长杆高速侵彻下装甲钢靶的等效强度

doi:10.12382/bgxb.2023.0619

摘要/Abstract

摘要：

装甲钢是复合装甲的主要组分之一,针对其抗长杆弹高速侵彻等效强度不明的问题,建立了三维SPH-FEM耦合模型。在验证模型可靠性的基础上,开展钨合金长杆弹在1000~1800m/s初速度范围内侵彻半无限300~600HBW装甲钢的仿真研究,基于侵彻阻力和Walker-Anderson(W-A)模型对高应变率-绝热工况下靶钢的等效强度进行探索。研究结果表明:侵彻过程分为初始瞬态、准定常和剩余侵彻3个阶段,W-A模型在大部分工况下可准确计算侵彻深度和准定常段头尾速度;准定常阶段杆体直径与靶体等效强度近似保持恒定,侵彻阻力可由Poncelet公式描述。基于以上分析建立装甲钢等效强度-硬度非线性换算模型,结合W-A模型能准确预测长杆弹对半无限靶的侵彻深度。此模型表明等效强度与硬度正相关,但热软化的增强与应变率强化的减弱使等效强度的增速逐渐放缓。

关键词: 长杆弹, 半流体侵彻, 半无限靶, 高硬度装甲钢, 光滑粒子流体动力学法

Abstract:

Armour grade steel is one of the main components of composite armour. A 3D SPH-FEM coupling model is developed to investigate the equivalent strength of armour grade steel against the penetration of long-rod projectile. On the basis of verifying the reliability of the model, a simulation study on tungsten alloy long-rod projectiles penetrating a semi-infinite 300-600HBW armour steel in the initial velocity range of 1000-1800m/s is carried out. The equivalent strength of armour steel under high strain rate-adiabatic conditions is explored based on the resistance force and Walker-Anderson model. The calculated results show that the penetration process of tungsten long-rod projectiles into semi-infinite steel targets can be divided into three stages: initial transient, quasi-steady and residual penetration. In most conditions, Walker-Anderson model can be used to accurately calculate the depth of penetration and head velocity of quasi-steady stage. the diameter of rod body and the equivalent strength of target are approximately constant in the quasi-steady stage, thus the penetration resistance can be described by the Poncelet formula. According to the above analysis, a nonlinear conversion model for the equivalent strength and hardness of armour steel is developed. Combined with Walker-Anderson model, it can accurately predict the depth of penetration of long-rod projectiles against semi-infinite targets. The model shows that equivalent strength is positively related to hardness, but its increase slows down due to the enhancement of thermal softening and the weakening of strain rate hardening.

Key words: long-rod projectile, semi-fluid penetration, semi-infinite target, high-hardness armour steel, smoothed particle hydrodynamics

中图分类号:

O347

王积锐, 王诚鑫, 王艺霓, 唐奎, 薄其乐. 长杆高速侵彻下装甲钢靶的等效强度[J]. 兵工学报, 2023, 44(12): 3755-3770.

WANG Jirui, WANG Chengxin, WANG Yini, TANG Kui, BO Qile. Equivalent Strength of Armour Steel against High-velocity Penetration of Long-rod Projectile[J]. Acta Armamentarii, 2023, 44(12): 3755-3770.

图/表 25

表1 弹靶Johnson-Cook模型参数

Table 1 Parameters of Johnson-Cookmodel of projectile and target

材料	A/MPa	B/MPa	n	C	m	D₁	D₂	D₃	D₄	D₅
钨合金^[20]	1275	624	0.12	0.016	0.94	2	1.77	-3.4	0	0
4340钢^[8]	719	456	0.093	0.008	1.03	-0.8	2.1	-0.5	0.002	0.61
Mars 190^[21]	1193	500	0.676	0.00435	1.17	0.21	7.2	-5.44	0	0
Armox 500^[22]	1470	702	0.199	0.00549	0.811	0.068	5.382	-2.554	0	0
Armox 600^[23]	1580	958	0.175	0.00877	0.712	-0.4	1.5	-0.5	0	0

表2 各材料状态方程参数

Table 2 Equation of state parameters of projectile and target

材料	ρ_i/ (kg·m^-3)	C₀/ (m·s^-1)	S₁	γ	a
钨合金^[20,25]	17700	4029	1.44	1.58	0.011
钢^[20,25]	7850	4578	1.33	1.93	0.47

图1 各材料实际应力-应变关系

Fig.1 True stress vs true strain of materials

图2 各硬度钢靶最大应力

Fig.2 Maximum stress and hardness of armour steels

表3 最大应力估算方法比较

Table 3 Comparison of strength estimation methods

H_t/ HBW	σ_JCmax/ MPa	σ_fit/ MPa	σ_m/ MPa	δ_fit/ %	δ_m/ %
300	1152	1139	1144	1.1	9.2
400	1450	1492	1370	2.9	5.5
500	1888	1845	1716	2.3	9.1
600	2182	2197	2180	0.7	0.1

图3 钨合金杆与半无限靶SPH-FEM模型

Fig.3 SPH-FEM model of tungsten rod and semi-infinite target

表4 网格尺寸对侵彻结果的影响

Table 4 Influence of mesh size on simulation results

粒子间距/mm	侵彻深度/mm	侵彻深度误差/%	背面变形量/mm	背面拉伸不稳定
0.80	34.3	14.3	3.9	无
0.61	36.8	8.0	4.7	无
0.47	39.9	0.25	6.1	弱
0.40	40.6	1.5	7.2	强
0.35	41.4	3.5	7.8	强

图4 网格尺寸对侵彻过程的影响

Fig.4 Influence of mesh size on penetration process

图5 不同网格尺寸弹靶Johnson-Cook损伤

Fig.5 Johnson-Cook damage of projectile and target with different mesh sizes

图6 1615m/s长杆弹侵彻300HBW靶J-C损伤

Fig.6 Johnson-Cook damage of 300HBW semi-infinite target penetrated by 1615m/s long rod projectile

图7 1000~1800m/s钨合金长杆弹侵彻300HBW靶仿真结果

Fig.7 Simulated results of 1000-1800m/s tungsten rod projectile penetrating 300HBW target

图8 头部速度-阻力关系

Fig.8 Relationship between head velocity and resistance force

图9 1600 m/s钨合金长杆弹侵彻300HBW靶头部变化过程

Fig.9 Head shape changing during penetration of tungsten long rod projectile into 300HBW target at 1600m/s

图10 1600m/s靶体Johnson-Cook损伤

Fig.10 Johnson-Cook damage of target at 1600m/s

图11 1000~1800m/s钨合金长杆弹侵彻300HBW靶体应力变化过程

Fig.11 Maximum effective stress of target during penetration of tungsten dart into 300HBW RHA at 1000-1800m/s

图12 1000~1800m/s钨合金长杆弹侵彻300HBW靶杆体最大应力变化过程

Fig.12 Maximum effective stress of tungsten long rod projectile during its penetration into 300HBW RHA at 1000-1800m/s

图13 400~600HBW靶体最大应力

Fig.13 Maximum effective stresses of 400~600HBW targets

表5 各硬度靶阻力拟合结果

Table 5 Fitting result of resistance force of armour steels

H_t/HBW	S_r	k_r	k_σ	σ_t/MPa
300	4.08	2.79	1.00	1152
400	4.16	2.48	0.89	1288
500	4.11	2.42	0.87	1637
600	4.07	2.30	0.82	1799

图14 400~600HBW阻力拟合结果

Fig.14 Resistance force fitting result of 300~600HBW

图15 侵彻300HBW靶仿真与W-A模型头尾速度

Fig.15 Head and tail velocities of simulation and W-A model of penetrating 300HBW target

表6 300HBW W-A模型计算与仿真结果比较

Table 6 Comparison of W-Amodel and simulated results of 300HBW target

v_i/ (m·s^-1)	中点头部速度/(m·s^-1)			侵彻深度/mm
v_i/ (m·s^-1)	仿真值	计算值	相对偏差/%	仿真值	计算值	相对偏差/%
1000	358	297	17.0	35.3	34.6	2.0
1200	497	463	6.8	57.9	59.7	3.1
1400	630	624	0.9	80.1	82.3	2.7
1600	776	776	0.1	101.0	101.0	0.5
1800	928	924	0.4	118.0	115.0	2.5

图16 300~600HBW强度仿真与W-A模型计算头部速度比较

Fig.16 Comparison of head velocities of simulation and W-A model of 300~600HBW target

图17 装甲钢等效强度拟合比较

Fig.17 Comparison of simulated and fitting results of equivalent strength of armor steel

图18 实验与计算侵彻效率比较

Fig.18 Comparison of experimental and calculated P/L

表7 等效强度计算方法比较

Table 7 Comparison of calculation methods of equivalent strength

H_t/HBW	σ_t/MPa
H_t/HBW	仿真值	Tate^[13]结果	Recht^[12]结果
300	1152	1260	1176
400	1288	1680	1568
500	1637	2100	1960
600	1799	2520	2352

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