陶瓷防弹板在多发打击下的损伤累积模拟与残余性能评估

何成龙; 霍子怡; 刘亚青; 杨可谞; 毛翔

doi:10.13801/j.cnki.fhclxb.20231121.002

陶瓷防弹板在多发打击下的损伤累积模拟与残余性能评估

doi: 10.13801/j.cnki.fhclxb.20231121.002

何成龙^{1, 2, ,},
霍子怡¹,
刘亚青²,
杨可谞¹,
毛翔¹

1.
中北大学机电工程学院，太原 030051
2.
中北大学纳米功能复合材料山西省重点实验室，太原 030051

基金项目: 中北大学纳米功能复合材料山西省重点实验室开放课题研究基金(NFCM202101)；山西省基础研究计划资助项目(20210302124197)；博士后科学基金(2021 M702981)

详细信息

通讯作者:
何成龙，博士，副教授，研究方向为冲击动力学　E-mail: hechenglong@nuc.edu.cn

中图分类号: TB332
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- 文章访问数: 240
- HTML全文浏览量: 146
- 被引次数: 0
出版历程
- 收稿日期: 2023-08-08
- 修回日期: 2023-10-26
- 录用日期: 2023-11-09
- 网络出版日期: 2023-11-22

Damage accumulation simulation and residual performance evaluation of ceramic ballistic plate under the multi-hit strikes

1.
College of Mechatronics Engineering, North University of China, Taiyuan 030051, China
2.
Shanxi Province Key Laboratory of Functional Nanocomposites, North University of China, Taiyuan 030051, China

Funds: Opening Project of Shanxi Province Key Laboratory of Functional Nanocomposites, North University of China (NFCM202101); Fundamental Research Program of Shanxi Province (20210302124197); China Postdoctoral Science Foundation (2021 M702981)

摘要

摘要: 陶瓷/纤维材料复合防弹板广泛应用于单兵防护装备，研究其抗多发冲击性能对于减少士兵伤亡有重要意义。基于53式7.62 mm穿燃弹冲击 SiC/超高分子量聚乙烯(UHMWPE)防弹板工况，利用数值模拟方法对多次冲击下防弹板的破坏分布和残余抗弹性能进行分析。利用陶瓷、纤维破坏及粘结面剥离程度表征整板损伤，并建立不同损伤区域下防弹板残余性能的分布规律。结果表明：第一次冲击下，防弹板损伤半径(R)为30 mm，当R<15 mm时，损伤(D)>0.6，靶板无法抵御第二发子弹冲击；两次冲击下，两发子弹间距(ΔL)<50 mm时，中间破坏区损伤有明显累加现象，当ΔL>50 mm时，损伤累加效应不显著。将防弹板以5 mm×5 mm网格离散，得到不同损伤面积占比，得出在两次冲击下整板穿透概率为0.94%。3次冲击下的整板穿透概率与第二次冲击位置有关，且当ΔL=20 mm时，3次冲击下整板穿透概率达到1.94%。
- 陶瓷/纤维防弹板 /
- 破坏特性 /
- 有限元分析 /
- 着弹点 /
- 抗多发弹
Abstract: The ceramic/fibre composite ballistic panels are widely used in personal protection equipment, and the performance of the ballistic plate under multiple impact loadings are important to keep soldiers safe. The numerical simulation was used to analyze the failure distribution and residual ballistic performance of ballistic panels subjected to multiple impacting, and specifically focusing on the operating condition of 53-type 7.62 mm armor-piercing bullet impacting SiC/ultra-high molecular weight polyethylene (UHMWPE) ballistic panels. The damage of the ballistic plate was characterized by the ceramic failure, fiber deformation and bond surface stripping, and the residual properties of the bulletproof plate with different damage were established. The results show that the damage radius (R) of ballistic panels is 30 mm under the first impact, and the damage (D) is greater than 0.6 when R<15 mm, and the target can't resist the second bullet impacting. Under two impacts, the damage in the middle zone becomes seriously when the distance between two bullets (ΔL) is less than 50 mm, and the cumulative effect of damage is not significant when ΔL>50 mm. Ballistic panels are discretized with 5 mm×5 mm grid, and the proportions of different damage areas are obtained. The penetration probability of the integral ballistic plate is 0.94% under the two impacts' loadings. The penetration probability of the integral ballistic plate under the third impacting is decided by the striking distance of the first two impacts, and the penetration probability by the third impacting is 1.94% when ΔL=20 mm.
- ceramic composite armor /
- failure characteristics /
- finite element analysis /
- impact point /
- multi-hit

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图 1 SiC/超高分子量聚乙烯(UHMWPE)板仿真模型示意图

Figure 1. Simulation model diagram of SiC/ultra-high molecular weight polyethylene (UHMWPE) plate

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图 2 几何间隔法示意图

Figure 2. Geometric interval method diagram

ΔH—Distance between the two bullets vertical to the plate; ΔL—Distance between the impact points of the two bullets

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图 3 SiC/UHMWPE板迎弹面破坏形态对比：(a) 实验结果；(b) 模拟结果

Figure 3. Comparison of damage patterns on the impact surface of SiC/UHMWPE: (a) Experimental results; (b) Simulation results

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图 4 SiC/UHMWPE板背面破坏形态对比：(a)实验结果；(b) 模拟结果

Figure 4. Comparison of damage forms on the back of SiC/UHMWPE: (a) Experimental results; (b) Simulation results

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图 5 单发冲击下SiC/UHMWPE板内应力传播及破坏分布

S—Stress

Figure 5. Stress propagation and damage distribution in SiC/UHMWPE plate under single bullet impact

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图 6 单发冲击SiC/UHMWPE板下相对破坏深度-子弹动能关系曲线

Figure 6. Relationship between kinetic energy of bullet and the broken depth under single bullet impact SiC/UHMWPE plate

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图 7 SiC/UHMWPE板内两发7.62 mm穿燃弹着弹点间距(ΔL)为35 mm的裂纹分布状况及应力场分布变化

Figure 7. Crack distribution and stress field distribution of two 7.62 mm armor-piercing projectile in SiC/UHMWPE plate impact point spacing (ΔL) is 35 mm

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图 8 侵彻SiC/UHMWPE板过程中破坏深度-子弹动能关系曲线

E_g—Energy gap

Figure 8. Damage depth-bullet kinetic energy relationship curves of SiC/UHMWPE plate penetrated

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图 9 侵彻SiC/UHMWPE板过程中破坏深度-动能差(E_g)曲线

Figure 9. Relationship between the gap of kinetic energy (E_g) and the broken depth of SiC/UHMWPE plate penetrated

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图 10 SiC/UHMWPE板内不同间距二次冲击下的破坏形态

Figure 10. Damage modes of SiC/UHMWPE plate under two impact with different spacing

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图 11 SiC/UHMWPE板材料破坏定义示意图

Figure 11. Definition of material damage of SiC/UHMWPE plate

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图 12 侵彻陶瓷板过程中动能-材料相对破碎深度关系

Figure 12. Relationship between kinetic energy of ceramic plate and layer and material relative crushing depth during penetration process

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图 13 侵彻UHMWPE过程中动能-材料相对破碎深度关系

Figure 13. Relationship between kinetic energy of UHMWPE and material relative crushing depth during penetration process

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图 14 SiC/UHMWPE板投影损伤程度分布图

Figure 14. Damage distribution map of SiC/UHMWPE plate projection

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图 15 第一发冲击下SiC/UHMWPE板损伤区域面积示意图

S_D—Total damage area; S_i—Area of the grid with damage degree of i; S₀—Total area of ceramic bulletproof plate

Figure 15. Diagram of damage area of SiC/UHMWPE plate under the first impact

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表 1 7.62 mm子弹材料参数^[14]

Table 1. Material constitutive parameters for type 7.62 mm bullet^[14]

Parameter	ρ/(g·cm⁻³)	G/GPa	A/GPa	B/GPa	n	C	$\dot \varepsilon _0/{ {\text{s} }^{ {{ - 1} } } }$	m
Steel	7.85	206	1900	1100	0.065	0.050	1.0	1.00
Copper	8.96	124	90	292	0.310	0.025	1.0	1.09
Parameter	t₀/K	t_m/K	D₁	D₂	D₃	D₄	D₅
Steel	300	1800	0.20	—	—	—	—
Copper	300	1356	0.54	4.89	–3.03	0.014	1.12
Notes: ρ—Density; G—Shear modulus; A—Yield stress constant; B—Strain hardening coefficient; n—Strain hardening exponent; C—Strain rate coefficient; ${\varepsilon }_{0}^{\dot{} }\text{ }$—Reference strain rate; m—Thermal softening exponent; t₀—Reference temperature; t_m—Melting temperature; D—Damage constant.

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表 2 UHMWPE纤维材料参数^[15]

Table 2. Material parameters of UHMWPE fiber laminates^[15]

Parameter	Value	Parameter	Value
E₁/GPa	153	X_c/MPa	2537
E₂=E₃/GPa	11.3	X_t/MPa	1580
ν₁₂=ν₁₃	0.3	Y_c/MPa	2537
ν₂₃	0.4	Y_t/MPa	1580
G₁₂/GPa	6	Z_c/MPa	340
G₁₃/GPa	6	Z_t/MPa	180
G₂₃/GPa	3.6
Notes：E₁, E₂, E₃—Elastic modulus in x, y and z directions, respectively; ν₁₂, ν₁₃, ν₂₃—Poisson's ratios; G₁₂, G₂₃, G₁₃—Shear modulus; X_c, X_t, Y_c, Y_t, Z_c, Z_t—Compressive and tensile strengths in x, y, z directions.

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表 3 SiC陶瓷材料参数^[12]

Table 3. SiC ceramic material parameters^[12]

Parameter	Value	Parameter	Value
ρ/(g·cm⁻³)	3.125	P_HEL/GPa	5.13
G/GPa	193	D₁	0.48
A	0.96	D₂	0.48
B	0.35	β	1.0
C	0.009	K₁/GPa	220
M	1.0	K₂/GPa	361
N	0.65	K₃/GPa	0
T/GPa	0.75
Notes：A—Intact strength coefficient; B—Fracture strength coefficient; M—Fracture strength exponent; N—Intact strength exponent; T—Maximum tensile pressure strength; P_HEL—Pressure at HEL; β—Bulking factor; K₁—Bulk modulus; K₂—Coefficient for 2nd degree term of Equation of State; K₃—Coefficient for 3nd degree term of Equation of State.

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表 4 Cohesive 单元材料参数^[20]

Table 4. Material parameters of Cohesive elements^[20]

Parameter	Numeric value
K/(MPa·mm⁻¹)	10⁶
$t_{{\mathrm{n}}}^{0} $/MPa	30
$t_{{\mathrm{s}}}^{0} $/MPa	80
$t_{{\mathrm{t}}}^{0} $/MPa	80
G_I/(kJ·mm⁻²)	0.31
G_II/(kJ·mm⁻²)	0.63
G_III/(kJ·mm⁻²)	0.63
Notes：K—Initial stiffness; $t_{{\mathrm{n}}}^{0} $, $t_{{\mathrm{s}}}^{0} $, $t_{{\mathrm{t}}}^{0} $—Corresponding normal and shear strengths; G_I, G_II and G_III—Critical energy release rates of model I, II and III.

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表 5 子弹冲击SiC/UHMWPE实验结果与数值模拟结果对比

Table 5. Comparison between experimental results of bullet impact SiC/UHMWPE with numerical simulation results

	Bullet velocity /(m·s^-1)	Depth of penetration/mm	Dorsal convex height/mm	Mean to diameter /mm
Citations	808	6.7	1.5	25.50
Numerical simulation	808	7.0	1.6	23.67

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表 6 第二发子弹穿透SiC/UHMWPE板概率

Table 6. Probability of the second bullet penetrate the SiC/UHMWPE plate

Penetration condition	Probability/%
P_s2	3.77
P_p2	25.00
P₀₂	0.94
Notes：P_s2—Probability that the second bullet will hit the damaged area; P_p2—Probability of a second bullet penetrating the damaged area; P₀₂—Probability of the second bullet penetrating.

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表 7 第三发子弹穿透SiC/UHMWPE板概率

Table 7. Probability of the third bullet penetrate the SiC/UHMWPE plate

Penetration condition		Probability/%
Penetration condition		P_s3	P_p3	P₀₃
ΔL/mm	15	5.92	26.07	1.54
	20	7.40	26.24	1.94
	35	7.42	25.53	1.89
	50	8.90	21.18	1.89
	80	9.20	20.49	1.89
Notes：P_s3—Probability of the third bullet hitting the damage area of the second bullet; P_p3—Probability of the third bullet penetrating the damage area of the second bullet; P₀₃—Probability of penetration of the third bullet.

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