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A theoretical investigation of the penetration properties of hollow particles


INTERNATIONAL JOURNAL OF IMPACT ENGINEERING PERGAMON
International Journal of Impact Engineering 26 (2001) 523-531 www.elsevier.condiocate/ijimpeng A THEORETICAL PENETRATION INVESTIGATIO

N OF HOLLOW OF THE PARTICLES PROPERTIES

J. T. M I L L S and J. P. C U R T I S Defence Evaluation and Research Agency, Fort Halstead, Sevenoaks,Kent TNI4 7BP, UK Abstraet-A novel investigation of the impact of hollow shaped charge jet particles on a steel target is made. The range of impact speeds considered is 2 to 8 kin/s, the upper limit of which is greatly above the ranges considered in previous studies of such impacts. An Eulerian hydrocode developed within DELIAis used. The code has been validated for this application by reproduction of previous work at lower impact speeds and by a large body of earlier work on shaped charges. Idealised particles having axisymmetric inner hollows and outer surfaces are considered. It is shown that the penetration achieved by a single individual hollow particle is much the same as that for a solid one of the same mass. However, we demonstrate the formation of a reverse jet travelling back through the hollow, analogous to the jets seen by earlier workers, but travelling much faster. This jet can cause significant disruption to the following particles. It is concluded that the presence of hollowness is likely to cause significant disruption to the penetration process in real jets. Crown copyright? 2001 Published by Elsevier Science Ltd. All rights reserved.

Keywords: shaped charge jets, hollow particles, penetration, reversejet
INTRODUCTION There are several factors that limit the penetration performance of shaped charge jets. This paper investigates one such potential mechanism of degradation - the presence of hollowness in the jet particles. Other mechanisms are known to be important. For example, lateral velocity components along the jet can cause the jet particles to collide with the side wall of the crater. Although such collisions may enlarge the crater the particles concerned will usually not reach its bottom and increase its length. Spallation may be created which will damage the jet. Other degradation mechanisms can include particle tumbling, particle shape and the necking in particle pairs and linked sets of higher numbers of particles. We do not address these other mechanisms here, but refer the reader to an accompanying paper at this Symposium [1] for a more detailed discussion. The aim of the work was to predict the effect on penetration performance that results from having a hollow, instead of a solid, particle impact on a target, with the goal of identifying degradation factors that could be applied in analytical penetration. In view of the multiple freesurfaces present, any attempt to model this time-dependent problem analytically poses significant challenges. Mention must be made here of analytical work by Franzen [2]. However, that work was limited to an investigation of the steady-state case. An Eulerian computational continuum dynamics (CCD) code was therefore used to allow a full treatment of transient effects. Later experimental and hydrocode work by Franzen and Schneidewind [3] was used to validate the code in this application. The hollow cylindrical particles studied are to be thought of as idealisations of fragments that can arise from the break-up of a shaped-charge jet. In the paper we will show that the depth of 0734-743X/01/$ - see front matter Crowncopyright? 2001 Publishedby ElsevierScienceLtd. All fightsreserved. PII: S 0 7 3 4 - 7 4 3 X ( 0 1 ) 0 0 1 0 9 - 9

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J.T. Mills, J.P. Curtis/International Journal of lmpact Engineering 26 (2001) 523-531

penetration is found to be almost unaffected by hollowness. However, another important prediction of the CCD code is the formation of a jet travelling in the reverse direction through the hollow. Although the penetration of a single particle is not greatly affected by being hollow, the effectiveness of a particle pair is significantly reduced if the leading particle was hollow. This is due to the reverse jet from the leading particle striking and disrupting the trailing particle. In a lower velocity regime (1.6 to 4 kin/s) Anderson et al. [4] and Sorenson et al. [5] discussed the corresponding phenomenon. They demonstrated that interference with subsequent segments could arise from the previous penetration of a tube. They stated that in each case the tube material is forced to the axis where it offers extra resistance to the penetration. In the higher velocity regime we have shown that this effect is significantly enhanced by the formation of the reverse jet. It should be emphasised that the results presented here are theoretical predictions and are therefore subject to experimental confirmation. A programme of work has been done to validate and to establish the mesh independence of the code predictions with satisfactory results.

MODELLING APPROACH As part of a more general study of the penetration properties of fragmented shaped-charge jets (el. [1]), the hydroeode Cast-Euler was used to investigate the penetration performance of hollow particles. The particles consisted of copper and the target of RHA (Rolled Homogeneous Armour), a high strength steel. To be specific, we begin with a solid fight-cylindrical particle of length 2cm and diameter 0.4cm. Then this is replaced by a series of hollow cylinders of the same length and volume of material but with increasing internal diameter. The internal diameters investigated were 0.1, 0.3 and 0.5 of the outside diameter. The incident velocities considered were mainly 5km/s and 8km/s. A range of mesh sizes was considered and details are given in the next section. Originally the intention was to determine the degradation of penetration that occurs as the internal diameter increases. The study showed that the penetration of a single particle was found to be almost unaffected by hollowness. At first sight it seemed that hollowness could not therefore be a degradation mechanism. However, a prediction of the hydrocode was the formation of a jet travelling in the reverse direction through the hollow. Penetration by a hollow projectile and the resulting reverse jet are shown schematically in figure 1.

--'~'~ ~ ~,--Innera e r Dme i l I pc m at Velocity
Fig. 1. Schematic diagram of penetration by a hollow projectile.

J.T. Mills, J.P. Curtis / International Journal of Impact Engineering 26 (2001) 523-531

525

This phenomenon has been reported previously, for example, by Franzen and Schneidewind [3]. Their paper gives a detailed description of the penetration mechanics of hollow particles at a range of impact velocities (1.5 to 4.0 km/s) substantially lower than in our work. Initially the jet consists mainly of target material and subsequently a mixture of target and particle materials.

VALIDATION OF CODE A check on the general validity of our code for this application was achieved by comparison with the Franzen and Sclmeidewind paper [3]. Their hydrOcode simulations were done with an Eulerian code and axisymmelric geometry. Our code, developed at DERA primarily for blast and shock wave applications, is also Eulerian, i.e. Franzen's and our computations are based on the same hydrodynamic model. The particular case chosen for comparison was that of a tungsten tube impacting a steel target. Our results appeared very similar to Franzen's. In his experiments, at normal incidence, in most cases a small piece of target material can be seen ahead of a slower moving jet. Franzen calls this leading particle the 'precursor'. We predicted a jet tip speed of 1.1 km/s, which corresponds to the speed of the precursor in some of Franzen's experimental data. Franzen's method of doing the calculations, to minimise the effect of inaccuracies resulting from material transport through the grid, is to move the target at the impact velocity towards a stationary projectile. We obtained little difference computationally between 'moving the target' and 'moving the penetrator'. Many other previous runs give further confidence in the accuracy of the code in the hypervelocity regime. Such runs include the modelling of the formation of shaped charge jets and of long rod penetration. Regarding possible mesh dependencies, the calculation in which the inner diameter of the hollow particle was one tenth (0.1) of the outside diameter presented difficulties as a very fine mesh was required to obtain even three cells across the radius of the hollow. This is probably the minimum required to avoid mesh dependent effects. For the case in which the inner diameter of the particle was half the outer diameter, the standard mesh had 11 cells across the radius of the hollow. The standard mesh cells were then sub-divided into two in both directions and the problem was re-calculated. Although the results obtained with the standard and refined meshes were quantitatively similar they were not quite identical, thus it is not certain that mesh dependencies have been entirely eliminated. This could be because of the fineness of the reverse jet. The values of the jet speeds may not be exact predictions at this time, but we are very confident of the qualitative features of the results to date.

COMPUTATIONAL RESULTS Figures 2(a) - (d) give plots of the logarithm of material pressure at 4~s after initial impact for an inner radius, ri, equal to 0.0 (solid), 0.1, 0.3 and 0.5 times the outer radius, ro, at 8km/s incident velocity. At this time the incident particles are almost completely exhausted. It will be seen that the character of the jet varies considerably with different hollow sizes: when ri = 0.1 and 0.5to the jet appears as a narrow well focussed stream; whereas, when ri = 0.3to, the jet is much more diffuse. It is possible that the differences could arise from the way in which the jet interacts with the inner surface of the hollow particle spallation. Although the penetration of a single particle was not greatly affected by being hollow, the effectiveness of a particle pair was significantly reduced if the leading particle was hollow. This was due to the reverse jet from the leading particle striking and disrupting the trailing particle. Figures 3(a) - (d) depict an example of this process for ri = 0.5to and an incident velocity of 8 km/s as it progresses at 2, 4, 6 and 81xs. The following particle was solid. This is to be contrasted with Figure 4 in which the leading particle is solid. The final crater depth was significantly greater for the solid compared to the hollow leading particle cases.

526

J.T. Mills, J.P. Curtis/International Journal of Impact Engineering 26 (2001) 523-531

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530

J.T. Mills, J.R Curtis / International Journal of lmpact Engineering 26 (2001) 523-531

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In some cases at least, an almost linear increase in the (reverse) speed of the jet from the particle end to the tip was predicted. Also it was seen that the jet tip speed could be considerably in excess of the incident speed of the particle. Speeds as high as 11 km/s were seen in the case of ri = 0.5ro. It remains to undertake experiments to validate our findings. It is also considered worthwhile to carry out further theoretical investigations to establish the maximum attainable jet speed when (for example) the leading profile of the particle and the contour of the target surface are varied. We emphasise that the formation of these very high speed 'reverse jets' is as yet a computer prediction and also that the results here are based on perfectly axisymmetric calculations. In any real situation departures from axisymmetry would inevitably be present and disturb the formation of a jet. Nonetheless the likelihood is very high that the presence of hollowness in the jet will cause disruption to the penetration process.

CONCLUSIONS A study was undertaken to determine by computational continuum dynamics the effect of hollowness on the penetration properties of a particle. In fact hollowness was found to have only slight effect on the penetration depth of a single particle. However, a significant outcome of the study was the prediction of the formation of a high-speed reverse jet. This jet can impinge on and degrade the penetration of a following particle. The results relating to jet formation assume an axisymmetric geometry. It is expected that even small departures from symmetry will lead to significant interactions between the jet and the particle wall. These interactions will in most cases disrupt both the jet and the part of the particle not yet consumed by the penetration process. It remains to validate these findings by suitable experiments.

J.Z Mills, J.P. Curtis/International Journal of Impact Engineering 26 (2001) 523-531

531

Acknowledgement-The authors thank Mr. A. Kesby for bringing the paper by R. Franzen and P. Schneidewind [3] to their attention.

REFERENCES [1] Cornish R, Mills JT, Curtis JP, Finch D. Degradation mechanisms in shaped charge jet penetration. Proc. Hypervelocity Impact Syrup., Galveston, TX, 2000. [2] Franzen RR. Notes on tubular hypervelocity penetrators, Proc. 10~h. Int. Syrup. Ballistics, San Diego, CA, 1987. [3] Franzen RR, Schneidewind PN. Observations concerning the penetration mechanics of tubular hypervelocity penetrators. Int. J. Impact Engng. 1991; 11(3): 289-303. [4] Anderson CE, Subramanian R, Walker JD, Normandia MJ, Sharron TR. Penetration mechanics of seg-tel penetrators, Int. J. Impact Engng. 1997; 20(1): 13-26. [5] Sorenson BR, Kimsey KD, Silsby GF, Schemer DR, Sherrick TM, De Rosset WS, High velocity penetration of steel targets, Int. J. Impact Engng. 1991; 11(1), 107-119.

?British Crown Copyright 2000, Defence Evaluation and Research Agency. This work was carried out as part of Technology Group 06 of the MoD Corporate Research Programme.


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