Dynamic responses of metal foam sandwich beams to repeated impacts
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摘要: 为了研究重复冲击载荷作用下泡沫金属夹芯梁的动态响应,采用Abaqus数值仿真软件,基于可压碎泡沫模型(crushable foam),建立了泡沫金属夹芯梁遭受楔形质量块冲击的有限元模型。通过将仿真获得的夹芯梁上下面板最终挠度与重复冲击实验结果进行对比,验证仿真方法的准确性。在此基础之上,分析了泡沫金属夹芯梁在楔形质量块重复冲击作用下的变形模式、加卸载过程以及能量耗散特性。结果表明,在重复冲击载荷作用下,夹芯梁的变形不断累积,上面板主要出现局部凹陷和整体弯曲,而芯层则是局部压缩,下面板表现为整体弯曲。在重复加卸载过程中,加卸载刚度随着冲击次数的增加而增大。随着冲击次数的增加,上面板和芯层的能量吸收增量不断减小,而下面板的能量吸收增量不断增加,且最终均趋于稳定。泡沫金属夹芯梁的塑性变形能增量不断减小,而回弹系数随着冲击次数逐渐增加,最后趋于稳定值。Abstract: The phenomena of repeated impacts are very common, especial in the field of ship and ocean engineering. When the ship structures suffering from repeated impact loadings, the deformation and damages will accumulate, leading to failure even damage of the structures, which may cause serious accident. In order to study the dynamic behaviors of metal foam sandwich beams (MFSBs) under repeated impact loadings, the nonlinear finite element model was established based on the material model of crushable foam by using Abaqus-Explicit, and the approach to achieve repeated impacts in the software was proposed. The accuracy of the numerical simulation was verified by comparing the permanent deflections of front and back face sheets. Based on the results of the numerical simulations, the deformation modes, loading and unloading process as well as the energy absorption behavior of the MFSBs under repeated impacts were analyzed. Results show that during repeated impacts, the deformation of the MFSBs is accumulated gradually, the front face sheet mainly experiences global bending and local indentation, and the metal foam core suffers from local compression, while the back face sheet is subjected to global bending. During the repeated impacts, the loading and unloading stiffness increases with the impact number. The energy absorption of front face is larger than that of back face and metal foam core in all the impacts. As the impact number increases, the energy absorbed by front face sheet and foam core declines gradually, while that of the back face sheet increases, approaching a constant value. The plastic deformation energy of the MFSBs decreases with the impact number, on the opposite, the rebound energy of the MFSBs increases gradually with the impact number, while both of them trends to be stable. The proposed finite element method can be applied to accurately predict the dynamic responses of the MFSBs suffering from repeated impact loadings, and provide technical supports for the anti-impact design of metal foam sandwich structures.
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冲击波作为爆破战斗部的主要毁伤方式之一,是评估武器毁伤威力的一项重要指标[1]。毁伤威力评估时,需要对战斗部炸点周围的冲击波场进行分布式测量,同时要求多测点实现同步触发。实战环境下战斗部落点及起爆时刻具有一定的随机性,且战斗部爆炸前具有一定的速度,战斗部的运动速度会改变爆炸冲击波的压力场分布。传统的触发方法如断线触发[2]、光触发[3]、无线触发[1]等均难以实现战斗部实战环境下冲击波超压的可靠触发,因此对战斗部动爆压力场的特性分析主要是通过仿真计算,并结合少量试验数据结果和爆炸相似律获得经验公式[4-6],缺少实战环境下的试验研究。
本文中,提出了一种基于地震波可靠触发的战斗部空中爆炸冲击波超压测试方法,对着靶速度为0、535和980 m/s的战斗部空中爆炸冲击波进行了测试分析。结果表明,基于地震波信号触发测试方法能可靠获取战斗部动爆冲击波超压峰值。试验成果可为实战复杂环境下基于实测数据研究动爆冲击波特性提供依据。
1. 基于地震波触发的冲击波超压测试系统
1.1 基于地震波触发的冲击波超压测试系统
为了验证基于地震波实现冲击波超压测试触发的可行性,设计了基于加速度信号触发的冲击波超压测试系统并进行了试验。测试系统主要包括传感器、信号调理电路、电源管理、无线通信和信号采集存储等五部分,测试系统组成如图1所示。进行冲击波超压测试时,信号调理电路对传感器获得的冲击波超压信号进行滤波、降噪,在进入FPGA (field programmable gate array)之前进行信号有无和是否达到触发阈值的判断,A/D控制模块将模拟信号转为数字信号后存储在外部同步动态存储器(synchronous dynamic random-access memory, SDRAM)中,最后通过USB (universal serial bus)或无线通信模块将数据上传到上位机上,在上位机上完成数据最终的显示、分析和处理。
1.2 基于地震波信号的冲击波测试触发原理
基于地震波信号的冲击波超压测试触发方法借助配置在各冲击波超压测试节点上的加速度计与信号调理电路,利用地震波传播速度比冲击波传播速度快的特点,在冲击波到达各测试节点之前,提前感应到的加速度信号,经专用调理电路处理后,触发该测试节点的冲击波超压信号存储。其触发原理如图2所示,冲击波超压信号采集缓存区划分为循环采集和时序采集两部分,通过加速度信号启动冲击波超压信号的循环采集完成第1步触发,通过预设超压阈值的比较进行第2步触发,满足触发条件时,立即固化循环采集区,并开始冲击波超压的时序采集。
爆炸时,形成以炸点为中心向四周传播的地震波,地震波传播速度最快的是纵波,其使地面发生上下振动,在地壳中的传播速度:
u0 =5.5~7 km/s。(1)根据金尼-格雷厄姆公式,计算冲击波超压峰值(
pp ,MPa):pppair=808[1+(fdR4.5)2]√1+(fdR0.048)2√1+(fdR0.032)2√1+(fdR1.35)2,fd=3√pairp0T0Tair (1) 式中:
R 为比例距离,是观测点到距爆炸中心的距离r(m)与炸药TNT当量W(kg)的立方根之比,即R=r/3√W ,本文中0.053m/kg1/3≤R≤500m/kg1/3 ;pair 为试验现场大气压;p0 为标准大气压,p0= 101.325kPa ;Tair 为试验现场大气温度;T0 为标准大气温度,T0=288.16K 。(2)根据Rankine-Hugoiot方程,爆炸点空气冲击波传播速度
u 与冲击波超压峰值pp 之间的关系为:u=√(ppp0×γ+12γ)+1⋅c0 (2) 式中:
p0 为大气压,γ 为空气的比热比,c0 为波阵面前的空气声速。(3)冲击波和地震波传播到观测点的平均时间差
Δt 为:Δt=r(1u−1u0) (3) 联立式(1)~(3)可得不同观测距离处冲击波传播平均速度及其与地震波传播平均时间差的关系,如图3所示。由图3(a)可以看出,冲击波超压值随爆距的增大而减小,当距离
r≥5m 时,冲击波的传播平均速度u≤995m/s ,该值远小于地震波的传播速度;由图3(b)可以看出,当距离r≥5m 时,冲击波与地震波传播到观测点的平均时间差Δt≥4.1ms ,而地震波信号触发该测点的冲击波信号只需要几十微秒,在该时间差内能够完成触发该测试节点的冲击波信号的存储。因此,当等效TNT装药量不大于100 kg、爆心距不小于5 m时,可以通过安装在测试终端的加速度计采集地震波信号,作为冲击波超压测试的可靠触发信号。图4是弹丸爆炸时在距爆心5 m处获取的加速度和冲击波超压信号,可以看出加速度信号的触发阈值先于冲击波信号到达测试节点,提前时长为12.42 ms,这进一步验证了基于地震波信号的冲击波测试触发方法原理的可行性。
2. 运动战斗部爆炸冲击波特性分析
2.1 动爆试验测试设置
为分析不同速度战斗部爆炸时冲击波场的分布规律,建立分布式动爆试验测试系统,采用球形裸装药,装药量为1.2 kg。比例距离R分别为4.71、9.41和14.12 m/kg1/3,战斗部着靶速度v0分别为0、535和980 m/s,火炮火药发射获得着靶速度,距目标炸点50 m处顺序放置4台天幕靶,每台间隔20 m,通过区截法获取弹丸在天幕靶处的飞行速度,再结合炮口靶获取的出炮口速度以及制式弹的外弹道模型,计算出目标炸点处弹丸速度。采用模块装药,速度为535和980 m/s弹丸的装药分别为3×B模块和6×B模块,每个B模块装药2.35 kg,引信采用瞬触发引信。战斗部与地靶平面的水平夹角β为45°,测点分布如图5所示,以爆炸中心为原点,建立三维坐标系Oxyz,分别在地靶平面距爆心5、10、15 m处安装冲击波超压测试装置。在Oxy平面上(即地靶平面),爆心到测试点的连线与x轴的夹角为θ,受试验条件限制,共24个测点。理论上测点越多,对爆炸冲击波的重建越有利。
2.2 爆炸冲击波特性分析
图6为比例距离R=4.71 m/kg1/3时不同方向上测得的冲击波超压时域曲线。由图6可知,以静爆条件下(v0=0 m/s)的冲击波超压时域曲线为参照,当θ=0°时,动爆冲击波超压远高于静爆冲击波超压;当θ增大到45°时,动爆冲击波超压有所下降,但是仍然高于静爆冲击波超压;当θ增大到90°时,动爆冲击波超压继续降低,v0对冲击波超压的影响变小,不同速度战斗部爆炸的冲击波超压趋于一致,与静爆冲击波压力相当;随着θ的进一步增大,动爆冲击波压力进一步降低,开始低于静爆冲击波压力;当θ增大到180°时,测点处于与战斗部速度完全相反的方向,为压力最低点,此时的冲击波超压远低于静爆冲击波超压。此外,在动爆冲击波超压高于静爆冲击波超压的方向上,即θ在0°~90°和270°~360°范围内时,v0越大,压力越高,冲击波到达时间越短;相反地,在动爆冲击波超压低于静爆冲击波超压的方向上,即θ在90°~270°范围内时,v0越大,压力越低,冲击波到达时间越长。
读取冲击波的超压峰值,得到不同速度战斗部的爆炸冲击波超压峰值对比曲线,如图7所示。由图7可知:(1)比例距离相同时,战斗部爆炸的冲击波超压峰值随θ的增大近似呈余弦衰减,当θ=0°时,超压峰值最大,θ=180°时,超压峰值最小,并且战斗部着靶速度v0越大,超压峰值衰减得越快;(2)以静爆冲击波超压峰值为参照,在与战斗部速度方向相同的区域(0°~90°和270°~360°),动爆冲击波存在较大的压力升,超压峰值大于静爆状态下的超压峰值,使得冲击波场呈现出局部高压区,而在与战斗部速度方向相反的区域(90°~270°),则存在较大的压力降。由此,可将运动战斗部的爆炸冲击波场分为压力升和压力降两个区域,分界点大约在θ=90°处。
根据战斗部动爆冲击波超压峰值pp,d与战斗部相对靶平面的速度
v′0 及静爆冲击波超压峰值pp,s的关系[4]:pp,dpp,s=(1+0.31+Rv′0c0cosθ)2 (4) 战斗部在靶平面的投影速度
v′0 为:v′0=v0cosβ (5) 由式(1)、(4)、(5)联合可得战斗部动爆冲击波超压峰值的经验公式计算值,实测战斗部动爆冲击波超压峰值pp,e与经验公式计算结果pp,d对比如表1所示,其中ε=(pp,e−pp,d)/pp,e。由表1可知,实测战斗部静爆冲击波超压峰值与经验公式计算结果一致性较好,除个别点外,实测战斗部动爆冲击波超压峰值与理论值较为接近,相对误差小于20%,且相对误差随着战斗部速度的增大而增大。此外,越靠近战斗部运动方向轴线(θ=0°和θ=180°)的实测冲击波超压峰值相对误差越大,垂直于战斗部运动方向轴线(θ=90°和θ=270°)的实测冲击波超压峰值相对误差较小。
表 1 试验结果与理论值对比Table 1. Comparison between experimental and theoretical resultsR/(m·kg−1/3) θ/(°) v0=0 m/s v0=535 m/s v0=980 m/s pp,e/kPa pp,d/kPa ε/% pp,e/kPa pp,d/kPa ε/% pp,e/kPa pp,d/kPa ε/% 4.71 0 321.39 317.35 1.26 434.86 355.57 18.23 483.16 389.02 19.48 45 343.49 317.35 7.61 384.34 344.15 10.46 392.65 367.28 6.46 90 342.92 317.35 7.45 285.10 317.35 −11.31 288.32 317.35 −10.07 135 335.52 317.35 5.41 270.90 291.64 −7.65 258.87 271.08 −4.72 180 320.94 317.35 1.12 228.45 281.30 −23.14 187.89 252.98 −34.64 225 294.20 317.35 −7.87 261.93 291.64 −11.34 215.23 271.08 −25.95 270 296.57 317.35 −7.01 285.98 317.35 −10.97 294.97 317.35 −7.59 315 319.73 317.35 0.74 368.50 344.15 6.61 402.27 367.28 8.70 9.41 0 112.04 104.86 6.41 127.36 111.70 12.30 149.08 117.54 21.15 45 110.61 104.86 5.19 110.62 109.67 0.86 118.86 113.76 4.30 90 100.10 104.86 −4.76 96.52 104.86 −8.65 96.21 104.86 −9.00 135 103.81 104.86 −1.02 88.96 100.16 −12.59 86.69 96.34 −11.13 180 106.88 104.86 1.89 90.35 98.25 −8.75 75.88 92.91 −22.44 225 102.12 104.86 −2.69 94.81 100.16 −5.64 88.06 96.34 −9.40 270 98.28 104.86 −6.70 99.25 104.86 −5.66 98.10 104.86 −6.90 315 111.00 104.86 5.53 118.45 109.67 7.41 123.47 113.76 7.86 14.12 0 63.87 63.04 1.31 74.87 65.85 12.05 78.23 68.24 12.77 45 63.23 63.04 0.30 66.35 65.02 2.01 69.56 66.69 4.12 90 57.72 63.04 −9.21 59.16 63.04 −6.55 59.03 63.04 −6.78 135 59.08 63.04 −6.70 57.75 61.08 −5.78 50.63 59.48 −17.48 180 60.51 63.04 −4.17 51.72 60.28 −16.56 45.73 58.04 −26.91 225 57.75 63.04 −9.16 53.69 61.08 −13.77 48.06 59.48 −23.77 270 57.78 63.04 −9.10 59.52 63.04 −5.92 57.52 63.04 −9.58 315 64.73 63.04 2.61 69.42 65.02 6.34 73.98 66.69 9.85 2.3 爆炸冲击波场重建
以表1中的冲击波超压峰值为插值点,利用MATLAB数据处理软件的薄板样条插值方法(thin-plate-spline interpolation)对实测数据进行插值(该插值方法可以使得三维超压曲面弯曲能量最小),得到战斗部速度分别为0、535、980 m/s的爆炸冲击波超压峰值场分布和等压曲线,如图8~10所示。由图8可知,战斗部静爆冲击波超压峰值在各个方向基本相同;由图9~10可知,战斗部动爆冲击波超压峰值在战斗部运动速度方向增强,在战斗部运动相反方向减弱,且战斗部速度越大,增强和减弱的程度越大。
3. 结 论
提出了一种基于地震波可靠触发的战斗部空中爆炸冲击波超压测试方法,并对速度为0、535和980 m/s的战斗部空中爆炸冲击波进行了测试研究,通过测试结果和经验公式计算值的对比分析,以及重建的战斗部动爆冲击波超压三维可视化模型,可以得出以下结论:
(1)本文中提出的测试方法能可靠获取战斗部动爆冲击波超压峰值;
(2)战斗部动爆冲击波超压峰值在战斗部运动速度方向增强,在战斗部运动相反方向减弱,且战斗部速度越大,增强和减弱的程度越大。
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