小口径弹丸侵彻双箭头负泊松比蜂窝夹芯结构的弹道特性

图1 双箭头结构与子弹尺寸

Fig.1 Arrowhead NPR structure and bullet size

双箭头单胞是由薄肋板和连接铰链组成的桁架结构,根据文献[18-19]设计单胞模型.单胞结构尺寸如图1所示.上水平胞元壁、长胞元壁、短胞元壁、下水平胞元壁的长度分别为L₁、L₂、L₃、L₄;长胞元壁和短胞元壁的厚度分别为L₂_T和L₃_T.α_C和β_C分别为厚度系数和长度系数,且满足L₂_T=α_CL₂,L₃_T=α_CL₃,L₁=β_CL₂=L₄.H为胞元高度,θ₁和θ₂分别为长胞元壁、短胞元壁与胞元对称轴之间的夹角,一般满足0<θ₁<θ₂<π/4.

α_C和β_C分别取0.10和0.25,夹角θ₁为研究变量,夹角θ₂取45°,长胞元壁L₂取17 mm,只要给定变量θ₁就能确定双箭头NPR胞元结构尺寸.当胞元受外力作用时,水平胞元壁L₁与L₄的间距将会变化,胞元的横向距离也同趋势变化.因此多个胞元构成的蜂窝结构也具有受到纵向压缩时横向发生收缩,受到纵向拉伸时横向发生扩张的负泊松比性质^[19].

相对密度指蜂窝结构的等效密度相对于所用基体材料的密度^[20].二维双箭头蜂窝结构相对密度的表达式为

$ρ_{2 R D} = \frac{(1 + β_{C} + \frac{s i n θ_{1}}{2 s i n θ_{2}} - \frac{β_{C}}{5 s i n θ_{2}}) α_{C}}{(β_{C} + s i n θ_{1}) (c o s θ_{1} - \frac{s i n θ_{1}}{t a n θ_{2}} + 1.5 α_{C})}$

(1)

本研究夹角θ₁取值范围为10°~30°,共9组(a~i).双箭头NPR蜂窝夹芯结构由8×7形式的单胞结构蜂窝、前板、背板3部分组成.面板厚度均为1.5 mm,夹芯结构的厚度、宽度根据θ₁值不同而改变.蜂窝夹芯结构面外高度为14 mm,夹角θ₁具体值及对应蜂窝的相对密度参数列于表1.

表1 蜂窝模型参数

Tab.1 Parameters of honeycomb model

组别	θ₁/(°)	ρ_2RD	厚度/mm	质量/g
a	10.0	0.319 8	122.9	179.0
b	12.5	0.313 9	117.1	187.6
c	15.0	0.312 4	111.3	195.4
d	17.5	0.314 8	105.2	206.5
e	20.0	0.321 1	99.0	108.4
f	22.5	0.331 5	92.6	113.9
g	25.0	0.346 8	86.1	119.6
h	27.5	0.367 8	79.5	125.3
i	30.0	0.396 1	72.8	130.8

弹丸以300~1 000 m/s的初速度正向撞击双箭头NPR蜂窝夹芯结构.为控制变量,使弹丸撞击夹芯结构的相同位置.依据文献[16],弹丸垂直于面板,撞击长胞元壁中点时的吸能效应相比其他撞击位置显著.因此选择“侧边撞击”为研究工况,如图2所示.

图2

图2 子弹与双箭头夹芯结构几何模型

Fig.2 Model of bullet and double-arrow sandwich structure

1.2 有限元模型

弹丸侵彻双箭头NPR蜂窝夹芯结构的数值模拟采用LS-DYNA软件进行.考虑到该模型的形状及载荷具有对称性,建立三维模型的1/2对称模型以减小计算规模,绝对坐标系的Y轴垂直于对称面.在对称面使用对称边界条件,建模采用单位为g-cm-us.弹丸、面板、芯层均使用实体单元建模 (*SECTION_SOLID).本研究不考虑侵彻过程中弹丸自身的变形,故弹丸采用(*MAT_RIGID)赋予刚体属性.对模型背板两端施加完全固定约束,约束位置如图3所示,芯层与上下面板之间连接处设置绑定接触(*TIED_SURFACE_TO_SURFACE).

图3

图3 蜂窝结构

Fig.3 Cellular structure

使用六面体网格对模型进行划分,弹丸与面板网格的尺寸保持不变,均为0.4 mm.划分芯层网格时,确保胞元壁厚度方向平均存在5层网格.网格分析表明,5层网格既可以保证较好的计算精度,亦能控制计算成本.所有网格雅可比系数大于0.7,通常雅可比系数大于0.7时可以认为有限元模型的网格质量较为优良,由网格划分产生的误差对数值计算的准确性影响较低.所有单元均应用沙漏控制 (*CONTROL_HOURGLASS)以避免网格单元的零能模式,提高数值模拟结果的可信度.

将弹体与芯层、前板与背板之间接触设置为侵蚀接触(*CONTACT_ERODING_SURFACE_TO_SURFACE),以模拟胞元贯穿失效.双箭头芯层自身设置为自接触(*AUTOMATIC_SINGLE_SURFACE).当胞元的塑性应变达到失效值时,相应单元被删除,从而形象地模拟侵彻时的结构损伤及变形.

1.3 材料参数与状态方程

子弹视为刚体,面板由45#钢制成,双箭头蜂窝材料为2024铝合金.均采用Johnson-Cook本构模型(J-C模型)^[21]用以模拟弹丸撞击过程中金属材料的动态力学行为.J-C模型常用于大应变、高应变率与材料热软化效应的问题中,能够较为理想地描述金属的力学行为,其流动应力描述为^[22]

$σ_{y} = (A_{1} + B_{1} {\bar{ε}}_{p}^{n}) (1 + C l n {\overset{\cdot}{ε}}^{*}) (1 - T^{* m})$

(2)

式中:A₁、B₁、C为材料输入常数; ${\bar{ε}}_{p}$ 为等效塑性应变; ${\overset{\cdot}{ε}}^{*}$ 为无量纲化的等效塑性应变率;T^*为无量纲温度,且T^*=(T-T_r)/(T_m-T_r),T_m为材料融点,T_r为参考温度;n是应变硬化指数;m是热软化指数.

面板与NPR结构均采用Gruneisen状态方程,方程是由S₁、S₂、S₃三个参数拟合的三次多项式.此状态方程定义材料的球应力σ_H为^[14,23-24]

$\begin{array}{l} σ_{H} = \frac{ρ_{0} C_{0}^{2} μ [1 + (1 - \frac{γ_{0}}{2}) μ - \frac{a}{2} μ^{2}]}{[1 - (S_{1} - 1) μ - S_{2} \frac{μ^{2}}{μ + 1} - S_{3} \frac{μ^{3}}{{(μ + 1)}^{2}}]} + \\ (γ_{0} + a μ) E \end{array}$

(3)

式中:E为初始内能;C₀为冲击绝热曲线的截距;S₁、S₂、S₃为冲击绝热曲线斜率的系数;γ₀为Gruneisen系数;a为γ₀的1阶体积修正系数;ρ₀为材料密度;μ为材料的受压系数.

J-C模型自带损伤断裂准则,损伤断裂模型定义为^[11]

$\begin{array}{l} ε_{f} = [D_{1} + D_{2} e x p (D_{3} σ^{*})] (1 + D_{4} l n {\overset{\cdot}{ε}}^{*}) \times \\ (1 + D_{5} T^{*}) \end{array}$

(4)

式中:σ^*为压力与有效压力σ_eff之比,σ^*=p/σ_eff; D₁~D₅为断裂常量.当破坏参数D达到1时即认为产生断裂:

$\begin{matrix} D = \sum \frac{Δ {\bar{ε}}_{p}}{ε_{f}} \end{matrix}$

(5)

式中:Δ ${\bar{ε}}_{p}$ 为等效塑性应变增量;ε_f为当前时刻的破坏应变.

45#钢、2024铝的具体材料参数如表2~4所示,均源自文献[11,25].表中:ρ代表材料密度.

表2 45#钢、2024铝Johnson-Cook本构参数

Tab.2 Johnson-Cook constitutive parameters of 45# steel and 2024 aluminum

材料	ρ/(g·cm^-3)	A₁/MPa	B₁/MPa	C	n	m	T_m/K	T_r/K
45#钢	7.82	507	320	0.064	0.28	1.06	1 795	300
2024铝	2.78	265	426	0.015	0.34	1.00	933	300

表3 45#钢、2024铝Gruneisen参数

Tab.3 Gruneisen parameters of 45# steel and 2024 aluminum

材料	C₀/(cm·μs^-1)	S₁	γ₀
45#钢	0.456 9	1.490	2.17
2024铝	0.532 8	1.338	1.97

表4 45#钢、2024铝Johnson-Cook失效参数

Tab.4 Parameters of Johnson-Cook failure model for 45# steel and 2024 aluminum

材料	D₁	D₂	D₃	D₄	D₅
45#钢	0.10	0.76	1.57	0.005	-0.84
2024铝	0.13	0.13	-1.50	0.011	0.00

1.4 数值模型验证

考虑双箭头NPR夹芯结构制造成本偏高,为证明本数值模拟模型的有效性,故建立与文献[26]中卵形弹侵彻2024铝靶的垂直侵彻实验相同的数值模型进行验证,弹体冲击过程如图4所示.弹体质量为121 g,直径为14 mm,长度168 mm,弹体头部系数CRH为3.圆柱形靶板厚度80 mm,直径为140 mm,四周施加固定约束.弹体垂直于铝靶表面入射.铝靶采用J-C模型,参数取自表2~4.计算中弹体设为刚体,密度取 7 830 kg/m³,数值模拟结果表明侵彻深度为24.3 mm.此结果与文献[26]中实验编号01-1的侵深结果25.8 mm基本一致,如图5所示,证明了数值方法的准确性.

图4

图4 弹体垂直侵彻2024铝靶数值模型

Fig.4 Finite element model of projectile body vertical penetration into 2024 aluminum target

图5

图5 与2024铝靶垂直侵彻结果对比(mm)

Fig.5 Normal penetration data of 2024 aluminum targets (mm)

2 数值模拟结果

2.1 双箭头NPR夹芯结构动能吸收率

评估NPR夹芯结构对弹丸的动能吸收可以用动能吸收率η来表示^[27]

$η = \frac{E_{t}}{E_{k}} = \frac{0.5 m_{p} v_{i}^{2} - 0.5 m_{p} v_{r}^{2}}{0.5 m_{p} v_{i}^{2}} = 1 - \frac{v_{r}^{2}}{v_{i}^{2}}$

(6)

式中:E_t为夹芯结构吸收的动能;E_k为弹丸初始动能;m_p为弹丸质量;v_i为弹丸初始速度;v_r为弹丸残余速度.

弹丸侵彻9种蜂窝夹芯结构时所对应的初始速度以及残余速度的数值模拟结果如表5所示,η=1表示弹丸未贯穿结构.弹丸初始速度与结构能量吸收率对应关系曲线如图6所示.

表5 弹体侵彻NPR夹芯结构的仿真结果

Tab.5 Simulation results of projectile body penetrating NPR sandwich structure

v_i/(m·s^-1)	组别a		组别b		组别c
v_i/(m·s^-1)	v_r/(m·s^-1)	η	v_r/(m·s^-1)	η	v_r/(m·s^-1)	η
300	0	1	0	1	0	1
400	0	1	0	1	0	1
500	0	1	0	1	0	1
600	0	1	0	1	0	1
700	0	1	265.24	0.856	233.41	0.888
750	0	1	372.82	0.753	374.24	0.751
800	277.78	0.879	332.41	0.827	383.00	0.770
850	437.62	0.735	65.34	0.994	381.34	0.798
900	141.40	0.975	137.48	0.976	116.05	0.983
950	486.52	0.737	135.29	0.979	333.83	0.876
1 000	417.90	0.825	240.63	0.942	439.17	0.807
v_i/(m·s^-1)	组别d		组别e		组别f
v_i/(m·s^-1)	v_r/(m·s^-1)	η	v_r/(m·s^-1)	η	v_r/(m·s^-1)	η
300	0	1	0	1	0	1
400	0	1	0	1	0	1
500	0	1	0	1	0	1
600	56.55	0.991	212.76	0.874	142.74	0.943
700	330.86	0.776	257.96	0.864	380.65	0.704
800	353.59	0.804	465.31	0.661	446.26	0.688
900	207.92	0.946	501.75	0.689	571.72	0.596
1 000	434.12	0.811	594.57	0.646	676.91	0.541
v_i/(m·s^-1)	组别g		组别h		组别i
v_i/(m·s^-1)	v_r/(m·s^-1)	η	v_r/(m·s^-1)	η	v_r/(m·s^-1)	η
300	0	1	0	1	0	1
400	0	1	0	1	0	1
500	0	1	64.94	0.983	0	1
600	300.80	0.748	301.22	0.747	286.41	0.772
700	408.43	0.659	423.92	0.633	414.33	0.649
800	511.09	0.591	534.17	0.554	519.61	0.578
900	635.61	0.501	654.95	0.470	634.17	0.503
1 000	737.72	0.455	763.98	0.416	740.85	0.451

图6

图6 双箭头夹芯结构能量吸收率-初始速度曲线

Fig.6 Energy absorption efficiency of double-arrow sandwich structure versus velocity

由图6可知,对于同种蜂窝夹芯结构,η与v_i之间并非存在线性关系.在g、h、i组夹芯结构中随着弹丸初速的增加,能量吸收率急剧下降至0.45附近,且它们之间较为接近.e、f组能量吸收率下降较g、h、i组小,f组下降至0.54附近,e组下降至0.64附近.a、b、c、d组随着弹丸初速增加,结构能量吸收率存在先减小后增加的规律;且这4组夹芯结构的能量吸收率均高于0.77,显著优于其余5组结构.因此双箭头NPR蜂窝夹芯结构的抗侵彻能力随着θ₁增加而降低.纵观所有曲线,当v_i=800~1 000 m/s时,a、b、c、d、e组结构的能量吸收率开始出现波动式增加,且θ₁越小波动程度越大.

2.2 双箭头NPR夹芯结构的弹道极限

一般认为结构的弹道极限越高,其抗侵彻能力越强.本研究试图通过弹道极限来评估双箭头NPR夹芯结构的抗侵彻性能,利用Jonal A改进的基于能量守恒和动量定理的R-I公式^[28]获取弹道极限,表达式如下

$\begin{matrix} v_{r} = A (v_{i}^{p} - v_{b l}^{p})^{1 / p} \end{matrix}$

(7)

式中: v_bl为弹道极限;A、p为模型参数,通过最小二乘法拟合得到.

将表5中的数据代入(7)式,得到9组双箭头NPR夹芯结构的弹道极限,列于表6.a、b、c三组的拟合结果未计入到表格中,原因是弹丸残余速度随着初始速度的增加而无单调规律,导致拟合结果偏差较大.但依据表5中的数据可以推测a组夹心结构的弹道极限在(750, 800) m/s区间内,b、c两组夹心结构的弹道极限均在(600, 700) m/s区间内.由表6可知随着θ₁增大,双箭头NPR夹芯结构的弹道极限存在降低的趋势.

表6 NPR蜂窝夹芯结构的弹道极限

Tab.6 Ballistic limits of NPR honeycomb sandwich structures

组别	v_b1/(m·s^-1)
a	(750, 800)
b	(600, 700)
c	(600, 700)
d	557.64
e	532.24
f	569.87
g	488.44
h	494.41
i	494.41

2.3 弹丸的弹道特性

本研究采用对称边界条件,弹丸偏转及速度矢量变化始终在X_tZ_t平面内.定义弹丸绕自身质心Y_t轴转动的角度γ为偏航角(当前时刻弹体轴线与初始弹体轴线位置夹角,方向符合右手螺旋定则).弹体轴线与速度方向夹角α为攻角,弹速与靶板法线夹角β为着角,弹轴与靶板法线夹角φ为姿态角.如图7所示,此时α、β、φ均为正,满足几何关系:φ=α+β.

图7

图7 弹靶几何关系

Fig.7 Projectile-target geometric relationship

由2.2节可知,v_i=800~1 000 m/s时夹芯结构的能量吸收率较高且波动较大,且制式小口径步枪弹的初始速度刚好处于该速度区间内^[15].为便于分析,将v_i=900 m/s的工况定义为典型速度工况.在LS-PrePost中绘制9组夹芯结构的弹道剖面图,如图8所示.图中:pid=1代表弹丸在有限元软件中的部件号,无实际物理意义.

图8

图8 弹丸侵彻9组夹芯结构的弹道剖面图

Fig.8 Trajectory profile of projectile penetrating a 9-group sandwich structure

对比弹道剖面图,同一弹丸以同一速度侵彻时,随着θ₁逐渐增大,弹丸最终贯穿夹芯结构时的姿态越不稳定.提取弹丸绕自身Y_t轴的角位移,如图9所示.发现弹丸偏航角与蜂窝夹芯结构的动能吸收率存在关联,弹丸贯穿姿态越稳定,双箭头NPR蜂窝夹芯结构的能量吸收率就越低.

图9

图9 弹丸偏航角和蜂窝夹芯结构动能吸收率

Fig.9 Bullet yaw angle and kinetic energy absorption rate of honeycomb sandwich structure

将b、h两组弹道剖面对比,如图10所示.随着初始速度的增加,弹丸在未穿透b组结构芯层时姿态角的改变量已经大于90°.而h组弹丸姿态角的变化相对较小,弹道一致性优于b组结构.这是由于h组结构的相对密度大于b组,胞元壁之间的距离较小,限制了弹丸的姿态变化.

图10

图10 b、h组弹道剖面对比

Fig.10 Comparison of ballistic profiles of Group b and h

弹丸姿态角的改变会导致弹-靶作用面积的改变,进而影响弹丸受到的侵彻阻力^[29].a、b、c三组结构中弹丸姿态角变化相对其他组较高,弹丸受到的侵彻阻力变化较大,最终导致弹丸残余速度产生较大波动,这也是2.2节中a、b、c三组弹道极限拟合结果不佳的原因.

3 弹丸侵彻双箭头NPR夹芯结构分析

3.1 侵彻过程分析

以典型速度工况中结构能量吸收率最高的c组与吸收率最低的h组进行分析.绘制c、h组的弹丸速度-时间曲线,如图11与图12所示.侵彻过程分为3个阶段:阶段1弹丸侵入前板但未侵彻双箭头NPR芯层;阶段2弹丸穿透双箭头NPR夹芯层但未侵彻背板;阶段3弹丸贯穿背板直至弹丸速度保持不变.

图11

图11 c组弹丸速度-时间曲线

Fig.11 Projectile velocity-time curve of Group c

图12

图12 h组弹丸速度-时间曲线

Fig.12 Projectile velocity-time curve of Group h

在c组结构中,阶段1弹丸速度从900 m/s降至878.99 m/s,该阶段历时10 μs.阶段2弹丸速度从878.99 m/s降至383.06 m/s,该阶段历时165 μs.阶段3速度从383.06 m/s降至116.05 m/s,该阶段历时75 μs.

在h组结构中,阶段1弹丸速度从900 m/s降至879.85 m/s,该阶段历时10 μs.阶段2弹丸速度从879.85 m/s降至717.71 m/s,该阶段历时87 μs.阶段3速度从717.71 m/s降至654.95 m/s,该阶段历时33 μs.

将c、h组不同阶段弹丸损失的动能比例列于表7.发现在双箭头NPR蜂窝夹芯结构中,芯层起到主要吸能作用,背板起到次要吸能作用,而前板对夹芯结构的吸能影响最小.

表7 弹体各阶段动能损失比例

Tab.7 Percentage of kinetic energy loss in each phase of penetration

组别	阶段1/%	阶段2/%	阶段3/%
c	4.7	78.6	16.7
h	9.4	68.0	22.6

3.2 弹丸偏转机理分析

由2.3节可知在弹丸侵彻时存在偏转现象.以典型速度工况时h组为例,提取弹丸角速度与角加速度曲线,如图13~14所示.

图13

图13 弹丸角速度-时间曲线

Fig.13 Projectile angular velocity-time curve

图14

图14 弹丸角加速度-时间曲线

Fig.14 Projectile angular acceleration-time curve

由图13可得,弹丸侵彻前板时角速度出现短暂负值,侵彻芯层时弹丸角速度虽有振荡,但恒为正值.这引起α的改变和β的增大,最终导致φ增大使弹丸沿着X正向偏移.

图中A、B两点间弹丸角速度急剧下降,绘制t=105~125 μs时刻的应力云图,如图15所示.发现弹丸周围存在应力分布不均的现象,虽然弹丸的角速度为正,但弹丸受到右侧胞元壁的挤压(黄色线框内)阻碍了弹丸的正向旋转,产生的侧向力矩导致弹丸角加速度为负值,如图14所示,t=105~125 μs时刻内D点加速度值最大.原因是弹丸受到背板的挤压,随着弹丸的运动,侧向力F的作用范围从弹肩移至弹尾,导致力臂h⁰逐渐增加,力矩也随之增大,故产生的角加速度逐渐增大.在整个侵彻过程中t=97.5 μs时刻C点的角加速度值最大,此时弹丸头部侵彻靶体的厚度是背板厚度与长、短胞元壁厚度的总和,导致弹丸头部存在较大的侵彻阻力,如图15所示.

图15

图15 弹丸的Mises应力云图

Fig.15 Mises stress cloud map of projectile

3.3 弹丸偏转力学模型

侵彻过程中弹丸的角速度存在振荡现象,该现象是双箭头NPR芯层的胞元壁与弹体的非对称作用造成^[16],下面对这一现象进行讨论.将弹丸与胞元特征尺寸对比,可知胞元壁厚远小于弹丸直径(L_2T/d<1),胞元高度略小于弹丸长度(H/L≈1).本研究中夹芯结构材料为金属,弹丸为刚体,而刚性弹丸对双箭头胞元的贯穿通常受到胞元的局部效应和胞元结构响应影响^[30],因此弹丸侵彻单个胞元壁结构的物理过程可看作弹丸侵彻金属薄板问题进行研究.

弹丸侵彻单个双箭头NPR胞元时的受力状态如图16所示.图中:C_p点为弹丸质心;a_w=dtan(α+β),为弹头接触面最大的接触距离;b_w=dtan(α+γ)为弹尾接触面最大的接触距离;γ₀为外侧边与x₀轴夹角;δ为穿透胞元后弹丸的攻角改变量;ω为内侧边与x₀轴夹角;σ_rb为尾部正应力分量.

图16

DOI:10.6052/0459-1879-20-333 [本文引用: 1]

图16 子弹侵彻胞元时的受力状态

Fig.16 Stress state of bullet when penetrating cells

当弹丸与胞壁接触时,由于材料的屈服作用产生应力,这些应力成为阻力的来源,所以冲击面会对弹丸质心产生力矩作用.接触面弹丸存在头部正应力分量σ_xx、σ_rr,尾部正应力分量σ_rb与周向切应力σ_rθ.正应力分量会对弹丸质心产生翻转力矩,切应力则不会^[23].头部径向应力σ_rr导致的力矩可表示为

$\begin{matrix} M_{r r} = S d a_{w} (L - a_{w}) / π \end{matrix}$

(8)

式中: S为胞元母材屈服应力.同理,轴向应力σ_xx导致的力矩可表示为

$\begin{matrix} M_{x x} = S d^{2} a_{w} / π \end{matrix}$

(9)

σ_rb导致的力矩可表示为

$\begin{matrix} M_{r b} = S d b_{w} (L - b_{w}) / π \end{matrix}$

(10)

头部径向应力σ_rr导致的力矩与其余两个力矩方向相反,剩余力矩M_c=M_rr-M_xx-M_rb产生弹丸的攻角加速度 $\ddot{α}$ .由动能定理分析弹丸贯穿单个胞元前后两种状态,∑W为过程中动能变化量总和,有∑W=T₂-T₁,其中T₁= $\frac{1}{2}$ m $v_{1}^{2}$ ,T₂= $\frac{1}{2}$ m $v_{2}^{2}$ + $\frac{1}{2}$ J ${\overset{\cdot}{α}}^{2}$ ,m为弹丸质量,v₁为弹丸侵彻胞壁时的速度,v₂为弹丸穿透胞元后的剩余速度,J为弹丸转动惯量.

$\sum W = \frac{1}{2} m g L [c o s (α + β) + b_{w} + c o s δ] - W_{1}$

(11)

式中: W₁为侵彻过程中消耗的能量^[23,31].

由式(11)可知弹丸贯穿单个胞元后获得的角速度与多重因素有关.依据上述弹丸侵彻双箭头NPR单胞结构的偏转模型可以描述弹丸在侵彻整个双箭头NPR蜂窝过程中的运动规律:弹丸以零攻角的正侵彻状态穿透第1层胞元后产生攻角;随着弹丸穿透的胞元层数增加,穿透前层胞元后弹丸的攻角又等于穿透后层胞元的初始攻角,剩余力矩M_c也随之增加,随之弹丸的角加速度 $\ddot{α}$ 增大,最终导致弹丸在双箭头NPR结构中的偏航角逐渐增大,与图8所展示弹丸在蜂窝结构中的运动规律一致.

4 结论

本研究建立了小口径弹丸侵彻双箭头NPR蜂窝夹芯结构的有限元模型,与实验结果对比确保了有限元模型参数的准确性.进而对弹丸侵彻夹芯结构的过程进行了分析,利用控制变量的方法研究了胞元设计参数对该夹芯结构的动能吸收率、弹道极限与弹道特性的影响.揭示了小口径弹丸侵彻双箭头NPR蜂窝夹芯结构的侵彻过程与机理,建立了弹丸侵彻双箭头胞元的动力学模型.

(1) 关于夹芯结构的抗侵彻能力,双箭头蜂窝芯层起主要吸能作用,背板起次要作用,而前板影响最低.

(2) 随着胞元夹角增大,双箭头NPR蜂窝夹芯结构的弹道极限越小,其抗侵彻能力越差.

(3) 对于同种胞元参数,弹丸初速与双箭头NPR蜂窝夹芯结构能量吸收率存在非线性关系;胞元夹角越小,该非线性关系就越强.

(4) 随着胞元夹角的增大,弹丸贯穿夹芯结构时偏航角愈小.弹丸偏航角与夹芯结构的动能吸收率存在一定关系,弹丸贯穿姿态越稳定,双箭头NPR蜂窝夹芯结构的能量吸收率越低.

(5) 侵彻时弹丸周向存在应力分布不均现象,促使弹丸受力变化,导致弹丸攻角的改变和弹靶着角的增大,最终引起弹丸姿态角增大.使弹丸在双箭头蜂窝芯层中发生偏转,其所受侵彻阻力发生改变.

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轻量化多功能负泊松比结构由于具有优异的可设计性、拉胀特性、剪切模量、断裂韧性、抗冲击吸能、减震降噪等特性,在车辆吸能结构设计和多功能优化方面具有巨大的应用潜力.本文详细综述了负泊松比结构的力学设计及其在车辆工程中的典型应用:(1)负泊松比基本概念及其力学特性, 以及近几十年来的快速发展趋势;(2)负泊松比材料与结构构型设计方法的基本分类、负泊松比泡沫材料微结构特征及制备工艺、负泊松比复合材料设计方法的基本发展历程以及前沿人工智能设计方法;(3)针对典型负泊松比结构的力学设计进行详细介绍, 主要包括手性结构、方格旋转结构、双箭头内凹结构、内凹蜂窝结构、拉伸扭转效应负泊松比结构等;(4)负泊松比材料与结构的冲击吸能特性及相关的实验、理论和模拟研究;(5)负泊松比材料与结构在汽车轻量化设计领域的典型应用, 主要包括汽车吸能盒、B柱、发动机罩、安全带、悬架、免充气轮胎等典型吸能结构件;(6)负泊松比结构在汽车工程中的应用前景, 所面临技术挑战和巨大应用潜力.

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研究了宏观负泊松比效应蜂窝夹芯结构胞元壁厚、胞元层数和胞元泊松比等参数对弹体侵彻及水下抗爆等防护性能的影响.模拟弹体在空气中对宏观负泊松比蜂窝夹芯舰船防护结构的侵入和穿透过程，以及蜂窝夹芯防护结构在水下爆炸冲击载荷作用下的破坏形式.计算结果表明：单纯依靠结构性的被动防御无法应对高速或超高速弹体的侵彻问题；负泊松比效应蜂窝夹芯防护结构较传统防护结构具有良好的水下抗爆性能，且其水下抗爆性能随蜂窝胞元层数和胞元泊松比的增大而增强.

YANG

Deqing

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