曲面碳纤维增强树脂复合材料点阵夹芯结构的弯曲和振动特性

唐玉玲; 韩露; 张峻霞; 任煜赫; 姜美姣

doi:10.13801/j.cnki.fhclxb.20220825.003

曲面碳纤维增强树脂复合材料点阵夹芯结构的弯曲和振动特性

doi: 10.13801/j.cnki.fhclxb.20220825.003

天津科技大学　轻工食品机械设备集成设计与在线监测天津市重点实验室，天津 300222

基金项目: 国家自然科学基金(11272105)；天津市科技计划项目(20JCYBJC01430)

详细信息

通讯作者:
张峻霞，博士，教授，博士生导师，研究方向为轻量化结构设计　E-mail：zjx@tust.edu.cn

中图分类号: TB332
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出版历程
- 收稿日期: 2022-06-08
- 修回日期: 2022-08-08
- 录用日期: 2022-08-11
- 网络出版日期: 2022-08-26
- 刊出日期: 2023-06-15

Bending and vibration performance of curved carbon fiber reinforced polymer pyramidal sandwich structure

Tianjin Key Laboratory of Integrated Design and On-line Monitoring for Light Industry & Food Machinery and Equipment, Tianjin University of Science & Technology, Tianjin 300222, China

Funds: National Natural Science Foundation of China (11272105); Science and Technology Planning Project of Tianjin (20JCYBJC01430)

摘要

摘要: 采用热压一次成型的工艺制备了曲面碳纤维增强树脂复合材料点阵夹芯结构，进行了三点弯试验探究了结构的弯曲破坏载荷与破坏模式。结果显示：结构的载荷位移曲线分为4个阶段，分别为线性阶段、损伤起始阶段、损伤演化阶段和失效阶段；破坏模式主要为面板压溃与节点失效。通过ABAQUS显示求解器建立了有效的弯曲和模态振动模型，得到弯曲破坏过程的失效模式、载荷位移曲线及结构振动模态与固有频率。讨论了不同参数(几何参数和材料性能)对弯曲和振动性能的影响，比较了不同边界条件对固有频率的影响。结果显示：相对密度(面板厚度、芯子直径)的增加会使结构的弯曲破坏载荷和固有频率增大，而芯子倾角ω的增大会使弯曲破坏载荷与固有频率的减小；材料的比刚度越大，固有频率越高。
- 碳纤维增强树脂复合材料 /
- 点阵夹芯结构 /
- 弯曲 /
- 振动 /
- 有限元分析
Abstract: The bending and vibration characteristics of the curved carbon fiber reinforced polymer pyramidal sandwich structure were studied. The hot pressing one-time molding process was used to prepare the curved carbon fiber reinforced polymer pyramidal sandwich structure. A three-point bending test was conducted to explore the bending damage load and damage mode of the structure. The results show that the load-displacement curve of the structure can be divided into 4 stages: Linear stage, damage initiation stage, damage evolution stage and failure stage. The main failure modes are panel collapse and node failure. The ABAQUS display solver was used to establish the effective bending and vibration model. The failure modes and load-displacement curves of the bending damage process, the structural vibration modes and natural frequencies were obtained. The effects of different parameters (geometric parameters, material properties) on the bending and vibration performance were discussed, and the natural frequencies were compared to the impact of various boundary conditions. The results show that an increase in relative density (panel thickness, core diameter) increases the bending failure load and natural frequency of the structure. But increasing the core angle ω leads to a decrease in the bending failure load and natural frequency. The greater the specific stiffness of the material is, the higher the natural frequency will be.
- carbon fiber composites /
- pyramidal sandwich structure /
- bending /
- vibration /
- finite element analysis

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图 1 曲面碳纤维增强树脂复合材料点阵夹芯结构和芯子单胞示意图

Figure 1. Schematic diagram of curved carbon fiber reinforced polymer pyramidal sandwich structure and core cell

α—Arc Angle; h—Height; ω—Angle; B—Panel width; d—Rod diameter; t—Panel thickness; k—Reserved distance; l_c—Length; r—Radius of curvature

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图 2 曲面碳纤维增强树脂复合材料点阵夹芯结构的制备过程

Figure 2. Preparation process of curved carbon fiber reinforced polymer pyramidal sandwich structure

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图 3 曲面碳纤维增强树脂复合材料点阵夹芯结构的三点弯曲载荷示意图

Figure 3. Schematic diagram of three-point bending load of curved carbon fiber reinforced polymer pyramidal sandwich structure

L—Base span; E—Reserved straight edge; U—Displacement load

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图 4 曲面碳纤维增强树脂复合材料点阵夹芯结构有限元示意图

Figure 4. Finite element diagram of curved carbon fiber reinforced polymer pyramidal sandwich structure

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图 5 曲面碳纤维增强树脂复合材料点阵夹芯结构常见的破坏模式

Figure 5. Common failure modes of curved carbon fiber reinforced polymer pyramidal sandwich structure

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图 6 典型曲面碳纤维增强树脂复合材料点阵夹芯结构试件(No.03)三点弯曲的载荷-位移曲线与破坏模式(相对密度为12.53%)

Figure 6. Load-displacement curves and failure modes of a typical curved carbon fiber reinforced polymer pyramidal sandwich structure specimen (No.03) under three-point bending (Relative density is 12.53%)

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图 7 曲面碳纤维增强树脂复合材料点阵夹芯结构(相对密度为12.53%)的破坏模式试验与数值模拟对比

Figure 7. Comparison of failure mode obtained from test and numerical simulation of curved carbon fiber reinforced polymer pyramidal sandwich structure (Relative density 12.53%)

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图 8 曲面碳纤维增强树脂复合材料点阵夹芯结构弯曲的应力分布演化过程

Figure 8. Stress distribution and evolution process of curved carbon fiber reinforced polymer pyramidal sandwich structure under bending

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图 9 曲面碳纤维增强树脂复合材料点阵夹芯结构弯曲载荷最终失效时的损伤情况

Figure 9. Damage of curved carbon fiber reinforced polymer pyramidal sandwich structure when bending load finally failure

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图 10 曲面碳纤维增强树脂复合材料点阵夹芯结构有限元的网格收敛性

Figure 10. Mesh convergence of curved carbon fiber reinforced polymer pyramidal sandwich structure finite element

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图 11 曲面碳纤维增强树脂复合材料点阵夹芯结构的工况：((a)、(b)) 受力与自由荷载工况；(c) 完全自由工况

Figure 11. Working conditions of curved carbon fiber reinforced polymer pyramidal sandwich structure: ((a), (b)) Stress and free load conditions; (c) Completely free working condition

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图 12 曲面碳纤维增强树脂复合材料点阵夹芯结构的前六阶模态：(a)一阶；(b)二阶；(c)三阶；(d)四阶；(e)五阶；(f)六阶

Figure 12. First six modes of curved carbon fiber reinforced polymer pyramidal sandwich structure: (a) First order; (b) Second order; (c) Third order; (d) Fourth order; (e) Fifth order; (f) Sixth order

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图 13 不同面板厚度t对曲面碳纤维增强树脂复合材料点阵夹芯结构弯曲破坏载荷的影响

Figure 13. Influence of different panel thickness t on the bending failure load of curved carbon fiber reinforced polymer pyramidal sandwich structure

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图 14 不同面板厚度t对曲面碳纤维增强树脂复合材料点阵夹芯结构固有频率的影响

Figure 14. Influence of different panel thickness t on natural frequency of curved carbon fiber reinforced polymer pyramidal sandwich structure

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图 15 不同芯子直径d对曲面碳纤维增强树脂复合材料点阵夹芯结构弯曲破坏载荷的影响

Figure 15. Effect of different core diameter d on bending failure load of curved carbon fiber reinforced polymer pyramidal sandwich structure

h—Hight

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图 16 曲面碳纤维增强树脂复合材料点阵夹芯结构芯子直径d对频率的影响

Figure 16. Effect of different core diameter d of curved carbon fiber reinforced polymer pyramidal sandwich structure on frequency

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图 17 不同芯子倾角ω对曲面碳纤维增强树脂复合材料点阵夹芯结构的影响

Figure 17. Different core angles ω influence on of curved carbon fiber reinforced polymer pyramidal sandwich structure

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图 18 不同材料对曲面碳纤维增强树脂复合材料点阵夹芯结构频率的影响

Figure 18. Influence of different materials on the structural frequency of curved carbon fiber reinforced polymer pyramidal sandwich structure

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表 1 碳纤维增强环氧树脂基复合材料(T300/BMP-316)单层预浸料的力学性能

Table 1. Mechanical properties of carbon fiber reinforced epoxy resin matrix composites (T300/BMP-316) monolayer prepreg

Property	Value
Longitudinal stiffness E₁₁/GPa	123
Transverse stiffness E₂₂/GPa	8.4
Out-of-plane stiffness E₃₃/GPa	8.4
Poisson’s ratio ν₁₂, ν₁₃, ν₂₃	0.32, 0.32, 0.3
Shear modulus G₁₂, G₁₃, G₂₃/MPa	5500, 5500, 3000
Longitudinal tensile strength X_T/MPa	2100
Longitudinal compressive strength X_C/MPa	800
Transverse tensile strength Y_T/MPa	25
Transverse compressive strength Y_C/MPa	120
Out-of-plane tensile strength Z_T/MPa	50
Density $ \rho $/(kg·m⁻³)	1560

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表 2 曲面碳纤维增强树脂复合材料点阵夹芯结构的弯曲破坏载荷(相对密度为12.53%)

Table 2. Bending failure load of curved carbon fiber reinforced polymer pyramidal sandwich structure (Relative density is 12.53%)

No.	Test/N	Average/N	Numerical simulation/N	Error/%
01	1751	1625	1581	−2.7
02	1680
03	1446

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表 3 曲面碳纤维增强树脂复合材料点阵夹芯结构在不同工况下的前六阶频率

Table 3. First six frequencies of curved carbon fiber reinforced polymer pyramidal sandwich structure under different working conditions

Natural frequency/Hz	Work condition
Natural frequency/Hz	CFCF	CFFF	FFFF
First order	1425.3	371.62	1.83
Second order	2061.8	409.46	2.33
Third order	2127.9	784.33	4.01
Fourth order	2639.3	1013.31	5.61
Fifth order	2716.3	1524.5	8.22
Sixth order	2953.6	1585.5	9.25

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表 4 曲面碳纤维增强树脂复合材料点阵夹芯结构试件参数

Table 4. Parameters of curved carbon fiber reinforced polymer pyramidal sandwich structure specimen

No.	Number of panel layers	Lay-up	Relative density/%	Quality/g
1	6	[0°/90°]₃	8.45	30
2	8	[0°/90°]₄	10.53	45
3	10	[0°/90°]₅	12.53	66
4	12	[0°/90°]₆	14.43	81

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表 5 不同复合材料的基本力学性能参数

Table 5. Basic mechanical property parameters of different composites

Symbol	T300/BMP-316	T700/Epoxy^[17]	T800 H/2500^[18]	IM6/Epoxy^[19]	Glass/Epoxy^[19]
E₁₁/GPa	123	132	155	203	60
E₂₂/GPa	8.4	10.3	9.0	11.2	13
E₃₃/GPa	8.4	10.3	9.0	11.2	13
ν₁₂, ν₁₃, ν₂₃	0.32, 0.32, 0.3	0.25, 0.25, 0.38	0.3, 0.3, 0.3	0.32, 0.32, 0.32	0.3, 0.3, 0.3
G₁₂, G₁₃, G₂₃/MPa	5500, 5500, 3000	6500, 6500, 3910	4550, 4550, 4550	8400, 8400, 8400	3400, 3400, 3400
X_T/MPa	2100	2100	2900	3500	1800
X_C/MPa	800	1050	1600	1540	650
Y_T/MPa	25	24	70	56	40
$ \rho $/(kg·m⁻³)	1560	1570	1600	1600	2100
E/$ \rho $	78.85	84.07	96.88	126.88	28.57
Note: E/$ \rho $—Specific stiffness.

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