Parametric and numerical Finite Element simulation of wind turbine blades subjected to thermal residual stresses

This study aims to contribute to the ongoing efforts to enhance the reliability and durability of wind turbine blades, a critical component in wind energy generation. Specifically, this research addresses the issue of tunneling cracking and severe damage that can occur in wind turbine blades due to cohesive failure of the trailing edge. To achieve this objective, the study employs a rigorous approach, utilizing a full three-dimensional (3D) modeling strategy with finite element analysis (FEA) to simulate the behavior of wind turbine blades. The effect of cohesive materials and layered simulation methods on the thermal residual stress and crack propagation is thoroughly investigated. In particular, the study assesses the influence of carbon fiber-reinforced polymer (CFRP) and glass fiber-reinforced polymer (GFRP) materials on the phenomenon under consideration. In addition, the study undertakes a comprehensive parametric analysis to identify the independent effects of material properties and numerical simulation on thermal residual stress. Moreover, the research explores the behavior of the cohesive zone model in terms of thermal residual stress and crack propagation. The findings of this study have significant implications for researchers and practitioners in the wind energy industry. The study’s outcomes can aid in the development of improved materials and simulation techniques to mitigate thermal residual stress and prevent the occurrence of tunneling cracking and other types of damage in wind turbine blades. As such, this research contributes to the broader efforts to advance the reliability, efficiency, and sustainability of wind energy generation.


Introduction
Fiber-reinforced polymers (FRPs) are attractive due to the weight to stiffness ratio, economical efficiency, chemical and humidity resistance, toughness, thermal, and electrical insulation.The advantages of FRP materials lead to extensive utilization in aerospace, mechanical, and civil engineering industries.In addition, adhesive bonding is required for the edges and connections of FRPs.Adhesively bonded joints offer advantages over traditional connection methods, including increased joint stiffness and higher fatigue resistance.Despite these benefits, there are also some drawbacks in terms of construction and service conditions.One of the most critical steps in the construction process is surface cleaning, which is highly sensitive.Furthermore, joint design typically results in greater shear, compressive, and tensile resistance, but may be vulnerable to peeling.Cohesive materials have a higher thermal constant than metals.Additionally, the relationship between cohesive material and temperature is nonlinear.Consequently, even minor deviations in thermal control and design conditions may result in significant changes in joint characteristics.This scenario is likely to occur under service thermal loading [1].The term "tunneling crack" refers to damage initiation of the bond line caused by cohesive failure [2].Carins and Peterson [3] and Struzziero and Teuwen [4] have investigated thick adhesive joints in terms of crack initiation and propagation.Samborsky et al. [5] studied mixed-mode fracture, crack growth characteristics, and fatigue growth resistance in thick adhesive joints between fiberglass laminates.The fracture behavior of the adhesive joint of the trailing edge has been evaluated by Eder and Bitsche [6].A new approach has been proposed by Jørgensen et al. [7] to determine the residual stress.The study shows that the difference in temperature in curing and testing leads to transverse crack formation in the adhesive layer.As a result, increasing the laminate thickness has a slight effect.Rosmeier et al. [8] considered the impact of thermal residual stress on fatigue and found significant effects on the initiation and growth of tunneling cracks.Although the tunneling crack has no direct effect on the structural integrity of turbine blades, its propagation into adjacent laminates can increase the probability of severe damage.
Figure 1 represents the general turbine blade shapes and tunneling cracking formation.The thermal residual stress can be calculated using finite element (FE) simulation.Nielsen [9] predicts the shape distortion of thick laminates by implementing cure hardening instantaneous elastic (CHILE) and a path-dependent approach.Rosemeier et al.
[10] determine the accuracy of the FE numerical model for a thick bond line.In their study, classical laminated plate theory (CLT) is implemented, along with FE plate models of different fidelities.Residual thermal stress also affects repaired wind turbine blades, leading to microstructural defects.Paul et al. [11] assess the occurrence of residual stress due to thermal cycles, by implementing a coupled temperature-displacement analysis in FE software.Hwang et al. [12] investigate the strength of the adhesive in a large turbine blade through real-scale simulation.The results indicate that by utilizing a smart curing process, the final curing temperature and hence residual thermal stress and thermal shear stress are reduced.Jørgensen et al. [13] evaluate the novel idea of embedding a buffer layer between the adhesive and the glass fiber laminate using a 2D tri-material FE model.The results show an improvement in joint design against tunneling cracks.
Despite the extensive experimental and numerical investigation, in many cases, the simplified plate model has been used as a delegacy of the full-scale turbine model.Furthermore, this simplified plate has simply supported boundary conditions which leads to contradiction with real blade loading conditions [14].Also, Carbon fiber-reinforced polymers (CFRP) and Glass fiber-reinforced polymers (GFRP) has different thermal constant.Therefore, connection with an adhesive layer in the trailing edge can result in different distortion and displacement values.Since the cohesive zone is considered employing different damage evolution models in FE simulation, this approaches lead to different crack propagation pattern.To overcome the abovementioned issues, this study proposed an extensive parametric study implementing a full-scale FE model to achieve a comprehensive study in terms of residual thermal stress induced by curing and operational temperature.

Numerical model and methodology
A three-dimensional finite element model in ABAQUS 2017 software is implemented to predict the behavior of the SSP blade [14] subjected to residual thermal stress.The model includes nonlinear and thermal characteristics of the materials for CFRP/GFRP and adhesive.The model is capable of capturing all six mechanical stress components along the trailing edge.The CFRP/GFRP laminae are modeled using shell element type SC8RT and the adhesive is modeled by means of COH3D8 elements.The general model, mesh pattern, and boundary conditions are demonstrated in Figures 2 and 3.The boundary condition is considered encast (fixed in all 6 degrees of freedom) in the blade root location.In this section, we present the results related to the thermal coefficients and material properties of the materials under investigation.Table 1 provides an overview of the thermal coefficients of the different materials, namely GFRP, CFRP, and cohesive materials.These coefficients represent the rate of change of material dimensions in response to temperature variations.The values are considered equal in all directions.Table 2 tabulates the material properties of GFRP, CFRP, and cohesive materials.These properties play a crucial role in determining the mechanical behavior and performance of the materials.For GFRP and CFRP, the table includes parameters such as Young's modulus, shear modulus, Poisson's ratio, and fracture energy in crack opening as well as in crack sliding.It is worth mentioning that CFRP and GFRP matrerials are considered elastic lamina for biaxial fiber configuration.These properties provide insights into the stiffness, strength, and fracture response of the composite materials.
The detailed analysis of these material properties will shed light on the characteristics and behavior of the materials under consideration, enabling a comprehensive understanding of their performance in the subsequent sections.By considering linear elastic behavior for CFRP/GFRP materials the relationship between stress and strain can be calculated as follows [10] where R i  are residual stress and R i  are residual strain components in the xz-plane of the adhesive layer.Moreover, E and  are module of elasticity, and Poisson's ratio, respectively.In the adhesive layer, the thermal residual strain is calculated as .Since the material model used is not temperature-dependent, the operating temperature was chosen as 1 T = 23 • C.This temperature corresponds to the standard class 1 room temperature [17], at which the material properties were originally determined.It is worth mentioning that static loading is considered according to Equations ( 4) and ( 5) by Mikkelsen [18] 2 8 27 where flap z q and edge z q are distributed flap and edge wind loads along the blade axis, respectively.
and g are air density, blade density, remote wind speed, area of the cross-section of blade materials, and gravitational constant, respectively.z indicates the axial blade coordinate measured from the root of the blade.

Equivalent stress
To account for the isotropic nature of the adhesive layer, the expression proposed by Betti [19] was utilized to calculate the residual equivalent stress.The following expression for calculating equivalent residual stress , R e  , (Equation 6) provided an accurate means of determining the stress distribution within the adhesive layer as where R ij  are shear stress components in corresponding directions, respectively.

Results
The results obtained from the comprehensive analysis of the turbine blade under thermal loading conditions provide valuable insights into the behavior and performance of the adhesive and CFRP/GFRP materials.In this section, we present and discuss the key findings and observations from the analysis, focusing on the effects of thermal loading on the stiffness, stresses, and displacement of the blade.

Figure 5. Stress versus relative span-wise position
The analysis of Figures 5 and 6 reveals interesting trends as we move from the root of the blade towards the tip, particularly in the region close to 80%-90% of the blade length.In the blade composed of GFRP material, it can be observed that this part of the blade experiences the highest levels of equivalent stress and displacement.Specifically, at this location, the equivalent stress reaches a magnitude of 15 MPa.Additionally, the thermal loading induces a displacement of -0.13 mm in the same region.It is noteworthy that the thermal effects diminish towards the tip of the blade due to the reduction in material length.Consequently, the impact of thermal stresses decreases accordingly.
Nevertheless, despite the lower thermal coefficient and higher stiffness of CFRP material compared to GFRP, unexpected results are observed.The CFRP blade exhibits approximately 4% higher displacement, 7% higher equivalent stress in comparison to the GFRP blade.This discrepancy can be attributed to the utilization of the same adhesive material at the trailing edge.Therefore, the choice of material and adhesive plays a crucial role in determining the stress and displacement characteristics of the blade under thermal loading conditions.Figure 7 provides insights into the behavior of the blade material under thermal loading conditions.It clearly demonstrates that the application of thermal loading leads to the generation of stress within the blade material.Moreover, it is noteworthy that this stress attains its maximum magnitude in the region extending from 80% of the blade length towards the blade tip in both GFRP and CFRP blade.8 presents a comprehensive visualization of the equivalent stress distribution within the adhesive material.It vividly illustrates how thermal loading influences the adhesive along its entire length, leading to the concentration of stress middle of the blade.This stress concentration phenomenon in the adhesive material in the middle of the blade is a direct consequence of the thermal loading applied to the structure.The application of thermal loading significantly affects the stiffness of the adhesive (in terms of SDEG, scalar damage in cohesive material), causing it to lose approximately 55% of its original stiffness (Figure 11a , SDEG=0.55).This reduction in stiffness makes the adhesive layer more susceptible to the applied loading conditions.Moreover, when considering the thermal loading, both the adhesive material and the GFRP and CFRP materials experience higher levels of stresses and strains compared to what was initially calculated during the design phase.These discrepancies in the loading conditions, coupled with the effects of thermal loading, can lead to unexpected failures in turbine blades.The results highlight a particular vulnerability near the blade tip, where a greater displacement is observed during the loading conditions.This increased displacement further contributes to the potential failure of the turbine blade.It is crucial to take into account these factors and accurately assess the impact of thermal loading to ensure the structural integrity and reliability of turbine blades under operating conditions.By conducting a parametric study on the adhesive material (Figure 11), it was observed that reducing the shear fracture energy from 0.6 N.mm to 0.4 N.mm in the softening region of the adhesive's behavior has significant effects.Specifically, this reduction in shear fracture energy results in higher stresses being exerted on the adhesive material located at the trailing edge.Consequently, the stiffness of the adhesive decreases.

Conclusion
In conclusion, the results obtained from the analysis of the turbine blade under thermal loading conditions have provided insights into the behavior and performance of the adhesive, GFRP and CFRP materials.The findings can be summarized as follows: • Moving from the root to the tip of the blade, the region close to 80%-90% of the blade length experienced the highest levels of equivalent stress and displacement.• Thermal loading induced stress within the blade material, with the maximum stress magnitude occurring from 60%-80% of the blade length towards the tip.• The thermal loading effects caused the adhesive to lose approximately 50% of its stiffness, making it more susceptible to applied loading conditions.• Reducing the shear fracture energy of the adhesive in the softening region had significant effects, resulting in higher stresses on the adhesive material at the trailing edge and a decrease in stiffness.Complete damage was observed in the cohesive element with lower fracture energy, leading to the detachment of the connected CFRP/GFRP sheets.
These findings underscore the importance of considering thermal loading effects, material properties, and adhesive behavior in the design and analysis of turbine blades.Accurate assessment and understanding of these factors are essential for ensuring the structural reliability and performance of the blades under operating conditions.Despite efforts that have been faced with this research, to have an accurate model it is essential to develop an extensive experimental program.Moreover, material-level experiments need to model validation and verification of the behavior of the adhesive.Therefore, this parametric study is useful just to know the comparison range of the displacement and stress for CFRP/GFRP blade shape structures.

Figure 1 .
Figure 1.Turbine blade details, a) general blade, b) blade section, c) adhesive joint and tunneling cracking location

2 . 1 .
layer and bond line laminate in x and z direction, thermal coefficient and T  is the difference of temperature between curing 1 T and operation 2 Thermal analysis of full-scale blade The models underwent thermal loading caused by a temperature difference T  , as described in Equation (3).The adhesive's curing temperature was 2 T = 70 • C [10]

Figure
Figure8presents a comprehensive visualization of the equivalent stress distribution within the adhesive material.It vividly illustrates how thermal loading influences the adhesive along its entire length, leading to the concentration of stress middle of the blade.This stress concentration phenomenon in the adhesive material in the middle of the blade is a direct consequence of the thermal loading applied to the structure.The application of thermal loading significantly affects the stiffness of the adhesive (in terms of SDEG, scalar damage in cohesive material), causing it to lose approximately 55% of its original stiffness (Figure11a, SDEG=0.55).This reduction in stiffness makes the adhesive layer more susceptible to the applied loading conditions.Moreover, when considering the thermal loading, both the adhesive material and the GFRP and CFRP materials experience higher levels of stresses and strains compared to what was initially calculated during the design phase.These discrepancies in the loading conditions, coupled with the effects of thermal loading, can lead to unexpected failures in turbine blades.The results highlight a particular vulnerability near the blade tip, where a greater displacement is observed during the loading conditions.This increased displacement further contributes to the potential failure of the turbine blade.It is crucial to take into account these factors and accurately assess the impact of thermal loading to ensure the structural integrity and reliability of turbine blades under operating conditions.

Figure 11 .
Figure 11.Scalar damage distribution in cohesive element with different fracture energy,a) 0.6 N.mm, b) 0.5 N.mm ,and c) 0.4 N.mm

Table 1 .
Thermal coefficient of materials Material

Table 2 .
Material properties