侵彻半无限厚靶的理论模型与数值模拟研究
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摘要
本文针对侵彻半无限厚靶问题,将其划分成刚性弹侵彻、长杆弹高速侵彻、大范围着速的侵彻问题等方面,系统地开展了理论分析和数值模拟研究。内容涉及理论分析模型、数值模拟方法、侵彻性能的影响因素和参数敏感性分析等。本文的研究工作对于侵彻毁伤评估、动能武器研制和防护工程设计,都有重要的理论和实际指导意义。研究内容主要有以下几个方面：
(1)系统分析了刚性弹侵彻半无限厚靶的相关理论,包括空腔膨胀理论、速度势和速度场理论,以及主要的半经验、经验公式。分别针对金属材料和混凝土类材料,讨论了常用的侵彻深度计算公式的优缺点和适用性,分析了屈服强度对计算结果的影响,以及弹头形状对侵彻深度的影响。研究表明,弹头形状对侵彻深度有较大的影响。
(2)总结了长杆弹高速侵彻半无限厚靶的理论模型,将6个主要的模型统一写成A-T模型的形式,编制了计算程序,研究了靶板阻力项随侵彻速度和撞击速度的变化关系,讨论了各模型的差异。系统分析了弹靶材料的动态屈服强度、杆弹的长径比对侵彻性能的影响。研究表明,靶的动态屈服强度比长杆弹的动态屈服强度对侵彻深度的影响更明显。
(3)对于大范围着速的侵彻问题,首先,基于对刚性弹到侵蚀弹过渡区间侵彻行为的分析,构造了过渡区靶板阻力的唯象模型和侵彻深度的计算公式,确定了过渡区边界速度的求解方法。其次,在分析三个响应区特征的基础上,构建了三段组合式的理论分析模型,组合模型的预测侵深与试验数据符合较好。
(4)针对钨合金杆高速侵彻半无限厚铝合金靶问题,使用Lagrange方法,开展了数值模拟研究,分析了钨合金杆的材料参数(失效应变、屈服强度和剪切模量)的敏感性,以及弹头形状和长径比对侵深的影响。研究结果表明,失效应变是影响侵彻深度的主要参数,而屈服强度和剪切模量对侵深的影响很小;在较低的撞击速度下,头部形状对侵彻深度的影响较大,而在高着速的情况下,影响很小；以杆长无量纲化的侵彻深度随长径比的增大而降低,表明采用增大长径比提高长杆弹侵彻能力的方式将随着长径比的不断增大,侵彻效率逐渐降低。
另外,对大范围着速的钨杆侵彻铝靶问题,划分成中低速和高速两个区间,选用不同的本构关系,分别建立计算模型进行了数值模拟。在低着速(<600m/s)与高着速(800-2000m/s)情况下,计算结果和试验数据较好地符合,同时,过渡区侵彻深度突然大幅下降的现象也有所反映。
(5)讨论了钢筋混凝土靶的建模问题,分析了三种钢筋和混凝土耦合建模方法的优缺点,以及材料失效判据对计算结果的影响。通过数值模拟研究了含筋率和弹着点对钢筋混凝土靶抗侵彻性能的影响。研究表明,钢筋越粗或者钢筋编织越密,即含筋率越高,钢筋混凝土靶板的抗侵彻能力越强,尤其对于动能弹直径大于靶板中钢筋间距的情况；同时,弹着点对动能弹侵彻能力有较大的影响。
针对均匀规则的靶网结构,构造了任意着靶位置的剩余速度或侵彻深度的预估公式。利用这个公式,只需得到三个典型位置动能弹穿靶后的剩余速度或侵彻深度,就可以有效地求解任意着靶位置的剩余速度或侵彻深度。
(6)对于动能弹侵彻多介质组合靶问题,通过数值模拟得到侵彻轨迹、弹体速度、减加速度以及侵彻深度的变化曲线,着重分析了入射倾角和攻角对侵彻毁伤的影响规律。对大倾角斜侵彻问题有了新的认识,弹体在侵彻过程中可能发生反向偏转,深入分析后得到,弹道偏转是由于弹体周围靶板的损伤程度不同引起。
In this paper, the problem of penetrating into semi-infinite thick target is divided into rigid projectiles penetration, high-speed long rods penetration, and penetration problems that impact speed changes in large range. Theoretical analysis and numerical simulations are carried out systematically to study these problems. The study involves theoretical analysis models, numerical simulation methods, and the factors affecting the performance of the penetration and parameter sensitivity analysis, etc. This research has important theoretical and practical significance for penetration damage assessment, kinetic energy weapon development and protection engineering design. The research focus mainly in the following areas:
(1) The theory of rigid projectile penetration of semi-infinite thick target was systematically analyzed, including the cavity expansion theory, the theory of velocity potential and velocity field, and the major semi-empirical and empirical formula. Respectively for metal materials and concrete materials, the common formulae for penetration depth calculation were comparatively analyzed, the advantages and disadvantages and the applicability of each formula were discussed. The effect of the yield strength on calculated results, and the effect of nose shape on the penetration depth were also analyzed. Studies have shown that the nose shape of rigid projectile has a great influence on the penetration depth.
(2) The theoretical model of high-speed long rods penetrating into semi-infinite thick target was summarized. Six major models were unified in the form of the A-T model, and the calculation procedures were compiled. The relations between target resistance item and penetration speed, between target resistance item and impact speed were analyzed, and the differences of each model were discussed. The effects of dynamic yield strength of the rods and target material, the ratio of length to diameter of the projectile on penetration performance were analyzed. Studies have shown that the dynamic yield strength of the target has a greater influence on the penetration depth than the dynamic yield strength of the rods.
(3) For penetration problems that impact speed changes in large range, based on the analysis of penetration behavior in rigid to erosion transition interval, phenomenological model of target resistance and formula of penetration depth calculation in the transition area were constructed, and the solving method for transition interval boundary were determined. After a detailed analysis of the three response region characteristics, three sections combined theoretical analysis model was built. Predictions of the penetration depth by combined model are in good agreement with the experimental data.
(4) Numerical simulations were carried out, using Lagrange method, to study the problem of tungsten alloy rods penetrating into semi-infinite aluminum alloy target with high velocity. This paper analyzes the sensitivity of tungsten alloy rod material parameters (failure strain, yield strength and shear modulus), as well as the effect of the nose shape and the ratio of length to diameter of the rod on penetration depth. The results show that the failure strain is the main parameter affecting the penetration depth, while the yield strength and the shear modulus are insensitive; in low impact velocity, the nose shape of the rod has a great influence on penetration depth, while in high impact velocity, the effect is negligible; the dimensionless penetration depth reduces with increasing the ratio of length to diameter. In addition, penetration problem that impact speed changes in large range, is divided into low-speed section and high-speed section, with different constitutive relationship, respective simulation is carried out.. In the low-speed (<600m/s) and high-speed (800-2000m/s) case, the calculated results agree well with experimental data, what's more, the phenomenon that penetration depth in the transition area declines suddenly is also reflected.
(5) After the modeling issue of reinforced concrete target was discussed, the advantages and disadvantages of three rebar and concrete coupling models, the influence of material failure criteria on the calculation results, as well as effects of reinforcement ratio and impact position on anti-penetration properties of reinforced concrete were analyzed by numerical simulations. Research shows that, increasing reinforcement ratio can enhance the anti-penetration property of reinforced concrete, especially in the case, where the diameter of projectile exceeds the distance of rebar. In addition, the influence of impact position is obvious. For concrete target with uniform-distributed rebars, estimate formula of the residual velocity or penetration depth in random impact position was built. Using this formula, just need to get the residual velocities or penetration depths of three typical position, then the residual velocity or penetration depth in random impact position can be solved effectively.
(6) For the problem of kinetic energy projectile penetrating into multi-media combination target, through the simulations, the penetration tracks, the history curves of velocity, acceleration and penetration depth were obtained. The influence laws of the incident angle and the attack angle on penetration damage were analyzed. For oblique penetration problem at a large incident angle, a new understanding is obtained that the projectile may occur reverse deflection, and after the deep analysis it is found that ballistic deflection is caused by different degree of damage of the target around the projectile.
(1)系统分析了刚性弹侵彻半无限厚靶的相关理论,包括空腔膨胀理论、速度势和速度场理论,以及主要的半经验、经验公式。分别针对金属材料和混凝土类材料,讨论了常用的侵彻深度计算公式的优缺点和适用性,分析了屈服强度对计算结果的影响,以及弹头形状对侵彻深度的影响。研究表明,弹头形状对侵彻深度有较大的影响。
(2)总结了长杆弹高速侵彻半无限厚靶的理论模型,将6个主要的模型统一写成A-T模型的形式,编制了计算程序,研究了靶板阻力项随侵彻速度和撞击速度的变化关系,讨论了各模型的差异。系统分析了弹靶材料的动态屈服强度、杆弹的长径比对侵彻性能的影响。研究表明,靶的动态屈服强度比长杆弹的动态屈服强度对侵彻深度的影响更明显。
(3)对于大范围着速的侵彻问题,首先,基于对刚性弹到侵蚀弹过渡区间侵彻行为的分析,构造了过渡区靶板阻力的唯象模型和侵彻深度的计算公式,确定了过渡区边界速度的求解方法。其次,在分析三个响应区特征的基础上,构建了三段组合式的理论分析模型,组合模型的预测侵深与试验数据符合较好。
(4)针对钨合金杆高速侵彻半无限厚铝合金靶问题,使用Lagrange方法,开展了数值模拟研究,分析了钨合金杆的材料参数(失效应变、屈服强度和剪切模量)的敏感性,以及弹头形状和长径比对侵深的影响。研究结果表明,失效应变是影响侵彻深度的主要参数,而屈服强度和剪切模量对侵深的影响很小;在较低的撞击速度下,头部形状对侵彻深度的影响较大,而在高着速的情况下,影响很小；以杆长无量纲化的侵彻深度随长径比的增大而降低,表明采用增大长径比提高长杆弹侵彻能力的方式将随着长径比的不断增大,侵彻效率逐渐降低。
另外,对大范围着速的钨杆侵彻铝靶问题,划分成中低速和高速两个区间,选用不同的本构关系,分别建立计算模型进行了数值模拟。在低着速(<600m/s)与高着速(800-2000m/s)情况下,计算结果和试验数据较好地符合,同时,过渡区侵彻深度突然大幅下降的现象也有所反映。
(5)讨论了钢筋混凝土靶的建模问题,分析了三种钢筋和混凝土耦合建模方法的优缺点,以及材料失效判据对计算结果的影响。通过数值模拟研究了含筋率和弹着点对钢筋混凝土靶抗侵彻性能的影响。研究表明,钢筋越粗或者钢筋编织越密,即含筋率越高,钢筋混凝土靶板的抗侵彻能力越强,尤其对于动能弹直径大于靶板中钢筋间距的情况；同时,弹着点对动能弹侵彻能力有较大的影响。
针对均匀规则的靶网结构,构造了任意着靶位置的剩余速度或侵彻深度的预估公式。利用这个公式,只需得到三个典型位置动能弹穿靶后的剩余速度或侵彻深度,就可以有效地求解任意着靶位置的剩余速度或侵彻深度。
(6)对于动能弹侵彻多介质组合靶问题,通过数值模拟得到侵彻轨迹、弹体速度、减加速度以及侵彻深度的变化曲线,着重分析了入射倾角和攻角对侵彻毁伤的影响规律。对大倾角斜侵彻问题有了新的认识,弹体在侵彻过程中可能发生反向偏转,深入分析后得到,弹道偏转是由于弹体周围靶板的损伤程度不同引起。
In this paper, the problem of penetrating into semi-infinite thick target is divided into rigid projectiles penetration, high-speed long rods penetration, and penetration problems that impact speed changes in large range. Theoretical analysis and numerical simulations are carried out systematically to study these problems. The study involves theoretical analysis models, numerical simulation methods, and the factors affecting the performance of the penetration and parameter sensitivity analysis, etc. This research has important theoretical and practical significance for penetration damage assessment, kinetic energy weapon development and protection engineering design. The research focus mainly in the following areas:
(1) The theory of rigid projectile penetration of semi-infinite thick target was systematically analyzed, including the cavity expansion theory, the theory of velocity potential and velocity field, and the major semi-empirical and empirical formula. Respectively for metal materials and concrete materials, the common formulae for penetration depth calculation were comparatively analyzed, the advantages and disadvantages and the applicability of each formula were discussed. The effect of the yield strength on calculated results, and the effect of nose shape on the penetration depth were also analyzed. Studies have shown that the nose shape of rigid projectile has a great influence on the penetration depth.
(2) The theoretical model of high-speed long rods penetrating into semi-infinite thick target was summarized. Six major models were unified in the form of the A-T model, and the calculation procedures were compiled. The relations between target resistance item and penetration speed, between target resistance item and impact speed were analyzed, and the differences of each model were discussed. The effects of dynamic yield strength of the rods and target material, the ratio of length to diameter of the projectile on penetration performance were analyzed. Studies have shown that the dynamic yield strength of the target has a greater influence on the penetration depth than the dynamic yield strength of the rods.
(3) For penetration problems that impact speed changes in large range, based on the analysis of penetration behavior in rigid to erosion transition interval, phenomenological model of target resistance and formula of penetration depth calculation in the transition area were constructed, and the solving method for transition interval boundary were determined. After a detailed analysis of the three response region characteristics, three sections combined theoretical analysis model was built. Predictions of the penetration depth by combined model are in good agreement with the experimental data.
(4) Numerical simulations were carried out, using Lagrange method, to study the problem of tungsten alloy rods penetrating into semi-infinite aluminum alloy target with high velocity. This paper analyzes the sensitivity of tungsten alloy rod material parameters (failure strain, yield strength and shear modulus), as well as the effect of the nose shape and the ratio of length to diameter of the rod on penetration depth. The results show that the failure strain is the main parameter affecting the penetration depth, while the yield strength and the shear modulus are insensitive; in low impact velocity, the nose shape of the rod has a great influence on penetration depth, while in high impact velocity, the effect is negligible; the dimensionless penetration depth reduces with increasing the ratio of length to diameter. In addition, penetration problem that impact speed changes in large range, is divided into low-speed section and high-speed section, with different constitutive relationship, respective simulation is carried out.. In the low-speed (<600m/s) and high-speed (800-2000m/s) case, the calculated results agree well with experimental data, what's more, the phenomenon that penetration depth in the transition area declines suddenly is also reflected.
(5) After the modeling issue of reinforced concrete target was discussed, the advantages and disadvantages of three rebar and concrete coupling models, the influence of material failure criteria on the calculation results, as well as effects of reinforcement ratio and impact position on anti-penetration properties of reinforced concrete were analyzed by numerical simulations. Research shows that, increasing reinforcement ratio can enhance the anti-penetration property of reinforced concrete, especially in the case, where the diameter of projectile exceeds the distance of rebar. In addition, the influence of impact position is obvious. For concrete target with uniform-distributed rebars, estimate formula of the residual velocity or penetration depth in random impact position was built. Using this formula, just need to get the residual velocities or penetration depths of three typical position, then the residual velocity or penetration depth in random impact position can be solved effectively.
(6) For the problem of kinetic energy projectile penetrating into multi-media combination target, through the simulations, the penetration tracks, the history curves of velocity, acceleration and penetration depth were obtained. The influence laws of the incident angle and the attack angle on penetration damage were analyzed. For oblique penetration problem at a large incident angle, a new understanding is obtained that the projectile may occur reverse deflection, and after the deep analysis it is found that ballistic deflection is caused by different degree of damage of the target around the projectile.
引文
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