一种考虑球体变形的钨球侵彻低碳钢深度计算模型

doi:10.12382/bgxb.2022.1013

摘要/Abstract

摘要：

为了研究钨球在高速撞击下的变形行为对侵彻效果的影响,对钨球侵彻半无限低碳钢靶进行试验研究,得到<1600m/s冲击速度下钨球变形特征和靶板侵彻深度随冲击速度的变化规律。在此基础上构建钨球侵彻塑性变形模型。将钨球变形模型和球形空腔膨胀阻力模型相结合,建立钨球变形侵彻深度计算模型。对比不同撞击速度下钨球变形侵彻模型、刚性侵彻模型的计算结果。对比结果表明,变形侵彻模型能够更加准确地计算钨球对半无限靶的侵彻深度,计算结果与试验相比最大误差20%(正误差15%,负误差5%),精度较刚性侵彻模型提升42.86%。

关键词: 钨球, 低碳钢, 塑性变形, 侵彻深度, 球形空腔膨胀

Abstract:

In order to study the influence of deformation behavior of tungsten ball on penetration effect under high-speed impact, the penetrationof tungsten ball into a semi-infinite low-carbon steel target is experimentally studied, and the deformation characteristics of tungsten ball and the change rule of penetration depth versus impact velocity of target plate at 1600m/s are obtained through experiment. On this basis, a plastic deformation model of tungsten ball is constructed.A calculation model of tungsten ball deformation penetration depth is established by combining the projectile deformation model with the spherical cavity expansion resistance model. The calculated results of the tungsten ball deformable penetration model and the rigid penetration model at different impact velocities are compared.The results show that the deformable penetration model can be used to more accurately calculate the penetration depth of tungsten ball into the semi-infinite target. The maximum error between the calculated results and test results is 20% (the positive error is 15% and the negative error is 5%), and the calculation accuracy of the deformable penetration model is 42.8% higher than that of the rigid penetration model.

Key words: tungsten ball, low-carbon steel, plastic deformation, depth of penetration, spherical cavity expansion

中图分类号:

TJ410.1

刘铁磊, 王晓锋, 徐豫新, 李永鹏, 张健. 一种考虑球体变形的钨球侵彻低碳钢深度计算模型[J]. 兵工学报, 2024, 45(5): 1625-1636.

LIU Tielei, WANG Xiaofeng, XU Yuxin, LI Yongpeng, ZHANG Jian. A Calculation Modelfor Penetration Depth of Tungsten Ball against Low-carbon Steel Considering Sphere Deformation[J]. Acta Armamentarii, 2024, 45(5): 1625-1636.

图/表 21

图1 试验布置

Fig.1 Experimental layout

图2 回收试验弹靶变形特征(上为靶板侵彻弹坑,下为回收弹丸)

Fig.2 Deformation characteristics of recovered projectile and target (upper: penetrated craters on target plate, and below: recovered projectiles)

表1 8mm直径93W钨球侵彻靶板后形状特征参数

Table 1 Shape characteristic parameters of 8mm-diameter 93W sphere after penetrating target plate

序号	剩余质量/ g	径向最大半径/ mm	轴向剩余长度/ mm	侵彻深度/ mm	靶板弹孔直径/ mm	冲击速度/ (m·s^-1)
(a)	4.76	8.08	7.7	3.85	7.7	377.09
(b)	4.75	8.13	7.65	4.65	8.47	457.63
(c)	4.74	8.32	7.3	6.83	8.5	605.04
(d)	4.74	8.41	7.01	6.69	8.42	637.92
(e)	4.71	8.72	6.61	7.54	8.77	727.76
(f)	4.7	8.77	6.53	8.05	8.93	732.7
(g)	4.73	8.92	6.3	8.41	9.13	791.21
(h)	4.74	9.23	5.98	8.41	9.43	817.56
(i)	-	-	-	9.14	9.54	892.56
(j)	-	-	-	9.11	10.06	980.04
(k)	-	-	-	8.75	10.06	988.61
(l)	-	-	-	9.3	11.81	1074.63
(m)	4.62	11.44	4.2	11.13	12.32	1220.34
(n)	4.63	11.56	4.18	12.11	12.74	1244.24
(o)	4.62	11.7	3.96	11.6	13.15	1291.87
(p)	4.55	11.65	4.41	12.06	13.11	1343.28
(q)	4.59	11.71	4.83	13.27	14.23	1441.92
(r)	4.52	11.69	4.59	13.78	14.28	1489.66

表2 弹靶材料本构参数

Table 2 Constitutive parameters of projectile and target materials

材料	ρ/(g·cm^-3)	E/GPa	G/GPa	υ	A/GPa
93W	17.6	350	160	0.284	1.506
Q235	7.80	210	86.1	0.22	0.235
材料	B/GPa	n	c	m	T_m/K
93W	1.506	0.12	0.016	1.00	1732
Q235	0.750	0.25	0.015	1.3	1520
材料	T_r/K	D₁	D₂	D₃
93W	294	3	0	0
Q235	294	2.2	0	0

图3 仿真网格尺寸划分

Fig.3 Simulated grid size division

图4 钨球侵彻后形状特征的试验和仿真对比(上为仿真结果,下为试验回收弹丸)

Fig.4 Comparison of shape characteristics of experimental and simulated tungsten balls(upper: simulated result; below: recovered projectile)

图5 仿真结果和试验结果对比

Fig.5 Comparison of experimental and simulated results

图6 钨球变形过程

Fig.6 Deformation process of tungsten ball

图7 钨球轮廓叠加图

Fig.7 Tungsten ball contour overlay

图8 钨球变形

Fig.8 Deformation of tungsten sphere

图9 力学模型

Fig.9 Mechanical model

图10 截球近似模型几何关系

Fig.10 Geometric relationship of approximate model of truncated sphere

图11 球体变形三维模型

Fig.11 Spherical deformation 3D model

图12 侵彻终点时刻钨球形状

Fig.12 Shape of tungsten sphere at the end of penetration

图13 截球受力分析

Fig.13 Stress analysis of truncated sphere

图14 球体开坑侵彻阶段

Fig.14 Spherical catering penetration stage

图15 截球体几何关系

Fig.15 Geometry of truncated sphere

表3 初始参数

Table 3 Initial parameters

r₀/m	ρ_p/(kg·m^-3)	ρ_t/(kg·m^-3)	E_t/Pa	Y_t/Pa
0.004	17500	7830	2.1×10¹¹	2.35×10⁸
n	ξ	μ	v₀/(m·s^-1)	Δt/s
0.12	0.1	0.1	377~1487	1×10^-8

图16 计算结果和计算误差分析

Fig.16 Analysis on calculated results and error

图17 不同ξ取值下的加速度、速度、侵彻深度、球体变形半径时变规律

Fig.17 Time-varying rule of acceleration, velocity, penetration depth and sphere deformation radius under different ξ values

图18 不同h2取值下的加速度、速度、侵彻深度、球体变形半径时变规律

Fig.18 Time-varying rule of acceleration, velocity, penetration depth and sphere deformation radius under different h2 values

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