侵彻作用下负泊松比蜂窝夹芯结构动态响应

doi:10.12382/bgxb.2022.0208

摘要/Abstract

摘要：

随着战争的不断加剧,弹丸对高价值设施有严重威胁,提高各类设施的抗侵彻性能尤为关键。通过弹道枪实验和数值模拟方法研究3D打印蜂窝夹芯结构的抗侵彻性能。通过弹道冲击实验对比分析7块试件的动态响应。夹芯结构由Q345钢顶板、碳纤维增强复合材料(CFRP)背板和铝合金蜂窝芯层组成。实验对比了3种蜂窝芯层构型:泡沫铝、正六边形及具有负泊松比效应的内凹六边形。对比结果表明,与蜂窝芯层为泡沫铝和正泊松比的蜂窝夹芯结构相比,负泊松比蜂窝夹芯结构残余速度较低,抗侵彻性能较强。通过数值模拟研究获得了负泊松比蜂窝夹芯结构的动态响应过程。通过参数分析进一步得到胞元内折角度、背板厚度以及背板类型对负泊松比蜂窝夹芯结构抗侵彻性能的影响规律。数值研究结果表明,3种因素对蜂窝夹芯结构抗侵彻性能均存在一定影响。运用非支配遗传算法对初始蜂窝夹芯结构进行多目标优化,在保证相同弹道极限速度的前提下使得其质量减轻21.1%。

关键词: 蜂窝夹芯结构, 碳纤维增强复合材料, 负泊松比, 抗弹性能, 遗传算法

Abstract:

With the intensification of war, projectiles pose a serious threat to high-value facilities, and improving the anti penetration performance of various facilities is particularly crucial. Study the anti penetration performance of 3D printed honeycomb sandwich structure through ballistic gun experiments and numerical simulation methods. Compare and analyze the dynamic response of 7 specimens through ballistic impact experiments. The sandwich structure consists of a Q345 steel top plate, a carbon fiber reinforced composite (CFRP) back plate, and an aluminum alloy honeycomb core layer. Three honeycomb core configurations are compared experimentally: foam aluminum, positive hexagon and concave hexagon with Negative Poisson’s ratio effect. The results show that compared with the honeycomb sandwich structure with foam aluminum core and positive Poisson’s ratio, the honeycomb sandwich structure with Negative Poisson’s ratio has lower residual velocity and stronger penetration resistance. The dynamic response process of honeycomb sandwich structure with Negative Poisson’s ratio is obtained through numerical simulation. Through parameter analysis, the influence of cell inflection angle, back plate thickness and back plate type on the anti penetration performance of honeycomb sandwich structures with Negative Poisson’s ratio is further obtained. The numerical research results indicate that all three factors have a certain impact on the anti penetration performance of honeycomb sandwich structures. The non dominated genetic algorithm is used to optimize the honeycomb sandwich structure with initial Negative Poisson’s ratio, and its mass is reduced by 21.1% under the premise of ensuring the same ballistic limit speed.

Key words: honeycombsandwich structure, carbon fiber reinforced composite, Negative Poisson’s ratio, ballistic resistance, genetic algorithm

刘彦, 王百川, 闫俊伯, 闫子辰, 时振清, 黄风雷. 侵彻作用下负泊松比蜂窝夹芯结构动态响应[J]. 兵工学报, 2023, 44(7): 1938-1953.

LIU Yan, WANG Baichuan, YAN Junbo, YAN Zichen, SHI Zhenqing, HUANG Fenglei. Dynamic Response of Honeycomb Sandwich Plate with Negative Poisson’s Ratio under Penetration[J]. Acta Armamentarii, 2023, 44(7): 1938-1953.

图/表 40

图1 蜂窝示意图以及相关尺寸(左为参数示意图,右为各参数尺寸)

Fig.1 Schematic diagram of honeycomb and relevant dimensions(left: schematic diagram of the parameters; right:parameter dimensions)

图2 实验构件构造示意图

Fig.2 Structural diagram of experimental components

表1 蜂窝尺寸

Table 1 Size of honeycomb structure

结构	胞元角度 θ/(°)	胞元壁厚度 t/mm	水平胞元壁长度 L₁/mm	斜胞元壁长度 L₂/mm	整体质量/ kg	整体厚度/ mm
传统	60	0.5	5	2.5	0.787	38.1
内凹	60	0.5	5	2.5	0.834	38.1

图3 蜂窝胞元壁材料应力-应变曲线

Fig.3 Stress-strain curve of basic materials of the cell wall

表2 Q345钢板基本力学参数

Table 2 Typical mechanical properties of Q345 steel plate

顶板	屈服应力/MPa	极限应力/MPa	断裂应变
Q345钢	370	520	0.21

表3 CFRP板基本力学参数

Table 3 Typical mechanical properties of CFRP

背板	抗拉强度/MPa	弹性模量/GPa	极限应变%
CFRP[0°/90°]	3140	260	1.2

图4 弹道枪测试装置设置

Fig.4 Setting of the ballistic gun test device

表4 各工况外场实验结果

Table 4 Field experiment results under various conditions

芯层类型	构型	面密度/ (g·cm^-2)	初始速度/ (m·s^-1)	毁伤情况	残余速度/ (m·s^-1)	冲击侧射孔直径/mm	后侧射孔参数/mm
泡沫铝^[19]	钢板-泡沫铝-CFRP	4.77	369.1	贯穿	152.8	7.73	11×27
			513.2	贯穿	256.8	7.61	39×73
			576.0	贯穿	299.0	7.85	54×110
正六边形结构	钢板-正六边形-CFRP	4.49	356.7	贯穿	67.4	7.70	16×29
内凹六边形结构	内凹六边形芯层	3.83	538.0	贯穿	237.0	7.81
	钢板-内凹六边形-CFRP	4.77	364.9	未贯穿	0(侵彻深度为31.3mm)	7.54	29×55
	钢板-内凹六边形-CFRP	4.77	616.2	贯穿	339.0	7.64	29×55

图5 370m/s左右冲击速度下的速度响应比较

Fig.5 Velocity responses comparison at impact speeds around 370m/s

图6 500m/s以上冲击速度下的速度响应比较

Fig.6 Velocity responses comparison at impact speeds above 500m/s

图7 正六边形和内凹六边形蜂窝夹芯结构横截面CT扫描图

Fig.7 CT scan of cross-section of the honeycomb structure

图8 单个蜂窝胞元毁伤模式

Fig.8 Damage mode of a single cellular cell

图9 各试件CFRP板毁伤模式

Fig.9 Damage mode of the CFRP sheet of different specimens

图10 不同弹道速度下各试件CFRP板损坏面积

Fig.10 Damage area of the CFRP sheet with of different specimens under different impact velocity conditions

图11 有限元模型

Fig.11 Finite element model

表5 钢板以及铝合金蜂窝芯层的材料模型及参数

Table 5 Characteristics of steel plate and Al-alloy honeycomb core

材料	密度/ (g·cm^-3)	杨氏模量/GPa	泊松比	屈服应力/ MPa	正切模量/ GPa	失效应变	DIF模型
Q345钢	7.8	200	0.3	基于参考文献[23]采用LCSS输入图12所示曲线			Malvar & Crawford模型^[22]
材料	密度/ (g·cm^-3)	杨氏模量/GPa	泊松比	屈服应力/ MPa	正切模量/ GPa	失效应变	DIF模型
铝合金	2.78	86.1	0.33	采用LCSS,输入基于图3测试应力-应变曲线			忽略

图12 Q345钢应力-应变曲线

Fig.12 Stress-strain curve of Q345 steel

图13 CFRP有限元模型

Fig.13 Finite element model of CFRP

表6 CFRP背板材料性能

Table 6 Material properties of CFRP

表7 数值模拟残余速度和实验残余速度比较

Table 7 Residual velocity of simulation and experimental results

类型	面板	弹道速度/ (m·s^-1)	残余速度/(m·s^-1)			偏差/%
类型	面板	弹道速度/ (m·s^-1)	v_{r_exp}	v_{r_num}	v_{r_num}/v_{r_exp}	偏差/%
泡沫铝	钢板-泡沫铝-CFRP	369.1	152.8	172	1.13	12.57
		513.2	256.8	220	0.86	-14.3
		576	299	265	0.89	-11.37
正六边形	钢板-正六边形-CFRP	356.7	67.4	85.7	1.27	27.15
内凹六边形	内凹六边形	538	237	265	1.12	11.81
	钢板-内凹六边形-CFRP	364.9	—(侵深为31.3mm)	—(侵深为35.7mm)	—(侵深之比为1.14)	14.06
		616.2	339	316	0.93	-6.78
		总体			1.05	14.01

图14 横截面破坏模式比较(上为实验所得侵彻示意图,下为仿真所得侵彻示意图)

Fig.14 Cross-section damage comparison (top: experimental penetration schematic diagram; bottom: simulated penetration schematic diagram)

图15 面板的破坏模式比较(左为实验结果,右为仿真结果)

Fig.15 Damage comparison of panels(experiment on the left and simulation on the right)

图16 弹丸侵彻内凹六边形蜂窝夹芯结构贯穿过程

Fig.16 Process of projectile penetrating the concave hexagonal honeycomb sandwich plate

图17 负泊松比蜂窝夹芯结构各部分吸收能量

Fig.17 Energy absorbed by various parts of honeycomb structure with Negative Poisson’s ratio

表8 芯层配置对弹道极限以及能量吸收的影响

Table 8 Effect of core configuration on ballistic limit and energy absorption

类型	弹道极限速度/ (m·s^-1)	极限时所吸收能量/J	弹道极限下单位质量吸收能量/ (J·kg^-1)
钢板-泡沫铝-CFRP	190	72.7	69.6
钢板-正六边形-CFRP	350	247	247.5
钢板-内凹六边形-CFRP	390	307	293.8

图18 芯层类型对弹道极限速度以及吸收能量的影响

Fig.18 Effects of core configuration on ballistic limit and energy absorption

图19 相同初速度下各类型蜂窝夹芯结构速度响应

Fig.19 Velocity response of four types of honeycomb panels with ballistic impact

图20 等面密度蜂窝夹芯结构弹道极限速度

Fig.20 Ballistic limit velocity of different structures of the same area density

图21 不同胞元角度的内凹六边形蜂窝夹芯结构横截面

Fig.21 Cross-section of honeycomb with different cell angles

表9 内凹蜂窝角度对弹道极限和能量吸收影响

Table 9 Influence of core configuration on ballistic limit and energy absorption

胞元角度/ (°)	弹道极限速度/ (m·s^-1)	弹道极限时的吸收能量/J	弹道极限时单位质量的吸收能量/(J·kg^-1)
30	400	322	308.1
45	390	307	293.8
60	390	307	293.8

图22 侵彻作用下各蜂窝夹芯结构弹道极限速度以及吸收能量

Fig.22 Ballistic limit and energy absorption at different angles

图23 600m/s冲击初速度下不同胞元角度的负泊松比蜂窝夹芯结构毁伤模式

Fig.23 Damage modes of honeycomb sandwich structures with Negative Poisson’s ratio at different cell angles under 600m/s initial impact velocity

表10 CFRP厚度对弹道极限及能量吸收的影响

Table 10 Influence of CFRP panel thickness on ballistic limit and energy absorption

CFRP 面板厚度/ mm	弹道极限速度/ (m·s^-1)	弹道极限时吸收能量/J	弹道极限时单位质量所吸收能量/(J·kg^-1)
1	390	307	293.8
2	480	464	490.2
3	620	775	828.8

图24 CFRP背板厚度对弹道极限速度及吸收能量影响

Fig.24 Influence of CFRP panel thickness on ballistic limit velocity and energy absorption

图25 不同面板厚度组合蜂窝夹芯结构弹道极限速度

Fig.25 Comparison of ballistic limit velocities of sandwich structures with different panel thickness combinations

表11 蜂窝夹芯结构弹道极限及吸收能量

Table 11 Ballistic limits and energy absorption of honeycomb sandwich structure

背板类型	弹道极限速度/ (m·s^-1)	弹道极限时所吸收能量/J	弹道极限时单位质量所吸收能量/(J·kg^-1)
3mm CFRP	620	775	828.8
等面密度0.6mmQ345钢板	250	125	133.7
3mm等体积Q345钢板	320	206	220.3

图26 背板类型对弹道极限以及能量吸收的影响

Fig.26 Influence of rear panel type on ballistic limit and energy absorption

图27 CFRP板和Q345钢板的破坏模式比较

Fig.27 Comparison of damage modes between CFRP sheet and Q345 steel plate

表12 仿真及实验所获得弹道极限速度

Table 12 Ballistic limit velocity obtained by simulation and experiment

t₁/mm	t₂/mm	t₃/mm	θ/(°)	弹道极限速度/ (m·s^-1)
0.5	1.4	3	30	398
0.5	1.0	1	45	200
0.5	1.2	2	60	360
1.5	1.4	2	45	466
1.5	1.0	3	60	600
1.5	1.2	1	30	475
2.0	1.4	1	60	750
2.0	1.0	2	30	659.5
2.0	1.2	3	45	644
1.0	1.4	2	45	367
1.0	1.0	1	30	400
1.0	1.2	3	60	500

图28 适应度进化过程

Fig.28 Fitness evolution process diagram

参考文献 34

[1]	HOU H L, ZHANG C L, LI M, et al. Damage characteristics of sandwich bulkhead under the impact of shock and high-velocity fragments[J]. Explosion and Shock Waves, 2015, 35(1):116-123.
[2]	EVANS K E, NKANSAH M A, HUTCHINSON I J, et al. Molecular network design[J]. Nature, 1991, 353(6340):124. doi: 10.1038/353124a0
[3]	LI X, ZHANG P W, WANG Z H, et al. Dynamic behavior of aluminum honeycomb sandwich panels under air blast: Experiment and numerical analysis[J]. Composite Structures, 2014, 108:1001-1008. doi: 10.1016/j.compstruct.2013.10.034 URL
[4]	任鑫, 张相玉, 谢亿民. 负泊松比材料和结构的研究进展[J]. 力学学报, 2019, 51(3):656-687. doi: 10.6052/0459-1879-18-381
	REN X, ZHANG X Y, XIE Y M. Researchprogress in auxetic material and structures[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3):656-687. (in Chinese)
[5]	QI C, REMENNIKOV A, PEI L Z, et al. Impact and close-in blast response of auxetic honeycomb-cored sandwich panels:experimental tests and numerical simulations[J]. Composite Structures, 2017, 180:161-178. doi: 10.1016/j.compstruct.2017.08.020 URL
[6]	JIN X C, WANG Z H, NING J G, et al. Dynamic response of sandwich structures with graded auxetic honeycomb cores under blast loading[J]. Composites Part B-Engineering, 2016, 106:206-217. doi: 10.1016/j.compositesb.2016.09.037 URL
[7]	IMBALZANO G, PHUONG T, NGO T D, et al. Three-dimensional modelling of auxetic sandwich panels for localised impact resistance[J]. Journal of Sandwich Structures & Materials, 2017, 19(3):291-316.
[8]	IMBALZANO G, LINFORTH S, TUAN DUC N, et al. Blast resistance of auxetic and honeycomb sandwich panels:Comparisons and parametric designs[J]. Composite Structures, 2018, 183:242-261. doi: 10.1016/j.compstruct.2017.03.018 URL
[9]	HOU S Y, LI T T, JIA Z, et al. Mechanical properties of sandwich composites with 3d-printed auxetic and non-auxetic lattice cores under low velocity impact[J]. Materials & Design, 2018, 160:1305-1321.
[10]	SARVESTANI H Y, AKBARZADEH A H, NIKNAM H, et al. 3D printed architected polymeric sandwich panels:energy absorption and structural performance[J]. Composite Structures, 2018, 200: 886-909. doi: 10.1016/j.compstruct.2018.04.002 URL
[11]	YANG C, VORA H D, CHANG Y. Behavior of auxetic structures under compression and impact forces[J]. Smart Materials and Structures, 2018, 27(2):025012. doi: 10.1088/1361-665X/aaa3cf URL
[12]	LI Y, CHEN Z H, XIAO D B, et al. The dynamic response of shallow sandwich arch with auxetic metallic honeycomb core under localized impulsive loading[J]. International Journal of Impact Engineering, 2020, 137:103442. doi: 10.1016/j.ijimpeng.2019.103442 URL
[13]	USTA F, TURKMEN H S, SCARPA F. Low-velocity impact resistance of composite sandwich panels with various types of auxetic and non-auxetic core structures[J]. Thin-Walled Structures, 2021, 163:107738. doi: 10.1016/j.tws.2021.107738 URL
[14]	QI C, YANG S, WANG D, et al. Ballistic resistance of honeycomb sandwich panels under in-plane high-velocity impact[J]. Scientific World Journal, 2013:892781.
[15]	YANG S, QI C, WANG D, et al. A comparative study of ballistic resistance of sandwich panels with aluminum foam and auxetic honeycomb cores[J]. Advances in Mechanical Engineering, 2013:589216.
[16]	WANG Y, YU Y, WANG C, et al. On the out-of-plane ballistic performances of hexagonal,reentrant,square,triangular and circular honeycomb panels[J]. International Journal of Mechanical Sciences, 2020, 173:105402. doi: 10.1016/j.ijmecsci.2019.105402 URL
[17]	王晓强, 胡方靓, 徐双喜. 蜂窝夹芯板的抗高速冲击性能研究[J]. 武汉理工大学学报(交通科学与工程版), 2021, 45(4):709-714.
	WANG X Q, HU F L, XU S X. Study on high speed impact resistance of honeycomb sandwich panel[J]. Journal of Wuhan University of Technology (Transportation Science & Engineering), 2021, 45(4):709-714. (in Chinese)
[18]	曹杰, 葛建立, 王浩, 等. 蜂窝铝冲击波形数值计算及分析[J]. 弹道学报, 2017, 29(4):58-63.
	CAO J, GE J L, WANG H, et al. Numerical simulation on shock waveform of aluminum honeycombs[J]. Journal of Ballistics, 2017, 29(4):58-63. (in Chinese)
[19]	贾然, 赵桂平. 泡沫铝本构行为研究进展[J]. 力学学报, 2020, 52(3):603-622. doi: 10.6052/0459-1879-20-020
	JIA R, ZHAO G P. Progress in constitutive behavior of aluminum foam[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(3):603-622. (in Chinese)
[20]	YANG J K, GU D D, LIN K J, et al. Optimization of bio-inspired bi-directionally corrugated panel impact-resistance structures:numerical simulation and selective laser melting process[J]. Journal of the Mechanical Behavior of Biomedical Materials, 2019, 91:59-67. doi: 10.1016/j.jmbbm.2018.11.026 URL
[21]	ZHANG Y, LU M, WANG C H, et al. Out-of-plane crashworthiness of bio-inspired self-similar regular hierarchical honeycombs[J]. Composite Structures, 2016, 144:1-13. doi: 10.1016/j.compstruct.2016.02.014 URL
[22]	MALVAR L J. Review of static and dynamic properties of steel reinforcing bars[J]. Aci Materials Journal, 1998, 95(5):609-616.
[23]	CHEN J L, SHU W Y, LI J W. Constitutive model of Q345 steel at different intermediate strain rates[J]. International Journal of Steel Structures, 2017, 17(1):127-137. doi: 10.1007/s13296-016-0122-8 URL
[24]	AFDHAL, JUSUF A, GUNAWAN L, et al. Numerical simulation of SHPB to measure the mechanical properties of aluminium foam material at high strain rate by using MAT 163 modified crushable foam[C]//Proceedings of the 7th International Conference on Mechanical and Manufacturing Engineering,Sustainable Energy Towards Global Synergy.Jogjakarta, Indonesia: AIP Publishing, 2017, 1831(1):020057.
[25]	CHENIAEV A, BUTCHER C, MONTESANO J. Predicting the axial crush response of CFRP tubes using three damage-based constitutive models[J]. Thin-Walled Structures, 2018, 129:349-364. doi: 10.1016/j.tws.2018.05.003 URL
[26]	GIANNAROS E, KOTZAKOLIOS A, KOSTOPOULO V, et al. Hypervelocity impact response of CFRP laminates using smoothed particle hydrodynamics method: Implementation and validation[J]. International Journal of Impact Engineering, 2019, 123:56-69. doi: 10.1016/j.ijimpeng.2018.09.016 URL
[27]	KIM Y C, YOON S H, JOO G, et al. Crash analysis of aluminum/CFRP hybrid adhesive joint parts using adhesive modeling technique based on the fracture mechanics[J]. Polymers, 2021, 13(19):3364. doi: 10.3390/polym13193364 URL
[28]	DONG S, GRAENING L, CARNEY K, et al. Analysis of crush-damaged carbon-fiber-reinforced-polymer(CFRP) composites with optimization-assisted post-peak-stress modeling[J]. Journal of Composite Materials, 2021, 55(6):759-774. doi: 10.1177/0021998320957702 URL
[29]	CHEN G M, LI S W, FERNNDO D, et al. Full-range FRP failure behaviour in RC beams shear-strengthened with FRP wraps[J]. International Journal of Solids and Structures, 2017, 125:21.
[30]	BAKAY R, SAYED-AHMED E Y, SHRIVE N G. Interfacial debonding failure for reinforced concrete beams strengthened with carbon-fibre-reinforced polymer strips[J]. Canadian Journal of Civil Engineering, 2009, 36(1):103-121. doi: 10.1139/L08-096 URL
[31]	MUTALI A A, HAO H. Numerical analysis of FRP-composite-strengthened RC panels with anchorages against blast loads[J]. Journal of Performance of Constructed Facilities, 2011, 25(5):360-372. doi: 10.1061/(ASCE)CF.1943-5509.0000199 URL
[32]	葛继科, 邱玉辉, 吴春明, 等. 遗传算法研究综述[J] 计算机应用研究, 2008(10):2911-2916.
	GE J K, QIU Y H, WU C M, et al. Summary of genetic algorithms research[J]. Application Research of Computers, 2008(10):2911-2916. (in Chinese)
[33]	边霞, 米良. 遗传算法理论及其应用研究进展[J]. 计算机应用研究, 2010, 27(7):2425-2434.
	BIAN X, MI L. Development on genetic algorithm theory and its applications[J]. Application Research of Computers, 2010, 27(7):2425-2434. (in Chinese)
[34]	马永杰, 云文霞. 遗传算法研究进展[J]. 计算机应用研究, 2012, 29(4):1201-1210.
	MA Y J, YUN W X. Research progress of genetic algorithm[J]. Application Research of Computers, 2012, 29(4):1201-1210. (in Chinese)