Analysis of local stress at hole edge of air-cooled blade with thermal barrier coatings
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摘要:
基于有限元法计算了热障涂层-基体系统热失配状态下的孔边应力，计算结果表明：涂层界面法向应力和界面切应力集中于孔边，孔边周向正应力较大，孔边涂层容易出现开裂和剥落。计算并分析了陶瓷层厚度、计算模型外径、氧化层厚度、孔径和温度分布对孔边局部应力的影响，结果表明：界面法向应力和界面切应力的作用范围随陶瓷层厚度的增加而增大，叶片冷却孔边应力计算子模型外径应大于4倍陶瓷层厚度与1/2孔径之和；冷却状态下，氧化层厚度的增加会增大界面法向正应力和界面切应力；高温下，孔径越小孔边陶瓷层周向正应力越大；在孔边温度非均匀分布的情况下界面应力和孔边周向正应力会增大。
Abstract:The stress distributions of the thermal barrier coating-substrate system with a hole under thermal mismatch were calculated using finite element method. Calculation results indicated that the interfacial normal/shear stress concentration occurred at the edge of the film hole, and higher circumferential stress existed near the edge of the hole. The coating near the hole edge was prone to cracking and spalling. The effects of the thickness of the ceramic layer, the outer diameter of the model, the thickness of the oxide layer, the hole diameter, and the temperature distribution on the local stress near the hole edge were calculated and analyzed. Results revealed that the region with interfacial normal and shear stress became larger while the thickness of the ceramic layer increased. The outer diameter of the sub-model, which was used to calculate the stress near the edge of the film hole, should be greater than the sum of four times of the ceramic layer’s thickness plus half of the diameter of the hole. Under the cooling condition, the interfacial normal and shear stress increased with the thickness of the oxide layer. At high temperature, the circumferential stress at the edge of the ceramic layer near the hole decreased with the diameter of the hole. The interfacial stress and circumferential stress near the hole edge increased in the case of non-uniform temperature distribution.
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图 1 涡轮叶片有限元模型、孔边子模型及含中心孔圆盘几何模型
Figure 1. Finite element model of the practical turbine blade, the submodel of the area near the film hole and the geometric model for numerical calculation in terms of the characteristics of the film hole
图 2 不同温度差及不同氧化层厚度时径向应力σx分布
Figure 2. Distributions of the radial stress σx for different temperature differences and the thicknesses of TGO
图 3 不同温度差及不同TGO厚度时切应力τxy分布
Figure 3. Distributions of the shear stress τxy for different temperature differences and the thicknesses of TGO
图 4 不同温度差及不同TGO厚度时TC界面切应力分布
Figure 4. Distributions of the shear stress at the TC interface for different temperature differences and thicknesses of TGO layer
图 5 不同温度差及不同TGO厚度时垂直于界面的轴向正应力σy分布
Figure 5. Distributions of the axial stress σy for different temperature differences and thicknesses of TGO layer
图 6 不同温度差及TGO厚度时TC界面法向正应力分布
Figure 6. Distributions of the normal stress σy at the TC interface for different temperature differences and thicknesses of TGO layer
图 7 Δtw=100 ℃时不同TGO厚度模型中周向正应力σz分布
Figure 7. Distributions of the circumferential stress σz for different thicknesses of TGO layer while Δtw=100 ℃
图 9 t=20℃时不同TC厚度时TC界面法向正应力及切应力分布
Figure 9. Distributions of the normal and shear stress at the TC interface for different thicknesses of TC layer while t=20℃
图 10 t=20 ℃时不同边界条件时TC界面法向正应力及切应力分布
Figure 10. Distributions of the normal and shear stress at the TC interface for different boundary conditions while t=20 ℃
图 11 t=20 ℃时不同TGO厚度时TC界面法向正应力及切应力
Figure 11. Distributions of the normal stress and shear stressat the TC interface for different thicknesses of TGO layer while t=20 ℃
图 12 t=20℃时不同孔径时TC界面法向正应力和切应力分布
Figure 12. Distributions of the normal and shear stress at the TC interface for different hole diameters while t=20℃
图 13 温度沿径向分布示意图
Figure 13. Illustration of the distribution of temperature along the radial direction
图 14 th= 1000 ℃时，沿径向温度差不同时，TC界面法向正应力及切应力分布
Figure 14. Distributions of the normal and shear stress at the TC interface for different temperature differences along the radial direction while th=1000 ℃
图 15 孔边温度不同，沿径向温度差为200 ℃时，TC界面法向正应力及切应力分布
Figure 15. Distributions of the normal and shear stress at the TC interface for different temperatures near the hole while the temperature difference of 200 ℃ along the radial direction
图 16 沿径向温度差为150℃，温度沿径向分布趋势不同时，TC界面法向正应力及切应力分布（th=900 ， 1100 ℃）
Figure 16. Distributions of the normal and shear stress at the TC interface while the temperature difference of 150℃ along the radial direction for different temperature distributions along the radial direction (th=900 ， 1100 ℃)
图 17 不同温度分布形式下TC层中周向应力σz
分布 Figure 17. Distributions of the circumferential stress σz in TC layer for different temperature distribution forms
表 1 热障涂层系统各层材料参数[12]
Table 1. Material parameters of each layer of the thermal barrier coating system[12]
涂层结构
（材料）弹性模量
E/GPa泊松比
ν线膨胀系数
α/（10−6·K−1）TC（YSZ） 48 0.1 9.0 TGO（Al2O3） 400 0.23 8.0 BC（MCrAlY） 200 0.3 13.6 基体
（PWA 1480）184 0.3 12.0 
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表 2 Δtw=100
$ {{\text{℃}}} $ ，各层径向应力理论解和有限元计算结果对比Table 2. Comparison of the radial stress obtained from analytical method and finite element method respectively while Δtw=100
$ {{\text{℃}}} $ 模型 位置 理论解
σx,a/MPa有限元解
σx,f/MPa$\left(\dfrac{ { {\sigma _{x,{\text{f} } } } - {\sigma _{x,{\text{a} } } } } }{ { {\sigma _{x,{\text{a} } } } } }\right)\Big/\text{%}$ 无氧化层 TC 16.345 16.334 −0.067 BC −43.883 −43.919 −0.082 基体 1.681 1.654 −1.606 有氧化层 TC 16.319 16.304 −0.092 TGO 210.877 210.765 −0.053 BC −44.020 −44.079 0.134 基体 1.556 1.506 −3.213
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表 3 1150
$ {{\text{℃}}} $ 下TC层内部径向应力及孔边周向应力的最大值Table 3. Radial stress inside TC layer and maximum value of the circumferential stress near the hole under 1150
$ {{\text{℃}}} $ Htc/μm TC内部径向
应力σx/MPaTC孔边周向应力
最大值σz,max/MPa100 24.90 27.34 200 24.61 32.83 250 24.46 35.26 300 24.31 37.15 400 24.03 39.83
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表 4 模型外径不同时应力计算结果及差异对比
Table 4. Comparison of stress calculation results and differences of different model outer diameters
模型
外半径Rt=20 ℃ t=1150 ℃ TC界面法向
正应力最大值
σy,max/MPa法向正应力
差异δσ,n/%TC界面
切应力最大值
τxy,max/MPa切应力
差异δτ/%外圆周面
节点径向位移
sx,o/mmTC层孔边周向
应力最大值
σz,,max/MPa周向正应力
差异δσ,c/%50Htc
（参考值）568.90 77.65 −147.86 35.26 30Htc 568.99 0.02 77.66 0.01 −88.62 35.26 0 10Htc 568.95 0.01 77.65 0 −29.54 35.26 0 6Htc 570.75 0.33 77.80 0.19 −17.72 35.38 0.34 5Htc 573.31 0.78 77.98 0.42 −14.77 35.48 0.62 4Htc 588.31 3.41 78.78 1.46 −11.81 35.33 0.20
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表 5 t=1 150
${{\text{℃}}}$ 时，不同TGO厚度下TC层内部径向应力及孔边周向应力最大值Table 5. Radial stress inside TC layer and the maximum value of the circumferential stress in the TC layer near the hole while t
=1 150 ${{\text{℃}}}$ for different thicknesses of TGO layerHtgo/μm TC内部径向应力
σx/MPaTC孔边周向应力
最大值σz/MPa1 24.55 35.26 2 24.48 35.39 3 24.42 35.53 5 24.28 35.79 8 24.09 36.17
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表 6 不同孔径时1150
${{\text{℃}}} $ 下陶瓷层内部径向应力及孔边周向应力最大值Table 6. Radial stress inside the TC layer and the maximum value of the circumferential stress in TC layer near the hole under 1150
${{\text{℃}}} $ against the diameter of the holeRh/Htc TC内部径向应力
σx/MPaTC孔边周向应力
最大值σz,max/MPa1 24.49 41.88 2 24.55 35.26 3 24.53 31.74 4 24.43 29.66
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