Given the difficulty in accurately evaluating the fatigue performance of large composite wind turbine blades (referred to as blades), this paper takes the main beam structure of the blade with a rectangular cross-section as the simulation object and establishes a composite laminate rectangular beam structure that simultaneously includes the flange, web, and adhesive layer, referred to as the blade main beam sub-structure specimen, through the definition of blade sub-structures. This paper examines the progressive damage evolution law of the composite laminate rectangular beam utilizing an improved 3D Hashin failure criterion, cohesive zone model, B-K failure criterion, and computer simulation technology. Under static loading, the layup angle of the anti-shear web has a close relationship with the static load-carrying capacity of the composite laminate rectangular beam; under fatigue loading, the fatigue damage will first occur in the lower flange adhesive area of the whole composite laminate rectangular beam and ultimately result in the fracture failure of the entire structure. These results provide a theoretical reference and foundation for evaluating and predicting the fatigue performance of the blade main beam structure and even the full-size blade.

As the energy shortage issue brought on by the global energy crisis has become more prominent, the demand for the new energy industry as well as support from many countries around the world has increased dramatically. As the largest wind power country in the world, China’s development of the new energy industry will reach unprecedented heights [

Blade in long-term complex, harsh working conditions, its internal structure will experience fatigue damage; with the continuous accumulation of damage, blade fatigue performance (such as stiffness) will then decrease, until the loss of bearing capacity [

However, it is costly to directly investigate the fatigue performance of the main beam structure using a full-size blade, so it has become a popular research topic to indirectly infer the overall performance of the blade by directly investigating the fatigue performance of a sub-structure formed by intercepting a specific segment of the blade [

Domestic and international researchers have conducted numerous studies on the sub-structure of wind turbine blades in recent years. Eder et al. [

Therefore, this paper uses the blade main beam with a rectangular cross-section as the research object, employs the definition of blade sub-structure, selects a composite rectangular beam with blade flange, web, and adhesive layer to simulate the blade main beam structure, and, within the framework of composite fatigue damage theory and continuous medium damage mechanics theory, takes the stiffness as the defining parameter to characterize the fatigue damage state of the composite. The FEA model of the composite rectangular beam is used to clarify the progressive damage evolution of the composite rectangular beam. This is to indirectly evaluate the fatigue performance of the simulated blade main beam structure and provide a theoretical foundation for investigating the evolution of the blade main beam structure’s fatigue performance.

Although the failure form of the blade under the influence of fatigue load is complex and diverse, the failure location of the blade along the spreading direction exhibits a degree of regularity. Specifically, the easy damage zone of the blade is primarily concentrated between 26.2% and 53.85% distance from the leaf root [

The rectangular beam sub-structure designed in this paper includes beam flanges, shear-resistant webs, and adhesive layers of the simulated blade main beam structure, with the beam flange including upper and lower flanges and the structural parameters of the rectangular beam structure cross-section, as shown in

In this figure, the joint between the rectangular beam flange and the shear-resistant web (i.e., the adhesive layer) is bonded with epoxy resin adhesive. Based on the shear test results of a specific epoxy resin structural adhesive under different adhesive thicknesses [

To maximize the high-strength performance brought by composite laminated structures and considering the actual working conditions of blade main beam structures, the following conditions are met simultaneously: 0° plies are used primarily to bear the main tensile and compressive loads along the fiber direction, and ±45° ply groups are applied to bear the shear load by decomposing it into tensile and compressive components along the fiber direction. A certain number of ±45° ply groups should be arranged at the flange of the spar cap to improve the compressive stability and anti-buckling performance of this part of the structure. It is preferable to locate the ±45° plies on the outer surface of the overall structure as much as possible to improve the compressive stability and impact resistance of the laminated structure. Unless otherwise required, balanced symmetric laminates are used for ply settings to avoid warping caused by coupling failure during blade curing or after loading [

In this paper, based on the above principles of lay-up design of composite laminates and the layer groups design of the simulated blade main beam structure, the total number of lay-ups of beam flanges of rectangular beam structure is set to 10 layers and the total number of lay-ups of shear resistant webs is set to 4 layers by equal scaling.

The composite laminates used for the beam flanges and shear webs are T300/6808 carbon fiber-reinforced composites; the material specifications are listed in

Elastic modulus/GPa | Poission’s ratio | Density/(kg.m^{−3}) |
Strength/MPa | |
---|---|---|---|---|

Since each component of the composite rectangular beam structure is by definition a composite laminate, the intrinsic structure model of the composite laminate applies to the composite rectangular beam structure as well. The intrinsic structure relationship in the elastic deformation phase of common materials is expressed as:

In the formula,

In the formula,

In the formula,

Based on the multilayer structural design characteristics of composite laminates, the internal damage can be categorized into two forms: single-layer intra-layer damage and inter-layer damage.

I. The initial damage emergence stage, wherein a significant number of microcracks are generated within each monolayer matrix, and there is no interaction between the cracks.

II. The quasi-saturated stage of relatively slow damage accumulation, wherein microcracks in the matrix further expand. Simultaneously, interfacial debonding occurs, resulting in the interaction of intra-ply and inter-ply damage, and the formation of damage localization in the severe zone. Interfacial debonding leads to interactions between intra- and inter-layer damage, resulting in damage localization in the severe zone. The number of cycles required to reach a certain stage of characteristic damage saturation (CDS). Loading continues, and after about 50% of the fatigue life, local delamination occurs. The delamination then continues to expand along with the random fiber fracture or extraction in a certain part.

III. Rapid failure and destruction stage, wherein the accumulation of various damages and interactions during the process leads to further expansion of cracks and instantaneous failure damage of the entire structure.

In this paper, a modified three-dimensional Hashin failure criterion is used to comprehensively describe the failure modes of fiber tensile failure, fiber compression failure, matrix tensile failure, matrix compression failure, and fiber-matrix shear failure.

Fiber tensile failure

Fibre compression failure

Matrix tensile failure

Matrix compression failure

Matrix fiber shear failure:

In

In this paper, the pros and cons of the existing damage accumulation models and their applicability in finite element numerical simulations are evaluated, and the modified three-dimensional Camanho stiffness degradation model is chosen as the stiffness reduction scheme for the progressive damage analysis of rectangular beam structures, as shown in

Failure mode | Modified camanho degradation factors |
---|---|

Fiber tension | |

Fiber compression | |

Matrix tension | |

Matrix compression | |

Shear |

This paper introduces a three-dimensional cohesive element with thickness based on the bilinear traction-separation law to simulate the delamination damage in the bonded area between the main beam flange and the shear-resistant web, i.e., interfacial debonding [

As shown in the following equation, the initial damage criterion for the cohesive zone model of the adhesive layer is determined by the maximum stress criterion:

In the formula,

In the formula,

Material property | Value |
---|---|

Elastic modules/GPa | |

Strength/MPa | |

Fracture energy/(N/mm) |

In this paper, we examine the adhesive layer and nonlinear characteristics of the composite rectangular beam structure. We analyze the progressive fatigue damage process of the composite rectangular beam (including the adhesive layer) using the continuous medium damage mechanics theory and the composite interface cohesive model by writing the UMAT subroutine. The foundation is the static model of the composite rectangular beam with the subroutine interface running platform of the Abaqus software, as shown in

As shown in

When it comes to mesh part, the COH3D6 cells are applied to the adhesive bonding zone and the C3D8R element is used to composite laminate structures such upper and lower flanges and shear resistant webs. In this instance, the adhesive bonding zone is delineated by sweeping the mesh in a direction parallel to the stacking direction of each flange layer. Hexahedral mesh is used for laminate structures, wedge mesh is used for bonding zones, and

According to the four-point bending test standard, a hinged fixed constraint is applied at points A and D to restrict rotation and displacement in directions 1, 2, and 3. At points B and C, a displacement load of 10 mm is applied in the opposite directions of 3, limiting all degrees of freedom of displacement and rotation, except for displacement in the 3-direction [

First, the shear-resistant webs of the composite rectangular beams are laid in a lay-up sequence with a lay-angle of [+45/−45]_{2S} facing up. As illustrated in

Based on

By analyzing the stress distribution of each layer of the upper and lower flange, it was determined that the stress concentration sites of the ±45° layers occurred predominantly at the intersection between the loading contact surface and the web side. Moreover, the maximum stress of the 0° layer occurred frequently at the locations on both sides.

Ply angle/° | Maximum stress on the upper flange/MPa | Maximum stress on the lower flange/MPa |
---|---|---|

Ply-1 (+45°) | 190.7 | 217.3 |

Ply-2 (−45°) | 148.0 | 166.1 |

Ply-3 (0°) | 445.9 | 393.9 |

Ply-4 (+45°) | 175.4 | 132.0 |

Ply-5 (−45°) | 218.5 | 141.4 |

As shown in

1. Both ±45° plies and 0° plies tend to fail under static load at the same displacement loading process point, while 0° plies are subjected to significantly higher stresses than other plies. This is because the loading direction of the four-point bending test is perpendicular to the fiber tensile direction;

2. The maximum stresses on the lower flange Ply-1 plies are greater than those on the other non-0° plies. This is due to the large tensile deformation of this ply under displacement load on the outermost side, whereas the composite material has superior tensile-compression resistance in the axial1 direction. In addition, the stress state of the composite rectangular beam’s shear-resistant web plies is not distributed axially symmetrically with the geometric center. As shown in

The shear-resistant web is subjected to the shear load from the rigid body pusher loading, i.e., the shear load is decomposed into ±45° axial load and transverse load, as shown in

The maximum stresses on the ±45° plies of shear-resistant webs are comparable, as depicted in the figure above.

Comparing the stress distribution of shear-resistant webs of composite rectangular beams with different layup angle settings (

Web ply angle/° | Maximum stress/MPa | Web ply angle/° | Maximum stress/MPa |
---|---|---|---|

Ply-1 (+45°) | 319.3 | Ply-1 (+0°) | 247.9 |

Ply-2 (−45°) | 361.4 | Ply-2 (−0°) | 220.6 |

Ply-3 (+45°) | 302.9 | Ply-3 (+0°) | 220.8 |

Ply-4 (−45°) | 306.5 | Ply-4 (−0°) | 256.2 |

Web ply angle/° | Displacement/cm | Web ply angle/° | Displacement/cm |
---|---|---|---|

Ply-1 (+45°) | 0.455 | Ply-1 (+0°) | 0.510 |

Ply-2 (−45°) | 0.470 | Ply-2 (−0°) | 0.510 |

Ply-3 (+45°) | 0.470 | Ply-3 (+0°) | 0.510 |

Ply-4 (−45°) | 0.460 | Ply-4 (−0°) | 0.510 |

Comparing

The static properties of shear-resistant webs of composite rectangular beams are concluded to be strongly related to the lay-up direction of the composite material. The transverse shear resistance of the ±45° lay-up group is significantly greater than that of the 0° lay-up group. In the longitudinal direction, the tensile and compressive properties of 0° lay-up are superior to those of ±45° lay-up. The arrangement of a small amount of 0° layer in the upper and lower flange layer can effectively improve the web’s axial tensile performance.

The progressive damage analysis of the composite rectangular beam was conducted using the explicit dynamics analysis mode of Abaqus. At the loading points B and C depicted in

As shown in

According to the simulation results, the progressive damage failure of the composite rectangular beam manifests primarily as fiber tensile damage failure.

From

This paper begins with an investigation into the fatigue performance of composite material blade main beam structures. Using a rectangular blade main beam structure as the simulation object, a composite material rectangular beam structure with beam flange, web, and the adhesive layer was designed. Based on the theory of composite material fatigue damage and the technology of finite element simulation, static and dynamic analyses were performed to investigate the progressive damage evolution law of the rectangular composite material beam. The following inferences have been made:

1. The web lay-up angles of composite rectangular beams have a close relationship with their static properties. Under the same loading conditions, it is preferable to adopt a lay-up angle of ±45° for the web structure to effectively increase the static load-carrying capacity of the composite rectangular beam.

2. In the process of progressive damage, the composite rectangular beam has a maximum load capacity of 32.5 kN, and its progressive damage law states that at 65% of the peak load, some of its structural elements will have initial damage, crack sprouting, and stiffness degradation; with the gradual increase of the load, the crack expands rapidly, and the stiffness decreases noticeably; and when the peak load is reached, some structural elements experience complete failure and lose all stiffness. When the peak load is reached, some of the structural elements will fail and lose their load capacity until the composite rectangular beam’s entire structure fails due to fatigue.

3. Under fatigue loading, the composite rectangular beam structure’s lower flange adhesive zone is the structure’s weakest area.

In summary, the probably point of failure under fatigue loading may be accurately depicted by the static numerical model, which is important for future proposals of new structures, the design of the number of layers and lay-up angle of composite laminates, and the improvement of the test equipment. The simplified main beam sub-structure has the benefits of high calculation speed and good convergence, which can significantly reduce the time and cost incurred by thorough experiments, provide the prediction and trend of structural design viability, and provide a rapid and indirect evaluation of the mechanical properties and fatigue damage mechanism of actual blades as a benchmark method.

The authors thank the journal editor and reviewers for their valuable comments, as well as all members and colleagues for their support and dedication to this work.

This work is supported by the Science and Technology Programs of Gansu Province (Grant Nos. 21JR1RA248, 23YFGA0050), the Young Scholars Science Foundation of Lanzhou Jiaotong University (Grant Nos. 2020039, 2020017), the Special Funds for Guiding Local Scientific and Technological Development by the Central Government (Grant No. 22ZY1QA005), the National Natural Science Foundation of China (Grant No. 72361019), and the Gansu Provincial Outstanding Graduate Students Innovation Star Program (Grant No. 2023CXZX-574).

The authors confirm contribution to the paper as follows: study conception and design: Haixia Kou; analysis and interpretation of results: Bowen Yang; draft preparation: Haixia Kou, Xuyao Zhang and Xiaobo Yang; data collection: Bowen Yang and Haibo Zhao. All authors reviewed the results and approved the final version of the manuscript.

The authors confirm that the research methods and resulting data used have been presented in the article.

The authors declare that they have no conflicts of interest to report regarding the present study.