Energy dissipation analysis of elliptical truncated oval rigid projectilepenetrating stiffened plate
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摘要: 为获得椭圆截面截卵形刚性弹体正贯穿加筋板的剩余速度，根据椭圆截面弹体贯穿靶板的破坏特征，认为贯穿过程中靶板的能量耗散方式主要为塞块剪切变形功与塞块动能、扩孔塑性变形功、花瓣动力功、花瓣弯曲变形功、靶板整体凹陷变形功、加强筋侧向凹陷变形功。推导了每种能量计算方法，计算中定量考虑了靶板扩孔、花瓣弯曲、凹陷变形的应变率效应。根据能量守恒关系，得到了椭圆截面弹体剩余速度和弹道极限速度预测公式。并通过实验结果对模型进行了验证。结果表明：考虑靶板应变硬化、应变率效应的贯穿模型可以准确预测弹体剩余速度；随着椭圆截面弹体长短轴之比的增大，靶板的弹道极限速度近似线性增大；长短轴之比小于3时，加筋板的主要耗能为花瓣弯曲变形能、整体凹陷变形能。Abstract: In order to obtain the residual velocity of elliptical section truncated oval rigid projectile penetrating stiffened plate, according to the failure characteristics of elliptical section projectile penetrating target plate, it is considered that the main energy dissipation modes of target plate during penetration are plug shear deformation work and kinetic energy, hole expanding plastic deformation work, petal dynamic work and bending deformation work, dishing deformation work and lateral dishing deformation of the stiffened plate. Each energy calculation method is deduced theoretically, and the strain rate effects of target hole enlargement, petal bending and sag deformation are quantitatively considered in the calculation. According to the energy conservation relationship, the prediction formulas of residual velocity and ballistic limit velocity of elliptical cross-section projectiles are obtained, and the model is validated by experimental results. The results show that the penetration model considering the strain hardening and strain rate effect of the target plate can accurately predict the residual velocity of the projectile. With the increase of the ratio of the long axis to the short axis of the elliptical cross-section projectile body, the ballistic limit velocity of the target plate increases approximately linearly. When the ratio of the long axis to the short axis is less than 3, the main energy dissipation of the stiffened plate is the petal bending deformation energy and dishing deformation energy.
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图 2 椭圆截面弹体撞击单加筋板示意图
Figure 2. Schematic diagram of single stiffened plate impactedby elliptic section projectile
图 4 靶板椭圆形扩孔变形示意图
Figure 4. Deformation diagram of elliptical hole enlargementof target plate
图 6 椭圆形扩孔动力功计算原理图
Figure 6. Schematic diagram of dynamical workduring elliptical hole enlargement
图 7 面板椭圆形整体凹陷变形计算原理图
Figure 7. Schematic diagram of elliptical dishing energy calculation
图 9 无量纲弹道极限速度随
${k_{{{ab}}}}$ 变化Figure 9. Dimensionless ballistic limit velocity vs
${k_{{{ab}}}}$ 
图 10 椭圆截面与“截面积等效”弹体各耗散能量比随
${k_{{{ab}}}}$ 的变化Figure 10. Variation of energy dissipation ratio of elliptical sectionand "section equivalent" projectiles with
${k_{{{ab}}}}$ 
图 11 平板和加筋板各能量耗散比随
${k_{{{ab}}}}$ 的变化Figure 11. Energy dissipation ratio of flat and stiffened plates vs
${k_{{{ab}}}}$ 表 1 截卵形弹体几何参数
Table 1. Geometry parameters oftruncated oval-nose projectiles
b1/mm b0/mm M/g L/mm CRH 12.5 4 165.3 27.5 1.42 
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表 2 加筋板结构和力学参数
Table 2. Geometry and mechanical parameters of stiffened plate
hp/mm hs/mm bs/mm ρ/(g·cm−3) σ0/MPa σy/MPa σu/MPa εf D P 5，10 25 5 7.85 410～420 510 585～610 0.2 1.14 ×104 5.8
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表 3 贯穿实验剩余速度与模型预测结果对比
Table 3. Comparison between the theoretical and experimental residual velocities
实验 板型 m n ${v_0}/({\rm{m}} \cdot {{\rm{s}}^{ - 1}})$ ${v_{\rm{f}}}/({\rm{m}} \cdot {{\rm{s}}^{ - 1}})$ $\Delta r/{\rm{mm}}$ ${w_0}/{\rm{mm}}$ ${v_{\rm{f}}}/({\rm{m}} \cdot {{\rm{s}}^{ - 1}})$ η/% ${v_{\rm{f}}}/({\rm{m}} \cdot {{\rm{s}}^{ - 1}})$ η/% 实验参数 刚塑性模型 本文模型 1 F 0 0 244 133 − 15 180.5 35.71 135.2 1.65 5 SI 0 0.5 247 156 12.5 10 191.3 22.63 151.8 2.69 10 SI* 1 0 388 144 − 5 252.3 75.21 140.8 2.22 13 CS 1 1 427 240 12.5 20 323.7 34.87 258.2 7.85 15 CS 1 1 417 157 12.5 18 311.8 98.60 243.5 55.10 16 QS 0 0 247 128 − 16 184.0 43.75 139.9 9.30
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