基于压电信号的复合材料疲劳寿命评估方法

肖玉善; 吴振; 任晓辉

基于压电信号的复合材料疲劳寿命评估方法

1.
西北工业大学　航空学院, 西安 710072
2.
西安航空学院　机械工程学院, 西安 710072

基金项目: 国家自然科学基金 (12172295)

详细信息

通讯作者:
吴振，博士，教授，博士生导师，研究方向为复合材料结构力学　E-mail: wuzhenhk@nwpu.edu.cn

中图分类号: TB333
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- 文章访问数: 127
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- 被引次数: 0
出版历程
- 收稿日期: 2023-10-30
- 修回日期: 2023-12-31
- 录用日期: 2024-01-11
- 网络出版日期: 2024-02-22

Fatigue assessment for composites by using piezoelectric signal

1.
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China
2.
School of Mechanical Engineering, Xi’an Aeronautical University, Xi’an 710072, China

Funds: National Natural Science Foundation of China (12172295)

摘要

摘要: 复合材料结构应变特征随着疲劳加载发生变化，因此本文尝试实时监测疲劳周期内复合材料结构的应变特征信号，通过应变信号评估结构疲劳寿命。然而已有研究表明，电阻式应变片在长时间动态测试中经常出现提前疲劳失效，不适合疲劳全周期内应变信号采集。为此，具有高耐疲劳性的新型聚偏氟乙烯压电薄膜(PVDF)被用于采集复合材料结构疲劳特征信号。通过在碳纤维增强树脂基复合材料(T700/9A16)层合板表面粘贴PVDF薄膜，获取层合板疲劳过程中的压电信号。基于压电效应，将表征疲劳损伤状态的应变信息转化为PVDF压电信号输出。基于试验生成的压电信号数据库，采用随机森林回归算法高效地建立压电信号与复合材料层合板疲劳循环次数之间的关联。通过不同循环次数下的PVDF压电信号可以准确预测试验件的实际疲劳加载次数，实现了对复合材料结构疲劳状态的有效评估。
- 复合材料 /
- 剩余刚度 /
- 疲劳 /
- PVDF压电薄膜 /
- 疲劳评估 /
- 随机森林回归
Abstract: Considering the strain characteristics of the composite structures changing with fatigue loading, so that this paper attempts to monitor the strain characteristics in real time during the fatigue cycle and assesses the fatigue life through the strain signals. However, from the published literatures, resistance strain gauge often suffered from early fatigue failure in the long-time dynamic testing, which is not suitable for strain signal acquisition during the full fatigue cycle. Therefore, the novel polyvinylidene fluoride piezoelectric film (PVDF) with high fatigue resistance is used to acquire fatigue characteristic signals of composite structures. The piezoelectric signals during the fatigue process of the composite laminates are obtained by pasting PVDF on the surface of carbon fiber reinforced plastic (CFRP) plates (T700/9A16). Based on the piezoelectric effect, the strain information during the fatigue process is converted into the piezoelectric signal from PVDF. Then, a Random Forest Regression (RFR) algorithm is trained based on the database generated from the experimental tests to efficiently establish the correlation between the piezoelectric signals and fatigue cycles of composite laminates. Through the trained RFR network, the actual fatigue cycles of the test pieces can be accurately predicted based on the piezoelectric signals, in which the maximum percentage error of logarithms of fatigue cycles is controlled within 5%. This paper provides a new research idea and technical support for the fatigue life assessment of composite materials.
- Composite plate /
- residual stiffness /
- Fatigue /
- PVDF /
- Fatigue assessment /
- Random Forest Regression

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图 1 碳纤维复合材料(T700/9A16)疲劳试验件尺寸

Figure 1. Geometry of CFRP fatigue test piece (T700/9A16)

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图 2 碳纤维复合材料(T700/9A16)试验件破坏模式示意图

Figure 2. Schematic diagram of damage mode of CFRP test piece subjected to fatigue loading (T700/9A16)

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图 3 加载n次疲劳载荷后的碳纤维复合材料(T700/9A16)试验件静力拉伸试验

Figure 3. Static tensile test of CFRP (T700/9A16) testing pieces after n number cycles of fatigue loading

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图 4 碳纤维复合材料(T700/9A16)试验件刚度退化曲线

Figure 4. Stiffness degradation curves of CFRP test pieces (T700/9A16)

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图 5 含聚偏氟乙烯压电薄膜(PVDF)的碳纤维复合材料(T700/9A16)疲劳试验件

Figure 5. CFRP (T700/9A16) test pieces with polyvinylidene fluoride piezoelectric film (PVDF) for fatigue test

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图 6 含PVDF的碳纤维复合材料(T700/9A16)疲劳试验

Figure 6. Fatigue test of the CFRP (T700/9A16) pieces with PVDF

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图 7 含PVDF的碳纤维复合材料(T700/9A16)试验件疲劳试验输出的压电信号

Figure 7. Piezoelectric signals from PVDF during fatigue test on CFRP test pieces (T700/9A16)

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图 8 疲劳周期内PVDF输出的归一化压电信号变化

Figure 8. Change of normalized piezoelectric signals from PVDF during fatigue test

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图 9 基于随机森林的含PVDF碳纤维复合材料(T700/9A16)试验件疲劳加载次数估计方法

Figure 9. RFR for predicting the number of fatigue cycles of CFRP (T700/9A16) pieces with PVDF

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图 10 预测疲劳循环次数与测试集原始数据相关性分析

Figure 10. Correlation between number of the predicted fatigue cycles and original data in testing set

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图 11 不同疲劳加载次数下含PVDF的碳纤维复合材料(T700/9A16)试验件输出的压电信号

Figure 11. Piezoelectric signals from PVDF during fatigue test on CFRP test pieces (T700/9A16) under different fatigue cycles

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算法I. 随机森林回归算法
输入：训练数据集D_Num，由当前压电信号V_i及对应循环次数n_i构成。
输出：预测的当前循环周次n_predict 。
Step1: For i = 1 to N_tree
(a) 从初始训练集D_Num中随机且有放回地抽取训练样本z；(b) 基于抽取样本z开展决策树训练。训练决策树模型节点时，在所有样本特征中随机选取部分特征，确定最优切分变量与切分点^[26]，完成最优决策树训练。
Step2: 基于Step1，完成所有最优决策树训练${\{ {T_{best}}\} ^{{N_{tree}}}} $。
Step3: 输入任意的电压信号V_t，输出疲劳循环周次预测结果$ {n_{predict}}({V_t}) $ = $ \sum\nolimits_{i = 1}^{{N_{tree}}} {{T_{best}}} ({V_t})/{N_{tree}} $。

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表 1 碳纤维复合材料(T700/9A16)基本材料参数

Table 1. Material properties of the CFRP (T700/9A16)

Material properties
E₁₁/GPa	126.97
E₂₂/GPa	8.52
G₁₂/GPa	3.41
X_T/MPa	2433.05
X_C/MPa	1063.25
Y_T/MPa	37.85
Y_C/MPa	118.30
S₁₂/MPa	61.30
Notes: E₁₁ and E₂₂ represent the tensile moduli in the fiber and matrix directions, respectively. G₁₂ denotes the shear modulus. X_T and Y_T represent tensile strength in the fiber and matrix directions. X_C and Y_C represent compression strength in the fiber and matrix directions. S₁₂ denotes the shear strength.

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表 2 碳纤维复合材料(T700/9A16)疲劳试验件疲劳寿命

Table 2. Fatigue life of the carbon fiber reinforced plastic laminates (T700/9A16)

Test piece number	Fatigue life	Logarithmic fatigue life
PL -1	9302	3.97
PL -2	25642	4.41
PL-3	26324	4.42
PL-4	-	-
PL-5	20175	4.30
PL-6	9715	3.99
Mean	18231.6	4.22
SD	8313.36	0.22
CoV	0.46	0.05
Notes: SD represents Standard Deviation and CoV denotes Coefficient of Variation.

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表 2 加载n次疲劳载荷后的碳纤维复合材料(T700/9A16)试验件剩余刚度以及剩余强度

Table 2. Residual stiffness and residual strength of CFRP (T700/9A16) test pieces after n number cycles of fatigue loading

Test piece number	Cyclic number (n)	Ultimate load/N	Residual strength/MPa	Residual stiffness/GPa
PLE-0-1	0	9646.8	643.1	34.48
PLE-0-2	0	10461.7	697.4	33.45
PLE-2000-1	2000	8806.4	587.1	21.77
PLE-2000-2	2000	9750.8	650.1	19.26
PLE-5000-1	5000	8773.8	584.9	21.77
PLE-5000-2	5000	9807.1	653.8	20.41
PLE-10000-1	10000	8336	555.7	19.08
PLE-10000-2	10000	9253.3	616.9	16.28
PLE-15000-1	15000	8964	597.6	11.29
Notes: The test piece number is defined as PLE-X-Y, in which PLE represents the residual properties of fatigue test pieces, X denotes the number cycles of fatigue loading and Y denotes the test number.

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表 4 含PVDF碳纤维复合材料(T700/9A16)试验件疲劳开始阶段与结束阶段输出的压电信号峰值平均值

Table 4. Average peak value of piezoelectric signals at starting /ending stage for CFRP (T700/9A16) test pieces with PVDF

Test piece number	Average peak voltage at starting stage /V	Average peak voltage at ending stage /V
PL-PVDF-1	3.02	3.49
PL-PVDF-2	2.63	2.76
PL-PVDF-3	3.09	3.23
PL-PVDF-4	3.63	3.80
PL-PVDF-5	3.05	3.42
PL-PVDF-6	3.17	3.52
PL-PVDF-7	3.07	3.56
PL-PVDF-8	3.08	3.48
PL-PVDF-9	2.68	2.84
PL-PVDF-10	2.84	3.12
PL-PVDF-11	3.08	3.47
PL-PVDF-12	3.56	3.88
PL-PVDF-13	3.11	3.52
PL-PVDF-14	3.04	3.48
Notes: The test piece number is defined as PL-PVDF-NN, in which PL represents fatigue test pieces, PVDF denotes the polyvinylidene fluoride piezoelectric film and NN denotes the test number.

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表 5 随机森林算法中超参数选取值

Table 5. The selected values for hyperparameters in RFR

NumTrees	Method	MinLeafSize	Surrogate
300	Regression	5	on

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表 6 数据驱动算法误差指标对比

Table 6. Comparison of error indicators for different models

Data-driven algorithm	MAE	MSE	R-square
RFR	0.0946	0.0200	0.9201
SVM	0.1315	0.0292	0.8845
XGBoost	0.0761	0.0065	0.9461
BPNN	0.3347	0.0672	0.8281
Notes: RFR denotes Random Forest Regression; SVM represents Support Vector Machine; XGBoost denotes EXtreme Gradient Boosting and BPNN represents Back propagation neural network. MAE, MSE and R-square denote the Mean Absolute Error, Mean Square Error and Coefficient of determination, respectively.

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表 7 基于压电信号的碳纤维复合材料试验件(T700/9A16)疲劳循环周次及剩余寿命估计结果

Table 7. The fatigue cycles and remaining life of CFRP test pieces (T700/9A16) predicted by using RFR

Test piece number	$ {n_{test}} $	${n_{pre}}$	Error	${\tilde n_{test}}$	${\tilde n_{pre}}$	Error
Piece 1	3.30	3.24	1.93%	4.39	4.21	4.10%
Piece 2	3.70	3.86	4.48%	4.18	4.03	3.59%
Piece 3	4.00	4.13	3.27%	3.92	3.65	6.89%
Notes: $ {n_{test}} $ denotes the logarithms of tested cycling number; ${n_{pre}}$ denotes the logarithms of predicted cycling number by using trained RFR; ${\tilde n_{test}}$ represents the tested remaining logarithmic fatigue life; ${\tilde n_{pre}}$ represents the predicted remaining logarithmic fatigue life.

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