the material. Subscripts eff, GPL, and m indicate effective material properties, GPL, and matrix, respectively.
Meanwhile, mechanical properties that are significantly affected by the geometry of the nanofillers, such as stiffness and strength, must be calculated through more precise,effective material property modeling techniques. Therefore, the effective elastic modulus of GPLRCs 
was calculated via the Halpin–Tsai micromechanics approach [27].
Table 3 shows the base material properties of GPLs and epoxy taken for calculating the effective material properties.
Here, L, T, GPL, and m denote the longitudinal and transverse directions, graphene platelets, and matrix, respectively. In addition,
,
, and
are the length, width, and thickness of GPLs, respectively, which were set by = 2.5 μm, = 1.5 μm, and = 1.5 nm [28].
2.3. Validation
In this study, midas NFX 2024R1, a commercial finite element analysis software, was used to conduct fatigue load spectrum analysis [29]. A four-node quad was used for the elements of the analysis model, and the element size was set at 0.08m × 0.08m, as in the report by Resor [26]. To validate the created finite element model, the mass, natural frequency, and bending and torsion deformations of the analysis model were compared with the results from the existing literature. As listed in Tables 4 and 5, the present analysis models and the previous studies have very similar masses and natural frequencies.
Figure 3 shows the results of comparing flapwise deflection and torsional deformation between the present analysis models and the reference solutions. The aerodynamic loads applied to the wind turbine blade model were calculated based on the rated wind speed(11.4 m/s). In this process, the BEMT to be introduced in Section 3 was utilized. The analysis model of this study showed high similarity to those of previous studies in terms of mechanical behavior, such as deflection and torsion, as well as the mass distribution and natural frequency of the blade, confirming that its results are sufficiently reliable.
3. Fatigue Life Assessment for Wind Turbine Blades
Fatigue life assessment is an essential step in the structural design process. It is particularly important for structures exposed to cyclic loads over an extended period of time, such as wind turbine blades. Fatigue life assessment for a structure is typically conducted by calculating the cumulative damage generated at each loading stage using the fatigue load spectrum according to design loads. In this study, cumulative fatigue damage was calculated based on the method proposed by Zhang et al. [21] to assess the fatigue life of the wind turbine blade. In this section, the procedure for assessing the fatigue life of the wind turbine blade is described in detail for each stage, and the results calculated at each stage are presented.
3.1. Aerodynamic Load Calculation
To improve the accuracy of the fatigue load spectrum, precisely calculated load data,as well as sophisticated finite element models, are essentially required. Computational fluid dynamics (CFD) and BEMT are typically used to estimate the aerodynamic loads acting on the wind turbine blade. Since CFD requires complex modeling and considerable computation time, BEMT-based load estimation methods have been widely adopted for practical applications. In this study, aerodynamic loads were calculated using BEMT, and the accuracy of calculation was further increased by applying tip loss correction [38] and turbulent windmill state correction [39].Detailed procedures for calculating aerodynamic loads using BEMT can be found in the studies by Kim and Cho [15] and Zhang et al. [21].
3.2. Sampling of Probable Wind Speed
To assess the accurate fatigue life of the wind turbine blade, it is ideal to use the fatigue load spectrum that corresponds to the entire design life. It is, however, an inefficient approach that requires excessive cost and time to secure long-term observation data in the time domain and conduct numerical analysis based on them. Therefore, the design of various engineered structures adopts a method for predicting long-term responses by combining stochastic approaches based on short-term data. In this study, the fatigue life of the wind turbine blade was predicted using 60 min wind speed data. The probability density distribution is mainly used to generate likely wind speed data. To secure similar wind speed distribution based on actual observation data, the long-term observation data of offshore wind farms in Europe were used (Weibull distribution, shape parameter α = 2.0,scale parameter β = 15.0 [21]). Equation (6) represents the Weibull distribution. The 60 min wind speed data, which are randomly extracted using it, are shown in Figure 4.
The tipspeed ratio presented in Figure 4 is calculated based on the experiment results of Jonkman et al. [40].
3.3. Fatigue Cycle Estimation
For simple loads with a single frequency, it is not necessary to additionally calculate the fatigue cycle. Actual structures, especially those that operate in complex dynamic environments (e.g., wind turbine blades), however, are exposed to complex load cycles that include various frequencies. In this case, stress and amplitude can be precisely defined by decomposing load cycles with frequencies. In this study, aerodynamic loads that correspond to the wind speed data generated earlier were calculated using BEMT, and they were applied to finite element analysis to extract fatigue loads in the time domain. The extracted fatigue load data were then converted into the frequency domain using a fast Fourier transform (FFT). Here, FFT is used for efficient calculation of the discrete Fourier transform presented in Equation (7). Figure 5 shows an example of a time-domain stress spectrum and its transformation into the frequency domain.
where X(k) is the signal in the frequency domain, k is the frequency index,
is the discrete signal samples in the time domain, N is the number of samples, and n is the time index
3.4. Equivalent Stress and Fatigue Life Calculation
An engineered structure is subjected to combined loads of static and dynamic loads,and it exhibits responses that combine mean stress and alternative loads. However, the S–N curve used for fatigue life assessment is generally derived under conditions with a mean stress of zero. Thus, it has limitations in accurately assessing fatigue life under combined load conditions. The equivalent stress concept was introduced to overcome the limitations, and the Goodman diagram is a representative method that effectively applies the concept. As such, equivalent stress was calculated in this study using the Goodman diagram presented in Equation (8) to consider fatigue behavior under combined load conditions.
where 
is the equivalent stress corresponding to the equivalent mean stress 
, which is set to zero in this study,
is the amplitude stress, and 
is the mean stress, and 
is the ultimate stress of the material.Next, the number of cycles to failure, N, can be calculated using Equation (9) by applying the equivalent stress calculated through the aforementioned method to the S–N curve of the material.
Figure 6 shows the Goodman diagram and the S–N curves of the glass fiber-reinforced polymer (GFRP), carbon fiber-reinforced polymer (CFRP), and GPLRCs used in this study. Here, the report by Resor [26] was referred to for the material properties of the GFRP and CFRP. The material properties of the GPLRCs were derived by extrapolating the properties presented in Shokrieh et al. [41].
Table 6 shows the material properties used in this study for fatigue life assessment. Here, the volume fraction of GPLRCs (2.7%) is a value set to the optimal ratio with the most similar mechanical characteristics to the conventional wind turbine blade, which was found through the previous studies [15,16] of the authors of the present study.
is the ultimate strength of the material, 
is the equivalent stress, b is the inverse of the slope of the S-N curve, and γ is the safety factor,which was set to 1.38 in accordance with Resor [24].3.5. 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
and minimum stress
are calculated based on the time-domain stress spectra, divided by the number of fatigue cycles. The equivalent stress 
can be determined using the mean stress and amplitude stress , as expressed in Equation (8).
with 
and 
being the numbers of the load cycles and cycles to failure, respectively. Here, is set to 1, since the concept of fatigue cycles is employed in this study, as indicated in Table 7.
4. Results and Discussion
4.1. Fatigue Life of Wind Turbine Blades with Conventional Fiberglass Composites Prior to assessing the fatigue life of the GPL-reinforced wind turbine blade, the fatigue life of the blade based on the conventional fiberglass composite was calculated using the aforementioned method to validate the method proposed in this study. It was then compared with the fatigue life results presented in Resor [24] to validate the proposed method. In general, the fatigue life of wind turbine blades is evaluated to be lower near the root when compared to the area near the tip. In this study, fatigue life was also assessed at the locations selected in Resor [24] (Table 8).
Figure 7 shows the fatigue life distribution of the fiberglass composite-based wind turbine blade according to the location in the span direction. It can be observed that the lowest fatigue life was calculated at location 5 for GFRP and CFRP. Compared with the fatigue life results presented in Resor [24],some differences were observed. This appears to be due to the difference in fatigue life assessment methods and applied loading conditions. Given that the changing tendency of the fatigue life of the blade in the span direction is generally similar to the results of Resor [24], however, the reliability and validity of the proposed method can be confirmed.
4.2. Fatigue Life of Wind Turbine Blades with GPLRC
Figure 8 shows the results of comparing fatigue life between the wind turbine blades with GPLRCs and traditional materials. From locations 1 to 4, the fatigue life of GPLRCs was evaluated to be higher than or similar to that of traditional materials. Between locations 5 and 8, however, the fatigue life of GPLRCs was evaluated to be lower than that of traditional materials. At location 5, the fatigue life of GPLRCs was notably lower than that of other materials. This is likely due to the maximum stress occurring at this location, combined with the fact that the fatigue failure stress (S–N curve) and tensile strength of GPLRCs are significantly lower compared to conventional materials, as shown in Figure 6 and Table 6. It is known that the non-uniform distribution of GPLs decreases the ultimate tensile strength of GPLRCs if the weight fraction of GPLs exceeds a certain level [42,43]. In this study, it was assumed that GPLs were ideally distributed inside the nanocomposite. If this criterion is not satisfied in the actual manufacturing process, the fatigue life of GPLRCs could be even lower than the results of this study
Table 9 summarizes the results of this study and the previous studies [15,16] by the authors of the present study. It compares the weight, material cost, natural frequency, and fatigue performance between the wind turbine blades made of traditional materials and GPLRCs. According to the comparison results, the total material cost of the wind turbine blade with GPLRCs is slightly higher. However, it is similar to traditional materials, as the difference is approximately 6%. On the other hand, the total weight of the blade with GPLRCs was more than 20% lower when compared to those of traditional materials, making it possible to significantly improve wind power generation efficiency. Furthermore, this is expected to reduce the cost of constructing support structures for wind turbines owing to the reduction in self-weight. In the case of wind turbine blades, the natural frequency is designed to be higher than the excitation frequency. Thus, it can be considered that GPLRCs with a higher natural frequency are safer in terms of resonance. The fatigue performance of GPLRCs, however, was found to be poor compared to that of traditional materials.Therefore, it is necessary to prepare measures that can supplement this at the design stage,such as developing hybrid materials by mixing conventional fiberglass composites with GPLs and optimizing the content and reinforcement location of GPLs. These measures are expected to ensure safety and durability while fully utilizing the potential of GPLRCs.
4.3. Fatigue Life of Wind Turbine Blades with Conventional Fiberglass Composites Reinforcedwith 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 Griffith and Ashwill [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 Yavari et al. [45], as the weight fraction ofGPLs 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.
5. Conclusions
In this study, the applicability of graphene platelet-reinforced composites (GPLRCs) to wind turbine blades as a next-generation material was examined by assessing the fatigue life of a wind turbine blade reinforced with graphene platelets (GPLs) using an effective and reliable numerical estimation method. The geometric dimensions and material properties of the finite element model were created based on the design of the SNL 61.5-m model, a 5 MW wind turbine blade. The effective elastic properties of GPLRCs were calculated by applying the Halpin–Tsai micromechanical model and modified linear rule of mixtures. The fatigue load spectrum was calculated based on 60 min wind speed data, and aerodynamic loads according to each wind speed were calculated using the BEMT. The fatigue load spectrum was then derived by applying the calculated loads to finite element analysis,and the fatigue cycle was calculated through an FFT. The equivalent stress acting on the blade was calculated based on the Goodman diagram, and cumulative fatigue damage was evaluated through the Palmgren–Miner rule. Finally, the reliability of the proposed analysis model and fatigue life assessment method was verified by comparing the fatigue life of wind turbine blades calculated in this study with the fatigue life results of Resor [26].
When the fatigue performance of the GPL-reinforced wind turbine blade was evaluated,GPLRCs exhibited similar or higher fatigue life compared to traditional materials in certain locations but showed poorer performance than traditional materials in other locations. In particular, the fatigue life of GPLRCs was significantly low near location 5 of the blade. This is due to the fact that the fatigue failure stress (S–N curve) and tensile strength of GPLRCs are lower than those of traditional materials. Additionally, an increase in the weight fraction of GPLs is highly likely to reduce tensile strength owing to their non-uniform distribution. This problem may have a more negative impact on fatigue performance in the actual manufacturing process.
Despite these challenges, GPLRCs showed promising results in terms of material cost, weight reduction, and natural frequency. However, their poor fatigue performance highlights the need for further development. Thus, it is necessary to explore measures such as developing hybrid materials by mixing conventional fiberglass composites with GPLs or optimizing the volume fraction and reinforcement locations of GPLs. To address the fatigue life limitations of wind turbine blades with GPLRC, this study proposed incorporating GPLs into fiberglass composites rather than completely replacing the matrix with GPLRC.As a result, the fatigue life of wind turbine blades was significantly improved by adding GPLs to fiberglass composites. Nevertheless, given the limited research on the application of GPL-reinforced fiberglass composites for wind turbine blades, further studies are needed to explore this approach in greater detail and advance its practical implementation.
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