1D And 2D Theory Of Long-Rod Hypervelocity Penetration

Made by high-density metals,long-rod penetrators have excellent performances on penetration and perforation when launched at hypervelocities around 1.5-3.0 km/s.Different from rigid penetrators,under high velocities,long-rod penetrators and targets erode dramatically during the penetration process.Due to the specificity of penetration mechanics and the military application,long-rod penetration at hypervelocity has become an active research focus.In the present paper,research advances up-to-date on long-rod penetration at hypervelocity are comprehensively reviewed firslty.Basic consepts,research methods and theoretical models are introduced.Highlighted issues which are focused in past studies and their applications,including rod and target materials,nose shape,L/D effect and segmented rods,ceramic targets and interface defeat,as well as non-ideal long-rod penetration,etc.Some future research proposals are also suggested.The Alekseevskii-Tate model is the most successful semi-hydrodynamic model applied to long-rod penetration into semi-infinite targets.However,due to the nonlinear nature of the equations,the rod(tail)velocity,penetration velocity,rod length and penetration depth were obtained implicitly as a function of time and solved numerically.By employing a linear approximation to the logarithmic relative rod length,we obtain two sets of explicit approximate algebraic solutions based on the implicit theoretical solution deduced from primitive equations.It will be very convenient in the theoretical prediction of Alekseevskii-Tate model by applying these simple algebraic solutions.In particular,the approximate solution 1 shows good agreement with the theoretical(exact)solution,and the first-order perturbation solution obtained by Walters et al.(2006)can be deemed as a special form of the approximate solution 1 in high-speed penetration.Meanwhile,with constant tail velocity and penetration velocity,the approximate solution 2 has very simple expressions,which will be applicable for the qualitative analysis of long-rod penetration.Differences among these two approximate solutions and the theoretical(exact)solution,and their respective scopes of application,have been discussed and the inferences with clear physical basis have been drawn.In addition,these two solutions and the first-order perturbation solution are applied to two cases with different initial impact velocity and different penetrator/target combinations to compare with the theoretical(exact)solution.The approximate solution 1 is much more close to the theoretical solution of Alekseevskii-Tate model than the first-order perturbation solution in both cases,whilst the approximate solution 2 brings us a more intuitive understanding of quasi-steady-state penetration.The relationship between the average penetration velocity,U,and the initial impact velocity,V0,in long-rod penetration has been studied recently.Experiment and simulation results all show the linear relationship between U and V0 over a wide range of V0 for different combinations of rod and target materials.However,the physical essence has not been fully revealed.In chapter 4,the U-V0 relationship is profoundly analyzed using hydrodynamic model and Alekseevskii-Tate model.Especially,the explicit U-V0 relationships are derived from approximate solutions of Alekseevskii-Tate model.Besides,the deceleration in long-rod penetration is discussed.The deceleration degree is quantified by a deceleration index,α=2μ/KΦJp≈Ypρp-1/2(ρp-1/2+ρt-1/2)V0-2.which is mostly related to the impact velocity,rod strength and rod/target densities.Thus,the state of penetration process can be identified and designed in experiments.Self-sharpenning has been observed in experiments and simulations of long-rod penetration.Different nose shapes may occur in the penetration of long rods made by different materials,which will have an effect on the penetration performances.This nose shape effect can not be considered and analyzed using present 1D model,thus 2D model needs to be established.By constructing the function of nose shapes,the resistance of rod nose is determined,and the 2D model of long-rod penetration is established in chapter 5.The ratio of nose and rod diameters η and the nose shape factor N*are two main parameters which can represent nose shape during the penetration process in the 2D model.The influences of η and N*on long-rod penetration and their mechanics are analyzed in case study.Base on the 2D model established in chapter 5,combining with the experimental and simulation results,the 2D effect of long-rod penetration is analyzed in chapter 6.According to the analysis of the experimental and simulation results of penetration into metallic targets,the basic assumption of the 2D model,the nose shape of long rods keeps invariant druing the primary pase,is verified,and the 2D model can briefly reflect the 2D effect shown in experiments and simulations.In adition,the special phenomenon of variation of nose shape is found in the simulation of long rods in ceramic targets,which is verified by a conducted experiment.As for the influence factors of the 2D effect,the influences of shear sensitivity of rod materials,strength of target materials and initial impact velocities are relatively siginificant while the influence of initial nose shape is relatively less.