Phenomenological aspects of a modified fragmentation test using small quantities of explosive

This paper describes the phenomenological aspects of a modified fragmentation test which utilizes an annulus of high explosive in contact with the inner wall of a cylinder of material under test. The shock interactions within the cylinder wall on detonation of the explosive are modelled using a one-dimensional Lagrangian computer code. Predictions of fragment velocities are made in this work. The velocities are found to be influenced by the spallation of the cylinder and this effect can be accounted for in the model by using the position of the spall surfaces which have been obtained from experimental firings of cylinders.

The fragment velocities are found to be much lower than those predicted for a conventional fragmentation test which utilizes a cylinder completely filled with high explosive and this suggests that the post-fragmentation damage of the fragments on recovery from the modified fragmentation test will be small. Experimental evidence from the steel cylinders tested in this work shows that the fragmentation mechanisms operating at the initiation of the test are similar to those reported for a conventional fragmentation test.     

圆柱形战斗部爆炸破片特性研究

有端部封盖的圆柱形战斗部爆炸产生破片的特征很难用理论公式确定,而在战斗部接近爆炸情况下,爆炸破片的分布将直接影响结构的破坏模式。该文采用数值计算方法对有端部封盖的圆柱形战斗部爆炸时壳体破裂形成自然破片的过程进行了数值模拟,研究了战斗部壳体产生的破片空间分布及速度特性,探讨了破片尺寸的影响因素,并将破片的速度分布特性与相关实验结果进行了对比分析。结果表明:有端部封盖的圆柱形战斗部爆炸时,远离起爆点的端部封盖形成的破片速度最大,圆柱形壳体高度方向上的破片的质量差异是由破片的长度尺寸引起,圆柱形壳体轴向(沿高度方向)的膨胀应变率的差值是破片长度的主要决定因素。远离起爆点的壳体轴向膨胀应变率差值较小,是破片长度尺寸较大的主要原因。     

Tungsten long-rod penetration into confined cylinders of boron carbide at and above ordnance velocities

The purpose was to investigate the influence of impact velocity and confinement on the resistance of boron carbide targets to the penetration of tungsten long-rod projectiles. Experimental tests with impact velocities from 1400 to 2600 m/s were performed using a two-stage light-gas gun and a reverse impact technique. The targets consisted of boron carbide cylinders confined by steel tubes of various thicknesses. Simulations were carried out using the AUTODYN-2D code and Johnson–Holmquist's constitutive model with and without damage evolution. The experimental results show that the penetration process had different character in three different regions. At low-impact velocities, no significant penetration occurred. At high-impact velocities, the relation between penetration velocity and impact velocity was approximately linear, and the penetration was steady and symmetrical. In between, there was a narrow transition region of impact velocities with intermittent and strongly variable penetration velocity. In the lower part of this region, extended lateral flow of the projectile took place on the surface of the target. The influence of confinement on penetration velocity was found to be small, especially at high-impact velocities. The simulated results for penetration velocity versus impact velocity agreed fairly well with the experimental results provided damage evolution was suspended below the transition region.     

Experimental observations and computer simulations for metallic projectile fragmentation and impact crater development in thick metal targets

Stainless steel (3.18 mm diameter) spherical projectiles impacting 2.5 cm thick targets of nickel, copper, 304 stainless steel, and 70/30 brass at velocities ranging from 0.52 to 5.12 km/s were observed by SEM to form decreasing average fragment sizes with increasing impact velocity, beyond a fragmentation onset velocity of 0.7 km/s. Crater observations by optical microscopy and SEM were qualitatively simulated using an AUTODYN numerical analysis code, which also illustrated a decrease in fragmentation density within the target craters with increasing impact velocity. However, extrapolated simulations corresponding to impact velocities as high as 10 km/s showed residual fragmentation within these craters in contrast to extrapolations of the experimental fragment size versus impact velocity data indicative of zero fragment size at 6 km/s.     

Analysis of high-explosive fragmenting shell impact into spaced plates

This paper describes an integrated experimental and numerical analysis approach to study the impact of an explosive-filled fragmenting shell into spaced plates. Although the initial impact velocity of the fragmenting shell into the first plate is around 1 km/s, the free-flight velocity of the fragment may become up to 2 km/s. For the first set of experiment impacting into spaced steel plates, the second compartment steel plate was perforated by the fragments and three holes were observed. A separate experiment was carried out with the support of S2-glass composite plate to the second plate. In this case, the second plate was able to capture the fragments. To acquire better understanding of the fragmenting shell impact into spaced plates, computational efforts were undertaken using both SPH and Lagrangian techniques with the support of the experimental data.     

Ballistic penetration of steel plates

This paper presents a research programme in progress where the main objective is to study the behaviour of Weldox 460 E steel plates impacted by blunt-nosed cylindrical projectiles in the lower ordnance velocity regime. A compressed gas gun is used to carry out high-precision tests, and a digital high-speed camera system is used to photograph the penetration process. A coupled constitutive model of viscoplasticity and ductile damage is formulated and implemented into the non-linear finite element code LS-DYNA, and the material constants for the target plate are determined. The proposed model is applied in simulations of the plate penetration problem and the results are compared with test data. Good agreement between the numerical simulations and the experimental results is found for velocities well above the ballistic limit, while the ballistic limit itself is overestimated by approximately 10% in the numerical simulations.     

Prediction of Distortion of Cylinders without Phase Transformations

The rule of Ameen whereby steel made cylinders with no phase transformations during quenching approach the spherical shape is contrary to the finding of Berger, who observes an elongation of thin and long work pieces. If the prediction of Ameen is correct, cylinders should decrease in length during heat treatment. This paper describes a first step of broader investigation of strain hardening and distortion of cylinders during gas quenching in a gas nozzle field. To make more general predictions about the distortion of cylinders which show no phase transformations during heat treatment, different dimensions of cylinders (lengths 50 mm, 100 mm and 200 mm, diameters 10 mm up to 100 mm) were investigated by means of numerical and experimental methods. The prediction of dimension and shape changes during gas quenching of steel cylinders has been performed by numerical simulation using the commercial Finite Element Program SYSWELD. The austenitic steel SAE30300 (German grade X8CrNiS18.9) was selected as investigated material; it shows no phase transformations during performed heating and cooling. The investigations show a good agreement between the kinematic strain hardening model and the experimental data, whereas the isotropic model is not in line with the experimental data. If the ratio of length and diameter is greater than 3, the relative changes in length displayed against the Biot number give uniform curves for all investigated geometries and heat transfer coefficients.     

Mixed convection of non-Newtonian nanofluid in an H-shaped cavity with cooler and heater cylinders filled by a porous material: Two phase approach

In the present problem, two-phase mixed convection of a non-Newtonian nanofluid in a porous H-shaped cavity is studied. Inside the enclosure there are four rotating cylinders, using the Boussinesq approximation, mixed convection is created. Nanofluid includes H₂O + 0.5% CMC and copper oxide nanoparticles. The mixture model was used to model physical phenomena. Different aspect ratios were used in order to achieve the best heat transfer rate. The Darcy and Richardson numbers ranges are 10⁻⁴ ≤ Da ≤ 10⁻² and 1 ≤ Ri ≤ 100 respectively. Also, the aspect ratio and dimensionless angular velocities of cylinders ranges are 1.4 ≤ AR ≤ 1.6 and −10 ≤ Ω ≤ 10 respectively. Streamlines and isotherm-lines contours have been obtained for the variation of Darcy and Richardson numbers, aspect ratio and angular velocity. The heat transfer rates have been obtained for various aspect ratios, Darcy and Richardson numbers, and the direction of the cylinder's rotation, and are compared with each other. The results show that the direction of cylinders rotation influences the strength and extent of the generation vortices. Also, the use of porous material in high permeability can be a good alternative to lowering the angular velocity of the cylinders and ultimately reducing the need for less energy.     

CFD modeling of dilute phase pneumatic conveying in a horizontal pipe using Euler–Euler approach

ABSTRACT

Computational fluid dynamics simulations were performed to investigate the behavior of dilute phase pneumatic conveying of plastic pellets in a horizontal circular pipe. The pellets are 200?µm in diameter and 1000?kg/m³ in density. A parametric study was performed to investigate the effects of turbulence model and model collision parameters on pressure drop, solid’s volume fraction and velocity profiles. Among model collision parameters, specularity coefficient has considerable effect on the pressure drop. Moreover, the results from simulations carried out for different solid loadings and velocities were compared with experimental data found in the literature. The air velocities range from 6 to 15?m/s and solids to air mass flow ratios range from 1 to 3. At higher air velocities, the pressure drops predicted by the standard k-omega turbulence model are higher than the pressure drops predicted by the standard k-epsilon model. In contrast, at lower gas velocities, the standard k-epsilon model predicts higher pressure drops compared to the standard k-omega turbulence model. However, no significant difference in solids and air velocity profiles is observed for the two different turbulence models.     

Drying of saturated lightweight concrete: an experimental investigation

The changes of moisture content during drying are experimentally investigated in the present work. Particular emphasis is placed on the initial stage of drying of saturated concrete, when moisture contents are high, since the resistance of the material to several deterioration processes is reduced at high moisture content levels, and experimental data for this stage of drying is lacking. The experimental investigation is performed for concrete cylinders of different lengths with one end exposed to drying. In this way, moisture flow is forced to be unidirectional. The gravimetric method is employed to obtain moisture content distribution in the material at different times of drying. The cylinders are made of lightweight concrete with varying water-to-cement ratios and moist curing times, and the influence of these variables upon the drying process is assessed. Higher initial water content and more rapid changes of water content occur in lightweight concrete with a higher w/c ratio. An increased moist-curing period results in a decrease of drying rates throughout the drying process.     

Introduce a new model for expansion behavior of thick‐walled cylinder under internal dynamic loading based on theoretical analysis

Given the numerous applications of thick‐walled cylinders, it is important to know the behavior of these structures. There are so many relationships for cylinders and spheres under dynamic loading which have been found mainly based on other experimental models. Hence derive an analytical model of the behavior of structures under internal and high‐rate loading is of great importance. The main objective of this paper is to derive a mathematical model of isotropic thick‐walled aluminum under internal high strain rate loading. The strength model the present analysis is based on the Cowper‐Symonds in which strain rate at each moment is used for calculation of dynamic strength according to that. Therefore, given the instantaneous internal loading pressure boundary conditions as well as instantaneous strain rate and its impact on the dynamic strength of the material, is of importance points in this paper. With employing equations of equilibrium in thick‐walled cylinders, the equations of radial and circumferential stresses and radial velocities derived. Given the instantaneous geometric and boundary conditions and correction the dynamic stress of material with respect to the strain rate, radial velocity by solving the differential equation, is calculated. After extraction of radial velocity, other stress equations will be evaluated. Furthermore, with considering the assumptions and in order to assess the overall results of the analytical modeling, computer simulation was done using Autodyn software, which shows good agreement with the analytical results.     

The effect of target strength on the perforation of steel plates using three different projectile nose shapes

The effect of target strength on the perforation of steel plates is studied. Three structural steels are considered: Weldox 460 E, Weldox 700 E and Weldox 900 E. The effects of strain hardening, strain rate hardening, temperature softening and stress triaxiality on material strength and ductility are determined for these steel alloys by conducting three types of tensile tests: quasi-static tests with smooth and notched specimens, quasi-static tests at elevated temperatures and dynamic tests over a wide range of strain rates. The test data are used to determine material constants for the three different steels in a slightly modified version of the Johnson–Cook constitutive equation and fracture criterion.Using these three steel alloys, perforation tests are carried out on 12 mm-thick plates with blunt-, conical- and ogival-nosed projectiles. A compressed gas gun was used to launch projectiles within the velocity range from 150 to 350 m/s. The initial and residual velocities of the projectile were measured, while the perforation process was captured using a digital high-speed camera system. Based on the test data the ballistic limit velocity was obtained for the three steels for the different nose shapes. The experimental results indicate that for perforation with blunt projectiles the ballistic limit velocity decreases for increasing strength, while the opposite trend is found in tests with conical and ogival projectiles. The tests on Weldox 700 E and Weldox 900 E targets with conical-nosed projectiles resulted in shattering of the projectile nose tip during penetration.Finally, numerical simulations of some of the experimental tests are carried out using the non-linear finite element code LS-DYNA. It is found that the numerical code is able to describe the physical mechanisms in the perforation events with good accuracy. However, the experimental trend of a decrease in ballistic limit with an increase in target strength for blunt projectiles is not obtained with the numerical models used in this study.     

Numerical and experimental studies of high-velocity impact fragmentation

Developments are reported in both numerical and experimental capabilities for characterizing the debris spray produced in penetration events. We have performed a series of high-velocity experiments specifically designed to examine the fragmentation of the projectile during impact. High-strength, well-characterized steel spheres (6.35 mm diameter) were launched with a two-stage light-gas gun to velocities in the range of 3 to 5 km/s. Normal impact with PMMA plates, thicknesses of 0.6 to 11 mm, applied impulsive loads of various amplitudes and durations to the steel sphere. The extent of fragmentation, loss in momentum, and divergence of the debris are shown to correspond to the impact conditions. Multiple flash radiography was used to monitor material motion and fragmentation of the steel sphere during the impact event. Dynamic fragmentation theories, based on energy-balance principles, were used to evaluate local material deformation and fracture state information from CTH, a three-dimensional Eulerian solid dynamics shock wave propagation code. The local fragment characterization of the material defines a weighted fragment size distribution, and the sum of these distributions provides a composite particle size distribution for the steel sphere. The calculated axial and radial velocity changes agree well with experimental data, and the calculated fragment sizes for a specific experiment are in qualitative agreement with the radiographic data.     

Propagation of hypervelocity impact fragment clouds in pressure gas

This study investigated the propagation of hypervelocity impact fragment clouds in pressure gas. Fragment clouds were generated through perforation of thin aluminium bumper plates by spherical aluminium projectiles. A thick aluminium backwall plate, placed inside a pressure container at a given distance from the bumper plate, caught the fragments to act as a witness plate for the residual damage potential of the fragments. Crater depth statistics are presented as a function of container pressure. The fragment cloud was photographed by means of an image converter camera. The images showed a strong deformation of the fragment cloud for increased container pressures and were used to extract residual velocities until up to 50 μs after impact. The deceleration of the velocity as a function of time after impact suggested an exponential decay function as the best fit to the curve. Thus, maximum fragment impact velocities on the backwall plate could be extrapolated from the axial cloud velocities. The extrapolated curves were compared with experimental time-of-flight measurements, and proved a good match. Fragment impact velocities and maximum crater depths were used to calculate maximum fragment particle sizes as a function of the container gas pressure.     

Numerical simulation of hypervelocity impact on CFRP/Al HC SP spacecraft structures causing penetration and fragment ejection

A representative carbon fiber reinforced plastic/aluminum honeycomb sandwich panel (CFRP/Al HC SP) spacecraft structure has been modeled in the hydrocode AUTODYN using the state-of-the-art ADAMMO material model [Riedel W, Harwick W, White D, Clegg R. Advanced material damage models for numerical simulation codes. ESA CR(P) 4397, 2003] to study the performance of the structure during impact events that cause perforation and fragment ejection. A new procedure combining a series of existing theoretical methods has been developed and applied to derive a full set of coarse material data. The data set has been implemented in AUTODYN, and the results of the numerical simulation have been compared to experimental impact test data. For impact tests performed near the structural ballistic limit, quantitatively accurate results were obtained over a range of impact velocities and angles. A further increase in the projectile size resulted in significant destruction of the sandwich panel front face-sheet and diversion from the experimental damage measurements. Inspection of the numerical model has shown non-localized propagation of inter-laminar delaminations, possibly caused by an under-prediction of the laminate dynamic inter-laminar tensile strength. The effects of the delamination propagation occur over an extended time scale and were not found to affect the state and trends of the fragment cloud ejected into the satellite interior. Accordingly, experimental trends of fragment cloud dispersion have been qualitatively reproduced.     

高能炸药驱动下弹体膨胀破碎过程试验研究

为了获得高能炸药驱动下战斗部壳体破碎机理,选取新型弹体材料30CrMnSiNi2A钢、40CrMnSiB钢以及典型弹体材料50SiMnVB钢,采用超高速摄影技术拍摄壳体静爆,获得了不同弹体材料壳体膨胀破碎过程,引入弹体径向膨胀系数,建立了考虑弹体材料性能影响的壳体径向膨胀距离随时间变化的函数关系式,并试验测定了三种材料弹体形成破片的最大初速。分析试验结果发现,新型弹体材料壳体膨胀速度和破片初速更大,相比50SiMnVB钢壳体,30CrMnSiNi2A钢和40CrMnSiB钢壳体形成破片的最大初速分别提高了19.0%和31.9%。不同合金钢材料壳体形成破片初速沿壳体轴向分布规律相同,最大初速出现在距起爆点约70%圆筒长度处。该研究结果将为杀爆战斗部壳体材料选取及设计提供参考依据。     

Gas–Liquid Interfacial Friction Factor for the Transition from Stratified to Slug Flow

Calculations based on the slug stability model and simplified stratified flow model provide predictions of the critical liquid height and the critical superficial velocities of a stratified flow for the transition to a slug flow in a horizontal pipe. Since slug flow derives from different interfacial waves patterns, previous interfacial waves model in stratified gas–liquid flows brings about the discrepancy between theoretical prediction and experimental data. A partial analysis for this behavior is given, which recognizes that the values of gas–liquid interfacial friction factor at the onset of slug flow have been underestimated, especially at high gas flows, and they should be obtained indirectly from other measured variables. Modified correlations for the interfacial friction factor are presented and better agreement between predicted and measured critical superficial velocities has been obtained.     

Agglomerating fluidization of group C particles: major factors of coalescence and breakup of agglomerates

An experimental study was carried out to determine the influence of different superficial gas velocities on the agglomerates of cohesive particles. The probability of agglomerate coalescence and breakup is proposed on the basis of the principle of force balance. Theoretical analysis shows that the higher superficial gas velocity and fluid density, the lower the particle cohesion, and that collisions between small and large agglomerates are advantageous for the agglomerating fluidization of cohesive particles. The average agglomerate size estimated by the model of force balance decreases with increasing superficial gas velocity, which is in agreement with experimental data.