爆炸成型弹丸贯穿靶板靶后破片空间分布模型

深空撞击载荷对探测小天体内部物质成分和结构特性具有重要意义,因此,在考虑爆炸成型弹丸(explosively formed projectile, EFP)可变截面的特性和区分靶后破片来源的基础上,建立了EFP贯穿靶板靶后破片空间分布模型。在靶板厚度30 mm至70 mm、EFP着靶速度1 650 m/s至1 860 m/s的条件下,该模型可以定量预测靶后破片云中各个破片的速度、质量、数量与空间位置的关系。结果表明,相对速度总是随相对空间位置的增加而呈线性增加,相对质量、相对数量总是随相对空间位置的增加而呈幂函数增加。     

Analysis of the mass of behind-armor debris generated by RHA subjected to normal penetration of variable cross-section EFP

Analyzing the mass of behind-armor debris (BAD) generated by Rolled Homogeneous Armor (RHA) subjected to normal penetration of variable cross-section Explosively Formed Projectile (EFP) is the purpose of this paper. So theoretical analysis, numerical simulation and experimental data are combined to analyze the influence of variable cross-section characteristic on the time history of crater radius. Moreover the relationships between time history of crater radius (as well as mass of BAD) and the thickness of RHA (from 30 mm to 70 mm) and the impact velocity of EFP (1650 m/s to 1860 m/s) are also investigated. The results indicate that: 1) being compared to the variable cross-section characteristic is ignored, the theoretical time history of crater radius is in better agreement with the simulation results when the variable cross-section characteristic is considered; 2) being compared to the other three conditions of plug, the theoretical mass of BAD is in the best agreement with the simulation results when the shape of plug is frustum of a cone and the angle between generatrix and bottom is 45° and the axial length of mushroom is considered.     

填充式波纹夹层结构超高速撞击特性仿真

基于航天器空间碎片被动防护需求,对一种新型填充式波纹夹层结构进行超高速撞击仿真研究,分析超高速撞击过程以及结构的穿孔破坏情况和所形成的碎片云的特性,并与相同面密度Whipple结构进行对比。其撞击现象与Whipple结构相似,但其碎片云的头部速度小于Whipple结构,而径向膨胀最大速度和膨胀半角均大于Whipple结构。随撞击初速从3 km/s~10 km/s不断增大,波纹夹层结构的撞击穿孔尺寸变大,形状也更不规则。此外,结构中的填充树脂对碎片撞击能量的吸收贡献最大,后面板所吸收的能量所占比重较大,而前面板和波纹板对碎片撞击能量的吸收贡献较小。研究结果对空间碎片防护结构的设计具有一定的参考意义。     

高速/超高速碰撞效应研究

高速/超高速碰撞会产生大量破片,并伴随闪光、等离子体等现象.高速碰撞材料受冲击产生射流及破片高温会引起碰撞闪光现象,获得了碰撞等离子体电磁场强度的变化规律.采用数值仿真与理论分析相结合的方法,获得了高速碰撞破片云团分布规律.     

Formation of explosively formed penetrator with fins and its flight characteristics

The ultimate goal of weapon system employing an explosively formed penetrator (EFP) is to defeat a target at the longest standoff. In order to do this, an EFP must be aerodynamically stable so as to strike the target at a small angle of obliquity, and the decay velocity per meter of EFP must be smaller at extended standoff. As the angle of attack increases, the penetration ability of EFP greatly reduces. The fins improve the EFP aeroballistic characteristics and decrease the flight drag of EFP as well. EFP with fins formed by three-point initiation is presented. The formation of EFP with fins is studied by LS-DYNA, and the aeroballistics is studied through experiment. The experimental results show that the decay velocity per meter of EFP with fins is much smaller than that of normal EFP, and the attitude angle steadily decreases.     

Estimation of the kinetic parameters for thermal decomposition of HNIW and its adiabatic time-to-explosion by Kooij formula

A differential/integral method to estimate the kinetic parameters (apparent activation energy E_a and pre-exponential factor A) for thermal decomposition reaction of energetic materials based on Kooij formula are applied to study the nonisothermal decomposition reaction kinetics of hexanitrohexaazaisowurtzitane (HNIW) by analyzing nonisothermal DSC curve data. The apparent activation energy (E_a) obtained by the integral isoconversional non-isothermal method based on Kooij formula is used to check the constancy and validity of apparent activation energy by the differential/integral method based on Kooij formula. The most probable mechanism function of thermal decomposition reaction of HNIW is determined by a logical choice method. The equations for calculating the critical temperatures of thermal explosion (T_b) and adiabatic time-to-explosion (t_TIad) based on Kooij formula are used to calculate the values of T_b and t_TIad to evaluate the thermal safety and heat-resistant ability of HNIW. All the original data needed for analyzing the kinetic parameters are from nonisothermal DSC curves. The results show that the kinetic model function in differential form and the values of E_a and A of decomposition reaction of HNIW are 3(1 − α)[−ln(1 − α)]^2/3, 152.73 kJ mol⁻¹ and 10^11.97 s⁻¹, respectively, and the values of self-accelerating decomposition temperature (T_SADT), T_b and t_TIad are 486.55 K, 493.11 K and 52.01 s, respectively.     

On maximization of the integral of a bell-shaped function over a symmetric set

Given a target T in Euclidean n-space Rⁿ and a point bomb whose point of impact in Rⁿ is governed by a probability distribution about the aim point a, what choice of a maximizes the probability of a hit v_a(T)? Of course, only in special cases is an exact solution of this problem obtainable. This paper treats targets T which are symmetric about the origin o and demonstrates conditions on the extent of T and the impact density f, a density with respect to Lebesgue measure, sufficient for v_a(T) to be monotone in the distance from a to o and maximized at a = o. The results are applied to various tactical situations.     

A study on the surface overpressure distribution and formation of a double curvature liner under a two-point initiation

The formation mechanism of an EFP(explosively formed projectile) using a double curvature liner under the overpressure effect generated by a regular oblique reflection was investigated in this paper.Based on the detonation wave propagation theory,the change of the incident angle of the detonation wave collision at different positions and the distribution area of the overpressure on the surface of the liner were calculated.Three-dimensional numerical simulations of the formation process of the EFP with tail as well as the ability to penetrate 45# steel were performed using LS-DYNA software,and the EFP ve-locity,the penetration ability,and the forming were assessed via experiments and x-ray photographs.The experimental results coincides with those of the simulations.Results indicate that the collision of the detonation wave was controlled to be a regular oblique reflection acting on the liner by setting the di-mensions of the unit charge and maintaining the pressure at the collision point region at more than 2.4 times the CJ detonation when the incident angle approached the critical angle.The distance from the liner midline to the boundary of the area within which the pressure ratio of the regular oblique reflection pressure to the CJ detonation pressure was greater than 2.5,2,and 1.5was approximately 0.66 mm,1.32 mm,and 3.3 mm,respectively.It is noted that pressure gradient caused the liner to turn inside out in the middle to form the head of the EFP and close the two tails of the EFP at approximately 120μs.The penetration depth of the EFP into a 45# steel target exceeded 30 mm,and there was radial expansion between the head and tail of the EFE increasing the penetration resistance of the EFP.Therefore,the structural size of the unit charge and the liner can be further optimized to reduce resistance to increase the penetration ability of the EFP.     

Research and development on hypervelocity impact protection using Whipple shield: An overview

Whipple shield, a dual-wall system, as well as its improved structures, is widely applied to defend the hypervelocity impact of space debris (projectile). This paper reviews the studies about the mechanism and process of protection against hypervelocity impacts using Whipple shield. Ground-based experiment and numerical simulation for hypervelocity impact and protection are introduced briefly. Three steps of the Whipple shield protection are discussed in order, including the interaction between the projectile and bumper, the movement and diffusion of the debris cloud, and the interaction between the debris cloud and rear plate. Potential improvements of the protection performance focusing on these three steps are presented. Representative works in the last decade are mentioned specifically. Some prospects and suggestions for future studies are put forward.     

Characteristics structure analysis on debris cloud in the hypervelocity impact of disk projectile on thin plate

In this paper, the gauge points setting is introduced in the SPH simulation to analyze the debris cloud structure generated by the hypervelocity impact of disk projectile on thin plate. Compared with the experiments, more detailed information of the debris cloud structure can be classified from the numerical simulation. However, due to the solitary dispersion and overlap display of the particles in the SPH simulation, accurate comparison between numerical and experimental results is difficult to be performed. To track the velocity and spatial distribution of the particles in the debris cloud induced from disk and plate, gauge points are locally set in the single-layer profile in the SPH model. By analyzing the gauge points’ spatial coordinate and velocity, the location and velocity of characteristic points in the debris cloud are determined. The boundary of debris cloud is achieved, as well as the fragments distribution outside the main structure of debris cloud.     

多爆炸成型弹丸性能参数灰关联分析

为了获得各参数对多爆炸成型弹丸毁伤性能的影响程度,以EFP速度和MEFP发散角为参考序列,以药型罩和装药参数为比较序列,运用灰关联理论对影响MEFP毁伤性能的参数进行了灰关联分析。在此基础上,应用灰关联分析结果完成了MEFP战斗部优化设计。结果表明:在较少样本空间前提下,采用灰关联理论可以分析获得影响多爆炸成型弹丸毁伤性能的各因素主次关系,而且经过优化后的MEFP战斗部,大大地提高了EFP的集聚性和毁伤性能。     

Graph distance‐dependent labeling related to code assignment in computer networks

For nonnegative integers d₁, d₂, and L(d₁, d₂)‐labeling of a graph G, is a function f : V(G) → {0, 1, 2, …} such that |f(u) − f(v)| ≥ d_i whenever the distance between u and v is i in G, for i = 1, 2. The L(d₁, d₂)‐number of G, λ(G) is the smallest k such that there exists an L(d₁, d₂)‐labeling with the largest label k. These labelings have an application to a computer code assignment problem. The task is to assign integer “control codes” to a network of computer stations with distance restrictions, which allow d₁ ≤ d₂. In this article, we will study the labelings with (d₁, d₂) ∈ {(0, 1), (1, 1), (1, 2)}. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Tuning the reactivity of Al–Ni by fine coating of halogen-containing energetic composites

In this paper, various core-shell structured Al–Ni@ECs composites have been prepared by a spray-drying technique. The involved ECs refer to the energetic composites (ECs) of ammonium perchlorate/nitrocellulose (AP/NC, NA) and polyvinylidene fluoride/hexanitrohexaazaisowurtzitane (PVDF/CL-20, PC). Two Al–Ni mixtures were prepared at atomic ratios of 1:1 and 1:3 and named as Al/Ni and Al/3Ni, respectively. The thermal reactivity and combustion behaviors of Al–Ni@ECs composites have been comprehensively investigated. Results showed that the reactivity and combustion performance of Al–Ni could be enhanced by introducing both NA and PC energetic composites. Among which the Al/Ni@NA composite exhibited higher reactivity and improved combustion performance. The measured flame propagation rate (v = 20.6 mm/s), average combustion wave temperature (T_max = 1567.0 °C) and maximum temperature rise rate (γ_t = 1633.6 °C/s) of Al/Ni@NA are higher than that of the Al/Ni (v = 15.8 mm/s, T_max = 858.0 °C, and γ_t = 143.5 °C/s). The enhancement in combustion properties could be due to presence of the acidic gaseous products from ECs, which could etch the Al₂O₃ shell on the surface of Al particles, and make the inner active Al to be easier transported, so that an intimate and faster intermetallic reaction between Al and Ni would be realized. Furthermore, the morphologies and chemical compositions of the condensed combustion products (CCPs) of Al–Ni@ECs composites were found to be different depending on the types of ECs. The compositions of CCPs are dominated with the Al–Ni intermetallics, combining with a trace amount of Al₅O₆N and Al₂O₃.     

The non-isothermal gravimetric method for study the thermal decomposition kinetic of HNBB and HNS explosives

The hexanitrostilben (HNS) is a thermally stable explosive that can be prepared from hexanitrobibenzyl (HNBB). Therefore, the investigation of thermal stability of HNBB can be important in the yield of preparation of HNS. The decomposition kinetic of HNBB and HNS are studied by non-isothermal gravimetric method. The TG/DTG curves in non-isothermal method are obtained in range of 25°C–400 °C at heating rates of 3 °C/min, 5 °C/min, 8 °C/min, 10 °C/min and 12 °C/min. The data of weight-temperature are used for calculation of activation energy (E_a) of thermal decomposition reactions by methods of Ozawa, Kissinger, Ozawa-Flynn-Wall (OFW) and Kissinger-Akahira-Sunose (KAS) as model-free methods and Strink's equation as model-fitting method. The compensation effect is used for prediction of mechanism and determination of pre-exponential factor (lnA) of the decomposition reaction. A reduction 60 kj/mol for the average of activation energy of thermal decomposition reaction of HNBB is obtained versus HNS. This result shows the lower thermal stability of HNBB in comparison to HNS. The Avrami equation (A_3/2) with function f(α) = 3/2(1-α)[-ln(1-α)]^1/3 indicates the predicted mechanism for thermal decomposition reaction both explosives.     

Analysis on the resistive force in penetration of a rigid projectile

According to the dimensionless formulae of DOP (depth of penetration) of a rigid projectile into different targets, the resistive force which a target exerts on the projectile during the penetration of rigid projectile is theoretically analyzed. In particular, the threshold V_c of impact velocity applicable for the assumption of constant resistive force is formulated through impulse analysis. The various values of V_c corresponding to different pairs of projectile-target are calculated, and the consistency of the relative test data and numerical results is observed.     

Statistical variability and fragility assessment of ballistic perforation of steel plates for 7.62 mm AP ammunition

The paper describes field test results of 7.62 × 51 mm M61 AP (armour piercing) ammunition fired into mild steel targets at an outdoor range. The targets varied from 10 mm to 32 mm in thickness. The tests recorded penetration depth, probability of perforation (i.e., complete penetration), muzzle and impact velocities, bullet mass, and plate yield strength and hardness. The measured penetration depth exhibited a variability of approximately ±12%. The paper then compared ballistic test results with predictive models of steel penetration depth and thickness to prevent perforation. Statistical parameters were derived for muzzle and impact velocity, bullet mass, plate thickness, plate hardness, and model error. A Monte-Carlo probabilistic analysis was then developed to estimate the probability of plate perforation of 7.62 mm M61 AP ammunition for a range of impact velocities, and for mild steels, and High Hardness Armour (HHA) plates. This perforation fragility analysis considered the random variability of impact velocity, bullet mass, plate thickness, plate hardness, and model error. Such a probabilistic analysis allows for reliability-based design, where, for example, the plate thickness with 95% reliability (i.e. only 1 in 20 shots will penetrate the wall) can be estimated knowing the probabilistic distribution of perforation. Hence, it was found that the plate thickness to ensure a low 5% probability of perforation needs to be 11–15% thicker than required to have a 50/50 chance of perforation for mild steel plates. Plates would need to be 20–30% thicker if probability of perforation is reduced to zero.     

Peak rate of occurrence of a poisson process

Suppose that a nonhomogeneous Poisson process is observed for a length of time T, say Let λ (t) denote the mean value function of the process. It is assumed that λ (t) is first increasing then decreasing inside the interval (0, T) with peak at t = t₀, say. Three methods are given for estimating to. One of these methods is nonparametric, and the other two methods are based on the standard regression technique and the maximum likelihood principle The given resull has application in a problem of determining the azimuth of a target from the radar-impulse data. The time series of incoming signals may be approximated by the occurrence of a nonhomogeneous Poisson process with mean value function λ (t). The azimuth of the target is reasonably determined from the direction of the axis of the radar beam at the instant to, corresponding to the peak value of λ (t).     

Investigating the surface integrity of aluminium based composites machined by EDM

In the present work, the surface characteristics of Electrical Discharge Machined (EDM) Al (6351)SiC and Al (6351)SiCB₄C composites are investigated. The composites are prepared by employing the conventional stir casting technique, as it can produce better particle dispersion in the matrix. The detailed experimental study is performed on the composites by varying current (I), duty factor (τ), pulse on time (T_on), and the gap voltage (V) in order to analyze the Heat Affected Zone (HAZ) formed in the sub surface and the average crater diameter formed on the machined surface of the composites as an output function. The formation of recast layers, presence of bubbles and the surface texture of the composites at various machining conditions are observed. The results show that the increased Metal Removal Rate (MRR) increases the depth of HAZ and the average crater diameter on the machined area. Further, the addition of B₄C particles to the composite produces more surface defect than the AlSiC composite.     

Evaluating cost and reliability integrated performance of stochastic logistics systems

The significance of integrating reliability into logistics performance has been established [The Logistics Performance Index and Its Indicators, World Bank International Trade and Transport Departments, (2010)]. Hence, as a response to the work by the World Bank, the present article aims to evaluate the performance index R_b,d of logistics systems as the probability that a specified demand d can be distributed successfully through multistate arc capacities from the source to the destination under the constraint that the total distribution cost should not exceed the cost limitation b. This article provides a pioneering approach for a straightforward computation of the performance index R_b,d. The proposed algorithm is a hybrid between the polynomial time capacity‐scaling algorithm, which was presented by Edmonds and Karp [JACM 19 (1972)], and the decomposition algorithm, which was presented by Jane and Laih [IEEE (2008)]. Currently, the proposed approach is the only algorithm that can directly compute R_b,d. An illustration of the proposed algorithm is presented. The results of the computational experiments indicate that the presented algorithm outperforms existing algorithms. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Estimating value in a uniform auction

Consider an auction in which increasing bids are made in sequence on an object whose value θ is known to each bidder. Suppose n bids are received, and the distribution of each bid is conditionally uniform. More specifically, suppose the first bid X₁ is uniformly distributed on [0, θ], and the i^th bid is uniformly distributed on [X_i?1, θ] for i = 2, …?, n. A scenario in which this auction model is appropriate is described. We assume that the value θ is un known to the statistician and must be esimated from the sample X₁, X₂, …?, X_n. The best linear unbiased estimate of θ is derived. The invariance of the estimation problem under scale transformations in noted, and the best invariant estimation problem under scale transformations is noted, and the best invariant estimate of θ under loss L(θ, a) = [(a/θ) ? 1]² is derived. It is shown that this best invariant estimate has uniformly smaller mean-squared error than the best linear unbiased estimate, and the ratio of the mean-squared errors is estimated from simulation experiments. A Bayesian formulation of the estimation problem is also considered, and a class of Bayes estimates is explicitly derived.