This study employs a data-driven methodology that embeds the principle of dimensional invariance into an artificial neural network to automatically identify dominant dimensionless quantities in the penetration of rod ...This study employs a data-driven methodology that embeds the principle of dimensional invariance into an artificial neural network to automatically identify dominant dimensionless quantities in the penetration of rod projectiles into semi-infinite metal targets from experimental measurements.The derived mathematical expressions of dimensionless quantities are simplified by the examination of the exponent matrix and coupling relationships between feature variables.As a physics-based dimension reduction methodology,this way reduces high-dimensional parameter spaces to descriptions involving only a few physically interpretable dimensionless quantities in penetrating cases.Then the relative importance of various dimensionless feature variables on the penetration efficiencies for four impacting conditions is evaluated through feature selection engineering.The results indicate that the selected critical dimensionless feature variables by this synergistic method,without referring to the complex theoretical equations and aiding in the detailed knowledge of penetration mechanics,are in accordance with those reported in the reference.Lastly,the determined dimensionless quantities can be efficiently applied to conduct semi-empirical analysis for the specific penetrating case,and the reliability of regression functions is validated.展开更多
In this study, a combined experimental, numerical and theoretical investigation is conducted on the penetration of semi-infinite 4340 steel targets by a homogeneous 93 W rod and two types of jacketed rods with strikin...In this study, a combined experimental, numerical and theoretical investigation is conducted on the penetration of semi-infinite 4340 steel targets by a homogeneous 93 W rod and two types of jacketed rods with striking velocities of 0.9-3.3 km/s. The results show that the jacketed rods produced typical“co-erosion” damage at all test velocities, except for the 93 W/1060 Al jacketed rod, which switched from an early “bi-erosion” damage to later “co-erosion” damage at a striking velocity of 936 m/s. However, the homogeneous 93 W rod always forms a large mushroom head during the penetration process. The damage mechanisms of these two types of jacketed rods differ for striking velocities of 0.9-2.0 km/s, but this difference gradually decreases with increased striking velocity. For velocities of 2.0-3.3 km/s, all three types of projectiles exhibit typical hydrodynamic penetration characteristics, and the damage mechanisms of the two types of jacketed rods are almost identical. For the same initial kinetic energy, the penetration performance of the jacketed rods is distinctly superior to that of the homogeneous 93 W rods.Compared with jacket density, jacket strength shows a more significant influence on the damage mechanism and penetration performance of the jacketed rod. Finally, an existing theoretical prediction model of the penetration depth of jacketed rods on semi-infinite targets in the co-erosion mode is modified. It transpires that-in terms of penetration depth-the modified theoretical model is in good agreement with the experimental and numerical observations for 93 W/TC4 and 93 W/1060 Al jacketed rods penetrating semi-infinite 4340 steel targets.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 effect of small variations of target hardness on the depth of penetration for nominally identical target material has not been addressed systematically in publications yet and is often neglected. An investigation ...The effect of small variations of target hardness on the depth of penetration for nominally identical target material has not been addressed systematically in publications yet and is often neglected. An investigation of this issue for laboratory-scale long rod projectiles penetrating into semi-infinite rolled-homogeneous-armor steel targets was conducted. The tungsten-heavy-alloy penetrators were of length 90 mm and diameter6 mm. Five lots of armor steel with a nominal hardness range of 280–330 BHN provided material for the targets. The pursued approach consisted of hardness testing of the targets, in total 17 ballistic experiments at velocities in between 1250 m/s and 1780 m/s and data analysis.A linear regression analysis of penetration vs. hardness shows that a target hardness increase within the given range of 280–330 BHN may result in a reduction of penetration depth of about 5.8 mm at constant velocity. This is equal to a change of-12% at an impact velocity of 1250 m/s. A multiple linear regression analysis included also the influence of yaw angle and impact velocity. It shows that small yaw angles and slight variations of impact velocities provide a smaller variation of the semi-infinite penetration depths than a variation of target hardness within a typical specification span of 50 BHN. For such a span a change in penetration of approximately-4.8 mm due to hardness variation is found, whereas 1°of yaw angle or-10 m/s of velocity variation gives a change of about-1.0 mm respectively-0.9 mm. For the given example, the overwhelming part of the variation is to be attributed to hardness effects – 4.8 mm out of 5.8 mm(83%). For nominally identical target material the target hardness thus influences the ballistic test results more severely than the typical scatter in impact conditions.展开更多
Analytical model is presented herein to predict the diameter of crater in semi-infinite metallic targets struck by a long rod penetrator. Based on the observation that two mechanisms such as mushrooming and cavitation...Analytical model is presented herein to predict the diameter of crater in semi-infinite metallic targets struck by a long rod penetrator. Based on the observation that two mechanisms such as mushrooming and cavitation are involved in cavity expansion by a long rod penetrator, the model is constructed by using the laws of conservation of mass, momentum, energy, together with the u-v relationship of the newly suggested 1D theory of long rod penetration (see Lan and Wen, Sci China Tech Sci, 2010, 53(5): 1364–1373). It is demonstrated that the model predictions are in good agreement with available experimental data and numerical simulations obtained for the combinations of penetrator and target made of different materials.展开更多
Analytical equations are presented herein to predict the penetration of semi-infinite metallic targets struck normally by long rods at high velocities for Yp<S where Yp is the rod strength and S is the static targe...Analytical equations are presented herein to predict the penetration of semi-infinite metallic targets struck normally by long rods at high velocities for Yp<S where Yp is the rod strength and S is the static target resistance.The equations are derived based on energy balance method.It is assumed that the kinetic energy loss of a long rod is related to the energy dissipated by the plastic deformations in the target,the energy consumed by the long-rod penetrator itself and the energy carried by the eroded rod debris.Secondary penetration is also examined in the present paper due to the fact that the eroded rod debris forms a tube which can penetrate the target further if the density of the rod is greater than that of the target and the impact velocity is high enough.The present analytical equation is found to be in good agreement with the experimental data for a wide range of impact velocities.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12272257,12102292,12032006)the special fund for Science and Technology Innovation Teams of Shanxi Province(Nos.202204051002006).
文摘This study employs a data-driven methodology that embeds the principle of dimensional invariance into an artificial neural network to automatically identify dominant dimensionless quantities in the penetration of rod projectiles into semi-infinite metal targets from experimental measurements.The derived mathematical expressions of dimensionless quantities are simplified by the examination of the exponent matrix and coupling relationships between feature variables.As a physics-based dimension reduction methodology,this way reduces high-dimensional parameter spaces to descriptions involving only a few physically interpretable dimensionless quantities in penetrating cases.Then the relative importance of various dimensionless feature variables on the penetration efficiencies for four impacting conditions is evaluated through feature selection engineering.The results indicate that the selected critical dimensionless feature variables by this synergistic method,without referring to the complex theoretical equations and aiding in the detailed knowledge of penetration mechanics,are in accordance with those reported in the reference.Lastly,the determined dimensionless quantities can be efficiently applied to conduct semi-empirical analysis for the specific penetrating case,and the reliability of regression functions is validated.
基金supported by the National Natural Science Foundation of China(Grant nos.:11672138,11602113)Foundation of National Key Lab.of Transient Physics(Grant no.:6142604180407,JCKYS2020606004).
文摘In this study, a combined experimental, numerical and theoretical investigation is conducted on the penetration of semi-infinite 4340 steel targets by a homogeneous 93 W rod and two types of jacketed rods with striking velocities of 0.9-3.3 km/s. The results show that the jacketed rods produced typical“co-erosion” damage at all test velocities, except for the 93 W/1060 Al jacketed rod, which switched from an early “bi-erosion” damage to later “co-erosion” damage at a striking velocity of 936 m/s. However, the homogeneous 93 W rod always forms a large mushroom head during the penetration process. The damage mechanisms of these two types of jacketed rods differ for striking velocities of 0.9-2.0 km/s, but this difference gradually decreases with increased striking velocity. For velocities of 2.0-3.3 km/s, all three types of projectiles exhibit typical hydrodynamic penetration characteristics, and the damage mechanisms of the two types of jacketed rods are almost identical. For the same initial kinetic energy, the penetration performance of the jacketed rods is distinctly superior to that of the homogeneous 93 W rods.Compared with jacket density, jacket strength shows a more significant influence on the damage mechanism and penetration performance of the jacketed rod. Finally, an existing theoretical prediction model of the penetration depth of jacketed rods on semi-infinite targets in the co-erosion mode is modified. It transpires that-in terms of penetration depth-the modified theoretical model is in good agreement with the experimental and numerical observations for 93 W/TC4 and 93 W/1060 Al jacketed rods penetrating semi-infinite 4340 steel targets.
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supported financially by the Bundesministerium der Verteidigung (BMVg)the Bundesamt für Ausrüstung, Informationstechnik und Nutzung der Bundeswehr (BAAINBw)
文摘The effect of small variations of target hardness on the depth of penetration for nominally identical target material has not been addressed systematically in publications yet and is often neglected. An investigation of this issue for laboratory-scale long rod projectiles penetrating into semi-infinite rolled-homogeneous-armor steel targets was conducted. The tungsten-heavy-alloy penetrators were of length 90 mm and diameter6 mm. Five lots of armor steel with a nominal hardness range of 280–330 BHN provided material for the targets. The pursued approach consisted of hardness testing of the targets, in total 17 ballistic experiments at velocities in between 1250 m/s and 1780 m/s and data analysis.A linear regression analysis of penetration vs. hardness shows that a target hardness increase within the given range of 280–330 BHN may result in a reduction of penetration depth of about 5.8 mm at constant velocity. This is equal to a change of-12% at an impact velocity of 1250 m/s. A multiple linear regression analysis included also the influence of yaw angle and impact velocity. It shows that small yaw angles and slight variations of impact velocities provide a smaller variation of the semi-infinite penetration depths than a variation of target hardness within a typical specification span of 50 BHN. For such a span a change in penetration of approximately-4.8 mm due to hardness variation is found, whereas 1°of yaw angle or-10 m/s of velocity variation gives a change of about-1.0 mm respectively-0.9 mm. For the given example, the overwhelming part of the variation is to be attributed to hardness effects – 4.8 mm out of 5.8 mm(83%). For nominally identical target material the target hardness thus influences the ballistic test results more severely than the typical scatter in impact conditions.
基金supported by the National Natural Science Foundation of China (Grant No. 10872195)
文摘Analytical model is presented herein to predict the diameter of crater in semi-infinite metallic targets struck by a long rod penetrator. Based on the observation that two mechanisms such as mushrooming and cavitation are involved in cavity expansion by a long rod penetrator, the model is constructed by using the laws of conservation of mass, momentum, energy, together with the u-v relationship of the newly suggested 1D theory of long rod penetration (see Lan and Wen, Sci China Tech Sci, 2010, 53(5): 1364–1373). It is demonstrated that the model predictions are in good agreement with available experimental data and numerical simulations obtained for the combinations of penetrator and target made of different materials.
基金supported by the National Natural Science Foundation of China(Grant No.11172298)
文摘Analytical equations are presented herein to predict the penetration of semi-infinite metallic targets struck normally by long rods at high velocities for Yp<S where Yp is the rod strength and S is the static target resistance.The equations are derived based on energy balance method.It is assumed that the kinetic energy loss of a long rod is related to the energy dissipated by the plastic deformations in the target,the energy consumed by the long-rod penetrator itself and the energy carried by the eroded rod debris.Secondary penetration is also examined in the present paper due to the fact that the eroded rod debris forms a tube which can penetrate the target further if the density of the rod is greater than that of the target and the impact velocity is high enough.The present analytical equation is found to be in good agreement with the experimental data for a wide range of impact velocities.
