Penetration Mechanisms in Glass Laminate-resin Structures

11
Penetration mechanisms in glass laminate/resin structures G.J. Appleby-Thomas a,, P.J. Hazell a , R. Cleave b a Cranfield Defence and Security, Cranfield University, Shrivenham, Swindon SN6 8LA, UK b Hamilton Erskine Ltd., 17 Moss Road, Ballygowan, Co. Down BT23 6JQ, UK article info Article history: Received 27 January 2011 Accepted 5 May 2011 Available online 13 May 2011 Keywords: A. Elastomers and rubbers B. Laminates E. Impact and ballistic abstract The ballistic response of composite structures comprising differing laminated float glass/polycarbonate replacement resin (PRR) elements was studied. In order to provide materials data for future modelling work, sphere-impact tests were employed to determine the high strain-rate response of the elastomeric resin. Larger-scale armour simulants comprising glass-laminate-fronted cylinders of PRR were also inves- tigated using lead antimony-cored 7.62 mm 51 mm NATO Ball rounds in order to interrogate their behaviour under impact. Penetration mechanisms were studied via the use of high-speed video equip- ment. Projectile defeat in the resin was observed to depend on the degree of projectile disruption, with a greater degree of comminution leading to enhanced behaviour. This confirmed the importance of the elastomeric properties of the resin in behaviour under ballistic impact in these structures. The interaction between the glass disrupting layer and the backing absorber was found to be key to minimising subse- quent penetration. The use of asymmetric float glass laminates incorporating a thinner disrupting outer surface was found to reduce subsequent depth of penetration by as much as 52% compared to similar areal density monolithic systems. High-speed video footage implied that the thinner outer layer acted to blunt the incident projectile, while the backing thick layer of glass exhibiting a Hertzian cone-like ‘‘plugging’’ failure mechanism. In addition analysis of high-speed video showed that the penetration rate in the resin was initially constant, implying penetration analogous to hydrodynamic behaviour. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction While monolithic armour solutions, such as Al 5083-H32 [1] and polycarbonate [2] are relatively commonplace, composite sys- tems allow more flexibility in design, with the potential to exploit useful properties of different elements in a complimentary manner [3–8]. Composite armour systems typically comprise two ele- ments: (1) a disrupter, ideally with a hardness > that of the likely threat, designed to fracture or otherwise break up an incident pro- jectile, and (2) an absorber, designed to dissipate the kinetic energy of an incident projectile [3,5,8,9]. In order to fully characterise such systems (e.g. for the purpose of simulation), knowledge of both material properties of the individual elements, and the way in which they interact under loading, is required. Very many novel combinations of armour have been employed. For example, Übeyli et al. [3] and Hetherington [10] both carried out similar studies investigating the ballistic response of alumina (Al 2 O 3 )/aluminium composite armours. Übeyli et al. conducted a series of experiments to compare the response of high strength low alloy (50CrV4) steel to the laminated alumina/aluminium composites (in varying configurations) following impact with 7.62 mm 51 mm M61 armour piercing (AP) rounds. The compos- ite systems considered were shown to provide weight savings of up to 26% whilst maintaining ballistic resistance. As well as high- lighting a variety of failure mechanisms in the composite, Übeyli et al. were able to show that an alumina (facing)/aluminium (back- ing) thickness ratio of 1:3 appeared optimal for ballistic purposes for a given armour areal density. Interestingly, via a comparison of numerical simulations and experiment (again, involving attack with 7.62 mm AP ammunition), a similar thickness ratio – in the range 1:2.5–1:2.9 – was identified by Hetherington [10] for a com- parable composite arrangement. In similar work, Jena et al. [4] investigated the ballistic response to impact with 7.62 mm AP rounds of a variety of steel (both as-received and heat-treated)/ Al-7017 aluminium and vacuum-bonded steel/Dyneema Ò (a high specific strength and high stiffness polyethylene fibre-based mate- rial) composite targets. The importance of target configuration – namely maintaining a gap between the steel and Al-7017 layers – was highlighted. Steel/Dyneema Ò systems were also shown to be extremely effective, with weight savings of c.55% achievable when the ballistic response of the composite inclined at 30° was compared to that of 380 BHN rolled homogenous armour under normal attack. While useful for applications such as vehicle armour, the solu- tions described above [3,4,10] are not applicable to situations where a tranparent solution is required. Transparent armour is 0261-3069/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2011.05.006 Corresponding author. Tel.: +44 (0) 1793 785731; fax: +44 (0) 1793 785772. E-mail addresses: g.applebythomas@cranfield.ac.uk (G.J. Appleby-Thomas), p.j.hazell@cranfield.ac.uk (P.J. Hazell), [email protected] (R. Cleave). Materials and Design 34 (2012) 541–551 Contents lists available at ScienceDirect Materials and Design journal homepage: www.elsevier.com/locate/matdes

Transcript of Penetration Mechanisms in Glass Laminate-resin Structures

Page 1: Penetration Mechanisms in Glass Laminate-resin Structures

Materials and Design 34 (2012) 541–551

Contents lists available at ScienceDirect

Materials and Design

journal homepage: www.elsevier .com/locate /matdes

Penetration mechanisms in glass laminate/resin structures

G.J. Appleby-Thomas a,⇑, P.J. Hazell a, R. Cleave b

a Cranfield Defence and Security, Cranfield University, Shrivenham, Swindon SN6 8LA, UKb Hamilton Erskine Ltd., 17 Moss Road, Ballygowan, Co. Down BT23 6JQ, UK

a r t i c l e i n f o

Article history:Received 27 January 2011Accepted 5 May 2011Available online 13 May 2011

Keywords:A. Elastomers and rubbersB. LaminatesE. Impact and ballistic

0261-3069/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.matdes.2011.05.006

⇑ Corresponding author. Tel.: +44 (0) 1793 785731;E-mail addresses: [email protected]

[email protected] (P.J. Hazell), rcc@hamiltoner

a b s t r a c t

The ballistic response of composite structures comprising differing laminated float glass/polycarbonatereplacement resin (PRR) elements was studied. In order to provide materials data for future modellingwork, sphere-impact tests were employed to determine the high strain-rate response of the elastomericresin. Larger-scale armour simulants comprising glass-laminate-fronted cylinders of PRR were also inves-tigated using lead antimony-cored 7.62 mm � 51 mm NATO Ball rounds in order to interrogate theirbehaviour under impact. Penetration mechanisms were studied via the use of high-speed video equip-ment. Projectile defeat in the resin was observed to depend on the degree of projectile disruption, witha greater degree of comminution leading to enhanced behaviour. This confirmed the importance of theelastomeric properties of the resin in behaviour under ballistic impact in these structures. The interactionbetween the glass disrupting layer and the backing absorber was found to be key to minimising subse-quent penetration. The use of asymmetric float glass laminates incorporating a thinner disrupting outersurface was found to reduce subsequent depth of penetration by as much as 52% compared to similarareal density monolithic systems. High-speed video footage implied that the thinner outer layer actedto blunt the incident projectile, while the backing thick layer of glass exhibiting a Hertzian cone-like‘‘plugging’’ failure mechanism. In addition analysis of high-speed video showed that the penetration ratein the resin was initially constant, implying penetration analogous to hydrodynamic behaviour.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

While monolithic armour solutions, such as Al 5083-H32 [1]and polycarbonate [2] are relatively commonplace, composite sys-tems allow more flexibility in design, with the potential to exploituseful properties of different elements in a complimentary manner[3–8]. Composite armour systems typically comprise two ele-ments: (1) a disrupter, ideally with a hardness > that of the likelythreat, designed to fracture or otherwise break up an incident pro-jectile, and (2) an absorber, designed to dissipate the kinetic energyof an incident projectile [3,5,8,9]. In order to fully characterise suchsystems (e.g. for the purpose of simulation), knowledge of bothmaterial properties of the individual elements, and the way inwhich they interact under loading, is required.

Very many novel combinations of armour have been employed.For example, Übeyli et al. [3] and Hetherington [10] both carriedout similar studies investigating the ballistic response of alumina(Al2O3)/aluminium composite armours. Übeyli et al. conducted aseries of experiments to compare the response of high strengthlow alloy (50CrV4) steel to the laminated alumina/aluminiumcomposites (in varying configurations) following impact with

ll rights reserved.

fax: +44 (0) 1793 785772..uk (G.J. Appleby-Thomas),skine.com (R. Cleave).

7.62 mm � 51 mm M61 armour piercing (AP) rounds. The compos-ite systems considered were shown to provide weight savings ofup to 26% whilst maintaining ballistic resistance. As well as high-lighting a variety of failure mechanisms in the composite, Übeyliet al. were able to show that an alumina (facing)/aluminium (back-ing) thickness ratio of 1:3 appeared optimal for ballistic purposesfor a given armour areal density. Interestingly, via a comparisonof numerical simulations and experiment (again, involving attackwith 7.62 mm AP ammunition), a similar thickness ratio – in therange 1:2.5–1:2.9 – was identified by Hetherington [10] for a com-parable composite arrangement. In similar work, Jena et al. [4]investigated the ballistic response to impact with 7.62 mm AProunds of a variety of steel (both as-received and heat-treated)/Al-7017 aluminium and vacuum-bonded steel/Dyneema� (a highspecific strength and high stiffness polyethylene fibre-based mate-rial) composite targets. The importance of target configuration –namely maintaining a gap between the steel and Al-7017 layers– was highlighted. Steel/Dyneema� systems were also shown tobe extremely effective, with weight savings of c.55% achievablewhen the ballistic response of the composite inclined at 30� wascompared to that of 380 BHN rolled homogenous armour undernormal attack.

While useful for applications such as vehicle armour, the solu-tions described above [3,4,10] are not applicable to situationswhere a tranparent solution is required. Transparent armour is

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an important niche, e.g. for windows in both armoured-vehiclesand buildings. However, by their nature, material choices for trans-parent armours are limited. Typically a composite of several ele-ments is employed, e.g. laminates of glass and/or transparentceramics (such as spinel or sapphire – e.g. single alumina crystals),and polycarbonate. Polycarbonate, as well as possessing an inher-ent degree of ballistic resistance [2], is typically employed as abacking layer to impede crack formation and catch residual projec-tile/comminuted target material. Inter-laminate bonds are a fur-ther important element and normally comprise a polymer filmsuch as polyvinyl butyrate (PvB) [8,9,11]. Unfortunately, in orderto meet likely threats, high laminate thicknesses are often re-quired. This increases armour weight and in the process can leadto degradation in optical transparency [12]. Reduction of the arealdensity of transparent armours either by optimising the architec-ture of current solutions or via the inclusion of more weight-efficient materials solutions is therefore desirable. Polyurethane,an elastomeric thermosetting resin, is a current candidate materialfor transparent armour systems. A transparent polyurethane-basedarmour system, known as Cleargard�, has been successfully devel-oped and brought to market by BAE Systems [13,14]. This materialhas, for a given areal density, shown superior ballistic performancecompared to both polycarbonate and acrylic and has been showneffective against threats ranging from fragmentation (in a mono-lithic layer) to Pb-cored 7.62 mm ammunition (as part of a com-posite solution). A similar material, from an alternate source, ispolycarbonate replacement resin (PRR); a polyurethane resin [8].PRR is a potential candidate for nano-reinforcement [15] and hasa similar refractive index to glass, rendering it transparent. Its ex-tended cross-linking imparts a high toughness, while the materialhas a lower density then glass, providing a direct weight saving ifsubstituted for other elements of a transparent armour system.When uncured PRR is a viscous liquid – a property which allowsit to be cast into complex geometries. Usefully, if cured in contactwith glass a strong chemical bond is formed. While suitable for theenergy-absorbing element of transparent armour, the low hard-ness of PRR means that a hard-faced disruptor is required on theface adjacent to the threat. Krell et al. [11] considered ceramicssuch as spinel and alumina for this application. Their high hardness(typically HV10 > 20 GPa) provides maximal ballistic strength. Fol-lowing a discussion of manufacturing routes leading to the produc-tion of a variety of different configurations of spinel and alumina,Krell et al. carried out a series of ballistic tests using7.62 mm � 51 mm AP ammunition which highlighted the impor-tance of using the lowest practical grain size. Not only does thisact to limit the potential for lattice-based elements of microplastic-ity (e.g. dislocations and twins) to migrate within the structure, butsmaller grain sizes also result in increased optical transparency.Klement et al. [9] studied a range of potential facing materialsincluding float glass, glass ceramic, quartz glass, ALON (aluminiumoxynitride) and sapphire. Depth of penetration (DOP) tests usingboth 7.62 mm � 51 mm WC–Co cored AP8 (NAMMO) and7.62 mm � 54 mm R B32 API hard steel cored (RAPI) AP projectileswere carried out on single materials as well as composites. Thesecomposite systems comprised glass and ceramic-faces with floatglass central sections backed by polycarbonate layers. Sapphire(HV0.1 = 2158) and ALON (HV0.1 = 1772) were shown to reduceDOP by 22% and 31% respectively compared to float glass(HV0.1 = 572) using NAMMO projectiles and by 57% and 38%respectively using RAPI projectiles (in the latter case comparedto glass ceramic – HV0.1 = 633). Similar results were found whencomparing the performance of the glass and sapphire faced com-posites considered. Overall, these results confirmed the advantagesof increased hardness in defeating incident projectiles.

As discussed above, many authors have considered individualelements of transparent armour systems [9,11]. However, as sug-

gested by the experimental and modelling work on glass-facedPRR-backed systems undertaken previously by Hazell et al. [8],the interaction between the various elements is also of importance.Hazell et al. showed that following impact with a lead antimony-cored 7.62 mm � 51 mm bullet, significant projectile disruptionoccurred during penetration, although interestingly the shape ofthe resultant penetration cavity was largely governed by the elas-tomeric nature of the PRR. Analysis of high-speed video of the pen-etration event plus recovered material – as well as comparison tocomputational simulations – indicated that both core and jacketmaterial were deposited along the penetration path, with the bulletessentially turning inside-out. In essence, these results showed thatat elevated strain-rates (e.g. at the tip of an impacting projectile),materials often behave in a hydrodynamic manner – i.e. strengtheffects become negligible [16]. The material response in suchstrain-rate regimes is largely governed by the equation-of-state,which allows pressure, energy, shock velocity, particle velocity(the continuum velocity of atoms or structures propagating a shock)and density to be related to each other. The authors of this paperpreviously experimentally derived the high strain-rate equation-of-state for PRR [17] via the impedance-matching technique[16,18,19]. At high particle velocities (uP)/impact pressures goodagreement with the behaviour of polyurethane was observed. Alinear relationship was apparent in the particle velocity–shockvelocity plane up to uP � 0.4 mm/ls. However, below this value(and particularly for uP < 0.2 mm/ls), the experimental data wasobserved to trend below the equation-of-state of polyurethane.Such non-linearity has been attributed elsewhere to disparity inthe strength of the backbone (polymer chain) and inter-chainforces, with the latter an order of magnitude smaller than the for-mer, leading to a multi-stage response to compression [20].

Such information, when combined with a suitable strengthmodel, can aid numerical simulation of impact phenomena. How-ever, in the ballistic impact regime strength and failure mecha-nisms are of greater importance. Consequently, in this paper thefailure and lead-cored projectile defeat mechanisms of a floatglass/PRR-based transparent armour concept are considered. ThisPRR-based solution was conceived in an attempt to reduce theareal density of such armours by c.20%. This work builds on thecomputational and experimental studies undertaken on similarsystems by Hazell et al. [8]. The overall aim was to extend under-standing of the mechanisms controlling both penetration into PRRand, unlike the pure float glass considered in Ref. [8], the effectsand projectile-defeat mechanisms associated with laminated floatglass disrupting layers. To this end, experiments have been under-taken to increase understanding of both the properties and interac-tion of the various elements of this composite armour system;preliminary results are reported here. Two different approacheswere adopted: (1) sphere-impact tests [21] to study the deforma-tion mechanisms of projectiles within the resin itself, with bothdeforming and non-deforming projectiles employed to maximisethe extent of information gained, and (2) ballistic impact testsinvolving single 7.62 mm � 51 mm NATO Ball rounds impactingthe centre of float glass-faced PRR targets to study, by comparisonto the sphere impact results, penetration mechanisms into thecomposite system.

2. Experimental

Two different types of tests were employed to investigate dif-ferent aspects of the ballistic response of glass/PRR compositestructures. Sphere-impact tests were used to investigate the natureof penetration into the PRR-only. Ballistic-impact tests were alsoconducted; these used 7.62 mm ammunition on an indoor firingrange to try and clarify the effect of differing glass-laminates. An

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outline of the experimental approach adopted for each type of testis presented in Sections 2.1 and 2.2 respectively.

2.1. Sphere-impact

Sphere-impact tests were conducted using a Ø30 mm smooth-bore, 5 m barrel, single-stage gas-gun. Both deforming Pb and morerigid (essentially non-deforming) WC–Co projectiles were selected.These materials were selected as they represent typical standard-issue bullet core materials. Impact velocities were chosen such thatboth projectiles possessed similar kinetic/impact energies ofc.1.8 kJ. Full details of the projectiles used and the associated im-pact conditions are set out in Table 1.

Projectiles were encased in acetal sabots which were strippedimmediately on exit from the muzzle. Targets comprised polycar-bonate boxes (with 6 mm thick sides) assembled to provide suffi-cient internal volume to cast 100 mm � 100 mm (impact face),95–100 mm deep, PRR in situ. These targets were placedc.20 mm from the exit of the sabot stripper, with impact phenom-ena recorded using a Phantom V12 high-speed camera. Frame ratesof 15,000–22,500 frames/s were employed with typical exposuretimes of 10 ls. Further via. the use of fiducial markers theserecordings also allowed calculation of the projectile impactvelocities. In addition to information obtained from high-speedvideo, the final depth of penetration and other key features wereassessed by visual analysis of the targets post-impact.

Fig. 1. Selected high-speed video frames showing the penetration of a Ø12 mmWC–Co sphere into a typical resin target at 515 ± 10 m/s.

2.2. Ballistic impact

Ballistic testing using 7.62 mm � 51 mm NATO Ball rounds wasundertaken using a proof barrel located 10 m from the targets frontface. A single bullet was fired into the centre of each target. Twodifferent geometries of target were employed: (1) outerØ170 mm tubes, and (2) outer Ø120 mm tubes, in both cases com-prising 4 mm thickness polycarbonate, filled with PRR and facedwith varying architectures of float glass laminates. Target assemblywas conducted by Hamilton Erskine Ltd. (N. Ireland, UK) and tookadvantage of the ability of PRR to chemically bond to glass on set-ting. Essentially, the required polycarbonate tube was placed ontothe rear surface of the face-down prepared laminate before beingfilled with resin. Further, to allow for resin cure times, the PRRwas typically cast in 3–4 layers, each of 30–50 mm thickness, withsuccessive layers only cast once the previous one had set. Due tothe proprietary nature of the laminate combinations employedspecific details of the float glass architectures tested are withheld.Instead, only the generic nature of the facing glass arrangementsare discussed. Further, specific results are only compared for sim-ilar areal density systems – with a maximum deviation of +25%from the monolithic layer employed as a standard. None-the-less,it is felt that this level of detail is sufficient to highlight key mech-anisms controlling transparent armour defeat in such systems. PvBinterlayers were employed between laminate layers unless other-wise stated. Bullet velocities were measured using a combinationof a Doppler-based measurement system and a series of light-gatesknown as a ‘sky screen’. An average impact velocity of c.812 m/swas recorded, in good agreement with BR6 standards [22,23]. Im-pact conditions were monitored using a Phantom V12 high-speed

Table 1Key properties of projectiles employed for sphere impact tests.

Projectile Mass (g) Vimpact (m/s)

Ø12.0 mm Tungsten carbide (WC–6Co) 13.5 515 ± 10Ø12.6 mm Lead (Pb) 11.7 550 ± 10

camera operating at a maximum frame rate of 120,171 frames/sand typical exposure of 8 ls.

3. Results and discussion

3.1. Sphere-impact

As expected, the morphology of penetration into PRR targetswas found to depend upon the choice of projectile. With non-deforming WC–Co projectiles, a post-impact penetration pathwas formed within the resin. This subsequently closed behindthe intact projectile. Interestingly, analysis of high-speed videofootage showed that the final depth of the projectile within the tar-get was significantly less than the maximum depth of penetration.Both the closure of the penetration path and subsequent bulkrecovery appear to be linked to the elastomeric nature of the resin.Both of these phenomena are clearly visible in Fig. 1.

Fig. 1 shows the penetration of a WC–Co projectile into a typicalresin target. Such results suggest that deformation of the resinleads to the build-up of stored elastic strain energy. Once thesphere had begun to penetrate the resin the penetration path be-gan to close behind. Finally, once a maximum depth of penetrationhad been reached, relaxation of the elastically deformed resin re-sulted in a notably lower final depth (e.g. the frame at 1558 ls inFig. 1 as opposed to that at 356 ls).

The significantly softer Pb projectiles, however, deformed onimpact/during subsequent penetration. Analysis of both the targetsand high-speed video captured during the impact indicated thatprojectile material was continually broken up during passagethrough the resin. This disrupted material was pushed to one sideas the projectile passed and was subsequently trapped in situwhen the deformed resin relaxed, leaving behind a series of char-acteristic ‘wings’ which pointed along the direction of formation ofthe penetration path (observed previously in PRR by Hazell et al.[8]). These structures are discernable in Fig. 2 which shows thepenetration of a Ø12.5 mm Pb projectile into a pure PRR target.Again, relaxation similar to that seen with the WC–Co projectileshown in Fig. 1 was apparent after the projectile had reached itsmaximum depth of penetration. This suggested that a large partof the penetration process is controlled by the elastomeric proper-ties of the resin. Further, the lower overall depth-of-penetrationcompared to the WC–Co case shown in Fig. 1, despite the similarity

Impact energy (kJ) Source

1.79 Atlas Ball & Bearing Co. Ltd., Walsall, UK (grade 25)1.77 G.E. Fulton & Son, Bisley Camp, Surrey, UK

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Fig. 2. Selected high-speed video frames showing the penetration of a Ø12.5 mm Pb sphere into a PRR target at 550 ± 10 m/s.

Fig. 3. Frames extracted from high-speed video showing the impact of an 822 m/s 7.62 mm NATO Ball round into a thinner-fronted bi-layer asymmetric float-glass faced PRRbacked cylindrical target.

544 G.J. Appleby-Thomas et al. / Materials and Design 34 (2012) 541–551

in impact energies (Table 1), suggested that the area of materialpresented to the resin by the penetrating projectile was important.

Essentially a larger incident projectile surface area (caused by pro-jectile disruption) appeared to dissipate the projectiles kinetic

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Table 2Ballistic impact experimental results – cylindrical laminated glass-fronted PRR-backed targets impacted in the centre by a single 7.62 mm � 51 mm NATO Ball round.

Exp. no. Glass arrangement (front ? back) Facing areal density relativeto monolithic layer

Depth-of-penetration (mm)

Vimpact (m/s) Final (meas.) Max. (HSV) Final (HSV) Elastic recovery

1 Thin/thick +25% 822 21.1 32.4 23.9 8.52 50:50 bi-layer = 836 68.2 71.2 68.2 3.03 Monolithic = 813 60.5 61.8 59.0 2.74 50:50 bi-layer = 806 61.1 64.2 60.5 3.75 Monolithic = 838 – 65.9 64.0 1.96 Thin/thick = 814 – 63.0 60.8 2.37 Thin/thick = 811 58.1 60.9 58.8 2.28 50:50 bi-layer = 810 – 69.6 67.4 2.29 50:50 bi-layer = 813 – 67.8 64.8 2.9

10 Thin/thick +25% 812 – 35.2 29.7 5.511 Thin/thick 50:50

(tri-layer)+25% 818 – 60.8 57.4 3.4

12 Thin/thick 50:50(tri-layer)

+25% 808 55.9 58.1 54.4 3.7

13 Thin/thick +25% 814 – 36.0 32.3 3.814 Thin/thick +25% 815 – 44.5 42.9 1.6

G.J. Appleby-Thomas et al. / Materials and Design 34 (2012) 541–551 545

energy over a larger surface area (and corresponding backing vol-ume) of PRR. This allowed the projectiles energy to be dissipatedover a shorter penetration distance within the PRR (albeit with awider area of damage across the targets face), leading to a reducedsubsequent depth-of-penetration.

3.2. Ballistic impact

A series of frames extracted from a typical high-speed videorecording of an impact into a cylindrical target are shown inFig. 3. The transparent area to the left of each frame is the PRR-filled polycarbonate tube, with the glass facing layer visible as darkbands towards the centre. This test involved impact of a single7.62 mm NATO Ball round, visible to the right of the target at0 ls, into the centre of a cylindrical PRR-filled polycarbonate tubefaced by a bi-layer asymmetric float-glass laminate (with a thinnerouter face). Just after impact at 41 ls comminuted glass is visibleflowing away from the impact site. By 83 ls the flow of ejectedmaterial has increased in volume and an area of disruption has be-come apparent within the backing resin. Subsequent studies athigher frame-rates showed that the width of this area grows beforenecking (apparent at 124 ls in Fig. 3) occurs and the area of dis-rupted material forms two different regions. It is postulated thatat this point stored elastic strain energy imparted to the resin bythe bullet impact has reached a sufficient level to allow the resinto recover about the point of greatest instability with in the flowof disrupted material. This lateral recovery/necking, analogous tothe closure of the penetration path behind WC–Co and Pb projec-tiles observed in the sphere-impact tests (Figs. 1 and 2 respec-tively), continues as penetration increases. One particularlyimportant observation is the large degree of recovery apparentalong the axis of penetration. Peak penetration occurs at around166 ls, reaching a depth behind the glass face of c.32.4 mm.However, by 373 ls recovery of at least 5 mm has occurred, withsubsequent recovery eventually reducing the final depth-of-penetration to c.24 mm. Again, this phenomenon is likely to belinked to release of stored elastic strain energy within the resin,showing that the elastomeric properties of the resin are key tothe manner in which it resists penetration.

Experimental results from the trial shown in Fig. 3 (test no. 1)and the first set of tests subsequently conducted are summarisedin Table 2. Key parameters recorded include bullet impact veloci-ties and depths-of-penetration, measured as required either fromhigh-speed video footage or directly from recovered targets. As dis-cussed, due to the proprietary nature of the glass-facing architec-

tures used only generic details are included. Here, the number oflaminated layers employed, their relative symmetry and the rela-tive magnitude of their areal density compared to the monolithicsystem employed in tests 3 and 5 are noted.

The data presented in Table 2 strongly suggested that the thinlayer-fronted asymmetric systems considered in tests 1, 6–7 and10 exhibited an enhanced ballistic response. Consequently, thedecision was taken to test a further series of these targets, althoughwith differing inter-glass laminate material composition and thick-ness. While interlayer thickness appeared to have a slight effect ondepth-of-penetration (at most optimisation led to a reduction ofc.20% compared to a similar system with a radically different inter-layer thickness) – a result encountered elsewhere [22] – discussionof the effects of this interlayer thickness is considered beyond thescope of this paper. Never-the-less as it represents a useful com-parison to results from the initial tests, experimental data fromthese tests is also included here in Table 3.

3.2.1. Penetration rate in the PRRFollowing passage through the facing glass laminates, the posi-

tion of the head of the region of disturbance within the PRR wasmonitored using captured high-speed video footage (e.g. Fig. 3)for a number of the ballistic impact tests detailed in Table 2. Thesetests involved a variety of different PRR-backed glass-laminatefaced targets. Fig. 4 shows the resultant variation in displacementwith time. The most important observation from this figure wasthat initial penetration largely occurred at a constant velocity(e.g. the gradient of the position–time curve was constant). Thisimplied that the resin initially behaved in a fluid-like manner,exhibiting minimal/no strength, suggesting that a hydrodynamictreatment of the resin under impact would be valid [16,17]. Inter-estingly, this constant-velocity penetration occurred independentof the architecture of the target. Following the initial hydrody-namic penetration in Fig. 4, a sudden cusp is apparent as storedelastic strain energy suddenly slows the penetrating projectile/material down. This is followed by a negative gradient indicativeof contraction before a constant line of zero gradient is establishedindicating that the final depth-of-penetration has been reached.This penetration/contraction morphology ties in with the post-penetration recovery of the resin highlighted in Fig. 3, discussedin more detail at the beginning of Section 3.2.

3.2.2. Laminate compositionAs shown in Table 2, a variety of different laminate composi-

tions were considered. These were chosen such-that glass and

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Table 3Ballistic impact experimental results – cylindrical thin glass-fronted thin/thick laminated PRR-backed targets, with a variety of different glass interlayers configurations, impactedin the centre by a single 7.62 mm � 51 mm NATO Ball round.

Exp. no. Interlayer Facing areal densityrelative tomonolithic layer

Depth-of-penetration (mm)

Vimpact

(m/s)Max.(HSV)

Final(HSV)

Elasticrecovery

15 0.38 mm PvB +25% 804 30.5 24.1 6.416 0.38 mm PvB +25% 808 38.7 36.2 2.517 0.76 mm PvB +25% 812 33.7 28.6 5.118 0.76 mm PvB +25% 813 30.5 24.1 6.419 1.14 mm PvB +25% 800 36.8 33.1 3.720 1.14 mm PvB +25% 811 38.7 36.2 2.521 1.52 mm PvB +25% 816 29.8 23.5 6.322 1.52 mm PvB +25% 807 31.7 22.2 9.523 1.52 mm Sentryglass� +25% 796 32.8 27.8 5.024 1.52 mm Sentryglass� +25% 808 27.9 19.7 8.225 2.28 mm Sentryglass� +25% 806 35.6 29.8 5.826 0.38 mm PvB = 809 50.3 49.3 1.027 0.38 mm PvB = 805 43.8 42.6 1.228 0.76 mm PvB = 805 52.5 51.4 1.129 0.76 mm PvB = 805 57.1 55.9 1.230 1.14 mm PvB = 809 59.3 57.1 2.231 1.14 mm PvB = 810 48.9 48.3 0.632 1.52 mm PvB = 809 54.9 52.7 2.233 1.52 mm PvB = 807 52.9 52.1 0.834 1.52 mm Sentryglass� = 807 55.6 50.5 5.135 1.52 mm Sentryglass� = 809 52.7 48.3 4.436 2.28 mm Sentryglass� = 802 50.8 48.3 2.537 2.28 mm Sentryglass� = 804 51.4 48.9 2.5

Fig. 4. Variation of depth-of-penetration with time for a single 7.62 mm NATO Ball round penetrating into PRR behind various glass laminate faces.

546 G.J. Appleby-Thomas et al. / Materials and Design 34 (2012) 541–551

laminate thicknesses were indicative of those expected for com-mercially-relevant bullet-resistant window architectures (e.g. Ref.[8]). From this table it is immediately apparent that targets 1, 10,13 and 14 – namely those with a bi-layer asymmetric laminatewith a higher areal density than the monolithic standard – per-formed between 55% and 70% more effectively than the other sam-ples. The key differences between the response of these targets andthe other arrangements considered, based on Table 2, appeared tobe a substantial increase in post-impact elastic recovery. E.g. recov-ery was observed to be consistently up to 8.5 mm, compared toconsistently <3.7 mm for the other configurations. Post-impactanalysis of targets combined with captured high-speed video foot-age as-shown in Fig. 3 identified two features which appeared toaccount for this improvement in ballistic resistance. In the firstcase visual analysis of impacted targets showed substantial regions

of delamination between laminated glass layers. While somewhatobscured by the transparent nature of the target, the edge of such aregion of delamination is visible/indicated by white arrows in thephotograph of the upper surface of target 12 (Table 2) shown inFig. 5.

In Fig. 6 the average radius of delamination (based on the meanof at least six manual measurements about the point-of-impact onpost-impact targets in each case) is plotted against maximumdepth-of-penetration data for a selection of the targets detailedin Table 2. This graph clearly shows a reduction in depth-of-pene-tration with enhanced interlayer delamination; for reference a 2ndorder polynomial best-fit is included which is found to be in goodagreement with the experimental data. From this curve, it is clearthat the depth-of-penetration is linked to the effective area ofdelamination (e.g. the square of the delamination radius). In other

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Fig. 5. Post-impact upper surface of target 12 (Table 2); visible edge of inter-laminate delamination defined by white arrows.

G.J. Appleby-Thomas et al. / Materials and Design 34 (2012) 541–551 547

words, maximising delamination – and consequent dissipation ofenergy – minimises the resultant depth-of-penetration.

However, subsequent analysis of high-speed video showed thatinterlayer delamination is not the only mechanism acting to en-hance projectile defeat. Figs. 7a and b show a series of frames fromhigh-speed video footage of penetration into asymmetric thinner-fronted glass-faced laminated targets (targets 16 and 22 detailed inTable 3 respectively) captured at approximately twice the framerate of the footage shown in Fig. 3. This higher frame rate footageappears to show evidence of a two-stage projectile defeat mecha-nism, separate to the delamination issue highlighted in Fig. 6, asthe projectile moves through the glass-facing and PRR-backing ele-ments. In Figs. 7a and b the bullet is visible at 0 ls to the right ofthe target prior to impact. The asymmetric glass-facing is the darkregion just to the right-of-centre in each frame. To the left of thisregion the transparent PRR is clearly visible as a saturated regionin each frame.

Red1 circles at 25 ls shown in both parts of Fig. 7 highlight twokey issues: (1) that deformation is occurring within the backingPRR ahead of the appearance of the bullet, and (2) the formationof a trapezoid-shaped area of (apparent) damage within the thickerbacking element of the glass laminate. The damaged glass is visibleas a white area in the centre of the aforementioned red circle inboth figures, with the larger trapezoid edge closest to the PRR. Inboth cases disrupted material is than pushed into the backingPRR. However, unlike Fig. 7b (and Fig. 3), in Fig. 7a the resultantPRR-penetration path is non-linear. A (highlighted) perturbationwithin the disrupted material is apparent in the PRR at 75 ls; thissubsequently disturbs the path of the penetrating projectile rem-nants. Analysis of recovered targets showed substantial disruptionof the thinner facing layer in these targets. Given the enhancedperformance of the laminates used in targets 1, 10 and 15–25 com-pared to other configurations investigated (as outlined in Tables 2and 3), based on the analysis of Fig. 7 above, it is postulated thatthe defeat mechanism in such systems involves the stages setout below:

1 For interpretation of colour in Fig. 7, the reader is referred to the web version ofthis article.

1. the outer thinner layer of glass blunts the incident bullet, lead-ing to the flat edge apparent in the trapezoid area of light mate-rial at 25 ls in Figs. 7a and b;

2. the blunted projectile pushes material from the second glasslayer ahead – forming a ‘plug’; this is apparent (i) from the trap-ezoid-like shape of disrupted material in the backing glasslayer, and (ii) the evidence of disruption within the backingPRR at 25 ls in both Figs. 7a and b. Analysis of recovered mate-rial suggests this plug of glass is likely a Hertzian cone – a con-cept backed by the trapezoid-like area of disruption. Thissuggests a strong link to indentation mechanisms [23];

3. the plug of glass leads to a large area of disruption (of width ‘W’in Fig. 7b) which pushes into the resin – along with disruptedprojectile material following behind/along with it – impartingelastic strain energy, and;

4. once the stored elastic strain energy reaches a certain levelnecking, followed by recovery, begins to occur (e.g. 100 and125 ls in Figs. 7a and b respectively); e.g. as seen previouslywith sphere impact tests in Section 3.1.

This concept is backed further by the improvement in ballisticresistance apparent in targets 1 and 10 compared to targets 6and 7 (Table 2). The only difference between these two sets of tar-gets was the higher areal density of the former pair, arising from athicker backing layer of float glass (both possessed identical facinglaminate layers). Assuming Hertzian-cone formation following ini-tial projectile disruption, the thicker backing layer would provide agreater depth of material for the Hertzian cone crack to propagatewithin – increasing the surface area of PRR behind exposed todisrupted material and, thereby, decreasing the resultant depth-of-penetration compared to the lower areal density case. Asevidenced by the consistent impact velocities, the ballistic impacttests detailed in Tables 2 and 3, were extremely repeatable. Ittherefore seems reasonable to assume that elements of the pene-tration process proposed above would likely have occurred in allcases.

Where a thinner front-facing layer was not present, the mainmodification to this process would likely be that the formation ofa blunted projectile and consequent extended Hertzian cone for-mation would not have occurred. Such a response would corre-spond to the observed greater depths-of-penetration comparedto the thin-fronted laminate cases. Fig. 8 shows similar high-speedvideo footage to that in Figs. 3 and 7, although in this case for a sys-tem fronted by a single monolithic layer of float glass (target no. 5,Table 2). Again, post-impact elastic recovery within the PRR isapparent (e.g. comparing the frames at 332 and 2033 ls). However,careful analysis of the video footage showed that the area of dis-ruption within the backing PRR had a much lower peak width thanfor the higher areal density asymmetric bi-layer configurationsconsidered in Figs. 3 and 7.

The decreased width of disrupted material within the backingPRR observed in Fig. 8 compared to Figs. 3 and 7 – a variable la-belled as W in Fig. 7b – was in good agreement with similar de-creased areas of disruption apparent in other non-thin/thickglass-fronted systems in other high-speed video footage not pre-sented here. It is postulated that the observed larger area of disrup-tion within the PRR in those cases where a thin front-layer of glasswas present is likely due to the aforementioned phenomena of pro-jectile blunting/plug formation. Essentially, where a thinner frontlayer of glass, backed by a thicker layer, is present the correspond-ing cone-like fracture (or plug formation) in the thicker rear layerwould maximise the resultant area of disruption in the backingPRR. In a similar manner to that discussed in Section 2.1, wherepenetration of spheres into PRR targets was shown to be influencedby the extent of projectile comminution, this enhanced area ofdisruption would then result in an increased surface-area being

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Fig. 6. An illustration of the relationship between interlayer delamination and resultant depth-of-penetration.

(a) (b)

Fig. 7. Frames extracted from high-speed video showing the impact of a single 7.62 mm NATO Ball round into the centre of bi-layer asymmetric thin-fronted glass laminatearrangements backed by pure PRR (detailed in Table 3): (a) target 16 and (b) target 22.

548 G.J. Appleby-Thomas et al. / Materials and Design 34 (2012) 541–551

presented to the PRR. This would lead to energy being dissipatedover a wider volume of material more quickly than if the projectilewas disrupted to a lesser extent, reducing the depth-of-penetrationalong the impact axis. Physically, such projectile disruption wouldlead to a more rapid build-up of elastic strain energy and a conse-quent quicker release; thereby reducing depth-of-penetration. Thepeak width of the penetration zone within the PRR element of bal-listic targets, e.g. W in Fig. 7b, was measured for all tests wherehigh-speed video footage was captured. This data is plotted againstthe resultant peak depth-of-penetration in Fig. 9. Data is included

for each of the tests detailed in Tables 2 and 3. However, due to thehigh quantity of data presented in Table 3, for clarity only meanwidths/depths-of-penetration based on each laminate architectureconsidered are included.

A linear relationship between the width of the penetration zonein the PRR (W) and the resultant maximum depth-of-penetrationinto the resin (determined from high-speed video footage) isclearly apparent in Fig. 9. The observed reduction in depth-of-penetration with increased W appears to confirm the suppositionthat more of the incident projectiles energy is dissipated in the

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Fig. 8. Frames extracted from high-speed video showing the impact of a 838 m/s 7.62 mm NATO Ball round into a monolithic glass-faced, PRR backed, cylindrical target(target no. 5 in Table 2).

Fig. 9. An illustration of the relationship between the extent of material disruption in the backing PRR and resultant depth-of-penetration.

G.J. Appleby-Thomas et al. / Materials and Design 34 (2012) 541–551 549

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Table 4Comparison of areal density and average ballistic response for different float glasslaminate configuration under impact from a single 7.62 mm NATO Ball round.

Laminate configuration

Monolithic Thick/thin

Thin/thick

qareal compared to monolithic layer = = >(+25%)Ave. max, depth-of-penetration (mm) 63.8 54.4 35.2Ave. max, depth-of-penetration (mm) 61.5 51.2 29.6

550 G.J. Appleby-Thomas et al. / Materials and Design 34 (2012) 541–551

PRR when a larger surface area of disrupted material is presentedto the resin. This strong correlation between depth-of-penetrationand W confirms the previous hypothesis that inter-laminatedelamination (e.g. Fig. 6) as well as projectile erosion by the frontglass face are not the only energy-dissipating processes operatingto enhance ballistic resistance. While there is a degree of scatter(not un-expected given the nature of ballistic tests), the lowestmeasured depths-of-penetration, corresponding to the largestvalues of W, occur for the high areal density asymmetric bi-layerlaminates. A significant reduction is also apparent where theasymmetric bi-layer laminates of the same areal density as themonolithic systems investigated were employed. Overall, for thenon bi-layer non-thin-fronted laminate systems an average maxi-mum depth-of-penetration of 64.9 mm was found. This comparesto average maximum depths-of-penetration of 35.2 mm and54.4 mm for the asymmetric thin-fronted bi-layer architectureswith a higher and lower areal density respectively. A betterpoint-of-comparison would be with the ballistic response of themonolithic layer float-glass targets. Consequently, using the datafrom Tables 2 and 3, the final and maximum depths-of-penetration(averaged across all tests with similar targets) of the two asymmet-ric bi-layer thin-fronted laminate architectures considered arecompared to those for the standard monolithic layer employed inTable 4.

Table 4 shows that replacing a monolithic glass layer with a thinfront-layer asymmetric bi-layer laminate led to improvements inmaximum/final depths-of-penetration of 14.9/16.8% respectivelyfor no change in areal density. Where similar composition lami-nates with a thicker backing layer were employed improvementsin ballistic resistance of 44.9% (maximum) and 51.9% (final) re-sulted compared to the monolithic arrangement, albeit accompa-nied by an increase in areal density. In this latter case theincrease in areal density is found to more-than outweighed bythe substantial increase in ballistic resistance (as discussed, abso-lute values are not quoted due to the proprietary nature of thearrangement considered).

4. Conclusions

The ballistic response of the different elements of a proposedglass-faced PRR-based transparent armour solution have beeninvestigated using a combination of sphere and ballistic impacttests. High-speed video footage of sphere impact experiments al-lowed interrogation of the influence of the elastomeric propertiesof PRR on penetration. In addition, high-speed video analysis ofballistic impact tests helped identify defeat mechanisms in bothfloat glass disrupting layers and composite glass-faced PRR-backedtargets. While the proprietary nature of the approach meant thatexact details of the proposed glass-facing solution were not pro-vided, the effect of modifying the glass facing by splitting it intoa thin-fronted asymmetric bi-layer configuration was considered.Further, the importance of the elastomeric resin in terms ofabsorbing incident projectile energy was highlighted. The key con-clusions which have emerged from the discussion of the experi-mental results presented here are highlighted below:

(1) The importance of monitoring impacts using high-speedvideo footage was highlighted as the final depth-of-penetra-tion in ballistic targets is significantly less than the maxi-mum depth due to elastic recovery in the PRR.

(2) High-speed video footage suggested that PRR behaves pre-dominantly hydrodynamically under impact, withstrength-effects only becoming important once the maxi-mum depth-of-penetration of an impacting projectile isreached (e.g. when elastic PRR recovery begins to occur).This result does not appear to the authors’ knowledge else-where in the literature.

(3) Energy dissipation, whether via inter-laminate delaminationor enhancing the surface area of contact between the pene-trating projectile and the PRR, is key to minimising depth-of-penetration – highlighting the importance of the elastomericproperties of PRR.

(4) Disrupting glass-laminates comprising a thin impact facebacked by a thicker glass layer were found to reduce thedepth-of-penetration compared to monolithic glass platesby up to c.52%, with a small increase in areal density. Thisapproach therefore appears to suggest that reductions inthe areal density compared to current transparent armoursolutions, combined with retention of the desired level ofprotection, are feasible.

(5) Thin/thick laminate systems were shown to maximise pro-jectile disruption and minimise subsequent depth-of-pene-tration via a two-stage mechanism involving (1) projectileerosion in the facing thin layer, followed by (2) plug-forma-tion in the thicker rear glass layer.

Acknowledgements

The authors would like to acknowledge provision of funding byHamilton Erskine Ltd., N. Ireland. In addition, Gareth Appleby-Thomas would like to recognise the contribution of his wife,Caroline Jane Appleby-Thomas, during the final stages of paperpreparation.

References

[1] Appleby-Thomas GJ, Hazell PJ, Millett J, Bourne NK. Deviatoric response of anarmour-grade aluminium alloy. Shock Compress Condens Matter 2009:533–6.

[2] Wright SC, Fleck NA, Stronge WJ. Ballistic impact of polycarbonate – anexperimental investigation. Int J Impact Eng 1993;13(1):1–20.

[3] Übeyli M, Orhan Yildirum R, Ögel B. On the comparison of the ballisticperformance of steel and laminated composite armours. Mater Des2007;28:1257–62.

[4] Jena PK, Ramanjeneyulu K, Siva Kumar K, Balakrishna Bhat T. Ballistic studieson layered structures. Mater Des 2009;30:1922–9.

[5] Hazell PJ. Ceramic armour: design and defeat mechanisms. 1st ed. Canberra,Australia: Argos Press; 2006.

[6] Hazell PJ, Roberson CJ, Moutinho M. The design of mosaic armour: theinfluence of tile size on ballistic performance. Mater Des 2008;29:1497–503.

[7] Özs�ahin E, Tolun S. Influence of surface coating on ballistic performance ofaluminium plates subjected to high velocity impact loads. Mater Des2010;31:1276–83.

[8] Hazell PJ, Edwards MR, Longstaff H, Erskine J. Penetration of a glass-facedtransparent elastomeric resin by a lead–antimony-cored bullet. Int J ImpactEng 2009;36:147–53.

[9] Klement R, Rolc S, Mikulikova R, Krestan J. Transparent armour materials. J EurCeram Soc 2008;28:1091–5.

[10] Hetherington JG. The optimization of two component composite armours. Int JImpact Eng 1992;12(3):409–14.

[11] Krell A, Klimke J, Hutzler T. Advanced spinel and sub-lm Al2O3 for transparentarmour applications. J Eur Ceram Soc 2009;29:275–81.

[12] Sturrock AJ. Investigation of protective glass laminates. MSc thesis.Shrivenham Campus: Cranfield University; 2003.

[13] Aircraft Armour Systems (BAE Systems publication) [cited 14 04 11]. <http://www.baesystems.com/BAEProd/groups/public/documents/bae_publication/bae_pdf_mps_oc_aircraft_armor.pdf>.

[14] Cleargard transparent polymer (BAE Systems publication) [cited 14 04 11].<http://www.baesystems.com/BAEProd/groups/public/documents/bae_publication/bae_pdf_mps_oc_cleargard.pdf>.

Page 11: Penetration Mechanisms in Glass Laminate-resin Structures

G.J. Appleby-Thomas et al. / Materials and Design 34 (2012) 541–551 551

[15] Chin SJ. Investigation of nanotechnology enhanced polyurethane replacementresin (PRR) as a transparent armour material. MSc thesis. Shrivenham Campus:Cranfield University; 2004.

[16] Meyers MA. Dynamic behaviour of materials. New York: John Wiley & SonsInc.; 1994.

[17] Appleby-Thomas GJ, Hazell PJ, Stennett C, Cooper G, Cleave R. The dynamicbehaviour of a modified polyurethane resin, DYMAT 2009. In: 9thInternational conference on the mechanical and physical behaviour ofmaterials under dynamic loading; 2009. p. 1081–87.

[18] Marsh SP. LASL shock Hugoniot data. University of California Press, Ltd.; 1980.[19] Vignjevic R, Bourne NK, Millett JCF, Vuyst TD. Effects of orientation on the

strength of the aluminum alloy 7010-T6 during shock loading: experiment andsimulation. J Appl Phys 2002;92(8):4342–8.

[20] Munson DE, May RP. Dynamically determined high-pressure compressibilitiesof three epoxy resin systems. J Appl Phys 1972;43(3):962–71.

[21] Hazell PJ, Appleby-Thomas G. A study of the energy dissipation of severaldifferent CFRP-based targets completely penetrated by a high velocityprojectile. Compos Struct 2009;91:103–9.

[22] López-Puente J, Arias A, Zaera R, Navarro C. The effect of the thickness of theadhesive layer on the ballistic limit of ceramic/metal armours. Anexperimental and numerical study. Int J Impact Eng 2005;32:321–36.

[23] Lawn BR. Indentation of ceramics with spheres: a century after Hertz. J AmCeram Soc 1998;81(8):1977–94.