Initial Velocity Of Fragments Research Articles

Influence of explosive type and constant γ in Mott’s stochastic model on terminal-ballistics parameters of high-explosive warheads using numerical simulations

The research examined the use of numerical simulations for high-explosive (HE) munitions. Lagrange and Euler solvers from Ansys Autodyn, whose brief theoretical synopsis is given, were utilized. Numerical program modeling of materials under dynamic loads (explosives and solid bodies) is also explained. The study also provides a brief summary of relevant research works that address numerical simulations of the fragmentation of HE projectiles (warheads). First, using data from other authors, the numerical model in this paper was effectively validated. The original research in the publication included an evaluation of the influence of explosive type on mass distribution, as well as velocity and the kinetic energy of fragments on cylindrical warheads, along with some recommendations and findings. Results show that ordered by values of initial fragment velocity are explosives: Trinitrotoluen (TNT), H6, Comp. B, Octol, PBX-9404-3, and LX-10-1. Explosives LX-10-1 and PBX-9404-3 showed similar performance because both explosives are HMX-based mixtures, with LX-10-1 having 0.5% more Octogen (HMX). The greatest (fastest) expansion of fragments (for the given time frame of 150 µs) is present in the most potent explosives (LX-10-1 and PBX-9404-3) since they have the largest detonation velocities. In the configurations with stronger explosives (Octol, LX-10-1, PBX-9404-3), the front and rear cover of the cylinder is more fragmented than in the case of weaker explosives. The highest number of fragments is obtained with PBX-9404-3 explosive, 142% higher than using TNT charge. Also, as part of the original research in the paper, an assessment of the influence of the constant γ in Mott’s stochastic fragmentation model on the mass distribution of fragments and their kinetic energy was made. Results indicate that constant γ has the greatest influence on the number of very small fragments, which can be used when calibrating this constant with experimental data. The masses of fragments are relatively uniform (for all γ values) up to the mass group of 50–100 g, above which the most massive fragments are obtained when γ = 5. Most of the fragments have relatively high energy where that is, fragments of mass 0.5–2 g have an average kinetic energy of 470–650 J, while fragments of masses 50–100 g have an average kinetic energy of 50–85 kJ. Described numerical simulations are a valuable tool for HE warhead designers, as they can minimize the time and expense associated with optimizing HE munition design and effectiveness evaluation when used in conjunction with available analytical techniques and experimentation procedures.

Experimental Study on the Effect of Buffer Layer on the Explosive Drive of Reactive Fragment

In order to study the influence of the buffer layer on the explosive drive of the reactive fragment, for the reactive fragment warhead of the same structure, the warhead static explosion test and the break-through target test method were used to test the fragment integrity and the fragment integrity of the reactive fragment warhead of the reactive fragment warhead with several different thickness silicone rubber buffer layers. The initial velocity of the fragment was measured, and its integrity and the variation law of the initial velocity were analyzed. The results show that with the increase of the thickness of the buffer layer, the integrity of the reactive fragments increases. When the thickness of the buffer layer is 2 mm, the fragment integrity rate is zero, and when the thickness of the buffer layer is greater than 8 mm, the integrity rate is greater than 0.85. The difference in the initial velocity of the warhead of the same reactive fragment is small, mainly because with the increase of the thickness of the buffer layer, the initial velocity of the fragment decreases mainly because the loading ratio of the warhead decreases; the buffer layer has a significant effect on reducing the initial velocity of the reactive fragment, and k=0.83 can be used The modified Gurney formula was used to estimate the initial velocity of the reactive fragments of the silicone rubber buffer layer.

Study on Axial Dispersion Characteristics of Double-Layer Prefabricated Fragments.

The axial distribution of initial velocity and direction angle of double-layer prefabricated fragments after an explosion were investigated via an explosion detonation test. A three-stage detonation driving model of double-layer prefabricated fragments was proposed. In the three-stage driving model, the acceleration process of double-layer prefabricated fragments is divided into three stages: "detonation wave acceleration stage", "metal-medium interaction stage" and "detonation products acceleration stage". The initial parameters of each layer of prefabricated fragments calculated by the three-stage detonation driving model of double-layer prefabricated fragments fit well with the test results. It was shown that the energy utilization rate of detonation products acting on the inner-layer and outer-layer fragments were 69% and 56%, respectively. The deceleration effect of sparse waves on the outer layer of fragments was weaker than that on the inner layer. The maximum initial velocity of fragments was located near the center of the warhead where the sparse waves intersected, located at around 0.66 times of the full length of warhead. This model can provide theoretical support and a design scheme for the initial parameter design of double-layer prefabricated fragment warheads.

Gurney velocity modification for detonation-driven steel cylindrical casings

Detonation-driven experiments for 2,4,6-trinitrotoluene in standard copper cylindrical casings and in 50SiMnVB and 45 steel cylindrical casings with three thicknesses were carried out in this study. The results showed that due to the influences of the coupled loading of the shock waves and the detonation products, the initial velocity of the fragments of the steel cylinders predicted using the Gurney formula and Gurney velocity obtained from a standard cylinder experiment significantly deviated from the experimental observations. This was caused by the difference in the cylinder density and the load coefficient β. Thus, a modified method and model of the Gurney velocity were proposed, and modification coefficients were obtained via a numerical simulation, which provided a means for a more accurate calculation of the initial velocity of fragments of the steel cylinder. Moreover, further analysis showed that at the same β value, the modified Gurney velocity of the copper cylinder was larger than that of the steel cylinder. The modified Gurney velocity of the same cylinders increased with the increase in the β value. The smaller the β value was, the larger the increase in the ratio was. When β > 0.8, the modified Gurney velocity became constant.

An overview of Gurney method for estimating the initial velocities of fragments for high explosive munition


 
 
 
 The literature survey, related to the initial velocity of fragments for HE ammunition is presented. The basic Gurney model for fragment initial velocity, that can be used for different munition configuration, is presented. The research we performed using the Gurney method for a different projectile types is given.
 
 
 

Method of evaluating energy released by a warhead charge based on average fragment quality

Abstract Limited initiation energy or external stimulation may cause incomplete detonation in a warhead. At present, there is no quantitative method to characterize the energy release of a warhead charge for incomplete detonation such as explosion and deflagration. We propose a method based on average fragment quality to characterize the energy released by a warhead charge. The theoretical study shows that the average fragment quality after warhead initiation is inversely proportional to the initial fragment velocity. The relationship between the average fragment quality and explosive energy release is established and verified by experiment. This relation can be used to determine the charge energy released after warhead initiation. It provides a theoretical basis for optimizing efficiency of charge energy use in high-energy conventional damage technology and warhead design, and provides a quantitative method for evaluating insensitive ammunition.

Experimental investigation on the velocity of the secondary fragments of reinforced concrete slabs under intensive dynamic load

The initial velocity of the secondary fragments of reinforced concrete slabs under blast loading is the basic data for the analysis of damage effect and it can also serve as important basis for the damage evaluation. In this study, three different types of reinforced concrete target slabs with different thicknesses were designed and prepared. These target slabs were investigated by local damage effect tests, the flying processes of the produced secondary fragments were recorded, and the velocities of the secondary fragments corresponding to different collapse coefficients were calculated by fragment back tracking. The results demonstrate that the initial velocity of the fragments was lower at a larger collapse coefficient. Based on the dimensional analysis results, the empirical formula of the initial velocity of the secondary fragments was derived. The errors between the calculated values according to the empirical formula and the experimental data were compared and found to be within 16% at a collapse coefficient in the range1.20–3.20m/kg1/3. Thus, the derived empirical formula can be used for predicting the initial velocity of the secondary fragments produced during the collapse of reinforced concrete slabs and also providing insightful reference for analyzing the damage power of the produced secondary fragments.

Optimization of the specific kinetic energy of the pre-grooved stun grenade fragments based on HyperMesh, LS-DYNA and Matlab

Large-scale fragments formed by packaging shell of stun grenade are easy to cause irreversible damage to human body in close range. In order to reduce the specific kinetic energy of shell fragments as much as possible, the pre-grooving method is proposed to optimize the safety of packaging shell. According to the process of fragment forming, flying and impacting, the shell breaking model, fragment dispersion model and average specific kinetic energy calculation model are established respectively. The non-grooved shell and inner grooved shell are simulated by the joint simulation method of HyperMesh, LS-DYNA and Matlab. The fragment mass distribution, initial velocity and average specific kinetic energy are obtained and compared. The results show that under the same main charge parameters, the mass distribution of fragments is more concentrated and the large mass fragments are less in the inner grooved shell than in the non-grooved shell; the average initial velocity of fragments in the inner grooved shell is lower than that in the non-grooved shell; the attenuation of average specific kinetic energy in the inner grooved shell is faster than that in the non-grooved shell, which is safer than that in the non-grooved structure.

Effect of the length-diameter ratio on the initial fragment velocity of cylindrical casing

The initial velocity of fragment from cylindrical casing, which detonates at one end along the central of the casing, is the key issue in the field of explosion technology and its protecting. Most of the formula available can predict the initial velocity or the velocity of fragments at middle part of the cylindrical casing with greater length-dimeter ratio (L/d>2). However, when the length-diameter ratio is less than two, the initial velocity of the cylindrical casing filled with explosives will have a big difference. In the present work, a numerical simulation model acknowledged by X-ray radiography experiments was used to determine the influence of the length-diameter ratio. The formula was built on top of the Gurney formula and made use of a correctional function to account for the effect of the length-dimeter ratio. The formula was further acknowledged with the established numerical simulation model. The results indicate that the calculation formula can accurately predict the initial fragment velocity with different length-diameter ratio (L/d⩽ 2).

Fragment Velocity Characteristics of Warheads with a Hollow Core under Asymmetrical Initiation

AbstractFragment velocity characteristics of warheads are key issues in the field of explosion technology and protection. However, the fragment velocity characteristics of a warhead with a hollow core under asymmetrical initiation are rarely touched. In this work, the effects of the diameter of the hollow core on the fragment velocities of warheads under asymmetrical initiation were investigated by experimentally verified numerical simulations. The results showed that the fragment velocity‐time curves exhibited a second time acceleration due to the collision of the shock/detonation wave and/or that of the detonation products. For warheads under symmetrical initiation, the second time acceleration becomes stronger, and then becomes slightly weaker with the increase of the diameter of the hollow core, due to the combined effects of bigger hollow core and less explosive charge mass. For warheads under asymmetrical initiation, the second time acceleration becomes more obvious with the increase of the diameter of the hollow core, because the larger shaped charge efficiency enhances the collision of the detonation products. A modified formula was proposed to predict the initial fragment velocity in the aiming direction of a warhead with a hollow core under asymmetrical initiation. Experimentally verified numerical simulations were then used to verify the formula and the results showed that the new formula could predict the velocity very well. This work could offer a good reference for the design of tunable effects warheads and aimable warheads.

Real-time calculation of fragment velocity for cylindrical warheads

Abstract To simulate explosion fragments, it is necessary to predict many variables such as fragment velocity, size distribution and projection angle. For active protection systems these predictions need to be made very quickly, before the weapon hits the target. Fast predictions also need to be made in real time simulations when the impact of many different computer models need to be assessed. The research presented in this paper focuses on creating a fast and accurate estimate of one of these variables - the initial fragment velocity. The Gurney equation was the first equation to calculate initial fragment velocity. This equation, sometimes with modifications, is still used today where finite element analysis or complex mathematical approaches are considered too computationally expensive. This paper enhances and improves Breech’s two-dimensional Gurney equation using available empirical data and the principals of conservation of momentum and energy. The results are computationally quick, providing improved accuracy for estimating initial fragment velocity. This will allow the developed model to be available for real-time simulation and fast computation, with improved accuracy when compared to existing approaches.

Experimental study on the expansion of metal cylinders by detonation

Detonation-driven metal cylinder acceleration is an important issue in the design of warheads, and calculating the initial velocity of fragments is an important part of this problem. In most previous experiments, the final expansion velocity and fracture behavior of the cylindrical casing were the main focus. However, the expansion and acceleration process of a cylindrical casing driven by internal explosion loading has not been well studied. To study the whole acceleration process of cylindrical casings under internal explosive load, a high-speed framing camera and an arrayed Doppler Photonic System (DPS) are used in the experiments in this paper. Three cylindrical casings made of TU1 copper, 50SiMnVB steel and ANSI 1045 steel were tested in the experiments. The velocity oscillations of the cylindrical casings were clearly captured in the experiments and analyzed theoretically. The experimental results show that the acceleration process of the cylindrical casings can be divided into two distinct phases: initial acceleration under the load of shock waves, and further acceleration under the load of detonation products. It was concluded that the acceleration process under the load of shock waves is highly dependent on the material of the cylindrical casings. The copper casing had higher wave impedance, and achieved higher velocity than the steel casings during the acceleration process under the load of shock waves. Furthermore, comparison of the two steel casings shows that the plasticity of the casing affects its rupture radius significantly, while the impact of the cylindrical casing on the final velocity is negligible.

General formula to calculate the fragment velocity of warheads with hollow core

In some novel warheads, the explosive charge is not compactly filled within the cylindrical casing but has a hollow core instead. However, most existing formulas can only predict the fragment velocity of warheads fully filled with explosive charge. In this work, through theoretical analysis and numerical simulations, a new formula was proposed to predict the initial fragment velocity of novel warheads with hollow core. The formula was built on top of the Gurney formula and made use of a correctional function to account for the effects of the rarefaction wave from the hollow core of the explosive charge on the fragment velocity. The formula showed good agreement with the experimental results in the validation tests. Hence, the proposed formula is suitable for predicting the initial fragment velocity of warheads with hollow core.

Velocity characteristics of fragments from prismatic casing under internal explosive loading

In this study, a prismatic casing, which is a part of a variable geometry device, is designed to improve the effectiveness of its impact distribution. The fragment velocity of the casing is investigated experimentally by high-speed photography. The experimental data indicate that the fragment velocities are influenced by the rarefaction wave from both the axial and transverse directions. In addition, the Parallel for Multi-material in Cell 3D (pMMIC-3D) hydrocode, coupled with the Lagrangian marker-point weighted method, is used to numerically investigate the fragmentation process of the prismatic casing. The numerical results confirm the considerable influence of the rarefaction wave on the fragment velocity. Therefore, a correction formula is proposed to calculate the initial fragment velocity on the basis of the experimental data. The agreement between the numerical results and corrected results confirms that the correction formula can be used to predict the fragment distribution of such prismatic casings.

Numerical Simulation of the Shell Fragments Damage-Field Based on ANSYS/LS-DYNA

Steinberg failure models based on Mott distribution in ANSYS/LS-DYNA was used on the formation of fragments.The forming process of the fragment damage field of the shell was simulated. The mass distribution、spatial distribution and the attenuation law of initial velocity of fragments are analyzed. The shell damage-field may serve as a basis for the future research on power of shell fragment to the targets.

Research on Initial Velocity and Penetration Ability of 50SiMnVB Steel Shell Formed Fragments

For 50SiMnVB steel shell formed fragments, AUTODYN-3D finite element software was applied to numerical simulate the process of fragment forming. The change law of velocity distribution of 50SiMnVB steel shell formed fragments under high energy explosive charge along the warhead axial was obtained. And the maximum velocity and penetration ability of 50SiMnVB steel shell formed fragments was researched by experiment. The result shows that, the whole process of shell breaking is about 70μs, and the velocity of shell expanding during it can be distributed to three phases called librating, accelerating and stability. The minimum initial velocity of fragments appears at where approaching detonation point, and its quantity is about 931.7m/s; The maximum initial velocity appears at where away from detonation point about 60% cylinder length, and its quantity is about 1488.3m/s. When fragment group penetrates 5mm thickness armor steel target with 1215m/s, its penetration probability is about 46.2%.

Numerical Study on Dispersion Characteristics and Damage Results of Pre-Fragment Warhead

The dispersion characteristics, damage region and destroy results of typical defending materials by pre-fragment warhead using explosively driven were numerical studied by non-linear finite code of LS-DYNA with fluid-structure interaction algorithm, meanwhile, the influence of different detonation types and explosive properties on dispersion characteristics and damage results of kinetic energy rod were analysed. Results show that: 1.fragments disperse symmetrically with greater damage region when center detonation and line detonate are adopted, and the dispersion velocity of fragments reach the maximum when line detonate is used; 2.explosive of higher detonation velocity in favour of improving the initial velocity of fragments, strengthing the damage ability; 3.the penetration kinetic energy of fragments increase with the decrease of axial angle between fragment and damage target.