
Acta Armamentarii ›› 2025, Vol. 46 ›› Issue (11): 250225-.doi: 10.12382/bgxb.2025.0225
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YANG Haowei1, WANG Junlong2, MIAO Zhenwei1,*(
), KANG Yue2,**(
), WEI Yanpeng1
Received:2025-03-31
Online:2025-11-27
Contact:
MIAO Zhenwei, KANG Yue
CLC Number:
YANG Haowei, WANG Junlong, MIAO Zhenwei, KANG Yue, WEI Yanpeng. Research on the Application of Shear-stiffening Gel Modified Foam Materials in Ballistic Helmets[J]. Acta Armamentarii, 2025, 46(11): 250225-.
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| 样品 | 硬度(SLX-C) | 密度/(g·cm-3) | 弹性模量/MPa |
|---|---|---|---|
| EVA泡沫 | 40 | 0.065 | 4.1 |
| EVA/SSG泡沫 | 48 | 0.068 | 5.2 |
Table 1 The fundamental material parameters of EVA and EVA/SSG foams
| 样品 | 硬度(SLX-C) | 密度/(g·cm-3) | 弹性模量/MPa |
|---|---|---|---|
| EVA泡沫 | 40 | 0.065 | 4.1 |
| EVA/SSG泡沫 | 48 | 0.068 | 5.2 |
| 失效模式 | 失效判据 |
|---|---|
| 纤维拉伸断裂 | σ11>0, |
| 基体碎裂 | σ22>0, |
| 基体压缩失效 | σ22<0, + |
| 纤维压缩失效 | σ11<0, |
Table 2 The failure criteria of MAT-54 constitutive model
| 失效模式 | 失效判据 |
|---|---|
| 纤维拉伸断裂 | σ11>0, |
| 基体碎裂 | σ22>0, |
| 基体压缩失效 | σ22<0, + |
| 纤维压缩失效 | σ11<0, |
| 材料参数 | 数值 |
|---|---|
| 密度ρ/(kg·cm-3) | 1230 |
| 弹性模量E11,E22/GPa | 18.5 |
| 弹性模量E33/GPa | 6 |
| 泊松比ν12 | 0.25 |
| 泊松比ν31,ν23 | 0.33 |
| 剪切模量G12/GPa | 0.77 |
| 剪切模量G23,G13/GPa | 2.5 |
| 平面方向的拉伸强度/GPa | 0.555 |
| 平面方向的压缩强度/GPa | 1.2 |
| 剪切强度/MPa | 77 |
Table 3 Material parameters of helmet shell
| 材料参数 | 数值 |
|---|---|
| 密度ρ/(kg·cm-3) | 1230 |
| 弹性模量E11,E22/GPa | 18.5 |
| 弹性模量E33/GPa | 6 |
| 泊松比ν12 | 0.25 |
| 泊松比ν31,ν23 | 0.33 |
| 剪切模量G12/GPa | 0.77 |
| 剪切模量G23,G13/GPa | 2.5 |
| 平面方向的拉伸强度/GPa | 0.555 |
| 平面方向的压缩强度/GPa | 1.2 |
| 剪切强度/MPa | 77 |
| 材料参数 | 铜外壳 | 铅芯 |
|---|---|---|
| 密度/(g·cm-3) | 8.96 | 11.31 |
| 屈服强度A/MPa | 510 | 10 |
| 硬化系数B/MPa | 496 | 50 |
| c | 0.009 | 0.23 |
| n | 0.42 | 0.098 |
| m | 1.03 | 1.03 |
| 损伤常数Di(i=1,2,3,…) | 0.6,0,0,0 | 0.25,0,0,0 |
Table 4 Material properties of copper jacket and core of 51-type pistol cartridge[23]
| 材料参数 | 铜外壳 | 铅芯 |
|---|---|---|
| 密度/(g·cm-3) | 8.96 | 11.31 |
| 屈服强度A/MPa | 510 | 10 |
| 硬化系数B/MPa | 496 | 50 |
| c | 0.009 | 0.23 |
| n | 0.42 | 0.098 |
| m | 1.03 | 1.03 |
| 损伤常数Di(i=1,2,3,…) | 0.6,0,0,0 | 0.25,0,0,0 |
| 部件 | 材料 | 本构模型 | 属性 |
|---|---|---|---|
| 皮肤 | 橡胶 | Second-order Ogden hyperelastic model | μ1=0.64 μ2=-4.01 α1=1.492 α2=-3.316 |
| 头骨 | 镁合金 | Linear elastic | ρ=1780kg/m3 E=45GPa |
| 头骨盖 | 镁合金 | Linear elastic | ρ=1780kg/m3 E=45GPa |
| 基座 | 铝合金 | Solid Rigid | ρ=2700kg/m3 |
| 颈部底座 | 铝合金 | Solid Rigid | ρ=2700kg/m3 |
Table 5 Details of the numerical model of Hybrid III headform
| 部件 | 材料 | 本构模型 | 属性 |
|---|---|---|---|
| 皮肤 | 橡胶 | Second-order Ogden hyperelastic model | μ1=0.64 μ2=-4.01 α1=1.492 α2=-3.316 |
| 头骨 | 镁合金 | Linear elastic | ρ=1780kg/m3 E=45GPa |
| 头骨盖 | 镁合金 | Linear elastic | ρ=1780kg/m3 E=45GPa |
| 基座 | 铝合金 | Solid Rigid | ρ=2700kg/m3 |
| 颈部底座 | 铝合金 | Solid Rigid | ρ=2700kg/m3 |
| 样品编号 | 子弹速度 | 被穿透芳 纶层数 | 实验 序号 |
|---|---|---|---|
| 芳纶盔壳+EVA(1) | 450.2 | 4 | Test 1 |
| 芳纶盔壳+EVA/SSG(2) | 448.9 | 4 | |
| 芳纶盔壳+EVA(3) | 453.6 | 3 | Test 2 |
| 芳纶盔壳+EVA/SSG(4) | 452.0 | 4 | |
| 芳纶盔壳+EVA(5) | 451.6 | 4 | Test 3 |
| 芳纶盔壳+EVA/SSG(6) | 449.3 | 4 |
Table 6 the number of failed laminates and the bullet’s velocity in tests
| 样品编号 | 子弹速度 | 被穿透芳 纶层数 | 实验 序号 |
|---|---|---|---|
| 芳纶盔壳+EVA(1) | 450.2 | 4 | Test 1 |
| 芳纶盔壳+EVA/SSG(2) | 448.9 | 4 | |
| 芳纶盔壳+EVA(3) | 453.6 | 3 | Test 2 |
| 芳纶盔壳+EVA/SSG(4) | 452.0 | 4 | |
| 芳纶盔壳+EVA(5) | 451.6 | 4 | Test 3 |
| 芳纶盔壳+EVA/SSG(6) | 449.3 | 4 |
| AIS评分 | 损伤严重程度 | 致死率/% |
|---|---|---|
| AIS 1 | 无 | 0.0 |
| AIS 2 | 轻微 | 0.1~0.4 |
| AIS 3 | 轻度 | 0.8~2.1 |
| AIS 4 | 中度 | 7.9~10.6 |
| AIS 5 | 重伤 | 53.1~58.4 |
| AIS 6 | 致命 | >90 |
Table 7 Explanation of AIS code
| AIS评分 | 损伤严重程度 | 致死率/% |
|---|---|---|
| AIS 1 | 无 | 0.0 |
| AIS 2 | 轻微 | 0.1~0.4 |
| AIS 3 | 轻度 | 0.8~2.1 |
| AIS 4 | 中度 | 7.9~10.6 |
| AIS 5 | 重伤 | 53.1~58.4 |
| AIS 6 | 致命 | >90 |
| 样品编号 | HIC值 | 对应时间窗口/ms |
|---|---|---|
| 芳纶盔壳+EVA(1) | 1052.6 | 4.65~5.05 |
| 芳纶盔壳+EVA(2) | 954.7 | 4.85~5.10 |
| 芳纶盔壳+EVA(3) | 1058.9 | 4.80~5.15 |
| 芳纶盔壳+EVA/SSG(1) | 702.8 | 4.85~5.45 |
| 芳纶盔壳+EVA/SSG(2) | 710.6 | 4.90~5.25 |
| 芳纶盔壳+EVA/SSG(6) | 844.5 | 4.80~5.15 |
Table 8 HIC value obtained from the test and the corresponding time window
| 样品编号 | HIC值 | 对应时间窗口/ms |
|---|---|---|
| 芳纶盔壳+EVA(1) | 1052.6 | 4.65~5.05 |
| 芳纶盔壳+EVA(2) | 954.7 | 4.85~5.10 |
| 芳纶盔壳+EVA(3) | 1058.9 | 4.80~5.15 |
| 芳纶盔壳+EVA/SSG(1) | 702.8 | 4.85~5.45 |
| 芳纶盔壳+EVA/SSG(2) | 710.6 | 4.90~5.25 |
| 芳纶盔壳+EVA/SSG(6) | 844.5 | 4.80~5.15 |
| 缓冲 系统 | HIC 平均值 | AIS1 | AIS2 | AIS3 | AIS4 | AIS5 | AIS6 |
|---|---|---|---|---|---|---|---|
| EVA | 1022.4 | 99.76 | 91.2 | 68.3 | 21.3 | 5.1 | 0.1 |
| EVA/SSG | 752.8 | 97.32 | 82.3 | 49.3 | 9.3 | 0.02 | 0 |
Table 9 Head injury criteria values and abbreviated injury scales
| 缓冲 系统 | HIC 平均值 | AIS1 | AIS2 | AIS3 | AIS4 | AIS5 | AIS6 |
|---|---|---|---|---|---|---|---|
| EVA | 1022.4 | 99.76 | 91.2 | 68.3 | 21.3 | 5.1 | 0.1 |
| EVA/SSG | 752.8 | 97.32 | 82.3 | 49.3 | 9.3 | 0.02 | 0 |
| 缓冲系统 | 峰值压力/N | 峰值加速度/g | ||||
|---|---|---|---|---|---|---|
| 实验值 | 仿真值 | 相对误 差/% | 实验值 | 仿真值 | 相对误 差/% | |
| EVA | 7870.9 | 7381.1 | 6.2 | 132.4 | 116.3 | 12.1 |
| EVA/SSG | 6015.5 | 6375.8 | 5.9 | 95.6 | 106.7 | 11.5 |
Table 10 Ballistic impact experiments and simulation results of headform model
| 缓冲系统 | 峰值压力/N | 峰值加速度/g | ||||
|---|---|---|---|---|---|---|
| 实验值 | 仿真值 | 相对误 差/% | 实验值 | 仿真值 | 相对误 差/% | |
| EVA | 7870.9 | 7381.1 | 6.2 | 132.4 | 116.3 | 12.1 |
| EVA/SSG | 6015.5 | 6375.8 | 5.9 | 95.6 | 106.7 | 11.5 |
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