Characterization of a short fiber-reinforced adhesive designed for wind turbine rotor blades

Wind turbine rotor blades are usually made of two half-shells and shear webs that are joined together by structural adhesives. The adhesive joints suffer from longitudinal strains from blade bending combined with shear strains from torsion and shear forces acting on the blade. It is thus important to provide an accurate and reliable characterization of the adhesive as a bulk material to account for cohesive failure. This work focusses on the characterization of a short fiber-reinforced adhesive used in wind turbine rotor blades under uniaxial tension, compression, and shear as well as biaxial tension-compression/shear for both static and fatigue loading. To obtain small scatter in measurement results, a specimen geometry was designed that ensures a clear maximum stress in the test section while minimizing stress concentrations in the transition between the load introduction regions and the test section. The manufacturing process was then designed in such a way that an optimum mixture of resin and hardener was obtained without the inclusion of voids. The latter was verified after manufacturing by means of micro-CT scanning for all specimens. A very extensive test campaign was then carried out in order to quantify stiffness, static strength, fatigue strength, and fatigue-related stiffness degradation. Excerpts of this test campaign are presented in this paper.


Introduction
Wind turbine rotor blades are multiaxially loaded structures subjected to loads from aerodynamics, gravitation, operation, gyroscopy, etc.These external loads excite deflections and vibrations of the blades and the entire turbine.The resulting deformations of the blades comprise mainly bending and (geometrically nonlinear) torsion.In the adhesive, a three-dimensional stress state is thus present [1] that is mainly governed by longitudinal strain (or stress) from blade bending and shear stresses from shear forces and torsion.
Failure of adhesive joints may occur due to loss of adhesion (i.e., failure in the interface between the adhesive and the adherend), loss of cohesion (failure of the adhesive itself), or a combination of both.There is a large variety of failure theories and simulation models available for adhesive joints, see e.g.[2] and the references therein.The strength of adhesive joints is normally characterized as a structural member comprising the adherends and the adhesive focussing on the shear strength of the connection, e.g., by means of lap joint testing [3], DCB testing [4], or subcomponent testing [5,6].
However, adhesive joints in wind turbine rotor blades are designed as thick adhesive layers [7,8,9].It is thus inevitable to characterize the cohesion failure behavior of the respective IOP Publishing doi:10.1088/1757-899X/1293/1/012010 2 adhesives as well, which can be done by bulk material characterization tests.As wind turbine rotor blades are subjected to very high ultimate and fatigue loads, the characterization needs to cover both (quasi-)static and fatigue scenarios and loading situations that are typical for the envisaged application.There are numerous specimen types and testing methods available for the multiaxial material characterization, ranging from plates [10,11] to cruciforms [12,13,14] and tubes [15,16,17], the choice of which depending on the available test machines, the material properties aimed for, and the material under investigation.
In this work, a paste-like, epoxy-based, short glass fiber-reinforced structural adhesive used in wind energy, namely Hexion Epikote TM Resin MGS TM BPR 135G3 in combination with Hexion Epikure TM Curing Agent MGS TM BPH 137G [18], is considered.A tubular specimen was chosen, as tension/compression and torsion applied to such specimen results in tensile, compressive, and shear stresses in the material.However, available specimen designs from literature [16,17] had to be modified and the manufacturing processes had to be optimized in order to obtain reliable test results [19].A very extensive test campaign was carried out including static and fatigue tests and both uni-and biaxial loadings to obtain static strengths and stiffnesses, fatigue strengths, S-N curves, and the fatigue-related stiffness degradation behavior [19,20,21,22].An excerpt of the respective test results is presented in this paper.

Specimen design and manufacturing
Due to the particular loading of an adhesive in a wind turbine rotor blade, it was important to investigate the following stress states in the adhesive: i) uniaxial normal stresses (both in tension and compression), ii) uniaxial shear stresses, and iii) biaxial tension/compression-shear stress combinations.
A tubular specimen was the most suitable choice, as the desired stress states could be introduced with one specimen type and one test machine (walter+bai LFV 100-T2000 [23] with cylindrical specimen grips and independent control in tension/compression and torsion, respectively) for all stress conditions.In this way, consistent material properties could be derived without the need of elaborate considerations on comparability.The specimens additionally needed to provide the following features: • a distinct test section with an expectable failure position; • absence of stress concentrations; • an excellent manufacturing quality.
The first two item points were realized by a thorough finite element-based geometry optimization.The procedure resulted in significantly higher stress ratios between the test section and other positions along the specimen compared to [16,17] and an almost constant and homogeneous stress distribution along the test section.Moreover, very smooth transitions from the clamping sections to the test section were obtained with optimum curvatures avoiding stress concentrations along the specimen.The final geometry with dimensions is depicted in Figure 1.Note that a clamping length of 43 mm and an outer clamping diameter of 30 mm were design boundary conditions from the testing machine.
The third item point was important to obtain reliable test results with clear mean values and minimized scatter, especially in fatigue.The specimen quality was ensured by optimization of the manufacturing processes, which includes the mixture of the resin with the hardener using a planetary centrifugal vacuum mixer [24] and the development of a 3D-printed injection nozzle avoiding the formation of voids.The absence of voids in the test section was guaranteed by micro-CT scanning of all specimens.For more details on the procedure for the design of the test specimen geometry and the steps in optimizing the manufacturing processes the reader is referred to [19].Image from [19] (modified, licensed under CC-BY-4.0).

Static test results
Static uniaxial tests in tension, compression, and torsion were carried out to determine the respective stiffness, yield point, ultimate strength, and strain to failure.In this paper, the major outcome of the static test campaign is presented.More details can be found in [19,20].Strain gauge rosettes were applied to each specimen on opposite sides in circumferential direction in the center of the test section.The load cell of the test machine was calibrated for class 0.5.
The tensile tests have been executed with displacement control at a displacement rate of 1 mm/min.The resulting frequency distribution functions of the ultimate tensile strength for the specimens of this work (both hand-mixed and machine-mixed specimens) are shown in Figure 2 assuming a Gaussian distribution in each case.Test results of other authors [16,17], who used other specimen geometries and hand mixing-based manufacturing processes are added for comparison.
The test results of the own test campaign [19,20]   Frequency distributions of the engineering tensile strength for hand-mixed and machine-mixed specimens and two reference specimens from [16,17] with different geometries and hand-mixing-based manufacturing.The 5% quantile engineering tensile strengths R k are indicated with vertical lines, n is the number of tested specimens.Image from [19] (modified, licensed under CC-BY-4.0).
of the machine-mixed specimens is much higher than that of the hand-mixed specimens.The reason is that in the hand-mixed specimens a high degree of porosity was present, which reduces the strength significantly, while the machine-mixed specimens were virtually porosity-free.It can also be seen that the standard deviation, is much lower for the machine-mixed specimens.The lower tensile strength and higher standard deviation for hand-mixed specimens is supported by the reference test results from [16,17].
The high strength obtained in the tests with the machine-mixed specimens is very close to that reported in the product data sheet [18].It can be concluded that this is the real material property unaffected by defects such as voids.On the contrary, a high porosity content decreases the strength substantially in the hand-mixed specimens, i.e., those specimens suffer from effects of defects.Another reason for the high tensile strength may be a very distinct fiber orientation in longitudinal direction in the machine-mixed specimens, which was identified by high-resolution micro-CT scanning [22].In the hand-mixed specimens, the voids may have affected the fiber orientation.However, this hypothesis was not yet verified by micro-CT scans.In fact, the tests may in turn have influenced the fiber orientation, e.g., due to plastic deformations.Another difference in test results was that the machine-mixed specimens exhibited a distinct elasto-plastic behavior, whereas the hand-mixed specimens were rather brittle in comparison, see [19].
In the uniaxial compression tests, the specimens failed by buckling, although buckling analyses were carried out in the design of the specimen geometry.However, the strong elastoplastic material behavior was not expected, as in literature a brittle behavior was reported [16,17].The higher failure strain and higher stiffness led to unexpected high stresses and consequently to buckling, so that the uniaxial compression strength cannot be evaluated.However, the transition from the elastic region to the plastic region was at lower strains than the onset of buckling.Hence, the uniaxial tension, compression, and shear tests as well as the biaxial tension-compression/shear tests were employed to derive a yield surface in [20].The experimentally derived yield surface was compared to well-known criteria from literature, i.e., the criteria of von Mises [25], von Mises-Schleicher [26], and Drucker-Prager [27], respectively.The results are plotted in Figure 3.
The test results imply an elliptical shape of the yield surface with a clear tension-compression asymmetry.An ellipsis fit hence shows very good agreement with the test results.The von Mises criterion cannot capture the tension-compression asymmetry.The von Mises-Schleicher criterion does capture the tension-compression asymmetry, but overestimates the yield strength in shear.For more details on the stress-strain curves, the extraction of yield stresses, the required elasto-plastic shear stress correction, the yield surface derivation, and for a thorough discussion of the results with respect to tension/compression bimodularity, viscoelasticity, comparison to existing yield criteria, the reader is referred to [20].

Fatigue test results
The fatigue tests were conducted using the same specimen design and testing machine as in the quasi-static tests in [21].To avoid heating of the specimens, the test frequencies at each load level was adjusted accordingly.The adaptation of the test frequency for different load levels also resulted in a reduction of viscoelasticity-related strain-rate effects.The cyclic loading in tension/compression was applied load-controlled, whereas the torsional load had to be applied displacement-controlled.For the reasoning and the implications in testing and postprocessing see [21].The determined cycles to failure enabled the extraction of S-N curves, see Figure 4.
Stiffness degradation measurements inspired by [28] accompanied the fatigue tests.Therein, the cyclic loading was stopped at pre-defined intervals, followed by a quasi-static cycle with very small amplitude in tension and torsion.On account of the small amplitudes, the additional   cycles of the stiffness degradation measurements had a negligible effect on the S-N results.From these intermediate measurements, the Young's and shear moduli could be extracted, enabling the formulation of moduli as a function of the cycle number and load level, see Figure 5.The R-ratio, which is defined by the ratio between the minimum and maximum stress, was R = −1 and R = 0 for tension/compression, and R = −1 for torsion.This paper focusses on the results for R = −1.The test results for R = 0 can be found in [21].S-N curve models according to Basquin [29], Sendeckyj [30], Stüssi [31], and Kohout & Věchet [32] were fitted to the test results for comparison.The test results together with the S-N curve fits are shown in Figure 4 on a double-logarithmic scale.
The test results form a sigmoidal shape.Three run-out specimens were observed (one in the tension/compression tests, two in the torsion tests).Residual strength tests were carried out with the run-out specimens (black triangles in Figure 4).In combination with the stiffness degradation model, these allowed for a prediction of the fatigue life of the run-out specimens.The results indicate the prescence of a fatigue limit, but due to a lack of data in the very high cycle fatigue (VHCF) regime, a final conclusion is not possible yet.[33] for VHCF (approximately half slope of the Basquin model) was proposed earlier [21].It does not predict a fatigue limit, but is also not as conservative as the Basquin model, especially considering the fatigue life prediction of the run-out specimens.The small scatter in test results on each load level is worth mentioning, and is a result of the very thorough specimen design and manufacturing.
The stiffness degradation test results together with model predictions are summarized in Figure 5.The degradation of the Young's modulus is shown in green, that of the shear modulus in blue.Test restults are indicated by black lines.In the top row, the fatigue load was uniaxial tension/compression with R = −1 and in the bottom row the fatigue load was uniaxial torsion with R = −1.In Figure 5, the relative Young's modulus Ẽ and relative shear modulus G (which are both a function of the cycle number n), the normalized cycle number Ñ , and the normalized load level L are defined by the expressions Herein, E(n) is the cycle number-dependent Young's modulus, E 0 is the initial Young's modulus, G(n) is the cycle number-dependent shear modulus, G 0 is the initial shear modulus, N is the number of cycles to failure, σ a is the (normal) stress amplitude (denoted by τ a for torsion), and R m is the static ultimate strength, respectively.The modeling approach consists of a power law given by The parameters A, B, p i , and q i , where i = 1, 2, ..., 4, are fitting parameters.For torsion, Ẽ needs to be replaced by G in Equation (2).
The test results show that the stiffness degradation increases with the number of cycles and is more severe for higher load amplitudes.The scatter is quite small in the primary load direction and is bigger in the secondary load direction.The primary load direction corresponds to the applied fatigue loading, i.e., the axial direction for the tension/compression fatigue test and the torsional direction for the torsion fatigue test, respectively.The magnitude of the stiffness degradation is approximately 5% for the secondary load directions, but is as much as 12.5% and 14.9% in the primary load directions tension/compression and torsion, respectively.In general, the modeling approach reflects the experimental results very well, both qualitatively and quantitatively.
For more details on the test setup, the S-N curve models, the experimental results, an engineering approach to very high cycle fatigue, the stiffness degradation model, a comparison with residual strength tests, and a run-out fatigue life estimation, the reader is referred to [21].Results for multiaxial and non-proportional fatigue tests have recently been published [22].

Conclusion
In this paper, an overview of an extensive testing campaign for the characterization of a pastelike, epoxy-based, short fiber-reinforced structural adhesive used in wind turbine rotor blades was presented.
A tubular specimen was chosen in order to carry out uniaxial tension/compression and shear tests as well as biaxial combinations of these using a testing machine with independent control for tension/compression and torsion.In this way, one specimen design could be used for all tests, resulting in a consistent dataset.The specimen was designed in such a way that a distinct test section with an expectable failure position was present in absence of stress concentrations.The manufacturing processes were optimized so that a homogeneous mixture and virtually defectfree specimens were obtained.Micro-CT scanning was used to guarantee a neglectable porosity content.
Static and fatigue tests have been carried out.The very good specimen quality resulted in extraordinarily low scatter of test results, high strength values that were similar to those reported in the manufacturer's data sheet, and a distinct plastic behavior in the static tests.A clear tension-compression asymmetry was present.The Drucker-Prager criterion was in very good agreement with the experimentally derived yield surface.In uniaxial fatigue, an S-N curve model was obtained that was also in very good agreement with the test results for all load levels.The fatigue-related stiffness degradation was also investigated and a cycle number-and load level-dependent degradation model was derived that was in very good agreement with experimental data.

Figure 1 .
Figure 1.Geometry of the test specimen.All numbers are in mm.Image from [19] (modified, licensed under CC-BY-4.0).

Figure 2 .
Figure 2. Frequency distributions of the engineering tensile strength for hand-mixed and machine-mixed specimens and two reference specimens from[16,17] with different geometries and hand-mixing-based manufacturing.The 5% quantile engineering tensile strengths R k are indicated with vertical lines, n is the number of tested specimens.Image from[19] (modified, licensed under CC-BY-4.0).

7 The
Basquin model fails to represent the test results well.It is non-conservative in the low cycle fatigue (LCF) regime and very conservative in the high cycle fatigue (HCF) regime.The Kohout-Věchet and the Stüssi model fit the experimental results very well.However, the Stüssi model is more conservative in the LCF and the HCF regimes.The Sendeckyj model coincides with the Kohout-Věchet model in the LCF regime and with the Basquin model in the HCF regime and is thus very conservative at low amplitudes.The tangential combination of the Stüssi model and the Haibach model The Drucker-Prager criterion is a very good fit to the test results, which almost coincides with the ellipsis fit.It is thus recommended to use the Drucker-Prager criterion, as it is well established in other engineering applications.
[20]re 3. Yield locus on the basis of uni-and biaxial test results (τ y : shear yield stress, σ y : normal yield stress).The Drucker-Prager criterion and the ellipsis fit are in very good agreement with the test results.Image from[20](licensed under CC-BY-4.0). 5