The effects of compressibility and strength on penetration of long rod and jet

The approximate compressible model is adopted to study the effects of strength and compressibility on the penetration by WHA long rod and copper jet into semi-infinite target in detail. For WHA rod penetrating PMMA at 2 km/s <V <5 km/s, the compressibility has a significant effect on the penetration efficiency. We clarify how compressibility affects the penetration efficiency by changing the stagnation pressures of the rod and target. For WHA rod penetrating 4340 Steel and 6061-T6 Al at 2 km/s < V < 10 km/s, the effect of strength is strong and the effect of compressibility is negligible at lower impact velocity, whilst the effect of strength is weak and the effect of compressibility becomes stronger at higher impact velocity. For the copper jet penetrating 4030 Steel, 6061-T6 Al and PMMA. the virtual origin model is adopted, and the compressibility and strength are implicitly considered by the linear relation between the penetration velocity and impact velocity. The effects of compressibility and target resistance on penetration efficiency are studied. The results show that the target resistance has a significant effect on the penetration efficiency. Howver PMMA is much more compressible than copper and the huge difference of compressibility has a significant effect on the penetration by hypervelocity copper jet into PMMA.

Effect of compressibility on the hypervelocity penetration

We further consider the effect of rod strength by employing the compressible penetration model to study the effect of compressibility on hypervelocity penetration.Meanwhile, we define different instances of penetration efficiency in various modified models and compare these penetration efficiencies to identify the effects of different factors in the compressible model. To systematically discuss the effect of compressibility in different metallic rod-target combinations, we construct three cases, i.e., the penetrations by the more compressible rod into the less compressible target, rod into the analogously compressible target, and the less compressible rod into the more compressible target. The effects of volumetric strain, internal energy, and strength on the penetration efficiency are analyzed simultaneously. It indicates that the compressibility of the rod and target increases the pressure at the rod/target interface. The more compressible rod/target has larger volumetric strain and higher internal energy. Both the larger volumetric strain and higher strength enhance the penetration or anti-penetration ability. On the other hand, the higher internal energy weakens the penetration or anti-penetration ability. The two trends conflict, but the volumetric strain dominates in the variation of the penetration efficiency, which would not approach the hydrodynamic limit if the rod and target are not analogously compressible. However, if the compressibility of the rod and target is analogous, it has little effect on the penetration efficiency.

A simplified approximate model of compressible hypervelocity penetration

A simplified approximate model considering rod/target material's compressibility is proposed for hypervelocity penetration.We study the effect of shockwaves on hypervelocity penetration whenever the compressibility of the rod is much larger,analogously,and much less than that of the target,respectively.The results show that the effect of shockwaves is insignificant up to 12 km/s,so the shockwave is neglected in the present approximate model.The Murnaghan equation of state is adopted to simulate the material behaviors in penetration and its validity is proved.The approximate model is finally reduced to an equation depending only on the penetration velocity and a simple approximate solution is achieved.The solution of the approximate model is in agreement with the result of the complete compressible model.In addition,the effect of shockwaves on hypervelocity penetration is shown to weaken material's compressibility and reduce the interface pressure of the rod/target,and thus the striking/protective performance of the rod/target is weakened,respectively.We also conduct an error analysis of the interface pressure and penetration efficiency.With a velocity change of 1.6 times the initial sound speed for the rod or target,the error of the approximate model is very small.For metallic rod-target combinations,the approximate model is applicable even at an impact velocity of 12 km/s.