A Combined Numerical And Theoretical Study Of Long Rod Penetration Into Semi-Infinite Targets

A combined numerical and theoretical study is presented in this thesis on the penetration of long rod penetrators into semi-infinite metallic targets. For different penetration configurations according to different combinations of penetrators and targets, numerical simulations and analysis are performed to obtain transient penetration images, deforming process of materials and distribution of physical parameters such as pressure, particle velocity, etc. Based on the insights into the penetration process from numerical simulation, corresponding theoretical models are established to predict the depth of penetration (DOP) and the diameter of the crater. The findings and conclusions of the investigations conducted in the thesis is helpful for the design of long rod kinetic energy weapons, protective structures and safety assessment, which mainly consists of following parts:Three types of long rod penetration are numerically simulated using ALE method and Steinberg constitutive model. (Ⅰ) For the penetration of eroding tungsten alloy long rod penetrators into semi-infinite armor steel targets, it is found that numerical predictions are in good agreement with available experimental observations in terms of DOP and four different penetration phases (i.e. transient phase, quasi-steady phase, phase three, and recovery phase). It is also found that the behavior of materials near the penetrator-target interface is controlled mainly by hydrostatic pressure. (Ⅱ) For the penetration of rigid rod penetrators into semi-infinite aluminum alloy targets, the solid-fluid coupling method is employed in numerical simulations. It is shown that numerically predicted DOP is in good agreement with the experimental data and that the cratering process includes two phases: first, the cratering by the penetrator head and followed by the inertia expansion of the target material. (Ⅲ) For the penetration of deforming 4340 steel long rod penetrators into semi-infinite aluminum alloy targets, it transpires that the numerical predictions are in reasonable agreement with the experimental observations. It also transpires that the head of the penetrator becomes bigger only in initial phase and followed by the subsequent thickening of the shank during which the velocity of the penetrator tail decreases rapidly whilst penetration velocity remains relatively steady.Theoretical models are suggested of long rod penetration into semi-infinite targets. It depends on the relative strength of the long rod penetrator (Y_p) and the target (S), There are two cases, viz. Y_p≤S and Y_p > S, which need to be dealt with separately: (1) Case 1: Y_p≤S. The penetrator can penetrate the target only in the eroding state with the transition from rigid to fluid being ignored. Based on the insights into the penetration process from the numerical simulations, the response regions in the target are constructed as flow region, plastic region, and elastic region; the material in the flow regions is treated as non-viscous incompressible fluids and described using the modified Bernoulli's equation whilst the cavity expansion model is employed for the material in the plastic and elastic regions. Hence, a new 1D model is proposed for long rod penetration, together with the expression for Interface Defeat Velocity. It is found that the theoretical predictions are in good agreement with experimental observations in terms of DOP.(2) Case 2: Y_p > S. There exist three types of penetration, namely, penetration by rigid long rods, penetration by deforming non-erosive long rods and penetration by erosive long rods. The critical conditions for the transition between these three penetration modes, i.e. rigid body velocity (V_r) and hydrodynamic velocity (V_H) are determined. For a rigid penetrator, the resistance force acting on the penetrator can be easily derived from the known relationship between pressure and penetration velocity at the penetrator-target interface; for a deforming non-erosive penetrator, based on the experiments performed by Forrestal and Piekutowski on 4340 steel long rod penetration into semi-infinite 6061-T6511 aluminum alloy targets, an empirical relation between crater area and impact velocity is suggested and then the u～v curve is obtained by using the laws of conservation of mass and momentum, together with the relationship between target resistance and u, where u and v are penetration velocity and the velocity of the penetrator tail, respectively. It is demonstrated that the present model predictions are in reasonable agreement with the experimental results and that both the models and the experiments follow the same trend as impact velocity increases.Models for the diameter of crater in semi-infinite targets by long rod penetrators are suggested based on the assumptions made about the deformation and the flow of the material of the penetrator, the u～v relation of the new 1D model, the laws of conservation of mass, momentum, and energy and the experimental observations. It is evident that the model predictions are in good agreement with available experimental data obtained for the combinations of penetrator and target made of different materials.Jacketed long rod penetration into semi-infinite targets is examined. Numerical simulations on the penetration of semi-infinite targets by jacketed long rods with different r_j0/r_c0 are first performed, where r_j0 and r_c0 are the radii of the jacket and the core, respectively. The numerical results show that for smaller r_j0/r_c0 ratio the u～v relation changes only a little compared to that of unitary long rod penetrator of the same core material, hence, the u～v relation of unitary (homogenous) long rod penetration is also applicable for jacketed long rod penetration. Model for cratering in semi-infinite targets by jacketed long rods is then suggested by using the laws of conversation of mass, momentum and energy, together with the u v relation of unitary (homogenous) long rod penetration. The critical condition (r_j0/r_c0)_C for co-erosion is also suggested. The present model is compared with the experimental data for EN24 steel jacketed tungsten alloy long rod penetration into semi-infinite armor steel targets and good agreement is obtained.