Introduction

Since the 1950s, the aviation and aerospace industry have constantly been developing thermal barrier coatings (Ref 1). These protective systems are commonly used for thermally stressed parts, which can be additionally loaded mechanically and tribologically under highly corrosive conditions. However, phenomena related to the TBC working conditions occur mainly at the coating interface (Ref 2), which is, therefore, responsible for the integrity of the whole TBC system. There is also a characteristic strong relation between the coating thermal performance and the coating interface as a result of the thermally grown oxides build-up at high temperatures (Ref 3, 4).

The influence of the bond coat/top coat interface on the TGO-related stresses is widely discussed in the literature. Song (Ref 5) investigated crack propagation in the EB-PVD and APS TBC systems considering different bond coat materials and physical properties, such as the as-sprayed roughness. He observed that the coating failure mechanism of rough TBC interfaces depends on the composition of MCrAlY coatings. In his work, Co-rich spinel oxides have been considered as a potential crack initiation sites when using CoNiCrAlY bond coats. On the other hand, Ni-based bond coats form rather pure alumina scales, thus not leading to an immediate TBC failure under the FCT test. However, the roughness of the MCrAlY interlayer performs a major role here. Gil et al. (Ref 3) investigated the behavior of polished and as-sprayed NiCoCrAlY coating during the isothermal oxidation and cooling cycle. A significant increase from 2 to 5 GPa in compressive stress was observed during air cooling for polished coatings compared to as-sprayed ones. This is consistent with the corresponding study by. Song (Ref 5), who observed an extended coating lifetime for porous TBCs sprayed on rough bond coats.

As discussed, the bond coat topography may considerably affect the durability and the cyclic performance of the TBC system. However, the as-sprayed roughness depends mainly on the production technology. Nowak et al. (Ref 6) investigated the mean roughness Ra and the maximum height Ry parameter of the APS/VPS and HVOF bond coats. A mean roughness of 11 µm was observed for HVOF and of 13 µm for APS/VPS. However, the maximum height parameter ranged from 65 µm for HVOF to 90 µm for APS/VPS. On the other hand, constant development in bond coat laser processing opens new possibilities for modifying the as-sprayed bond coat topography. Zhou et al. (Ref 7) presented promising laser pretreatment techniques such as laser cleaning, shock peening, and microtexturing. Laser texturing can be applied directly to the substrate to increase its roughness and coating adhesion (Ref 8) or to the bond coat to control the bond coat/top coat interface and the top coat structure (Ref 9, 10). Another promising technique is the interference pattering (Ref 11), which uses the phenomenon of the laser beam interference for precise texturing at a scale of the laser source wavelength.

This work considers the laser microtexturing as a promising tool to control the TBC structure, i.e., the formation of the columnar top coat. The mechanism of the columnar coating build-up on substrate asperities was first proposed in 2011 by VanEvery et al. (Ref 12). They considered the shadowing effect as a factor determining the structure of the coating. This idea was further developed by Bernard et al. (Ref 13, 14) and Sokolowki (Ref 9, 15). Bernard et al. (Ref 13) investigated the geometry of columns growing on differently prepared substrates and tested such TBCs under the TCF test (Ref 14). It was proven that well-separated columns grown on a well-developed substrate surface provide a better cyclic fatigue lifetime. Additionally, Sokołowski et al. (Ref 9) considered this build-up mechanism and introduced bond coat laser microtexturing discussed in this section to control the TBC structure.

As mentioned, experimental approaches to surface pretreatment have been widely discussed in the literature. On the other hand, numerical research into thermal spray processes is dynamically evolving toward the understanding of plasma spraying processes and coating deposition phenomena. There are advanced plasma generation models proposed in the literature (Ref 16, 17) as well as complex plasma flow analyses focused on plasma jet thermophysical properties (Ref 17) including the interaction with flat (Ref 18), curved (Ref 19), and microtextured substrate (Ref 10). The movement of the substrate was also introduced to the plasma spray simulations by Melilot et al. (Ref 20), complementing the numerical approach to the analysis of the plasma jet behavior.

This work is focused on the behavior of the coating material in the closest proximity to the substrate. Before the feedstock reaches the substrate, it is injected into the plasma jet. At this stage, arc voltage fluctuations affect the plasma flow and the feedstock trajectory according to Marchand (Ref 21). Then, the coating material distribution in the plasma jet is further affected by the droplet break-up phenomenon, which was thoughtfully studied by Kharlamov et al. (Ref 22) and others (Ref 16, 19, 23). The heat transfer between the plasma jet and the coating material should also be considered here in addition to the physical interaction according to Vardelle et al. (Ref 24). Mariaux et al. (Ref 25) extended this study and considered also the heat transfer to the substrate as it affects the plasma jet and droplet thermophysical properties in the substrate boundary layer. However, the deposition location depends mostly on the droplet size. Bigger droplets are preferably deposited close to the centerline due to relatively high Stokes number (St ≫ 1), while smaller droplets are more likely to reach the substrate outer regions (Ref 26). The analysis of A. Dolmaire et al. (Ref 27) shows that the off-normal angle of impinging the droplets increases from 6 degrees close to the centerline to 80 degrees in the 10 mm distance from the centerline. This creates optimal conditions for the shadowing effect to perform a major role in the columnar coating build-up mechanism. This has been further confirmed by G. Mauer (Ref 3) and P. Wang et al. (Ref 28), who performed the 2D Monte Carlo simulation of coating material deposition over the flat surface, and Azar (Ref 29, 30) who extended the mentioned studies with a splat shape analysis, as well as the 3D Monte Carlo simulation.

Based on the discussed state-of-the-art, there is still room for the analysis of the behavior of the coating material in the microtextured boundary layer. This work extends the previous own numerical study on the plasma jet behavior (Ref 10) with the introduction of a coating material injection. The interaction between YSZ droplets, plasma jet, and the microtextured substrate is investigated to better understand and control the columnar TBC build-up mechanism. Additionally, the computational domain was located at three different distances from the plasma jet centerline to investigate the intensity of the shadowing effect for different droplet geometries and impinging angles. The time-dependent 2D axisymmetric model included heat transfer equations and specific plasma flow boundary conditions for the microscale computational domain taken from the previous analysis (Ref 10).

Methods of Mathematical Modeling

Experimental Reference

The experimental approach in this work consisted of Atmospheric Plasma Spraying of NiCrAlY bond coat later subjected to laser texturing. Then, the zirconia top coat was produced over the microtextured interlayer by Suspension Plasma Spraying.

The bond coat was sprayed on nickel supper alloy coupons with a thickness of 3 mm and a diameter of 25 mm using an SG-100 (Praxair, Indianapolis, US) plasma torch. The commercial feedstock powder -90 + 45 µm AMDRY 963 (OC Oerlikon, Freienbach, Switzerland) was used for this purpose.

Then, the as-sprayed interlayer was microtextured with a F20 Varia (Coherent, Santa Clara, USA) fiber laser. The engraving pattern was designed to be possibly dense, with a groove width of 15-20 µm and a mean depth of approximately 30 µm. The geometry of the mentioned pattern was adjusted to the mean bond coat thickness of 80 µm and the impinging zirconia droplet of 1 µm. Additionally, the pattern pith was limited to 40 µm, while the groove width of 20 µm remained much larger than the droplet size.

The next step was the deposition of AuerCoat® YSZ 25E T1 (Treibacher Industrie AG, Althofen, Austria) suspension to produce a ceramic top coat. Finally, the as-sprayed columnar coating was inspected under Tescan Vega3 Scanning Eletron Microscopy (Tescan Orsay Holding, Brno-Kohoutovice, Czech Republic). Figure 1 shows the cross section of the resulting TBC taken with SEM. The columnar structure is controlled by the microtextured bond coat topography as shown in Fig. 1(a). It is seen that the coating build-up is initialized periodically from each of the bond coat asperities (Fig. 1b), as discussed in detail later in the article.

Fig. 1
figure 1

Reference TBC sprayed on a microtextured bond coat, (a) overview of the as-sprayed TBC, (b) detail view of the bond coat / top coat interface

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Initial and Boundary Conditions

As mentioned in the Introduction section, this paper discusses the numerical analysis of the microtextured bond coat boundary layer. The most promising bond coat topography was modeled based on the inspection of the reference TBC interface (Fig. 1) and a previous preliminary study (Ref 10). Figure 2 shows the locations of the computational domain in which the trajectory and concentration of the landing droplets were analyzed. In this work, the numerical analysis is performed in a microscale domain (Fig. 2) including the deposition of zirconia particles and the heat flux to the substrate during the coating deposition. The heat transfer equations introduced to the boundary conditions consider the convective heat transfer law as (Ref 31)

$$q = h_{f} (T_{w} - T_{f} ) + q_{{{\text{rad}}}} = h_{{{\text{ext}}}} (T_{{{\text{ext}}}} - T_{w} )$$
(1)

where

Fig. 2
figure 2

Draft of the spraying domain in the reference SPS process; all dimensions are given in mm

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\({h}_{\mathrm{ext}}=1100\frac{w}{{m}^{2}K}-\) taken from G. Mariaux et. al (Ref 25), \({T}_{\mathrm{ext}}=2500K.\)

The discretization of the geometrical model was very fine to ensure a proper discrete phase tracking, which results from the fluid phase flow resolution. The 2D axisymmetric discrete model contained 39,456 uniform QUAD4 type cells. With the discretization density shown in Fig. 3, the additional local mesh refinement was redundant. The values of y* and y+ did not reach 1, which is far below the critical 5 according to the Fluent Theory Guide (Ref. 32). Figure 4 shows y* value 6.250 mm from the plasma jet centerline. However, at 3.125 mm and 9.375 mm, a corresponding level of y* was observed. Low y* parameter ensured high-resolution mapping of turbulence and viscosity-related phenomena. The high-quality mesh allowed to track also the droplet trajectory in the closest proximity of the grooves and just before the contact with the microtextured surface.

Fig. 3
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Discrete model of a microtextured substrate boundary layer and the groove geometry

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Fig. 4
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Mesh-related y* value 6.250 mm from the plasma jet centerline

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As mentioned, the behavior of the coating material was investigated in three different locations corresponding to the results of the own preliminary study (Ref 10). This allowed to investigate the relation between the distance from the plasma jet centerline and the behavior of the droplets impinging the microtextured substrate. To do so, three sets of boundary conditions were introduced to the governing equations, including location-specific properties of the coating material and the plasma flow. BCs related to the plasma flow were taken from the corresponding sections of the whole spraying domain. Figure 5 shows the components of the plasma flow BCs specific for the section located 6.250 mm from the plasma jet centerline. The variable plasma flow properties for each boundary were considered here to better reproduce the deposition condition of the whole spraying domain in the extracted sections. The maximum values of the respective BC for each section are shown in Table 1. The entire domain simulation is more widely discussed in the previous studies (Ref 10, 33) considering the plasma generation, free-jet flow, and the interaction between the plasma jet and the microtextured substrate. Figure 6 shows the scheme of computational domain BCs related to the plasma flow and the coating material modeling.

Table 1 Boundary conditions for extracted sections of the spraying domain
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Fig. 5
figure 5

Plasma flow boundary condition components for the computational domain located 6.250 mm from the plasma jet centerline; plasma radial inlet: (a) radial component of velocity profile, (b) axial component of velocity profile, (c) temperature profile, (d) pressure profile, plasma axial inlet: (e) radial component of velocity profile, (f) axial component of velocity profile, (g) temperature profile, (h) pressure profile: domain outlet: (i) pressure profile, (j) backflow temperature profile

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Fig. 6
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Computational domain boundary conditions scheme (Ref 10, 26, 27, 34)

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The discrete phase properties were verified with the current knowledge on the behavior of the coating material in the closest proximity to the substrate. The impinging droplet angle was taken from the numerical analysis of the stagnation zone under SPS conditions by A.Dolmaire (Ref 27). Due to the different plasma gun used in the mentioned study, namely TriplexPro 210 cascaded arc gun, the injected droplet velocity was reduced by the correction factor \(C_{v} = 67.5\frac{m}{s}\) when compared to ADolmaire (Ref 27). The correction intensity was determined based on the particle image velocimetry provided by Mohammandi (Ref 34) and other numerical simulations considering single-cathode plasma guns (Ref 19, 23, 35). The size distribution of the droplets in the plasma jet was also considered here using the two-parameter Rosin–Rammler size distribution. Table 1 shows the particle size range and distribution considered for respective substrate sections according to the literature (Ref 26, 27).

Material properties

The continuous phase was defined as the compressible mixture of inert gases, thus considering the occurrence of dynamic diffusion phenomena. The composition of the mixture consisted of 90% vol. of Ar and 10% vol. of H2., which is related to the typical plasma gases flow rate when using the SG-100 plasma torch – 45 slpm of Ar and 5 slpm of H2. The thermophysical properties of plasma were taken after Boulos et al. (Ref 36) and applied to the plasma gases definition. On the other hand, the discrete phase was considered as molten YSZ with the required material properties (Table 2) taken after Kang et al. (Ref 35) and Pourang et al. (Ref 23). For droplet trajectory mapping, the spherical drag law was used as it is suitable for most smooth particles including droplet shape. This law defines the drag coefficient as

$$C_{D} = a_{1} + \frac{{a_{2} }}{{\text{Re}}} + \frac{{a_{3} }}{{{\text{Re}}^{2} }}$$

where a1, a2, and a3 constants are taken after Morsi et al. (Ref 37).

Table 2 Feedstock material properties – molten YSZ
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Governing Equations

Time-dependent governing equations (Table 3) were solved under pressure-based solver with fixed time advancement for both fluid flow modeling and discrete phase tracking. Considering the unsteady plasma flow and the interaction between phases, the PISO scheme was used for pressure–velocity coupling. Compared to coupled schemes, PISO-based models are more resistant to convergence issues when solving unsteady multiphase flow equations (Ref 32).

Table 3 Model governing equations
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The interaction between the discrete and the continuous phase, as well as the DPM sources, was updated for every fluid flow timestep. However, the droplets injection was defined by a specific particle timestep size regardless of the continuous phase time advancement. The simulation time and the timestep interval were optimized for particle trajectory mapping and computational cost reduction. Table 4 shows the discussed time advancement for fluid flow and DPM simulation.

Table 4 Simulation time advancement
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Results and Discussion

As mentioned, this work considers the trajectory analysis of impinging droplets. The first step assumed the validation of the plasma thermophysical properties. It was done by the plasma flow comparison in the substrate boundary layer. The results obtained here were compared to own full spraying domain simulations and other corresponding studies (Ref 19, 35) for reference. Then, the droplet behavior was investigated in three different locations, under microscale computational domain, which refer to the previous own study on the plasma jet interaction with the microtextured boundary layer (Ref 10).

Validation of the Plasma Flow Model

The plasma stream behavior in the substrate boundary layer was investigated based on the velocity and temperature field analysis at 3.125 , 6.250 , and 9.375 mm from the plasma jet centerline.

Figure 7 and 8 show the difference between the domain remodeled at 6.250 mm from the centerline and the results of the reference entire spraying domain. There are no major differences between these simulations in terms of the velocity field (Fig. 7). The velocity magnitude in the substrate boundary layer is also comparable to the results presented by Jadidi et al. (Ref 19) and Kang et al. (Ref 35) in all cases. However, the temperature field is not equal to the results of the preliminary study (Fig. 8). Figure 9 shows the comparative analysis of temperature inside the grooves from the entire spraying domain and the remodeled domain cases. The temperature was analyzed at the point marked with the cross in Fig. 8. The temperature difference at the substrate surface level was roughly 500 K close to the plasma jet centerline, and 1000 K was observed at the outer regions. However, the free-jet temperature of 2500 K was maintained in all cases. This inaccuracy was acceptable in the analysis of the plasma jet behavior, namely temperature and velocity gradients. However, heat flux to the substrate performs a significant role when investigating the interaction between feedstock and the substrate, as mentioned in the section Molten droplet trajectory analysis. The droplet behavior depends on the energy which is transferred from the plasma jet flow to the feedstock. This energy, in turn, is partially transferred to the substrate after the impact, which cannot be neglected here.

Fig. 7
figure 7

Comparison of velocity contours, (a) results of the remodeled substrate boundary section, (b) results of the preliminary study

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Fig. 8
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Comparison of temperature contours, (a) results of the remodeled substrate boundary section, (b) results of the preliminary study

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Fig. 9
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Comparative analysis of the temperature field inside the grooves of the microtextured substrate

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Molten Droplet Trajectory Analysis

As mentioned, the YSZ feedstock was modeled as a discrete phase using the DPM. Thus, the domain discretization did not have to meet the scale of the tiniest considered droplet, namely 0.3 µm here (see the Initial and Boundary Conditions section), which is roughly half of the mesh cell size. Figure 10, 11 and 12 show the concentration of landing droplets at 3.125, 6.250, and 9.375 mm from the plasma jet centerline, respectively. It can be seen that the amount of coating material deposited on the substrate is the highest close to the centerline. However, the largest difference in the mean concentration of the landing droplets is observed between the 3.125 and 6.250 mm distances (Fig. 13). Also, the pick value of 0.5 g/m3 was reached on the leading side of the grooves located at 3.125 mm.

Fig. 10
figure 10

Landed droplet concentration along the 0.3 mm section of microtextured substrate surface located between 3.125 mm and 3.425 distance from the plasma jet centerline

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Fig. 11
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Landed droplet concentration along the 0.3 mm section of microtextured substrate surface located between 6.250  and 6.550 mm distance from the plasma jet centerline

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Fig. 12
figure 12

Landed droplet concentration along the 0.3 mm section of microtextured substrate surface located between 9.375  and 9.675 mm distance from the plasma jet centerline

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Fig. 13
figure 13

Mean concentration of landed droplets recorded along the microtextured surface at different distances from the plasma jet centerline

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This is roughly twice the value observed at the groove top and leading side when considering the 6.250 mm offset. The further increase in the distance from the centerline does not reduce the number of deposited droplets at such a rate. The distribution of the size of the droplets in the plasma jet plays a major role here. As mentioned, larger droplets are carried close to the plasma jet core and are more likely to reach the substrate close to the centerline. Due to the relatively high Stokes number, St ≈ 1 for 1 µm YSZ droplets under SPS conditions (Ref 26, 38), they do not follow the surface jet easily, which results in a more efficient deposition at 3.125 mm offset from the centerline when compared to the other cases. This, in turn, may affect the growth of the columnar coating structure in the macroscale. Intensive coating build-up close to the centerline provides columns initialized at the groove leading side rather than at the very top of the substrate asperities, which is discussed in detail later in the paragraph.

However, the microscale distribution of the coating material over the microtextured substrate seems to affect the columnar coating build-up mechanism directly. Figure 10, 11, and 12 show that, in all cases, the pattern of concentration peaks and drops corresponds to the substrate topography. The peaks of the DPM concentration can be seen at the top of the grooves with marginal deposition at the bottoms of the grooves. This periodical initiation of the coating build-up results in the occurrence of the shadowing effect, which is an important factor in obtaining columnar-like TBCs (Ref 12). However, the intensity of the effect depends on the distance from the centerline. This relation is experimentally proven by Caio and Moreau (Ref 39), who sprayed the rod sample with the YSZ feedstock by means of SPS. It was observed that the shadowing effect increases with the off-normal angle of the impinging droplets. In this study, peaks of the concentration of landed droplets are observed at the leading edges and inner walls of the grooves at the 3.125 mm offset (Fig. 10, 14(a)), which is specific for this case. When moving away from the plasma centerline, the intensity of the shadowing effect increases and the coating material is deposited only at the top of the substrate topography. This effect can also be seen in Fig. 14, which shows the droplet trajectories in three sections of the microtextured substrate. Although the particles were injected into the plasma jet in the full range of size, in Fig. 14, trajectories of particles larger than 0.9 µm and smaller than 0.45 µm are given separately (Fig. 14a, b, c and d, e, f, respectively). This allowed to observe that only small droplets, characterized by low Stokes number St ≪ 1, are dragged by the surface jet in the case of 3.125 mm distance from the plasma jet centerline. Furthermore, at further distances from the centerline (Fig. 14b, c, e, f), the majority of the injected droplets follow the surface jet due to increasing off-normal angle and the higher content of droplets with a low Stokes number. This also results in no movement of the particles inside the grooves for the 9.375 mm (Fig. 14c, d) and 6.250 mm cases (Fig. 14b, e). However, Fig. 14a shows that the coating material reached the leading edge of the groove and the inner wall in the case of 3.125 mm offset, which is confirmed by the analysis of DPM concentration, as already discussed.

Fig. 14
figure 14

YSZ droplet trajectory in the microtextured substrate boundary layer for droplet size > 0.9 µm, at (a) 3.125 mm, (b) 6.250 mm, and (c) 9.375 mm from the plasma jet centerline, and droplet size < 0.45 µm, at (d) 3.125 mm, (e) 6.250 mm, and (f) 9.375 mm from the plasma jet centerline

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The analysis of the YSZ droplet trajectory together with its periodic concentration on the microtextured substrate confirms that the substrate topography is crucial in the formation of columnar coatings. The coating deposition is periodically initialized from the groove tops and leading sides, which proves the predictions from the previous own study (Ref 10). In the mentioned work, the pressure filed distribution was investigated in the substrate’s closest proximity. Local pressure peaks were observed therein on the groove leading side and pressure drops on the groove trailing side. This periodical effect of local pressure field disturbance additionally increases the probability of the occurrence of the columnar structure. However, the impinging inclination angle seems to be critical here, as the shadowing effect is considered here as the key build-up mechanism for columnar TBC. Finally, the study suggests that columnar-structured TBCs may be effectively controlled by substrate topography, which, in turn, may be well designed and precisely pretreated by laser microtexturing, even under the micrometer regime.

Conclusions

In this study, the 2D time-dependent numerical model was used to predict the behavior of the plasma-sprayed YSZ during the deposition. To do so, the plasma jet’s thermophysical properties were first compared to the literature and own preliminary study. Then, the feedstock interaction with the microtextured bond coat was modeled at three different locations on the substrate, varying the distance from the plasma jet centerline. The analysis was oriented on the columnar TBC deposition conditions resulting from the bond coat pretreatment.

It can be concluded from the analysis of the landed droplet concentration that the initiation of columnar TBC build- up is periodic and follows the microtextured pattern. However, feedstock deposition on the leading edge of the groove and the inner wall was observed only close to the centerline. The YSZ droplets did not reach the inside of the grooves at the outer regions of the sample as a result of intensive shadowing. For this reason, the impinging inclination angle and the droplet size should be considered together with the resulting intensity of the shadowing effect when planning the bond coat’s laser processing. The discussed droplet behavior also proves that columnar formation can be effectively controlled by the bond coat laser microtexturing. In the future works, different substrate topographies will be modeled to optimize the bond coat laser processing for different TBC deposition conditions discussed in this paper and confirmed experimentally.