Transient Heat-Transfer Analysis
Experimental and simulated temperatures at the surface of the top coat and the center of the substrate are shown in Fig. 4. In this figure, the experiment was conducted with the loop pattern, 50 mm/s in torch velocity, 6 s in loop interval, 28 kW in the plasma power and without pre-heating. The simulation was conducted with T
s = 6000 K condition. The substrate temperature was precisely represented because the boundary conditions were adjusted to fit the simulated temperature to the experimental temperature at this point. On the contrary, the simulated surface temperature became higher than the experimental one, especially at the local maximum. One of the reasons of the high surface temperature in simulation might be the layer-by-layer deposition despite the continuous and gradual deposition in real experiments. The surface temperature was easy to elevate when some amount of high temperature material was deposited at once. Furthermore, the surface temperature might be higher than the measured value because the response of the thermocouple was slower than the actual temperature elevation (Ref 7).
The stress distributions were obtained from elastic and elasto-plastic analyses until the substrate temperature was cooled down to 100 °C after the finish of deposition (see Fig. 5). Stress in radial direction on the interface between the top and bond coats is shown in this figure. The elastic analysis showed significantly larger stress distribution than the elasto-plastic analysis. Of course, such large stress could not be generated in the real coating because of the strength of the sprayed top coat. Furthermore, it was reported that the residual stress in the top coat after spraying was several tens of MPa by x-ray diffraction method (Ref 13, 20, 21). Then, a consideration of stress relaxation due to crack generation was necessary for analysis of the deposition process of ceramic coatings. Therefore, elasto-plastic analysis in this study is one of the effective methods.
Figure 6 shows the stress and the strain distributions in radial direction by elasto-plastic analysis on the interface between the top and bond coats when the deposition was just finished. The stress level in the elasto-plastic analysis was almost constant by changing the initial temperature of the substrate because the material reached to the plastic zone. On the contrary, the strain depended on the initial temperature of the substrate. The experimental and simulated results can be corresponded to the strain because the crack development degree depended on the pre-heating temperature in experimental results. The strain which corresponded to the vertical cracks was radial or circumferential direction because the most of the observed cracks especially from the experiments with the loop pattern were vertical ones. The analysis results were evaluated using the radial strain because the radial and circumferential strains became almost the same value.
Figure 7 shows the temperature history of the specimen and the strain history on the interface between the top and bond coats. The strain (dotted line in the figure) showed a significant increase tendency during temperature increasing although the specimen temperature showed cyclic increasing and decreasing during spraying. Generally in plasma spraying process, thermal stress is considered to be generated by mismatch of thermal expansion coefficient between the top coat, bond coat and substrate or temperature gradient in the top coat. The thermal strain should be the same manner. Tensile strain occurs in the top coat, especially around the interface between the top and bond coats when the surface is heated by spraying because the thermal expansion coefficient of the bond coat and the substrate is larger than the top coat. Therefore, the strain is considered to be large when the initial temperature of the substrate is low because the effect of mismatching of the thermal expansion coefficient also becomes large.
Vertical Cracking Behavior
Figure 8 shows the schematic of generation of temperature gradient in the top coating during spraying. The temperature distribution before one-time of spraying was almost uniform. Then, a large temperature gradient would be generated in the top coat when the surface was heated by spraying (Ref 7). Figure 9(a) is an example of vertical crack, which suggests that the crack developed upward by the shape of branching. Figure 9(b) is a sample contour plot of the strain in the top coat when the deposition was finished. The radial strain reached the peak on the interface between the top and bond coats and gradually diminished to the surface of the top coat. Furthermore, the radial strain on the top surface was negative. Distribution of the strain was estimated as Fig. 9(b) because the strain in the top coat became large nearby the bond coat due to the mismatch of the thermal expansion coefficient and the temperature gradient in the top coat. This tendency of the crack propagation to the surface was explained by this strain distribution because a crack would be considered to be generated at the maximum strain point.
Effect of the Initial Temperature
Figure 10 shows the effect of the initial temperature of the substrate on the maximum radial strain on the interface between the top and bond coats. The radial strain became larger and smaller when the specimen was heated and cooled, respectively. Our previous result of laser AE monitoring showed that the most of cracks were generated during rapid heating by spraying (Ref 7). Therefore, the simulation results were corresponded to the experimental results of crack generation due to heating.
Furthermore, the strain after the deposition process became larger when the initial temperature was low. It can be considered that the strain became larger because the effect of the mismatching of the thermal expansion coefficient also became larger when the initial temperature of the substrate was low. Figure 11 shows the relationship among the initial temperature of the specimen, the total AE energy in each experiment, and the simulated radial strain. The AE energy and the strain became larger when the pre-heating temperature was low. Therefore, a relationship between development of vertical cracks and the initial temperature was explained by the radial strain because cracks were more developed in the lower initial temperature experiments.
Effect of the Atmospheric Temperature
Figure 12 shows the effect of the atmospheric temperature T
s (see section 2.4) on the strain on the interface between the top and bond coats. The temperature fluctuation during spraying became larger when T
s was large. Then, the strain is considered to be larger because of the effect of the mismatch of the thermal expansion coefficient. The tendency of the final strain in Fig. 12 was affected by temperature gradient in the top coat when the surface was heated by spraying because the temperature gradient in the top coat became large when T
s was high.
Figure 13 shows the relationship among the average of temperature fluctuation during spraying T
f, the total AE energy in each experiment and the simulated radial strain. Temperature history during spraying was expressed by T
f. The diamond marks show the total AE energy of each experiment, and the square marks show the simulated radial strain on the interface between the top and bond coats when the deposition was finished. In this study, the temperature history during spraying was controlled by T
s in the simulation and the strain of each simulated condition was plotted at the position of T
f of the corresponded experiment of the center temperature of the specimen. Then, this figure showed a tendency that the AE energy in the experiment and the strain in the simulation were increased when T
f was increased.
Furthermore, it was also revealed that the total AE energy in each experiment was corresponded to the crack development degree in the top coat. Especially, the almost all of the AE energy in Fig. 13 was due to vertical cracking and the radial strain was corresponded to this vertical cracks. Therefore, the simulated strain amount in this study can be corresponded to the crack development degree in the experiments.