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。     

On hypervelocity penetration of the mesh-bumper strings into a projectile

An elastic–plastic model describing hypervelocity penetration of a mesh-bumper string by an arriving projectile is presented. An analytical solution for the case of rigid penetration is derived whereby the dependence between penetration depth and impact velocity is established. A comparative analysis between rigid penetration and penetration with a spreading string is performed. The mesh strings interact between each other with the aid of flow arising during penetration. The model which is developed allows us to estimate destruction depth of the projectile during its interaction with the mesh strings.     

弹体冲击混凝土半无限靶的侵彻阻力与深度计算

假设弹体是刚性的,将弹体侵彻冲击作用下的混凝土靶体划分为粉碎区、径向裂缝弹性区与原始弹性区,并认为侵彻粉碎区域内的混凝土材料处于类似于流体动力学状态,可采用水动力模型.根据伯努利方程推得了细长杆弹侵彻阻抗力的公式,进而求出锥形弹头侵彻阻抗力的等效平面解,得到了弹体的侵彻深度.利用实弹进行了以不同速度侵彻不同强度的混凝土靶体的验证计算,并与多个经验公式做了对比.结果表明,该模型是合理的,与经验公式相比计算结果趋于保守.     

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。     

Deep penetration of a non-deformable projectile with different geometrical characteristics

A general non-dimensional formula based on the dynamic cavity-expansion model is proposed to predict penetration depth into several mediums subjected to a normal impact of a non-deformable projectile. The proposed formula depends on two dimensionless numbers and shows good agreement with penetration tests on metal, concrete and soil for a range of nose shapes and impact velocities. The validity of the formula requires that the penetration depth is larger than the projectile diameter and the projectile nose length while projectile remains rigid without noticeable deformation and damage.     

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。     

Normal penetration of an eroding projectile into an elastic–plastic target

The main objective of the present work is to describe normal penetration of a deformable projectile into an elastic–plastic target. The force imposed on the projectile by the target is generally a complex function of the strength of the target material, the projectile velocity, its diameter and shape, as well as the instantaneous penetration depth. When this force exceeds a certain critical value the projectile begins to deform. At moderate-to-high values of the impact velocity, the projectile's tip material flows plastically with large deformations causing the formation of a mushroom-like configuration. This process is accompanied by erosion of the projectile material. In the rear (“elastic”) part of the projectile the deformations remain small and the region can be approximated as a rigid body being decelerated by the projectile's yield stress. The general model allows one to predict the penetration depth, the projectile's eroded length and the crater diameter. It has been shown that in the limit of very high impact velocities the present model reduces to the well-known form of the hydrodynamic theory of shaped-charge jets. Also, a simplified asymptotic formula for the crater radius has been derived which includes the effect of the target's yield stress and compares well with experimental data for very high impact velocities.     

Penetration of a rigid projectile into an elastic-plastic target of finite thickness

This paper considers the problem of non-steady penetration of a rigid projectile into an elastic-plastic target of finite thickness. A specific blunt projectile shape in the form of an ovoid of Rankine is used because it corresponds to a reasonably simple velocity field which exactly satisfies the continuity equation and the condition of impenetrability of the projectile. The target region is subdivided into an elastic region ahead of the projectile where the strains are assumed to be small, and a rigid-plastic region near the projectile where the strains can be arbitrarily large. Using the above mentioned velocity field, the momentum equation is solved exactly in both the elastic and the rigid-plastic regions to find expressions for the pressure and stress fields. The effects of the free front and rear surfaces of the target (which is presumed not to be too thin) and the separation of the target material from the projectile are modeled approximately, and the force applied to the projectile is calculated analytically. An equation for projectile motion is obtained which is solved numerically. Also, a useful simple analytical solution for the depth of penetration or the residual velocity is developed by making additional engineering approximations. Moreover, the solution procedure presented in this paper permits a straight forward approximate generalization to accommodate a projectile with arbitrary shaped tip. Theoretical predictions are compared with numerous experimental data on normal penetration in metal targets, and the agreement of the theory with experiments is good even though no empirical parameters are used. Also, simulations for conical and hemispherical tip shapes indicate that the exact shape of the projectile tip does not significantly influence the prediction of integral quantities like penetration depth and residual velocity.     

Numerical–analytical model of penetration of long elastically deformable projectiles into semi-infinite targets

A new numerical–analytical model of penetration of long axisymmetric elastically deformable projectiles in semi-infinite targets is presented. A background of this model is the integral–differential equation of ballistics for non-deformable projectile. This equation is obtained on the basis of the Lagrange–Cauchy integral for non-stationary irrotational motion of an incompressible fluid, as well as the solutions for the quasi-static spherical cavity expansion problem in an infinite medium. The velocity field in a target is defined by actual projectile shape. The functional dependence of penetration velocity is determined for both elastic and rigid projectiles. The effect of forced elastic longitudinal oscillations on penetration velocity is estimated. An estimate is made for the critical impact velocity at which point the projectile plastically deforms causing irreversible changes in its shape, and also leads to instability of its trajectory in the target. This velocity depends on both elastic and strength characteristics of the projectile and target, their densities and projectile shape. Results from our penetration modeling are compared with existing experimental and calculated data.     

A fuzzy model of the penetration resistance of concrete targets

The penetration resistance of a concrete target varies greatly with the strike velocity of the projectile from low and intermediate impact velocities to high impact velocities. A fuzzy model of the penetration resistance of a concrete target is proposed to describe this characteristic. A complete analysis is conducted of the penetration process during which a rigid projectile penetrates a semi-infinite concrete target based on the proposed fuzzy model. Good agreement is observed between the experimental and predicted results based on the proposed fuzzy model.     

Multiple impact penetration of semi-infinite concrete

An experimental study was performed to gather multiple impact, projectile penetration data into concrete. A vertical firing range was developed that consisted of a 30-06 rifle barrel mounted vertically above a steel containment chamber. 0.41 m cubes of an Air Force G mix concrete were suspended in wet sand and positioned in the steel chamber. The concrete targets were subjected to repeated constant velocity impacts from 6.4 mm diameter steel projectiles with an ogive nose shape and a length to diameter ratio of 10. A laser sight was adapted to the rifle to ensure alignment, and a break screen system measured the projectile velocity. After each impact, the projectile penetration and crater formation parameters were recorded. The penetration and crater formation data were consistent with single impact penetration data from previous studies conducted at Sandia National Laboratories. In addition, an analytic/empirical study was conducted to develop a model that predicted the penetration depth of multiple impacts into concrete targets. Using the multiple impact penetration and crater formation data, a single impact penetration model, developed by Forrestal at Sandia National Laboratories, was extended to account for the degradation of the target strength with each subsequent impact. The degradation of the target was determined empirically and included in the model as a strength-modifying factor. The model requires geometry parameters of the ogive nose projectile, projectile velocity, the number of impacts, and target compressive strength to calculate the overall penetration depth of the projectile.     

主控因素对异型头弹丸半侵彻金属靶深度的影响特性研究

为研究异型头弹丸半侵彻金属靶的侵深特性,基于量纲方法对影响侵深的主控因素进行了分析,采用弹道枪加载和LS-DYNA软件对异型头弹丸半侵彻金属靶的作用过程进行了试验和数值模拟研究,分析了异型头弹丸结构、弹丸初速、靶板厚度等因素对侵彻深度的影响规律,获得了侵深随弹丸初速以及靶板厚度的变化曲线。研究结果表明,弹丸初速和靶板厚度是影响侵彻深度的关键因素,并拟合得到了弹丸初速和靶板厚度综合影响下的半侵彻侵深经验公式。研究结果可为半侵彻作用的研究及新型侵彻的工程计算方法等提供参考。     

岩石Holmquist-Johnson-Cook模型参数的确定方法

Holmquist-Johnson-Cook(HJC)本构模型在混凝土冲击爆炸数值模拟中应用广泛, 该文将其推广到岩石类材料中, 为合理确定岩石材料的HJC本构模型参数, 从塑性屈服面理论出发, 得到了特征化黏性强度系数与帽盖模型参数的关系。基于三轴围压实验、Hugoniot实验和Hopkinson压杆实验数据, 分别得到了Salem石灰岩极限面参数、压力参数和率效应参数的取值。基于上述模型参数利用有限元程序LS-DYNA对Salem石灰岩的弹体侵彻实验进行了数值模拟, 侵彻深度的计算结果与实验数据对比表明了本文所提出的HJC本构模型参数确定方法的合理性和有效性。以相对侵彻深度为目标函数, 对Salem石灰岩HJC模型所涉及的19个参数的敏感性进行了分析, 并对一般岩石材料的HJC模型参数的确定给出了建议方法, 并通过模拟高强花岗岩和Sidewinder凝灰岩弹体侵彻实验, 进一步验证了该文提出方法的合理性。     

Resistance of high-strength concrete to projectile impact

This paper presents the results of an experimental study on the impact resistance of concrete with compressive strengths of 45–235 MPa when subjected to impact by 12.6 mm ogive-nosed projectile at velocities ranging from ∼620 to 700 m/s. The results indicate that the penetration depth and crater diameter in target specimens exhibit an overall reduction with an increase in the compressive strength of the concrete. However, the trend is not linear. Further increase in the compressive strength requires a reduction in the water-to-cementitious material ratio and the elimination of coarse aggregates. However, doing these does not result in reduction of the penetration depth and crater diameter. The presence of coarse granite aggregates appears to be beneficial in terms of reducing penetration depth, crater diameter, and crack propagation, thus contributing to impact resistance. Incorporation of steel fibers in the concrete reduced the crater diameter and crack propagation, but did not have a significant effect on penetration depth. An increase in the curing temperature from 30°C to 250°C did not alter the impact resistance of the concrete significantly. Based on the present findings and cost consideration, high-strength fiber-reinforced concrete with a compressive strength of ∼100 MPa appears to be most efficient in protection against projectile impact.     

Oblique penetration of a rigid projectile into a thick elastic–plastic target: theory and experiment

A model of oblique penetration of a rigid projectile into a thick elastic–plastic target has been developed (Roisman et al., Int J Impact Engng 1997; 19: 769–95) which incorporates stress-free boundary conditions at the rear surface of the target. The main objective of the present work is to validate the theoretical model by comparison with new experimental results for normal and oblique penetration of a rigid projectile into a thick plate of Al 6061-T651. Good agreement between theory and experiment is exhibited for the projectile residual velocity and the crater shape.     

An investigation on mass loss of ogival projectiles penetrating concrete targets

Mass loss of an ogival projectile during its normal penetration in concrete target was investigated in this paper. Experiments of 38CrSi short-rod projectiles with ogival nose shape penetrating into concrete targets were conducted in the striking velocity range of 500–1500 m/s. Discussions revealed that projectile mass loss derives mainly from the nose part for both short-rod and long-rod projectiles during the penetration process. Furthermore, an engineering model was proposed to determine upper limit of rigid penetration regime as the maximum value of the striking velocity, which was based on the feature of projectile mass loss in the hydrodynamic transition between rigid penetration regime and semi-hydrodynamic penetration regime. Good agreements are obtained between engineering predictions and experimental results.     

Depth of penetration of high-speed penetrator with including the effect of mass abrasion

Mass abrasion is observed on the nose of projectile when a projectile strikes concrete target at high velocity. To evaluate the influence of the mass abrasion on the depth of penetration (DOP) limit, the relationship between the nose factor of the residual projectile after abrasion and the initial impact velocity is suggested according to the experimental data. Based on the dynamic cavity expansion theory, with considering the effects of varying nose factor and mass of projectile, a modified model is proposed to calculate the depth of penetration of kinetic energy penetrator. The model predicts that a theoretical maximum DOP exists due to the mass abrasion of the projectile. The model is checked by the different experimental data.     

强度失配对铝合金板焊接接头抗弹性能影响的有限元分析

通过建立7.62mm穿甲弹侵彻铝合金板的模型,采用Johnson-Cook材料模型模拟研究了焊接接头的强度失配对铝合金板抗弹性能的影响。研究结果表明:当子弹侵彻铝合金焊接接头附近时,由于材料的不均匀变形,子弹会改变侵彻方向,其方向角的改变大小与子弹速度、侵入位置、弹头形状、强度失配比、靶板厚度有关;当子弹以低速侵彻铝合金板中间的软焊缝材料时,由于变形局部化,出现材料的抗弹性能低于纯焊缝材料的情况;由于子弹侵彻方向的改变,出现部分区域的抗弹性能高于铝合金基体材料的情况。研究结果为不均匀材料的抗弹性能研究提供参考。     

A modified model for the penetration into moderately thick plates by a rigid,sharp-nosed projectile

The deep penetration model based on cavity expansion analysis (Int. J. Impact Eng. 27 (2002) 619) is modified to take account of the increase of the contact area between the projectile nose and the target medium before the projectile nose fully penetrates into the target. The modified penetration model is applicable to those penetration problems where the length of the projectile nose is comparable to the penetration depth. The predicted results are in good agreement with experimental results from Diskshit and Sundararajan (Int. J. Impact Eng. 12(3) (1992) 373) and Diskshit et al. (Int. J. Impact Eng. 16(2) (1995) 293).