考虑多因素协同作用的单晶高温合金高周疲劳强度预测模型

刘星月; 刘海燕; 张晓杰; 胡殿印; 刘茜; 毛建兴; 张斌

doi:10.13224/j.cnki.jasp.20250200

考虑多因素协同作用的单晶高温合金高周疲劳强度预测模型

doi: 10.13224/j.cnki.jasp.20250200

刘星月^1,,
刘海燕¹,
张晓杰^2,*, ,,
胡殿印^{1, 3, 4},
刘茜²,
毛建兴^{1, 4},
张斌⁵

1.
北京航空航天大学航空发动机研究院，北京 100191
2.
北京航空航天大学能源与动力工程学院，北京 100191
3.
北京航空航天大学航空发动机结构强度北京市重点实验室，北京 100191
4.
中小型航空发动机联合研究中心，北京 100191
5.
杭州市北京航空航天大学国际创新研究院（北京航空航天大学国际创新学院），杭州 311115

基金项目: 国家自然科学基金（52205081）

详细信息

作者简介:
刘星月（1999-），女，硕士，主要研究方向为结构强度与可靠性。E-mail：lxytxb0@163.com

通讯作者:
张晓杰（1994-），女，副教授，博士，主要研究方向为结构强度、振动和气动弹性。E-mail：zxjbuaa@buaa.edu.cn

中图分类号: V232.4
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- 被引次数: 0
出版历程
- 收稿日期: 2025-04-24
- 网络出版日期: 2025-11-04

High-cycle fatigue strength prediction model of single crystal superalloy considering multi-factor synergy

LIU Xingyue^1
,,
LIU Haiyan¹,
ZHANG Xiaojie^{2,*
, ,},
HU Dianyin^{1, 3, 4},
LIU Xi²,
MAO Jianxing^{1, 4},
ZHANG Bin⁵

1.
Research Institute of Aero-Engine，Beihang University，Beijing 100191，China
2.
School of Energy and Power Engineering，Beihang University，Beijing 100191，China
3.
Beijing Key Laboratory of Aero-Engine Structure and Strength，Beihang University，Beijing 100191，China
4.
United Research Center of Mid-Small Aero-Engine，Beijing 100191，China
5.
Hangzhou International Innovation Institute of Beihang University，Hangzhou 311115，China

摘要

摘要:
通过开展不同一次取向偏角（1.5°～7.1°）、温度（850 ℃和980 ℃）和应力比（−1、−0.33、0.1、0.5、0.8和0.9）条件下的气膜孔模拟件高周疲劳试验，结合疲劳断口宏微观形貌分析，系统揭示了晶体取向、温度场与载荷参数对疲劳强度的影响规律。基于Kitagawa-Takahashi（K-T）图法框架，结合EI-Haddad模型与平均应力修正理论，构建了多因素协同作用的高周疲劳强度预测模型。结果表明：疲劳断口均呈现类解离断裂特征，未观察到缩颈或明显伸长现象，疲劳裂纹主要萌生于气膜孔附近，并沿{111}晶体学滑移平面扩展。当一次取向偏角小于7.1°时，疲劳强度的差异不超过2%，显示该阈值范围内的取向不敏感性。温度效应表现为显著的高周疲劳强度衰减规律，980 ℃下的疲劳强度较850 ℃下降了12.4%。恒寿命曲线（2×10⁷循环周次）呈现典型外凸特性：低应力比区（R<0.5）平均应力增速为高应力比区（R>0.5）的3.44倍，而应力幅值衰减速率呈现相反规律。建立的疲劳强度模型显示预测值与试验值相比误差小于7.7%，表明该模型在复杂多因素耦合条件下的工程适用性，可以为先进航空发动机单晶涡轮叶片的抗疲劳优化设计提供重要理论支撑。
- 单晶高温合金 /
- 气膜孔 /
- 应力集中 /
- 高周疲劳 /
- 疲劳强度预测
Abstract:
The influences of crystal orientation, temperature field and load parameters on fatigue strength were systematically revealed by carrying out high-cycle fatigue tests of film cooling hole simulants under different primary orientation declination angles (1.5°—7.1°), temperatures (850 ℃ and 980 ℃) and stress ratios (−1, −0.33, 0.1, 0.5, 0.8 and 0.9). Based on the Kitagawa-Takahashi (K-T) diagram framework, combined with the EI-Haddad model and the average stress correction theory, a high-cycle fatigue strength prediction model with multi-factor synergy was constructed. The results showed that the fatigue fractures all presented the characteristics of dissociation-like fractures, and no necking or obvious elongation was observed, and the fatigue cracks mainly originated near the film cooling hole and propagated along the {111} crystallographic slip plane. When the primary orientation declination angle was less than 7.1°, the difference in fatigue strength did not exceed 2%, indicating that the orientation within this threshold range was insensitive. The temperature effect showed a significant attenuation law of high-cycle fatigue strength, and the fatigue strength at 980℃ decreased by 12.4% compared with 850 ℃. The constant life curve (2×10⁷ cycles) showed typical convex characteristics: in the low stress ratio region (R<0.5), the average stress growth rate was 3.44 times of the high stress ratio region (R>0.5), while the stress amplitude decay rate showed an opposite law. The established fatigue strength model showed that the error of the predicted value was less than 7.7% compared with the experimental value, indicating that the engineering applicability of the model under the condition of complex multi-factor coupling can provide important theoretical support for the fatigue optimization design of single crystal turbine blades of advanced aero engines.
- single crystal superalloys /
- film cooling holes /
- stress concentration /
- high cycle fatigue /
- fatigue strength prediction

HTML

图 1 高周疲劳强度预测流程图

Figure 1. Flow chart of high-cycle fatigue strength prediction

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图 2 试样尺寸（单位：mm）

Figure 2. Sample size （unit：mm）

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图 3 试样1在不同一次取向偏角下的升降数据图

Figure 3. Data of the up-down method of sample 1 at different primary orientation declination angles

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图 4 试样2在不同一次取向偏角下的升降数据图

Figure 4. Data of the up-down method of sample 2 at different primary orientation declination angles

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图 5 不同温度下的升降数据图

Figure 5. Data of the up-down method at different temperatures

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图 6 不同应力比下的升降图

Figure 6. Data of the up-down method at different stress ratios

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图 7 寿命为2×10⁷循环周次的恒寿命图

Figure 7. Constant life diagram with a lifetime of 2×10⁷ cycles

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图 8 不同一次取向偏角下的断口侧面形貌

Figure 8. Fracture side morphology under different primary orientation declination angles

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图 9 不同应力比下的断口侧面形貌

Figure 9. Fracture side morphology under different stress ratios

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图 10 断口表面形貌

Figure 10. Fracture surface topography

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图 11 不同一次取向偏角下的γ′相形貌

Figure 11. γ′ phase morphology under different primary orientation declination angles

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图 12 不同应力比下的γ′相形貌

Figure 12. γ′ phase morphology at different stress ratios

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图 13 网格模型示意图

Figure 13. Diagram of the meshed model

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图 14 试样等效应力分布

Figure 14. Equivalent stress distribution of the specimen

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图 15 缺陷尺寸参数与应力集中系数的关系

Figure 15. Relationship between the notch size parameter and the stress concentration coefficient

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图 16 平均应力模型在2×10⁷循环周次下的恒寿命图

Figure 16. Constant life plot of the average stress model at2×10⁷ cycles

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图 17 基于Gerber模型建立修正的平均应力模型

Figure 17. Lateral morphology of the fracture under different primary orientation declination angles

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表 1 试验条件

Table 1. Test conditions

试样形式	气膜孔倾角/ （°）	取向偏角/ （°）	温度/ ℃	应力比	数量/ 件
试样1	90	1.5	850	−1	16
试样1	90	5.5	850	−1	16
试样2	40	1.6	850	−1	15
	40	1.6	850	−0.33	15
	40	2.2	850	0.1	15
	40	2.2	850	0.5	15
	40	2.3	850	0.8	15
	40	2.3	850	0.9	15
	40	7.1	850	−1	12
	90	5.5	850	−1	15
	90	5.5	980	−1	15

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表 2 不同一次取向偏角下试样的疲劳强度

Table 2. Fatigue strength of the specimen at different primary orientation declination angles

试样形式	气膜孔倾角/（°）	一次取向偏角/（°）	温度/ ℃	应力比	疲劳强度/ MPa
试样1	90	1.5	850	−1	230
试样1	90	5.5	850	−1	232
试样2	40	1.6	850	−1	225
试样2	40	7.1	850	−1	229

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表 3 不同温度下试样的疲劳强度

Table 3. Fatigue strength of the specimen at different temperatures

试样形式	气膜孔倾角/（°）	一次取向偏角/（°）	温度/ ℃	应力比	疲劳强度/ MPa
试样2	90	5.5	850	−1	235
试样2	90	5.5	980	−1	209

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表 4 不同应力比下试样的疲劳强度

Table 4. Fatigue strength of the specimen at different stress ratios

试样形式	气膜孔倾角/（°）	一次取向偏角/（°）	温度/℃	应力比	平均应力/MPa	应力幅值/MPa
试样2	40	1.6	850	−1	0	225.0
	40	1.6	850	−0.33	109.0	216.5
	40	2.2	850	0.1	260.4	213.0
	40	2.2	850	0.5	545.6	182.0
	40	2.3	850	0.8	688.5	76.5
	40	2.3	850	0.9	704.0	37.0

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表 5 气膜孔模拟件的疲劳强度

Table 5. Fatigue strength of a simulated film cooling hole part

试样形式	气膜孔倾角/（°）	一次取向偏角/（°）	温度/ ℃	应力比	疲劳强度/MPa
试样1	90	1.5	850	−1	230
试样2	40	1.6	850	−1	225
	40	7.1	850	−1	229
	90	5.5	850	−1	235

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表 6 第二代单晶高温合金材料参数

Table 6. Material parameters of the second generation of single-crystal superalloys

材料参数	数值
材料参数	t=850 ℃	t=980 ℃
E_[001]/GPa	98.0	80.5
E_[011]/GPa	137.5	145.0
E_[111]/GPa	205.0	217.5
ν_[001]	0.383	0.390
C₁₁/GPa	186.8	160.6
C₁₂/GPa	116.0	102.7
C₄₄/GPa	80.4	74.2

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表 7 不同试样的应力集中系数${\boldsymbol{K}}_{\bf{t}}' $

Table 7. Stress concentration coefficient ${\boldsymbol{K}}_{\bf{t}}' $ of different specimens

试样形式	气膜孔倾角/（°）	一次取向偏角/（°）	温度/℃	应力比	疲劳强度/MPa	应力集中系数$K_{\rm{t}}' $
试样1	90	1.5	850	−1	230	1.378
试样2	40	1.6	850	−1	225	1.547
	40	7.1	850	−1	229	1.444
	90	5.5	850	−1	235	1.381

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表 8 气膜孔模拟件的疲劳强度

Table 8. Fatigue strength of a simulated film cooling hole part

试样形式	气膜孔倾角/（°）	一次取向偏角/（°）	温度/℃	应力比	疲劳强度/MPa
试样2	40	1.6	850	−1	225
	40	2.2	850	0.1	213
	40	2.2	850	0.5	182
	40	2.3	850	0.9	37

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表 9 不同试验条件下的疲劳强度预测

Table 9. Fatigue strength prediction under different test conditions

试样形式	气膜孔倾角/（°）	一次取向偏角/（°）	温度/℃	应力比	试验值/MPa	预测值/MPa	误差/%
试样1	90	5.5	850	−1	232.0	232.1	0.04
试样2	40	1.6	850	−0.33	216.5	220.5	1.85
	40	2.3	850	0.8	76.5	74.5	2.61
	90	5.5	980	−1	209	224.9	7.61

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