*3.1. Case 1. Analysis of a LEP Multilayer System Rain Erosion Testing Based on ASTM G73-10*

This analysis case considers the rig features used at University of Limerick based on ASTM G73-10 [37] (Figure 6), with two set of coupons comparing the inclusion of a primer layer and another one with the coating LEP application directly to the sanded filler (see [3] for details). The modelling input data are defined in Table 1.

**Figure 6.** Reference multilayer configuration for rain erosion testing (RET) coupons (ASTM G73-10). Liquid droplet and each material layer are defined by the input mechanical parameters of Table 1.


**Table 1.** Reference Input data used for the Lifetime Springer modelling in Case1. ASTM G73-10.

Figure 7 shows the simulated analysis and the testing results tested at the WARER U.Limerick [3,7], comparing for two experimental batches of given top coating material prototypes, with primer and without primer, only with a filler substrate layer, as depicted in Figure 6. On the left vertical axes, one can observe the mass loss for the simulated results (in straight lines). On the right vertical axes, the box and whispers plots (in red for wear and in blue for debonding) are shown for each batch of the rain erosion testing (RET) tested coupons (developed over five coupons size batches). Horizontal axes define the incubation time for the experimental and simulated coupons. It is observed that since the primer and the filler have very similar impedance values, the expected lifetime is also comparable. Moreover, it is assumed that both materials have semi-infinite thickness (in the case of the primer, only a 50 μm thickness is applied in real). The experimental testing anticipates the wear damage showing inaccuracy on the modelling results. The simulated outcomes include important uncertainties due to fundamental properties values used as input data on the modelling. In this case, LEP top coating material ultimate strength was estimated with numerical extrapolation at high strain rates from [18].

**Figure 7.** Rain erosion testing lifetime analysis for experimental tested and simulated material LEP configuration comparing coating LEP configuration with No-primer layer (application directly to the filler), and coating LEP configuration with intermediate primer layer.

The modelling approach nevertheless is useful to quantify how the expected lifetime of a given configuration correlates with a given fundamental property variation, as introduced in Figure 5. In Figure 8 is shown the lifetime consequence of a LEP material properties variation of 20%, such are the computation of 80% and 120% values of the reference system. In this analyzed case, the wave speed of the coating, *cc* (in green dotted) and is compared with the Ultimate Strength of the coating, σ*uc*, (in blue line). One can realize that a variation on the ultimate strength of the material influences more significantly on the expected LEP lifetime (and so its determination by appropriate testing, but out of the scope of this work). An example of that issue is quantified for the speed of sound values that the Springer modelling requires as input data used in this research.

**Figure 8.** Lifetime analysis for experimental tested and simulated material LEP prototype comparing 20% variation of LEP Speed of Sound and Ultimate Strength.

Other analysis is due to the relative impedance values on the interfaces liquid-coating and coating-substrate that affect directly the lifetime performance results, see Figure 9. The parameters ϕ*Lc* and ϕ*sc* defined in Equation (2) (see Figure 5 for complete reference of the used equations), allow one to identify suitable combinations to optimize lifetime performance by means of acoustic matching.

**Figure 9.** Relative impedance values comparing lifetime prediction due to 20% variation (computing 80% and 120% values) of the Coating cc and Substrate cs Speed of Sound.

It is important to note that the stress history and the criteria to consider how the stress waves affect fatigue damage is based on a simplified one-dimensional and pure elastic single impact analysis as introduced in previous section. Figure 10 shows the considered stress evolution at coating LEP surface due to consecutive reflections defined in Equations (3)–(5), introduced in [15] and depicted in Figure 5, for our reference system comparing lifetime prediction due to 50% variation of the coating speed of sound *cc* (computing 50% and 150% of the reference values). The key parameter in this case is the averaged stress σ*<sup>o</sup>* calculated for the estimated impact duration. It is defined as a constant value in Equation (8), introduced in [15], and directly applies in lifetime prediction with the number of impacts estimation during incubation time, Equation (15). It is observed that a reduction and an increment of the reference value reduce, in both cases, the coating LEP lifetime estimation. This is due that the coating speed of sound values affect not only the coating-substrate reflections, also the liquid-coating interface and hence to the waterhammer pressure at surface.

Figure 11 shows the equivalent analysis when the variation is due to the filler-substrate speed of sound cs. In this case, that a 50% reduction on its value may yield and improvement of lifetime estimation and a 150% of its reference value consequences an abrupt loss on erosion lifetime. Figure 12 depicts the stress history with the same assumptions, but at the interface coating-substrate, calculating σ*<sup>h</sup>* with Equation (9), introduced in [15].

The analysis allows one to define appropriate criteria for evaluate the coating LEP capability to reduce or enhance the surface and interface stress, depending on its relative coating-substrate impedance (or speed of sound). Its optimization in terms of fatigue lifetime may be coupled with another parameter analysis, as discussed later in this section. By using other numerical simulation techniques and more complex material models, the accurateness on this estimation may be also improved.

**Figure 10.** Surface stress evolution analysis for simulated material LEP prototype comparing 50% variation of LEP coating Speed of Sound.

**Figure 11.** Surface stress evolution analysis for simulated material LEP prototype comparing 50% variation of Filler Substrate Speed of Sound.

**Figure 12.** Interface stress evolution analysis for simulated material LEP prototype comparing 50% variation of Filler Substrate Speed of Sound.

*3.2. Case 2. Relative Coating-Substrate Impedance Variability. Analysis of a LEP Multilayer System Rain Erosion Testing Based on DNVGL-RP-0171*

This second case ponders a batch of three coupons with a LEP configuration definition used for testing based on DNVGL-RP-0171 [38], following the modelling introduced and implemented in [15,39] and validated at PolyTech [40], as depicted in Figures 13–15.


**Table 2.** Reference Input data used for the Lifetime Springer modelling in Case2. DNVGL-RP-0171.

The modelling input data is defined in Table 2 that correspond to the speed of sound testing measurements developed for this research, in which the results are exposed in Figure 3. The objective is to validate the Springer modelling capabilities in regard to frequency-dependent speed of sound measurements.

Figure 16 shows RET testing data results tested at Polytech facilities. The two experimental coupons are configured with an intermediate primer layer to avoid delamination and to observe wear damage uniquely. It is observed the two RET test coupons (referenced S445-178R#2 and S445-178R#3) showing wear erosion damage progression at intermediate time intervals.

**Figure 13.** Reference multilayer configuration for RET coupons (DNVGL-RP-0171). Liquid droplet and each material layer are defined by the input mechanical parameters of Table 2.

**Figure 14.** Application execution steps of RET testing coupons used in this work (DNVGL-RP-0171).

**Figure 15.** Rain erosion test facility and three specimens used at PolyTech Test and Validation A/S according to DNV-GL-RP-0171 [38], for the analysis and experimental validation.

**Figure 16.** RET images of coupons S445-178R#2 and S445-178R#3 at intermediate testing time and zoom details to appreciate erosion damage.

The testing results data are also plotted in Figure 17 with a velocity-time representation (equivalent to V-N number of impacts until failure), where the velocity varies for each coupon depending on the location distance to the root of the rotating arm (see [38] for details on such a testing procedure) defining a slope introduced in Equation (15), from [15]. Simulated performance results are observed when using speed of sound measured values as input data at different UT frequencies of 5 or 2.5 MHz. It is detected that both cases offer the same simulated results, noting no influence on such impedance measurement deviations. The modelling results predict erosion damage earlier than RET testing. The accuracy of this modelling is reasonable, since many other material and operational parameters uncertainties are involved. Nevertheless, considering, in our problem, the unique variation due to the coating wave speed Cc, see Figure 18, the incubation time estimation (number of impacts until failure) is obtained for each simulated *Cc* value. It is observed the effect of increasing the coating speed of sound value *Cc* produces an improvement in erosion performance for a range of *Cc* values. One may also observe that, for the optimum value of *Cc*, a change in *Cc* becomes negative for this upper range values. Figure 19 shows the equivalent analysis but for a substrate speed of sound value *Cs* variation range. Both results allow one to define optimum values for material stiffness design reference. Figure 20 illustrates the limits of erosion performance deviation when considering a 10% value of its original reference for the speed of sound variation, in the coating and in the substrate. It is pointed out the stronger influence of the substrate speed of sound, mainly due to its responsibility on transferring the energy of impact to the blade laminate (in the Springer model, it is considered of semi-infinite thickness).
