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。     

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。     

有限柱形空腔膨胀理论及其应用

为研究有限平面尺寸金属厚靶侵彻问题,提出了有限柱形空腔膨胀理论.考虑侧面自由边界,将理想弹塑性材料的空腔膨胀过程分为弹塑性阶段和塑性阶段,得到了空腔壁径向压力的解析解.基于Tate磨蚀杆模型,应用有限柱形空腔膨胀理论计算靶的侵彻阻力,建立了长杆弹侵彻有限直径圆柱形金属厚靶工程模型.与现有文献试验比较表明,文中工程模型计算的侵彻深度与弹道试验结果吻合较好.     

长杆弹超高速侵彻半无限靶理论模型的对比分析与讨论

分别基于六组典型长杆弹超高速侵彻金属靶体以及三组长杆弹侵蚀侵彻混凝土靶体的实验数据,对经典一维AT模型及其五个改进模型对弹体侵彻深度的预测能力进行了评估,并讨论了靶体等效强度(Rt)变化以及弹体的轴线速度变化。计算结果表明,对于长杆弹高速侵彻金属靶体的分析计算,应首选AW模型,其次为LW模型。而对于混凝土靶体,已有有限的实验数据表明,上述六个模型对于长杆弹侵蚀侵彻混凝土靶体侵彻深度预测均不适用,其主要原因在于Rt不能反映超高速侵彻下混凝土靶体的响应。最后基于分析结果,给出了长杆弹侵蚀侵彻混凝土靶体进一步的研究方向。     

中低速长杆弹侵彻半无限岩石靶的动态响应研究

该文将统一强度理论与岩石材料动力强度依赖应变率效应的物理模型相结合,建立了岩石材料在侵彻等动力荷载作用下的率型动态统一强度准则。基于修正的土盘浮动锁应变模型,考虑应变率效应、中间主应力效应、强度准则差异和弹头滑动摩擦的影响,推导了土盘整体平均锁应力和整体平均锁应变的表达式。采用MATLAB数值计算软件和四阶Runge-Kutta算法编制计算程序,求解了中低速（V ≤ 900 m/s）长杆弹侵彻条件下弹体的侵彻深度,研究了侵彻过程中弹体的运动规律及靶体的动态响应,分析了各参数对弹体侵深的影响特性。研究表明:该文计算方法可以较好地描述整个侵彻过程中弹、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深度的解析解,有效地预测弹体侵深的上限值和下限值;中间主应力效应、强度准则差异和弹头滑动摩擦对岩石靶的抗侵彻性能具有重要影响。     

半球头长杆弹高速侵彻半无限厚靶临界速度理论模型

高速/超高速侵彻问题一直是武器设计者和防护工程专家关注的焦点问题之一。随着撞击速度的提高,弹体由刚体侵彻转入变形、流体侵彻状态,进而导致侵彻深度不再随速度呈单一上升趋势。为预测大着速范围下弹体的侵彻状态,基于弹体质量守恒、动量守恒及弹体动态强度计算方法,建立了弹体侵彻过程中的动力学平衡方程,进而确定高速侵彻临界速度。在与已有实验结果对比验证的基础上,分析了不同弹靶参数对侵彻临界速度的影响规律。结果表明:随着弹体静态屈服强度增大,弹体的变形长度减小,弹体的临界侵彻速度增大;弹靶塑性波波速等参数对高速侵彻状态临界速度也有显著影响。     

刚性弹体对素混凝土厚靶侵彻响应的LDPM数值模拟研究EI北大核心CSCD

基于一种新的细观离散元模型Lattice Discrete Particle Model(LDPM),该研究建立了刚性弹侵彻素混凝土厚靶的数值仿真模型。对LDPM基本假设和细观模型构建简单介绍,结合三轴压缩响应曲线,对23 MPa强度素混凝土进行LDPM参数标定。通过对比弹体减速度和侵彻深度试验值,验证数值模型对于混凝土厚靶侵彻问题的适用性。LDPM模拟弹体恒定速度侵彻混凝土厚靶,获得侵彻行程中侵彻阻力变化曲线,结合Forrestal阻力公式得到靶体静态阻应力。仿真结果表明,尖卵形弹头不同CRH值以及侵彻速度对靶体静态阻应力基本没有影响;弹径为最大骨料直径3倍、6倍和8倍的弹体受到靶体静态阻应力分别为260 MPa、175 MPa和163 MPa。该结果对混凝土侵彻缩比实验研究具有重要的实际工程意义。     

刚性弹体对素混凝土厚靶侵彻响应的LDPM数值模拟研究

基于一种新的细观离散元模型Lattice Discrete Particle Model(LDPM),该研究建立了刚性弹侵彻素混凝土厚靶的数值仿真模型。对LDPM基本假设和细观模型构建简单介绍,结合三轴压缩响应曲线,对23 MPa强度素混凝土进行LDPM参数标定。通过对比弹体减速度和侵彻深度试验值,验证数值模型对于混凝土厚靶侵彻问题的适用性。LDPM模拟弹体恒定速度侵彻混凝土厚靶,获得侵彻行程中侵彻阻力变化曲线,结合Forrestal阻力公式得到靶体静态阻应力。仿真结果表明,尖卵形弹头不同CRH值以及侵彻速度对靶体静态阻应力基本没有影响;弹径为最大骨料直径3倍、6倍和8倍的弹体受到靶体静态阻应力分别为260 MPa、175 MPa和163 MPa。该结果对混凝土侵彻缩比实验研究具有重要的实际工程意义。     

“上帝之杖”天基动能武器毁伤效应评估

作为未来化战争条件下打击地下深层战略目标的一种重要武器装备,“上帝之杖”天基动能武器对维护国家利益和领土完整意义重大。综合考虑了外界温度、压强、海拔高度、大气密度、飞行速度等因素对弹体在大气层中所受空气阻力的影响,分析计算出“上帝之杖”动能弹的入地速度达3 401.7 m/s;目前,受到实验技术和方法的限制,只有Gold取得了几组动能弹高速侵彻混凝土靶的实验数据,且最高侵彻速度不足2 km/s,对诸如“上帝之杖”这么高侵彻速度的动能弹侵彻混凝土靶的实验研究还是空白;因此,进行了“上帝之杖”动能弹侵彻C60半无限混凝土靶的数值模拟和理论研究。研究结果表明:数值模拟所得的最终侵彻深度(18.9 m)与理论计算结果(17.3 m)的误差在允许的范围内,混凝土靶的最终开坑直径达7.333倍弹径;不同于刚性弹侵彻过程中侵彻速度持续衰减的特点,“上帝之杖”超高速动能弹侵彻的瞬态高压阶段弹头侵彻速度锐减,动能损失率极高,相应侵彻深度小;稳定侵彻阶段弹头侵彻速度和弹长消蚀速度保持稳定,弹体动能损失率基本不变,侵彻深度却线性增加;当动能弹着靶速度足够大时,最终侵彻深度主要受弹靶材料密度控制,受弹靶强度影响不大,高密度分层防护结构在抗超高速动能弹侵彻领域优势显著。     

对弹体侵彻混凝土靶体阻力函数计算公式的探讨

基于动态球形空腔膨胀理论,探讨了混凝土材料的单轴抗压强度、弹性模量、泊松比、压力硬化系数对阻力函数的影响,并指出,混凝土靶体的弹性模量和单轴抗压强度对阻力函数影响较明显,而泊松比和压力硬化系数的影响可以忽略不计。在此基础上,该文忽略泊松比和压力硬化系数的影响,通过引入弹性模量与单轴抗压强度的关系式,分别建立了基于弹性-断裂-塑性和弹性-塑性两种靶体响应模型下,同时考虑单轴抗压强度和弹性模量影响的阻力函数理论公式,并建立了弹体侵彻靶体的加速度时程计算模型。通过与不同尺寸弹体侵彻实验数据对比,验证了该文提出阻力函数表达式的适用性及其在加速度时程以及较大尺寸弹体侵彻深度计算中的优 越性。     

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 analysis for geo-material based on unified strength criterion

A unified strength criterion is applied for penetration analysis of geo-materials. Based on the cylindrical cavity-expansion theory the relation between the radial traction on the cavity surface and the impact velocity of a rigid projectile is derived. The finial penetration depth of the projectile is analytically obtained and the effect of strength criterion on the penetration depth is investigated. By comparing with existing test results, it is found that the proposed penetration model is effective in the analysis of a rigid projectile penetrating into a semi-infinite geo-material target.     

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.     

CAVITY MODELS FOR SOLID AND HOLLOW PROJECTILES

Two analytical models for the crater size generated by long-rod and thick-walled tube projectiles are presented. The first is based on energy; in a steady-state penetration, the kinetic energy loss of a projectile is related to the total energy deposited in the target. This simple approach provides an upper bound for the crater size. The second approach is based on the observation that two mechanisms are involved in cavity growth due to long projectiles: flow of projectile erosion products, which exerts radial stress on the target and opens a cavity, and radial momentum of the target as it flows around the projectile nose (cavitation). This analysis includes the centrifugal force exerted by the projectile, radial momentum of the target, and the strength of the target. Thus, it can estimate the extent of cavity growth due to projectile mushrooming, which cannot be predicted by other analyses. This model is shown to be in good agreement with experimental data.     

基于颗粒流离散元模型的弹丸侵彻细观混凝土数值模拟方法研究

利用颗粒离散单元法,研究弹丸侵彻细观混凝土模型中弹丸受到介质的阻应力与侵彻速度的关系。采用蒙特卡罗法随机生成并投放混凝土骨料且骨料的粒径分布满足级配曲线。通过对混凝土颗粒离散元细观力学模型进行单轴压缩实验、巴西劈裂实验和双轴压缩实验的参数反演,确定细观模型参数,能使细观混凝土模型具有和一般混凝土等效的力学性能。分析了骨料、过渡层和砂浆三相材料各细观参数对混凝土单轴压缩应力应变关系影响以及锥形弹和平头弹弹丸直径对侵彻阻应力的影响。将颗粒离散元细观力学模型方法计算的弹丸阻应力与空腔膨胀理论计算模型相比较,表明计算离散元方法具有良好的精度和实用性。     

A generalized formula for the penetration depth of a deformable projectile

A simple analytical algebraic formula is developed for predicting the penetration depth of a deformable projectile into a semi-infinite target. This formula is a simplified version of more general equations that have been developed to predict the time-dependent penetration process in finite thickness targets. Specifically, the formula generalizes the classical hydrodynamic theory to include dependence on elastic properties of the target and on the yield strengths of both the target and the projectile. Moreover, the formula is limited to the case of long-rod penetration where both the projectile and the target experience significant plastic flow. The limiting values of the location of the elastic–plastic boundary in the target have been determined, and a single empirical constant has been introduced to characterize the transition between these limiting values. A value for this empirical constant has been determined which produces theoretical predictions that are in reasonable agreement with experimental data for moderate to high values of the impact velocity of steel and tungsten projectiles penetrating a steel target.     

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.