Fatigue S-N curve approach for impact loading of hyper- and visco-elastic leading edge protection systems of wind turbine blades

Computational evaluation of leading edge erosion remains challenging due to the high-strain rate loading conditions caused by impact of the wind turbine blade leading edge with rain droplets and other environmental particles. Here, a methodology is proposed for obtaining an S-N curve which can be used for impact fatigue evaluation of hyper- and viscoelastic leading edge protection systems for wind turbine blades, in the relevant strain rate domain. Two material systems (hard and soft polyurethane (PU)) are characterised experimentally by dynamic mechanical analysis (DMA) and static tensile tests. Time-temperature superposition is applied to the raw DMA data in order to obtain the material’s mastercurve, describing its visco-elastic behaviour in an expanded strain rate domain. The Yeoh (hyperelastic) and prony series (vis-coelastic) material model parameters are calibrated and form the input for a 2D-axisymmetric finite element model, in which Single Point Impact Fatigue Test (SPIFT) testing conditions are simulated. The stress field experienced by the coating during SPIFT testing is obtained and combined with the experimental measurements, allowing the determination of the material systems S-N curve, in the relevant strain rate domain. Results for a hard and soft PU coating system are compared with rain erosion test (RET) data. The RET data shows higher lifetime for the hard PU systems, a tendency that can be predicted when comparing the S-N curve for the hard and soft PU system. This methodology can be utilised in computational lifetime evaluation of leading edge coating systems. Furthermore, the methodology has the potential to partly alleviate the need of RET in the development and comparison of next-generation leading edge protection systems.


Introduction
Leading edge erosion (LEE) constitutes the degradation of a wind turbine blade's leading edge due to impact with environmental particles.Causing AEP losses of up to 5% and leading to expensive maintenance campaigns, LEE is one of the biggest challenges in the wind industry [1].This is further emphasised by the tendency to larger and more powerful turbines [2], increasing the blade length, potentially leading to higher tip-speeds.This means more erosion resistant and durable leading edge protection systems will be required in the future.
Different solutions have been proposed such as erosion shield, tapes and protective coatings.Of these, elastomeric coating systems are the most common practise in industry today [3,4].The 1293 (2023) 012021 IOP Publishing doi:10.1088/1757-899X/1293/1/012021 2 mechanical properties of these materials show dependency on strain rate and should therefore be evaluated in the relevant strain rate domain.Different studies have been performed in which the lifetime of such systems has been predicted [5,6,7].However, only limited studies exist on the evaluation of impact fatigue performance in the relevant strain rate domain.
Here, a methodology is proposed to obtain an S-N curve, describing the materials fatigue properties in the relevant strain rate domain.Two polyurethane (PU) systems, a soft and a hard system, are characterised based on dynamic mechanical analysis (DMA) and static tensile tests.Both systems are experimentally evaluated using the single point impact fatigue test (SPIFT).The experimental results are combined with a numerical evaluation of the SPIFT conditions [8] in order to obtain the material's stress based damage criteria in the form of a S-N curve.The relative material's performance is validated by comparison with the performance in rain erosion whirling arm test conditions.

Material Characterisation
Two PU systems are investigated for this study.They are distinguished by their respective hardness with one system relatively soft and one relatively hard to the touch.Furthermore, the nitrile rubber used as the projectile material in SPIFT experimental testing is discussed.The material systems are characterised by Yeoh model (hyperelastic) and prony series (viscoelastic), calibrated based on experimental results which are described below.

Materials
The basic material properties of both PU systems are displayed in Table 1.Furthermore, the properties of the projectile material used in SPIFT (nitrile rubber) are shown.The Poisson's ratio at high strain rate is taken from [8].The density of the systems are based on measurements according to Archimedes principle [9].

Tensile test
Tensile tests for the soft and hard PU were carried out in accordance to ISO 527-2 (specimen 1A) [10] at test speeds corresponding to a strain rate of ε = 10 −4 /s.The test results are visualised in Figure 1 and serve as one of the inputs for the Yeoh hyperelastic material model calibration.

Dynamic Mechanical Analysis (DMA)
DMA testing was carried out in order to obtain the material systems visco-elastic properties, expressed by the storage (G') and loss (G") shear modulus.Furthermore, the loss factor (Tanδ) is determined according to Equation 1.
A constant amplitude, cyclic shear loading frequency sweep ([10 −2 ,10 3 ] Hz) was performed at constant, discrete temperature levels ranging from -70 • C to +140 • C.These frequency sweeps are post processed by utilising the time-temperature superposition (TTS) principle.This allows  the construction of the material's mastercurves describing the visco-elastic properties over an increased ([10 −5 , 10 5 ] Hz) frequency range, for a given reference temperature.For this purpose, a python based post-processing script was developed which calculates horizontal shift factors based on the overlapping range of the storage modulus data of adjacent temperature level's frequency sweeps.For adjacent frequency sweeps, the shift factor is determined according to Equation 2. Here, a T represents the shift factor of the frequency sweep for temperate T i , while ω T i+1 and ω T i represent the frequency at which equal storage modulus is found for respective temperature levels T i+1 and T i .
Figure 2 visualises the working mechanism of this tool as well as illustrates the increase in frequency range when comparing the raw DMA data with the mastercurve.Figure (a) shows the raw DMA data for the soft PU system, as well as its corresponding mastercurve, while Figure (b) visualises the horizontal shift factors applied to the respective temperature levels frequency sweeps.In the extreme temperature ranges, the material's behave increasingly unpredictable, resulting in a large scatter in the data.This data is disregarded from the analysis and are not included in the mastercurve.

Material model calibration
The software MCalibration by PolymerFEM [11] is used to calibrate the Yeoh-Prony hyperviscoelastic material models.The calibration is carried out based on the storage and loss modulus mastercurves and the static tensile test data.The software utilises the tensile data at the slow strain rate and the mapped strain amplitudes of the DMA data covering a larger strain range to calibrate the hyperelastic material model.The viscoelastic part of the material

Methodology
Here the methodology for determination of the materials impact fatigue S-N curve is discussed.
The experimental evaluation of the PU systems is elaborated upon in subsection 3.1, while subsection 3.2 discusses the numerical evaluation of the testing conditions.Both results are combined, allowing for the construction of the material systems impact fatigue S-N curve as discussed in subsection 3.3

SPIFT: V-N curve
The SPIFT is a electro-pneumatic projectile firing device as described in [12] [13].The main goal of testing with the SPIFT is to establish V-N curves (Velocity -Number of impacts to failure).As can be seen on Figure 3 the SPIFT allows for a wide array of instrumentation i.e. high-speed, optical and thermal cameras.In order to generate V-N curves, a suitable impact rate must be chosen.This is done using the thermal imaging system (Optris Pi 640 recording 120 Hz with a 0.1 °C temperature resolution) to empirically determine an impact interval that allows for the dissipation of the thermal energy imparted by each impact [13] at a given impact speed.The impact velocity (V impact ) is set by adjusting the air pressure via the regulator and the Optical speed trap is used to measure the mean impact velocity.The impact rate and desired maximum number of impacts is then input into the controller and the test is started.During the test the surface of the sample is monitored for damage using the inline microscope camera (M7915MZTL long working distance USB microscope from Dino-lite) with 3.1 Megapixel (2048 × 1534 @10 Hz ).A continuous video of the sample is made and the test is terminated once a significant damage is observed on the sample.After the conclusion of the test, the recorded video is analysed, and the time to a given failure state as defined in [13] is measured.The number of impacts is calculated in Equation 3, with N 0 as the number of impacts until failure, t as the testing time and R i as the impact rate.
After the V-N data is recorded the data is fitted following ASTM E739 − 10[14], using N 0 as the dependent parameter

SPIFT: FE model evaluation
SPIFT testing conditions are modelled in an Abaqus/Explicit axisymmetric finite element model, from which the stress states experienced during SPIFT testing are obtained.The model is schematically shown in Figure 4 (a) and described in [8].The calibrated material models describing the hard and soft PU systems are used as input and the model is evaluated for V impact ϵ [50, 190] m/s with a step size of 10 m/s.The impact material experience a stress wave moving away from the centre of impact.Figure 4 (b) visualises such a stress state in terms of the Von Mises stress criteria.The maximum stress amplitude experienced by one of the nodes is extracted and used for subsequent analysis.The stress criteria considered is the signed von mises (SVM) stress criteria.

V-N to S-N curve
The experimental SPIFT results provide a V-N (Velocity vs. Number of impacts) relation for the coating system, while the numerical evaluation provides a S-V (Stress amplitude -Velocity) relation.Both results are combined and the following relation is fitted to the newly established S-N relation: Here, S represents the maximum stress amplitude experienced by the coating system following impact, N the number of impacts until failure.A and B are fitted to the relation and describe the coating systems stress based damage criteria.

Results and discussion
The material characterisation and corresponding model parameters used for subsequent analysis are discussed in subsection 4.1.The S-N curve established for the hard and soft PU system is discussed and validated in subsection 4.2.A discussion on the methodologies and limitation of this work is included in subsection 4.3.

Material Characterisation
The master curves for the storage and loss modulus as well as Tanδ for both material systems is visualised in Figure 5.These form the basis for the material model calibration.The resulting Yeoh-prony model parameters are displayed in Appendix A, Table 2.The relevant strain rates for rain erosion ( (>10 4 /s) [8] can be linked to the high frequency domain (>10 4 Hz) of the mastercurves.Here, the soft PU system shows a higher degree of energy dissipation, as compared to the hard system.

S-N curve
Figure 6 visualises the SPIFT experimental results in the form of the materials VN curve (a) and maximum stress amplitude, expressed by the SVM stress criteria (b).The soft PU system shows higher lifetime in SPIFT when compared to the hard system.Furthermore, it can be seen that the soft system experiences lower stress amplitude over the analysed impact velocities, indicating a higher degree of energy dissipation during the test.This can be recognised in the respecive materials master curves.Combining these results leads to the materials S-N curve, visualised in Figure 7, (a).It can be seen under similar loading conditions, the soft PU system shows lower lifetime then the hard PU system.This behaviour is opposite to the results found in the experimental SPIFT analysis, confirming the necessity to consider the stress states in the material.To get an insight into the relative material performance in terms of impact fatigue resistance, Figure 7, (b) shows RET experimental data for both material systems.It can be seen that the relative performance of both systems corresponds to the relative position of respective material systems S-N curve.

Discussion and limitations
The S-N curves for the material systems can be used for computational lifetime evaluation of impact fatigue problems.Direct validation with RET data is not valid since the stress states during impact fatigue loading, as experienced in RET, are dependent on the visco-elastic material properties.Furthermore, the same equivalent stress criteria (SVM) should be used when expressing the loading history.Alternatives such as the Von Mises, Tesca or Principle stress (maximum, minimum, absolute maximum) could be used.Here the choice for SVM provides a simplistic approach while considering the directionallity of the loading conditions.Due to the nature of the loading (multi-axial, non-proportional), the equivalent stress damage accumulation approach might provide overestimated lifetime results.

Conclusion
A methodology is presented for the determination of a S-N curve, relevant for impact fatigue (high strain rate) loading conditions.A hard and soft PU system are characterised based on tensile test and DMA analysis.The master curves indicate the soft PU system to show relatively high energy dissipation during impact loading, leading to lower amplitude stress waves in the coating system.However, when combining the SPIFT experimental and numerical evaluation of both systems, the respective S-N relations shows that, under the same stress conditions, the hard PU system will experience a longer lifetime.This tendency is recognised with RET data in which the same relative material performance is seen.Indications are seen that the relative material performance can be predicted by the presented methodology, however further analyses is required to conclusively validate the results.

Figure 1 :
Figure 1: Tensile test experimental data for the hard and soft PU systems, corresponding to a strain rate of ε = 10 −4 /s

Figure 2 :
Figure 2: DMA storage modulus experimental data before and after mastercurve construction (a) and shift factor a T as a function of temperature used in mastercurve construction (b) for the soft PU system with T ref = 20 • C.

Figure 3 :
Figure 3: Illustration of the SPIFT, with instrumentation and control systems relevant for the conducted experiments.

Figure 4 :
Figure 4: Model geometry and boundary conditions for simulating SPIFT testing conditions with V 0 as the impact velocity indicated on the ball (a) and stress field in terms of the Von Mises stress criteria for the soft PU system, with V impact = 110 m/s approximately 1 µs following impact initiation (b)

Figure 5 :Figure 6 :
Figure 5: Mastercurves for T ref = 20 • C, for hard and soft PU material system, in terms of the storage and loss modulus (a) and Tanδ (b)

Figure 7 :
Figure 7: S-N curve relation (a) and RET data (b) for the hard and soft PU system

Table 1 :
Basic assumed material properties used in current study