A Calculation Modelfor Penetration Depth of Tungsten Ball against Low-carbon Steel Considering Sphere Deformation

doi:10.12382/bgxb.2022.1013

Abstract

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

CLC Number:

TJ410.1

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.

Figures/Tables 21

Fig.1 Experimental layout

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

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

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

Fig.3 Simulated grid size division

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

Fig.5 Comparison of experimental and simulated results

Fig.6 Deformation process of tungsten ball

Fig.7 Tungsten ball contour overlay

Fig.8 Deformation of tungsten sphere

Fig.9 Mechanical model

Fig.10 Geometric relationship of approximate model of truncated sphere

Fig.11 Spherical deformation 3D model

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

Fig.13 Stress analysis of truncated sphere

Fig.14 Spherical catering penetration stage

Fig.15 Geometry of truncated sphere

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

Fig.16 Analysis on calculated results and error

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

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

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