*3.3. Influence of Coating-Substrate Thickness Variations*

In this section, the strain-stress analysis ponders first the effect of considering a variation on the coating thickness over the reference case for the initial testing coupon of Table 1. Two cases of study are related with variations of the given parameter multiplying its value by 1,4 for Cases 1 and 2 respectively as shown in Table 2


**Table 2.** Modelling input data for variation cases in **Coating thickness**.

Figure 20 shows the influence of the Coating thickness on the stress developed at surface (s\_0) and interface (s\_100) for the Case 1 (reference LEP configuration). The peak values observed at interface depends also on the acoustic matching with the filler. Since the material develops different stress-strain values through its thickness, a proper layer location for comparing the strain evolution is considered to be defined at its intermediate 50% thickness location i.e., e\_50, s\_50. Figures 21 and 22 for Cases 1 and 2 comparison.

**Figure 20.** Stress-Time evolution for Case 1 at surface (s = 0) and interface (s = 100).

**Figure 21.** Spectrogram for strain evolution at the middle coating layer. Comparison for coating thickness variation respect to the reference LEP multilayer configuration (Case 1).

**Figure 22.** Spectrogram for strain evolution at the middle coating layer. Comparison for coating thickness variation respect to the reference LEP multilayer configuration (Case 2).

It is important to observe the high values of the reflection stresses developed due to the multilayer interfaces effect due to the low value of the substrate thickness of the reference LEP multilayer configuration. Springer model limits this assuming that the substrate (filler) layer has to be considered semi-infinite, hs > 2d Cs CL , which means in fact that the reflections are not considered in the fatigue analysis for computing the average stress values on surface. Other additional effect is considering very thick coatings with hC <sup>&</sup>gt; 2d Cc CL by means of shells or tapes. Cases 1–3 analyze the effect of increasing 20 times the filler thickness and 1, 10 and 20 times the coating thickness compared to the initial reference LEP multilayer configuration of Table 1, detailed variation input data is defined on Table 3.

**Table 3.** Modelling input data for variation cases in semi-infinite substrates, hs > 2d Cs CL , in substrate (filler) thickness and in thick coatings (shells and tapes), hC <sup>&</sup>gt; 2d Cc CL .


It is observed in Figures 23 and 24 the lower value of stress at surface (s\_0) and middle location layer (s\_50) due to the increment of coating thickness (so its damping capabilities). It is also appreciated the delay on wave stress reflections due to the increase on the substrate-filler thickness.

**Figure 23.** Stress-Time evolution for Cases 1–3 at surface, 0% of Coating thickness, considering the substrate filler as semi-infinite with increased thickness (shells, tapes).

**Figure 24.** Stress-Time evolution for Cases 1–3 at middle coating layer, 50% thickness, considering substrate-filler as semi-infinite with increased thickness (shells, tapes).

Figures 25–27 show the corresponding influence on the strain frequency spectrum where the higher strain-rate variations are developed in the periods of time closer to the impact pulse and the wave traveling reflections.

**Figure 25.** Spectrogram for strain evolution at the middle coating layer, 50% thickness, considering substrate-filler as semi-infinite with defined coating thickness for reference LEP configuration. Case 1.

**Figure 26.** Spectrogram for strain evolution at the middle coating layer, 50% thickness, considering substrate-filler as semi-infinite with increased thickness (shells, tapes). Case 2.

**Figure 27.** Spectrogram for strain evolution at the middle coating layer, 50% thickness, considering substrate-filler as semi-infinite with increased thickness (shells, tapes). Case 3.

#### *3.4. Influence of Coating Viscoelastic Property Variations*

In this section, the strain-stress analysis considers the influence of pondering a variation on the coating stiffness over the reference case for the testing coupon of Table 1. Three cases of study are related with variations of the given parameter multiplying its value by 1, 0.5 and 1.5 for Cases 1, 2, and 3, respectively as shown in Table 4.

**Table 4.** Modelling input data for variation cases in coating modulus (stiffness) and considering semi-infinite substrates, hs > 2d Cs CL .


Figure 28 show the strain in the coating layer due to a variation on the modulus for the three different cases. It is detected an abrupt variation in the strain-rate values and its corresponding effect on the strain frequency spectrum, Figures 29 and 30. The dominant working strain frequency range is increased in the periods of time closer to the impact pulse is increased from 1 MHz, to 3–7 MHz for Cases 2 and 3.

**Figure 28.** Strain-Time evolution for Case 1,2,3 at middle coating layer, 50% thickness, considering the substrate-filler as semi-infinite with variation in coating modulus.

**Figure 29.** Spectrogram for strain evolution at the middle coating layer, 50% thickness, considering substrate-filler as semi-infinite with variation in coating modulus. Case 2.

**Figure 30.** Spectrogram for strain evolution at the middle coating layer, 50% thickness, considering substrate-filler as semi-infinite with variation in coating modulus. Case 3.
