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A study of the effect of target thickness on the ballistic perforation of glass-fibre-reinforced plastic composites
International Journal of Impact Engineering 24 (2000) 445}456
A study of the e!ect of target thickness on the ballistic perforation of glass-"bre-reinforced plastic composites E.P. Gellert, S.J. Cimpoeru*, R.L. Woodward1 DSTO Aeronautical and Maritime Research Laboratory, P.O. Box 4331, Melbourne 3001, Australia Received 19 January 1999; received in revised form 3 December 1999
Abstract Ballistic tests were conducted using hard-steel cylinders of two diameters and three nose shapes against glass-"bre-reinforced plastic (GRP) composite plates of various thicknesses. The data when plotted as energy to penetrate as a function of target thickness exhibit simple bi-linear relationships. This is also found to be the case for a broad range of reported composite ballistic impact data. A simple model is developed to explain the bi-linear behaviour and to provide the basis for geometrical scaling of composite ballistic perforation data, and also to help with the interpretation of material parameter and bond strength in#uences on ballistic resistance. The study also shows that energy absorption in thin GRP targets is largely independent of projectile nose geometry and that thin GRP and Kevlar targets respond similarly on a thickness basis to impact by fragment simulating projectiles. Measurements on geometric damage parameters in the perforated composites are presented. Crown copyright ( 2000 Published by Elsevier Science Ltd. All rights reserved.
1. Introduction A major step forward in the protection of personnel against ballistic threats, particularly irregular fragments, has been the introduction of impregnated glass "bre and synthetic textiles [1]. This has been aided by the commercialisation of "bres and resins, resulting in the use of glass-"bre-reinforced plastic (GRP), Kevlart, Nylont 66 and Polyethylene in personal armour vests, helmets, pilot seats and spall liners. Studies of ballistic penetration of fabrics and composites have examined "bre response [2,3], mechanisms of deformation [4,5] and failure [6] as well as energy absorption [6}11] and dynamic loading [12]. Despite elucidating many characteristic features of fabric and composite behaviours, no single model has emerged which allows a * Corresponding author. 1 Deceased. 0734-743X/00/$ - see front matter. Crown copyright ( 2000 Published by Elsevier Science Ltd. All rights reserved. PII: S 0 7 3 4 - 7 4 3 X ( 9 9 ) 0 0 1 7 5 - X
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Nomenclature C , C@ , C , 1 1 2 C@ , C , C 2 3 4 D D B D E D I E G C h 0 H E ¸ n S = ,= , B D = , =, = F I T / p B p C p ,e . .
constants projectile diameter minimum diameter of damage at boundary between dishing and indentation/compression deformation diameter of delamination on target exit side diameter of delamination on target impact side modulus of composite (in-plane direction) fracture toughness target thickness measured thickness of target on exit side which dishes diameter of delaminated conical dish on exit side of target number of delaminated layers displacement of idealised beam in bending work of bending, of dishing, of fracture, of indentation, and of tension, respectively theoretical thickness of target on exit side which dishes, or the target thickness at which a change in slope in energy absorption vs target thickness occurs maximum tensile stress in composite due to bending compressive stress in composite (through-thickness direction) mean tensile stress and strain, respectively, in composite (in-plane direction)
quantitative description of the ballistic perforation process. This is partly a consequence of the di!erences in behaviour between "bre types and between fabric and composite constructions, and the great diversity in thermomechanical properties, ductility, anisotropy and rate sensitivity, etc. Composites respond di!erently to the `ideala materials (metals) upon which the fundamentals of the mechanics of high strain deformation are based. It is clear that there are large di!erences in the nature of the deformation processes as the projectile proceeds through the target, the early phase being dominated by acceleration of target material, compression and crushing ahead of the projectile, and the latter stages being characterised by stretching of "bres, delamination and dishing which continues during and after perforation [4,11]. This study examines the thickness dependence of perforation of GRP composites for three projectile nose shapes by measuring ballistic resistance and by the examination of sectioned, perforated specimens. An attempt is made at analytically understanding deformation processes by comparison with observations on metallic laminates. Fragment simulator perforation data is also used to illustrate the generality of the approach.
2. Experimental Targets were constructed from woven roving E-Glass GRP of 11 plies (&4.5 mm, &27 wt% resin), 22 plies (&9 mm, &28}29 wt% resin), 33 plies (&14 mm, &27 wt% resin) and 44 plies
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Fig. 1. Kinetic energy at ballistic limit vs. target thickness for the target/projectile combinations examined in this study. The dashed line is the predicted curve for the 6.35 mm #at-ended projectile (refer text). Note that a precise ballistic limit was not obtained for the thickest target for the 453 cone angle projectiles due to severe projectile yaw within the target, hence there is some uncertainty in the position of the line of best "t. It was suspected that the ballistic limit was higher than estimated, hence the upward pointing arrow.
(&20 mm, 29}30 wt% resin) of a nominal 608 g m~2 woven cloth and DerakaneTM 411-45 vinylester resin. The laminate panels were hand layed up and cured with 1.2% of Butanox M60 methyl ethyl ketone peroxide catalyst and 0.3% of cobalt octoate co-catalyst, autoclave cured at 303C and 100 kPa for 1 h, and "nally post cured for 2 h at 903C. The average bulk density of all panels was 1.85 g cm~3. Hardened steel penetrators consisting of 6.35 mm #at-ended cylinders (of 3.84 g, 15.6 mm length), 4.76 mm #at-ended cylinders (of 3.33 g, 24.5 mm length), and 90 and 453 conically nosed 4.76 mm diameter projectiles of 3.21 g, 25.1 mm length and 2.92 g, 25.1 mm length, respectively, were used for a total of sixteen di!erent projectile/target combinations. The penetrators were "red from a commercial stud gun, and impact velocity was measured by the interruption of electromagnetic "elds. The ballistic limit, < , for each target combination was 50 calculated as the average velocity of impacting penetrators that just perforated and were just stopped by the target. Each target was at least 100 mm]100 mm and was clamped along two edges. Targets were impacted no more than four times, with the impacts spaced so that any delamination produced did not overlap with delamination damage from previous impacts. 3. Results Because the penetrators of di!erent geometry were of slightly di!erent masses, the projectile kinetic energy to just defeat the target was calculated from the ballistic limit data, and this was plotted as a function of target thickness. In this way the results from di!erent penetrators can be validly represented on the same scales for comparison. The data, shown in Fig. 1, can have two intersecting straight lines "tted for the case of each projectile, with the straight line for the thin
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Fig. 2. Kinetic energy at ballistic limit vs. target thickness for fragment simulators impacting GRP and Kevlar resin-impregnated composites [13]: (***) refers to 5.59 mm; (} } }) refers to 7.62 mm; and ( ) ) ) ) ) ) ) ) ) ) refers to 12.7 mm fragment simulating projectiles. The data have been linearly scaled by dividing by energy and thickness measures for the ordinate and the abscissa, respectively.
targets being e!ectively common for the three 4.76 mm diameter projectiles of di!erent nose geometry. The simplicity of this plot encouraged a wider search and Fig. 2 shows fragment simulator data [13] plotted for GRP and Kevlar polyester composites, for 5.59 mm (1.1 g), 7.62 mm (2.9 g) and 12.7 mm diameter (13.4 g) fragment simulators [12]. Intersecting straight lines represent the data over an extremely wide range of thicknesses and bi-linear relationships are seen for all three sizes of fragment simulator. It is notable that a common straight line was able to be "tted through both the GRP and Kevlar thin target data for each of the 5.59 and 7.62 mm projectile data sets. Similarly, fragment simulator data on bonded and unbonded Aramid fabrics [14,15] are replotted as a function of number of plies (proportional to target thickness) in Fig. 3, but using the ballistic limit velocity squared (proportional to kinetic energy) instead of ballistic limit as was presented originally. Again, bi-linear relationships are evident. Sectioning of perforated samples, Fig. 4, indicated two characteristic patterns of damage or delamination, as illustrated schematically by the horizontal hatching in Fig. 5. For thin targets the damage was in the form of a cone of delamination opening towards the target exit side, Figs. 4(a) and 5(a). This cone increased in diameter and height with increasing target thickness, until with su$ciently thick targets a cone of delamination opening towards the impact side was also added, Figs. 4(b) and 5(b). Measurements of damage geometry, de"ned in Fig. 5 as a function of target thickness and projectile geometry, are given in Table 1 along with target impact velocities and ballistic limits. These measurements should only be seen as indicative as it was often di$cult to make precise measurements, and it was suspected that the dimensions of the damage would be subject to experimental scatter. Additional targets were impacted signi"cantly above and below the ballistic limit and were sectioned to examine the variation of cone dimensions with impact velocity.
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Fig. 3. Velocity squared (proportional to kinetic energy) at ballistic limit vs. target thickness for unspeci"ed [sic] fragment simulating projectiles impacting fabric and resin-impregnated Aramid composites [14,15].
Fig. 4. Sectioned targets that have been impacted by 4.76 mm 903 conically tipped projectiles: (a) thin 4.5 mm target (187 m s~1) and (b) thick 20 mm target (464 m s~1). The impact face is the upper edge of each target.
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Fig. 5. De"nition of damage geometry dimensions speci"ed in Table 1. A thin target, (a), and a thick target, (b), are illustrated. The impact face is the upper edge of each diagram. Table 1 Target thickness, impact velocity, ballistic limit (< ) and test outcome (P"perforation and NP"no-perforation) 50 combined with damage geometry parameters de"ned in Fig. 5, and / (estimated from Fig. 1) Projectile diameter (mm)
Target thickness (h ) (mm) 0
Velocity (m s~1) Impact
Damage geometry dimensions (mm) < 50
/
Outcome
D I
D B
D E
H E
55 90 106 95
* 7 11 12.5
7.3
6.35 mm #at
4.5 9 14.5 19
216 343 482 566
210 327 473 563
P P P P
* 18 30 37
6.5 17 18.5 12
4.76 mm #at
4.5 9 14 20 20.5 19
188 319 406 399 533 566
175 293 389 505 505 505
P P P NP P P
* 15.5 31 42 42 42
5 12 19 16 20 20
53 68 82 46 81 76
* 7.5 9 12.5 9.5 11
5.8
4.76 mm 903 cone
4.5 9.5 14 20
187 277 360 464
186 274 355 452
P P P P
* 23 31 41
16 15 16 13
54 59 61 68
* 6.5 9.5 9
8.8
4.76 mm 453 cone
4.5 9.5 14.5 20.5
172 265 351 470
173 263 351 '471
P P P P
* 20 30 45
15 11 10 10
36 49 53 55
* 7 8.5 8
12.5
Table 1 lists such additional measurements for the 20 mm thick target, 4.76 mm #at-ended projectile condition. The D (diameter of delamination on the target exit side) and H (measured E E thickness of cone of delamination on target exit side) parameters were found to vary the most with impact velocity. For consistency, all other measurements of cone geometry in Table 1 were made on perforated targets that had been impacted as close as possible to their ballistic limits. Fig. 6(a) shows that D (diameter of delamination on target impact side) increases linearly with I target thickness from when it is "rst apparent on the impact face of the target. Fig. 6(b) suggests that D increases with target thickness and eventually plateaus. Greater exit-side delamination is E
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Fig. 6. Variation of damage geometry dimensions de"ned in Fig. 5: D , (a); D , (b); and h }H , (c), as a function of target I E 0 E thickness.
observed for larger projectile diameters and as nose geometry becomes blunter. D was di$cult to B measure but most values were in the range between 10 and 20 mm. H was found to increase with E thickness (refer to Table 1) and eventually plateaus for the 4.76 mm targets. Fig. 6(c) shows that the parameter h !H , a measure of the thickness of the cone of damage extending towards the impact 0 E side of the targets, was found to increase approximately linearly with increasing thickness for the 4.76 mm projectiles.
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4. Discussion Figs. 1}3 show that a transition in energy absorption occurs at a certain target thickness for both GRP and Kevlar composites and that this transition depends on projectile diameter and nose geometry as well as target material. This transition is postulated to be due to a change in perforation mechanism from largely dishing in thin targets, Figs. 4(a) and 5(a), to a combination of indentation and dishing, Figs. 4(b) and 5(b). This bi-linear dependence of energy absorption on thickness does not appear to have been previously identi"ed. This relationship could easily be interpreted as non-linear, or even linear, if a su$ciently wide range of experimental conditions was not examined. Bi-linear behaviour in terms of a change in damage area, i.e. delamination pattern, has previously been identi"ed as a function of impact energy and velocity in impacted GRP targets (e.g. [16,17]). Fig. 1 demonstrates that for thick GRP targets, pointed projectiles are more e!ective against GRP, i.e. less energy is absorbed. However, Fig. 1 also shows that energy absorption is largely independent of projectile nose geometry for thin GRP targets. It is also of interest that the response of thin GRP and Kevlar composite targets to fragment simulator projectiles, Fig. 2, appears to be independent of target material. The damage geometry in perforated GRP targets can be interpreted by analogy with the behaviour of ductile metallic targets where the deformation geometry is `frozen ina by plastic deformation [18]. Damage in GRP targets is manifested as delamination and is conveniently assessed as it is observed as an opaque area in the target and easily distinguished from the undamaged laminate. It is important to be aware that shearing [5] and fragmentation [19] have been identi"ed as important phenomena in the initial stages of perforation of GRP targets. The cone of damage on the impact side of a thick target is interpreted as being a consequence of compression of material ahead of the penetrator. This leads to radial pressure due to displacement of fragmented material, which causes an upthrust of laminae to compensate. As the projectile nears the exit side of the target, it is easier for layers to delaminate and bend away from the oncoming projectile in the direction of projectile motion. Dishing occurs and forms the cone of the damage opening towards the exit side of the target. The measurements made of D , D , D and I E B H , de"ned in Fig. 5, characterise the separate zones of compression and dishing in the various E targets. The work done in perforation of a target is therefore the sum of the work of all the deformation mechanisms. However, kinetic energy is also given to moving layers at the rear of the target [11] and ejected debris [19]. Both of these e!ects are important but were not accounted for in the current modelling exercise as they require specialised instrumentation for characterisation, e.g. high-speed cine photography, and thus the development of a suitable model for this phenomenon is beyond the scope of the current study. For a thin target which forms a delaminated conical dish, as seen in high-speed cine images [11], the work of tension is the mean tensile stress in the composite, p , times the mean strain, . e (e "p /E, where E is the composite modulus) times the deformed volume. If ¸ is the diameter . . . of the delaminated conical dish on the outside of the target and h the thickness of the deforming 0 target, then the work of tension, = , is given by T = "C ¸2h p2 /E, T 1 0 .
(1)
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where the constant C accounts for the through thickness geometry of the delaminated region of 1 the target as illustrated in Figs. 4(a) and 5(a). For composites with a brittle binder, delamination will occur with work done estimated from the fracture toughness, via G , where shear or opening modes are not speci"ed here, times the area of C delamination (proportional to ¸2) times the number of layers (proportional to h ) times a geometry 0 dependant constant, C , which accounts for the through-thickness variation in the radius of 2 delamination, as per Figs. 4(a) and 5(a). Fracture of the binder phase will be more general than simple delamination, being better described as fragmentation, however this more general break-up can be also captured in the three terms: strain energy release rate, G ; volume; and the geometrical C constant. Thus the work of fracture, = , becomes F = "C G h ¸2. (2) F 2 C 0 The work of bending can be examined by treating the dish as a beam of width p¸, with the hinge at a position ¸/2 from the applied load. If S is the displacement of the load and the yield moment is given by p¸h2p /6 [20], then the bending work, = , is given by 0 . B = "C h2p S, (3a) B 3 0 B where p is the maximum composite tensile stress due to bending. Once matrix fracture and B delamination occur, the beam is e!ectively con"gured of n-independent layers, each of thickness h /n, so that the work of bending is then expressed as 0 = "C h2p S/n. (3b) B 3 0 B Substitution of typical material and geometric parameters into Eq. (3b) shows = is small in B comparison to = . Whilst the work of bending may be small, the resistance to bending before T delamination as represented by the derivative with respect to displacement, S, of Eq. (3a) can be large. After delamination, the resistance to bending is much less as the derivative with respect to displacement of Eq. (3b) is smaller than that of Eq. (3a), allowing the dishing mechanism to develop. It is the initial resistance to bending that determines whether dishing will occur upon impact or later during the perforation process, even though the bending work does not contribute at the same magnitude as the other terms in the total work of perforation. Analogous studies on metallic laminates have shown that despite bending work being small, the bending resistance of the target will determine whether or not dishing occurs as well as in#uence the degree of dishing on the target exit-side [18]. For a thin composite target, with = small, using Eqs. (1) and (2), the work of B dishing, = , becomes D = += #= "¸2h (C p2 /E#C G ). (4) D T F 0 1 . 2 C As the diameter of the dished region, ¸, is expected to increase in proportion to the diameter of the projectile, D, Eq. (4) becomes = +D2h (C@ p2 /E#C@ G ), (5) D 0 1 . 2 C where the modi"ed constants C@ and C@ include the proportionality constant ¸/D. 1 2 For a su$ciently thick target, the initial resistance to bending will be high enough to prevent dishing until the penetrator nears the target exit side. Penetration will therefore initially occur by
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an indentation mechanism. The work of indentation, = , is the presented area times the compresI sive stress, p , times the displacement. Account is taken of con"nement of the compressed material C [5] by increasing the e!ective material #ow stress by a constant, and with this and the geometrical constants included in a constant C , the work becomes 4 = "C D2p (h !/), (6) I 4 C 0 where h is the total target thickness and / is the thickness on the exit side which dishes instead of 0 being indented. The work of perforation of a thick target then becomes the sum of = , Eq. (6), and I = , Eq. (5) where h in Eq. (5) is equal to /. Thus / is assumed to be the target thickness at which D 0 the change of slope occurs as in Figs. 1}3. The analysis results in the work of perforation being bi-linearly proportional to target thickness with di!erent slopes for thin and thick targets, as observed experimentally (Figs. 1}3). The two slopes would suggest that complete perforation of thin composite targets should be by one mechanism, that represented by the lower slope, which is dishing rather than indentation and compression. The analysis has therefore provided a de"nition of a thin composite target. This is not the case for thick bonded composites because of their high initial resistance to bending. Thick composites will therefore initially be penetrated by the indentation mechanism until fracture of the matrix phase at the ply interfaces can be achieved, which then allows the dishing mechanism to develop at the rear of such targets. There is, in fact, some evidence to suggest that reducing the resistance to bending in composites by using separate impregnated plies reduces ballistic performance [15]. For unbonded layered targets the slope of the work versus target thickness curve is high for thin targets as shown in Fig. 3. This is probably a consequence of a very large diameter of dished region, ¸, [21] in Eq. (4) leading to large values of C@ and C@ in Eq. (5). The material and geometric 1 2 parameters in Eqs. (5) and (6) are not well understood from this analysis, because average strength parameters are used in lieu of a better knowledge of the mechanics of large-deformation composite behaviour. However, these equations give a basis for understanding the linear relationships evident in Figs. 1}3 and an appropriate method of scaling with projectile diameter and target thickness. Similar projectile nose shapes must be compared when scaling ballistic data. For instance, Eqs. (5) and (6) specify that the slope (energy/thickness) for both thin and thick targets should depend on the square of projectile diameter. Fig. 1 is used as an example, where the slopes for the #at-ended 4.76 mm projectile and the ratio of the squares of the projectile diameters are used to predict the curve for the 6.35 mm #at-ended projectile (shown as a dashed line), assuming / is known for this latter projectile. The theory appears to be adequate for relative scaling purposes in this instance as the predicted slopes for the #at-ended 6.35 mm projectile are within 10% (for thin targets) and 4% (for thick targets) of those determined experimentally. It is expected that the change in slope at a target thickness / as speci"ed in the model of Eqs. (5) and (6) and from Fig. 1 relates to the parameter H determined by post-perforation measurements. E Table 1 compares these measurements and shows that notable di!erences exist. The model also predicts that / remains constant once indentation and compression deformation become signi"cant, i.e. beyond a target thickness of /. Experimentally, it was found that a constant value of H was not reached for the 6.35 mm projectiles and for the 4.76 mm projectiles a constant value E was only apparent for the 14 mm and 20 mm targets. Any correlation between the measured post-perforation microstructural information and the transition points represented in Fig. 1 is at best approximate. This is partly because of simple idealisation in the modelling and partly because
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of post-perforation deformation and recovery in the experimental materials. Fig. 6(c) does, however, demonstrate that an approximate linear increase in h !H (i.e. the thickness of target 0 E that is penetrated by indentation and compression deformation) occurs beyond certain critical thicknesses. In reality there may be a somewhat gradual transition from dishing to indentation and compression, beginning at target thicknesses less than 9 mm. In the present instance this is probably masked by the absence of targets between 4.5 and 9 mm in thickness. It should be noted that the H values could easily vary by a millimetre or so because of the subjective nature and E imprecision of the H measurements and the expected shot-to-shot scatter. This makes precise E correlations di$cult, especially for the 9 mm targets where H is small. E The analysis has also shown that the indentation phase is a more signi"cant absorber of energy and indicates that it should be maximised in any bonded composite armour design. This indicates that thicker bonded composite armours would be more e$cient ballistically, especially against blunt projectiles. It is also interesting that smaller cone angle projectiles were found to have larger values of /, i.e. greater thicknesses of dishing. The model predicts that this translates to a greater proportion of a given target thickness deforming by a lower energy dishing mode. Presumably, this is one reason for such target/projectile combinations having lower ballistic limits. 5. Conclusions Ballistic perforation data and post-perforation microstructural measurements are presented for a range of projectile shapes impacting GRP targets. The ballistic data, when plotted as energy to penetrate the target as a function of target thickness, can be "tted to simple bi-linear plots. A simple model is developed to explain the relationship and it gives a basis for geometrical scaling of ballistic perforation data for composite targets and a de"nition of a thin target. The relationships established are also seen in other data sets for composite targets. Importantly, the analysis has shown that the indentation phase is a more signi"cant absorber of energy and should be maximised in any bonded composite armour design, indicating that thicker targets are more e$cient ballistically, especially against blunt projectiles. It was of interest that energy absorption in thin GRP targets is largely independent of projectile nose geometry and that thin GRP and Kevlar targets respond similarly on a thickness basis against fragment simulator projectiles. Acknowledgements The authors wish to acknowledge the contributions of Mr Jim Dimas and Mr Stephen Pattie for their e!orts in ballistic testing. Mr Alban Cole and Mrs Karen Challis are also to be thanked for their patient sectioning and polishing. References [1] Laible RC. In: Laible RC, editor. Ballistic materials and penetration mechanics. Amsterdam: Elsevier, 1980. p. 9. [2] Petterson DR, Stewart GM, Odell FA, Maheux RC. Dynamic distribution of strain in textile materials under high speed impact, part I: experimental methods and preliminary results on single yarns. Textile Res J 1960;30:411}21.
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[3] Jameson JW, Steward GM, Petterson DR, Odell FA. Dynamic distribution of strain in textile materials under high speed impact, part III: strain-time-position history in yarns. Textiles Res J 1962;32:858}60. [4] Egglestone GT, Gellert EP, Woodward RL, Perforation failure mechanisms in laminated composites. In: Davies RD, Hatcher DI, editors. Materials united in the service of man, IMMA, Perth, Australia, 17}21 September, 1990, Vol. 1, p. 2.1}11. [5] Woodward RL, Egglestone GT, Baxter BJ, Challis K. Resistance to penetration and compression of "brereinforced composite materials. Composites Engng 1994;4:329}41. [6] Zhu G, Goldsmith W, Dharan CKH. Penetration of laminated Kevlar by projectiles*I. Experimental investigation. Int J Solids Struct 1992;29:399}420. [7] Jang BZ, Chen LC, Hwang LR, Hawkes JE, Zee RH. The response of "brous composites to impact loading. Polym Compos 1990;11:144. [8] Zee RH, Hsieh CY. Energy loss partitioning during ballistic impact of polymer composites. Polym Compos 1993;14:265. [9] O'Donnell RG. Deformation energy of Kevlar backing plates. J Mater Sci Lett 1993;12:1485}6. [10] Scott BR, Brunner Jr RF. Transient distributed loading of ballistic panels. Proceedings of the 14th International Symposium on Ballistics, ADPA, Quebec. Canada, September 1993. p. 729. [11] Gellert EP, Pattie SD, Woodward RL. Energy transfer in ballistic perforation of "bre reinforced composites. J Mat Sci 1998;33:1845}50. [12] Mascianica FS. In: Laible RC, editor. Ballistic materials and penetration mechanics. Amsterdam: Elsevier, 1980. p. 41. [13] Mascianica FS. Ballistic technology of light weight armour (U), AMMRC TR 81}20, 1981. Con"dential. [14] Savage GM, Fabric and "bre reinforced laminate armours. Metals and Mater 1989; May: 285}90. [15] Shephard RG, The use of polymers in personal ballistic protection. International Conference on Polymers in Defence. The Plastics and Rubber Institute, Bristol, March 1987. p. 21/1-21/10. [16] Wu E, Chang LC. Woven glass/epoxy laminates subject to projectile impact. Int J Impact Engng 1995;16:607}19. [17] Thaumaturgo C, Da Costa Jr. AM. Shock waves on polymer composites. J Mater Sci Lett 1997;16:1480}2. [18] Woodward RL, Cimpoeru SJ. A study of the perforation of aluminium laminate targets. Int J Impact Engng 1998;21:117}31. [19] Greaves LJ. Defence research agency memorandum 12/92, Chertsey memorandum 92003. Chertsey, Surrey, March 1992. [20] Johnson W, Mellor PB. Plasticity for mechanical engineers. London: Van Nostrand, 1962. p. 96. [21] Morrison CE, Bowyer WH. Factors a!ecting the ballistic impact resistance of Kevlar laminates. In: Bunsell AR, editor. Advances in composite materials, Vol. 1. Oxford: Pergamon Press, 1980. p. 233.
A study of the e!ect of target thickness on the ballistic perforation of glass-"bre-reinforced plastic composites E.P. Gellert, S.J. Cimpoeru*, R.L. Woodward1 DSTO Aeronautical and Maritime Research Laboratory, P.O. Box 4331, Melbourne 3001, Australia Received 19 January 1999; received in revised form 3 December 1999
Abstract Ballistic tests were conducted using hard-steel cylinders of two diameters and three nose shapes against glass-"bre-reinforced plastic (GRP) composite plates of various thicknesses. The data when plotted as energy to penetrate as a function of target thickness exhibit simple bi-linear relationships. This is also found to be the case for a broad range of reported composite ballistic impact data. A simple model is developed to explain the bi-linear behaviour and to provide the basis for geometrical scaling of composite ballistic perforation data, and also to help with the interpretation of material parameter and bond strength in#uences on ballistic resistance. The study also shows that energy absorption in thin GRP targets is largely independent of projectile nose geometry and that thin GRP and Kevlar targets respond similarly on a thickness basis to impact by fragment simulating projectiles. Measurements on geometric damage parameters in the perforated composites are presented. Crown copyright ( 2000 Published by Elsevier Science Ltd. All rights reserved.
1. Introduction A major step forward in the protection of personnel against ballistic threats, particularly irregular fragments, has been the introduction of impregnated glass "bre and synthetic textiles [1]. This has been aided by the commercialisation of "bres and resins, resulting in the use of glass-"bre-reinforced plastic (GRP), Kevlart, Nylont 66 and Polyethylene in personal armour vests, helmets, pilot seats and spall liners. Studies of ballistic penetration of fabrics and composites have examined "bre response [2,3], mechanisms of deformation [4,5] and failure [6] as well as energy absorption [6}11] and dynamic loading [12]. Despite elucidating many characteristic features of fabric and composite behaviours, no single model has emerged which allows a * Corresponding author. 1 Deceased. 0734-743X/00/$ - see front matter. Crown copyright ( 2000 Published by Elsevier Science Ltd. All rights reserved. PII: S 0 7 3 4 - 7 4 3 X ( 9 9 ) 0 0 1 7 5 - X
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Nomenclature C , C@ , C , 1 1 2 C@ , C , C 2 3 4 D D B D E D I E G C h 0 H E ¸ n S = ,= , B D = , =, = F I T / p B p C p ,e . .
constants projectile diameter minimum diameter of damage at boundary between dishing and indentation/compression deformation diameter of delamination on target exit side diameter of delamination on target impact side modulus of composite (in-plane direction) fracture toughness target thickness measured thickness of target on exit side which dishes diameter of delaminated conical dish on exit side of target number of delaminated layers displacement of idealised beam in bending work of bending, of dishing, of fracture, of indentation, and of tension, respectively theoretical thickness of target on exit side which dishes, or the target thickness at which a change in slope in energy absorption vs target thickness occurs maximum tensile stress in composite due to bending compressive stress in composite (through-thickness direction) mean tensile stress and strain, respectively, in composite (in-plane direction)
quantitative description of the ballistic perforation process. This is partly a consequence of the di!erences in behaviour between "bre types and between fabric and composite constructions, and the great diversity in thermomechanical properties, ductility, anisotropy and rate sensitivity, etc. Composites respond di!erently to the `ideala materials (metals) upon which the fundamentals of the mechanics of high strain deformation are based. It is clear that there are large di!erences in the nature of the deformation processes as the projectile proceeds through the target, the early phase being dominated by acceleration of target material, compression and crushing ahead of the projectile, and the latter stages being characterised by stretching of "bres, delamination and dishing which continues during and after perforation [4,11]. This study examines the thickness dependence of perforation of GRP composites for three projectile nose shapes by measuring ballistic resistance and by the examination of sectioned, perforated specimens. An attempt is made at analytically understanding deformation processes by comparison with observations on metallic laminates. Fragment simulator perforation data is also used to illustrate the generality of the approach.
2. Experimental Targets were constructed from woven roving E-Glass GRP of 11 plies (&4.5 mm, &27 wt% resin), 22 plies (&9 mm, &28}29 wt% resin), 33 plies (&14 mm, &27 wt% resin) and 44 plies
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Fig. 1. Kinetic energy at ballistic limit vs. target thickness for the target/projectile combinations examined in this study. The dashed line is the predicted curve for the 6.35 mm #at-ended projectile (refer text). Note that a precise ballistic limit was not obtained for the thickest target for the 453 cone angle projectiles due to severe projectile yaw within the target, hence there is some uncertainty in the position of the line of best "t. It was suspected that the ballistic limit was higher than estimated, hence the upward pointing arrow.
(&20 mm, 29}30 wt% resin) of a nominal 608 g m~2 woven cloth and DerakaneTM 411-45 vinylester resin. The laminate panels were hand layed up and cured with 1.2% of Butanox M60 methyl ethyl ketone peroxide catalyst and 0.3% of cobalt octoate co-catalyst, autoclave cured at 303C and 100 kPa for 1 h, and "nally post cured for 2 h at 903C. The average bulk density of all panels was 1.85 g cm~3. Hardened steel penetrators consisting of 6.35 mm #at-ended cylinders (of 3.84 g, 15.6 mm length), 4.76 mm #at-ended cylinders (of 3.33 g, 24.5 mm length), and 90 and 453 conically nosed 4.76 mm diameter projectiles of 3.21 g, 25.1 mm length and 2.92 g, 25.1 mm length, respectively, were used for a total of sixteen di!erent projectile/target combinations. The penetrators were "red from a commercial stud gun, and impact velocity was measured by the interruption of electromagnetic "elds. The ballistic limit, < , for each target combination was 50 calculated as the average velocity of impacting penetrators that just perforated and were just stopped by the target. Each target was at least 100 mm]100 mm and was clamped along two edges. Targets were impacted no more than four times, with the impacts spaced so that any delamination produced did not overlap with delamination damage from previous impacts. 3. Results Because the penetrators of di!erent geometry were of slightly di!erent masses, the projectile kinetic energy to just defeat the target was calculated from the ballistic limit data, and this was plotted as a function of target thickness. In this way the results from di!erent penetrators can be validly represented on the same scales for comparison. The data, shown in Fig. 1, can have two intersecting straight lines "tted for the case of each projectile, with the straight line for the thin
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Fig. 2. Kinetic energy at ballistic limit vs. target thickness for fragment simulators impacting GRP and Kevlar resin-impregnated composites [13]: (***) refers to 5.59 mm; (} } }) refers to 7.62 mm; and ( ) ) ) ) ) ) ) ) ) ) refers to 12.7 mm fragment simulating projectiles. The data have been linearly scaled by dividing by energy and thickness measures for the ordinate and the abscissa, respectively.
targets being e!ectively common for the three 4.76 mm diameter projectiles of di!erent nose geometry. The simplicity of this plot encouraged a wider search and Fig. 2 shows fragment simulator data [13] plotted for GRP and Kevlar polyester composites, for 5.59 mm (1.1 g), 7.62 mm (2.9 g) and 12.7 mm diameter (13.4 g) fragment simulators [12]. Intersecting straight lines represent the data over an extremely wide range of thicknesses and bi-linear relationships are seen for all three sizes of fragment simulator. It is notable that a common straight line was able to be "tted through both the GRP and Kevlar thin target data for each of the 5.59 and 7.62 mm projectile data sets. Similarly, fragment simulator data on bonded and unbonded Aramid fabrics [14,15] are replotted as a function of number of plies (proportional to target thickness) in Fig. 3, but using the ballistic limit velocity squared (proportional to kinetic energy) instead of ballistic limit as was presented originally. Again, bi-linear relationships are evident. Sectioning of perforated samples, Fig. 4, indicated two characteristic patterns of damage or delamination, as illustrated schematically by the horizontal hatching in Fig. 5. For thin targets the damage was in the form of a cone of delamination opening towards the target exit side, Figs. 4(a) and 5(a). This cone increased in diameter and height with increasing target thickness, until with su$ciently thick targets a cone of delamination opening towards the impact side was also added, Figs. 4(b) and 5(b). Measurements of damage geometry, de"ned in Fig. 5 as a function of target thickness and projectile geometry, are given in Table 1 along with target impact velocities and ballistic limits. These measurements should only be seen as indicative as it was often di$cult to make precise measurements, and it was suspected that the dimensions of the damage would be subject to experimental scatter. Additional targets were impacted signi"cantly above and below the ballistic limit and were sectioned to examine the variation of cone dimensions with impact velocity.
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Fig. 3. Velocity squared (proportional to kinetic energy) at ballistic limit vs. target thickness for unspeci"ed [sic] fragment simulating projectiles impacting fabric and resin-impregnated Aramid composites [14,15].
Fig. 4. Sectioned targets that have been impacted by 4.76 mm 903 conically tipped projectiles: (a) thin 4.5 mm target (187 m s~1) and (b) thick 20 mm target (464 m s~1). The impact face is the upper edge of each target.
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Fig. 5. De"nition of damage geometry dimensions speci"ed in Table 1. A thin target, (a), and a thick target, (b), are illustrated. The impact face is the upper edge of each diagram. Table 1 Target thickness, impact velocity, ballistic limit (< ) and test outcome (P"perforation and NP"no-perforation) 50 combined with damage geometry parameters de"ned in Fig. 5, and / (estimated from Fig. 1) Projectile diameter (mm)
Target thickness (h ) (mm) 0
Velocity (m s~1) Impact
Damage geometry dimensions (mm) < 50
/
Outcome
D I
D B
D E
H E
55 90 106 95
* 7 11 12.5
7.3
6.35 mm #at
4.5 9 14.5 19
216 343 482 566
210 327 473 563
P P P P
* 18 30 37
6.5 17 18.5 12
4.76 mm #at
4.5 9 14 20 20.5 19
188 319 406 399 533 566
175 293 389 505 505 505
P P P NP P P
* 15.5 31 42 42 42
5 12 19 16 20 20
53 68 82 46 81 76
* 7.5 9 12.5 9.5 11
5.8
4.76 mm 903 cone
4.5 9.5 14 20
187 277 360 464
186 274 355 452
P P P P
* 23 31 41
16 15 16 13
54 59 61 68
* 6.5 9.5 9
8.8
4.76 mm 453 cone
4.5 9.5 14.5 20.5
172 265 351 470
173 263 351 '471
P P P P
* 20 30 45
15 11 10 10
36 49 53 55
* 7 8.5 8
12.5
Table 1 lists such additional measurements for the 20 mm thick target, 4.76 mm #at-ended projectile condition. The D (diameter of delamination on the target exit side) and H (measured E E thickness of cone of delamination on target exit side) parameters were found to vary the most with impact velocity. For consistency, all other measurements of cone geometry in Table 1 were made on perforated targets that had been impacted as close as possible to their ballistic limits. Fig. 6(a) shows that D (diameter of delamination on target impact side) increases linearly with I target thickness from when it is "rst apparent on the impact face of the target. Fig. 6(b) suggests that D increases with target thickness and eventually plateaus. Greater exit-side delamination is E
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Fig. 6. Variation of damage geometry dimensions de"ned in Fig. 5: D , (a); D , (b); and h }H , (c), as a function of target I E 0 E thickness.
observed for larger projectile diameters and as nose geometry becomes blunter. D was di$cult to B measure but most values were in the range between 10 and 20 mm. H was found to increase with E thickness (refer to Table 1) and eventually plateaus for the 4.76 mm targets. Fig. 6(c) shows that the parameter h !H , a measure of the thickness of the cone of damage extending towards the impact 0 E side of the targets, was found to increase approximately linearly with increasing thickness for the 4.76 mm projectiles.
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4. Discussion Figs. 1}3 show that a transition in energy absorption occurs at a certain target thickness for both GRP and Kevlar composites and that this transition depends on projectile diameter and nose geometry as well as target material. This transition is postulated to be due to a change in perforation mechanism from largely dishing in thin targets, Figs. 4(a) and 5(a), to a combination of indentation and dishing, Figs. 4(b) and 5(b). This bi-linear dependence of energy absorption on thickness does not appear to have been previously identi"ed. This relationship could easily be interpreted as non-linear, or even linear, if a su$ciently wide range of experimental conditions was not examined. Bi-linear behaviour in terms of a change in damage area, i.e. delamination pattern, has previously been identi"ed as a function of impact energy and velocity in impacted GRP targets (e.g. [16,17]). Fig. 1 demonstrates that for thick GRP targets, pointed projectiles are more e!ective against GRP, i.e. less energy is absorbed. However, Fig. 1 also shows that energy absorption is largely independent of projectile nose geometry for thin GRP targets. It is also of interest that the response of thin GRP and Kevlar composite targets to fragment simulator projectiles, Fig. 2, appears to be independent of target material. The damage geometry in perforated GRP targets can be interpreted by analogy with the behaviour of ductile metallic targets where the deformation geometry is `frozen ina by plastic deformation [18]. Damage in GRP targets is manifested as delamination and is conveniently assessed as it is observed as an opaque area in the target and easily distinguished from the undamaged laminate. It is important to be aware that shearing [5] and fragmentation [19] have been identi"ed as important phenomena in the initial stages of perforation of GRP targets. The cone of damage on the impact side of a thick target is interpreted as being a consequence of compression of material ahead of the penetrator. This leads to radial pressure due to displacement of fragmented material, which causes an upthrust of laminae to compensate. As the projectile nears the exit side of the target, it is easier for layers to delaminate and bend away from the oncoming projectile in the direction of projectile motion. Dishing occurs and forms the cone of the damage opening towards the exit side of the target. The measurements made of D , D , D and I E B H , de"ned in Fig. 5, characterise the separate zones of compression and dishing in the various E targets. The work done in perforation of a target is therefore the sum of the work of all the deformation mechanisms. However, kinetic energy is also given to moving layers at the rear of the target [11] and ejected debris [19]. Both of these e!ects are important but were not accounted for in the current modelling exercise as they require specialised instrumentation for characterisation, e.g. high-speed cine photography, and thus the development of a suitable model for this phenomenon is beyond the scope of the current study. For a thin target which forms a delaminated conical dish, as seen in high-speed cine images [11], the work of tension is the mean tensile stress in the composite, p , times the mean strain, . e (e "p /E, where E is the composite modulus) times the deformed volume. If ¸ is the diameter . . . of the delaminated conical dish on the outside of the target and h the thickness of the deforming 0 target, then the work of tension, = , is given by T = "C ¸2h p2 /E, T 1 0 .
(1)
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where the constant C accounts for the through thickness geometry of the delaminated region of 1 the target as illustrated in Figs. 4(a) and 5(a). For composites with a brittle binder, delamination will occur with work done estimated from the fracture toughness, via G , where shear or opening modes are not speci"ed here, times the area of C delamination (proportional to ¸2) times the number of layers (proportional to h ) times a geometry 0 dependant constant, C , which accounts for the through-thickness variation in the radius of 2 delamination, as per Figs. 4(a) and 5(a). Fracture of the binder phase will be more general than simple delamination, being better described as fragmentation, however this more general break-up can be also captured in the three terms: strain energy release rate, G ; volume; and the geometrical C constant. Thus the work of fracture, = , becomes F = "C G h ¸2. (2) F 2 C 0 The work of bending can be examined by treating the dish as a beam of width p¸, with the hinge at a position ¸/2 from the applied load. If S is the displacement of the load and the yield moment is given by p¸h2p /6 [20], then the bending work, = , is given by 0 . B = "C h2p S, (3a) B 3 0 B where p is the maximum composite tensile stress due to bending. Once matrix fracture and B delamination occur, the beam is e!ectively con"gured of n-independent layers, each of thickness h /n, so that the work of bending is then expressed as 0 = "C h2p S/n. (3b) B 3 0 B Substitution of typical material and geometric parameters into Eq. (3b) shows = is small in B comparison to = . Whilst the work of bending may be small, the resistance to bending before T delamination as represented by the derivative with respect to displacement, S, of Eq. (3a) can be large. After delamination, the resistance to bending is much less as the derivative with respect to displacement of Eq. (3b) is smaller than that of Eq. (3a), allowing the dishing mechanism to develop. It is the initial resistance to bending that determines whether dishing will occur upon impact or later during the perforation process, even though the bending work does not contribute at the same magnitude as the other terms in the total work of perforation. Analogous studies on metallic laminates have shown that despite bending work being small, the bending resistance of the target will determine whether or not dishing occurs as well as in#uence the degree of dishing on the target exit-side [18]. For a thin composite target, with = small, using Eqs. (1) and (2), the work of B dishing, = , becomes D = += #= "¸2h (C p2 /E#C G ). (4) D T F 0 1 . 2 C As the diameter of the dished region, ¸, is expected to increase in proportion to the diameter of the projectile, D, Eq. (4) becomes = +D2h (C@ p2 /E#C@ G ), (5) D 0 1 . 2 C where the modi"ed constants C@ and C@ include the proportionality constant ¸/D. 1 2 For a su$ciently thick target, the initial resistance to bending will be high enough to prevent dishing until the penetrator nears the target exit side. Penetration will therefore initially occur by
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an indentation mechanism. The work of indentation, = , is the presented area times the compresI sive stress, p , times the displacement. Account is taken of con"nement of the compressed material C [5] by increasing the e!ective material #ow stress by a constant, and with this and the geometrical constants included in a constant C , the work becomes 4 = "C D2p (h !/), (6) I 4 C 0 where h is the total target thickness and / is the thickness on the exit side which dishes instead of 0 being indented. The work of perforation of a thick target then becomes the sum of = , Eq. (6), and I = , Eq. (5) where h in Eq. (5) is equal to /. Thus / is assumed to be the target thickness at which D 0 the change of slope occurs as in Figs. 1}3. The analysis results in the work of perforation being bi-linearly proportional to target thickness with di!erent slopes for thin and thick targets, as observed experimentally (Figs. 1}3). The two slopes would suggest that complete perforation of thin composite targets should be by one mechanism, that represented by the lower slope, which is dishing rather than indentation and compression. The analysis has therefore provided a de"nition of a thin composite target. This is not the case for thick bonded composites because of their high initial resistance to bending. Thick composites will therefore initially be penetrated by the indentation mechanism until fracture of the matrix phase at the ply interfaces can be achieved, which then allows the dishing mechanism to develop at the rear of such targets. There is, in fact, some evidence to suggest that reducing the resistance to bending in composites by using separate impregnated plies reduces ballistic performance [15]. For unbonded layered targets the slope of the work versus target thickness curve is high for thin targets as shown in Fig. 3. This is probably a consequence of a very large diameter of dished region, ¸, [21] in Eq. (4) leading to large values of C@ and C@ in Eq. (5). The material and geometric 1 2 parameters in Eqs. (5) and (6) are not well understood from this analysis, because average strength parameters are used in lieu of a better knowledge of the mechanics of large-deformation composite behaviour. However, these equations give a basis for understanding the linear relationships evident in Figs. 1}3 and an appropriate method of scaling with projectile diameter and target thickness. Similar projectile nose shapes must be compared when scaling ballistic data. For instance, Eqs. (5) and (6) specify that the slope (energy/thickness) for both thin and thick targets should depend on the square of projectile diameter. Fig. 1 is used as an example, where the slopes for the #at-ended 4.76 mm projectile and the ratio of the squares of the projectile diameters are used to predict the curve for the 6.35 mm #at-ended projectile (shown as a dashed line), assuming / is known for this latter projectile. The theory appears to be adequate for relative scaling purposes in this instance as the predicted slopes for the #at-ended 6.35 mm projectile are within 10% (for thin targets) and 4% (for thick targets) of those determined experimentally. It is expected that the change in slope at a target thickness / as speci"ed in the model of Eqs. (5) and (6) and from Fig. 1 relates to the parameter H determined by post-perforation measurements. E Table 1 compares these measurements and shows that notable di!erences exist. The model also predicts that / remains constant once indentation and compression deformation become signi"cant, i.e. beyond a target thickness of /. Experimentally, it was found that a constant value of H was not reached for the 6.35 mm projectiles and for the 4.76 mm projectiles a constant value E was only apparent for the 14 mm and 20 mm targets. Any correlation between the measured post-perforation microstructural information and the transition points represented in Fig. 1 is at best approximate. This is partly because of simple idealisation in the modelling and partly because
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of post-perforation deformation and recovery in the experimental materials. Fig. 6(c) does, however, demonstrate that an approximate linear increase in h !H (i.e. the thickness of target 0 E that is penetrated by indentation and compression deformation) occurs beyond certain critical thicknesses. In reality there may be a somewhat gradual transition from dishing to indentation and compression, beginning at target thicknesses less than 9 mm. In the present instance this is probably masked by the absence of targets between 4.5 and 9 mm in thickness. It should be noted that the H values could easily vary by a millimetre or so because of the subjective nature and E imprecision of the H measurements and the expected shot-to-shot scatter. This makes precise E correlations di$cult, especially for the 9 mm targets where H is small. E The analysis has also shown that the indentation phase is a more signi"cant absorber of energy and indicates that it should be maximised in any bonded composite armour design. This indicates that thicker bonded composite armours would be more e$cient ballistically, especially against blunt projectiles. It is also interesting that smaller cone angle projectiles were found to have larger values of /, i.e. greater thicknesses of dishing. The model predicts that this translates to a greater proportion of a given target thickness deforming by a lower energy dishing mode. Presumably, this is one reason for such target/projectile combinations having lower ballistic limits. 5. Conclusions Ballistic perforation data and post-perforation microstructural measurements are presented for a range of projectile shapes impacting GRP targets. The ballistic data, when plotted as energy to penetrate the target as a function of target thickness, can be "tted to simple bi-linear plots. A simple model is developed to explain the relationship and it gives a basis for geometrical scaling of ballistic perforation data for composite targets and a de"nition of a thin target. The relationships established are also seen in other data sets for composite targets. Importantly, the analysis has shown that the indentation phase is a more signi"cant absorber of energy and should be maximised in any bonded composite armour design, indicating that thicker targets are more e$cient ballistically, especially against blunt projectiles. It was of interest that energy absorption in thin GRP targets is largely independent of projectile nose geometry and that thin GRP and Kevlar targets respond similarly on a thickness basis against fragment simulator projectiles. Acknowledgements The authors wish to acknowledge the contributions of Mr Jim Dimas and Mr Stephen Pattie for their e!orts in ballistic testing. Mr Alban Cole and Mrs Karen Challis are also to be thanked for their patient sectioning and polishing. References [1] Laible RC. In: Laible RC, editor. Ballistic materials and penetration mechanics. Amsterdam: Elsevier, 1980. p. 9. [2] Petterson DR, Stewart GM, Odell FA, Maheux RC. Dynamic distribution of strain in textile materials under high speed impact, part I: experimental methods and preliminary results on single yarns. Textile Res J 1960;30:411}21.
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[3] Jameson JW, Steward GM, Petterson DR, Odell FA. Dynamic distribution of strain in textile materials under high speed impact, part III: strain-time-position history in yarns. Textiles Res J 1962;32:858}60. [4] Egglestone GT, Gellert EP, Woodward RL, Perforation failure mechanisms in laminated composites. In: Davies RD, Hatcher DI, editors. Materials united in the service of man, IMMA, Perth, Australia, 17}21 September, 1990, Vol. 1, p. 2.1}11. [5] Woodward RL, Egglestone GT, Baxter BJ, Challis K. Resistance to penetration and compression of "brereinforced composite materials. Composites Engng 1994;4:329}41. [6] Zhu G, Goldsmith W, Dharan CKH. Penetration of laminated Kevlar by projectiles*I. Experimental investigation. Int J Solids Struct 1992;29:399}420. [7] Jang BZ, Chen LC, Hwang LR, Hawkes JE, Zee RH. The response of "brous composites to impact loading. Polym Compos 1990;11:144. [8] Zee RH, Hsieh CY. Energy loss partitioning during ballistic impact of polymer composites. Polym Compos 1993;14:265. [9] O'Donnell RG. Deformation energy of Kevlar backing plates. J Mater Sci Lett 1993;12:1485}6. [10] Scott BR, Brunner Jr RF. Transient distributed loading of ballistic panels. Proceedings of the 14th International Symposium on Ballistics, ADPA, Quebec. Canada, September 1993. p. 729. [11] Gellert EP, Pattie SD, Woodward RL. Energy transfer in ballistic perforation of "bre reinforced composites. J Mat Sci 1998;33:1845}50. [12] Mascianica FS. In: Laible RC, editor. Ballistic materials and penetration mechanics. Amsterdam: Elsevier, 1980. p. 41. [13] Mascianica FS. Ballistic technology of light weight armour (U), AMMRC TR 81}20, 1981. Con"dential. [14] Savage GM, Fabric and "bre reinforced laminate armours. Metals and Mater 1989; May: 285}90. [15] Shephard RG, The use of polymers in personal ballistic protection. International Conference on Polymers in Defence. The Plastics and Rubber Institute, Bristol, March 1987. p. 21/1-21/10. [16] Wu E, Chang LC. Woven glass/epoxy laminates subject to projectile impact. Int J Impact Engng 1995;16:607}19. [17] Thaumaturgo C, Da Costa Jr. AM. Shock waves on polymer composites. J Mater Sci Lett 1997;16:1480}2. [18] Woodward RL, Cimpoeru SJ. A study of the perforation of aluminium laminate targets. Int J Impact Engng 1998;21:117}31. [19] Greaves LJ. Defence research agency memorandum 12/92, Chertsey memorandum 92003. Chertsey, Surrey, March 1992. [20] Johnson W, Mellor PB. Plasticity for mechanical engineers. London: Van Nostrand, 1962. p. 96. [21] Morrison CE, Bowyer WH. Factors a!ecting the ballistic impact resistance of Kevlar laminates. In: Bunsell AR, editor. Advances in composite materials, Vol. 1. Oxford: Pergamon Press, 1980. p. 233.