考虑靶背自由表面和开裂影响的刚性尖头弹贯穿金属靶板模型

将靶体视为不可压缩材料，假定空腔膨胀产生塑性-弹性响应分区，构造了靶背自由表面效应的衰减函数。将衰减函数乘以可压缩幂次硬化材料的阻力方程，得到了弹体贯穿金属靶板的阻力函数。基于弹性衰减-塑性衰减-开裂3个阶段，建立了同时考虑靶体可压缩性、靶背自由表面和开裂影响的弹体贯穿有限厚金属靶板的分析模型，推导得出了弹体瞬时速度的解析方程，并采用数值方法计算得到了弹体的过载、瞬时速度和残余速度。通过与6组实验数据和已有模型的对比得到，当靶板厚度和弹体冲击速度在一定范围内时，需要考虑自由表面效应的影响。

A model for rigid sharp-nosed projectile perforating metallic targets considering free-surface and cracking effects

Treating the target as the incompressible material, by assuming that the cavity expansion produce plastic-elastic response region, the decay function for the back free-surface effect of target is constructed. The forcing function of metallic targets for perforation is obtained by multiplying the forcing function of compressible Strain-Harding targets with the decay function. Based on the three stage of elastic-decaying, plastic-decaying and cracking, the analytical model considering the compressibility, the back free-surface effect of target and cracking is established, and the analytical equation of instantaneous velocity of projectile is deduced. The deceleration, instantaneous and residual velocity of projectile is calculated by numerical methods. Through comparison with six sets of experimental data and other existing models, with the target thickness and impact velocity in a certain range, the free-effect should be considered.