基于开裂能密度的柔性接头摆动疲劳寿命预测

张金尧; 任军学; 薛牧遥; 童悦; 郑庆; 汤海滨

doi:10.13224/j.cnki.jasp.20220826

基于开裂能密度的柔性接头摆动疲劳寿命预测

doi: 10.13224/j.cnki.jasp.20220826

张金尧^{1, 2,},
任军学^1,*, ,,
薛牧遥³,
童悦³,
郑庆³,
汤海滨¹

1.
北京航空航天大学宇航学院，北京 100191
2.
西安航天动力技术研究所，西安 710025
3.
上海航天动力技术研究所，上海 200125

基金项目: 基础加强计划技术领域基金（2020JCJQJJ014）

详细信息

作者简介:
张金尧（1997-），男，助理工程师，硕士，主要从事航空宇航推进理论与工程研究

通讯作者:
任军学（1980-），男，副教授，博士，主要从事航空宇航推进理论与工程研究。E-mail：rjx_buaa@163.com

中图分类号: V431
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出版历程
- 收稿日期: 2022-10-31
- 网络出版日期: 2023-11-30

Prediction of the swing fatigue life of flexible joint based on cracking energy density

ZHANG Jinyao^{1, 2
,},
REN Junxue^{1,*
, ,},
XUE Muyao³,
TONG Yue³,
ZHENG Qing³,
TANG Haibin¹

1.
School of Astronautics，Beihang University，Beijing 100191，China
2.
Xi’an Aerospace Solid Propulsion Technology Institute，Xi’an 710025，China
3.
Shanghai Space Propulsion Technology Research Institute，Shanghai 200125，China

摘要

摘要:
为准确预测柔性接头的摆动疲劳寿命，将开裂能密度作为驱动弹性件疲劳裂纹扩展的损伤参量，借助材料的疲劳裂纹扩展试验和单轴拉伸疲劳试验建立了柔性接头的摆动疲劳寿命预测模型，并用有限元分析结果计算了柔性接头在12.3 MPa、6°摆角工况下的开裂能密度，进而对柔性接头的摆动疲劳寿命进行预测。结果表明：预测试验工况下柔性接头的摆动疲劳寿命为107次，实测寿命为120次，两者较为一致，且预测的裂纹位置和开裂平面与实际试验的失效位置较为吻合。模型预测柔性接头的摆动疲劳寿命与实测疲劳寿命之比为1/1.12，分布在2倍分散因子之内，满足工程疲劳寿命的预测要求。
- 疲劳寿命预测 /
- 柔性接头 /
- 开裂能密度 /
- 裂纹扩展 /
- 有限元分析 /
- 固体火箭发动机
Abstract:
In order to accurately predict the swing fatigue life of flexible joint, the cracking energy density (CED) was used as the damage parameter to drive the fatigue crack growth of elastomers. The swing fatigue life prediction model of flexible joint was established by means of fatigue crack growth test and uniaxial tensile fatigue test. The CED of flexible joint under 12.3 MPa and 6° swing angle was calculated by using the finite element analysis results, and then the swing fatigue life of flexible joint was predicted. The results showed that the predicted swing fatigue life of the flexible joint under the test condition was 107 cycles, which was consistent with the measured fatigue life of 120 cycles, and the predicted crack location and crack plane were in good agreement with the failure position of test. The ratio of predicted life to measured life was 1/1.12 within the double dispersion factor, which was acceptable in engineering.
- fatigue life prediction /
- flexible joint /
- cracking energy density /
- crack propagation /
- finite element analysis /
- solid rocket motor

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图 1 橡胶疲劳裂纹受力状态示意图

Figure 1. Stress state of rubber fatigue crack

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图 2 单边预制裂纹的纯剪试件

Figure 2. Pure shear specimen with unilateral prefabricated crack

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图 3 电磁动态疲劳试验系统

Figure 3. Electromagnetic dynamic fatigue test system

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图 4 疲劳裂纹扩展试验变幅加载形式

Figure 4. Variable amplitude loading of fatigue crack growth test

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图 5 裂纹扩展速率随撕裂能峰值的变化关系

Figure 5. Relationship between crack growth rate and tear energy maximum

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图 6 双对数坐标系下裂纹扩展速率随撕裂能峰值的拟合关系

Figure 6. Fitting relationship between crack growth rate and tear energy maximum in double logarithmic coordinate

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图 7 哑铃形试件卸载段的应力应变曲线

Figure 7. Stress-strain curves in unloading section of dumbbell specimen

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图 8 双对数坐标系下不同应变峰值的单轴拉伸疲劳预测寿命与计算寿命的比较

Figure 8. Comparisons of the predicted uniaxial tensil fatigue life and calculated uniaxial tensil fatigue life with different strain maximum in double logarithmic coordinate

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图 9 柔性接头摆动试验装置

Figure 9. Swing test device for flexible joint

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图 10 摆动疲劳寿命试验后的柔性接头

Figure 10. Flexible joint after swing fatigue life test

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图 11 柔性接头有限元模型

Figure 11. Finite element model of flexible joint

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图 12 实际加载下的柔性接头有限元模型

Figure 12. Finite element model of flexible joint in fatigue test

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图 13 柔性接头疲劳寿命试验实际失效位置与预测开裂位置结果对比

Figure 13. Comparison between actual failure position and predicted failure position in fatigue life test of flexible joint

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表 1 纯剪试件静强度试验结果

Table 1. Static strength test results of pure shear specimens

试件编号	拉断应变ε_sb/%	拉断应力 σ_st/MPa	拉断应变能密度W_b/MPa	临界撕裂能 T_c/（kJ/m²）
a1（h₀=7.06 mm）	87.57	0.5103	0.4410	3.1136
a2（h₀=7.45 mm）	95.64	0.5015	0.4666	3.4759
a3（h₀=6.51 mm）	85.23	0.5108	0.4333	2.8206

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表 2 硅橡胶单轴拉伸疲劳试验结果

Table 2. Results of uniaxial tensile fatigue test of silicone rubber

编号	ε_max/%	ε_min/%	N_f,max/cycles	N_f,min/cycles	N_f,avg/cycles
1	200	0	4536	3657	4088
2	250	0	3065	2435	2776
3	300	0	1923	1437	1660
4	350	0	1593	1177	1349
5	400	0	1108	786	963

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表 3 柔性接头摆动疲劳寿命试验工况信息

Table 3. Condition of swing fatigue life test of flexible joint

环境温度/℃	试验压强/MPa	摆动频率/Hz	摆角幅值/(°)
23±2	12.3	1	±6

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表 4 弹性件材料本构模型拟合参数

Table 4. Constitutive parameter of elastomer

本构参数	μ₁/10⁻⁵	α₁	μ₂	α₂
拟合值	1.83663	10.303	21.539	0.02659

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表 5 柔性接头预测疲劳寿命与实测寿命对比

Table 5. Comparison between predicted fatigue life and measured fatigue life of flexible joint

预测开裂单元	开裂能密度峰值 W_c,max/MPa	开裂方位角 θ/rad	预测寿命 N_f,pre/cycles	实测寿命 N_f,test/cycles	N_f,pre/N_f,test
No.7505	5.585	θ=0，±π	107	120	1/1.12

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参考文献(21)

[1]	李太安. 固体火箭发动机柔性喷管使用性能分析[D]. 呼和浩特: 内蒙古工业大学,2015. LI Taian. Performance analysis of flexible nozzles for solid rocket motor[D]. Hohhot: Inner Mongolia University of Technology,2015. (in Chinese LI Taian. Performance analysis of flexible nozzles for solid rocket motor[D]. Hohhot: Inner Mongolia University of Technology, 2015. (in Chinese)
[2]	万诺,史宏斌,屈转利,等. 柔性接头疲劳摆动寿命分析研究[J]. 推进技术,2022,43(5): 269-277. WAN Nuo,SHI Hongbin,QU Zhuanli,et al. Analysis of fatigue properties and vectoring life of flexible joint[J]. Journal of Propulsion Technology,2022,43(5): 269-277. (in Chinese WAN Nuo, SHI Hongbin, QU Zhuanli, et al. Analysis of fatigue properties and vectoring life of flexible joint[J]. Journal of Propulsion Technology, 2022, 43(5): 269-277. (in Chinese)
[3]	RAVI CHANDRAN K S. Mechanical fatigue of polymers: a new approach to characterize the SN behavior on the basis of macroscopic crack growth mechanism[J]. Polymer,2016,91: 222-238. doi: 10.1016/j.polymer.2016.03.058
[4]	TEE Y L,LOO M S,ANDRIYANA A. Recent advances on fatigue of rubber after the literature survey by Mars and Fatemi in 2002 and 2004[J]. International Journal of Fatigue,2018,110: 115-129. doi: 10.1016/j.ijfatigue.2018.01.007
[5]	MARCO Y,HUNEAU B,MASQUELIER I,et al. Prediction of fatigue properties of natural rubber based on the descriptions of the cracks population and of the dissipated energy[J]. Polymer Testing,2017,59: 67-74. doi: 10.1016/j.polymertesting.2017.01.015
[6]	王小莉,上官文斌,曾祥坤,等. 基于开裂能密度及裂纹扩展特性的橡胶隔振器疲劳特性预测[J]. 振动与冲击,2016,35(6): 70-74. WANG Xiaoli,SHANGGUAN Wenbin,ZENG Xiangkun,et al. A method to predict fatigue performances of rubber isolator based on the cracking energy density and the fatigue crack growth characteristic of rubber material[J]. Journal of Vibration and Shock,2016,35(6): 70-74. (in Chinese WANG Xiaoli, SHANGGUAN Wenbin, ZENG Xiangkun, et al. A method to predict fatigue performances of rubber isolator based on the cracking energy density and the fatigue crack growth characteristic of rubber material[J]. Journal of Vibration and Shock, 2016, 35(6): 70-74. (in Chinese)
[7]	MARS W V. Cracking energy density as a predictor of fatigue life under multiaxial conditions[J]. Rubber Chemistry and Technology,2002,75(1): 1-17. doi: 10.5254/1.3547670
[8]	BELKHIRIA S,HAMDI A,FATHALLAH R. Cracking energy density for rubber materials: computation and implementation in multiaxial fatigue design[J]. Polymer Engineering & Science,2020,60(9): 2190-2203.
[9]	PAN Zheng,LAI Yaling,WANG Yanping,et al. Fatigue life prediction and effects of cerium oxide-filled vulcanized natural rubber on fatigue life under multiaxial loading[J]. Fatigue & Fracture of Engineering Materials & Structures,2021,44(12): 3349-3362.
[10]	金状兵. 基于开裂能的橡胶动态疲劳寿命预报[D]. 湖南湘潭: 湘潭大学,2014. JIN Zhuangbing. Fatigue life evaluation of rubber material based on crack energy density and dynamical mechanical analysis[D]. Xiangtan Hunan: Xiangtan University,2014. (in Chinese JIN Zhuangbing. Fatigue life evaluation of rubber material based on crack energy density and dynamical mechanical analysis[D]. Xiangtan Hunan: Xiangtan University, 2014. (in Chinese)
[11]	王小莉. 橡胶隔振器多轴疲劳寿命预测方法研究[D]. 广州: 华南理工大学,2014. WANG Xiaoli. Studies on life prediciton of multiaxial fatigue for rubber isolators[D]. Guangzhou: South China University of Technology,2014. (in Chinese WANG Xiaoli. Studies on life prediciton of multiaxial fatigue for rubber isolators[D]. Guangzhou: South China University of Technology, 2014. (in Chinese)
[12]	LAKE G J,LINDLEY P B. Cut growth and fatigue of rubbers Ⅱ: experiments on a noncrystallizing rubber[J]. Journal of Applied Polymer Science,1965,38(2): 301-313.
[13]	王昊,危银涛. 橡胶疲劳研究综述[J]. 轮胎工业,2015,35(10): 579-585. WANG Hao,WEI Yintao. Summary of rubber fatigue research[J]. Tire Industry,2015,35(10): 579-585. (in Chinese doi: 10.3969/j.issn.1006-8171.2015.10.001 WANG Hao, WEI Yintao. Summary of rubber fatigue research[J]. Tire Industry, 2015, 35(10): 579-585. (in Chinese) doi: 10.3969/j.issn.1006-8171.2015.10.001
[14]	THOMAS A G. Rupture of rubber V cut growth in natural rubber vulcanizates[J]. Rubber Chemistry and Technology,1959,32(2): 477-489. doi: 10.5254/1.3542412
[15]	LINDLEY P B. Non-relaxing crack growth and fatigue in a non-crystallizing rubber[J]. Rubber Chemistry and Technology,1974,47(5): 1253-1264. doi: 10.5254/1.3540497
[16]	MARS W V,FATEMI A. Fatigue crack nucleation and growth in filled natural rubber[J]. Fatigue & Fracture of Engineering Materials & Structures,2003,26(9): 779-789.
[17]	American Society for Testing and Materials (ASTM). Standard test method for rubber property-extension cycling fatigue: D4482-11[S]. West Conshohocken,US: ASTM,2021: 4-5.
[18]	AÏT-BACHIR M,MARS W V,VERRON E. Energy release rate of small cracks in hyperelastic materials[J]. International Journal of Non-Linear Mechanics,2012,47(4): 22-29. doi: 10.1016/j.ijnonlinmec.2012.03.001
[19]	GREENSMITH H W. Rupture of rubber X: the change in stored energy on making a small cut in a test piece held in simple extension[J]. Journal of Applied Polymer Science,1963,7(3): 993-1002. doi: 10.1002/app.1963.070070316
[20]	MARS W V,FATEMI A. A literature survey on fatigue analysis approaches for rubber[J]. International Journal of Fatigue,2002,24(9): 949-961. doi: 10.1016/S0142-1123(02)00008-7
[21]	张金尧. 基于开裂能的柔性接头摆动疲劳寿命预测[D]. 北京: 北京航空航天大学,2022. ZHANG Jinyao. Prediction of the swing fatigue life of flexible joint based on cracking energy density[D]. Beijing: Beihang University,2022. (in Chinese ZHANG Jinyao. Prediction of the swing fatigue life of flexible joint based on cracking energy density[D]. Beijing: Beihang University, 2022. (in Chinese)