考虑多源不确定性的复合材料风扇叶片高周疲劳失效概率评估

唐旭; 陈勇; 欧阳华; 田杰

doi:10.13224/j.cnki.jasp.20240654

考虑多源不确定性的复合材料风扇叶片高周疲劳失效概率评估

doi: 10.13224/j.cnki.jasp.20240654

唐旭^1,,
陈勇^{1, 2},
欧阳华^{1, 2},
田杰^{1, 2}

1.
上海交通大学机械与动力工程学院，上海 200240
2.
上海交通大学燃气涡轮与民用航空发动机教育部工程研究中心，上海 200240

基金项目: 国家重点研发计划（2023YFB3709805）

详细信息

作者简介:
唐旭（1996-），男，博士生，主要从事复合材料风扇叶片结构完整性概率分析方法研究。E-mail：t1996422@sjtu.edu.cn

中图分类号: V231.3
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- 文章访问数: 88
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- 被引次数: 0
出版历程
- 收稿日期: 2024-09-20
- 网络出版日期: 2026-03-23

High cycle fatigue failure probability assessment including multi source uncertainties with application to composite fan blades

TANG Xu^1
,,
CHEN Yong^{1, 2},
OUYANG Hua^{1, 2},
TIAN Jie^{1, 2}

1.
School of Mechanical Engineering，Shanghai Jiao Tong University，Shanghai 200240，China
2.
Engineering Research Center of Gas Turbine and Civil Aero Engine，Ministry of Education，Shanghai Jiao Tong University，Shanghai 200240，China

摘要

摘要:
为研究多源不确定性作用下铺层复合材料风扇叶片高周疲劳失效概率，并揭示复合材料单向带竞争损伤模式，采用非局部Weakest-link模型描述材料疲劳极限固有分散性；基于非平稳高斯随机场表征制造缺陷，建立关于多源不确定性随机向量的代理模型；最后使用蒙特卡洛法求解失效概率和Sobol敏感性系数。各典型模态的设计曲线均表明：在设计转速，叶片相对疲劳强度比95%分位数为0.142，纤维间损伤是主要失效模式；相比扭转模态和弦向弯曲模态，一阶弯曲模态具有最低的分位数。全局一阶敏感性系数说明：总阻尼比对纤维间损伤条件失效概率影响最大，其次是气动激励幅值。稳健性分析结果显示：总阻尼比认知和随机不确定性均占据主导；随着铺层厚度变异性增大，纤维间损伤总失效概率趋于一致。
- 高周疲劳 /
- 复合材料风扇叶片 /
- 随机过程 /
- Weakest-link模型 /
- 失效概率
Abstract:
To investigate the influence of multi-source uncertainties on failure probability of high cycle fatigue of laminated composite fan blade in response to the forced vibrations, and to capture the competing damage modes of laminas, aleatory uncertainty of material fatigue limit was evaluated by non-local Weakest-link model. Non-stationary Gaussian random field was employed to represent manufacturing defects. Surrogate model between stochastic input vector and conditional failure probability was constructed, and failure probability was computed by drawing samples of the joint probability density function using Monte Carlo method. Then, sensitivity indices by Sobol’s decomposition were obtained. All design curves with weak-link points as references of critical modal vibratory stresses showed that 95% quantiles of fatigue strength ratio at design rotation speed was 0.142 after considering typical vibration modes, and the failure mechanism was inter-fiber damage mode, in which the bending mode had the lowest value than torsional and chordwise shapes. The first-order Sobol’s indices indicated that the total damping ratio exerted the most significant effect on conditional failure probability, followed by unsteady aerodynamic pressure. Moreover, result from robustness analyses illustrated their uncertainties, and also had a significant influence on total probability of inter-fiber damage. Probability was approximate to the same level when the coefficient of variation for ply thickness increased.
- high cycle fatigue /
- composite fan blade /
- stochastic process /
- weakest-link model /
- failure probability

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图 1 防止转子叶片高周疲劳失效确定性设计方法

Figure 1. Deterministic design method against HCF failure for rotor blades

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图 2 Weakest-link理论示意图

Figure 2. Schematic of Weakest-link theory

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图 3 铺层厚度不确定性表征

Figure 3. Uncertainty representation for thickness of layers

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图 4 铺层厚度非平稳高斯随机过程2条轨迹

Figure 4. Two sample trajectories of ply thickness from non-stationary Gaussian stochastic process

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图 5 名义设计工况气动压力幅值

Figure 5. Amplitude of harmonic aero-forcing in nominal design operating condition

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图 6 复合材料风扇叶片高周疲劳条件失效概率评估流程

Figure 6. Flowchart for evaluating HCF conditional failure probability of composite fan blades

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图 7 复合材料风扇盘片旋转周期子结构

Figure 7. Substructure of composite fan blade-disk assembly with rotational symmetry

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图 8 参考最大振动应力点的高周疲劳失效概率设计曲线

Figure 8. Failure probability design curve of HCF design by the critical vibratory stress points

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图 9 参考薄弱点的高周疲劳失效概率设计曲线

Figure 9. Failure probability design curve of HCF design by the weak-link points

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图 10 各损伤模式概率设计曲线

Figure 10. Probability design curve for each damage mode

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图 11 两个层合板最里侧铺层纤维间损伤叠加等效应力

Figure 11. Superimposed equivalent stresses corresponding to inter-fiber damage mode for the innermost ply of two laminates

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图 12 代理模型多项式拟合系数

Figure 12. Coefficients of polynomials in surrogate model

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图 13 高周疲劳条件失效概率全局一阶敏感性系数

Figure 13. First-order global sensitivity indices of conditional HCF probability

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图 14 不同认知不确定性总体高周疲劳失效概率

Figure 14. Total HCF failure probability within the value range from epistemic uncertainties

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图 15 不同变异系数总体高周疲劳失效概率

Figure 15. Total HCF failure probability at different coefficients of variation

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表 1 单向带极限拉伸强度（UTS）、临界应力比和疲劳强度比

Table 1. Homogeneous ultimate tensile strengths （UTS）, critical stress ratios and fatigue strength ratios

铺层应力分量	UTS/MPa	χ	Ψχ
σ₁	2586	−0.533	0.255
σ₂	129.1	−2.623	0.331
σ₃	75.2	−2.896	0.331
σ₄	126.2	−1	0.350
σ₅	140.6	−1	0.350
σ₆	120.6	−1	0.350

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表 2 气动激励幅值和叶片阻尼不确定性

Table 2. Uncertainties from aerodynamic excitation amplitude and damping of blades

物理量	名义值	分布	区间
F	见图4	N（0, 0.1）	[−0.29, 0.29]
ζ	0.93%N（0, 0.1） [−0.1, 0.1]	N（0, 0.1）	[−0.29, 0.29]

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表 3 Puck纤维间断裂面强度准则参数

Table 3. Parameters of Puck’s action plane strength criterion for inter-fiber fracture

$ f_{\text{w}}^{{ （{\mathrm{if}}） }} $	$ R_{\bot }^{ （+） } $	$ R_{\bot }^{ （-） } $	$ {R}_{\bot \parallel } $	$ p_{{}_{\bot \bot }}^{ （+） } $	$ p_{{}_{\bot \bot }}^{ （-） } $	$ p_{{}_{\bot \parallel }}^{ （{+}） } $	$ p_{{}_{\bot \parallel }}^{ （{-}） } $
0.85	UTS（σ₂）	UCS（σ₂）	UTS（σ₅）	0.25	0.2	0.35	0.3

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表 4 不确定性参数和条件高周疲劳失效概率取值

Table 4. Values of uncertain parameters and conditional HCF failure probability

z₅/1	z₆/1	z₇/1	z₈/1	z₉/1	z₁₀/1	P_f（$\sigma^{\mathrm{crit}}_{\mathrm{a}} $\|z）
0.1043	0.4971	0.1266	−1.650	−0.6	−0.6	9.484×10⁻⁶
−2.083	0.5671	0.7916	0.8798	−0.6	−0.6	9.539×10⁻⁶
0.1970	−0.0302	0.4178	0.3484	−0.6	−0.6	8.981×10⁻⁶
1.733	−0.6513	−1.668	−1.521	−0.6	−0.6	9.573×10⁻⁶
−0.5885	−0.3413	0.4257	−2.188	0.9	0.9	2.294×10⁻³
0.2305	1.252	−2.245	−0.5123	0.9	0.9	3.128×10⁻³
−0.2289	0.1488	−0.4780	0.0244	0.9	0.9	2.939×10⁻³
−0.7097	0.8967	−0.8985	0.3552	0.9	0.9	2.404×10⁻³

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