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。     

A time-dependent model for long-rod penetration

The one-dimensional, quasi-steady-state, modified Bernoulli theory of Tate [J. Mech. Phys. Solids, 15, 287 (1967)] is often used to examine long-rod penetration into semi-infinite targets. In general., the time histories of penetration predicted by the Tate model can be in good agreement with those computed from numerical simulations. However, discrepancies exist between the model and numerical simulations at the beginning and at the end of penetration. From insights provided by numerical simulations, assumptions are made concerning the velocity and stress profiles in the projectile and the target. Using these assumptions, the time-dependent, cylindrically-symmetric, axial momentum equation is explicitly integrated along the centerline of the projectile and target to provide the equation of motion. The model requires the initial interface velocity—which can be found, for example, from the shock jump conditions-and material properties of the projectile and target to compute the time history of penetration. Agreement between the predictions of this one-dimensional, time-dependent penetration model are in good agreement with experimental results and numerical simulations.     

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.     

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。     

Determination of an empirical model for the prediction of penetration hole diameter in thin plates from hypervelocity impact

The purpose of this work is to identify an empirical relationship that describes the size of the hole created in a thin plate from a hypervelocity impact in terms of the material properties and geometry of both the projectile and target. A multivariable power series was selected as the form of the mathematical model to develop this empirical relationship. Material properties and geometry of both the projectile and target were selected as the independent variables of this model to predict the hole diameters in targets. Comparison with historical equations reveals that these new models are more accurate predictors of target hole diameters. This statement is based on a one-to-one comparison of the equations using both the data utilized in developing the new models and “new”, independent data.     

Oblique penetration of a rigid projectile into an elastic-plastic target

The main objective of the present work is to develop an approximate solution of the problem of oblique penetration of a rigid projectile into an elastic-plastic target of finite thickness. This is accomplished by generalizing the work on normal penetration reported in [1]. Here, an irrotational isochoric velocity field is considered that consists of three parts, each of which together satisfy the condition of impenetrability at the projectile's surface. The first part is associated with the longitudinal motion of the projectile, the second part with the transverse motion, and the third part with the projectile rotation in the plane defined by the initial longitudinal projectile velocity and the normal to the target surface. The target material is assumed to be incompressible and the target region is subdivided into an elastic region ahead of the projectile, and a rigid-plastic region near the projectile. Using the above potential velocity field, inertia effects are included and the linear momentum equation is solved exactly in the elastic region. In the plastic region, the linear momentum equation is integrated numerically along the instantaneous streamlines to determine the pressure field on the projectile surface. Then the decelerating force and moment applied to the projectile are solved numerically. The model developed here predicts the residual velocity, the ballistic limit, as well as the residual angle of obliquity. Moreover, this model is able to describe the phenomenon of ricochet. It is shown that the agreement of the theory with experiments is good even though no adjustable parameters are used. Also, a user-friendly computer program has been developed that is available for distribution along with a Users' Manual.     

The influence of confinement on the penetration of ceramic targets by KE projectiles at 1.8 and 2.6 km/s

This paper presents the results of scale size experiments using a tungsten-alloy long-rod projectile fired against 97.5% Al₂O₃ ceramic targets at 1.8 and 2.6 km/s. Two targets were used, one having lateral steel confinement; the other without. The projectile overmatched the target, and residual projectile length and velocity were recorded using ballistic-syncro photography. Flash radiography was used during penetration of the unconfined target to obtain the penetration velocity. Manganin pressure gauges were also used to obtain additional data on the response of the ceramic target during penetration. Results from the eight experiments indicate that the confinement reduced the residual energy of the projectile at both impact velocities. Expressed in terms of the projectile impact energy, 55–56% was lost in the unconfined target at 2.6 km/s compared with 60% for the confined design. The same trend was found at 1.8 km/s with 68% and 72–73% for the unconfined and confined, respectively. Predictions using the QinetiQ GRIM2D hydrocode and a simplified form of the Johnson–Holmquist ceramic material model agreed well with the experiments for three out of the four test configurations. The predicted projectile erosion and retardation against the confined target at 1.8 km/s was excessively high. Analytical predictions using the Tate modified Bernoulli equation also gave reasonably accurate predictions for three of the tests, but values for the Tate target ‘strength’ extracted from experiments using a different target configuration were not accurate for the target design used in this paper.     

The effect of geometric scale on impact induced fragmentation, and its application to the design of dual plate armor

An analysis is presented which predicts that, for a fixed impact velocity, impact induced fragmentation becomes more severe as geometric scale increases. Test data is presented which supports this prediction, and which allows calculation of material dependent coefficients. The analysis was based on a minimization with respect to radius, for an expanding body, of a total energy density term (expansion kinetic energy per unit volume plus surface energy per unit volume). The test configuration was a steel sphere impacting an aluminum plate, with fragmentation recorded by a stack of spaced witness panels. The tests were run at full and half scale. Correlation between testing and analysis was achieved for the number of fragments perforating the front witness panel when a term analogous to a threshold energy was introduced. While the fragment count showed a dependence on geometric scale, the relative depth of penetration (number of witness panels perforated) did not. This suggested that the targets were fragmented, but that the projectile remained in one piece. A reduction in penetration depth with increasing impact velocity was seen, and was attributed to increased projectile deformation. For cases where the projectile would fragment (for example, if a harder target material were used), the effect of geometric scale on the performance of dual plate armor is predicted by analysis. The prediction is that, for impact velocities where projectile breakup at the outer plate of dual plate armor is a factor, the armor required to stop a large scale projectile can be lighter, on a relative basis, than the armor required to stop a small scale projectile.     

A new analytical model of normal penetration of projectiles into the light-weight ceramic–metal targets

In this paper based on Zaera and Sanchez-Galvez [4] model, a new analytical model has been presented for penetration of deformable projectiles into ceramic–metal targets. By considering erosion and flattening of projectile tip, the one-dimensional equation of motion has been established. The momentum equation has been employed to describe the fragmented ceramic conoid. Considering work hardening material behavior, energy conservation equation has also been used for modeling the deformation of back-up metallic plate. Semi-angle of ceramic conoid is modified based on Wilson and Hetherington [8] experiments. The ballistic limit and residual velocity of projectile predicted by new analytical model have a good agreement with the experimental results.     

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.     

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。     

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。     

Steady-state flow of compressible rigid–viscoplastic media

Computational methods for modeling steady-state flow of compressible rigid viscoplastic fluids are proposed. The constitutive equation used captures the combined effects of high-strain rate and high-pressure on the behavior of porous materials.A mixed finite-element and finite-volume strategy is developed. Specifically, the variational inequality for the velocity field is discretized using the finite element method and a finite volume method is adopted for the hyperbolic mass conservation equation. To solve the velocity problem a decomposition–coordination formulation coupled with the augmented lagrangian method is used. This approach is accurate in detecting the viscoplastic regions and permit us to handle the locking medium condition.The proposed numerical method is then applied to model the penetration of a rigid projectile into cementitious targets. The numerical model accurately describes the density changes around the projectile, the stress field, as well as the shape and location of the deformation zone (viscoplastic region) in the target.     

An analytical model for tumbling projectile perforation of thin aluminum plates

An analytical model for the perforation of thin aluminum targets by tumbling cylindrical projectiles was developed. The target material was considered to be rigid—perfectly plastic without strain hardening, while the projectile was treated as undeformable. The perforation process was experimentally found to consist of three stages: plugging, hole enlargement, and front petaling. Both conservation of energy and conservation of momentum laws were used for modeling the plugging stage, while a lower bound method was employed during the hole enlargement stage. The energy dissipated during the petaling stage consists of shearing fracture of the petal, localized plastic shear in a zone contiguous with the edges, the momentum of the petal and the bending energy of the petal. The analytical results provided generally good agreement with the corresponding experimental data in terms of the final velocity and final oblique angle of the projectile as well as the crater length of the target.     

Projectile penetration and perforation of high performance concrete: experimental results and macroscopic modelling

Experiments and simulations of penetration and perforation of high performance concrete targets by steel projectiles have been carried out. A Doppler radar monitored the projectile pre-impact velocity history and a high-speed camera captured the projectile residual velocity. A continuum mechanical approach and the finite-element method were used for the simulations. The targets were modelled with the K&C concrete model. For perforation the computational results show acceptable agreement with the experimental results, but not for penetration. The article is concluded with suggestions on how to better model concrete material for the current application.     

On the ballistic performance of metallic materials

The paper presents a ballistic performance index for metallic armour materials in terms of the commonly determined mechanical properties such as strength and modulus. The index is derived using an energy-balance approach, where the kinetic energy of the projectile is assumed to be absorbed by the elastic and the plastic deformation involved in the penetration process as well as the kinetic energy imparted to the target material during deformation. The derivation assumes two distinct stages to exist during the penetration of the projectile. At the striking face of the armour, the material is assumed to flow radially in a constrained deformation region but longitudinally at the rear surface leading to typically observed bulging of the armour without constraint. The index is validated using the available experimental and empirical data obtained in the case of small arm projectiles for an impact velocity of about 800 m/sec. This index is expected to facilitate the development of metallic armour, since the number of the ballistic experiments can be reduced significantly and only the promising materials need to be considered.     

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。     

An examination of long-rod penetration

The one-dimensional modified Bernoulli theory of Tate [J. Mech. Phys. Solids 15, 287–399 (1967)] is often used to examine long-rod penetration into semi-infinite targets. The theory is summarized and the origins of the target resistance term examined. Numerical simulations were performed of a tungsten-alloy, long-rod projectile into a semi-infinite hardened steel target at three impact velocities sufficiently high to result in projectile erosion. The constitutive responses of the target and projectile were varied parametrically to assess the effects of strain hardening, strain-rate hardening, and thermal softening on penetration response. The results of one of the numerical simulations were selected to compare and contrast in detail with the predictions of the Tate model.     

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.