Theoretical Model And Numerical Study On Penetrating Into Semi-Infinite Targets

In this paper, the problem of penetrating into semi-infinite thick target is divided into rigid projectiles penetration, high-speed long rods penetration, and penetration problems that impact speed changes in large range. Theoretical analysis and numerical simulations are carried out systematically to study these problems. The study involves theoretical analysis models, numerical simulation methods, and the factors affecting the performance of the penetration and parameter sensitivity analysis, etc. This research has important theoretical and practical significance for penetration damage assessment, kinetic energy weapon development and protection engineering design. The research focus mainly in the following areas:(1) The theory of rigid projectile penetration of semi-infinite thick target was systematically analyzed, including the cavity expansion theory, the theory of velocity potential and velocity field, and the major semi-empirical and empirical formula. Respectively for metal materials and concrete materials, the common formulae for penetration depth calculation were comparatively analyzed, the advantages and disadvantages and the applicability of each formula were discussed. The effect of the yield strength on calculated results, and the effect of nose shape on the penetration depth were also analyzed. Studies have shown that the nose shape of rigid projectile has a great influence on the penetration depth.(2) The theoretical model of high-speed long rods penetrating into semi-infinite thick target was summarized. Six major models were unified in the form of the A-T model, and the calculation procedures were compiled. The relations between target resistance item and penetration speed, between target resistance item and impact speed were analyzed, and the differences of each model were discussed. The effects of dynamic yield strength of the rods and target material, the ratio of length to diameter of the projectile on penetration performance were analyzed. Studies have shown that the dynamic yield strength of the target has a greater influence on the penetration depth than the dynamic yield strength of the rods.(3) For penetration problems that impact speed changes in large range, based on the analysis of penetration behavior in rigid to erosion transition interval, phenomenological model of target resistance and formula of penetration depth calculation in the transition area were constructed, and the solving method for transition interval boundary were determined. After a detailed analysis of the three response region characteristics, three sections combined theoretical analysis model was built. Predictions of the penetration depth by combined model are in good agreement with the experimental data.(4) Numerical simulations were carried out, using Lagrange method, to study the problem of tungsten alloy rods penetrating into semi-infinite aluminum alloy target with high velocity. This paper analyzes the sensitivity of tungsten alloy rod material parameters (failure strain, yield strength and shear modulus), as well as the effect of the nose shape and the ratio of length to diameter of the rod on penetration depth. The results show that the failure strain is the main parameter affecting the penetration depth, while the yield strength and the shear modulus are insensitive; in low impact velocity, the nose shape of the rod has a great influence on penetration depth, while in high impact velocity, the effect is negligible; the dimensionless penetration depth reduces with increasing the ratio of length to diameter. In addition, penetration problem that impact speed changes in large range, is divided into low-speed section and high-speed section, with different constitutive relationship, respective simulation is carried out.. In the low-speed (<600m/s) and high-speed (800-2000m/s) case, the calculated results agree well with experimental data, what’s more, the phenomenon that penetration depth in the transition area declines suddenly is also reflected.(5) After the modeling issue of reinforced concrete target was discussed, the advantages and disadvantages of three rebar and concrete coupling models, the influence of material failure criteria on the calculation results, as well as effects of reinforcement ratio and impact position on anti-penetration properties of reinforced concrete were analyzed by numerical simulations. Research shows that, increasing reinforcement ratio can enhance the anti-penetration property of reinforced concrete, especially in the case, where the diameter of projectile exceeds the distance of rebar. In addition, the influence of impact position is obvious. For concrete target with uniform-distributed rebars, estimate formula of the residual velocity or penetration depth in random impact position was built. Using this formula, just need to get the residual velocities or penetration depths of three typical position, then the residual velocity or penetration depth in random impact position can be solved effectively.(6) For the problem of kinetic energy projectile penetrating into multi-media combination target, through the simulations, the penetration tracks, the history curves of velocity, acceleration and penetration depth were obtained. The influence laws of the incident angle and the attack angle on penetration damage were analyzed. For oblique penetration problem at a large incident angle, a new understanding is obtained that the projectile may occur reverse deflection, and after the deep analysis it is found that ballistic deflection is caused by different degree of damage of the target around the projectile.