复合材料夹芯结构准静态稳定性性能现状概述

邓晓星; 朱子旭; 陈长海; 胡年明

复合材料夹芯结构准静态稳定性性能现状概述

1.
海军工程大学舰船工程系, 武汉 430033
2.
华中科技大学船舶与海洋工程学院, 武汉 430074

基金项目: 国家自然科学基金 (52201391)

详细信息

通讯作者:
朱子旭，博士，讲师，研究方向为复合材料耐压结构强度和稳定性　E-mail: 769986641@qq.com

中图分类号: TB332
计量
- 文章访问数: 50
- HTML全文浏览量: 30
- 被引次数: 0
出版历程
- 收稿日期: 2023-12-13
- 修回日期: 2024-03-01
- 录用日期: 2024-03-09
- 网络出版日期: 2024-04-16

Research status of quasi-static stability performance of composite sandwich structures

1.
Department for Naval Architecture and Ocean Engineering, Navy University of Technology, Wuhan 430033, China
2.
School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

Funds: National Natural Science Foundation of China(No.52201391)

摘要

摘要: 复合材料夹芯结构由于其优异的比强度，比刚度及较小的表观密度的优点而广泛应用于航空航天、船舶等各个领域。本文从理论研究、仿真分析、实验研究这三个方面出发，综述了蜂窝、泡沫、点阵、褶皱四种夹芯结构在准静态稳定性研究方面的现状。蜂窝夹芯结构的研究较为成熟，进一步的研究应集中于应用领域；泡沫夹芯结构在面芯问题方面有待增强，可考虑纤维缝合技术；褶皱夹芯结构理论方面有待进一步研究，潜力巨大；点阵夹芯结构较其它结构抗屈曲能力更强，但是依然存在面芯粘接问题。复合材料夹芯结构在准静态稳定性方面的问题主要集中在面芯粘接方面，纤维缝合技术可以有效增强面芯性能，该方面的研究对增强复合材料夹芯结构稳定性有较强的潜力。
- 复合材料 /
- 夹芯结构 /
- 稳定性 /
- 蜂窝夹芯结构 /
- 泡沫夹芯结构 /
- 点阵夹芯结构 /
- 褶皱夹芯结构
Abstract: Composite sandwich structures are widely used in aerospace, shipbuilding and other fields due to their excellent strength-and stiffness-to-weight ratio and small apparent density. From the three aspects of theoretical research, simulation analysis and experimental research, this paper summarizes the current situation of quasi-static stability research of honeycomb , foam, lattice and foldcore sandwich structures. The research on honeycomb sandwich structure is relatively mature, and further research should focus on the application field. The foam sandwich structure needs to be strengthened in the panel/core interface, and the fiber stitching technology can be considered. The theory of foldcore sandwich structure needs further study and has great potential. The lattice sandwich structure has stronger anti-buckling ability than other structures, but there is still a problem of face/core bonding. The problem of the quasi-static stability of the composite sandwich structure is mainly focused on the bonding of the face/core. The fiber stitching technology can effectively enhance the performance of the face/core. The research in this area has a strong potential for enhancing the stability of the composite sandwich structure.
- composite material /
- sandwich structure /
- stability /
- honeycomb sandwich structure /
- foam sandwich structure /
- lattice sandwich structure /
- folded sandwich structure

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图 1 四种典型夹芯结构示意图

Figure 1. Schematic diagram of four typical sandwich structures

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图 2 分层蜂窝结构示意图^[34]

Figure 2. Hierarchical honeycombs structure diagram^[34]

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图 3 $k$对临界屈曲应变的影响^[48]

Figure 3. The effect of $k$ on the critical buckling strain^[48]

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图 4 三种不同点阵夹芯结构示意图^[52]

Figure 4. Schematic diagram of three different lattice sandwich structures^[52]

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图 5 三点弯曲载荷作用下金属点阵夹芯梁的失效机制图^[54]

Figure 5. Collapse mechanism map of metallic lattice truss core sandwich beams under threepoint bending^[54]

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图 6 破坏载荷有限元与试验曲线^[68]

Figure 6. Failure load of finite element and experiment curve^[68]

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图 7 Kagome 构型碳纤维点阵材料结构有限元模型^[84]

Figure 7. The finite element model of Kagome configuration carbon fiber lattice material structure^[84]

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图 8 理想超轻夹芯结构平压强度与相对密度之间的关系^[86]

Figure 8. The relationship between the compressive strength and relative density of the ideal ultralight sandwich structure^[86]

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图 9 等效应力-应变曲线^[87]

Figure 9. Equivalent stress-strain curves^[87]

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图 10 压缩载荷下碳纤维复合材料褶皱夹芯结构失效机理^[90]

Figure 10. Failure mechanism map for woven carbon fiber composite curved-creaseorigami foldcore sandwich under compression^[90]

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图 11 蜂窝夹层复合材料压缩试件破坏照片^[92]

Figure 11. Photo of experimental failure mode of honeycomb sanwich composite compression specimens^[92]

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图 12 TGHSS钎焊组件示意图^[95]

Figure 12. Schematic diagram of brazing assembly for TGHSS^[95]

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图 13 三种失效模式照片^[99]

Figure 13. Three failure mode photos^[99]

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图 14 短切纤维增韧示意图^[39]

Figure 14. Toughening schematic diagram of chopped fiber^[39]

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图 15 泡沫夹层结构的缝合工艺^[106]

Figure 15. Stitching process for foam sandwich structures: (a) stitching (b) locking (c) tightening^[106]

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图 16 复合材料金字塔点阵夹芯板的制造路线^[108]

Figure 16. the manufacturing route for making composite pyramidal lattice core sandwich panels^[108]

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表 1 四种典型夹芯结构特点

Table 1. Four typical sandwich structure characteristics

Structure Type	Strength	Carrying capacity	Application	Manufacture
Honey-comb	○	○	√	×
Foam	√	×	○	○
Lattice	○	○	○	×
Folded	○	√	×	√
Notes: ○=very good , √=good , ×=not good.

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表 2 金字塔点阵夹芯结构不同边界条件下的屈曲临界载荷理论公式^[55]

Table 2. Theoretical formula of buckling critical load of pyramid lattice sandwich structure under different boundary conditions^[55]

boundary condition	critical buckling load $ {P_{{\text{cr}}}} $/N
Simply-supported at both ends	$ {P_{{\text{cr}}}} = \dfrac{{2{c^2}\left({A^{\text{t}}}{D^{\text{t}}} - {B^{\text{t}}}{B^{\text{t}}}\right){{\left(n{\text{π}}/L\right)}^4} + 4 S{D^{\text{t}}}{{\left(n{\text{π}}/L\right)}^2}}}{{{C^{\text{2}}}{A^{\text{t}}}{{\left(n{\text{π}}/L\right)}^2} + 2 S}} $
Clamped at one end, and free at the other end	$ {P}_{\text{cr}}={\scriptstyle \dfrac{2{c}^{2}\left({A}^{\text{t}}{D}^{\text{t}}-{B}^{\text{t}}{B}^{\text{t}}\right){\left({\left(2n-1\right){\text{π}}/2L}\right)}^{4}+4 S{D}^{\text{t}}{\left(\left(2n-1\right)n{\text{π}}/2L\right)}^{2}}{{C}^{\text{2}}{A}^{\text{t}}{\left(\left(2n-1\right)n{\text{π}}/2L\right)}^{2}+2 S}} $
Clamped at one end, and free to slide in the longitudinal direction at the other end	$ {P_{{\text{cr}}}} = \dfrac{{2{c^2}({A^{\text{t}}}{D^{\text{t}}} - {B^{\text{t}}}{B^{\text{t}}}){{\left(2n{\text{π}}/L\right)}^4} + 4 S{D^{\text{t}}}{{\left(2n{\text{π}}/L\right)}^2}}}{{{C^{\text{2}}}{A^{\text{t}}}{{\left(2n{\text{π}}/L\right)}^2} + 2 S}} $
Clamped at one end, and free to slide in oth the longitudinal and transverse directions at the other end	$ {P}_{\text{cr}}={\scriptstyle \dfrac{2{c}^{2}\left({A}^{\text{t}}{D}^{\text{t}}-{B}^{\text{t}}{B}^{\text{t}}\right){\left(\left(2n-1\right){\text{π}}/L\right)}^{4}+4 S{D}^{\text{t}}{\left(\left(2n-1\right){\text{π}}/L\right)}^{\text{2}}}{{C}^{\text{2}}{A}^{\text{t}}{\left(\left(2n-1\right){\text{π}}/L\right)}^{2}+2 S}} $
Notes: $n$ represents the buckling mode order ; $S$ represents the shear stiffness of the core ; $c$ represents the thickness of the core ; $A$ represents the tensile stiffness of the face sheet ; $B$ represents the coupling stiffness of the face sheet ; $D$ represents the bending stiffness of the face sheet ; The superscript $t$ represents the upper panel ; The subscript represents the lower panel .

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表 3 多层锥体点阵夹芯结构在面内压缩载荷作用下的四种失效模式^[57]

Table 3. Four failure modes of multi-layer cone lattice sandwich structure under in-plane compressive load^[57]

In-plane compressive failure mode	Analytical collapse load expression
Macro elastic buckling	$ {P_{{\text{cr}}}} = \dfrac{{\dfrac{{2{k^4}{\pi ^4}{D_{\text{f}}}{D_0}}}{{{L^4}}} + \dfrac{{{k^2}{\pi ^2}D}}{{{L^2}}}S}}{{\dfrac{{{k^2}{\pi ^2}{D_0}}}{{{L^2}}} + S}} $,when$ {P_{{\text{cr}}}} < \dfrac{{4 bh{\sigma _y}}}{{\sqrt 3 }} $
Macro inelastic buckling	$ {P_{{\text{cr}}}} = \dfrac{{\dfrac{{2{k^4}{\pi ^4}{D_{\text{f}}}{D_0}}}{{{L^4}}} + \dfrac{{{k^2}{\pi ^2}D}}{{{L^2}}}S}}{{\dfrac{{{k^2}{\pi ^2}{D_0}}}{{{L^2}}} + S}} $,when$ {P_{{\text{cr}}}} \geqslant \dfrac{{4 bh{\sigma _y}}}{{\sqrt 3 }} $
Local elastic face buckling	$ {P_{{\text{FB}}}} = \dfrac{{{k^{'2}}{\pi ^2}{E_{\text{s}}}b}}{{6(1 - {\nu ^2})}}\dfrac{{{h^3}}}{{{d^2}}} $,when$\dfrac{h}{d} < \sqrt {\dfrac{{24(1 - {v^2}){\sigma _y}}}{{\sqrt 3 {k^{'2}}{\pi ^2}{E_{\text{s}}}}}} $
Local inelastic face buckling	$ {P_{{\text{FB}}}} = \dfrac{{{k^{'2}}{\pi ^2}{E_{\text{t}}}b}}{6}\dfrac{{{h^3}}}{{{d^2}}} $,when$\dfrac{h}{d} < \sqrt {\dfrac{{24(1 - {v^2}){\sigma _y}}}{{\sqrt 3 {k^{'2}}{\pi ^2}{E_{\text{s}}}}}} $
Notes: $\nu $ represents the poisson's ratio ; $k$ represents the shear coefficient ; ${k^{'}}$ represents the shear correction factor for face sheet ; ${E_{\text{t}}}$ represents the tangent modulus ; ${E_{\text{s}}}$ represents the solid material modulus ; ${\sigma _y}$ represents the yield strength ; ${D_{\text{f}}}$ represents the face sheet stiffness ; ${D_0}$ represents the core stiffness;$S$ represents the shear stiffness of the core ;$h$ represents the facesheet thickness ; $d$ represents the inter-node spacing ; $b$ represents the width of the core ; $L$ represents the length of the core .

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表 4 层级褶皱结构夹层梁压缩载荷作用下失效模式分类

Table 4. Failure modes of the hieratchical structure with second order corrugated under transverse^[65]

Destructed sites	mode of failure	Basic solution of failure criterion
First-level hierarchical structure	Sandwich plate buckling	${P_x} \geqslant {P_{{\text{cr}}}}$
	Euler beam buckling	${P_x} \geqslant {P_{{\text{cr}}}}$
	Surface plastic buckling	$\sigma \geqslant \left[ \sigma \right]$
	Surface plate buckling	${P_x} \geqslant {P_{{\text{cr}}}}$
	Surface beam wrinkle	${P_x} \geqslant {P_{{\text{cr}}}}$
	Shear failure	${P_x} \geqslant {P_{\text{s}}}$
Second-level hierarchical structure	plastic buckling	$\sigma \geqslant \left[ \sigma \right]$
	buckling of thin plates	${P_x} \geqslant {P_{{\text{cr}}}}$
	Euler beam buckling	${P_x} \geqslant {P_{{\text{cr}}}}$
Notes: ${P_{{\text{cr}}}}$ represents the critical buckling load;${P_x}$ represents in-plane compressive load;$\sigma $ represents the stress of the component;$\left[ \sigma \right]$ represents the yield stress of materials

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表 5 理论分析总结

Table 5. Theoretical analysis summary

Structure type	Theory name	Identification number
Plate	Reissner type theory	[24]
	Hoff type theory	[25]
	Du Qinghua type theory	[26]
Honeycomb	Honeycomb plate theory	[30][31]
	Sandwich theory	[32]
	Hierarchical honeycomb theory	[34]
	Quasi-honeycomb theory	[35]
	Mixed honeycomb core theory	[36]
	Refined Shear Deformation Theory	[37]
Foam	Buckling theory based on rod	[41]
	Fiber reinforcement theory based on Rayleigh-Ritz method	[48]
	Modified buckling theory of columns	[49]
	The formula for calculating the overall stability coefficient	[50]
Lattice	Tetrahedron theoretical formula	[55]
	Pyramid theoretical formula	[53][55][56]
	The theoretical formula of multi-layer cone	[57]
Folded	Zeta fold structure theory	[61]
	Isotropic fold structure theory	[63]
	M-type fold structure theory	[64]
	Hierarchical fold structure theory	[65][66]
	Carbon fiber reinforced wrinkle theory	[67]

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表 6 混杂蜂窝夹芯板与单层蜂窝夹芯板在不同工况下的临界屈曲载荷比较^[69]

Table 6. Comparison of critical buckling loads of hybrid honeycomb sandwich panels and single-layer honeycomb sandwich panels under different working conditions^[69]

Type of load	Single-layer honeycomb sandwich panel/ (N·mm^-1)	hybrid honeycombsandwich panel/ (N·mm^-1)	Critical load growth rate/%
Subjected to axial compressive load	895.8	988.2	10.31
Subjected to shear load	2040.7	2212.3	3.34
Under the combined load of shear and compression ratio of 1 : 1	778.3	839.1	7.83

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表 7 三种方法下的屈曲载荷与极限承载对比^[71]

Table 7. Comparison of buckling load results and limit load results under three methods^[71]

Method	Buckling load/N	Relative accuracy	Limit load/N	Relative accuracy
Eigenvalue method	13.11	13.98	——	——
Arc length method	12.50	17.98	17.95	2.97
Experiment	15.24	0	18.50	0

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表 8 屈曲应力计算结果与试验结果的对比^[78]

Table 8. Contrast for buckling stress between results of present model and experiments^[78]

		Failure mode	Strength/kN
Experiment	Sample1	Buckling	20.13
	Sample2	Buckling	20.00
	Sample3	Buckling	21.96
	Sample4	Buckling	19.14
	Sample5	Buckling	19.29
	Sample6	Buckling	20.74
	Mean		20.21
	Present mode		18.32

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表 9 不同树脂柱弹模下夹层板的屈曲临界载荷^[83]

Table 9. Critical buckling loads of sandwich plates for different elastic modulus of resinic columns^[83]

Elastic modulus of resinic columns/MPa	Critical buckling load/N
1500	218.98
2000	220.54
2500	221.72
3500	223.43
4500	224.62

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表 10 不同树脂柱间距下夹层板的屈曲临界载荷^[83]

Table 10. Critical buckling loads of sandwich plates for different cell sizes^[83]

Adjacent resinic columns distance/mm	Critical buckling load/N
40	223.43
80	209.49
160	199.78

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表 11 仿真模型总结

Table 11. Simulation model summary

structure type	model name	identification number
Honeycomb	Honeycomb sandwich panel with transition zone	[68]
	Hybrid honeycomb sandwich panel	[69]
	Honeycomb cylinder model	[70]
	a novel improved star-shaped honeycomb sand-wich panel	[72]
	Two-Dimensional Dimensional Reduction Model	[73]
	Two-dimensional equivalent plate model	[74]
Foam	Model of grid reinforced foam sandwich webs	[76]
	Foam sandwich plate model simulating sutures	[77]
	Type I sandwich web model filled with aluminum foam	[79]
	Asymmetric Sandwich Panels	[80]
Lattice	Pyramid lattice sandwich plate model	[82]
	3 D-Kagome lattice sandwich plate model	[82]
	Resin column reinforced lattice sandwich plate model I-type pyramid lattice sandwich panel model Double triangular lattice sandwich plate model with reinforcing frame	[83] [87] [88]
Folded	Folded core plate model with defects	[89]
	S-shaped fold sandwich plate model	[90]
	Carbon fiber reinforced folded truncated cone shell model	[91]

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表 12 不同特征角度下试件的刚度与极限承载对比^[120]

Table 12. Comparison of stiffness and limit load under different characteristic angles

Characteristic angle/(º)	Stiffness/(N·mm^-1)	Limit load/kN
0	8023	25.30
1	7042	20.67

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