*3.3. Case 3. Substrate Impedance Variability. Analysis of a LEP Multilayer System Rain Erosion Testing Based on DNVGL-RP-0171*

This third case ponders the effect of considering different substrate materials with the same coating LEP. Figure 21 shows a blade section in reparation. It is observed different substrate material layers from the structural laminate where a filler (putty) layer between the laminate and the coating is included. Some manufacturers also include a primer layer under the coating and over the filler to improve adhesion. Depending on each industrial solution, the inclusion of interfaces may accelerate erosion by delaminating between layers. It is important in terms of repairing that the LEP configuration keeps uniform through the thickness with the appropriate substrate. In this section, the possible different erosion lifetime is analyzed due to the substrate layer impedance variation. Upon impingement, the wave front in the top coating 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 impedances, and the remaining part is transmitted to the substrate layer and hence to the blade.

In this worked case are used two batches of three coupons, each with two LEP configurations, as depicted in Figure 13, for rain erosion testing based on DNVGL-RP-0171. The modelling input data are defined in Table 2 that correspond to the speed of sound testing measurements developed for this research and of which the results are exposed in Figures 3 and 4. Particularly, the simulation is different to previous case 2, mainly because of the use of a different coating LEP; see Table 3 for its input data. The analysis considers RET testing results obtained at ORE-Catapult [41] with a configuration of coating LEP19B layer with a Primer layer (without filler layer) and then the laminate (glass fiver reinforced epoxy). The second test ponders the RET testing results obtained at PolyTech [40] with a configuration of coating LEP19B, primer layer and filler B as an intermediate substrate before the fourth GFRE-laminate layer.

**Figure 17.** V-Time plot for simulated coating LEP prototype, comparing both the effect of the droplet impact velocity variations through the RET coupon from the root to the tip, according to DNVGL-RP-0171 and the comparing the simulated results when UT measuring at 2.5 and 5 MHz.

**Figure 18.** Incubation time estimation due to a unique variation of the coating wave speed Cc.

**Figure 19.** Incubation time estimation due to a unique variation of the substrate (primer or filler) wave speed Cs.

**Figure 20.** V-Time plot for simulated LEP prototype, comparing both the effect of a 10% variation on the coating and substrate speed of sound variations.

**Figure 21.** Blade section in reparation showing different areas with different substrates. Droplet impact reflected/transmitted stress on interface due to relative impedance.


**Table 3.** Reference Input data used for the Lifetime Springer modelling in Case 3. DNVGL-RP-0171.

Figures 22 and 23 show the RET data testing results of the two LEP configurations, evaluating the effect of using (primer-laminate) or (primer-fillerB-laminate) as substrate layers with LEP19B as the coating layer. The damage points are depicted in a V-N plot with the number of droplets impacts, until failure for each impact velocity.

We may calculate and fit the erosion strength *Sec*\_ *fit* from the RET data as described in Equations (12) and (15), see [15] and Figure 5, in terms of number of droplet impacts N, and observed velocity. The erosion strength *Sec*\_ *fit* of both LEP systems are derived using their RET data by matching the *Vfit* and *nic*\_ *fit* values for a given RET data VN plot result as

$$S\_{cc,fit} = \sigma\_o \left(\frac{n\_{ic,fit} \, d^2}{8.9}\right)^{\frac{1}{2.7}} \sigma\_o = V\_{f\bar{t}t} \frac{Z\_L \cos(\theta) (\psi\_{\&\{\bar{t} < \bar{t}\}} + 1)}{\left(\frac{Z\_L}{Z\_c} + 1\right) (1 - \psi\_{Lc} \psi\_{\&\{\bar{t} < \bar{t}\}})} \left(1 - \frac{(1 - e^{\bar{t}}) (\psi\_{Lc} + 1) \psi\_{\&\{\bar{t} < \bar{t}\}}}{\gamma (\psi\_{\&\{\bar{t} < \bar{t}\}} + 1)}\right) \tag{2}$$

In our case, all the *Sec*\_ *fit* values were obtained for all the damages (coupling *Vfit* and *nic*\_ *fit*) of each tested batch. The mean value of each set of initial failure points defined *Sec*\_*set* was obtained and plotted in a V-N curve for a complete range of V and N values with Equation (15), as introduced in [15]. See experimental RET data results in Figure 22 with V-N curve in dotted lines for the primer-laminate or primer-fillerB-laminate used as substrate layers for each configuration. Subsequent intermediate progression of damages until breakthrough are also plotted as aforementioned. It is perceived that Springer V-N curve slope obtained for the aforementioned fit erosion strength follows the experimental data for the initial damages (incubation time).

It is observed in Figure 22 for comparison and modelling accuracy validation that Springer modelling simulations from fundamental properties (filled lines) of wear damage are also plotted, considering the three cases of LEP19B as the coating layer combined with fillerB or primer or laminate as substrate layer (with labelling LEP19B-fillerB, LEP19B-primer, LEP19B-laminate, respectively). This is due to the fact that the Springer model only accounts for a semi-infinite substrate layer, and does not consider a multilayer configuration as depicted in Figure 13. Since our tested systems contemplate all a thin primer layer and then a filler or a laminate layer, the three possibilities were simulated, and the results are plotted for comparison. The modelling results predict erosion damage earlier than RET testing for the laminate and the filler B cases. In the contrary, Primer simulation shows that the RET damages occur later than predicted. These results are as expected and are justified that in reality the RET coupons have a multilayer configuration, where the primer is the first substrate layer, but only with a thickness of 500 μm. That means that the overall mechanical effect is a mixture between the thicker substrates (laminate or fillerB) and the primer. A worse performance is expected when considering a pure primer layer and better for pure laminate substrate or pure fillerB substrate (in agreement with the modelling results shown).

Figures 24 and 25 show that the incubation time estimation (number of impacts until failure) is obtained for each simulated *Cc* and *Cs* value respectively. It is observed again (as in the previous case 2) the effect of increasing the coating speed of sound value *Cc* and the substrate speed of sound value *Cs* in a variation range. Both results allow one to define the influence of the substrate material responsibility on transferring the energy of impact to the blade laminate, when considering its reparation with added filler or putty layers. We can determine that the modelling estimates well wear failure and it is

validated with the erosion strength derivation from RET testing data, which in fact is assumed to be necessary within performance estimation methodology for correct erosion analysis.

**Figure 22.** V-N plot for RET testing and simulated coating LEP prototype comparing both the effect of the droplet impact velocity variations though the RET coupon from the root to the tip according DNVGL-RP-0171 and comparing the simulated results when varying the substrate impedance.

**Figure 23.** RET images of coupons at intermediate testing time for the two configurations: left, (LEP19B-Primer-Laminate) and right, (LEP19B-Primer-FillerB-Laminate).

**Figure 24.** Incubation time (Number of impacts until failure) numerical estimation, due to a unique variation of the coating wave speed Cc when considering the Primer as the substrate layer.

**Figure 25.** Incubation time (Number of impacts until failure) numerical estimation, due to a unique variation of the substrate wave speed CS when considering the LEP19B material as the substrate layer.
