A calculation of penetration resistance during cratering for ogive-nose projectile into concrete
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摘要: 为了研究弹体开坑过程中，弹头表面应力的表达形式，采用高速摄影仪记录弹体在开坑区的位移和时间关系，得到卵形弹体在开坑区的速度和侵深关系。采用最小二乘法对开坑区结束时消耗的弹体动能和侵深关系进行分析，提出开坑过程中弹头表面的应力形式。计算结果表明，该应力形式能较好地描述高速条件下开坑区的侵深和速度关系。Abstract: Penetration experiments were conducted to explore an expression formula for the stress endured by the nose of the projectile during cratering.To obtain the relation between penetration velocity and penetration depth, the relation between penetration depth and time was recorded by using a high-speed camera.And the least square method was used to analyze the relation of the kinetic energy consumed by the projectile with the penetration depth at the end of cratering.Thereby, an expression formula was proposed for the stress endured by the nose of the projectile during cratering.The calculation results display that the proposed stress formula can describe the relation between the penetration velocity and the crater depth under high-velocity impact.
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图 4 最小二乘法对弹体开坑过程中耗能的拟合分析
Figure 4. Fitted curves of kinetic energy decrease during cratering
图 5 OP2型弹开坑区侵彻速度和侵深的关系
Figure 5. Relation between penetration velocity and penetration depth during cratering
图 6 OP5型弹开坑区速度和侵深的关系
Figure 6. Relation between penetration velocity and penetration depth during cratering
表 1 开坑区在侵彻过程中的数据
Table 1. Experimental data of crater region during penetration process
zc/m v/(m·s-1) zc/m v/(m·s-1) OP2(Ⅰ) OP2(Ⅱ) OP2(Ⅲ) OP2(Ⅰ) OP2(Ⅱ) OP2(Ⅲ) OP5(Ⅰ) OP5(Ⅱ) OP5(Ⅲ) OP5(Ⅰ) OP5(Ⅱ) OP5(Ⅲ) 0 0 0 431.2 607.6 431.2 0 0 0 419.3 608.3 780.0 0.020 0.026 0.020 427.2 599.2 427.2 0.018 0.032 0.016 416.2 601.3 779.9 0.040 0.061 0.040 418.6 583.2 418.6 0.041 0.064 0.034 412.9 581.2 771.1 0.060 0.094 0.060 410.7 568.5 410.7 0.065 0.094 0.052 406.0 569.5 749.5 0.078 0.124 0.078 397.1 550.0 397.1 0.087 0.124 0.070 398.0 560.6 734.7 0.097 0.097 383.0 383.0 0.109 0.153 0.087 385.3 537.3 720.9 0.115 0.115 378.1 378.1 0.130 0.104 972.0 707.0 0.132 0.132 363.6 363.6 0.151 0.120 354.6 692.9 0.136 678.5 0.152 663.8 
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表 2 最小二乘法拟合用的数据
Table 2. Parameters for least square fitting
OP2 OP5 zc/m vs/(m·s-1) vc/(m·s-1) ΔEi/kJ zc/m vs/(m·s-1) v/(m·s-1)c ΔEi/kJ 0.132 431.2 363.6 37.610 0.151 419.3 354.6 35.050 0.124 607.6 550.0 46.674 0.153 608.3 537.3 56.936 0.126 767.7 661.5 106.247 0.152 780.0 663.8 117.439
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