Materials of large wind turbine blades: recent results in testing and modeling

ABSTRACT

The reliability of rotor blades is the pre-condition for the development and wide use of large wind turbines. In order to accurately predict and improve the wind turbine blade behavior, three main aspects of the reliability and strength of rotor blades were considered: (i) development of methods for the experimental determination of reliable material properties used in the design of wind turbine blades and experimental validation of design models, (ii) development of predictive models for the life prediction, prediction of residual strength and failure probability of the blades and (iii) analysis of the effect of the microstructure of wind turbine blade composites on their strength and ways of microstructural optimization of the materials. By testing reference coupons, the effect of testing parameters (temperature and frequency) on the lifetime of blade composites was investigated, and the input data for advanced design of wind turbine blades were collected. For assessing the residual strength and stiffness of wind turbine blades subjected to irregular cyclic loads, a shell-based finite element numerical methodology was developed, taking into account the non-linear response of plies, and experimentally validated. Two methods of structural reliability estimation of the blade, which take into account the stochastic nature of the anisotropic material properties and loads, were developed on the basis of the response surface method and the Edgeworth expansion technique, respectively. The effects of fiber clustering, misalignments, interface properties and other factors on the strength and lifetime of the wind turbine blade materials were investigated in the micromechanical finite element simulations. The results described in this paper stem from the Rotor Structure and Materials task of the UPWIND project. Copyright © 2011 John Wiley & Sons, Ltd.

1 INTRODUCTION

For larger wind turbines, the potential power yields scales with the square of the rotor diameter, but the blade mass scales to the third power of rotor diameter (square-cube law). With the gravity load induced by the dead weight of the blades, this increase of blade mass can even prevent successful and economical employment of larger wind turbines.[1-3] In order to meet this challenge and allow for the next generation of larger wind turbines, higher demands are placed on materials and structures. This requires more thorough knowledge of materials and structural response, as well as further development of reliability estimation methods. Previous projects have emphasized the necessity for improved and detailed fatigue life modeling for reliable and optimal blade design.[4]

In this paper, the recent results on the structural reliability and mechanical behavior predictions and testing of blade materials and components are reported. In order to make it possible both to predict the wind turbine blade service properties and ultimately to improve the blade materials, three main questions should be answered:

• How are the material mechanical properties required for the advanced design of wind turbine rotor blades consistently collected?
• How is the accuracy in the prediction of the failure and the structural reliability of wind turbine blades on the basis of the material layer properties improved?
• How do the microstructures of blade materials influence their strength, and can the service properties of the materials be improved by modifying the microscale structures?

To solve these problems, advanced experimental methods (reference blade component testing, scanning electron microscopy in situ static and fatigue experiments), theoretical approaches (kinetic strength theory, etc.) and numerical methods (3D finite elements (FEs)) and micromechanical models) were employed. As a result, material testing procedures were established, a progressive damage prediction tool was developed and probabilistic strength analysis of wind turbine blades was carried out. The effects of different microstructural parameters and loading conditions on the strength of the wind blade materials were studied. The detailed state-of-art overview of the materials for wind turbines was given in Brøndsted et al.[1] and the references therein. In this paper, focus is given on the recently developed methods and ideas that give the possibility to answer the questions above.

2 HOW TO COLLECT MATERIAL PROPERTIES FOR BLADE DESIGN

In the process of blade design, various input parameters are required for reliable design. As design tools become more sophisticated, the number of required material characteristics increases. The results from the experimental program described in this part can be used by manufacturers and designers as reference data.

An important new concept in blade design is to use not only data collected from flat, uniaxial coupons, but from realistic structural details. This concept was developed in the subcomponent tasks of the UPWIND project, through testing and modeling of I-beams.

The main aim, however, of the static and fatigue experiments on coupons and subcomponents was to facilitate the development and validation of models described in the following sections. In addition, test methods were developed, and existing methods were compared in terms of numeric value of the results. Effects of temperature and testing frequency on the strength degradation and life time of blade materials were studied.

2.1 Testing methods

A large part of the test program described here, which is reported from the UPWIND program (subtask Rotor Structures and Materials), is based on the use of a reference coupon. This means that based on general consensus among the project partners, a typical laminate representative for the rotor blade industry was chosen as the project reference. Subsequently, a preliminary test program of (slightly) different specimen geometries was conducted to find an optimal combination of planform and tab configuration that leads to acceptable results in all required tests methods.[5] Finally, test methods, notably the frequencies used in the fatigue tests, were fixed to a large extent.

The advantages of this reference specimen lie in the consistency of methods (e.g. performance at different R-values can be compared in a straightforward manner, without the need to account for severe geometry differences). Disadvantages are that in order to obtain the highest values for certain material characteristics (compression and shear), dedicated geometries are still necessary and that the rectangular geometry selected is prone to failure in the tabbed area.

Details on the reference specimen and material and recent results are documented in e.g. Nijssen et al.[6] The reference specimen geometry, fatigue behavior in the form of a constant life diagram (CLD) and fatigue test setup are illustrated in Figure 1.

Figure 1. Reference coupon geometry, CLD and test configuration. The legend refers to the constant life lines, describing number of cycles to failure.

Apart from the reference coupons, scores of other test geometries were used. Mechanical tests were carried out on servohydraulic test frames of various calibers and by using various dedicated load fixtures; results are discussed e.g. in van Leeuwen et al.[7] and briefly in the next section.

2.2 Results of fatigue tests

Approximately 250 static and fatigue tests were performed on the reference specimen at ambient conditions and various R-values to describe the specimen fatigue life behavior in considerable detail (see the CLD in Figure 2). Different fatigue models were fitted to the CA fatigue dataset to evaluate performance of these models statistically (see Figure 2).[8, 9]

Figure 2. Fit of piecewise continuous (dashed) and continuous (solid line) CLD models to constant amplitude (CA) data (dots indicate experimental data).

2.2.1 Temperature and frequency

The effect of temperature and frequency on fatigue life was investigated experimentally on the reference material. Tests were performed at reference and increased frequencies and at low (−40°C), room (approximately 25°C) and high (60°C) temperatures. Ambient and surface temperatures were measured during these tests. For tension fatigue, the test frequency was increased from reference frequencies of 2 and 6 Hz at load levels corresponding to approximately 1000 and 10⁶ cycles, respectively, to 24 Hz for both load levels. This leads to lower lifetimes at ambient temperature, but no detrimental effect of this frequency increase is seen when testing at low temperatures. In both cases, an increase in temperature difference between the surface and the environment was observed in the high-frequency tests, but the temperature rise was, in most cases, less than 10°C, maximum 15°C.

A temperature difference between the specimen surface temperature and the room temperature, which was limited to the above-mentioned 10–15°C, results in significantly deteriorated fatigue performance, both in the tension–tension (see Raijmaekers et al.[10]) and tension–compression fatigue. The observation that this decreased performance did not occur at low temperatures, albeit with similar surface temperature increase, gives rise to the hypothesis of a threshold temperature, potentially related to the glass transition temperature, above which the fatigue performance of the reference laminate decreases significantly. Sufficiently below this threshold, the effect of testing temperature is negligible.

2.2.2 Adhesive testing

In order to determine shear strength properties of an epoxy structural adhesive [Hexion BPR 135 (Hexion, Columbus, OH, USA)] representative for manufacturing composite wind turbine blades, a series of experiments was conducted, partly within the framework of the UPWIND project. The objective of the research included a comparison of shear test methods, viz. bonded tubes in torsion, full adhesive tubes in torsion, V-notched rail shear, Iosipescu and strap joints. Shear strength results of adhesives depend strongly on test methods. Employing a bonded tube in torsion gives the highest average shear strength (>40 MPa), and this geometry allows for investigation of thickness effects and bi-axial loading. Other methods give lower results, but e.g. the V-notched rail shear method yields similar values (approximately 10% lower than the bonded tube) and is less labor intensive, since multiple specimens can be manufactured from a single flat panel, whereas the molding of a single composite tube as the adherent for the tube bonding paste tests requires significantly more effort. A method that allows investigation of thickness effects is the strap joint, but the shear strengths measured with this method were the lowest of all investigated methods.

The bonded tubes were used in an evaluation of the effect of the bondline thickness on the shear strength, where, within the range of bondline thicknesses investigated (0.5 to 10 mm), no significant effect was observed.

Shear strength values obtained for bonding paste resin (double strap joint, bonded tubes, full adhesive tube and adhesive using notched specimens) and fiber-reinforced plastic (FRP; the UPWIND glass/epoxy reference material) are shown in Figure 3.

Figure 3. Summary of shear test results and test setup for bonded tube tests in tension–torsion frame at Knowledge Centre WMC.

2.2.3 Subcomponents

The subcomponent concept developed in the UPWIND project is aimed at bridging the gap between coupon tests and full-scale testing. This is a new approach in wind turbine blade engineering. The main objective of the subcomponent program was to develop a cost-effective test representative of blade structural detail(s). Such a subcomponent can be used for various purposes, such as the evaluation of critical structural details, material tests, modeling and validation, investigating influence of manufacturing methods, testing of repair methods and improvement of full-scale blade tests by prior assessment of critical structural details. To limit the scope of evaluating this concept, this project focuses on the assessment of bondline behavior in a load carrying spar. Two types of prismatic I-beams were manufactured and distributed over various laboratories. Test methods were developed and executed by various partners, who investigate symmetric three-point and four-point bending as well as cantilever beam bending. In parallel, advanced simulations of the static and fatigue beam tests were performed to predict the beam behavior,[11, 12] using as input the material properties, including the adhesive properties, as determined within the previously described testing programs. An example of the comparison of a static test with numerical simulation results is shown in Figure 4. Some results on three-point bending fatigue correlating with the adhesive fatigue are shown in Nijssen et al.[13] and Figure 5. This figure shows the fatigue curves of beams in three-point bending (the red and green lines). These curves are slightly different because of the difference in geometry of the bondline between the beam web and flanges. Since the beam fatigue behavior was expected to depend significantly on the adhesive shear performance, V-notched rail shear tests were performed on flat bonding paste specimens in fatigue. These results are shown as black dots in the figure. Slightly different beams were tested in Sayer et al.[14] and related projects. Ample comparison of measurements taken during static beam testing with numerical results demonstrated the necessity of detailed input data (strengths and stiffnesses of constituent materials). Failure predictions in static tests were made and in some cases could predict strength and failure mode.

Figure 4. FE analysis of beam in symmetric three-point bending.

Figure 5. Normalized S–N diagram of bonding paste (shear) and I-beams (three-point bending); blue arrows refer to load introduction/direction. The black arrows associate the left photo with the bonding paste data and the right photo with the beam data.

3 HOW TO PREDICT THE STRENGTH AND FAILURE OF WIND TURBINE BLADES

In this task, the concepts and methods for exact and reliable life prediction, residual strength and stiffness prediction, as well as estimation of failure probability for the structural reliability assessment of wind turbine rotor blades, are developed.

3.1 Damage tolerant design concept

Nowadays, FRP rotor blades are designed according to regulations based on the very first principles of composite mechanics, in which ply failure of a multilayer element in an FE model is not followed by property degradation, and thus, investigation of post first ply failure load bearing capability is not implemented. Furthermore, material constitutive equations are considered linear, although it is common knowledge that in-plane shear and transverse compressive response of a unidirectional (UD) layer is from moderately to highly non-linear.[16] No advantage is taken this way of damage tolerant features of composite materials, and all design-related decisions refer to ‘safe life’ principles, i.e. no account is taken for progressive damage development. This is due among other reasons to the lack of generally applicable damage assessment schemes and suitable as well as reliable non destructive inspection (NDI) techniques. It also reflects to formulation weaknesses of most commercial FE shell elements, which do not possess possibilities for fatigue life prediction or estimation of residual strength and stiffness. These shortcomings of state-of-the-art numerical tools and existing formulations of composite mechanics result in uncertainty levels that imply high values of partial safety factors, hence rotor blades of increased weight and cost.

Here, reliable methods to assess residual strength, stiffness, load bearing capacity and mechanical response of the rotor blade after a number of operating years are developed on the basis of formulating a shell-based FE numerical methodology suitable for the analysis of irregular cyclic loads. Development of such a tool for predicting the mechanical response of the rotor blade consists of several major tasks: (i) non-linear stress analysis of the multilayer structure, (ii) failure prediction of the building layer under static or cyclic loads by giving the option of using a number of different new generation failure criteria not available in commercial codes, (iii) modeling of both progressive property degradation due to fatigue and sudden property change due to failure and finally, (iv) formulation of an ‘overall structural failure’ condition, resulting in the prediction of remaining life, residual strength and stiffness.

The concept of modeling damage development in multilayer laminates under quasi-static loads has been discussed theoretically to some extent (see Antoniou et al.[15-17] for recent account). However, very limited research results are available from modeling damage accumulation as a result of cycling. One of the reasons for the lack of work in this field, besides the considerable inherent difficulties associated with the multitude of failure mechanisms and their interaction, is the huge effort required to create comprehensive material property databases with test results from static, cyclic and residual strength experiments under multi-axial loading conditions. The simulation procedure that was implemented in FE shell code took advantage of the OPTIDAT database.[4]

A continuum damage mechanics method was implemented in a ply-to-laminate life prediction scheme for composite laminates under cyclic CA or variable amplitude (VA) loading. According to theoretical foundations of distributed damage,[18-21] instead of considering the geometric description of a type of defect induced by local failure, a set of appropriate stiffness degradation rules is applied, resulting in a modified stiffness tensor, i.e. an equivalent homogeneous continuum description, such that either the resulting strain field or strain energy density under the same load is similar to that of the damaged medium. Thus, instead of adapting the mesh of an FE model and introducing new boundaries for progressing cracks or other defect types, the stiffness tensors at elements where damage onset was predicted are suitably modified.

This effective medium description also requires, besides sudden stiffness degradation due to failure onset, progressive strength and stiffness degradation expressed as a function of load cycles, n. Hence, residual strength and stiffness after cycling become of importance for this approach of progressive damage mechanics and certainly require a great experimental effort, besides efficient modeling, to cover the various loading conditions, e.g. tension–tension (T-T), tension–compression (T-C), etc., at various stress ratio values and material principal directions.

To assess conditions for incipient failure in a specific mode, compatible with certain defect type and respective stiffness degradation strategy, appropriate failure criteria considering separately the various failure modes[22-25] were implemented in the numerical procedure.

The material model consists also of the detailed description of fatigue strength in each principal material direction and in-plane shear, for the basic building ply, for several R values to ease the implementation of CLD formulations.

For accuracy, a detailed load step-by-step simulation of each cycle is foreseen in the realization of the algorithm, although this could be extremely time-consuming, especially when the routine is implemented in FE formulations. Alternatively, calculations are performed in steps for a complete cycle and then after a block, Δn, of cycles again, a detailed complete cycle and so forth. The size of cycle jump is defined by the user.

Non-linear response of the UD ply especially under in-plane shear and normal loading transversely to the fibers is also taken into account, introducing appropriate models derived by fitting experimental data. In the numerical analysis, non-linearity is modeled by implementing an incremental stress–strain constitutive law.[16]

An extensive comparison of life prediction numerical results with experimental data from CA or VA tensile cyclic testing of a [±45]_S plate and loading at various R-ratios of a multidirectional (MD) Glass/Epoxy laminate [(±45/0)₄/±45]_T has been performed. As an example, in Figure 6, the numerically predicted S–N curve for the MD laminate under CA at R = 0.1 along with experimental data is presented, whereas in Figure 7, damage patterns in the outer three layers after 700,000 cycles are shown. Coupons cut from the MD plate were loaded either on-axis, where fiber dominated failure modes were observed, or off-axis at various directions where matrix damage had also significant contribution in the observed failure. Predictions of tensile residual strength after cyclic loading of [±45]_S coupons were also compared with test results (see Figure 8). In all cases, the agreement of numerical predictions and test results was very good. More details on the mechanics formulations, numerical procedures and results can be found in Philippidis and Eliopoulos.[26]

Figure 6. Comparison of the fatigue damage simulator predictions and experimental data; MD Gl/Ep under R ;= 0.1.

Figure 7. Damage modes according to Puck failure criteria of a [(±45/0)₄/±45] Gl/Ep MD coupon, at a stress level of σ_max = 193 (MPa), R = 0.1.

Figure 8. Fatigue damage simulator predictions versus residual strength test data after R ;= 0.1 cyclic loading; [±45]_S Gl/Ep.

3.2 Probabilistic modeling of wind turbine blades

Quantification and assessment of the structural reliability level of the wind turbine blade with respect to its strength, stiffness and elastic stability should be performed in probabilistic terms by relying both on load uncertainty quantification as well as on material, because of the use of composite materials, exhibiting great inherent variability of mechanical properties. Substantial efforts have been directed toward load uncertainty investigation,[27-32] with results already incorporated in the relevant design standard IEC 61400-1.[33]

The structural reliability analysis of the wind turbine blade was addressed up to now (e.g. Braam,[34] Ronold and Larsen[35] and Veldkamp[36]), limiting the analysis to the failure of the root section of the blade, taking into account only the developed stress in the axial direction due to bending in the flap direction and the respective strength of the laminate, disregarding the multi-axial stress state of the anisotropic composite material.

For permitting the estimation of failure probability on the level where the material properties are certified, i.e. the layer, two independent methodologies were developed in parallel within the UPWIND project; the first[37] enables the connection with currently employed aero-elastic wind turbine design codes and is based on the Edgeworth expansion methodology (EDW), whereas the second[38] employs the response surface method (RSM) with direct Monte Carlo (MC) simulation and is combined with an FE shell model. In both methodologies, the stochastic nature of the anisotropic material properties, as well as the loads, is considered for the reliability estimation of the layer and thereupon extended to the laminate, the blade section and the overall blade.

3.2.1 Stochastic variables and failure functions

Common to both developed methodologies is that the probability estimations are developed by performing a ply-by-ply analysis using the quadratic version of the failure tensor polynomial, Tsai–Hahn.[39] Since the numerical models of the rotor blade consist of a great number of layered elements, each with a stacking sequence composed of numerous plies, it is considered that each element forms a series system of layers, implying a first ply failure criterion for the element.[37] It is further assumed that the failure modes of the different layers are positively correlated. The same convention applies for the failure probability of the rotor blade, by considering it as a series system of elements with the failure modes of the elements presenting positive correlation. Thus, the maximum probability of failure of all the layers in all the elements defines the probability of failure of the rotor blade.

For the statistical characterization of the variability of the material parameters, experimental databases are used, covering information not only for the strength properties of the orthotropic media but also for the relevant elastic properties, such as that in Philippidis et al.[40]

Statistical analysis is also necessary to model the time series for the stress resultants at various sections of the blade derived from aero-elastic simulations by the extreme maximum value distributions.[38] IEC 61400-1[33] describes the procedure for the estimation of the extreme distribution using extrapolation.

3.2.2 PRE-THIN, THIN AND POST-THIN

The tool has been divided into three modules (PRE-THIN, THIN and POST-THIN) in order to facilitate the use of the available aero-elastic codes, accurately represent the mechanical properties of the full 3D blade in the 1D beam element used in aero-elastic codes and enable the performance of the necessary detailed strength assessment after stress resultants at each section have been calculated. PRE-THIN uses material layer properties and information on the lamination sequences for the calculation of the effective properties of each laminate. The basic processor, THIN, is based on thin wall beam theory, taking into account the inhomogeneity and elastic anisotropy of the cross-sectional elements, described in detail in Philippidis et al.[41] for the deterministic case and Lekou and Philippidis[37] for the probabilistic. THIN estimates for each section of the blade all sectional properties necessary for input to the aero-elastic codes, e.g. the bending and torsional stiffness, in statistical terms. The aero-elastic simulation codes provide (for each load case) the internal resultant axial and shear forces and bending and torsional moments for each section of the blade. Using this as an input, the normal stress resultants, as well as the shear flows due to torsion and shear forces, are calculated for each ‘homogenized’ element on the multi-cell section within THIN,[41] including hygrothermal effects. These normal and shear stress resultants of each node on every element of the section are provided as input to the POST-THIN module, where the stress field and reliability of each layer in the lamination sequence is calculated.

For the probabilistic analysis, the EDW, as described for application with composite material laminates under multi-axial loading in Lekou and Philippidis,[42, 43] was verified through crude MC simulations with indicative results presented in Lekou and Philippidis.[37] An example output of the developed tool is shown in Figure 9, where the results of the EDW methodology are compared with MC simulations for the case when only the material layer properties (strength and elasticity) are assumed to be stochastic (denoted as EDW_mat and MC_mat, respectively) and for the case where also the variability of the loading is taken into account (marked EDW_mat&load and MC_mat&load, respectively). It should be noted that the results presented are derived for a load case having an average value especially designed to cover both high and low probabilities of failure around the section, so as to check the validity of the method throughout the design space. Moreover, the load variance assumed for the present stochastic analysis is considered to be high, making the presented case a conservative one. Taking into account the fact that the computational cost of the EDW methodology is comparable to that of a pure deterministic analysis, the applicability of the method within the design process, requiring a large number of loops and load cases before reaching the final structure, is evident. Regarding the sectional properties estimation, results of the EDW method are within 1% for both the average values and the standard deviations outcome of the MC simulation.

Figure 9. Indicative output of the probability of failure using PRE-THIN, THIN and POST-THIN(left) and element numbering on the blade section (right).

3.2.3 Response Surface Method

The RSM was used in Bacharoudis and Philippidis[38] to estimate the reliability of the wind turbine blade using a 3D detailed FE model. To this end, instead of repeatedly solving the FE model, following an MC simulation approach, approximation (regression) models were formed through the use of RSM. Stress analysis is performed with a refined shell element formulation of a commercial FE code, ANSYS (ANSYS, Inc., Canonsburg, PA). Because of computational complexity and code limitations, only part of the reliability computation, specifically part of the ‘Design of Experiment’, is accomplished with the commercial code, whereas the remaining computational tasks were developed and implemented in external user routines in FORTRAN. Special care was taken in defining the stochastic character of the concentrated loads applied on a 3D shell element FE model starting from load series of sectional stress resultants from aero-elastic beam simulations.

The RSM involves central composite design composed of three different designs for the design of experiment (DoE): second order polynomial models with or without cross terms, regression analysis and testing of model accuracy. DoE provides the appropriate sample points that are used for a limited number of FE simulation experiments (e.g. for seven input variables, 79 FE analyses are required). These results are then fed into a regression analysis to estimate the unknown coefficients of the approximation models. Contrary to the common application of RSM, instead of approximating the limit state function, in this case, the RSM is used for the derivation of approximate models for the in-plane strains developed at any ply of any element in the blade, thus avoiding time-consuming FE solution repetitions.

The validity of the method, which could be used in the future as a design tool, was proved through comparison of failure probability predictions with typical MC simulation results, focusing in the limit condition in the design space. In Figure 10, a typical output representation of the application is shown.

Figure 10. Indicative output of the probability of failure using the RSM.[38]

Summarizing the results presented in Section 3.2, it is emphasized that both developed methods enable the reliability estimation of the wind turbine blade on the layer level in every location of the blade taking into account the variability of the anisotropic material properties, as well as that of the multi-axial loading acting on the blade. The computational cost of the EDW methodology developed having as output the probability of failure on the layer level is comparable to that of deterministic analysis methods. Although the statistical results for the elasticity sectional properties and the layer stresses provided by the EDW methodology are in accordance with MC simulation results,[37] if the variance of the stochastic variables is quite high, the EDW underestimates the reliability of the structure. The EDW method as applied enables direct link with aeroelastic computational tools used for wind turbine simulations. The work conducted on the RSM methodology presented showed that use of 3D FE models, with an accurate representation of the structure, using load data as delivered by aero-elastic computational tools for wind turbines involves a number of assumptions, introducing uncertainties in the final model estimations. Nevertheless, the RSM method results in probability of failure estimates in good agreement with MC simulation outputs. Further work on direct comparison of the two stochastic analysis methodologies developed in the frame of UPWIND project is under way.

4 HOW DO THE MICROSTRUCTURES OF WIND TURBINE BLADE MATERIALS INFLUENCE THEIR STRENGTH?

The strength and reliability of wind turbine blades depend on the properties, mechanical behavior and strengths of the material components (glass or carbon fibers and polymer matrix) and the interaction between them under loading. In this task, the micromechanisms of strength, degradation and failure of the rotor blade materials are studied experimentally, theoretically and numerically. The answers on the following questions were sought: Which physical mechanisms control the strength and failure of the wind turbine blade materials? Which parameters of microstructures of the materials influence the strength of wind turbine blade materials? How can the service properties of the materials be improved by modifying the microscale structures? The sensitivity of the strength of the composites toward different microstructure parameters and loading conditions has been studied with respect to static and cyclic strengths, and the most significant ones are identified.

4.1 Effect of microstructural parameters on the strength and lifetime of composites

4.1.1 Effect of fiber orientation on damage mechanisms under static and cyclic loading: scanning electron microscopy in situ experiments

In order to clarify the effect of the loading direction on the wind blade strength, scanning electron microscopy in situ experimental investigations of damage growth in glass FRPs under three-point bending, tensile, compressive and (tension–tension) cyclic loadings under different angles between the loading and fibers have been carried out. The detailed conditions of the experiments are described elsewhere.[44] It was observed in the three-point bending experiments that the peak strengths, elastic strengths and elastic modulus of the composites decrease when increasing the angles between load vector and fibers almost linearly. Under compression, the peak strengths, elastic strengths and elastic modulus of the composites decrease when increasing the angles of fibers at first and slightly increase thereafter. Under tension–tension cyclic loading, it was observed that the cracks develop most often along the interface between main fibers and matrix.[44]

4.1.2 Effect of variability of fiber strengths, viscosity of matrix and competition of damage modes: 3D micromechanical FE analysis

In order to study the effect of microscale parameters of wind turbine blade composites on their strength, a special software for the automatic generation of 3D computational micromechanical models of the composites was developed[45] and used in the numerical experiments. Figure 11 shows the micrograph of a composite and the 3D FE model as well as the crack growth scheme. The effects of the statistical variability of fiber strengths, viscosity of the polymer matrix and the interaction between the damage processes in matrix, fibers and interface are investigated numerically, by testing different multifiber unit cell models of the composites.[46, 47] It was demonstrated in the simulations that fibers with constant strengths ensure the higher strength of a composite at the pre-critical load, whereas the fibers with randomly distributed strengths lead to the higher strength of the composite at post-critical loads. In the case of randomly distributed fiber strengths, the damage growth in fibers seems to be almost independent from the crack length in matrix, whereas the influence of matrix cracks on the beginning of fiber cracking is clearly seen for the case of the constant fiber strength. Competition between the matrix cracking and interface debonding was observed in the simulations: in the areas with intensive interface cracking, both fiber fracture and matrix cracking are delayed. Reversely, in the area, where a long matrix crack is formed, the fiber cracking does not lead to the interface damage.[45, 48]

Figure 11. Micrograph of the composite, 3D FE micromechanical model, crack growth between the fibers and fiber bridging over the matrix crack.[45, 46]

4.1.3 Fiber misalignment and clustering and their effect on the compressive and fatigue strength of rotor blade materials

In compression, the dominating failure mode of carbon fiber reinforced polymer composites is a so-called kink band formation. In order to study the compressive strength of composites, statistical computational model was developed on the basis of the MC method and the Budiansky–Fleck fiber kinking condition[49] (see the schema of the multifiber unit cell with random misalignments in Figure 12, left). The effects of fiber misalignment variability, fiber clustering, load sharing rules on the damage in composite are studied numerically. It is demonstrated that the clustering of fibers has a negative effect on the damage resistance of a composite (Figure 12, right). Further, the static compressive loading model is generalized for the case of cyclic compressive loading, with and without microdegradation of the matrix and with and without random variations of loading.[49] It was observed that the random variations of loading shorten the lifetime of the composite: the larger the variability of applied load, the shorter the lifetime. The model was further generalized to include the irregular fiber waviness and the interface defects. Considering the cases of small and large interface defects with different density, it was observed that the small interface microcracks do not lead to the sufficient reduction of compressive strength even at unrealistically high microcrack density. In contrast, large interface defects have a strong effect on the compressive strength of the composite.

Figure 12. Left: Schema of statistical models of fibers with randomly distributed misalignments. Right: Comparison of damage (density of kinked fibers, D) for random and clustered fiber distributions (top view).[49]

4.1.3.1 Mesoscale ply stiffness degradation model

In order to provide the link between microscale structure damage analysis and macroscale wind turbine blade reliability studies and design, a ply level stiffness degradation model has been developed.[50] A theoretical solution linking the stiffness of the damaged UD composite with average opening displacement of fiber breaks and its sliding displacement was obtained. Using this solution, it was demonstrated that sliding displacement of a crack in a cracked layer of a laminate does not affect the longitudinal stiffness, and the effect of the crack opening displacement of fiber breaks on the transverse and shear modulus is negligible as well. The significant effect of the debond length on the stiffness reduction was observed.

4.2 Combined microstructure and loading conditions effect: computational analysis

4.2.1 Moisture-induced degradation of composites

Moisture-induced interface damage evolution and debonding for different fiber realizations are studied numerically using the FE method and micromechanical modeling.[51] The interplay of the two time scales (diffusion time scale and the time scale of the applied load) is considered by applying a strain rate comparable to the moisture diffusion rate. In the simulations, it was observed that moisture-induced degradation of the interfacial properties brought in substantial increase in the interface damage. It was observed that the unit cell model of composite subjected to loading after being saturated with moisture has shown a decrease in the nominal stress achieved and the initial tangent modulus that is dependent on the fiber distribution in the composite (Figure 13).

Figure 13. Schema of the model of the moisture-induced degradation and the snapshots of the of moisture diffusion profiles (from Abhilash et al.[51]).

4.2.2 Loading frequency effect on fatigue lifetime

A new approach to the modeling of material degradation under cyclic loading has been developed on the basis of the kinetic theory of strength.[52] In the model, it was assumed that the stress (and not stress increase) is responsible for the damage growth in the materials under cyclic loading (what is characteristic for the viscous materials). With the use of the kinetic theory, it has been shown that the damage growth per cycle decreases (and the lifetime decreases) when increasing the loading frequency under such conditions. If, however, the damage is caused by stress increase (rate dependent damage), the inverse effect will be observed: in this case, the lifetime should increase when increasing the loading frequency.

Summarizing the research described in this section, we can state that the strength of fiber/matrix interface, fiber misalignment and variability of fiber properties, as well as clustering of fibers, are important parameters influencing the strength of the blade materials. Controlling these parameters, one can improve the strength and lifetime of blade materials.

5 CONCLUSIONS

The work performed regarded material and modeling related issues of the wind turbine blade, covering experimental and theoretical (numerical) investigations from the material microscale to the overall behavior of the structure. It should be noted that the approaches and solutions developed in this work are also applicable to other composite structures.

A comprehensive program of experimental testing of different composites for wind turbine blades has been realized, which includes the investigations of loading, temperature, frequency and orientation effect on the strength and lifetime of composites including statistical analysis of CLD for the unidirectional glass/epoxy reference laminate.

In the collection of experimental data, the philosophy of using a ‘reference specimen’ was used to enable the construction of a consistent database, containing data that can be used e.g. in assessment of fatigue models at various loading types. To obtain the best possible material characteristics, however, it is necessary to perform dedicated tests on optimal specimen geometries.

The temperature and frequency investigation led to the hypothesis that there exists a threshold temperature above which the fatigue performance of the UPWIND reference laminate decreases significantly. The value of this threshold temperature and a potential relation to e.g. the glass transition temperature is yet to be determined.

Shear strength of adhesives, which is required for the detailed analysis of the wind turbine blade, depends strongly on test methods. This implies that some test methods might be more sensitive to multi-axial stress states, reducing their apparent shear strength values. Full-field strain measurement techniques are recommended to further quantify this. Employing a bonded tube in torsion gives the highest average shear strength, and this geometry allows for investigation of multi-axial and thickness effects. Other methods give lower results, but e.g. the V-notched rail shear method yields similar values (approximately 10% lower than the tubes) and is less labor intensive.

An important new concept in blade design is to use data collected not only from flat, uni-axial coupons but from realistic structural details. This concept was developed in the subcomponent tasks of the UPWIND project, through testing and modeling of I-beams.

The development of the subcomponent concept from the UPWIND project shows promising results in terms of test improvement including measurement techniques and validation of advanced structural models. Ample comparison of measurements taken during static beam testing with numerical results demonstrated the necessity of detailed input data (strengths and stiffnesses of constituent materials). Failure predictions in static tests were made and in some cases could predict strength and failure mode.

An anisotropic non-linear constitutive model implementing progressive damage concepts to predict the residual strength/stiffness and life of composite laminates subjected to static or cyclic multi-axial loading was formulated. In-plane mechanical properties of the material were fully characterized at the ply level whereas static or fatigue strength of any MD stacking sequence was predicted. The computational implementation of the theoretical model in an FE thick-shell formulation routine, simulating fatigue damage progression in a composite laminate by means of a ply-to-laminate approach, was achieved as well. The in-plane residual strength of the UD layer was used as fatigue damage metric. Strength and stiffness degradation was modeled using simple and cost-effective schemes, whereas the failure criteria of Puck along with post failure behavior of the material were implemented. The model was set up for a Glass/Epoxy material typical of the wind turbine rotor blade industry and has been verified through a series of CA and VA fatigue tests on different lay-ups, simulating a variety of plane stress combinations and failure modes. Including progressive damage modeling in blade design procedures could enhance the exploitation of material potential and increase confidence in structural design, especially with respect to remaining strength and stiffness of a rotor blade during its operational life.

Two methodologies for the structural reliability assessment of the wind turbine blade were developed within the UPWIND project, where the probability of failure is estimated on the layer level, taking into consideration the variability of applied loads, in addition to the variability of the material strength and elasticity properties. One,[37] based on the Edgeworth expansion method, allows for direct connection with currently employed aero-elastic wind turbine design codes, while being based on thin wall beam theory, taking into account the inhomogeneity and elastic anisotropy of the cross-sectional elements sectional analysis. The other,[38] employing the RSM, is combined with an FE shell model, more accurately representing the blade structure. Although each method presents its own limitations, extensively discussed within Lekou and Philippidis[37] and Bacharoudis and Philippidis,[38] respectively, the advantages attained by enabling the structural reliability evaluation of the wind turbine blade on the layer level at an early stage in the design process are apparent.

In the computational studies of the effects of microstructures of rotor blade materials on their strength and damage resistance, it was observed that a weaker fiber/matrix interface prevents the development of matrix cracks in the composites. Further, replacement of fiber reinforcements by clusters or bundles of thinner fibers can ensure higher strength of the composite. The effect of the loading frequency on the lifetime of materials depends strongly on the damage mechanisms: whether it is rate dependent or creep-related damage. Generally, the microscale analysis and microstructure optimization represent an important source of the optimization of the wind blade materials.

Summarizing the research and results described above, one can state that new approaches and methodologies of testing and assessing wind turbine blade materials were developed, the prediction of lifetime, residual strength and structural reliability of rotor blades were enabled and improved and the effects of material properties and loading conditions on the strength and lifetime of blade materials were analysed.

ACKNOWLEDGEMENTS

Research presented was partly funded by the European Commission within the 6th Framework Programme, under research project ‘Integrated Wind Turbine Design (UPWIND)’, contract number SES6-019945.