碳纤维/环氧树脂拉扭多耦合效应层合板设计与试验验证

崔达; 张鸣昊; 李道奎

碳纤维/环氧树脂拉扭多耦合效应层合板设计与试验验证

崔达^{1, 2, 3},
张鸣昊^{1, 3},
李道奎^{1, 3, ,}

1.
国防科技大学　空天科学学院, 长沙 410073
2.
兰州大学　土木工程与力学学院, 兰州 730000
3.
空天任务智能规划与仿真湖南省重点实验室, 长沙 410073

基金项目: 国家自然科学基金 (12302197)；国防科技大学青年自主创新科学基金项目(ZK2023-38)

详细信息

通讯作者:
李道奎，博士，教授，博士生导师，研究方向为航天结构分析与设计、复合材料结构力学　E-mail: lidaokui@nudt.edu.cn

中图分类号: TB33; O341
计量
- 文章访问数: 42
- HTML全文浏览量: 30
- 被引次数: 0
出版历程
- 收稿日期: 2024-05-16
- 修回日期: 2024-06-22
- 录用日期: 2024-07-04
- 网络出版日期: 2024-07-19

Design and experimental verification of carbon fiber/epoxy resin multi-coupling laminates with extension-twisting coupling effect

CUI Da^{1, 2, 3},
ZHANG Minghao^{1, 3},
LI Daokui^{1, 3
, ,}

1.
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China
2.
School of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, China
3.
Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions, Changsha 410073, China

Funds: National Natural Science Foundation of China(12302197); Youth Independent Innovation Science Fund project of National University of Defense Technology (ZK2023-38)

摘要

摘要: 针对碳纤维/环氧树脂(Carbon fiber reinforced epoxy resin，CF/EP )拉扭多耦合效应层合板湿热稳定机制不明、耦合效应不强的问题，开展碳纤维/环氧树脂拉扭多耦合效应层合板设计与试验验证研究。引入复合材料层合板的几何因子，推导了拉扭多耦合效应层合板湿热稳定条件。基于湿热稳定条件，建立了拉扭多耦合效应层合板的非对称铺层优化设计模型，利用遗传算法-序列二次规划(Genetic algorithm-sequential quadratic program，GA-SQP)混合优化算法求解得到了拉扭耦合效应最大的层合板的铺层角度规律。基于三维数字图像相关方法(Three-dimension digital image correlation，3D-DIC)完成了层合板拉扭耦合效应的测量试验。数值仿真和试验结果表明，当拉扭多耦合效应层合板的铺层角度满足其湿热稳定条件时，层合板不会发生固化变形；多耦合效应的引入能够显著提升层合板的拉扭耦合效应，最大可达30%以上。
- 湿热稳定 /
- 拉扭多耦合效应层合板 /
- 优化设计 /
- 试验验证 /
- 几何因子 /
- 鲁棒性分析
Abstract: In order to reveal the mechanism of hygro-thermal stability and solve the problem of insufficient coupling effect, the design and experimental verification of carbon fiber/epoxy resin (CF/EP) multi-coupled laminates with extension-twisting coupling effect were carried out. The geometric factors of the laminates were introduced, and the conditions for hygro-thermal stability of the multi-coupled laminates with extension-twisting coupling effect were deduced. Based on these conditions, the optimal design model of multi-coupled laminates with extension-twisting coupling effect was established. Genetic algorithm-sequential quadratic program (GA-SQP) hybrid optimization algorithm was used to optimize the stacking sequence of the laminates with the maximum extension-twisting coupling effect. Based on three-dimension digital image correlation (3D-DIC), the extension-twisting coupling effect of the laminates was measured. The numerical simulation and experimental results show that the multi-coupled laminates with extension-twisting effect will not undergo curing deformation when the stacking sequences meet the conditions of hygro-thermal stability. The introduction of multi-coupling effects can significantly improve the extension-twisting coupling effect of laminates and maximum increase is over 30%.
- hygro-thermal stability /
- multi-coupled laminates with extension-twisting coupling effect /
- optimization design /
- experimental verification /
- geometrical factor /
- robust analysis

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图 1 层合板各层坐标图

Figure 1. Coordinates of each layer

H—Total thickness of laminates; z_i—Out-of-plane coordinates of laminates

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图 2 CF/EP拉扭耦合层合板降温自由收缩位移云图

Figure 2. Cooling free displacement cloud image of CF/EP extension-twisting coupled laminates

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图 3 CF/EP拉扭耦合层合板轴向拉伸时的位移云图

Figure 3. Displacement of four types of CF/EP extension-twisting coupled laminates under axial tension

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图 4 CF/EP层合板几何模型示意图

Figure 4. Geometric model of CF/EP carbon fiber/epoxy resin multi-coupled laminates

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图 5 多耦合效应层合板试验加载装置示意图

Figure 5. Loading device for multi-coupled laminates

1—Test stand; 1a—The body of test stand; 1b—Connecting disc; 1c—The beam of the test stand; 2—Connecting device; 2a—Upper fixture; 2b—Lower fixture; 2c—Outer clamping block; 2d—Outer clamping block; 3—Test pieces; 4—Loading device; 4a—Connecting rod; 4b—Weight tray; 4c—Weights

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图 6 层合板耦合效应测量系统

Figure 6. Test system for coupling effect of laminates

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图 7 CF/EP拉扭耦合层合板试验件

Figure 7. Test pieces of CF/EP laminates

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图 8 CF/EP拉扭耦合层合板试验件扭转角变形试验结果

Figure 8. Test results of torsion deformation of CF/EP extension-twisting coupled laminates

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图 9 CF/EP层合板试验件有限元模型

Figure 9. Finite element model of CF/EP test pieces

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图 10 CF/EP层合板试验件在不同拉力下的扭转角变化率

Figure 10. Change rate of torsion angle of CF/EP extension-twisting coupled laminates under different tensile forces

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图 11 CF/EP层合板拉扭耦合效应的鲁棒性分析结果

Figure 11. Robustness analysis results of extension-twisting coupling effect of CF/EP laminates

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表 1 层合板耦合类型下标表示

Table 1. Subscripts representing the coupling types of laminates

Subscripts	Coupling effects	Subscripts	Coupling effects
A_S:$ \left[ {\begin{array}{*{20}{c}} {{A_{11}}}&{{A_{12}}}&0 \\ {{A_{21}}}&{{A_{22}}}&0 \\ 0&0&{{A_{66}}} \end{array}} \right] $	—	A_F:$ \left[ {\begin{array}{*{20}{c}} {{A_{11}}}&{{A_{12}}}&{{A_{16}}} \\ {{A_{21}}}&{{A_{22}}}&{{A_{26}}} \\ {{A_{61}}}&{{A_{62}}}&{{A_{66}}} \end{array}} \right] $	E-S
B₀:$ \left[ {\begin{array}{*{20}{c}} 0&0&0 \\ 0&0&0 \\ 0&0&0 \end{array}} \right] $	—	B_l:$ \left[ {\begin{array}{*{20}{c}} {{B_{11}}}&0&0 \\ 0&{{B_{22}}}&0 \\ 0&0&0 \end{array}} \right] $	E-B
B_t:$ \left[ {\begin{array}{*{20}{c}} 0&0&{{B_{16}}} \\ 0&0&{{B_{26}}} \\ {{B_{61}}}&{{B_{62}}}&0 \end{array}} \right] $	E-T S-B	B_lt:$ \left[ {\begin{array}{*{20}{c}} {{B_{11}}}&0&{{B_{16}}} \\ 0&{{B_{22}}}&{{B_{26}}} \\ {{B_{61}}}&{{B_{62}}}&0 \end{array}} \right] $	E-T S-B E-B
B_S:$ \left[ {\begin{array}{*{20}{c}} {{B_{11}}}&{{B_{12}}}&0 \\ {{B_{21}}}&{{B_{22}}}&0 \\ 0&0&{{B_{66}}} \end{array}} \right] $	E-B S-T	B_F:$ \left[ {\begin{array}{*{20}{c}} {{B_{11}}}&0&{{B_{16}}} \\ 0&{{B_{22}}}&{{B_{26}}} \\ {{B_{61}}}&{{B_{62}}}&0 \end{array}} \right] $	E-B E-T S-B S-T
D_S:$ \left[ {\begin{array}{*{20}{c}} {{D_{11}}}&{{D_{12}}}&0 \\ {{D_{21}}}&{{D_{22}}}&0 \\ 0&0&{{D_{66}}} \end{array}} \right] $	—	D_F:$ \left[ {\begin{array}{*{20}{c}} {{D_{11}}}&{{D_{12}}}&{{D_{16}}} \\ {{D_{21}}}&{{D_{22}}}&{{D_{26}}} \\ {{D_{61}}}&{{D_{62}}}&{{D_{66}}} \end{array}} \right] $	B-T
Notes: E-T—Extension-twisting coupling effect; S-B—Shear-bend coupling effect; E-B—Extension-bending coupling effect; S-T—Shear-twist coupling effect; E-S—Extension-shearing coupling effect; B-T—Bend-twist coupling effect.

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表 2 拉扭耦合层合板的耦合类型

Table 2. Coupling types of extension-twisting coupled laminates

Laminate type	Coupling type
A_SB_tD_S	E-T
A_SB_tD_F	E-T、B-T
A_SB_ltD_S	E-T、E-B
A_FB_tD_S	E-T、E-S
A_SB_ltD_F	E-T、E-B、B-T
A_SB_FD_S	E-T、E-B、S-T
A_FB_tD_F	E-T、E-S、B-T
A_FB_ltD_S	E-T、E-B、E-S
A_SB_FD_F	E-T、E-B、S-T、B-T
A_FB_ltD_F	E-T、E-B、E-S、B-T
A_FB_FD_S	E-T、E-B、S-T、E-S
A_FB_FD_F	E-T、E-B、S-T、E-S、B-T
Notes: E-T—Extension-twisting coupling effect; S-B—Shear-bend coupling effect; E-B—Extension-bending coupling effect; S-T—Shear-twist coupling effect; E-S—Extension-shearing coupling effect; B-T—Bend-twist coupling effect.

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表 3 拉扭多耦合效应层合板的耦合效应几何因子解析条件

Table 3. Conditions for geometric factors satisfying coupling effects of multi-coupled laminates with E-T

Type	Conditions
A_SB_ltD_S	$ {\xi _3} = {\xi _4} = {\xi _6} = {\xi _{11}} = {\xi _{12}} = 0,\left\| {{\xi _5}} \right\| + \left\| {{\xi _6}} \right\| \ne 0,\left\| {{\xi _7}} \right\| + \left\| {{\xi _8}} \right\| \ne 0 $
A_SB_tD_F	$ {\xi _3} = {\xi _4} = {\xi _5} = {\xi _6} = 0,\left\| {{\xi _7}} \right\| + \left\| {{\xi _8}} \right\| \ne 0,\left\| {{\xi _{11}}} \right\| + \left\| {{\xi _{12}}} \right\| \ne 0 $
A_SB_FD_S	$ {\xi _3} = {\xi _4} = {\xi _{11}} = {\xi _{12}} = 0,{\xi _6} \ne 0,{\text{ }}\left\| {{\xi _7}} \right\| + \left\| {{\xi _8}} \right\| \ne 0{\text{ }} $
A_SB_ltD_F	$ {\xi _3} = {\xi _4} = {\xi _6} = 0,{\text{ }}{\xi _5} \ne 0,\left\| {{\xi _7}} \right\| + \left\| {{\xi _8}} \right\| \ne 0,{\text{ }}\left\| {{\xi _{11}}} \right\| + \left\| {{\xi _{12}}} \right\| \ne 0 $
A_SB_FD_F	$ {\xi _3} = {\xi _4} = 0,{\text{ }}{\xi _6} \ne 0,\left\| {{\xi _7}} \right\| + \left\| {{\xi _8}} \right\| \ne 0,{\text{ }}\left\| {{\xi _{11}}} \right\| + \left\| {{\xi _{12}}} \right\| \ne 0 $

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表 4 拉扭多耦合效应层合板湿热稳定的几何因子解析条件

Table 4. Conditions for hygro-thermally stable multi-coupled laminates with extension-twisting coupling effect

Type	Conditions for geometric factors
A_SB_tD_S	$ {\xi _1} = {\xi _3} = {\xi _4} = {\xi _5} = {\xi _6} = {\xi _7} = {\xi _{11}} = {\xi _{12}} = 0,{\xi _8} \ne 0 $
A_SB_tD_F	$ {\xi _1} = {\xi _3} = {\xi _4} = {\xi _5} = {\xi _6} = {\xi _7} = 0,{\xi _8} \ne 0,\left\| {{\xi _{11}}} \right\| + \left\| {{\xi _{12}}} \right\| \ne 0 $
A_SB_FD_S	$ {\xi _1} = {\xi _3} = {\xi _4} = {\xi _5} = {\xi _7} = {\xi _{11}} = {\xi _{12}} = 0,{\xi _6} \ne 0,{\xi _8} \ne 0 $
A_SB_FD_F	$ {\xi _1} = {\xi _3} = {\xi _4} = {\xi _5} = {\xi _7} = 0,{\xi _6} \ne 0,{\xi _8} \ne 0,\left\| {{\xi _{11}}} \right\| + \left\| {{\xi _{12}}} \right\| \ne 0 $

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表 5 IM7/8552型碳纤维/环氧树脂单层板材料属性

Table 5. Properties of carbon IM7/8552 single layer

Parameter		Value
Young’s modulus/GPa	E₁	161.0
Young’s modulus/GPa	E₂	11.38
Shear modulus/GPa	G₁₂	5.17
Poisson’s ratio	ν₂₁	0.38
Thickness of single layer/mm	t	0.1397
Thermal expansivity/10⁻⁶℃⁻¹	α₁	−0.0181
Thermal expansivity/10⁻⁶℃⁻¹	α₂	24.3

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表 6 湿热稳定的CF/EP拉扭耦合层合板

Table 6. Hygro-thermally stable CF/EP laminates with extension-twisting coupling effect

Type	Optimization results/(°)	\|b₁₆\|/ N⁻¹
A_SB_tD_S	[69.8/−6.7/−17.1/79.4/−30.4/ 76.9/−53.0/37.3/13.8/81.5/ −63.2/8.5/16.9/−72.2]_T	1.69×10⁻⁵
A_SB_tD_F	[12.9/−64.1/−63.5/−58.9/ 29.5/−3.3/40.3/55.6/51.3/ −43.0/84.7/70.3/−19.7/ −26.2]_T	2.25×10⁻⁵
A_SB_FD_S	[−8.5/73.8/−24.6/64.8/64.1/ −38.3/−48.6/29.5/−88.0/0.8/ 24.9/−75.1/−72.7/12.0]_T	2.17×10⁻⁵
A_SB_FD_F	[−11.3/83.4/−16.7/65.7/−23.5/ 70.9/86.9/−57.8/33.8/7.2/ 28.8/−70.8/5.9/−66.3]_T	2.07×10⁻⁵
Note: \|b₁₆\|—Absolute value of extension-twisting coupling flexibility coefficient.

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表 7 CF/EP层合板扭曲率变形解析解与数值解

Table 7. Analytical and numerical solutions of the distortion rate of CF/EP laminates

Type	Analytical ${\kappa _{xy}}$	Numerical ${\kappa _{xy}}$	Promotion
A_SB_tD_S	0.68×10⁻²	0.68×10⁻²	-
A_SB_tD_F	0.90×10⁻²	0.90×10⁻²	32.35%
A_SB_FD_S	0.87×10⁻²	0.87×10⁻²	27.94%
A_SB_FD_F	0.83×10⁻²	0.83×10⁻²	22.06%
Note: ${\kappa _{xy}}$—The torsional curvature of laminates.

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表 8 CF/EP试验件的材料属性

Table 8. Properties of CF/EP test pieces

Young’s modulus/GPa	E₁	135.0
Young’s modulus/GPa	E₂	9.0
Shear modulus/GPa	G₁₂	3.9
Poisson’s ratio	ν₂₁	0.3
Thickness of single layer/mm	t	0.155

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