基于频率变化预测玻璃纤维增强树脂复合材料层合板的剩余疲劳寿命

廖兴升; 梁智洪; 傅继阳; 江剑; 王财政; 张芝芳

doi:10.13801/j.cnki.fhclxb.20201215.010

基于频率变化预测玻璃纤维增强树脂复合材料层合板的剩余疲劳寿命

doi: 10.13801/j.cnki.fhclxb.20201215.010

廖兴升^1,,
梁智洪^1,,
傅继阳^1,,
江剑^1,,
王财政^2,,
张芝芳^1, ,

1.
广州大学　广州大学-淡江大学工程结构灾害与控制联合研究中心，广州 510006
2.
清华大学　航天航空学院，北京 100084

基金项目: 广东省自然科学基金(2019A1515011116)；广州市“121人才梯队工程”后备人才项目

详细信息

通讯作者:
张芝芳，博士，副研究员，硕士生导师，研究方向为复合材料结构健康监测和疲劳寿命评估　 E-mail：zfzhang@gzhu.edu.cn

中图分类号: TB332；TQ327.1
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出版历程
- 收稿日期: 2020-10-08
- 录用日期: 2020-11-30
- 网络出版日期: 2020-12-16
- 刊出日期: 2021-10-01

Prediction of remaining fatigue life of glass fiber reinforced polymer laminates based on frequency change

1.
Guangzhou University-Tamkang University Joint Research Center for Engineering Structure Disaster Prevention and Control, Guangzhou University, Guangzhou 510006, China
2.
School of Aerospace Engineering, Tsinghua University, Beijing 100084, China

摘要

摘要: 复合材料结构在疲劳过程中的累积损伤将导致结构刚度下降，并进一步引起结构的动态参数如频率发生衰减。因此，可以将结构疲劳状态与结构频率联系起来，基于频率预测结构的剩余疲劳寿命。本文首先基于复合材料在纵向、横向和面内剪切三个方向的疲劳特性，结合ABAQUS与Umat子程序开发了三维有限元模型模拟复合材料层合板中的疲劳损伤演变，并构建了不同疲劳状态下对应的模态分析模型，由此获得了疲劳过程中的频率衰减曲线。之后，基于疲劳过程的频率变化量训练了人工神经网络，用于预测玻璃纤维增强复合材料层合板的剩余疲劳寿命。特别地，在当前的数值模型中为每个单元分配了符合高斯正态分布的材料属性，以模拟实际情况下复合材料性能的离散性。结果表明，疲劳模型数值模拟结果与已有文献的疲劳实验数据吻合，基于频率变化量训练的人工神经网络可以成功预测玻璃纤维增强复合材料试件的剩余疲劳寿命。
- 复合材料 /
- 疲劳寿命 /
- 频率衰减 /
- 人工神经网络 /
- 离散性 /
- 数值模拟
Abstract: The cumulative damage in the composite structures during the fatigue process will lead to decrease in the stiffness of structures. This will further cause the changes in the dynamic parameters of the structure, such as the frequencies. Therefore, the fatigue status can be related to the frequencies of structures, and inversely, the frequencies can be used to predict the fatigue life of the structures. In this paper, by incorporating Umat subroutines in ABAQUS, a three-dimensional finite element model was developed to simulate the evolution of fatigue damage in glass fiber reinforced polymer (GFRP) laminates. The fatigue characteristics of composite materials in the longitudinal, transverse and in-plane shear directions have been considered in the model. The fatigue state of the glass fiber reinforced polymer laminates was exported from the fatigue model and then was imported into a second model to apply modal analysis for obtaining the frequencies which are corresponding to the fatigue status. An artificial neural network was trained based on the frequency data during the fatigue process, with the frequency shifts as the input and the remaining fatigue life as the output. The training data for ANN was generated from the finite element (FE) models, based on which the remaining fatigue life of the GFRP laminates was predicted. In particular, to consider the discreteness of material properties of fiber reinforced polymer (FRP) composite materials, each element in the finite element model (FEM) was individually assigned the material properties randomly distributed in the Gaussian normal distribution. The results show that the numerical simulation results of the present fatigue model are consistent with the fatigue test data in the existing literature. The trained artificial neural network can successfully predict the remaining fatigue life of the GFRP laminates.
- composite materials /
- fatigue life /
- frequency shift /
- artificial neural network /
- discreteness /
- finite element model

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图 1 疲劳模型模拟流程

Figure 1. Simulation scheme of fatigue model

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图 2 玻璃纤维增强树脂复合材料(GFRP)层合板疲劳退化区域的有限元模型

Figure 2. FEM of fatigue degradation zone of glass fiber reinforced polymer (GFRP) plate

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图 3 [0]₈ GFRP层合板未进行正态分布的疲劳模型

Figure 3. Fatigue model without normal distribution of [0]₈ GFRP laminates

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图 4 [0]₈ GFRP层合板进行正态分布的疲劳模型

Figure 4. Normally distributed fatigue model of [0]₈ GFRP laminates

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图 5 六种铺层GFRP层合板的S-N曲线

Figure 5. S-N curves of six types of GFRP laminates

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图 6 六种GFRP层合板的剩余刚度曲线

Figure 6. Residual stiffness curves of six types of GFRP laminates

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图 7 模态模型建模流程

Figure 7. Built-up process of FE model for modal analysis

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图 8 不同分网密度下的[0]₈ GFRP层合板

Figure 8. GFRP plate ([0]₈) with different mesh densities

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图 9 [0]₈ GFRP层合板振型图

Figure 9. [0]₈ Vibration shape diagram of GFRP laminate

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图 10 GFRP层合板模态分析模型

Figure 10. FE model for modal analysis of GFRP laminate

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图 11 [0]₈层合板0.6应力水平下剩余频率曲线

Figure 11. Residual frequency curves of [0]₈ laminate under 0.6 stress level

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图 12 [90]₈层合板0.5应力水平下剩余频率曲线

Figure 12. Residual frequency curves of [90]₈ laminate under 0.5 stress level

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图 13 [45/−45/45/−45]_S层合板0.5应力水平下剩余频率曲线

Figure 13. Residual frequency curves of [45/−45/45/−45]_S laminate under 0.5 stress level

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图 14 [0/90/90/0]_S层合板0.6应力水平下剩余频率曲线

Figure 14. Residual frequency curves of [0/90/90/0]_S laminate under 0.6 stress level

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图 15 [45/0/0/−45]_S层合板0.53应力水平下剩余频率曲线

Figure 15. Residual frequency curves of [45/0/0/−45]_S laminate under 0.53 stress level

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图 16 [45/90/−45/0]_S层合板0.55应力水平下剩余频率曲线

Figure 16. Residual frequency curves of [45/90/−45/0]_S laminate under 0.55 stress level

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图 17 1^#~4^#GFRP层合板剩余频率曲线

Figure 17. Residual frequency curves of GFRP laminate 1^#~4^#

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图 18 GFRP层合板神经网络结构图

Figure 18. Neural network structure diagram of GFRP laminate

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图 19 GFRP层合板预测模型训练误差曲线

Figure 19. Training error curves of ANN model of GFRP laminate

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表 1 材料参数突降方案

Table 1. Degradation scheme of material parameters

Failure mode	Parameter degradation scheme
Fiber tensile failure	${E_{11}}$, ${E_{{\rm{22}}}}$, ${G_{1{\rm{2}}}}$, ${G_{{\rm{13}}}}$, ${G_{{\rm{23}}}}$, ${\nu_{1{\rm{2}}}}$, ${\nu_{{\rm{13}}}}$, ${\nu_{{\rm{23}}}}$ reduced to 0.07 times the initial value
Fiber compressive failure	${E_{11}}$, ${E_{{\rm{22}}}}$, ${G_{1{\rm{2}}}}$, ${G_{{\rm{13}}}}$, ${G_{{\rm{23}}}}$, ${\nu_{1{\rm{2}}}}$, ${\nu_{{\rm{13}}}}$, ${\nu_{{\rm{23}}}}$ reduced to 0.14 times the initial value
Matrix tensile failure	${E_{{\rm{22}}}}$, ${G_{1{\rm{2}}}}$, ${G_{{\rm{23}}}}$ reduced to 0.2 times the initial value
Matrix compression failure	${E_{{\rm{22}}}}$, ${G_{1{\rm{2}}}}$, ${G_{{\rm{23}}}}$ reduced to 0.4 times the initial value
Fiber/matrix shear failure	${G_{1{\rm{2}}}}$. ${\nu_{1{\rm{2}}}}$ reduced to 0.2 times the initial value
Delamination failure	${E_{{\rm{33}}}}$, ${G_{{\rm{13}}}}$, ${G_{{\rm{23}}}}$, ${\nu_{{\rm{13}}}}$, ${\nu_{{\rm{23}}}}$ reduced to 0.2 times the initial value
Notes: E₁₁, E₂₂, E₃₃—Young’s moduli; G₁₂, G₁₃, G₂₃—Shear moduli; ν₁₁, ν₁₂, ν₂₃—Poisson’s ratios.

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表 2 GFRP层合板试件的铺层角度与静拉伸强度^[7]

Table 2. Layup and static tensile strength of GFRP laminate specimens^[7]

Sample No.	Stacking sequence	Strength/MPa
A	[0]₈	900
B	[90]₈	36
C	[0/90/90/0]_S	470
D	[45/−45/45/−45]_S	118
E	[45/0/0/−45]_S	592
F	[45/90/−45/0]_S	372

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表 3 GFRP层合板剩余刚度-剩余强度关联模型参数^[7]

Table 3. Parameters for the correlated model of the remaining stiffness-remaining strength^[7] for GFRP laminate

	Parameter	Magnitude
Longitudinal	$u$	0.8
	$v$	60
	$a$	0.25
	E_11rc/E₁₁₀	0.95
Transverse	$w$	1.2s²−1.85s+0.85
	$u$	0.6
	$v$	2
	$a$	80
	E_22rc/E₂₂₀(E_33rc/E₃₃₀)	0.9
Shear	$w$	1.57s²−2.43s+1.12
	$u$	0.5
	$v$	0.3
	$a$	15
	G_12rc/G₁₂₀	0.3
	$w$	10.86s²−16.2s+7.3
Note: E_11rc/E₁₁₀, E_22rc/E₂₂₀ (E_33rc/E₃₃₀), G_12rc/G₁₂₀—Ratio of critical residual stiffness to initial stiffness along longitudinal, transverse and shear direction, respectively.

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表 4 不同分网下GFRP层合板的模态频率

Table 4. Modal frequencies of GFRP laminate under different mesh densities

Mode No.	1^# mesh density-21140 elements/Hz	2^# mesh density -81800 elements/Hz	Discrepancy between 1^# and 2^# mesh density/%
1	699.4	699.32	0.01
2	2379.6	2378.4	0.05
3	5669	5664.8	0.07
4	10141	10136	0.05
5	14241	14240	0.01
6	18097	18091	0.03
7	23443	23426	0.07
8	29688	29676	0.04

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表 5 铝片的材料参数

Table 5. Material parameters of aluminum

Material	Elastic modulus/MPa	Poisson's ratio	Density/ (g·cm⁻³)
Aluminum	70000	0.32	2.7

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表 6 [0]₈层合板0.6应力水平下最终寿命

Table 6. Fatigue life of [0]₈ laminate under 0.6 stress level

Number	1^#	2^#	3^#	4^#
Fatigue life	36000	36000	33000	25000

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表 7 神经网络预测3^#GFRP层合板剩余疲劳寿命结果

Table 7. Neural network prediction of the remaining fatigue life of GFRP laminate 3^#

Abaqus simulation actual value N_r/%	Neural network algorithm prediction ${N_{\rm{r}}}'$/%	Prediction error ${N_{\rm{r}}}$−${N_{\rm{r}}}'$/%
100.00	99.88	0.12
96.97	97.16	−0.19
93.94	94.36	−0.42
87.88	88.59	−0.71
81.82	82.90	−1.08
75.76	77.02	−1.26
69.70	71.29	−1.59
60.61	62.61	−2.01
51.52	53.92	−2.41
42.42	45.05	−2.62
36.36	39.01	−2.64
27.27	30.18	−2.91
18.18	21.38	−3.20
9.09	13.29	−4.19
3.03	6.12	−3.09
0	0	0

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