Modelling and Experimental Validation of the Flame Temperature Profile in Atmospheric Plasma Coating Processes on the Substrate

Abstract

This work presents a characterisation model for the temperature distribution at different substrate depths during the atmospheric plasma spray (APS) coating process. The torch heat flow in this model is simulated as forced convection defined by a surface, a temperature profile, and a convection coefficient. The simulation model considers three plasma temperature profiles of the Al₂O₃ coating on a 5 mm thickness flat aluminium substrate. The simple and low-cost experimental procedure, based on a thermocouple, measures the plasma plume temperature distribution of the APS coating system, and their results are used to obtain the parameter values of each of the three proposed plasma temperature profiles. The experimental method for in situ non-contact temperature measurements inside the substrate is based on an infrared pyrometry technique and validates the simulation results. The Gaussian temperature profile shows excellent accuracy with the measured temperatures. The Gaussian approach could be a powerful tool for predicting residual stress through a coupled one-way thermal-mechanical analysis of the APS process.

1. Introduction

Thermal spray coating processes improve the mechanical, electrical, optical, and thermophysical properties while maintaining high geometric tolerances of a surface or a piece [1]. Thermal spray coating is a surface coating process that consists of depositing material (powder, wire or suspension) by heat with a highly energetic gas flow until reaching a molten or partially molten state. The subsequently atomised particles are projected onto the surface to be coated, resulting in so-called splats without the fusion of the substrate material during the process [2]. Different thermal spraying processes are depending on the energy source used. The atmospheric plasma spraying (APS) process is of particular interest due to the high temperatures reached in the plasma of up to 15,000 K. Such high temperatures enable great flexibility in the processing of a wide variety of materials, from metals to metal oxides or the mixture of ceramic materials and cermets, among others. On the other hand, a protective atmosphere around the molten particles during the process forms coatings of metallic materials with low oxide concentrations or a controlled degree of chemical reaction [3].

There are heat and mass transfer processes between highly energetic gases, the particles of coating materials and the substrate during the coating process. The final properties of the coating are determined by the oxide layer, adhesion, porosity, compound inclusions, hardness, and residual stresses [4]. Due to the complexity of the coating process, different authors divided the process into four main phases, as shown in Figure 1 [5,6].

Theoretical studies of the first phase are focused on modelling the generation of high-energy gases, such as the combustion of the fuels (liquid or gas) or the generation of thermal plasma, from the most simplified 1-D models to more complex and precise 3-D models [7]. The behaviour of the projected particles and the shapes of the obtained splats depends mainly on the mass and heat transfer between the gas and the particles, which defines the velocities and temperatures of the in-flight particles, as well as their diameter, morphology, and chemical composition [8], from which studies are included in the second phase. Current 3-D models obtain the velocity and temperature profiles of the carrier gas and estimate the in-flight particle properties [9]. The kinetic and thermal energies of the particles determine the deposition. Several factors influence the deposition, such as particle impact, surface flattening and solidification, splat formation, and substrate adhesion. The deposition involves mechanical, physical, and chemical adhesion mechanisms [10], the studies of which are included in the third phase. Analytical models defining a degree of flattening based on dimensionless parameters are presented in 3-D simulation models, including the formation of microstructures and multiple porosity generation mechanisms [11].

The definition of coating build-up and its properties are studied in models of the fourth phase to determine the characteristics of the coating, such as microstructure, cracks, or residual stresses. Including the heterogeneity of the particle deposition in the model presents a high degree of difficulty, particularly for simulating adhesion, heat transfer and mechanical behaviour between the coating and the substrate [12]. The substrate analysis and coating temperature evolution during the process are of main interest in this work. The sudden contraction and solidification of the splats and the mismatch between the thermal expansion coefficients of the coating and substrate influence the formation of residual stresses and its relaxation by cracks [1].

A numerical model solved using finite element methods (FEMs) is presented for the study of temperature and stress evolutions during the coating deposition process. This model is based on a coupled one-way thermal-mechanical analysis. This model simulates residual stresses generated in the coating by atmospheric plasma spraying on flat surfaces. Firstly, the thermal analysis is solved to obtain the temperature field. The resulting temperature field serves as the input condition for the mechanical analysis. Finally, the mechanical analysis determines the stress field [12]. However, this work uses a constant profile for flame plume temperature distribution. The temperature and stress results from this model are far from the real measurement due to a simple approximation of the flame plume temperature profile. Previous works determined the heat flow using calorimetric measurements [13] or Optical Emission Spectroscopy [14,15]. In the case of the method based on calorimetric measurements, the results obtained give overestimated temperatures when using very high powers on the applied area with orders of MW/m². The Optical Emission Spectroscopy method does not determine the radial distribution of the temperature, and it is also a very complex method to implement.

The main objective of this work is to implement a thermal model that predicts the temperature distribution at different substrate depths during the APS coating process, taking into account the effect caused by flame profiles that have not been studied in [12]. It is important to correctly define the heat flux contributed by the plasma plume (flame temperature, dimensions of the plasma area, and shape) to fit the simulation results with the experiments. To achieve this goal, Section 2 introduces the thermal simulation model of a flat plate for the APS process.

Section 3 defines three proposed flame plume profiles and proposes an experimental procedure to measure the plasma plume temperature distribution based on thermocouple in situ measurements. This procedure finds out all important parameters of the flame plume of an APS coating process, which will be included in the proposed flame temperature profile of the simulation model. This experimental procedure proposed by thermocouple is a simple and low-cost method to implement, improving the weak points present in other methods based on calorimetric measurements [13] or Optical Emission Spectroscopy [14,15] previously discussed.

Section 4 describes the experimental method for in situ non-contact temperature measurements at different substrate depths. This experimental method is based on an infrared pyrometry technique. Other techniques based on infrared thermography [13,16,17,18] have been used to measure the substrate temperature during the APS coating process, which are able to measure only the temperature on the substrate but not inside it.

Finally, Section 5 compares the simulation results with three flame profiles and the experimental results of the infrared pyrometry procedure.

2. Flat Plate Simulation Model

A flat plate model of dimensions 38.4 × 38.4 × 5 mm³ has been proposed. The mesh is refined towards the surface, with the smallest elements on the surface representing the coating/substrate interface, for greater precision in the region close to the coating surface, as shown in Figure 2 [12,19]. For this purpose, a total of five layers of nodes have been defined, with a depth scale ratio of 1.735. Figure 2 shows the depth of each layer of nodes for a total thickness of 5 mm.

The first and second layers of the mesh were distributed in 64 × 64 elements. The mesh is denser in the region close to the coating surface. In the successive layers, the number of elements has been reduced by half to reduce the computational cost and time, with a total of 9472 elements. Each mesh element is defined by its vertices or nodes.

A thermal analysis of the model was performed in ANSYS Mechanical APDL 2024 R1 software (ANSYS Inc., Canonsburg, PA, USA) [20]. The heat flow from the spray torch was simulated as forced convection, defined by a surface, a temperature profile, and a convection coefficient. A surface of 36 × 16 elements, equivalent to 21.6 × 9.6 mm², was defined in the model. At each load step, 16 elements in front of the torch flame begin to receive the heat flow, and 16 elements left the area covered by the torch.

The load step, $t_{step}$, is defined by the relation between the torch speed, $vtorch,$ and the X-axis surface element dimensions, $dx$, as follows: $t_{step}=dx/vtorch$. The process parameters have been set in the experimental coating process. The geometric and process parameters defined in the model are specified in

Table 1. Geometric parameters and simulation model definition process.

Parameter	Value
Substrate dimensions (DX × DY × DZ), mm3	38.4 × 38.4 × 5
Number elements: first layer (MTX × MTY)	64 × 64
Number of node layers	5
Surface element dimensions (dx × dy × dz), µm3	600 × 600 × 460
Analysed elements (Ne)	9472
Torch speed (vtorch), mm/s	100
Torch line change time (timetor), s	1
Ambient temperature (TAmb), K	300
Number elements of the line offset (ΔLZ)	4
Total number of spray lines (TLs)	19

.

The definition of the heat flow provided by the torch conditions the temperature field inside the component. The Fourier–Biot equation provides a basic tool for heat conduction analysis [21]. This equation is used to study the heat balance inside the substrate and on the surfaces in this work.

$$-{\displaystyle \frac{\partial }{\partial x}}\left(k_x·{\displaystyle \frac{\partial T}{\partial x}}\right)-{\displaystyle \frac{\partial }{\partial y}}\left(k_y·{\displaystyle \frac{\partial T}{\partial y}}\right)-{\displaystyle \frac{\partial }{\partial z}}\left(k_z·{\displaystyle \frac{\partial T}{\partial z}}\right)+q_V+q_S=\rho ·C·{\displaystyle \frac{\partial T}{\partial t}},$$

(1)

where k_x, k_y, and k_z are the material’s conductivity in W/m²·K, $\rho$ is the material density in kg/m³, C is the specific heat capacity in J/kg·K, $q_V$ is the heat loss by convection in W/m³, and $q_S$ is the heat loss by radiation in W/m³.

To define the convection, it is necessary to determine the temperature and convective coefficient of the plasma plume in the area covered by the torch, which is explained in more detail in Section 3.

A path is defined as a motion sequence of the torch and/or substrate during the coating process to cover the entire surface. In this case, a robot is employed to move the torch. The torch follows each line or trajectory of the path with a line offset, ΔLZ, as shown in Figure 3. The ΔLZ is the distance between two consecutive parallel lines or trajectories. The total number of spray lines, TL, is the total length of the path.

3. Plasma Plume Temperature Profile

The thermal simulation model proposed in Section 2 of this work has the temperature flame profile as the input parameter. For this, it is necessary to know the important parameters of the plasma plume profile, such as the temperatures at the centre and the edges of the flame, the dimensions of the plasma area, and its shape. Depending on which parameters are included in the temperature flame profile, the simulation results of temperature evolution at different substrate depths during the coating process are closer to reality.

This section proposes three different flame profiles (constant, incremental step and Gaussian). Later on, Section 4 compares the temperature temporal evolution on the substrate during the coating process using these flame profiles. The motivation behind these three proposed profiles comes from the knowledge of the flame profile we want to simulate. The simplest case is when the temperature at the centre of the flame and flame footprint are only known (constant profile), and the most complete case is when all flame parameters (temperature at the centre and edges, flame footprint, and shape profile) are known, such as the Gaussian profile. A procedure for experimental measurements of plasma plume temperature distribution by the thermocouple is proposed in Section 3.4. All flame parameters could be extracted with this experimental method.

3.1. Constant Temperature Profile

The heat transfer of the plasma plume is defined by a constant temperature, as shown in Figure 4.

The model presents the advantage of lower computational times but with higher errors in the obtained substrate temperatures. The parameters necessary to define this model are the maximum plasma temperature, THigh, and the X-axis and Y-axis dimensions of the plasma area or footprint in terms of the number of elements employed in the simulation model, BlockX and BlockY, respectively.

3.2. Incremental Steps Temperature Profile

In this profile, the temperature distribution increases fixed incremental steps from the border to the centre of the plasma plume, as shown in Figure 5.

This model better matches the real temperature profile of the plasma plume on the component surface than the constant parameter model. However, it does not produce a uniform distribution with a low number of BlockX elements. The parameters necessary to define this model are the same as for constant temperature and include the parameter defined as the minimum temperature on the border of the plasma area, TLow.

3.3. Gaussian Temperature Profile

The last definition of the temperature profile uses a Gaussian distribution as an approximation function, as shown in Figure 6. It is defined by the following equation based on the study described in [13]:

$$T(x,y)=TLow+\left(TLow-THigh\right)·e^{\left(-{\displaystyle \frac{x^2}{2{\sigma }_x^2}}-{\displaystyle \frac{y^2}{2{\sigma }_y^2}}\right)}$$

(2)

where the initial temperature is TLow, the maximum temperature is THigh, and the X-axis and Y-axis standard deviations are represented as σ_x and σ_y.

In this case, the temperature variation is smoother and more progressive than the incremental step profile, allowing a weighted adjustment of the temperature curve. As shown in the subsequent analysis, the temperature distribution represents a normal distribution throughout the cross-section and approximates the real flame profile in more detail.

3.4. Experimental Measurement of Plasma Plume Temperature Distribution

As justified above, the heat flow is simulated as the convective heat transfer between the plasma gas and the substrate surface. Therefore, it is essential to define the temperature profile of the plasma plume during the path. First, it is necessary to establish the temperature limits that define the plasma plume during the movement. In previous studies, plasma plumes have been simulated, and temperature distributions in the substrate surface have been determined, but the results obtained have not been validated with experimental data [22].

In this work, experimental tests are implemented to determine in situ the temperature profiles of the plasma plume, taking into account the impinging jet from a round nozzle to the substrate surface, as shown in Figure 7. A calibrated type K thermocouple of the Ni/Cr alloy with fibreglass insulation material from TC Mess und Regelungstechnik GmbH (Mönchengladbach, Germany) has been used. The fibreglass insulation protects the wires from the plasma plume, and only the tip is exposed to the heat flow (allowing fast response and avoiding interferences during the test).

The thermocouple tip has been placed on the surface of the water-cooled disk, allowing the performance of stationary measurements of different positions radially in the plasma plume without the melting of the surface. Fibreglass insulation tape is used to fix and insulate the thermocouple, reducing the heat transfer between the sensor and the cooled disk, which would affect the measured temperature. The plasma torch parameters are defined in

Table 2. Plasma torch parameters.

Parameter	Value
Torch distance to the plate, mm	120
Torch speed, mm/s	550
Hydrogen, slpm	10
Argon, slpm	44
Current, A	500
Voltage, V	75
Power, kW	37.5

. It should be noted that the experimental measurements were carried out without the spraying of the coating material to avoid interferences in the temperature measurement due to the deposition of a coating. The experimental X-axis dimension flame profile was measured using the next procedure. First, the torch was moved to the measurement centre, which is defined as the thermocouple placement. After that, it was moved with a 5 mm X-axis incremental step to the measurement centre before waiting 10 s for thermocouple temperature stabilisation and acquiring the temperature directly from the thermocouple. This process was repeated every 5 mm X-axis incremental step until the total plasma footprint was covered in the X-axis. In this case, it ranged from −60 mm to +60 mm in the thermocouple placement. The measured experimental X-axis dimension plasma profile is shown by the black line in Figure 8. The experimental parameters of the flame profile were a maximum plasma temperature, THigh = 1476 K, minimum temperature on the border of the plasma area, TLow = 634 K, and a 60 mm radial dimension of the plasma area or footprint.

3.5. Parameters of the Proposed Profiles

The parameters of the three proposed flame temperature profiles of the simulation model are extracted from the experimental results of plasma plume temperaturedistributions (Section 3.4). The THigh and TLow parameters are 1476 K and 634 K, respectively, from the plasma plume temperature measurements. The X-axis and Y-axis dimensions of the plasma area or footprint were fixed to BlockX = 36 and BlockY = 16 elements in the simulation model. The X-axis dimension of the simulation flame profile, BlockX, was scaled relative to the X-axis dimension of the experimental flame. To increase the accuracy and reduce the computational time of the simulation, the 550 mm/s experimental flame velocity (Table 2) was divided by 5.5 to define the model flame velocity of 100 mm/s (Table 1). Proportionally, the experimental flame size was scaled to the model, fitting the 120 mm of the experimental flame profile to the 36 elements of the model flame profile, keeping the heat flux per area constant.

Additionally, the three proposed profiles include the maximum convective coefficient in the centre of the plasma plume, FilmHigh, and the minimum convective coefficient on the border of the plasma area, FilmLow. These coefficients have been obtained from an analysis of the estimated heat flow in the thermal spraying process [13] and the experimental plasma plume temperature distribution. The parameters of the constant, incremental step, and Gaussian flame temperature profiles used in the simulations are summarised in

Table 3. Definition of the model flame profile parameters.

Parameter	Constant Profile	Incremental Steps Profile	Gaussian Profile
Number of elements for the X-axis dimension of the plasma area or footprint (BlockX)	36	36	36
Number of elements for the Y-axis dimension of the plasma area or footprint (BlockY)	16	16	16
Maximum plasma plume temperature (THigh), K	1476	1476	1476
Minimum plasma plume temperature (TLow), K	--	634	634
σx2 = (3 · BlockX − 10)/2	--	--	49
σy2 = (2 · BlockY − 3)/2	--	--	14.5
Maximum convective coefficient (FilmHigh), W/m2·K	2500	2500	2500
Minimum convective coefficient (FilmLow), W/m2·K	2000	2000	2000

.

Figure 8 compares experimental results with the three proposed temperature profiles of the flame. The curve of the Gaussian temperature profile (red line) represents a closer temperature profile to the measured temperatures (black line). For this, X-axis and Y-axis standard deviations, σ_x and σ_y, respectively, are defined in Table 3 to fit the Gaussian profile with the measured values. The incremental steps profile (green line) is overestimated in the central region, reducing accuracy. To obtain better results with the incremental steps profile, it is necessary to increase the number of elements in the X-axis dimension of the footprint, BlockX, which increases the number of steps and the computational time cost. As expected, the constant temperature flame profile is the furthest from the experimental results.

4. Experimental Temperature Measurement inside the Substrate

An experimental method of non-contact temperature measurements using an infrared pyrometer validated the simulation results. This method is based on the phenomenon of infrared thermal radiation, in which a body with a temperature greater than 0 K (−273.15 °C) emits electromagnetic radiation. The temperature of a body can be determined without contact by a correlation with the radiated intensity. The most interesting range for measurements is between a 0.7 and 20 μm wavelength. As thermography is an optical measurement method, a direct view from the sensor is required. Multiple factors should be considered to avoid measurement errors, such as the object material, the surface finishing, the measurement section, the intermediate medium, and the presence of interfering radiation in the environment. These errors can be corrected by calibrating the equipment to obtain valid results. In our test, the measurement equipment was arranged at the back of the component to avoid interference from the radiation generated by the plasma plume. In the case of metal surfaces, the surface finish quality and a relatively constant emissivity were of great importance for the experimental test. Four flat aluminium AL99 AW 1050A H14 plates with dimensions of 100 mm × 100 mm and 5 mm thickness were used for the experimental test. Black paint was applied to the rear surface of the plates, which has a known emissivity value of 0.89. To determine the temperature at different substrate depths, a 2 mm diameter hole was made on the centre of the back face of each plate with a specific depth, Hole_depth, of 1, 3, 4, and 4.5 mm, which defines the distance from to the surface to be coated, Point_depth = Plate _{thickness −} Hole_depth, of 4, 2, 1, and 0.5 mm, respectively, as detailed in Figure 9.

An infrared pyrometer model Optris 3MH1-CF3-CB3 (Optris GmbH, Berlin, Germany) was used. The calibration of the pyrometer was carried out by measuring the known temperature on the surface and its comparison using a contact thermometer in a temperature-controlled oven. The pyrometer was aligned with the hole made in the plates using a laser pointer. The measurement was started at the same time as the robot performed the first line or trajectory of the path. Since the operating range of the pyrometer is from a 150 °C temperature, the first transition had to be made without applying a layer for preheating the substrate surface. After that, a coating process was applied with a path of 52 total spray lines or trajectories, TL, a line offset, ΔLZ, of 2.4 mm, and Al₂O₃-coated material (Al₂O₃ 99.7%, melted and acid washed from Ceram GmbH Ingenieurkeramik, Albbruck, Germany) deposited on the surface of each plate. Table 2 describes the plasma torch parameters used for this experiment.

The temperature evolutions at different depths of the measuring point during each trajectory or line of the path are shown in Figure 10a. First, an increase in the temperature of the homogeneous substrate as the torch advanced along the path was observed. Specifically, an increase in temperature was observed from 575 K approx. to 675 K approx., from trajectory number 14 (m14) to number 40 (m40). The temperature peaks during each line or trajectory of the spray path were observed in temperature evolution. A typical pattern of temperature evolution generated for all lines of the path was due to the plasma plume movement during each trajectory or line of the path. In each path trajectory, the temperature increased as the plasma plume moved from the beginning to the centre of the trajectory. The peak of this pattern corresponded when the plasma plume was over the point of the trajectory of the path that was Y-axis-aligned with the placement of the point under test (the plasma plume crosses the dotted red line B in Figure 10b and in Figure 10a inset), and subsequently decreases as it moved away from it. These temperature peaks increased as the torch approached trajectory number 26 (m26), corresponding to the passage of the torch flame over the measurement point, which is point P_B in Figure 10b and in the Figure 10a inset. Then, the peaks decreased as the trajectories move away from the measurement point. On the other hand, the inset of Figure 10a showed the temperature values for different depths, Point_depth. The temperature peaks were lower as Point_depth increased. A small time delay for the peaks appeared due to conduction heat transfer through the substrate with the depth.

5. Results and Discussion

Initial simulation works with constant temperature profiles were performed for a plate dimension of 115.2 × 115.2 mm², which defines a mesh of 192 × 192 elements on the substrate surface, corresponding with an element size of 0.60 × 0.60 mm² [12]. Due to computational resource limitations in the case of incremental steps and the Gaussian temperature profiles, it was necessary to reduce the simulation model to a size of 1/3 of the original dimension. Therefore, the complete component was defined with a plate dimension of 38.4 × 38.4 mm², establishing a mesh of 64 × 64 elements on the substrate surface, corresponding with an element size of 0.60 × 0.60 mm². The simulation covered the centre area of the original plate with a total size of 1/3 of the original plate and a path of 19 trajectories.

As shown in the graphic representation of pyrometer measurements, the more relevant experimental results correspond with a depth of 0.5 mm due to the more immediate effect of the plasma plume in the temperature evolution. Figure 11 compares the temperature evolution of the three temperature profiles in the numerical model at a depth of 0.46 mm within the experimental results.

From the analysis of Figure 11, we obtained two main conclusions. The evolution of the mean temperature of the plates for the incremental steps and Gaussian temperature profiles were close to the experimental results. On the other hand, the temperature evolution for the constant temperature profile presented a high deviation due to the higher heat transfer, as expected.

To compare the influence of plasma plume trajectory over the measurement point, simulations of a single trajectory pass were performed for the three temperature profiles with two considerations. First, the simulation time corresponding to the experimental time was set in the range between 50 ms and 50.5 ms. Second, the initial simulation temperature was the mean experimental temperature obtained at 50 ms. These considerations allow for a standard initial condition to compare the results of the temperature peak in the three temperature profiles.

Figure 12 shows the temperature dependence over time in the constant temperature model. The temperature constantly increases during the complete passage of the plasma plume, where it continues to heating the substrate after the torch centre line crosses the point in the analysis. After the footprint is out of the region under study, the temperature decreases exponentially due to a sudden cool-down by convection. This model presents a significant deviation of the peak temperature, with a ΔT of 31 K in simulations and 15 K in the experimental results. The mean temperature field in the substrate presents a temperature increase of 21 K compared to the 4 K obtained in the experiment. Figure 11 previously showed that simulating successive trajectories leads to even higher errors.

Figure 13 shows the simulation results for the incremental steps temperature profile and the Gaussian temperature profile. The temperature smoothly increases in the first phase. The torch continues to heat the substrate until the torch centre line crosses the point in analysis and decreases smoothly once the footprint moves out of the region under study. The temperature decrease is a gradual cool-down by convection. Both modelled temperature evolutions are close to the experimental results. The peak temperature in the simulation presents a ΔT of 19 K and 16 K, respectively, compared with the 15 K obtained in the experimental results. The mean temperature field in the substrate presents a temperature increment of 7 K and 4 K, respectively, compared to the 4 K obtained in the experimental results. Figure 11 shows that the Gaussian temperature profile is more accurate than the incremental steps temperature profile, particularly for the mean temperature field.

6. Conclusions

This work presents a numerical model for the thermal analysis of atmospheric plasma spray processes not only on the surface of the substrate but also inside it. The heat flux was simulated as the convective heat transfer between the plasma plume and the substrate, defining the temperature profile of the plasma plume in the substrate temperature and the associated convective coefficient. For this purpose, a constant, incremental step and Gaussian temperature profiles were proposed. The three profiles evaluated the influence of the type of plasma profile over the substrate temperature simulation. A simple and low-cost experimental setup based on a calibrated type K thermocouple of the Ni/Cr alloy with fibreglass insulation was used to extract all key parameters of the plasma plume of the IMTCCC’s APS coating system. In this case, the experimental parameters of the flame profile were a maximum plasma temperature, THigh = 1476 K, minimum temperature on the border of the plasma area, TLow = 634 K, and a 60 mm radial dimension of the plasma footprint. The measured plasma parameters were used to fit the parameters of each proposed flame profile. From the three proposed profiles, the Gaussian plasma temperature profile was the only one that matched the shape of the measured plasma profile. The fitted plasma temperature profiles were included in the numerical model to study the temperature evolution inside a 5 mm thickness flat aluminium plate during the Al₂O₃ coating of the APS process. An experimental method for in situ non-contact temperature measurements inside the substrate validated the simulation results. The experimental method was based on an infrared pyrometry technique. The plasma plume movement during the APS coating path generates a typical temperature pattern for all path trajectories. This pattern has a temperature peak, and its amplitude decreases with the substrate depth. The peak amplitude is at its maximum when the torch passes over the measurement point, corresponding with the centre of trajectory number 26 in this experiment and trajectory number 19 in the simulations. For the central trajectory, the measured peak amplitudes are 15 K, 10 K, and 6 K at 0.5 mm, 1 mm and 2 mm substrate depths. The simulated results for the temperature peak amplitudes with Gaussian flame temperature profiles in the central trajectory are 19 K, 15 K, 9 K, and 5 K at 0 mm (for the coated surface of the substrate) with 0.46 mm, 1.25 mm, and 2.62 mm substrate depths, respectively. These temperature peak amplitudes for the same substrate depths are 22 K, 19 K, 11 K, and 8 K with the incremental step flame temperature profile; they are 35 K, 31 K, 26 K, and 21 K with the constant flame temperature profile. From the simulation and measurement results, the maximum peak amplitudes between the simulations at 0.46 mm substrate depth and the measurement at a 0.5 mm substrate depth are 0 K, 4 K, and 16 K with the Gaussian, incremental steps, and constant flame temperature profiles, respectively. The simulation results with the Gaussian flame temperature profile fit the peak values and the temperature pattern to the experimental results.

A coupled one-way thermal-mechanical analysis used the flame temperature profile to obtain the residual stress in the coating–substrate interface during the APS process. The Gaussian temperature profile studied in this work could be a powerful tool for this purpose.