3.1. Residual Stress in the TGO Layer
Regional differences in the oxidation process can cause complications in oxide growth. In this study, three representative regions within the TGO, namely, the peak region (EU), the valley region (EB), and the ramp region (ER), were analyzed separately.
Figure 7 shows the schematic diagram of typical regions within the TGO.
The TGO layers under different thermal cycles were tested using a Raman microscope (Horiba LabRAM HR, Kyoto, Japan) with an excitation of 532 nm. The TGO stress was characterized by tracking the frequency shift of R2 of Cr
3+ in α-Al
2O
3 [
21].
Figure 8a shows a schematic of the PLPS test area, and
Figure 8b shows the tested PLPS spectra of the TGO [
22].
The collected spectral curves were fitted with the Gaussian Lorentz function by Labspec 6 spectral analysis software, and the fitting accuracy was about 0.5 cm
−1. The TGO can be considered under biaxial stress due to its flat structure. Lipkin and Clarke et al. [
23,
24] discussed the stress tensor of TGO in more detail. The residual stress σ in the TGO can be calculated by Equation (6) [
25].
where Δυ is the frequency shift of R2 fluorescence. All the Raman measurements were carried out at room temperature(20 °C).
The stresses in each region in the TGO were calculated for different numbers of thermal cycles.
Figure 9 shows the magnitude of residual stresses in the TGO region after 50, 200, 400, 550 and 750 thermal cycles of the TBCs.
Figure 10 shows the regional biaxial stress diagram in the TGO during thermal cycling.
The test results from
Figure 9 showed that the stress states of TGO under the cooling stage were compressive stresses. The residual stresses in the three regions were relatively close to each other after 50 thermal cycles. A dense layer of TGO was formed at 200 thermal cycles, and the compressive stress reached the maximum at this time, then began to decrease slowly. The compressive stress reached the minimum after 750 thermal cycles. The test results were consistent with the results of Xu [
26] and with the biaxial stress results (The biaxial stress is the sum of the principal stress vectors in both directions) for each region at room temperature in the FE model, as shown in
Figure 10. The result can further verify the accuracy of the constructed model and stress evolution based on oxidation kinetics in this work, and also provide the basis for analyzing the dangerous loading in the coating.
3.2. Effect of Thermal Cycling Process on Stress Distribution in TGO Layer
The failure of coatings is mostly defined by crack initiation and the crack generation drived by two stresses σ
xx and σ
yy in the TGO layer [
27,
28]. Therefore, the study first examined the evolution of stresses σ
xx and σ
yy in the TGO layer during thermal cycling.
Figure 11 shows the stress diagram of the TGO in the ungrown state. In the
X direction, the TC layer in the original state was in a compressive stress state. The stress in the coating was released and the compressive stress near the TC/BC interface started to decrease as the thermal cycle started (
Figure 11b).
In the Y direction, the tensile stress in the peak region (Peak 1) in the original state was the largest at +108 MPa. The stress gradually changes from tensile stress to compressive stress from the peak region to the valley region. The tensile stress in the peak area (Peak 2) was gradually released as the thermal cycle started.
Figure 12 shows the stress diagram under the Al
2O
3 initiation process. In the
X direction, high-pressure stress concentrations appeared in the peak and valley regions due to the Al
2O
3 initiation. The compressive stresses and their areas increased as the TGO grew.
In the Y direction, the stress distribution near the interface becomes very heterogeneous during the Al2O3 initiation process. The tensile stress in the peak region (Peak 3, 4) of the TGO layer kept rising. The high tensile stress region also appeared in the near peak region (Near Peak 1, 2) near the TC/TGO interface and moved with the TC/TGO interface.
Figure 13 shows the stress diagram under the longitudinal “layer” growth phase of Al
2O
3. With the longitudinal growth of Al
2O
3, the compressive stress in the valley region (Valley 1, 2, 3) near the TGO/BC interface gradually decreased in the
X direction.
In the
Y direction, the maximum tensile stress remained in the peak region near the TGO/BC interface (Peak 5, 6, 7). The relatively even compressive stress distribution in the ramp region (Ramp 1) can protect the thermal barrier coating more effectively [
29].
Figure 14 shows the stress diagram for the rapid growth phase of MO. The transition from compressive stress (−298 MPa) to tensile stress (+158 MPa) occurred in the valley region near the TGO/BC interface (Valley 4 to 6), eventually maintaining a high tensile stress concentration zone in the
X direction.
The maximum tensile stress in the peak region near the TGO/BC interface (Peak 7, 8, 9) increased from +243 MPa to +291 MPa in the Y direction. The “compressive stress zone” remained in the ramp area of the Al2O3 layer (Ramp 2), but the stress decreased sharply, causing the protection of the coating to also decrease.
The stress distribution of the above thermal cycles observed that the maximum tensile stress σyy occurred in the near-peak region close to the TC/TGO interface (Near Peak 1–2) during the initial few thermal cycles (3–4 cycles) of the Al2O3 initiation. Maximum tensile stress σyy changes the position to the peak region near the TGO/BC interface (Peak 1–9) with the increasing number of thermal cycles (5–20 cycles). The stress σxx changed from compressive to tensile stresses in the valley region near the TGO/BC interface (Valley 1–6) during the rapid growth of MO. It can be inferred that the continuously growing tensile stresses in both regions tended to be the driving force for crack initiation.
3.3. Stress Evolution Law in Typical Regions
For a clearer analysis of the correlation between the TGO growth behavior and the stress evolution under different regions, the stresses σ
xx and σ
yy in typical regions were investigated separately in this work (
Figure 15). The stress changes in the three regions were similar and relatively small in the TGO ungrown state in
Figure 15a. The maximum compressive stress under all three regions during Al
2O
3 initiation tended to increase, especially in EU. The maximum compressive stress in the three regions slowly decreased during the slow growth of the “layer” of Al
2O
3. With the appearance of the difference in oxide growth rate in the TGO region, the stresses in the EU and EB regions gradually changed from compressive stresses to tensile stresses during the holding period, and the EB tensile stress growth rate was larger in
Figure 15b. EB was increasingly affected by tensile stress from the beginning of the explosive growth of MO. Thus, it can be shown that the tensile stress concentration region appeared in the valley region since the beginning of the oxidation layer uneven growth compared to other regions. The tensile stress also increased gradually with the growth of MO, which is more prone to crack initiation and propagation under stress σ
xx.
As shown in
Figure 15c, it can be seen that the maximum tensile stress of EU was around +100 MPa at no TGO. The tensile stress of EU increases slowly with Al
2O
3 initiation, from 97 MPa to 108 MPa. The ER generated enormous compressive stress due to the extrusion of the initiated TGO. The maximum tensile stress in the EU increased with the TGO thickness at the beginning of the “layer” growth of Al
2O
3. With the rapid growth of MO, the maximum tensile stress of the EU kept growing. It can be concluded that the oxide growth had a significant effect on the growth of tensile stress in the peak region within the TGO, especially at the uneven growth of Al
2O
3, which was more prone to microcracking under stress σ
yy.
The regional stress evolution law above speculated that the peak region of the TGO layer was more prone to microcracking at Al
2O
3 uneven thickening. The microcracks in the valley region were prone to appear under the MO rapid growth phase. The presence of crack initiation and propagation in the peak and valley regions can be seen in the samples after long thermal cycling (
Figure 16). The phenomenon was consistent with the conclusion reached by Karadge et al. [
30].
The average crack length was calculated for each group of samples using five typical SEM images of successive cracks selected at TGO/BC interface. As shown in Equation (7).
where L is the average crack length, L
TC is the sum of all crack lengths, and N is the number of cracks near the interface. To summarize the relationship between various factors according to the number of thermal cycles, TGO growth behavior, stress and crack initiation and propagation are shown in
Table 6. The effect of thermal cycling on the evolution of stresses and cracks was reflected in a quantitative way. The stresses in both directions were essentially unchanged at the early stage of the thermal cycle (C ≤ 4) in the table. The stress growth rate in both directions was larger in the middle of the thermal cycle (4 < C ≤ 10). The stress growth rates in both directions were larger, however the maximum failure strength was not reached in the middle of the thermal cycle (4 < C ≤ 10). The crack propagation rate was slower in the peak and valley regions. The growth rate of tensile stress was slowed down by the appearance of spinel. Tensile stresses exceed the maximum failure strength at the late stage of thermal cycling (C > 10). The rate of interfacial crack propagation was significantly higher. The presence of the valley region produced σ
xx above +1500 MPa and σ
yy above +250 MPa in the peak region eventuallyaccording to Wang et al. [
31]. This was consistent with the numerical results in the current model. This indicated that there was a strong correlation between the elevation of tensile stress, crack propagation rate, TGO composition and morphology.