Coupled Thermo-Mechanical Modeling of Crack-Induced Stress Fields in Thermal Barrier Coatings with Varying Crack Geometries
Abstract
1. Introduction
2. Materials and Methods
2.1. Structural Characterization and Crack Geometry Extraction
- (1)
- Tube voltage: 150 kV;
- (2)
- Tube current: 15 μA;
- (3)
- Integration time: 6000 ms;
- (4)
- Magnification: 130×;
- (5)
- Focus-to-sample distance: 11.4 mm;
- (6)
- Focus-to-detector distance: 12 mm;
- (7)
- Number of projections: 1801 over 360°.
2.2. Finite Element Modeling
2.2.1. Geometric Model and Boundary Conditions
- (1)
- The dynamic growth of the TGO layer is neglected.
- (2)
- Residual stress generated during coating preparation is not considered.
- (3)
- Phase transition-induced thermal effects are excluded from the calculations.
- (4)
- Interfaces between layers are fully bonded with no relative displacement.
2.2.2. Grid Division and Material Parameters
2.3. Simulation Methodology
3. Results and Discussion
3.1. Temperature Field Calculation Results
3.2. Effect of Crack Characteristics on Local Stress Distribution
3.2.1. Effect of Crack Length on Stress Distribution
3.2.2. Effect of Crack Depth on Stress Distribution
3.2.3. Effect of Crack Inclination on Stress Distribution
3.3. Optimization Analysis of Surface Scoring Strategy
3.3.1. Analysis of Crack Stress Response at Different Lengths
3.3.2. Analysis of Crack Stress Response at Different Locations
3.3.3. Analysis of Crack Stress Response at Different Inclination Angles
4. Conclusions
- (1)
- Crack length, depth, and inclination angle significantly influence crack-tip stress. Under thermo-mechanical loading, thermal expansion inhomogeneity leads to strong stress concentration at the crack tip. Specifically, as the crack length increases from 400 to 1000 μm, the maximum tensile stress rises from 104.02 to 238.51 MPa. In contrast, increasing crack depth results in reduced crack-tip stress, indicating a negative correlation.
- (2)
- When crack depth increases from 50 to 200 μm, the maximum crack-tip stress decreases from 205.89 to 101.65 MPa. Shallow cracks are less constrained by surrounding material, resulting in higher local stress concentration, whereas deeper cracks are more constrained, promoting a more uniform stress field. Crack inclination also significantly affects stress behavior. As inclination increases, the crack-tip stress decreases, and the stress direction transitions from tensile to compressive.
- (3)
- When the inclination angle reaches 40°, the stress drops sharply and changes from tensile to compressive. With further increases in inclination, the compressive stress intensifies and becomes more uniformly distributed, indicating that higher inclination angles help mitigate stress concentration and reduce the risk of crack propagation.
- (4)
- Laser scoring treatment was shown to effectively reduce crack-tip stress by shortening the effective crack length and modifying the local stress direction. At a crack length of 1000 μm, the post-scoring stress was comparable to that of a 400 μm crack, confirming the scoring’s regulatory effect. Additionally, scoring reversed the stress direction from tensile to compressive, suppressing crack extension.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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ElementSize/μm | Grid Size Near Crack/μm | Number of Elements | Maximum Mises/GPa | Time Step Range/s | ElementSize/μm | Grid Size Near Crack/μm | Number of Elements |
---|---|---|---|---|---|---|---|
10 | 0.2–0.3 | 51966 | 2.68 | 10–20–30 | 10 | 0.2–0.3 | 51966 |
15 | 0.3–0.4 | 24834 | 2.69 | 20–30–40 | 15 | 0.3–0.4 | 24834 |
25 | 0.4–0.5 | 10345 | 2.67 | 30–40–50 | 25 | 0.4–0.5 | 10345 |
45 | 0.5–0.6 | 4299 | 2.69 | 40–50–60 | 45 | 0.5–0.6 | 4299 |
Material | Temperature /°C | Elastic Modulus /GPa | Poisson’s Ratio | Coefficient of Thermal Expansion/10−5°C−1 | Density /kg·m−3 | Specific Heat/J·kg−1°C−1 | Conductivity/W·m−1K−1 |
---|---|---|---|---|---|---|---|
LaMgAl11O19 | 20 | 28.83 | 0.23 | 0.83 | 3321 | 578.4 | 1.53 |
200 | 25.47 | / | 0.95 | / | 805.4 | 1.18 | |
400 | 22.11 | / | 1.05 | / | 913.2 | 0.82 | |
600 | 18.75 | / | 1.10 | / | 1007.9 | 0.65 | |
800 | 15.37 | / | 1.15 | / | 1055.3 | 0.52 | |
1000 | 12.01 | / | 1.20 | / | 1089.6 | 0.41 | |
1200 | 8.65 | / | 1.30 | / | 1094.5 | 0.32 | |
YSZ | 20 | 48 | 0.1 | 1.04 | 5280 | 450 | 1.80 |
200 | 47 | / | 1.05 | / | 491 | 1.76 | |
500 | 43 | / | 1.07 | / | 532 | 1.75 | |
700 | 39 | / | 1.08 | / | 573 | 1.72 | |
1100 | 25 | / | 1.09 | / | 615 | 1.69 | |
1200 | 22 | / | 1.10 | / | 656 | 1.67 | |
TGO | 20 | 3978 | 0.27 | 0.8 | 1000 | / | 10 |
200 | 390 | / | 0.82 | / | / | 7.8 | |
400 | 380 | / | 0.84 | / | / | 6.0 | |
1000 | 325 | / | 0.93 | / | / | 4.4 | |
NiCoCrAlY | 25 | 225 | 0.30 | 1.20 | 7320 | 501 | 4.30 |
400 | 186 | / | 1.39 | / | 592 | 6.40 | |
600 | 166 | / | 1.48 | / | 670 | 8.00 | |
800 | 147 | / | 1.55 | / | 781 | 10.20 |
Material | Temperature/°C | Stress/MPa | Plastic Strain | A (10−11·MPa−n·s−1) |
---|---|---|---|---|
NiCoCrAlY | 25 | 1000 | 0 | / |
400 | 2500 | 0.23 | / | |
600 | 2200 | 0.3 | / | |
800 | 375 | 0.022 | / | |
900 | 60 | 0.02 | / | |
1000 | 19 | 0.01 | / | |
1100 | / | / | 1.35 | |
TGO | 1100 | / | / | 5.0299 |
Material | B/MPa−n·s−1 | N | Temperature/°C |
---|---|---|---|
TC | 1.8 × (10−11–10−5) | 1 | 1000 |
TGO | 7.3 × (10−12–10−4) | 1 | 1000 |
BC | 6.54 × 10−19 | 4.57 | ≤600 |
2.2 × 10−12 | 2.99 | 700 | |
1.84 × 10−7 | 1.55 | 800 | |
2.15 × 10−8 | 2.45 | ≥850 | |
SUB | 4.85 × 10−36 | 1 | 10 |
2.25 × 10−9 | 3 | 1200 |
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Zhang, L.; Dou, R.; Liu, N.; Sun, J.; Liu, X.; Wen, Z. Coupled Thermo-Mechanical Modeling of Crack-Induced Stress Fields in Thermal Barrier Coatings with Varying Crack Geometries. Coatings 2025, 15, 785. https://doi.org/10.3390/coatings15070785
Zhang L, Dou R, Liu N, Sun J, Liu X, Wen Z. Coupled Thermo-Mechanical Modeling of Crack-Induced Stress Fields in Thermal Barrier Coatings with Varying Crack Geometries. Coatings. 2025; 15(7):785. https://doi.org/10.3390/coatings15070785
Chicago/Turabian StyleZhang, Linxi, Ruifeng Dou, Ningning Liu, Jian Sun, Xunliang Liu, and Zhi Wen. 2025. "Coupled Thermo-Mechanical Modeling of Crack-Induced Stress Fields in Thermal Barrier Coatings with Varying Crack Geometries" Coatings 15, no. 7: 785. https://doi.org/10.3390/coatings15070785
APA StyleZhang, L., Dou, R., Liu, N., Sun, J., Liu, X., & Wen, Z. (2025). Coupled Thermo-Mechanical Modeling of Crack-Induced Stress Fields in Thermal Barrier Coatings with Varying Crack Geometries. Coatings, 15(7), 785. https://doi.org/10.3390/coatings15070785