A review of sacrificial claddings in multilayer protective structure
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摘要: 成层式防护结构通常由伪装层、遮弹层、分散层和主体结构组成，现已被广泛应用于地面、浅埋以及坑道口部的防御工事中。其中分散层作为降低侵彻后爆炸毁伤效应的功能单元，其作用机理主要包括：借助波阻抗失配效应以降低向下部结构传播的能量占比、延长应力波传播路径；利用分层界面产生面波以改善荷载集中状态；通过基体材料不可逆塑性破坏以吸收耗散冲击波能量；增大结构阻尼以减轻主体结构震动效应。开展分散层的相关研究，对提高工程整体防护水平具有重要的现实意义。基于此，从分散层材料与结构型式两个方面较为系统地介绍了国内外成层式防护结构中分散层的研究现状，分析了分散层的结构及物性参数对其防护效能的影响，提出分散层选型及设计需关切的几点问题，并对目前分散层研究中存在的问题进行了探讨与展望，以期为今后分散层的研究发展提供参考。Abstract: The multilayer protective structure has been widely used in fortifications located above-ground, shallow burial, and tunnel entrances. And this type of structure usually consists of four parts: camouflage layer, shelter layer, sacrifice layer and protection structure. Among them, the sacrifice layer is the main functional unit to reduce the damage effect of strong explosion after penetration. Its action mechanism mainly includes: reducing the proportion of energy propagating to the substructure and extending the propagation path of stress wave by means of the wave impedance mismatch effect; using the layered interface to generate surface waves to reduce the load concentration; absorbing and dissipating shock wave energy through irreversible plastic failure of the matrix material; increasing the structural damping to reduce the vibration effect of the protection structure. Thus, it is of great practical significance to carry out relevant research to improve the overall level of engineering protection. Taking the materials and structure of sacrifice layer as clues, the current status of research on sacrifice layer in multilayer protective structure at home and abroad is systematically sorted out. On this basis, the influence of structural parameters such as the density, wave impedance, thickness, unit shapes and sizes, moisture content and other physical parameters of the sacrifice layer on the protective performance is analyzed. Moreover, several issues that need to be considered in the selection and design of the sacrifice layer are proposed. The perfect sacrifice layer should be economical, reliable, and have a low wave impedance, sufficient static compressive strength and a certain yield strength, which be able to undergo a large plastic deformation under the condition that the yield stress remains essentially constant. Finally, the problems existing in the current research on the sacrifice layer are discussed and prospected, in order to provide a reference for the research and development of the sacrifice layer in the future.
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抗爆门是防止爆炸传播及冲击波、破片、碎片毁伤的关键设施，同时也是抗爆结构的薄弱点。目前，抗爆门基本采用钢材料制作，由于钢自身密度大，导致抗爆结构自重大，安装、开闭不便，长时间使用后导致门栓等关键承重构件变形严重。因此，针对目前抗爆门存在的弊端，抗爆材料轻量化逐渐成为抗爆结构的研究方向。轻质合金材料、陶瓷材料对冲击波具有良好的防护作用，但在破片侵彻作用下极易形成破片、碎片等二次伤害。如何对已有轻质材料进行抗破片侵彻防护，成为亟需解决的问题。
目前针对轻质材料较多采用复合防弹板的结构，比如复合板有陶瓷/金属复合板[1-2]、陶瓷/纤维复合板和金属/纤维复合板等。这些研究中包含了大量的实验、数值计算及理论推导。Johnson等[3]指出，复合靶板侵彻破坏分为两个阶段：第一个阶段为剪切冲塞阶段，该阶段以纤维的横向剪切破坏为主；第二个阶段为背部凸起变形阶段，以纤维拉伸变形破坏为主。根据此理论，一般将迎弹面材料选择抗剪切强的材料，背弹面采用抗拉伸强的材料。Bürger等[4]开发了3种由氧化铝与超高分子聚乙烯组成的有限元模型，对比数值预测与实验结果后得出：黏合剂模型可以正确预测对冲击的响应、复合失效模型可准确预测能量吸收。这为侵彻复合板的数值验证提供了可靠的分析方法。
针对多层复合板的抗侵彻性能，学者们从不同方面进行了研究。Zukas等[5]研究了多层钢板的冲击效应，发现靶板吸能性能随着钢板层数增加而变差。Corran等[6]和Dey等[7]研究发现钝形弹头侵彻时，在总厚度不变的情况下，多层复合靶板的吸能性能要优于单层均质靶板，这说明由不同材料组成的复合板对于提升吸能性能是有帮助的。而针对纤维复合板，马小敏等[8]通过对铺层数的优化，能够有效地减小后面板挠度，提高结构的能量吸收效率。李茂等[9]发现间距的存在有利于复合装甲结构综合抗侵彻性能的提高。秦溶蔓等[10]研究发现纤维层的铺层角度也对复合板抗侵彻性能有影响，45°铺层结构吸收动能高出90°结构6.86 %。谢文波等[11]研究破片入射角度时发现在冲击能量较低时，靶板在正冲击下的能量吸收率比斜冲击高，而当冲击能量较高时则恰好相反。何业茂等[12]将碳纳米粒子加入超高分子聚乙烯（ultra-high molecular weight polyethylene, UHMWPE）纺丝原液中，采用水性聚氨酯作为树脂基体，发现由该纤维丝制成的纤维板提高了抗单发破片侵彻性能，但由于碳纳米粒子原位改性降低了 UHMWPE纤维/水性聚氨酯（waterborne polyurethane, WPU）复合材料的层间剪切强度，使得抗多发破片侵彻性能下降。王敏等[13]根据前人实验，建立了纤维增强复合材料（fiber reinforced polymer, FRP）本构模型，数值模拟结果能够预测碳纳米粒子/碳纤维（carbon nanoparticle/carbon fiber, CNT/CFRP）层合板在低速冲击载荷作用下的响应、破坏过程和分层形貌。通过以上研究结果可以发现，靶板层数、靶板材料、靶板间隙、纤维铺层角度、破片入射角度、纺丝原液成分等都会对靶板抗侵彻性能产生影响。这些研究都建立在破片初速较为单一，且UHMWPE复合板实验样本厚度较小的情况下，UHMWPE复合板在不同速度且不同厚度下抗侵彻性能是否一致还有待考证。
本文中以2024铝合金和超高分子聚乙烯为复合板材料，对涂敷不同厚度UHMWPE背板的Al/UHMWPE复合板进行研究。利用低、中、高速度的球形破片侵彻不同厚度PE复合板，通过数字图像相关方法（digital image correlation method, DIC）与X射线电子计算机断层扫描（computed tomography, CT）分析得到Al/PE复合板受到侵彻后的应变动态响应及微观破坏，分析不同PE背板厚度下复合板的抗侵彻性能及造成这种抗侵彻性能差异的原因。采用断通靶和六路电子测时仪对破片初速、末速进行测量，以研究不同UHMWPE背板厚度的Al/UHMWPE复合板吸能性能。同时基于Johnson-Cook材料模型及Abaqus Explicit/Dynamic求解器对应材料子程序对不同背部UHMWPE板厚度下Al/UHMWPE复合板的低、中、高速度球形破片侵彻过程开展数值模拟。
1. 现场实验方案
1.1 靶板制作流程
Al/UHMWPE复合靶板的迎弹面铝板材料型号为2024铝合金，背弹面UHMWPE材料为超高分子量聚乙烯纤维平纹布，由北京同益中新材料科技股份有限公司提供。黏结剂采用环氧树脂。
Al/UHMWPE靶板制作流程如图1所示，先打磨铝板表面毛刺，揭去表面防腐膜，再用纱布打磨光滑。然后采用无水乙醇清洗、擦拭铝板表面。在考虑胶凝固后纺布会收缩产生误差量的基础上，将单向超高分子聚乙烯等纺布裁剪成所需尺寸（0.25 m×0.25 m）。环氧树脂胶调配时，室内温度为23 ℃。粘贴立面纤维复合材料时，要按照由上到下的顺序进行。粘贴后用滚筒将纤维复合材料从一端向另一端滚压，除去胶体与纤维复合材料之间的气泡，使胶体渗入纤维复合材料。当采用多层纤维复合材料加固时，在前一层纤维布表面用手指触摸感到干燥后，立即涂胶粘贴后一层纤维复合材料。最后一层纤维复合材料施工结束后，在其表面放置UHMWPE薄膜，将8 kg重物放在其表面，静置24 h。
1.2 实验场地布置
滑膛枪的破片冲击复合板实验如图2所示。利用口径14.5 mm身管进行弹道发射，通过调节发射药药量来控制破片侵彻速度。发射药采用14.5 mm滑膛枪制式药，装填药量在10～37 g范围内，破片采用直径8 mm、质量4 g的钨合金球，初速度在400～1500 m/s范围内。
采用2台高速摄像机观测复合板动态响应如图2(b)，拍摄速度15000 s−1，利用LED照明设备保障光照强度条件，相机前通过设置防弹玻璃以保护相机。采用断通靶（图2(c)）和六路电子测时仪（图2(d)）对破片初速、末速进行测量；通过同步触发器使得击发破片时同时触发测试设备实验场地布置。破片配置尼龙弹托如图2(e)所示，尼龙弹托与枪膛为过盈配合，膛内与破片共同加速运动，能够保持破片姿态的稳定性。靶板平面应与弹道枪中心轴线垂直，并调整至适度的射击距离，以保证破片与弹托及时分离。
靶板通过夹具对四周进行全固定，夹具通过螺栓固定在实验平台，如图3所示。高速相机的拍摄区域面积为200 mm×200 mm，如图3所示。为了便于后期形变分析，制作了散斑，散斑的质量会影响后期计算的准确性，因此散斑图案必须随机分布，并具有适当的密度和良好的对比度。实验散斑直径约大于2 mm，在喷漆面标记200 mm×200 mm分析区域如图3所示，采用Match ID软件计算分析von Mises应变场。
图 3 靶板固定方式与高速相机拍摄示意图Figure 3. Schematic diagram of target plate fixing method and high-speed camera shooting2. 数值模拟实验方法
2.1 数值模拟模型
通过Abaqus/Explicit对实验场景进行数值模拟，并对比分析数值模拟结果与实验结果，通过理想化数值模型探究超高分子抗破片侵彻性质。
建立的破片侵彻Al/UHMWPE复合板模型如图4所示，包括铝合金板、Cohesive层和UHMWPE板，靶板长宽均为250 mm，铝板厚度为10 mm，PE板根据具体要求选择不同厚度。由于高速撞击具有局限性，故对靶板中心区域作加密处理，通过多次调试，发现加密处采用1 mm×1 mm的细化网格，8 mm直径破片网格采用0.8 mm时能有效保证模型计算效率和计算精度。 最小计算时长为0.03 ms，最大计算时长为0.1 ms。
2.2 材料模型
铝合金靶板与钨合金破片采用Johnson-Cook材料模型，其中铝合金材料参数来源于文献[14]，钨合金材料参数来源于文献[15]。
材料屈服模型（损伤）：
σeq=(A+Bεeqn)(1+Clnε∗eq)(1−T∗m) (1) 式中：A为材料在参考应变率下的初始屈服应力，B为材料的应变硬化模量，n为材料应变硬化系数，C为应变率敏感系数，m为温度敏感系数，εeq为等效塑性应变，
ε∗eq 为无量纲化等效塑性应变率，T*为无量纲化温度， T*=(T−Tr)(Tm−Tr)，其中T为当前温度，Tr为参考温度，Tm为材料的熔点。材料失效模型：
εf=[D1+D2exp(D3(σmσeq))][1+D4ln(ε∗eq)](1+D5T∗) (2) 式中：D1、D2、D3、D4、D5 为材料损伤参数，σeq为等效应力（von Mises应力），σm为球应力(静水压力)。
所用UHMWPE材料模型是基于Abaqus用户子程序VUMAT编写的本构模型[16]。该本构模型中根据UHMWPE材料正交各向异性特性所用的柔度矩阵：
(εxεyεzγyzγzxγxy)=(1E11−ν12E22−ν13E33000−ν21E111E22−ν23E33000−ν31E11ν32E221E330000001G230000001G130000001G12)(σxσyσzτyzτzxτxy) (3) 式中：E11、E22、E33分别为轴向、切向、法向方向的弹性模量，ν12、ν13、ν23为泊松比，G12、G13、G23为剪切模量。
纤维增强树脂复合材料的失效判断准则采用 Hashin 3D失效准则，遵循以下4个失效准则分析叠层复合材料的失效破坏。
纤维拉伸破坏:
(σ11Xt)2+σ212+σ213S12≥1σ11＞0 (4) 纤维压缩失效：
σ11Xc≥1σ11＜0 (5) 基体拉伸失效：
(σ22+σ33Yt)2+σ223−σ22σ33S223+σ212+σ213S212≥1σ22+σ33＞0 (6) 基体压缩失效：
[(Yc2S23)2−1](σ22+σ33)+14S223(σ22+σ33)2+σ223−σ22σ33S223+σ212+σ213S212≥1σ22+σ33＜0 (7) 式中：Xt、Yt、Zt为极限拉伸强度(极限张应力)，Xc、Yc、Zc为极限抗压强度，S12、S13、S23为极限剪应力，具体参数见表1所示。
表 1 UHMWPE材料参数Table 1. Material parameters of UHMWPEρ/(kg·m−3) E11/MPa E22/MPa E33/MPa ν12 ν13 ν23 970 95000 95000 11300 0.3 0.3 0.4 G12/MPa G13/MPa G23/MPa Xt/MPa Xc/MPa Yt/MPa 6000 6000 3600 3048 1580 130 Yc/MPa Zt/MPa Zc/MPa S12/MPa S13/MPa S23/MPa 650 340 180 130 130 130 数值模拟模型所用子程序在Hashin准则和孕育时间准则的基础上考虑了应变率效应的失效准则，与Hashin准则的不同之处在于静态荷载下，动态增强因子δ为1，此时该失效准则与Hashin准则完全一致；动态荷载下，动态增强因子δft(纤维拉伸)、δfc(纤维压缩)、δmt(基质拉伸)、δmc(基质压缩)为：
{δft=1+τfXtσ11Xtδfc=1+τfXcσ11Xcδmt=1+τm2σ22Ytδmc=1+τm2σ22Yc (8) 式中：τf和τm分别为纤维方向和横向的孕育时间。这里不考虑纤维方向和横向的拉压性能差异，压缩相关的孕育时间与拉伸一致。
为了表征失效模式和材料的弱化影响，引入了损伤变量或退化因子。目前主要有衰减退化和折减退化两种方式。衰减退化是指材料的退化是一个渐变的过程，一般适用于具有明显塑性段的材料。折减退化是指材料的退化是一个突变的过程，在满足一定条件后，相关参数折减为初始值一定比例。FRP损伤力学中一般采用折减退化的方式，其中最常用的模型是Chang-Chang折减模型[17]和Camanho折减模型[18]，本文中采用Camanho折减模型，因为该模型对材料的模量不完全折减为零，可避免有限元中出现矩阵奇异所造成的数值问题，详细内容见表2。表中
Ed11 、Ed22 为材料失效后退化的轴向、切向弹性模量，Gd12 为材料失效后退化的剪切模量。表 2 Camanho 折减模型Table 2. Camanho reduction model失效模型 折减方法 纤维拉伸失效 Ed11=0.07E11 纤维压缩失效 Ed11=0.14E11 基体拉伸或剪切失效 Ed22=0.2E22，Gd12=0.2G12 基体压缩或剪切失效 Ed22=0.4E22，Gd12=0.4G12 基于应力应变关系、失效准则和退化模型，利用Fortran语言编写的子程序，其分析流程如图5所示。
黏合剂材料采用内聚力（Cohesive）材料模型，材料模型参数来源于文献[19]，本构模型采用双线性模型，公式为：
t=(tntstt)=(Knn000Kss000Ktt)(εnεsεt)=Kε (9) 式中：tn、ts、tt为名义应力，εn、εs、εt为名义应变（张开位移），Knn、Kss、Ktt为３个方向的刚度。
Cohesive初始损伤准则采用二次名义应力准则（quads damage），公式为：
(tnS)2+(tsS)2+(ttT)2=1 (10) 式中：N、S、T为相应方向的法向强度与剪切强度。
损伤演化规律为：
(GⅠGⅠC)2+(GⅡGⅡC)2+(GⅢGⅢC)2=1 (11) 式中：GⅠ、GⅡ和GⅢ分别为模型Ⅰ、Ⅱ和Ⅲ的能量释放率。GⅠC、GⅡC和GⅢC分别为模型Ⅰ、Ⅱ和Ⅲ。通过双悬臂试样和端部缺口弯曲试样确定的黏结层的内聚断裂韧性参数
3. 高速冲击下复合板响应及失效分析
3.1 破片速度衰减规律
通过设置与实验相同破片初速以及靶板厚度以模拟实验情况，对比破片速度衰减情况以及能量衰减情况判断数值模拟模型的可靠性。由于有限元数值模拟的不连续性导致得到的子弹末速存在波动，故对所得数据取平均值，具体数据参见表3。
表 3 侵彻靶板数值模拟与实验数据对比Table 3. Comparison between simulation and experiment in penetration process靶板厚度/mm 靶板结构 破片初速/(m·s−1) 破片末速/(m·s−1) 误差/% 数值模拟 实验 速度 动能 10.02 Al 1027.49 823.83 844.88 2.5 4.92 10.01 Al 861.67 682.44 658.75 3.6 7.32 10.01 Al 1020.48 822.30 835.62 1.6 3.16 10.01 Al 1283.26 1043.31 1093.19 4.6 8.92 10.00 Al 1091.24 879.88 856.74 2.7 5.47 12.00 Al/UHMWPE 1031.03 815.47 815.51 0.0 0.01 13.30 Al/UHMWPE 1109.26 837.90 882.61 5.1 9.87 14.40 Al/UHMWPE 1015.25 736.59 721.04 2.2 4.36 15.60 Al/UHMWPE 1071.68 725.44 736.71 1.5 3.04 17.40 Al/UHMWPE 988.45 517.27 500.82 3.3 6.68 对比数值模拟数据与实验数据，可以发现两者存在误差波动，误差都在10%以内，在允许误差范围内。这证明该铝合金材料模型与超高分子聚乙烯材料模型对破片的吸能性能与实验所用铝合金材料与聚乙烯材料基本一致。
图6所示为实验得到的靶板吸收破片动能与数值模拟靶板吸收动能的对比，从图6中可以发现，厚度为12 mm的Al/UHMWPE复合板在1031.03 m/s初速破片侵彻下动能吸收量要小于10 mm铝板在1283.26 m/s初速破片侵彻下的动能吸收量。这是由于加载速率的增加将导致材料强度的提高，这也意味着具有较高冲击速度的破片将受到较大的阻力，从而损失更多的动能。由此可见，影响靶板对破片动能的因素除了靶板自身厚度，破片速度也会影响靶板动能吸收。破片速度越高，相同靶板所能吸收的动能就越多。
图 6 靶板吸收破片动能的实验和数值模拟结果对比Figure 6. Comparison between experimental and simulated kinetic energy absorption of the target plate3.2 复合板应变动态响应分析
Al/UHMWPE复合板厚度为12 mm，其中铝板厚度为10 mm，UHMWPE板厚度为2 mm。对1020、1431 m/s冲击下复合板动态响应进行DIC分析，如图7所示。破片侵彻12 mmAl/UHMWPE复合板，鼓包呈现以着弹点为中心的不规则椭圆形。除明显的鼓包外，由于最外层纤维铺设角度为0°，故出现了呈0°的纤维凸起，且形成以弹孔为中心呈十字形应变带分叉的现象。破片较高的冲击强度使得位于破片侵彻弹道上的纤维被破片冲击而出现剪切及拉伸破坏，拉伸作用下使得应力沿着纤维继续传播，导致纤维出现凸起。由于纤维层之间为0°与90°角度交替铺设，故在破片侵彻过程中被破坏的0°与90°铺设角度的纤维凸起导致了十字形应变带分叉现象。
图 7 1020和1431 m/s初度破片侵彻下PE复合板DIC分析Figure 7. DIC analysis of PE composite plate penetrated by fragment at the velocities of 1020 and 1431 m/s通过观察速度1431 m/s下工况，发现在67 μs时，十字形应变带较明显，随着时间推移，十字形应变带逐渐消失，333 μs时，十字形应变带中的纵向应变带基本消失，这说明实验中出现的十字形应变带属于弹性变形。造成高速度侵彻产生的十字应变不如低速度时明显的原因是因为弹靶速度差，破片速度较低使得正交铺设纤维拉伸时间充足，会造成明显的十字凸起，破片速度较高使得十字凸起反而由于纤维拉伸时间短而不明显[20]。由此可见1431 m/s初速破片侵彻下，12 mmAl/UHMWPE复合板中的纤维并未得到充分拉伸。
为验证数值模拟自由界面纤维破坏的可靠性，对相同工况进行数值模拟，所得应变随时间变化结果如图8所示。从数值模拟结果可以发现自由表面纤维出现了与实验中相似的十字形应变，且随着应变带向边界传播，1020 m/s速度下的24 μs与1431 m/s速度下的18 μs出现十字形应变带分叉现象，这证明数值模拟模型对于模拟自由面纤维应变的可靠性。
图 8 1020和1431 m/s初度破片侵彻下Al/UHMWPE复合板应变传播云图Figure 8. Strain propagation cloud diagrams of Al/UHMWPE composite plate penetrated by fragments with the velocities of 1020 and 1431 m/s3.3 Al/UHMWPE复合板应力动态响应分析
通过对初速为1431 m/s破片侵彻厚度12 mm的Al/UHMWPE复合板进行数值模拟，得到了破片侵彻过程中Al/UHMWPE复合板的von Mises应力传播云图（图9）。从图9中可以看出，着弹孔周围形成应力集中现象，由于迎弹面面板材料为2024铝合金，金属各向同性的材料性质使得应力波在铝合金上呈同心圆状传播，应力波峰值超过280 MPa，大于铝合金屈服应力150 MPa。应力波在铝合金板面传播过程中，应力值逐渐减弱，应力波到达边界后与之后的应力波在边界处叠加，这使得边界的应力波峰值出现少许的提升，从约70 MPa短暂提升到约100 MPa。
图 9 1431 m/s初速破片侵彻下Al/UHMWPE复合板中 Mises应力传播云图Figure 9. Mises stress propagation distribution of Al/UHMWPE composite plate penetrated by the fragment with the velocity of 1431 m/s纤维具有各向异性的材料性质，这使得应力波在纤维各个方向上的传播速度与大小不一致，破片侵彻过程中沿着纤维方向产生的拉伸应力波以材料声速传播，其余方向应力波则会在拉伸应力波作用后出现扰动并以较低的速度传播 [21-22]。纤维层之间以0°与90°交替铺设使得强应力波在纤维面板上呈现十字形传播，弱应力波以同心菱形的形状以着弹点为中心向边界传播。与铝合金板上应力波传播方式不同点还在于纤维上十字形传播的应力波值较大，且十字形传播的应力波到达边界后一部分向两边传播，另一部分沿着相同传播路径反射，并与之后产生的应力波相互作用、耦合，从而使得纤维层出现前后波动，这种波动随着应力波的衰减而逐渐减弱并最终消失。
3.4 Al/UHMWPE复合板微观破坏分析
图10展示了通过CT分析得到的球形破片侵彻后的孔壁微观破坏及数值模拟弹孔破坏。观察图10可以发现Al/UHMWPE复合板的迎弹面铝板在与破片侵彻过程中，铝板在冲击作用下发生绝热剪切破坏，且孔壁由于压剪失效呈现毛刺状的不规则孔壁。背弹面UHMWPE板出现了两种破坏状态，先受到侵彻的纤维层断口平整，出现轻微分层现象，另一部分纤维层断口不平整，出现拉伸破片产生的絮状纤维，且出现明显分层现象。说明该工况下UHMWPE板的纤维层在破片侵彻过程中，先受到的主要破坏方式为剪切破坏，后受到的主要破坏方式为拉伸破坏。纤维破坏与所受冲击强度有关，所受冲击强度较小时，能更有效地发挥超高分子聚乙烯的高抗拉伸强度的效果，从而起到更好的抗侵彻效果，但当所受冲击强度较大时，纤维在高速破片冲击下产生挤压、剪切破坏，无法通过大幅度的拉伸变形吸收更多能量。
图 10 PE复合板弹孔周围局部破坏Figure 10. Local destruction around the bullet hole of the PE composite plate对比相同工况的数值模拟结果可以发现，该数值模型能较好地模拟铝板受到破片侵彻后产生的冲塞效应及压剪破坏产生的毛刺状不规则孔壁。对于PE板受到侵彻后，纤维出现的拉伸破坏、剪切破坏也能较好地模拟。
4. UHMWPE背板厚度对抗侵彻性能影响研究
4.1 不同侵彻速度下背板厚度对应变的影响
为了研究不同速度下背板厚度对应变的影响，选取侵彻速度500、1000和1500 m/s贯穿不同厚度的靶板时的应变云图进行对比分析，其中8、14 mm分别为500、1000 m/s的极限侵彻厚度，如图11所示。从图中可以观察到相同速度的破片侵彻靶板，UHMWPE板较薄时出现的应变大于0.01的区域呈现十字形，出现十字形的原因与靶板固定方式为四周全固定有关[23]。随着厚度的增加，破片在UHMWPE板中侵彻时间增加，纤维有更充足的时间通过拉伸变形吸收动能，这使得超过0.01的应变区域也从近似于十字形逐渐过渡为X形。
图 11 贯穿靶板前后应变云图Figure 11. Runs through the target plate successively strain cloud mapLong[24]曾对这种X形鼓包进行研究，国内学者的实验中也曾出现这种现象。出现这种现象的原因是由于正交铺设的正方形UHMWPE板自由面纤维拉伸过大，且靶板固定方式为四周全固定，离着弹点近的边界部分先向内收紧，并逐渐向四个边角扩展，形成了紧缩现象。最终这将导致出现的纤维鼓包类似于金字塔形[25]。这说明侵彻边界全固定下的UHMWPE复合板在较薄厚度下，主要形变区域呈现十字形。而当厚度更接近或超过破片侵彻极限厚度时，由于纤维层吸收能量更多，隆起形变影响范围更大，侵彻时间以及拉伸变形程度随着厚度的增加而增加，最终主要形变区域会形成类似于X形。数值模拟中出现的纤维撕裂也表现出了不同的形状。较薄时纤维沿着铺设角度发生径向撕裂，随着纤维层厚度增加，受到破坏的纤维层增加，被破坏的部分形成冲塞物，随着冲塞物增多从而形成纤维堆积，以及破片速度降低后，纤维有更多的拉伸时间，从而出现更大的纤维拉伸变形。这将导致后受到破坏的纤维层出现严重的撕裂开花现象[26]。
4.2 背部UHMWPE 板厚度对吸收破片动能的影响
为探究破片侵彻过程中复合板对破片各个阶段动能吸收情况，特选取1500 m/s侵彻速度下10 mm Al/2 mm UHMWPE、10 mm Al/8 mm UHMWPE、10 mm Al/18 mm UHMWPE等种复合板为对象，得出了破片侵彻过程中动能随时间变化历程图，如图12。而破片侵彻过程中的复合板剖面图，如图13所示。从图中可以看出，复合板的吸能情况可以根据破片动能-时间曲线斜率及数值模拟中复合板损伤演化大致分为3个阶段。第一阶段为面板损伤阶段，在穿透铝板时，破片分别消耗了大约1350.8、1788.6和2039.2 J，而时间分别用了8、10和12 μs。通过对比3组工况破片穿透铝板时所消耗的动能与时间可以发现随着纤维层的加厚，破片侵彻相同厚度的铝板所需的动能与时间不断提高，这是因为背板厚度增加从而增强了背板对迎弹面铝板的支撑作用，说明增加背弹面UHMWPE板厚度有利于破片在侵彻迎弹面铝板过程中消耗更多动能。
图 12 破片侵彻过程中动能吸收时程曲线Figure 12. Kinetic energy absorption history during fragment penetration process
图 13 破片侵彻过程中的复合板剖面图Figure 13. Cross-sectional view of the composite panel during fragment penetration第二阶段为破片开始侵彻UHMWPE板至UHMWPE板背部出现凸起阶段，该阶段由于UHMWPE板背部未出现大变形，所以纤维所受拉伸破坏较小，且结合图11可以判定该阶段纤维主要破坏方式剪切破坏。
第三阶段为UHMWPE板背部出现凸起至结束。从数值模拟图可以发现复合板出现了较明显的脱胶现象，且背部纤维变形程度持续增大，说明该阶段纤维受到了较大的拉伸破坏，主要破坏方式为拉伸破坏。同时UHMWPE板两侧比中间部分先出现了明显的破坏，出现这样的原因是因为破片侵彻过程中形成的应力波到达UHMWPE板自由表面（背弹面）后立即产生相应的反射拉伸应力波。反射的拉伸波以相同的波速反向传播与之后传播的应力波重叠出现应力叠加，使得自由表面附近的拉伸应力超过某截面纤维材料本身的断裂强度且持续一定时间以后，这使得该截面产生破坏。而在10 mm Al/18 mm UHMWPE工况中可以看出，从18 μs开始，由于自由表面纤维层持续破坏，曲线斜率不断下降，说明单位时间内复合板吸能效果也持续下降。由此可以得出UHMWPE板对破片侵彻的阻抗力大小与UHMWPE板厚度和完整性有直接关系，越厚且越完整的UHMWPE板所能提供的对破片侵彻的阻力越大。
4.3 破片速度与靶板厚度对吸能性能的影响
对500、1000和1500 m/s的钨球破片侵彻Al/UHMWPE复合板进行数值模拟，迎弹面统一采用10 mm铝合金板，通过对背弹面增加不同厚度超高分子聚乙烯涂层的方式探究破片速度与背弹面UHMWPE板厚度对吸能性质的影响。对于初速为500 m/s的破片，由于破片速度相对较低，能够消耗掉全部破片动能的靶板厚度也较小。为能够得到足够的样本数量，通过依次增加厚度为0.8 mm的UHMWPE板来探究低速下破片对UHMWPE复合板的侵彻性质。对于初速为1000、1500 m/s的破片，通过依次增加厚度为2 mm的UHMWPE板来探究低速下破片对UHMWPE复合板的吸能特质。由于数值模拟得到的500和1000 m/s破片初速侵彻下，UHMWPE板的极限侵彻厚度为8和14 mm。为确保得出数据为靶板吸收破片动能的极限值，因此在500和1000 m/s速度工况下选取的UHMWPE板厚度分别为7.4 和13 mm 。
目前，常用的表示靶板吸能性能的方法有比吸能和面密度吸能。二者的区别在于靶板的比吸能是通过弹道极限获得的，而面密度吸能是通过弹体穿透靶板后的动能减少量来获得的。二者在物理本质上没有本质区别[27]，但鉴于数值模拟中已有破片初速与末速，故采用面密度吸能来描述靶板吸能性能：
ES=EbρA (12) 式中：Eb为靶板吸收的弹体动能，ρA为靶板的面密度。
将初速为500、1000和1500 m/s的破片侵彻下靶板面密度吸能随厚度变化的数据按三阶多项式拟合，所得曲线如图14所示。从图中可知，3种速度侵彻PE复合板的面密度吸能变化趋势基本符合三阶多项式曲线规律，这使得PE板厚度对于面密度吸能的影响呈非线性。500 m/s破片冲击下，面密度吸能随着PE板厚度的增加而持续提升，虽然部分阶段存在波动，但整体增长趋势并未放缓。复合板的面密度吸能在涂敷了约6.4 mm的PE板时达到最大，为14.55 J/(kg·m2)，随后便不断降低，直至达到极限侵彻厚度8 mm。对于1000 m/s的破片，PE板厚度在12 mm之前，面密度吸能都呈现上升趋势，PE板厚度在12 mm时，面密度吸能达到最大值49.51 J/(kg·m2)。而对于1500 m/s的破片，PE板厚度在10 mm之前，面密度吸能呈现上升趋势，但在厚度超过10 mm时，面密度吸能增速开始变缓，PE板厚度在16 mm时面密度吸能达到最大（为98.07 J/(kg·m2)）。从500、1000和1500 m/s的吸能性能随厚度的关系可以发现，吸能性能随着PE板厚度增加，而不断增长，但达到一定厚度后再继续增加厚度，PE板扩散冲击能量的效果减弱，单位面密度吸收冲击动能减小，从而导致复合板吸能性能将停滞甚至下降。因此，在达到一定程度厚度后，提高靶板厚度对提高吸能性能的作用有限。
图 14 500、1000和1500 m/s侵彻速度下靶板的吸能性能与靶板厚度关系Figure 14. Relation between energy absorption performance of the target plate and its thickness at the penetration velocity of 500, 1000 and 1500 m/s5. 结 论
针对Al/PE复合板在低、中、高速冲击下的防护，开展了14.5 mm滑膛枪的破片冲击复合板实验，基于Abaqus用户子程序VUMAT编写的超高分子聚乙烯的本构模型及金属J-C损伤本构模型进行数值模拟，得出以下结论。
(1)正交纤维受到正撞击后，应力呈十字形扩散。在破片侵彻弹道上的纤维被破片冲击而出现剪切及拉伸破坏，拉伸作用下应力沿着纤维方向继续传播，使得被剪切拉断的0°与90°铺设角度的纤维凸起并出现十字形应变带分叉现象。
(2)侵彻边界全固定下的Al/PE复合板，随着PE板厚度增加，破片在PE板中侵彻时间增加，纤维有更充足的时间通过拉伸变形吸收动能，这使得超过0.01的主要应变区域从近似于十字形逐渐过渡为X形。
(3)背板对面板的支撑性随着背部PE板厚度增大而增强，这阻碍了破片对铝板的冲塞运动，使得破片在迎弹面消耗动能与时间也随之增加。且PE板抵抗力与其自身厚度和完整性有关，出现破损后PE板对破片侵彻的阻抗力便会减弱。
(4) PE复合板厚度对吸能性能影响趋势呈先快速上升至阈值，后缓慢下降的趋势。当冲击速度为500、1000和1500 m/s时，最优面密度吸收能厚度分别为6.4、12和16 mm，最优面密度吸收能分别为14.55、49.51和98.07 J/(kg·m2)。
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图 1 典型的成层式防护结构示意图
Figure 1. Schematic diagram of typical multilayer protective structure
图 2 准静态压缩下泡沫混凝土典型的应力应变曲线示意图
Figure 2. Typical stress-strain curves of foam concrete under quasi-static compression
图 3 空气夹层成层式结构破坏演化过程示意图
Figure 3. Failure evolution process of the multilayer protection structure with an air distribution layer
图 7 不同空间尺度下金属泡沫的结构特征
Figure 7. Structural features of metal foams at different spatial scales
图 10 不同密度多孔混凝土的抗压强度
Figure 10. Compressive strength of cellular concrete with different density
图 11 不同密度多胞材料的典型应力-应变曲线示意图
Figure 11. Typical stress-strain curves of cellular materials with different densities
Table 1. Physical and mechanical parameters of the medium under the ground impact of explosion[9-10]
介质 波速c/（m·s−1） 波阻抗ρc /（kg·m-2·s-1） 衰减指数n 低相对密度松散干砂、黄土和砂砾 180 0.26×106 3.00～3.50 密实的不良级配干砂 274～396 0.57×106 2.50～2.75 相对密度接近100%的极密干砂 488 1.00×106 2.50 黏土、松散不良级配湿砂（含自由水） 152～183 0.28×106～0.34×106 3.00 湿的泥质黏土 213～274 0.41×106～0.57×106 2.75～3.00 砂质填土、回填土、潮湿黏土 300 0.50×106 2.75～3.00 密实的不良级配湿砂（含自由水） 305 0.50×106 2.75 潮湿黄土、粉土 300 0.63×106 2.75～3.00 地下水位以上的潮湿粉土 549 1.09×106 2.50 饱和土 550～1500 1.09×106～3.05×106 1.50～2.50 
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表 2 铺设泡沫混凝土分散层后结构层动态响应参数峰值衰减率
Table 2. Peak attenuation rate of dynamic response parameters of protection structure with foam concrete
工况 泡沫混凝土分散层 装药量/kg 结构层动态响应参数类型 峰值衰减率/% 数据来源 密度/（kg·m−3） 厚度/cm 1 450 6～10 44 压力峰值 79.1～89.9 文献[14] 2 475 3 0.014 54 文献[15] 3 610 15 0.2 48.9 文献[13] 4 788 20～120 306 23～28.8 文献[16] 5 799 5～15 − 20.1～40.5 文献[17] 6 788 40～120 − 加速度峰值 30.9～40.2 文献[18] 7 450 6～10 44 速度峰值 62.1～73.3 文献[14] 8 799 5～15 − 7.3～13.3 文献[17] 9 400 20 0.025～0.03 形变量峰值 66.7～83.7 文献[19] 10 475 2～4 0.014 11.9～23.9 文献[15] 11 799 15 − 8.3 文献[17]
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