**1. Introduction**

Rain erosion damage, caused by repeated droplet impact on wind turbine blades, is a major cause for concern, even more so at offshore locations with larger blades and higher tip speeds, see Figure 1. In most cases, since the surface protection plays a decisive role in the blade manufacture and overall performance, it has been identified as an area where a solution may be obtained. There are various protection solutions used by industry that can reduce the effect of erosion and increase the turbine expected lifetime. Four main surface protection technologies may be considered: In-mould coatings (Gel coating) applied during moulding on the entire blade surface but not specifically on the Leading Edge location where the protection is crucial; post-mould coatings specifically developed for Leading Edge Protection (LEP) and considering a multilayer system with optional configurations based on

top-coatings, filler and primer materials, depending on blade manufacturing and operational settings; tapes based on post-mould applications circumventing the issues related with liquid-based materials; shells that as tapes are manufactured in controlled conditions and applied in pre-cast solid modules over the Leading Edge surface. In order to analyze and evaluate the relative positive facts and faults of a given protection system, we will consider the common issues related with rain erosion failure for any of these technologies.

**Figure 1.** Examples of leading edge erosion across a range of years in service, from [1].

Industrial processes state that LEP systems can be outlined as a multi-layered system with varying layer thickness and material configurations. A particular case, used here to sketch the problem, with a post-mould coating-based LEP system is shown where the blade manufacturer includes a putty layer between the composite laminate and the coating, see Figure 2. It also can be included a primer layer under the coating and over the filler to improve adhesion mainly to avoid layer debonding and circumvent application related defects.

**Figure 2.** Leading Edge Protection (LEP) system configuration on the blade surface as a post-mould application multilayer system.

In the top coating material system, two main different types of erosion failure are mainly observed (see Figure 3) in used Rain Erosion Testing coupons: pits and cracks that progress with mass loss caused by direct impact and stress on surface and delamination indirectly caused by the interface stresses [1,2].

The analysis of erosion caused by rain droplets is considered, as first approach, a single impact event as it is shown in Figure 4. The damage is in fact a 3D dynamic consequence resulting in the propagation of shock waves [3,4]. The droplet numerical modelling has been broadly studied by different authors [5–8]. As the water droplet impinges on the surface, a longitudinal compressional normal stress wave front in the top surface material further advances towards the coating-substrate interface, where a portion of the stress wave is reflected back into the coating with a different amplitude (depending on the relative material acoustic impedance) and yields a transverse shear wave. The remaining part is transmitted to the substrate. The impact gives rise to a third wave due to the water droplet deformation itself, called the Rayleigh wave, which is confined to the surface of the top coating. Depending on the relative acoustic properties through the liquid-coating-substrate, the propagation of the stresses and, consequently, the erosion lifetime can be optimized.

**Figure 3.** Two different types of erosion failure: Coating surface wear erosion with pits and cracks that progress with mass loss caused by direct impact and stress on surface and coating interface delamination indirectly caused by the coating-substrate interface stresses. The coupons were tested at Whirling arm rain erosion test facility (WARER) at University of Limerick.

**Figure 4.** (**a**) Standard blade structure sketch with a filler intermediate layer showing stress wave behavior under impingement and (**b**) Liquid droplet-solid surface impact interaction depicted from numerical simulation developed by the authors.

The analysis (or design) of Leading-Edge Protection systems depends on the material properties in the configuration and the operational load to which it is designed during its realistic life, that is, it must be able to withstand accelerated loads and also fatigue field regimes [6,9]. To make a selection or design of a specific coating protection system, appropriate modelling requires to be defined [10–12]. Numerical or analytical models can be constructed with their own capabilities and limitations, [13–15].

Springer analytical model [13] has been widely referenced and industry validated [15]. The model quantitatively predicts the erosion lifetime of coated materials under the previously untested conditions. The model is limited to erosion failures such as progressive failure mode or coating wear. To use the Springer model, material test data is needed to derive the erosion performance properties of a selected system. The formulation examines the impact of a liquid droplet treating the problem only

as a pure elastic 1D tensile-compression event. This simplification is applicable since shear stresses and shear material characterization directly related with other important damage mechanisms as peeling, debonding, delamination or crack evolution are out of the wear fatigue analysis case involved.

Wear fatigue failure analysis based on Springer model requires coating and substrate speed of sound measurements as input material parameters. The model does not account for a very high-rate transient pressure build-up and the viscoelastic effects are frequency dependent for the materials involved [16–18]. The main objective of this research is to fully apply the Springer model but considering the effect of the viscoelastic stress-strain development during the impact event in the LEP multilayer system by means of the appropriate frequency range definition for the coating layer impedance characterization.

In this work, as the first part of the research, it is proposed a modelling methodology that allows one to evaluate the single droplet impingement taking into consideration the highly transient material behavior during waterdrop collisions. The computational tool ponders with different application cases the operational conditions (impact velocity, droplet size, layer thickness, etc.) with the variable working frequency range that the material develops. We will introduce in this work a complementary numerical modelling tool (developed in openmodellica [19]) including suitable material models that allow us to observe the viscoelastic behavior (with consideration for high transient strain rate deformation, and variable stiffness and damping with frequency) and not as a pure elastic event. The complete analysis is used then to define the frequency range for the corresponding impedance measurements with Ultrasonic testing. The paper is organized considering first a review of the aforementioned Springer erosion lifetime prediction modelling, then the state of the art is completed for taking into account the viscoelastic effects of the stress-strain development under single droplet impingement for elastomeric materials. In last sections, different modelling analysis cases are discussed to ponder the effect of the operational and material configurations on the frequency range definition for appropriate material properties testing.

The coating characterization is developed in a second part of the research in a complementary reference [20] for different viscoelastic coatings and the methodology validated for the input material data definition of the erosion lifetime modelling based on Springer.

In this research the model is used then to carry out studies as a computational framework that allows a parametric analysis to examine the impact of the selected coating impedance variation on the erosion performance. This provides also a guidance in the selection and modulation of coating properties and to identify suitable coating and substrate combinations due to their acoustic matching optimization. At this point, the proposed modelling methodology should reduce the scope of Rain Erosion Testing [21,22] to verify and evaluate the rain erosion resistance of coating systems.
