On the design of containment shields

Computers & Structures Vol. 16, No. 1-4, pp. 563-572. 1983 Printed in Great Britain.

0045--7949/831010563-10503.00/0 © 1983 Pergamon Press Ltd.

ON THE DESIGN OF CONTAINMENT SHIELDS R. S. J. CORRANand C. RuIZ Oxford University, Department of Engineering Science, Parks Road, Oxford, OXl 3PJ, England and P. J. SHADBOLT Esso, Fawley, Southampton,England Abstract--The failure mechanisms of shields for the containment of subordinance velocity missiles is briefly described. Based on test data, conclusionsare drawn on the advantages that may be gained by using multi-layered constructions. Suggestionsfor further improvementsin design and future research directions are finally made. INTRODUCTION

The study of projectile impact against metal targets has long been of interest to military engineers. It is also of increasing interest to the designers of shields for the containment of missiles at subordinance velocities such as shed turbine blades in aero engines, valve stems and other fragments resulting from an explosion in process or power plants, etc. Typically, impact velocities in these situations do not exceed 200 m/s. While the field of ordinance velocity impact has received considerable attention[l] there is little information on sub-ordinance impact in the published literature. The behaviour of metal plates under impact has been studied by Zaid[2], Beynet[3] and Shadbolt[4]. As the impact velocity increases, the plate damage ranges from indentation to perforation through part-penetration. At sub-ordinance velocities damage is usually associated with considerable widespread plastic deformation, termed dishing, and with localised bulging at the point of impact. For a particular test configuration the dishing increases with velocity until perforation occurs at some critical velocity. For higher velocities, the dishing decreases. Shadbolt[4] distinguished between four different energy dissipation mechanisms: (a) Elastic vibrations in the impacted plate that dissipate the missile kinetic energy at the clamps or supports. (b) Plastic deformation in membrane stretching, bending and shear. (c) Local plastic deformation around the missile as the plate material is forced aside (plugging). (d) Plastic deformation in the missile, i.e. mushrooming of blunt missiles, buckling of plates or wedges. Of these, the first three are the most important when using hard missiles. While it is possible to consider each mechanism separately, the process of deformation and perforation is complicated by the effect of the overall target elastic and plastic deformation; in contrast, at ordinance velocities, targets may be assumed to be rigid, thus simplifying the analysis [5, 6]. CONTAINMENT AND FAILURE MECHANISMS IN SINGLE-LAYER SHIELDS

In a series of tests, cylindrical steel missiles were fired at targets by a compressed gas gun. The missiles had a 12.5 mm dia. and a total length equal to 50 ram. The front

end was blunt. At the back, a circumferential groove, engaging into the gun firing mechanism was cut. The mass was 35 gm and the hardness exceeded 320 HNV in the as-machined condition, 850 HNV in the quenched and tempered condition. In all the tests reported here, the hardness was sufficient to prevent gross plastic deformations of the missile. The targets were circular plates, 300 mm dia., clamped round their circumference by two rigid rings with a total clamping force of 400 kN in the tests described in this paper. Other edge conditions, ranging from the full clamping load to free support, were tested and the results are fully documented elsewhere[4,7]. A number of materials have also been investigated but reference will only be made to mild steel plates since their behaviour illustrates the principles of design of containment shields and provides enough information to draw conclusions of general validity. Targets were cut from low carbon mild steel sheets, 1.3, 2, 3, 5 and 6.4 mm thick with nominally identical chemical composition. For all the plates, the yield point and tensile strength were found to be 260N/mm 2+- 15% and 337 N/mm:±7% respectively. Chemical analysis revealed that the percent carbon content was within the range 0.05 to 0.068. A small number of 0.15%, 6.4 mm thick plates with yield point 360 N/ram: and tensile strength 500 N/mm: were also tested. The impact velocity was measured by means of two photodiodes, mounted 150ram apart, opposite narrow light sources, along the path of the missile, and the velocity after perforation by two induction coils, mounted behind the target. From the velocity measurements, the kinetic energy at impact and after perforation were calculated and hence the energy absorbed by the target plate. Figure 1 shows that the velocity required to produce perforation increases rapidly at first but tends to level off as the thickness exceeds 3 ram. It will be noted that this observation, of general validity for the materials tested[7], does not take into account the improved mechanical properties of the 0.15% C steel used for some of the thick plates. To investigate further the absorption of energy by the target, energy balances were performed, considering the various mechanisms listed in the introduction to this paper. The elastic energy was estimated assuming that the deformation is linear until the plastic collapse load is reached. The elastic stiffness S is, 4.17"

Eh 3

s= T ~

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80

60

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1

2

,

1

I

I

I

3

4

5

6

PlQte thickness (ram)

Fig. I. Variationof perforation velocity with plate thickness for mild steel plate targets,

where E is Young's modulus, v the Poisson's ratio, h the plate thickness and r the plate radius[8]. The limit load, Plim, is,

stress resultants respectively, No=cr~h

h: Mo=o'y T .

Blim = ~ro'yh 2

where #, is the yield stress or a "flow stress" intermediate between yield and tensile stren~h[9l. The maximum elastic energy is then,

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(l - ~),,,:hr ~,

(1)

The plastic energy of dishing and of bulging was calculated from the permanent deformation of the plate. Expressing the strains in the usual form in terms of the deflection w, the plastic energy is given by, E , = f (Noe, + MoK, + MoKo)2~rr dr

(2)

where the integral sign implies summation over the whole plate, the radial strain e, is,

. \dr~

the bending strains K, and ~, are, d2w K~ = - - ~

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and No and Mo are ultimate membrane and bending

A computer was used to calculate Ep from eqn (2), measuring the deflection w along two perpendicular diameters and averaging the results. E~ was divided into a membrane component, corresponding to stretching, and a bending component. The energy associated with mushrooming is calculated, assuming ideally plastic behaviour, from the measured deformation[10] and that due to plugging is obtained as the difference between the total energy and the sum of the other terms. The variation of absorbed energy with plate thickness is shown in Fig. 2. Mushrooming, even when using the comparatively soft as-machined missiles, accounts for a relatively small proportion of the total energy, increasing gradually as the thickness increases. Elastic energy accounts for between 10 and 20% of the total, gomg through a minimum at 4ram thickness. The plastic energy is the main component. It starts by accounting for 78% of the total, but, as the thickness increases, less energy is absorbed in this form and more as elastic. mushrooming and plugging energies. The maximum of the plastic bending energy term is found near the miramum of the elastic energy but the membrane plastic energy decreases rapidly as the thickness increases. This variation in the way in which energy is absorbed is accompanied by a variation in the impact containment efficiency of the plate, defined as the ratio between the

On the design of containment shields

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Fig. 2. Variation of absorbed energy with plate thickness.

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PLote t h i c k n e s s ( r a m ) Fig. 3. Variation of (Pedoration energy)l(Plate thickness) with plate thickness.

R, ~';. J CORRAN et aL

566

perforation energy and the plate thickness. Figure 3 clearly shows that above 3 ram, there is a significant reduction in the containment efficiency, implying that plastic deformation is a much more efficient way of absorbing energy than either of the others; easily deformable targets are preferable to thick, rigid targets in which the missile is either rapidly decelerated to a standstill or perforates through plugging. Even when the plate fails to stop the missile, it still absorbs a proportion of the impact energy. Figure 4 shows the variation of energy absorbed and the residual velocity against impact velocity for the 3 mm thick plates, similar results being obtained for the other thicknesses. It is noteworthy that the maximum energy absorbed does not correspond to the condition of containment, at a critical velocity of 145 m/s but to one of perforation at 190 m/s. Since the relative importance of dishing and bulging decreases as the impact velocity increases, as shown in Fig. 4, it follows that methods of analysis developed for ordinance impact of rigid targets may become applicable. A particularly simple method, due to Recht and Ipson[ll], assumes a constant average dynamic shear stress and predicts the residual velocity of the missile after perforation by the equation,

V. =

1 (V 2_ V = ., . ) ,,: ' (D)'h

(3)

l+a7

where V, is the residual velocity of the missile; V is the impact velocity; V,,i, is the minimum impact velocity for perforation: [1 is the ratio of missile to target densities, (D/d) the ratio between plug and missile diameter; h is the plate thickness and L the missile length. The denominator therefore represents the ratio between the mass of the missile and that of missile and plug. In Fig. 5 the results of tests with 1.2, 2 and 3 mm thick plates are

plotted and the residual velocity is compared with the values predicted by eqn (3). Given the good agreement between the experimental and the predicted values, it is possible to apply eqn (3) once the perforation velocity has been found experimentally, to calculate residual velocities after perforation at higher impact velocities. ~l"bt~vgli sllmL~ c o s s m ' l ~ oF WmgLYSPAC~.aPLAr~. Equation (31 can be combined with the experimental data to predict the perforation velocity of a multi-layer shield consisting of a series of widely spaced parallel plates. Consider, for example, the case of two 2 mm thick plates. The missile hits the front plate at, say, 120 m/s. Since the perforation velocity is (Fig. I) 95 m/s, the residual velocity, from eqn (3) is found to be 70 m/s. The missile, carrying now a 2 mm thick plug in front of it, hits the back plate causing deformation without perforation, The residual velocity that may be allowed will be slightly below the perforation velocity for the back plate to maintain the kinetic energy constant,

V,: =

v ~..

I*

T

In this example, the perforation velocity for the twin 2 mm plate shield is found to be 135 m/s. This value compares unfavourably with 165 m/s, obtained experimentally, and 180 m/s for a single 4 ram thick plate. One reason that explains the difference between predicted and experimental values is that the plug detached from the front plate forms a slightly curved surface that softens the blow of the blunt missile on the back plate. Experiments conducted with missiles having a spherical front--Fig. 6--illustrate this effect very clearly. The blunt missile is the most difficult to stop, producing a sharp, clean, shear in the target. As the spherical radius decreases, tensile tearing rather than through-thickness

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Fig. 4. Residual velocity after perforation and energy absorbed in 3 mm thick plate.

On the design of containment shields

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shear becomes predominant, with large bulging. Below a given radius, on the other hand, the missile penetrates more easily, punching its way through the plate. A second reason is that the plug is softer than the missile and absorbs a certain amount of energy through mushrooming. Although in the example treated there is no advantage in the twin shield, rather the opposite, the situation changes for combined thicknesses of 6 mm or more, as shown in Fig. 7. where curves for 2-, 3- and 4-layer shields have been plotted and compared to the experimental data for the single layer shield. The experimental prints are always above the corresponding predicted values. MULTI-LAYERSHIELDSCONSISTINGOF PLATESIN CONTACT

l

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Fig. 6. Variation of perforation energy with missile nose radius in 1.2 mm plates.

Consider a multi-layer shield consisting of n plates of equal thickness (h/n). The elastic bending stiffness is (1/n 2) of the stiffness for a single plate of thickness h and, for the same deformation, the elastic energy (eqn (I) is.

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Fig. 7. Estimated perforation velocities for multi-layer shields and comparison to experimental results for the single layer shield.

In eqn (2), No is the same for both types of shield, but, i Thus, the multi-layer shield has the same membrane (stretching) properties as its single layer equal, but it is more flexible in bending and has a lower ultimate bending stress resultant. This increased tlexibih'ty results in greater elastic and plastic deflections for a given load: in a 4 mm thick plate the central deflections observed were of the order of the plate thickness[7] while in a twin 2 mm shield the deflection of the rear plate was around 12 ram. The reasons already advanced to explain the enhanced resistance to pluuing of a seres of non-contactin~ plates hold for these multilayer laminated shields. The combination of enhanced plugging s t r e n ~ and greater flexibility help to promote energy absorption through dishing and bulging, an effect observed by Maron and Bodner[12] who, by laminating beams, were able to absorb the kinetic energy of a missile by bending rather than by perforating the target. Their method of analysis, successful in interpreting their results, was not found to be applicable to the clamped circular plates used as tarots in this investigation mainly because of the differences between the structural behaviour of beams and plates. Experimental results, summarised in Fig. 8, do however show that it is advantageous to laminate the shields above a thickness of 5-6 mm but that for thinner shields lamination either does not improve the impact strength or may even be detrimental, The results are compared to the best fit curve, Ep,,fo,~,,o. = 41.8 hz (J) which assumes implicitly that most of the energy is absorbed in bending (dishing and bulging). It will be noted that separated plates behave less well than plates

in contact and that, as predicted by the plots of Fig. 7, increasing the number of layers does not increase the strength of a shield for a given total thickness. The inferiority of targets with many layers has also been observed by Marom and Bodner[12] and by Honda[13]. The tests on the targets with 1.2 and 3 ram thick elements show that the shield consisting of a 1.2 mm plate followed by a 3 mm plate is superior to one with two elements of equal thickness and to the one in which the thicker plate is at the front and the thinner one at the back, This confirms that in the most efficient shield the front layer is sufficiently flexible to gradually decelerate the missile while being sufficiently hard to take a significant amount of energy through plusging before it perforates. The plug formed rounds off the blunt nose of the missile which, together with the velocity reduction, promotes overall plastic deformation in the rear plate rather than plugging.

Alternative designs The process of containment or perforation in non-rigid shields under sub-ordinance velocity impact, i.e. missiles travelling at up to 200.-250 m/s, may be described by reference to the experimental results obtaioed from the mild steel test plates. When the missile hits the shield, energy is first absorbed through elastic deformation, damped by the shield material itseff and by friction at the supports. The energy that can he absorbed in this manner is relatively small with respect to the energy associated with widespread plastic deformation, but as the velocity increases, inhibition of plastic deformation makes the elastic energy play a more important part in decelerating the missile. Upon impact, the deformation, initially elastic, first spreads at the wave velocity, ~/(EIg) where p is the material density, but for the deflection at the point of impact to become significant it is necessary to develop plastic hinges or bands of intense bending, travelling at the much lower speed of k/(cr-da). Plastic energy absorption is therefore only possible in relatively stow

On the design of containment shields

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Fig. 8. Perforation energy for single- and multi-layer shields.

processes. While plastic deformation spreads towards the supports, a plug is formed through shear, as shown in Fig. 9. In plugging, following an initial period of compression, narrow shear bands appear resulting in the separation of a part of the plate with very small absorption of energy. The two processes, plugging and plastic deformation, occur simultaneously; which of the two is dominant depends on the times taken for the missile to shear through the plate thickness and for the plastic hinges to spread to the supports. Deformation of the plate upon impact reduces the deceleration of the missile and hence the shear force available for plugging, but the two processes are largely independent, as illustrated by the failure diagram in Fig. 10. Referring to Fig. 10, and for an impact velocity V, the final mode of failure may consist of plugging accompanied by some plastic deformation or excessive dishing and bulging leading to tearing. As V increases, the final deflection decreases and, for a critical velocity V,,i,, plugging occurs with virtually no plastic deformation. On the other hand, at low impact velocity, no plugging takes place. An envelope or failure line may be drawn, consisting of two branches: (a) Failure due to plugging or to mixed mode. The rapidity of the process does not give time for the plastic hinges to spread the load. Low energy absorption.

(b) Failure due to large plastic deformation. High energy absorption. The problem in designing a single layer is that, to prevent plugging, the shell thickness has to be increased over the theoretical minimum for containment by plastic deformation. As the thickness increases, so does the shell stiffness and the deformation becomes more concentrated while the relative missileshield velocity increases. The shield becomes less and less efficient. The improved strength of multi-layer shields, consisting of a thin front plate backed by a thicker rear plate, is essentially due to the fact that plastic deformation is promoted while plugging is inhibited. While only single metal shields have been tested, it may be expected that further improvements will be achieved by a thin, flexible and hard front plate backed by a low-yield thick plate capable of absorbing energy with large plastic deformations. In a single layer metal shield, internal damping is virtually non-existent. Damping can be introduced as an important means of energy absorption in multi-layer shields, in which the various layers are in frictional contact, by using elastomeric materials, woven fabrics, coiled wires or ropes or by inducing Iocalised plastic deformation, e.g. with collapsing elements. Plugging remains the critical failure mechanism. Full

570

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(b) Fig. 9. Formation of plug through shear, (a) initiation, (b) shear surfaces. exploitation of plastic deformation and damping requires that early failure by plotting should be avoided. This can he achieved by: (a) Reducing the relative velocity during the early stages of impact. This requires avery low stiffness at the beginning of the displacement, increasing later as the missile decelerates. (b) Spreading the impact load over a wide area and thus reducing the energy density. One alternative worth considering is multilayer construction of various types: (i) Core-mainly to maintain shape; outer layers-to absorb energy in stretching, bending, friction and/or internal damping. Mechanical properties of core are largely irrelevant, the resistant outer layers must have a suitable combination of strength and toughness at high strain rate.

(ii) Core-.only resistant element, the purpose of the outer layers is to inhibit plugging, possibly by settin8 up advantageous residual compressive stresses. The material chosen must be resistant to plugging. (iii) Intermediate between these two extremes is the case where both core and outer layers participate in the absorption of energy (Fig. I1). A different type of shield consists of an inner skin easily deformable, in which plugging is avoided by the low relative velocity that can be developed. The load is spread by an intermediate structure to an outer skin that absorbs energy through widespread plastic deformation. Alternatively, the inner skin may consist of interlocking elements or be easily fragmented into "tiles" by means of premachined fracture lines. As before, the easy displacement of each element inhibits plngsing, while the increased area spreads the load to the outer skin through the intermediate structure (Fig. 12).

On the design of containment ~hields

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0

~160 Vrnin 12,0

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L.C

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I

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I 8

10 Defiection(rnm)

Fig. 10. Failure diagram for 3 mm thick plates.

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CONCLUSIONS The investigation reported here is only a part of a programme of research conducted in Oxford under the sponsorship of Rolls Royce. It has helped to understand the complex mechanism of failure of single layer shields and provided new data on the behaviour of metals other than mild steel at the high strain rates occurring at impact. A reduction of weight is unlikely to be achieved for the single layer shield design. Two-layer shields where different metals are used for the inner and for the outer

R, S J. CoRgiS et aL

572

layer have been tested sucessfully at ordinance velocities but there is virtually no published information on their behaviour at low velocities. It is however clear that they are potentially interesting. From the results of this investigation, improvements are noticeable above a certain thickness, when the rigidity of the single layer shield promotes plugging, thus a 6 mm shield consisting of two 3 mm plates absorbs 900 J at perforation while the single 6 mm thick plate perforates at less than 600 J. Saving in weight is also illustrated by comparing, in Fig. 8, the 1.2 + 3 mm two-layer shield to the 5 or the 6.4 mm single plates. This saving, of the order of 20%, is particularly important in aerospace applications. The optimum design is likely to be one of the alternatives suggested. Some have been tested and one, indeed, in use, but their behaviour is not at all well understood because the tests have only attempted to reproduce the exact conditions existing in the actual structure rather than to provide any fundamental knowledge. Simple tests, in which the experimenter can control and isolate variables, are needed before the designs that are at present only validated, can be optimised but the potential weight saving makes the additional effort involved in doing such tests very worth while. REI~P,~NC~

1. M. E. Baekman and W. Goldsmith, The mechanics of i~netration of projectiles into targets, Int. J. Mectt ScL 16, 1-99 (1978).

2. A. I. O. Zaid, investigations into the containment o~ highspeed projectiles. Ph.D. Thesis. Paisley College of Technology (1972). 3. P. Beynet. Plastic plate impact without perforation. ?h.D. Thesis,University of Minnesota (1970). 4. P. J. Shadbolt, Impact loading of plates. D.PhiL Thesis, Oxford University (1981). 5. J. Awerbuch and S. R. Bodner, Experimental investigation of normal perforation of metal plates by projectiles in metallic plates. Int. J. Solids Structures I0, 685--699(1974). 6. J. Awerbuch and S. R. Bodner, Analysis of the mechanics of perforation of projectiles in metallic plates. Int. J. Solids Structures I0, 671-684 (1974). 7. P. J. Shadbolt, R. S. J. Con:an and C. Ruiz, A preliminary investigation of plate perforation by projectiles in the subordinance range. OUEL Reports 1372--4/81, Department of Engineering Science, Oxford. 8. S, P. Tiinoshenko and S. Woinowsky-Krieger, Theo~ o[ Plates and Shells. McGraw-I-!ill,New York (1959). 9. C. Ruiz and F. Kownigsberger, Design for Strength and Production. Macmillan, London (1970). 10. W. Johnson and P. B. MeUor. Plasticity for Mechanical Engineers. Van Nostrand, London (1962). 11. R. F. Recht and T. W. Ipson, Ballistic perforation dynamics. Trans ASME, J. Appl. Mech, 30, 384-380 (1963). 12. I. Marom and S. R. Bodner, Projectile perforation of multilayered beams. Int. J. Mech. Sci. 21,489-50,1 (1979). 13. K. Honda, G. Takamae and T. Watanabe, On the measurement of the resistance of shield plates to penetration by a rifle bullet. Tohoku Imperial University, I st series 19, 703-725 (1930).