刚性尖头弹侵彻圆柱形金属厚靶分析模型

考虑金属厚靶侧面自由边界的影响,研究了刚性尖头弹侵彻有限平面尺寸金属厚靶问题。基于有限柱形空腔膨胀理论和线性硬化材料模型,得到了空腔壁径向压力的解析式,建立了刚性尖头弹侵彻有限直径圆柱形金属厚靶工程模型。与试验和数值模拟比较表明,该文工程模型计算精度很好。基于所建立的工程模型,研究了靶板半径对侵彻深度和侵彻阻力的影响,结果表明:当靶板与弹丸半径比值小于20时,靶板半径对侵彻阻力和侵彻深度有显著影响,不能按无限尺寸靶板计算;当靶板与弹丸半径比值大于20时,靶板半径对侵彻阻力和侵彻深度影响较小,可近似按无限尺寸靶计算。     

基于Hoek-Brown准则的混凝土-岩石类靶侵彻模型

基于空腔膨胀理论建立工程模型是研究侵彻问题的常用方法。针对射弹侵彻岩石-混凝土类脆性材料半无限靶问题,基于靶体的弹性-裂纹-粉碎响应模式,粉碎区采用考虑围压的Hoek-Brown准则,得到了准静态球形空腔膨胀的空腔壁压力。在Forrestal两个阶段侵彻模型中,用所得空腔壁压力代替隧道侵彻阶段的侵彻阻力,得到刚性弹侵彻岩石-混凝土类脆性材料半无限靶的侵彻深度预估公式,与文献侵彻试验以及现有典型侵彻深度预估公式比较表明,预估公式适用范围更广,对于(超)高强混凝土和岩石材料靶的预测精度更高。     

高速长杆弹对有限直径金属厚靶的侵彻分析EI北大核心CSCD

采用基于统一强度理论的有限柱形空腔膨胀理论,结合Tate磨蚀杆模型,考虑中间主应力、靶体侧面自由边界的影响及高速(1500 m/s~2200 m/s)侵彻弹体的变形和消蚀现象,推导线性硬化有限直径金属厚靶在长杆弹高速侵彻时的空腔壁径向应力,建立侵彻阻力和侵彻深度计算模型,并利用MATLAB软件编程求解,分析包括强度准则差异在内的弹道终点效应的一系列影响因素。结果表明:该文计算方法可以更好地描述弹靶的动态响应,还可以得到一系列基于不同强度准则的侵彻阻力和深度的解析解、对不同靶弹半径比的靶材侵彻深度的区间范围进行有效预测;强度参数、弹体撞击速度和靶体半径对有限直径金属靶体的抗侵彻性能均有较大的影响,其中强度参数值由1减小为0时,侵彻阻力可减小33.33%,侵彻深度可增加15.93%;当靶弹半径比小于等于20时,侵彻深度增大的程度显著,当靶弹半径比由19.88减小至4.9时,侵彻阻力减小了41.30%,侵彻深度增长了32.61%,此时靶体边界尺寸对侵彻性能的影响很大,不能继续按照半无限靶体进行计算。     

刚性弹侵彻有限直径金属厚靶的机理与模型研究

采用统一强度理论,考虑靶板中间主应力效应和靶体侧面自由边界的影响,得到线性硬化靶材在弹塑性阶段和塑性阶段的空腔壁径向应力的表达式,建立线性硬化靶材的统一侵彻模型,求出中低速(v₀≤1000 m/s)刚性弹体侵彻有限直径金属厚靶时侵彻阻力、侵彻深度计算公式,并利用Simpson算法对其进行求解,分析了包括强度准则差异在内的弹道终点效应的一系列影响因素。结果表明:该文计算方法可以更好地描述侵彻过程中弹靶的动态响应,还可以得到一系列基于不同强度准则的侵彻阻力和深度的解析解、对靶材在不同撞击速度下侵彻深度的区间范围进行有效预测;强度参数、弹体撞击速度、靶体半径和弹头形状对有限直径金属厚靶的抗侵彻性能均有较大的影响,其中强度参数值由1减小为0时,侵彻深度增加了22.45%;随着靶弹半径比的减小,侵彻深度不断增大,当靶弹半径比小于等于16时,侵彻深度增大的程度显著,此时靶体边界尺寸对侵彻性能的影响很大,不能继续按照半无限靶体进行计算。     

分析金属装甲弹道极限的两阶段模型

基于大量弹道试验分析,考虑靶板背面自由边界的影响,提出一个分析刚性尖头弹垂直撞击中等厚度理想弹塑性材料靶板弹道极限的两阶段工程模型。由圆柱形空腔膨胀理论和功能原理导出第一阶段延性扩孔耗能表达式,按薄靶板最小穿透能量的简化分析模型计算第二阶段耗能,由两阶段总的耗能最小确定第一阶段的侵彻深度,从而得到最小穿透能量的解析解。经与金属装甲弹道试验比较,表明两阶段工程模型计算结果与试验吻合较好,比现有单一延性扩孔模型精度高。     

尖头弹侵彻延性金属靶板弹道极限的解析模型

现有的尖头弹侵彻金属靶板的弹道极限计算模型往往需要大量的试验数据和靶板材料的动态性能参数,且没有考虑侵彻速度对侵彻效果的影响,这给工程应用带来了很大的不便和误差。基于这一问题,考虑速度效应和靶板材料参数对侵彻的影响,结合流体动力学原理与动态空穴膨胀理论,分别提出了双模式和单模式侵彻模型。双模式侵彻模型的侵彻过程可分为两个阶段：流体动力变形阶段和塑性变形阶段,当侵彻速度小于靶材产生流体动力变形的临界速度时,侵彻进入塑性变形阶段,根据功能原理,建立了计算弹道极限的解析模型;单模式侵彻模型仅考虑塑性变形阶段。解析模型计算的弹道极限与弹道试验结果吻合的较好,且模型中不涉及弹道试验数据和靶板材料的动态性能参数,易于迅速求解,便于工程应用,可用于对延性金属靶板抗尖头弹侵彻能力的评估。     

弹体高速侵彻陶瓷复合厚靶的计算模型研究

针对平头弹高速撞击陶瓷复合厚靶的问题,以集中质量法为基础并考虑靶体的内摩擦效应对Fellows模型加以改进,建立侵彻过程的理论计算模型并利用Matlab编程求得不同撞击速度下弹体侵彻复合靶体的侵彻深度,模型得到了试验结果和数值计算结果的验证。参数分析的结果表明,陶瓷厚度的增加可提高复合靶体的抗侵彻能力,但随着初始撞击速度的提高,弹体的侵彻深度增长曲线趋于平缓。     

弹体撞击半无限金属靶极限侵彻深度分析

基于空腔膨胀理论和修正的流体动力学理论,提出了球形弹头弹体侵彻半无限金属靶深度的计算方法.进而根据侵彻极限状态得出的极限撞击速度,得到了极限侵彻深度计算公式,并与试验数据进行对比分析,验证了此种方法的实用性.     

基于加速度测试及模糊模型的弹丸侵彻混凝土深度实时预测方法

为了对卵形弹垂直侵彻半无限厚混凝土目标的侵深进行实时预测,提出了一种基于实测加速度值及模糊模型的计算方法。该方法根据瞬时速度的不同将侵彻过程分成了高速侵彻、中速侵彻和低速侵彻三个阶段,并分别采用不同的模型对每个阶段的减加速度、速度和侵彻深度进行了描述。通过判断减加速度的计算误差,自动确定了高速侵彻阶段与中速侵彻阶段以及中速侵彻阶段与低速侵彻阶段的截点速度。同时,利用实测的全弹道加速度曲线,实时计算了侵彻过程的初始冲击速度。将实验后所测得的侵彻深度与模型预测的侵彻深度进行比较,结果表明该预测方法可以对侵彻深度进行准确地实时计算。     

柱形波纹压溃元件轴向冲击力学行为研究

针对冲击载荷作用下多层柱形波纹压溃元件的力学特性分析非常困难的问题,结合柱形波纹压溃元件的冲击压溃变形特征,将柱形波纹压溃元件的变形划分为弹性变形阶段、壁面接触前的塑性变形阶段、混合塑性变形阶段、壁面接触过程中的塑性变形阶段,研究了轴向冲击下柱形波纹压溃元件变形抗力的理论计算方法。利用Matlab Simulink软件编程,计算分析了不同高度落锤冲击柱形波纹压溃元件产生的变形抗力与压溃量之间的映射特性,并与实验结果进行了比较。研究结果表明,在不同跌落高度冲击下,理论计算的变形抗力与实验结果吻合较好,证明所提出的理论分析方法是合理的,对波纹压溃缓冲元件的工程应用具有指导意义。     

Validation and calibration of a lateral confinement model for long-rod penetration at ordnance and high velocities

In designing targets for laboratory long-rod penetration tests, the question of lateral confinement often arises, “How wide should the target be to exert enough confinement?” For ceramic targets, the problem is enhanced as ceramics are usually weak in tension and therefore have less self-confinement capability. At high velocities the problem is enhanced even more as the crater radius and the extent of the plastic zone around it are larger. Recently we used the quasistatic cavity expansion model to estimate the resistance of ceramic targets and its dependence on impact velocity [1]. We validated the model by comparing it to computer simulations in which we used the same strength model. Here we use the same approach to address the problem of lateral confinement.

We solved the quasistatic cavity expansion problem in a cylinder with a finite outside radius “b” at which σ_r (b) = 0 (σ_r = radial stress component). We did this for three cases: ceramic targets, metal targets, and ceramic targets confined in a metal casing. Generally, σ_r (a) is a decreasing function of “a” (“a” = expanding cavity radius, and σ_r (a) = the stress needed to continue opening the cavity). In the usual cavity expansion problem b → ∞, σ_r (a) = const., R =−σ_r (a) (R = resistance to penetration). For finite “b” we estimate R by averaging σ_r (a) over a range o ≤ a ≤ a_r, (where a_r, the upper bound of the range, is calibrated from computer simulations).

We ran 14 computer simulations with the CTH wavecode and used the results to calibrate a_r for the different cases and to establish the overall validity of our approach.

We show that generally for D_t/D_p > 30, the degree of confinement is higher than 95% (D_t = target diameter; D_p = projectile diameter; and degree of CONFINEMENT = R/R_∞; R∞ = resistance of a laterally infinite target). We also show the tensile strength of ceramic targets (represented by the spall strength P_min) has a significant effect on the degree of confinement, while other material parameters have only a minor effect.     

On the hydrodynamic theory of long-rod penetration

The hydrodynamic theory of long-rod penetration is reexamined by applying the modified Bernoulli equation to the forces acting on both sides of the moving rod-target interface. Using a ratio of 2 for the effective cross sectional areas of the mushroomed and rigid parts of the rod, it is shown that analytical expressions can be used to calculate the resistance to target penetration. The analytical expression used to calculate this resistance is the cylindrical cavity expansion, which yields resistance values of 3–4 times the compressive yield strength of the target material. Calculations based on our model show good agreement with experimental data, for steel and tungsten long rods penetrating various steel targets.     

A numerical study of the cavity expansion process and its application to long-rod penetration mechanics

The paper describes a series of 2D numerical simulations which followed the cavity expansion process in an elasto- plastic solid. The results from these simulations, in terms of cavity wall motion as a function of the applied pressures inside the cavity, highlighted several issues concerning cavity expansion process and the terminal ballistics of both rigid and eroding long rods. These issues include the form of the relation between the dynamic radial stress on the cavity wall and its velocity, which can be written in a simple, normalized form, at least for the materials we simulated here. Also, the difference between target resistance to the penetration of rigid and eroding-rod penetration, was quantified with a series of simulations in which the pressures in the cavity were applied on an angular section, rather than on its whole surface. Finally, we explored the inherent differences between spherical and cylindrical cavity expansion processes, which can be helpful for analytical models of the penetration of rigid rods with different nose shapes.     

Effect of the static strength of a metal on long-rod penetration at low velocities

The effect of the static strength (yield stress) of a material on major penetration parameters (specific work of cavity formation and pressure at the contact surface) was examined. The analytical equations and the quantitative evaluation of the specific work spent for the formation of a spherical or cylindrical cavity and of the pressure at the surface of such cavities upon their static expansion were obtained for rigid-plastic and elastoplastic materials. The evaluation of the specific work of deformation upon the formation of the spherical cavity in the plate and the cylindrical one upon the penetration of a rigid rod are shown to be adequate. The influence of strain hardening on maximum radial stresses on the cavity surface was evaluated. The resistance to penetration and the expansion of a cavity are shown to be influenced by the elastic compressibility of a material in the inelastic region. The kinetics of the stress-strain state of the material upon the formation of the cavity was analyzed for the case of considerable deformation of a rod at penetration. Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev Ukraine. Translated from Problemy Prochnosti, No. 1, pp. 93–110, January–February, 2000.