Fragment spatial distribution of prismatic casing under internal explosive loading

Non-cylindrical casings filled with explosives have undergone rapid development in warhead design and explosion control. The fragment spatial distribution of prismatic casings is more complex than that of traditional cylindrical casings. In this study, numerical and experimental investigations into the fragment spatial distribution of a prismatic casing were conducted. A new numerical method, which adds the Lagrangian marker points to the Eulerian grid, was proposed to track the multi-material interfaces and material dynamic fractures. Physical quantity mappings between the Lagrangian marker points and Eulerian grid were achieved by their topological relationship. Thereafter, the fragment spatial distributions of the prismatic casing with different fragment sizes, fragment shapes, and casing geometries were obtained using the numerical method. Moreover, fragment spatial distribution experiments were conducted on the prismatic casing with different fragment sizes and shapes, and the experimental data were compared with the numerical results. The effects of the fragment and casing geometry on the fragment spatial distributions were determined by analyzing the numerical results and experimental data. Finally, a formula including the casing geometry parameters was fitted to predict the fragment spatial distribution of the prismatic casing under internal explosive loading.     

Influence of Al2O3 particles on the microstructure and mechanical properties of copper surface composites fabricated by friction stir processing

The influence of three factors, such as volume percentage of reinforcement particles (i.e. Al₂O₃), tool tilt angle and concave angle of shoulder, on the mechanical properties of Cu–Al₂O₃ surface composites fabricated via friction stir processing was studied. Taguchi method was used to optimize these factors for maximizing the mechanical properties of surface composites. The fabricated surface composites were examined by optical microscope for dispersion of reinforcement particles. It was found that Al₂O₃ particles are uniformly dispersed in the stir zone. The tensile properties of the surface composites increased with the increase in the volume percentage of the Al₂O₃ reinforcement particles. This is due to the addition of the reinforcement particles which increases the temperature of recrystallization by pinning the grain boundaries of the copper matrix and blocking the movement of the dislocations. The observed mechanical properties are correlated with microstructure and fracture features.     

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.     

Parametric study of single confined fragment launch explosive device

In this article, parametric study of single confined fragment launch device was carried out. The configuration proposed was further studied to derive the empirical relationship for effect of fragment size, charge size, confinement thickness on fragment velocity. The simulations were carried out using ANSYS-AUTODYNE explicit solver. Fragment velocities were estimated as a function of different parametric combinations of explosive quantities, charge length to diameter ratio, fragment height to diameter ratio, confinement thickness, fragment material and fragment mass. The data was further converted to charge to metal ratio under fragment and confinement. It was observed that, increase in confinement thickness, charge quantity and decrease in fragment height increases the fragment velocity. It is also noted that, charge to metal mass ratio under fragment significantly affects the fragment velocity. At the end, an empirical relationship for fragment velocity interms of all these parameters was established. Using these relations, two velocities 1831.92 m/s and 2523.9 m/s required for NATO STANAG 4496 IM test were estimated. The design parameters for these velocities are presented. Also, the results estimated using the empirical relationship has been compared with published experimental data. Error in the predicted velocities is within the acceptable range. The empirical relationship proposed will be useful for finalization of design of the fragment launch device.     

On computing the expected discounted return in a markov chain

The discounted return associated with a finite state Markov chain X₁, X₂… is given by g(X₁)+ αg(X₂) + α²g(X₃) + …, where g(x) represents the immediate return from state x. Knowing the transition matrix of the chain, it is desired to compute the expected discounted return (present worth) given the initial state. This type of problem arises in inventory theory, dynamic programming, and elsewhere. Usually the solution is approximated by solving the system of linear equations characterizing the expected return. These equations can be solved by a variety of well-known methods. This paper describes yet another method, which is a slight modification of the classical iterative scheme. The method gives sequences of upper and lower bounds which converge mono-tonely to the solution. Hence, the method is relatively free of error control problems. Computational experiments were conducted which suggest that for problems with a large number of states, the method is quite efficient. The amount of computation required to obtain the solution increases much slower with an increase in the number of states, N, than with the conventional methods. In fact, computational time is more nearly proportional to N², than to N³.     

Approximating partial inverse moments for certain normal variates with an application to decaying inventories

This paper considers the problem of computing E(X^?n; X > t) when X is a normal variate having the property that the mean is substantially larger than the standard deviation. An approximation is developed which is determined from the mean, standard deviation, and the cumulative standard normal distribution. Computations comparing the approximate moments with the actual are reported for various values of the relevant parameters. These results are applied to the problem of computing the expected number of shortages in a lead-time for a single product which exhibits continuous exponential decay.     

基于轮廓特征的空间目标识别算法

高分辨力单脉冲雷达通过对三个通道回波成像可以获取各个散射中心的方位角和俯仰角,结合距离信息就可以得到各个散射中心在垂直于雷达天线轴的平面上的投影,形成方位-俯仰二维像.由于卫星的尺寸通常大于碎片的尺寸,因此卫星的方位-俯仰二维像的轮廓面积较大.提出了基于轮廓特征的空间目标识别算法,首先通过高分辨力单脉冲雷达对目标进行方位-俯仰二维像成像,然后从方位-俯仰二维像中提取目标轮廓,最后根据轮廓面积特征对卫星和碎片进行识别.经过计算机仿真实验,该算法取得了比较好的识别效果.     

Problem of the reference height of the projectile trajectory as a reduced meteo-ballistic weighting factor

This paper deals with the issue of preparation of the aiming angles with the use of tabular firing tables and needed determination of the ballistic elements μ_B (ballistic wind w_B, w_xB, w_ZB, ballistic (virtual) temperature τ_B, ballistic density ρ_B) from the standardized met messages. The weighting factors are used for the calculation of ballistic elements μ_B that are incorporated into the trajectory calculations characteristics of weapon and ammunition. Two different methodologies practically used in the praxis are analysed and compared. For the comparison of the two methodologies the reference height of trajectory determined from the weighting factor functions is employed. On the basis of the analyses conducted, the potential for further increase in accuracy of these aiming angles preparation methods is pointed out.     

爆轰波斜冲击作用下破片飞散特性研究

为研究非对称结构战斗部的破片飞散特性,利用斜激波理论对爆轰波作用于壳体表面的过程进行研究,并利用自由面速度倍增定律对波在自由面反射后质点速度的计算进行简化,得到了破片飞散角的计算模型。利用D型战斗部试验数据对计算模型进行验证,结果表明,斜激波理论计算得到的破片飞散与试验结果吻合很好;当入射角较小时,壳体飞散角与入射角成线性关系。     

Fullerene bisadduct stabilizers: The effect of different addition positions on inhibiting the autocatalytic decomposition of nitrocellulose absorbed nitroglycerin

To explore the effect of different positions and number of pyrrolidine bound to the carbon cage on the stabilization effect of fulleropyrrolidine derivatives to nitrocellulose (NC)/nitroglycerine (NG), we synthesized N-(4-methoxy) phenylpyrrolidine-C₆₀ and four different of bis(N-(4-methoxy) phenylpyrrolidine)-C₆₀ compounds through Prato reaction. Their structures were characterized by UV–vis, ¹H NMR, ¹³C NMR, high-resolution mass spectroscopy, and single-crystal X-ray diffraction. Their stabilization effect to NC/NG were investigated using differential scanning calorimetry, methyl violet, vacuum stabilization effect, weight loss, and accelerating rate calorimeter tests. The results indicated these compounds had excellent stabilization effect to NC/NG. The stabilization effect of the fulleropyrrolidine bisadducts to NC/NG is significantly better than that of fulleropyrrolidine monoadduct and C₆₀. Moreover, the position where pyrrolidine binds to fullerene in fulleropyrrolidine bisadducts is different, and its stabilization effect to NC is also different. The stabilization effect order of different bisadduct isomers to nitrocellulose is as follows: e-edge > trans-2> cis-2> trans-3. Electron paramagnetic resonance (EPR) and FT-IR were used to study the stabilization mechanism of fulleropyrrolidine derivatives to NC/NG. The EPR results also show that fulleropyrrolidine bisadducts with different addition sites have different abilities to absorb nitroxide, and their ability is better than that of the monoadduct and C₆₀, which is consistent with the results of stabilization effect performance test.     

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.     

Structure design and property adjustment of new cage rich-nitrogen pentazolyltetraazacubanes as potential high energy density compounds

In this study, based on two attractive energetic compounds pentazole (PZ) and tetraazacubane (TAC), a new family of high energy and high nitrogen compounds pentazolyltetraazacubanes were designed. Then, a different number of NH₂ or NO₂ groups were introduced into the system to further adjust the property. The structures, properties, and the structure-property relationship of designed molecules were investigated theoretically. The results showed that all nine designed compounds have extremely high heat of formation (HOF, 1226-2734 kJ/mol), good density (1.73–1.88 g/cm³), high detonation velocity (8.30–9.35 km/s), high detonation pressure (29.8–39.7 GPa) and acceptable sensitivity (ΔV: 41-87 ų). These properties could be effectively positive adjusted by replacing one or two PZ rings by NH₂ or/and NO₂ groups, especially for the energy and sensitivity performance, which were increased and decreased obviously, respectively. As a result, two designed pentazolyltetraazacubanes were predicted to have higher energy and lower sensitivity than the famous high energy compound in use 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane, while two others have better combination property than 1,3,5-Trinitro-1,3,5-triazacyclohexane. In all, four new pentazolyltetraazacubanes with good combination performance were successfully designed by combining PZ with TAC, and the further property adjustment strategy of introducing a suitable amount of NH₂/NO₂ groups into the system. This work may help develop new cage energetic compounds.     

A note on circular error probabilities

An approximation for P(X² + Y² ≤ K²σ²₁) based on an unpublished result of Kleinecke is derived, where X and Y are independent normal variables having zero means and variances σ²₁ and σ²₂ and σ₁ ≥ σ₂. Also, we provide asymptotic expressions for the probabilities for large values of β = K²(1 - c²)/4c² where c = σ₂/σ₁. These are illustrated by comparing with values tabulated by Harter [6]. Solution of K for specified P and c is also considered. The main point of this note is that simple and easily calculable approximations for P and K can be developed and there is no need for numerical evaluation of integrals.     

Investigation on the spatial distribution characteristics of behind-armor debris formed by the perforation of EFP through steel target

The behind-armor debris (BAD) formed by the perforation of an EFP is the main damage factor for the secondary destruction to the behind-armor components. Aiming at investigating the BAD caused by EFP, flash X-ray radiography combined with an experimental witness plate test method was used, and the FEM-SPH adaptive conversion algorithm in LS-DYNA software was employed to model the perforation process. The simulation results of the debris cloud shape and number of debris were in good agreement with the flash X-ray radiographs and perforated holes on the witness plate, respectively. Three-dimensional numerical simulations of EFP's penetration under various impact conditions were conducted. The results show that, an ellipsoidal debris cloud, with the major-to-minor axis radio (a/b) smaller than that caused by shaped charge jets, was formed behind the target. With the increase of target thickness (h) and decrease of impact velocity (v₀) and obliquity (θ), the value of a/b decreases. The number of debris ejected from target is significantly higher than that from EFP. Based on the statistical analysis of the spatial distribution of the BAD, An engineering calculation model was established considering the influence of h, v₀ and θ. The model can with reasonable accuracy predict the quantity and velocity distribution characteristics of BAD formed by EFP.     

Estimation of ordered parameters from k stochastically increasing distributions

There are given k (? 2) univariate cumulative distribution functions (c.d.f.'s) G(x; θ_i) indexed by a real-valued parameter θ_i, i=1,…, k. Assume that G(x; θ_i) is stochastically increasing in θ_i. In this paper interval estimation on the i^th smallest of the θ's and related topics are studied. Applications are considered for location parameter, normal variance, binomial parameter, and Poisson parameter.     

Estimating the accuracy of the coverages of outer β-content tolerance intervals,which control both tails of the normal distribution

Tolerance limits which control both tails of the normal distribution so that there is no more than a proportion β₁ in one tail and no more than β₂ in the other tail with probability γ may be computed for any size sample. They are computed from X? - k₁S and X? - k₂S, where X? and S are the usual sample mean and standard deviation and k₁ and k₂ are constants previously tabulated in Odeh and Owen [3]. The question addressed is, “Just how accurate are the coverages of these intervals (– Infin;, X? – k₁S) and (X? + k₂S, ∞) for various size samples?” The question is answered in terms of how widely the coverage of each tail interval differs from the corresponding required content with a given confidence γ′.     

Shock-induced reaction behaviors of functionally graded reactive material

In this paper, the ballistic impact experiments, including impact test chamber and impact double-spaced plates, were conducted to study the reaction behaviors of a novel functionally graded reactive material (FGRM), which was composed of polytetrafluoroethylene/aluminum (PTFE/Al) and PTFE/Al/bismuth trioxide (Bi₂O₃). The experiments showed that the impact direction of the FGRM had a significant effect on the reaction. With the same impact velocity, when the first impact material was PTFE/Al/Bi₂O₃, compared with first impact material PTFE/Al, the FGRM induced higher overpressure in the test chamber and larger damaged area of double-spaced plates. The theoretical model, which considered the shock wave generation and propagation, the effect of the shock wave on reaction efficiency, and penetration behaviors, was developed to analyze the reaction behaviors of the FGRM. The model predicted first impact material of the FGRM with a higher shock impedance was conducive to the reaction of reactive materials. The conclusion of this study provides significant information about the design and application of reactive materials.     

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.     

Confidence intervals for ranked means

Suppose that observations from populations π₁, …, π_k (k ≥ 1) are normally distributed with unknown means μ₁., μ_k, respectively, and a common known variance σ². Let μ_[1] μ … ≤ μ_[k] denote the ranked means. We take n independent observations from each population, denote the sample mean of the n observation from π₁ by X _i (i = 1, …, k), and define the ranked sample means X _[1] ≤ … ≤ X _[k]. The problem of confidence interval estimation of μ₍₁₎, …,μ_[k] is stated and related to previous work (Section 1). The following results are obtained (Section 2). For i = 1, …, k and any γ(0 < γ < 1) an upper confidence interval for μ_[i] with minimal probability of coverage γ is (? ∞, X _[i]+ h) with h = (σ/n^1/2) Φ^?1(γ^1/k-i+1), where Φ(·) is the standard normal cdf. A lower confidence interval for μ_[i] with minimal probability of coverage γ is (X _i[i] – g, + ∞) with g = (σ/n^1/2) Φ^?1(γ^1/i). For the upper confidence interval on μ_[i] the maximal probability of coverage is 1– [1 – γ^1/k-i+1]ⁱ, while for the lower confidence interval on μ_[i] the maximal probability of coverage is 1–[1– γ^1/i] ^k-i+¹. Thus the maximal overprotection can always be calculated. The overprotection is tabled for k = 2, 3. These results extend to certain translation parameter families. It is proven that, under a bounded completeness condition, a monotone upper confidence interval h(X ₁, …, X _k) for μ_[i] with probability of coverage γ(0 < γ < 1) for all μ = (μ_[1], …,μ_[k]), does not exist.     

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.