The modified hydrodynamic theory of long rod penetration into semi-infinite targets was established independently by Alek-seevskii and Tate over forty years ago and since then many investigators contributed much to th...The modified hydrodynamic theory of long rod penetration into semi-infinite targets was established independently by Alek-seevskii and Tate over forty years ago and since then many investigators contributed much to the development of the high speed penetration mechanics.However,in all the models proposed so far,the target resistance Rt is not well defined and usually determined by adjusting it until the predicted depth of penetration comes to an agreement with experimental data.In this paper,assumptions are first made about particle velocity and pressure profiles together with response regions in the target and then an extension is made to the modified hydrodynamic theory of long rod penetration into semi-infinite targets,in which Rt has explicit form and is dependent on penetration velocity as well as thermo-mechanical properties of target material.The present model is compared with long rod penetration tests for different material combinations.It transpires that the present model predictions are in good agreement with the experimental data and numerical simulations in terms of penetration depth although many assumptions and simplifications are introduced into the paper.展开更多
A theoretical study is presented herein on the pen- etration of a semi-infinite target by a spherical-headed long rod for Yp 〉 S, where Yp is the penetrator strength and S is the static target resistance. For Yp 〉 S...A theoretical study is presented herein on the pen- etration of a semi-infinite target by a spherical-headed long rod for Yp 〉 S, where Yp is the penetrator strength and S is the static target resistance. For Yp 〉 S, depending upon initial impact velocity, there exist three types of penetration, namely, penetration by a rigid long rod, penetration by a deforming non-erosive long rod and penetration by an erosive long rod. If the impact velocity of the penetrator is higher than the hydrodynamic velocity （VH）, it will penetrate the target in an erosive mode; if the impact velocity lies between the hydrodynamic velocity （VH） and the rigid body velocity （VR）, it will penetrate the target in a deformable mode; if the impact velocity is less than the rigid body velocity （VR）, it will penetrate the target in a rigid mode. The critical conditions for the transition among these three penetration modes are proposed. It is demonstrated that the present model predictions correlate well with the experimental observations in terms of depth of penetration （DOP） and the critical transition conditions.展开更多
The relationship between the average penetration velocity,UˉUˉ,and the initial impact velocity, V0V0,in long-rod penetration has been studied recently. Experimental and simulation results all show the linear relatio...The relationship between the average penetration velocity,UˉUˉ,and the initial impact velocity, V0V0,in long-rod penetration has been studied recently. Experimental and simulation results all show the linear relationship between UˉUˉ and V0V0 over a wide range of V0V0 for different combinations of rod and target materials. However, the physical essence has not been fully revealed.In this paper, the Uˉ?V0Uˉ?V0relationship is profoundly analyzed using hydrodynamic model and Alekseevskii-Tate model. Especially, the explicitUˉ?V0Uˉ?V0 relationships are derived fromapproximate solutions of Alekseevskii-Tate model. Besides, the decelerationin long-rod penetration is discussed. The decelerationdegree is quantified by adeceleration index,α=2μˉ/(KΦJp)≈Ypρ?1/2p(ρ?1/2p+ρ?1/2t)V?20α=2μˉ/(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.展开更多
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, pe...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 theoretica solution deduced from primitive equations. It is very convenient in the theoretical prediction of the Alekseevskii–Tate model to apply these simple algebraic solutions. In particular, approximate solution 1 shows good agreement with the theoretical(exact) solution, and the first-order perturbation solution obtained by Walters et al.(Int. J. Impac Eng. 33:837–846, 2006) can be deemed as a special form of approximate solution 1 in high-speed penetration. Meanwhile, with constant tail velocity and penetration velocity approximate solution 2 has very simple expressions, which is 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. Approximate solution 1 is much closer to the theoretical solution of the Alekseevskii–Tate model than the first-order perturbation solution in both cases, whilst approximate solution 2 brings us a more intuitive understanding of quasi-steady-state penetration.展开更多
基金supported by the National Natural Science Foundation of China (Grant No.10872195)
文摘The modified hydrodynamic theory of long rod penetration into semi-infinite targets was established independently by Alek-seevskii and Tate over forty years ago and since then many investigators contributed much to the development of the high speed penetration mechanics.However,in all the models proposed so far,the target resistance Rt is not well defined and usually determined by adjusting it until the predicted depth of penetration comes to an agreement with experimental data.In this paper,assumptions are first made about particle velocity and pressure profiles together with response regions in the target and then an extension is made to the modified hydrodynamic theory of long rod penetration into semi-infinite targets,in which Rt has explicit form and is dependent on penetration velocity as well as thermo-mechanical properties of target material.The present model is compared with long rod penetration tests for different material combinations.It transpires that the present model predictions are in good agreement with the experimental data and numerical simulations in terms of penetration depth although many assumptions and simplifications are introduced into the paper.
基金supported by the National Natural Science Foundation of China (10872195)
文摘A theoretical study is presented herein on the pen- etration of a semi-infinite target by a spherical-headed long rod for Yp 〉 S, where Yp is the penetrator strength and S is the static target resistance. For Yp 〉 S, depending upon initial impact velocity, there exist three types of penetration, namely, penetration by a rigid long rod, penetration by a deforming non-erosive long rod and penetration by an erosive long rod. If the impact velocity of the penetrator is higher than the hydrodynamic velocity （VH）, it will penetrate the target in an erosive mode; if the impact velocity lies between the hydrodynamic velocity （VH） and the rigid body velocity （VR）, it will penetrate the target in a deformable mode; if the impact velocity is less than the rigid body velocity （VR）, it will penetrate the target in a rigid mode. The critical conditions for the transition among these three penetration modes are proposed. It is demonstrated that the present model predictions correlate well with the experimental observations in terms of depth of penetration （DOP） and the critical transition conditions.
基金The work was supported by the National Natural Science Foundation of China (Grant 11872118)The authors want to express deep gratitude to the reviewers for their sound comments and helpful suggestions.
文摘The relationship between the average penetration velocity,UˉUˉ,and the initial impact velocity, V0V0,in long-rod penetration has been studied recently. Experimental and simulation results all show the linear relationship between UˉUˉ and V0V0 over a wide range of V0V0 for different combinations of rod and target materials. However, the physical essence has not been fully revealed.In this paper, the Uˉ?V0Uˉ?V0relationship is profoundly analyzed using hydrodynamic model and Alekseevskii-Tate model. Especially, the explicitUˉ?V0Uˉ?V0 relationships are derived fromapproximate solutions of Alekseevskii-Tate model. Besides, the decelerationin long-rod penetration is discussed. The decelerationdegree is quantified by adeceleration index,α=2μˉ/(KΦJp)≈Ypρ?1/2p(ρ?1/2p+ρ?1/2t)V?20α=2μˉ/(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.
基金supported by the National Outstanding Young Scientist Foundation of China (Grant 11225213)the Key Subject "Computational Solid Mechanics" of China Academy of Engineering Physics
文摘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 theoretica solution deduced from primitive equations. It is very convenient in the theoretical prediction of the Alekseevskii–Tate model to apply these simple algebraic solutions. In particular, approximate solution 1 shows good agreement with the theoretical(exact) solution, and the first-order perturbation solution obtained by Walters et al.(Int. J. Impac Eng. 33:837–846, 2006) can be deemed as a special form of approximate solution 1 in high-speed penetration. Meanwhile, with constant tail velocity and penetration velocity approximate solution 2 has very simple expressions, which is 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. Approximate solution 1 is much closer to the theoretical solution of the Alekseevskii–Tate model than the first-order perturbation solution in both cases, whilst approximate solution 2 brings us a more intuitive understanding of quasi-steady-state penetration.
