长杆弹侵彻半无限靶的数值模拟和理论研究
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摘要
本论文对长杆弹侵彻半无限金属靶板的问题进行了较全面地数值模拟和理论研究。对不同弹靶组合产生的不同侵彻形态,均进行了数值模拟和分析,获得了清晰的侵彻图像、材料变形过程和一些物理量如压力、质点速度等的分布、变化。然后在对数值模拟结果分析的基础上分别建立了理论模型,并成功地以材料性能和初始打击参数来预测侵彻深度和开坑直径。本文的研究和结论对长杆弹动能武器、防护结构的设计和安全评估有重要的理论和实际指导意义,主要内容包括以下几个方面:
用ALE方法和Steinberg本构模型模拟了三类长杆弹侵彻问题。(Ⅰ)对消蚀的钨合金长杆弹侵彻装甲钢靶,得到不同打击速度下均与实验数据吻合的侵彻深度,成功地再现了实验观察到的四个侵彻阶段(瞬态高压段、准定常阶段、惯性扩展阶段和弹性回弹阶段),模拟结果表明弹靶界面附近的材料行为主要由静水压力控制。(Ⅱ)对刚体长杆弹侵彻铝合金靶,使用流固耦合的方法,得到的侵彻深度也与实验数据吻合,发现弹体的横向开坑可分为两阶段-弹体头部开坑和随后靶体材料的惯性运动。(Ⅲ)对变形非消蚀的钢长杆弹侵彻铝合金靶,模拟得到的侵彻深度与实验数据具有相同的变化趋势。撞击初期主要是弹头变粗,其后杆身变粗,变形期间弹尾速度下降较快,侵彻速度较稳定。
建立了长杆弹侵彻半无限靶的理论模型。弹靶组合可根据弹体强度Y_p与靶板静阻力S的关系分为两类:
(1)Y_p≤S。弹体只能以消蚀的状态侵彻靶板,并且直接从刚体状态转变为消蚀状态。基于数值模拟分析结果,靶板在高速侵彻下的响应区被划分为流动区、塑性区和弹性区,流动区内材料视为无粘流体,用修正Bernoulli方程描述,塑性区和弹性区的材料行为用空穴膨胀模型描述,从而建立了长杆弹侵彻的新一维模型并给出了界面失效速度(Interface Defeat Velocity)的表达式。模型的预测侵彻深度与实验数据非常吻合。
(2)Y_p＞S。根据打击速度的大小,长杆弹可能存在三种状态,即刚性弹、变形非消蚀弹和消蚀弹。针对这三种状态,确定了临界转化条件即刚体速度(V_R)和流体动力学速度(V_H)的确定方法。对刚体侵彻,由之前得到的弹靶界面压力与侵彻速度的关系容易得到弹体受到的阻力;对于变形非消蚀弹侵彻,根据Forrestal和Piekutowski的4340钢长杆弹侵彻半无限6061-T6511铝合金靶实验结果提出了开坑面积随打击速度变化的关系,利用质量和动量守恒定律以及靶板阻力随侵彻速度的变化规律建立了变形非消蚀状态的弹体的u～v关系(其中u、v分别为侵彻速度和弹尾速度),进而根据运动学关系求解了侵彻深度。结果表明:模型预测与实验结果较吻合,体现了相同的变化趋势。
建立了长杆弹侵彻半无限靶的横向开坑模型。对弹体的变形和材料流动引入假定,利用新的一维模型得到的u～v关系和质量、动量、能量三大守恒定律并结合实验观察分别给出了Y_p≤S和Y_p＞S的开坑直径计算公式,模型应用于不同弹靶材料,均得到与实验数据一致的预测结果。
研究了夹心长杆弹侵彻半无限靶问题。首先对不同外套-弹芯外径比的夹心长杆弹侵彻进行了数值模拟,模拟结果表明在r_(j0)/r_(c0)(外套外半径与弹芯半径之比)不太大的情形下,夹心长杆弹的u～v关系与去掉外套(或外套与弹芯材料相同)时的均质长杆弹差别很小,可直接用均质长杆弹的u～v关系代替。然后利用三大守恒定律和新的一维模型的u～v关系建立了夹心长杆弹开坑模型,并给出了产生co-erosion状态的临界条件(r_(j0)/r_(c0))_C的计算方法。理论模型较准确地预测了外套为EN24钢的钨合金夹心长杆弹侵彻装甲钢靶的开坑半径,并指出(r_(j0)/r_(c0))_C随打击速度增大而增大,可用减小r_(j0)/r_(c0)和增大打击速度来避免产生bi-erosion状态。
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.
用ALE方法和Steinberg本构模型模拟了三类长杆弹侵彻问题。(Ⅰ)对消蚀的钨合金长杆弹侵彻装甲钢靶,得到不同打击速度下均与实验数据吻合的侵彻深度,成功地再现了实验观察到的四个侵彻阶段(瞬态高压段、准定常阶段、惯性扩展阶段和弹性回弹阶段),模拟结果表明弹靶界面附近的材料行为主要由静水压力控制。(Ⅱ)对刚体长杆弹侵彻铝合金靶,使用流固耦合的方法,得到的侵彻深度也与实验数据吻合,发现弹体的横向开坑可分为两阶段-弹体头部开坑和随后靶体材料的惯性运动。(Ⅲ)对变形非消蚀的钢长杆弹侵彻铝合金靶,模拟得到的侵彻深度与实验数据具有相同的变化趋势。撞击初期主要是弹头变粗,其后杆身变粗,变形期间弹尾速度下降较快,侵彻速度较稳定。
建立了长杆弹侵彻半无限靶的理论模型。弹靶组合可根据弹体强度Y_p与靶板静阻力S的关系分为两类:
(1)Y_p≤S。弹体只能以消蚀的状态侵彻靶板,并且直接从刚体状态转变为消蚀状态。基于数值模拟分析结果,靶板在高速侵彻下的响应区被划分为流动区、塑性区和弹性区,流动区内材料视为无粘流体,用修正Bernoulli方程描述,塑性区和弹性区的材料行为用空穴膨胀模型描述,从而建立了长杆弹侵彻的新一维模型并给出了界面失效速度(Interface Defeat Velocity)的表达式。模型的预测侵彻深度与实验数据非常吻合。
(2)Y_p＞S。根据打击速度的大小,长杆弹可能存在三种状态,即刚性弹、变形非消蚀弹和消蚀弹。针对这三种状态,确定了临界转化条件即刚体速度(V_R)和流体动力学速度(V_H)的确定方法。对刚体侵彻,由之前得到的弹靶界面压力与侵彻速度的关系容易得到弹体受到的阻力;对于变形非消蚀弹侵彻,根据Forrestal和Piekutowski的4340钢长杆弹侵彻半无限6061-T6511铝合金靶实验结果提出了开坑面积随打击速度变化的关系,利用质量和动量守恒定律以及靶板阻力随侵彻速度的变化规律建立了变形非消蚀状态的弹体的u～v关系(其中u、v分别为侵彻速度和弹尾速度),进而根据运动学关系求解了侵彻深度。结果表明:模型预测与实验结果较吻合,体现了相同的变化趋势。
建立了长杆弹侵彻半无限靶的横向开坑模型。对弹体的变形和材料流动引入假定,利用新的一维模型得到的u～v关系和质量、动量、能量三大守恒定律并结合实验观察分别给出了Y_p≤S和Y_p＞S的开坑直径计算公式,模型应用于不同弹靶材料,均得到与实验数据一致的预测结果。
研究了夹心长杆弹侵彻半无限靶问题。首先对不同外套-弹芯外径比的夹心长杆弹侵彻进行了数值模拟,模拟结果表明在r_(j0)/r_(c0)(外套外半径与弹芯半径之比)不太大的情形下,夹心长杆弹的u～v关系与去掉外套(或外套与弹芯材料相同)时的均质长杆弹差别很小,可直接用均质长杆弹的u～v关系代替。然后利用三大守恒定律和新的一维模型的u～v关系建立了夹心长杆弹开坑模型,并给出了产生co-erosion状态的临界条件(r_(j0)/r_(c0))_C的计算方法。理论模型较准确地预测了外套为EN24钢的钨合金夹心长杆弹侵彻装甲钢靶的开坑半径,并指出(r_(j0)/r_(c0))_C随打击速度增大而增大,可用减小r_(j0)/r_(c0)和增大打击速度来避免产生bi-erosion状态。
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.
引文
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