基于芯条胶粘弹性本构的芳纶纸蜂窝拉伸孔格形态研究

夏思禹; 李岩; 付昆昆; 李朝蓬

基于芯条胶粘弹性本构的芳纶纸蜂窝拉伸孔格形态研究

1.
同济大学　航空航天与力学学院, 上海, 200092
2.
黑龙江众合鑫成新材料有限公司, 黑龙江, 151500

基金项目: 国家重点研发计划(编号：2020YFB0311500)

详细信息

通讯作者:
李岩，博士，教授，博士生导师，研究方向为复合材料设计与制造　E-mail:liyan@tongji.edu.cn

中图分类号: TB332
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- 文章访问数: 224
- HTML全文浏览量: 106
- 被引次数: 0
出版历程
- 收稿日期: 2023-08-01
- 修回日期: 2023-09-17
- 录用日期: 2023-09-29
- 网络出版日期: 2023-11-03

Study on Stretched Aramid Honeycomb cell Structure Based on the Viscoelastic Constitutive Model of Adhesive

XIA Siyu¹,
LI Yan^{1
, ,},
FU Kunkun¹,
Li Zhaopeng²

1.
School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
2.
Heilongjiang Zhonghe Xincheng New Materials Co., Ltd, Hei Longjiang 151500, China

Funds: National Key Research and Development Program of China (No.2020YFB0311500)

摘要

摘要: 拉伸工艺是影响芳纶纸蜂窝孔格形态最关键的工序之一。本研究基于纳米压痕法确定了芯条胶粘弹性力学本构关系，建立了芳纶纸蜂窝双边拉伸工艺有限元模型。通过蜂窝拉伸-保载实验验证了该模型的有效性。研究发现，芯条胶的应力松弛行为导致了蜂窝两端孔格内切圆直径增大，使得蜂窝中部孔格内切圆直径减小。同时，在保载过程中纸-胶粘接处孔格粘结圆角半径减小导致蜂窝孔格内角减小。最后，基于该有限元模型探索了涂胶工艺参数对拉伸后蜂窝孔格尺寸的影响规律。研究表明涂胶宽度和涂胶厚度的增加会导致蜂窝孔格内切圆直径的减小，而蜂窝孔格内角仅受涂胶宽度的影响，随涂胶宽度的增加而增大。
- 芳纶纸蜂窝 /
- 芯条胶 /
- 粘弹性 /
- 蜂窝孔格形态 /
- 有限元模型
Abstract: Stretching process is one of the critical procedures that affect the honeycomb cell structure of Aramid honeycomb. In this study, the viscoelastic constitutive relationship of node bond adhesive was determined by a fitting method based on nanoindentation, and a finite element model of honeycomb biaxial stretching process was established. The validity of the model was verified by the honeycomb stretching-holding experiment. The study found that the stress relaxation behavior of the adhesive caused an increase in the radius of the inscribed circles at both ends of the honeycomb and a decrease in the middle. Meanwhile, during the holding process, the node bond adhesive fillet radius decreased, leading to a decrease in the internal angle of the honeycomb cell. Finally, the influence of gluing process parameters on the size of honeycomb cell after stretching was explored based on the finite element model. The study showed that the increase in gluing width and thickness would lead to a decrease in the diameter of the inscribed circle of the honeycomb cell, and the honeycomb cell's internal angle was only affected by the gluing width, which increased with the gluing width.
- Aramid honeycomb /
- Adhesive /
- Viscoelasticity /
- Honeycomb cell structure /
- Finite element model

HTML全文

图 1 芳纶纸蜂窝拉伸-保载测试过程:(a)蜂窝拉伸过程；(b)保载中蜂窝内切圆直径测量过程

Figure 1. Stretching-Holding Test Process of Aramid Honeycomb：(a) Honeycomb stretching process; (b) In-process measurement of the diameter of the inscribed circle of the honeycomb during holding.

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图 2 有限元模型网格划分示意图

Figure 2. Demonstration of finite element model and meshing

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图 3 纳米压痕测试所获得的不同加载速率下J80芯条胶载荷-位移曲线

Figure 3. Load-Displacement curves of J80 adhesive at different loading rates obtained by nanoindentation

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图 4 不同加载速率下的拟合曲线：(a)2 mN/s；(b)1 mN/s；(c)0.5 mN/s

Figure 4. Fitting Curves Under Different Loading Rates: (a) 2 mN/s; (b) 1 mN/s; (c) 0.5 mN/s

$ {h}^{2}\left(t\right) $-square of indentation depth; $ P\left(t\right) $- indentation load

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图 5 松弛模量拟合曲线

Figure 5. Fitting Curves of Relaxation Modulus

$ E\left(t\right) $-relaxation modulus;t-time

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图 6 芳纶蜂窝拉伸成型过程中有限元仿真结果与实验结果对比：(a)拉伸开始；(b)拉伸中；(c)拉伸结束

Figure 6. Comparison between Simulation Model and Stretching Test Process: (a) Start of Stretching Test; (b) Middle of Stretching Test; (c) End of Stretching Test

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图 7 蜂窝孔格尺寸参数^[32]

Figure 7. Parameters of Honeycomb Cell Size^[32]

$ {d}_{r} $-diameter of the incircle of honeycomb cell; $ {t}_{w} $-cell wall thickness; $ {t}_{a} $-adhesive thickness; $ {d}_{i} $-distance between opposite walls; $ {d}_{f} $-length of adhesive bondline; $ {R}_{c} $-radius at intersections; $ {R}_{f} $-fillet radius; $ {\theta }_{w} $-internal angle; $ {\theta }_{c} $-angle between inclined and horizontal wall

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图 8 仿真模型计算获得的保载过程$ \Delta \stackrel{-}{d} $尺寸变化与实验结果对比

Figure 8. Comparison of $ \Delta \stackrel{-}{d} $ change in Simulation Model and Stretching-Holding Test

$ \Delta \stackrel{-}{d} $-change in diameter of the incircle of honeycomb cell during the holding process

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图 9 保载前后蜂窝孔格参数在蜂窝拉伸方向上的分布：(a)$ \delta d $；(b)$ {\theta }_{w} $

Figure 9. Distribution of Honeycomb cell Size Parameters in the Direction of Honeycomb Stretching before and after Holding: (a)$ \delta d $；(b)$ {\theta }_{w} $

$ \delta d $- deviation from the standard value of the diameter of the incircle of a honeycomb cell; $ {\theta }_{w} $-internal angle

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图 10 保载前后蜂窝孔格粘结圆角对比 (a) 保载开始；(b)保载150 s

Figure 10. Comparison of Node Bond Adhesive Fillet Radius of Honeycomb Cell before and after Holding： (a) Start of Holding; (b) Holding 150 s

$ {R}_{f1} $,$ {R}_{f2} $-fillet radius before and after holding

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图 11 不同涂胶宽度下的蜂窝孔格形态：(a)涂胶宽度2.55 mm；(b)涂胶宽度2.75 mm；(c)涂胶宽度2.95 mm

Figure 11. Mophology of Honeycomb Cell under Different Gluing Widths: (a) Gluing Width of 2.55 mm; (b) Gluing Width of 2.75 mm;(c) Gluing Width of 2.95 mm

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图 12 不同涂胶厚度下的蜂窝孔格形态：(a)涂胶厚度0.005 mm；(b)涂胶厚度0.01 mm；(c)涂胶厚度0.015 mm

Figure 12. Mophology of Honeycomb Cell under Different Gluing Thicknesses: (a) Gluing Thickness of 0.005 mm; (b) Gluing Thickness of 0.01 mm; (c) Gluing Thickness of 0.015 mm

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图 13 涂胶工艺参数对保载后$ \delta d $的影响：(a)涂胶宽度的影响；(b)涂胶厚度的影响

Figure 13. Effects of Gluing Process Parameters on δd after Holding:(a) Effects of Gluing Width; (b) Effects of Gluing Thickness

$ \delta d $- deviation from the standard value of the diameter of the incircle of a honeycomb cell

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图 14 涂胶工艺参数对保载后$ {\theta }_{w} $的影响：(a)涂胶宽度的影响；(b)涂胶厚度的影响

Figure 14. Effects of Gluing Process Parameters on θw after Holding:(a) Effects of Gluing Width; (b) Effects of Gluing Thickness

$ {\theta }_{w} $-internal angle

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表 1 有限元模型的材料参数

Table 1. Material Parameters of Finite Element Model

Material	Density/ (g*cm⁻³)	Modulus/ GPa	Poisson’s ratio
Aramid paper	0.842	2.46	0.32
Node bond adhesive	1.12×10⁻³	0.089	0.39

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表 2 蠕变柔量相关参数

Table 2. Parameters Related to Creep Compliance

Parameter	$ {J}_{0}/\mathrm{M}\mathrm{P}{\mathrm{a}}^{-1} $	$ {J}_{1}/\mathrm{M}\mathrm{P}{\mathrm{a}}^{-1} $	$ {J}_{2}/\mathrm{M}\mathrm{P}{\mathrm{a}}^{-1} $	$ {J}_{3}/\mathrm{M}\mathrm{P}{\mathrm{a}}^{-1} $	$ {\tau }_{1}/\mathrm{s} $	$ {\tau }_{2}/\mathrm{s} $	$ {\tau }_{3}/\mathrm{s} $
Value	0.01416	0.06	0.04275	0.00655	8×10^-4	60	25000
Notes: $ {J}_{0} $ is the initial creep compliance; $ {J}_{i} $ (i=1,2,3) is the creep compliance of the i-th Maxwell element; $ {\tau }_{i}(\mathrm{i}=\mathrm{1,2},3) $ is the relaxation time of the i-th Maxwell element.

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表 3 $ h\left(t\right) $与$ P\left(t\right) $的关系参数

Table 3. Relationship Parameters between h(t) and P(t)

Loading rate$ {v}_{0} $/(mN·s⁻¹)	$ {J}_{0}+{\displaystyle\sum }_{i=1}^{3}{J}_{i} $	$ {J}_{1}{v}_{0}{\tau }_{1} $	$ {J}_{2}{v}_{0}{\tau }_{2} $	$ {J}_{3}{v}_{0}{\tau }_{3} $	$ {v}_{0}{\tau }_{1} $	$ {v}_{0}{\tau }_{2} $	$ {v}_{0}{\tau }_{3} $
2	$ 0.12346 $	9.6×10⁻⁵	5.13	327.5	1.6×10⁻³	120	50000
1	$ 0.12346 $	4.8×10⁻⁵	2.565	163.75	8×10⁻⁴	60	25000
0.5	$ 0.12346 $	2.4×10⁻⁵	1.2825	81.875	4×10⁻⁴	30	12500

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表 4 松弛模量拟合参数

Table 4. Fitting Parameters of Relaxation Modulus

$ {E}_{\mathrm{\infty }} $(MPa)	$ {E}_{1} $(MPa)	$ {E}_{2} $(MPa)	$ {E}_{3} $(MPa)	$ {\tau }_{1} $(s)	$ {\tau }_{2} $(s)	$ {\tau }_{3} $(s)	$ {R}^{2} $
2.75	69.68	3.75	13.21	12	357	1750	0.99
Notes: $ {E}_{\mathrm{\infty }} $ is the equilibrium relaxation modulus, $ {E}_{\mathrm{i}} $ (i=1,2,3) is the relaxation modulus of the spring in the i-th Maxwell element; $ {R}^{2} $ is the correlation coefficient.

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表 5 芯条胶的三阶Prony级数参数

Table 5. Third-order Prony series parameters of node bond adhesive

i	$ {G}_{i} $	$ {K}_{i} $	$ {{\tau }_{i}}^{G} $
1	0.7795	0	12
2	0.0419	0	357
3	0.1477	0	1750
Notes: $ {G}_{i} $ is the shear modulus; $ {K}_{i} $ is the bulk modulus; $ {{\tau }_{i}}^{G} $ is the relaxation time of each component in the Prony series.

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表 6 有限元模型AH-W与AH-T系列涂胶工艺参数

Table 6. Gluing Process Parameters of AH-W and AH-T finite element model series

	Gluing width/mm	Gluing thickness/mm
AH-W2.55	2.55	0.01
AH-W2.75	2.75	0.01
AH-W2.95	2.95	0.01
AH-T0.005	2.75	0.005
AH-T0.01	2.75	0.01
AH-T0.015	2.75	0.015

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