International Journal of Impact Engineering 110 (2016) 123�137

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International Journal of Impact Engineering

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

Effect of confinement on the static and dynamic indentation response of

model ceramic and cermet materials

TaggedPD1X XE.G. Pickering D2X Xa, D3X XM.R. O'Masta D4X Xa, D5X XH.N.G. WadleyD6X Xb, D7X XV.S. DeshpandeD8X Xa,*TaggedP

aDepartment of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UKbDepartment of Material Science & Engineering, School of Engineering and Applied Science, University of Virginia, Charlottesville VA 22904, USA

TAGGEDPA R T I C L E I N F O TAGGEDEND

* Corresponding author.E-mail address: vsd@eng.cam.ac.uk (V.S. Deshpande)

http://dx.doi.org/10.1016/j.ijimpeng.2016.12.0070734-743X/© 2016 Elsevier Ltd. All rights reserved.

TAGGEDPA B S T R A C T

The effect of confinement on the localized impact response of ceramic and cermet tiles is investigated. Ascoping study was first conducted using alumina and TiC/Ni cermet tiles encased in a metal matrix compos-ite (MMC) and impacted by high velocity steel balls. The investigation revealed that increasing the MMCcasing thickness reduced the cracking in the ceramic (alumina) tile but had a much smaller effect on the cer-met tile. This motivated a detailed experimental investigation of the effect of lateral confining pressure onthe static and dynamic indentation response of granite and Corian� tiles that serve as model ceramic andcermet materials, respectively. Quasi-static indentation resulted in comminution under the indenter andthe formation of radial cracks in the granite tiles, with the number of radial cracks decreasing with increas-ing confining pressure. By contrast, the plastic indentation and small shallow radial cracks observed in theCorian� tiles were unaffected by variations in the confining pressure. The loading imposed by the highvelocity impact of a steel ball resulted in conical and lateral cracks as well as radial cracks and comminutionin the granite tiles. Intriguingly, while the cone and radial cracks were suppressed by confining pressure,the lateral cracks appeared only at the higher confining pressures. By contrast, the strain rate sensitivity ofthe yield strength of the Corian� reduced the plastic indentation under dynamic loading, but this in turnpromoted the formation of radial cracks which decreased in number with increasing confining pressure. Nolateral cracks, conical cracks or comminution was observed in the Corian� . The study shows that confiningpressure has a less significant effect on cermets compared to ceramics. Since confinement systems add con-siderable weight to ceramic-based ballistic protection systems, this study suggests that the use of lightlyconfined cermets could reduce the overall weight of ballistic protection systems.

© 2016 Elsevier Ltd. All rights reserved.

TaggedPKeywords:CeramicCermetImpactConfinementCracking

.

1. Introduction

TaggedPCeramic-based armour systems can offer significant weightreductions compared to traditional metallic systems for similar bal-listic protection performances [1]. The efficacy of a material fordefeating an impacting projectile is primarily governed by twomaterial characteristics: (i) its resistance to plastic deformation,characterized by its yield strength (including susceptibility to adia-batic shearing) and hardness; and (ii) its resistance to cracking, char-acterized by its dynamic fracture toughness. When both materialcharacteristics are high, the material is able to sustain high projectilecontact pressures, leading to deformation and fracture (defeat) of theimpacting projectile. While most metals have a much higher tough-ness compared to ceramics, their hardness is significantly less. As aresult, increasing the impact velocity of hard projectiles eventuallyresults in the penetration of the metallic target rather than the

TaggedPdefeat of the projectile. On the other hand, impacts with hardceramics can fracture the projectile but the low toughness results inextensive micro-cracking (typically called comminution) near theimpact site and longer radial, circumferential and cone crack pat-terns. While the comminuted material can remain effective indefeating the projectile (provided the time associated with the arrestprocess is less than the time required to move the damaged materialaway from the impact site), the radial and other macro-crack pat-terns typically propagate throughout the ceramic target, resulting insignificantly reduced impact resistance to subsequent projectileimpacts. By contrast, metallic targets typically suffer only localizeddamaged, and thus offer significant resistance to a second projectileimpacting at a different location. To compensate for the limitationsresulting from these crack patterns in ceramics, several methodshave been developed to increase the time associated with the flowof the comminuted material and to reduce the density/length of themacro-cracks.

TaggedPThe most common approach for improving ceramic impact resis-tance is to use a confinement mechanism such as front and/or

Fig. 1. (a) A sketch of the samples comprising of an alumina or TiC/Ni cermet tile of thickness h encased in a Nextel 610 fabric/aluminium metal matrix composite of thickness tc.The casing on two sides of the tile is not shown in order to clearly mark the relevant dimensions. (b) Sketch of the fixture used to clamp the encased tiles in the ballistic impactexperiments in which the target was impacted normally and centrally by a 12.7mm diameter steel ball at an incident velocity of 950 ms-1.

1 CPS Technologies, Norton, Massachusetts, USA.2 CoorsTek, Golden, Colorado, USA.3 Davis Defense Group, Fredericksburg, Virginia, USA.

124 E.G. Pickering et al. / International Journal of Impact Engineering 110 (2016) 123�137

TaggedPbacking plates [2�4], lateral confinement [5,6] or even more com-plex assemblies comprising metallic sandwich panels with latticecores containing ceramic inserts [7]. These concepts attempt to bothincrease the flow resistance of the comminuted material and reducethe formation of radial cracks and other macro-cracks such a conecracks [8]. Whilst these confining mechanisms can be highly effec-tive, they add considerable weight (and cost) to ceramic protectionsystems. This has driven the interest in alternative materials such asmetal-ceramic composites with sufficiently high toughness to avoidsignificant macro-cracking and a hardness capable of fracturing animpacting projectile.

TaggedPCeramic-metal composites comprise a broad class of materialsthat combine the high toughness of metals with the high hardnessand stiffness of ceramics. They can be broadly distinguished on thebasis of the volume fractions and the topologies of the constituentphases. Following Compton and Zok [9], we classify materials con-taining more than 50 vol.% metal as metal-matrix composites(MMCs) and those containing more than 50 vol.% ceramic as cer-mets. Because of their higher ceramic content and hence higherhardness, cermets have been widely investigated for ballistic appli-cations [9�12]. The principal aim in cermet design is to increase thetoughness of the primary ceramic phase without a substantial reduc-tion in hardness. For example, several studies [13�15] have shownthat a TiC/steel cermet comprising 30 vol.% 1080 carbon steel has astatic and dynamic fracture toughness of 20 and 68 MPa m1/2,respectively, and a Vickers hardness of 13 GPa. By comparison, thetoughness of polycrystalline TiC is expected to be 2�4 MPa m1/2,while its hardness is approximately 20 GPa [16]. The increasedtoughness of the cermet therefore comes with an appreciable reduc-tion in hardness. It thus remains unclear if such cermets are superiorballistic materials as compared to confined ceramics.

TaggedPA limited number of studies [6,17,18] have attempted to quantifythe role of confinement on the dynamic impact performance ofceramics. For example, Sherman [6] investigated the influence ofthree levels of lateral confinement, namely: no lateral confinement,lateral confinement without any laterally applied compressive stressand lateral confinement with a laterally applied compressive stress.These studies showed that the application of a lateral confiningstress reduced the number of radial cracks but no systematic studiesinvestigating the role of increasing confining pressure on crackingpatterns in ceramics have been reported. Moreover, the effect ofconfinement on the impact response of cermets has received almostno attention in the literature. The lack of understanding of the effectsof confining stresses on the impact response of cermets is importantto quantify and motivates the primary goal of this experimentalinvestigation.

TaggedPThe outline of this paper is as follows. First, we report on a pre-liminary study of the observed variations in macro-crack patternscreated during the impact of ceramic and cermet tiles with differentlevels of confinement. Motivated by these initial findings we thenconduct a fundamental experimental investigation of the effect of

TaggedPconfining pressure on the deformation and fracture mechanisms ofmodel ceramic and cermet materials subjected to both quasi-staticand dynamic indentation. These model materials are chosen sincethey have similar microstructures to engineering ceramics and cer-mets, but have significantly lower strengths allowing for a quantita-tive laboratory scale investigation of the effects of confining stresses.We conclude with a discussion of the implications of these findingsfor the use of cermets in impact loading scenarios, such as ballisticarmour systems.

2. Scoping study on engineering ceramics and cermets

TaggedPThere is significant literature on the improved ballistic resistanceof hot-isostatic pressed metal encapsulated ceramics as compared tobare ceramics; see for example Gooch [8]. However, the metal encas-ing required for the system to show significant performanceimprovements adds a large parasitic weight due to the relatively lowstrength of the metal encasing compared to the ceramic. Thus, weadopt an alternative strategy of encasing ceramic and cermet tiles inan aluminium matrix/alumina fibre composite that has a signifi-cantly higher strength to weight ratio than metallic materials.

2.1. Manufacture of targets

TaggedPTargets comprising 100 mm£100 mm tiles of a ceramic or cer-met wrapped in a metal matrix composite (MMC), as sketched inFig. 1a, were manufactured1 and tested in this study. We first detailthe tile materials and then proceed to describe the wrapping proce-dure and the MMC.

TaggedPThe two types of tiles were:

TaggedP(i) A hD11.7 mm thick alumina tile (grade AD-995)2. Details of

the mechanical properties of AD-995 are reported in Wadleyet al. [7].

TaggedP(ii)

A hD8.3 mm thick TiC/Ni cermet tile (DDG-X)3 comprising 83vol.% TiC and 17 vol.% Ni. Details of the mechanical propertiesof DDG-X are reported in Compton and Zok [9] and Keene [19].

TaggedPThe tiles thicknesses were selected so that both tiles had thesame areal density of raD46 kg m-2. The MMC reinforcement com-prised a 2£2 twill weave with approximately 3 tows per cm. Eachtow comprised »5k Nextel 610 fibres so that the fabric had a dryareal mass of about 1.3 kg m-2 and a “squeezed” thickness of0.91 mm. Samples with 1, 2 and 4 layers of MMC fabric were thenmanufactured as follows. First the MMC fabric was wrapped overthe top and the bottom of the tiles with oversized fabric sheets andthe excess fabric folded along the sides of the tiles. Next a strip with

Fig. 2. A matrix of post-impact X-ray tomographic scans of the ceramic and cermet ballistic targets. The scans show the surfaces of the alumina and TiC/Ni tiles just below frontlayer of the MMC for the three thicknesses tc of MMC casings considered here.

E.G. Pickering et al. / International Journal of Impact Engineering 110 (2016) 123�137 125

TaggedPa width equal to the tile thickness was wrapped around the sides ofthe tiles. This process was repeated to give 2 and 4 layers of fabricwrapping. These wrapped tiles were then pressure infiltrated usinga molten Al 2 wt.% Cu matrix to produce the final targets. Post-man-ufacture X-ray tomography and sectioning revealed that the 1, 2 and4 layers MMC wrappings resulted in MMC encasing layers of thick-ness tc � 1 mm, 2 mm and 4 mm respectively. In line with datareported by the manufacturer of the Nextel weave, the tensilestrength of the metal infiltrated woven composite was about 3 GPa,i.e. considerably higher than that of the metals typically used inceramic confinement systems.

2.2. Ballistic tests on targets and observations

TaggedPThe square targets were clamped in a fixture with a central circu-lar opening of diameter 60mm as sketched in Fig. 1b. The fixturewas made from hardened AISI 4130 steel and the targets wereclamped within this fixture by six clamping bolts. The impactresponse of the targets was evaluated by impacting the targets cen-trally and normally with a 12.7 mm diameter hardened AISI 52100steel ball at an incident velocity v0D950 ms-1.

TaggedPPost-test X-ray computed tomograms (XCT) showing the frontfaces of the tiles (i.e. the plane perpendicular to the impact directionjust below the front layer of the MMC casing) are shown in Fig. 2 forall six specimen types. First consider the targets with the aluminatiles. The impact created a crater in the tile that is seen as the darkcentral circular patch due to loss of comminuted ceramic. For thelowest level of confinement corresponding to the tcD1 mmMMC casing, this crater is the largest and a few radial cracks arealso observed. With increasing thickness of the MMC casing

TaggedP(i.e. increasing confinement), the crater size decreases and radialcracks can no longer be observed. Next consider the cermet tile tar-gets. While the number of radial cracks for the cermet tiles is seen tosomewhat decrease with increasing MMC thickness, there is negligi-ble effect on the crater diameter. Overall the effect of confinementvia the MMC casing seems much less significant for the targets withcermet tiles. This finding suggests that ballistic systems with cermettiles can offer their optimal performance with lower levels of con-finements and hence lower overall mass.

TaggedPThe results in Fig. 2 suggest a significantly larger influence of con-finement on the impact response of ceramic targets as compared tocermets. However, there remain significant uncertainties in the find-ings which include: (i) the level of confining pressure exerted by theMMC casing is unknown and (ii) the effect of the MMC casing inreducing the impact velocity of the projectile on the tile as it passesthrough the MMC front layers versus the effect of the MMC in pro-viding confinement is not quantified. Given these uncertaintieswe use model materials and loading systems to quantify the effectof confinement on the response of model ceramic and cermetmaterials.

3. Model ceramic/cermet materials

TaggedPThe alumina and TiC/Ni cermets used in Section 2 have very highyield strengths, 4.6 GPa [7] and 3.9 GPa [19] respectively. In orderfor the confining pressure to have an observable effect on the mate-rials, pressures on the order of their yield strengths need to beapplied onto the tiles. This makes a systematic laboratory investiga-tion impractical on tiles of the size typically employed in ballistictargets. Hence, we employ model ceramic and cermet materials that

Fig. 3. (a) Photograph of a 90 mm £ 90 mm tile granite tile. (b) Optical micrograph of a 2.8 mm £ 2.1 mm region of the granite tile showing the grain structure. (c) SEM micro-graph of an etched Corian

�sample showing the aluminium trihydrate particles in a PMMA matrix. In (a) we include the co-ordinate system xi used to subsequently identify the

faces of the tiles.

Table 1.Summary of the key mechanical properties of the granite andCorian

�. The listed properties include density, Young's modulus E,

compressive strength Sc, tensile strength ST, hardness Hm and frac-ture toughness KIc.

Granite Corian�

Density (kg m-3) 2588 1745Young's modulus E (GPa) 10.2§0.04 9.1§0.03Compressive strengthSc (MPa) 84§11.2 96.2§0.5Tensile strength ST (MPa) 16.8§1.9 65.8§1.82Hardness Hm (MPa) 1524§62 353§19Fracture toughness KIc (MPa m1/2) 0.35§0.04 1.66§0.02

126 E.G. Pickering et al. / International Journal of Impact Engineering 110 (2016) 123�137

TaggedPhave microstructures and mechanical characteristics that are analo-gous to engineering ceramics and cermets but with significantlylower strengths.

3.1. Materials

TaggedPThe model materials need to replicate some key microstructuraland mechanical properties of the alumina and TiC/Ni cermets. Thesecan be summarised as:

TaggedP(i) Alumina is a polycrystalline material comprising ceramic grains

4 H

with a relatively low fracture toughness of 4.5 MPa m1/2 buthigh hardness of 14.1 GPa [7].

TaggedP(ii)

The TiC/Ni cermet is a composite comprising a high volumefraction of ceramic particles (85 vol.%) in a ductile matrix. Com-pared to alumina, this material has higher fracture toughness20 MPa m1/2 but a lower hardness 11.8 GPa [9].

TaggedPThe two model materials selected with the required microstruc-tural features and contrast in mechanical properties are a domesticgrade granite4 and the polymer matrix composite material Corian�

supplied by DuPont, UK. Granite is a natural ceramic material with arelatively random microstructure and grain size of »300mm; seeFig. 3a and b. On the other hand, Corian� is reasonably homogenoussynthetic composite material comprising of approximately 66 vol.%particles of aluminium trihydrate derived from bauxite in a PMMA(Poly-Methyl Meth-Acrylate) resin matrix. A SEM micrograph of theCorian� is included in Fig. 3c and indicates that the average alumin-ium trihydrate particle size is »55 mm. The microstructures of thegranite and Corian� thus resemble the alumina and TiC/Ni respec-tively, with the Corian� similar to the TiC/Ni cermet in the sense ofbeing a composite with a high volume fraction of ceramic particlesin a ductile matrix. A range of mechanical properties of these twomodel materials were also measured (details provided in Section3.2) and are listed in Table 1. Like alumina and TiC/Ni, the graniteand Corian� have contrasting values of hardness and toughness.However, both the bending strength (which is a measure of the ten-sile strength) and hardness of these materials is relatively low mak-ing them ideal candidates for a laboratory investigation of the effectof confinement on ceramic and cermet-like materials. We alsoemphasize here that dynamic properties such as acoustic impedancez�

ffiffiffiffiffiEr

p, where E and r are the Young's modulus and density, respec-

tively and the wave speed cDffiffiffiffiffiffiE=r

palso have similar contrasts in the

model materials compared to commercial grade ceramics and cer-mets. For example, the ratio of the acoustic impedance between thealumina and TiC/Ni cermets is 0.8 while this ratio is 1.3 between the

omebase (www.homebase.co.uk).

TaggedPgranite and Corian�. Similarly, the ratio of the wave speeds is 1.1and 0.9 for the commercial grade and model materials respectively.

3.2. Quasi-static mechanical properties

TaggedPQuasi-static mechanical properties of the granite and Corian�

were measured in order to (i) ensure that these two materials havethe required contrast of mechanical properties for them to serve asmodel ceramics and cermets, and (ii) aid in the interpretation of theindentation measurements reported in Section 4. The specimens forall the different tests were water-jet cut from hD10 mm and 12 mmthick granite and Corian� tiles, respectively.

TaggedPThe uniaxial compressive stress versus strain response of thegranite and Corian� materials was measured by compressing cylin-ders of diameter 6.7 mm and height 10 mm. The axes of the cylin-ders were along the x3 direction (Fig. 3a) and the cylinders werecompressed at axial strain rates H � F=A ranging from 10-5 s-1 to1 s-1. The nominal compressive stress S versus axial straine responses for the Corian� are shown in Fig. 4a. With increasing_e, the peak compressive strengthSc increased as a result of the strainrate sensitive behaviour of the polymeric matrix in the Corian� [20].Moreover, the material also displayed a post-peak strength softeningresponse � with the softening rate increasing with increasing strainrate. By contrast, the granite displayed an elastic-brittle compressiveresponse over the whole range of strain rates investigated here. Thevariation of the measured peak strengths Sc for both the Corian�

and granite are included in Fig. 4b: the contrast between the Corian�

and granite is highlighted here with the granite displaying negligiblestrain rate sensitivity compared to the strongly strain rate sensitiveresponse of the Corian�.

TaggedPWhile the uniaxial compression tests are adequate for measuringthe compressive strength, such tests are unsuitable for accuratemeasurements of the Young's modulus. Hence the Young's moduluswas determined independently by measuring the frequencies of thefirst three vibration modes of granite and Corian� beams of length

Fig. 4. (a) The measured compressive nominal stress S versus nominal strain e responses of Corian�for applied nominal strain rates in the range _e D10¡5 s¡1¡1 s¡1. (b) The peak

compressive stresses Sc for granite and Corian�as a function of the applied strain rate _e . (c) The variation of the hardness H with contact area A for the granite and Corian

�tiles

indented by a 12.5mm diameter hemispherical indenter.

E.G. Pickering et al. / International Journal of Impact Engineering 110 (2016) 123�137 127

TaggedP250 mm and thickness as well as breadth h. Using these measure-ments we estimate the Young's modulus of the granite and Corian�

as ED10.2 GPa and 9.1 GPa, respectively.TaggedPThe brittle nature of the granite implied that the compression

test was unsuitable for the measurement of its plastic yieldresponse. We thus also performed hardness tests by indenting thegranite and Corian� tile in the x3 direction (Fig. 3a). The heteroge-neous grain structure of the granite with relatively large length scaleheterogeneities implied that traditional Vickers hardness test do notyield a macroscopic representative hardness as the indentation sam-ples only a few grains. Hardness tests were thus performed byindenting the tiles with a DD12.5 mm diameter hardened steelindenter with a hemispherical tip. The indenter was displaced at arate _dD0:1 mm min¡1 and the indentation periodically interruptedand unloaded from known loads F. The area A of the indented regionwas measured in these unloaded specimens using an optical micro-scope and the hardness defined as H � F/A. A plot of the measuredhardness H versus A is included in Fig. 4c. A strong size effect wasobserved in the hardness of the granite with H converging withincreasing A as a more representative region of the granite micro-structure was included in the indented region. We define the mate-rial hardness HmD1524 MPa as the H value for A � 8 mm2 when Hattains an approximately constant value. The hardness

TaggedPmeasurements for Corian� were insensitive to the indented area,with a constant HmD353 MPa. We note in passing that the hardnessof Corian� is consistent with plastic indentation theory Hm � 3Sc,where Sc is interpreted as the peak compressive strength at the rep-resentative strain rate of _eD _d=D � 10¡4 s¡1.

TaggedPThe fracture toughness was measured using three-point bendtests as per ASTM E399. Briefly, beams with height equal to the tilethickness h, breadth BDh/2 and length LD5h were cut from thegranite and Corian� tiles. Notches of length aDh/2 were then water-jet cut into these specimens such that the normal to the plane of thenotch was along either the x1 or x2 directions as defined in Fig. 3a.The roots of the notches were sharpened with a razor blade (notchsharpening by fatigue cycling resulted in either no sharpening orsudden catastrophic crack growth) before conducting a three-pointbend test on specimens with a span SD4h. The fracture toughnesswas then calculated as

KIc¼Pf SBh3=2 f

ah

� �; ð3:1Þ

where f(a/h) is the K-calibration factor as given in ASTM E399 and Pfis the failure load. To within experimental variability, the fracturetoughness of both granite and Corian� was insensitive to the orien-tation of the crack, i.e. whether the crack plane normal was in the x1

Fig. 5. (a) Top view and (b) elevation sketches of the fixture used to apply an equi-biaxial confining stress sc on the granite and Corian�tiles. The main components are labelled

and leading dimensions marked. The inset view in (a) shows the nylon washer and locknut arrangement used to apply compressive force Q onto the frame. The indenter used inthe quasi-static tests is included in the elevation view. (c) Schematic of the experimental setup used in the dynamic impact experiments.

128 E.G. Pickering et al. / International Journal of Impact Engineering 110 (2016) 123�137

TaggedPor x2 directions and the measured values of KIc are 0.35 MPa m1/2 and1.66 MPa m1/2 for granite and Corian� respectively.

TaggedPThe tensile strength was estimated from three-point bend testson specimens of identical geometry as the fracture toughness testsexcept that no notch was present in these specimens. Again the peakload at fracture Pf was recorded and the tensile strength ST esti-mated from elastic beam theory using

ST D 3Pf S2Bh2 : ð3:2Þ

TaggedPThis approach gave STD16.8 MPa and 65.8 MPa for the graniteand Corian�, respectively. These strengths were not dependent onwhether the beam span is parallel to the x1 or x2 axes as defined inFig. 3a. The key mechanical properties of these two model materialsare tabulated in Table 1 with the peak compressive strength of theCorian� listed for an applied strain rate _eD10¡4s¡1

.

4. Static and dynamic indentation of granite and Corian� tiles

TaggedPThe indentation study was performed on water-jet cut90 mm£90 mm granite and Corian� tiles of thickness hD10 mmand 12mm, respectively. These tiles were supported on a rigid foun-dation and subjected to equi-biaxial compression. Top view and ele-vation sketches of the fixture used to apply the equi-biaxialcompression are included in Fig. 5a and b, respectively. The fixturewas made of AISI 3140 steel and comprised of a 10 mm thick back-ing plate and an adjustable square frame mounted on this backingplate. The tile was placed within the frame and in-plane compressiveforces were applied to the tile by tightening the frame onto the sidesof the tile via a set of bolts. These bolts applied compressive forcesthrough a set of nylon washers of known stiffness as shown in theinset of Fig. 5a. The deformation of these washers was optically mon-itored in order to calculate the force applied by each bolt and eachbolt was tightened to give the same applied force Q. The appliedbiaxial compressive stress was then estimated as sc � 3Q/(Lh),where LD90 mm is the length of the side of the square tile.

TaggedPA key aim of the experiments was to observe the damage in thetiles after loading. However, a large number of the tiles sustainedextensive cracking and hence fragmented upon removal from the

TaggedPloading setup. To avoid this, a thin steel strip was placed around theperimeter of the tiles in-between the tile and the confining frame(Fig. 5a). After the tile was tested, but prior to the removal of theconfining stress sc, this steel strip was tightened in order to apply asmall equi-biaxial stress. This maintained the structural integrity ofthe tiles and avoided the loss of the cracking pattern information.The tiles within the thin steel confining strip were then mounted incoloured epoxy which upon setting maintained the structural integ-rity of the tiles; see Compton et al. [21] for a description of a similarprocedure. The tiles were then polished and imaged with the col-oured epoxy highlighting the cracks.

4.1. Quasi-static indentation

TaggedPThe tiles were indented normally and centrally via a hemispheri-cal indenter of diameter 12.5mm as sketched in Fig. 5b. The indenterwas displaced at a rate of 0.1 mm min-1 in a screw driven testmachine and the applied load F measured via the load cell of the testmachine. Tests were conducted keeping the initial applied confiningstress sc constant at 0, 2.8 and 5.6MPa. In order to observe the dam-age as a function of the applied load F, a series of tests were con-ducted where for each sc the test was halted at recorded values of Fand the tiles were mounted in epoxy to optically observe the dam-age. Thus, a matrix of images in sc¡F space was generated in orderto understand the interaction of the applied indentation load andconfining pressure on the cracking modes.

TaggedP4.1.1. Indentation of the granite tilesTaggedPA matrix (in sc¡F space) of images showing the damage on the

front (indented) and rear surfaces of the granite tiles is included inFig. 6a and b, respectively. First consider the case of no confinementwith scD0. Radial cracks are observed on both the front and rearfaces, with the number of radial cracks increasing with increasingapplied load F. Moreover, with increasing F a comminuted region isseen immediately under the indenter on the front face. Similar tothe indentation observations of Gamble et al. [22] for the indentationof alumina, nearly every grain boundary is cracked in this regionresulting in a damaged zone that resembles a particulate medium. Inthe images in Fig. 6a, this region is a uniformly coloured region as

Fig. 6. Images showing the (a) front and (b) rear surfaces of the granite tiles after quasi-static indentation testing. The cracks are highlighted with a red coloured epoxy and nineimages are shown for each surface corresponding to the different combinations of the indentation force F and confining stress sc. (For interpretation of the references to colour inthis figure legend, the reader is referred to the web version of this article.)

Fig. 7. Images of central sections through the granite tiles after quasi-static indentation testing for the different combinations of the indentation force F and confining stress sc.The cracks are highlighted with a red coloured epoxy in each case. Samples were loaded at the centre of the upper face. (For interpretation of the references to colour in this figurelegend, the reader is referred to the web version of this article.)

E.G. Pickering et al. / International Journal of Impact Engineering 110 (2016) 123�137 129

TaggedPthe epoxy has spread into all voids in between the fragmented gran-ite particles. Such a comminuted region is not observed on the rearface. With increasing confining pressure sc for a given value of F, thenumber of radial cracks decreases but the size of the comminutedzone is less affected. In fact for FD19 kN, radial cracking iscompletely switched off for sc > 2.8 MPa but the size of commi-nuted zone is approximately the same as for scD0.

TaggedPAfter imaging the front and rear surfaces, the tiles were sectionedusing a water-jet cutter to produce 90 mm£45 mm tiles. This enabledthe visualisation of the damage through the thickness of the tiles. A setof images of this central sectioned plane is included in Fig. 7. No clearconical cracking or lateral cracking is observed as reported in the litera-ture for engineering ceramics [5,23,24]. Rather only the distributeddamage corresponding to the comminuted zone and radial cracksintersecting the sectioned plane are visible. This demonstrates thatcomminution under the indenter and radial cracking are the two domi-nant cracking modes under quasi-static indentation.

TaggedPThe radial cracks are mainly through-thickness cracks, and it isinstructive to quantify the interaction between sc and F on the num-ber of radial cracks. We plot in Fig. 8a the number of radial cracks5

as a function of the applied load F for the three levels of sc investi-gated here. Clearly n increases with increasing F for a given sc and

5 Only cracks � 45 mm in length emanating from the indented region are includedin the count.

TaggedPdecreases with increasing sc for a given F. The dependence of n on sc

and F can be rationalized using a semi-quantitative extension of themodel introduced by Seagraves and Radovitzky [25].

TaggedPThe tensile radial stresses s within the tiles can be written as asuperposition of the tensile stress s0 generated by the bending ofthe tiles on the foundation due to the applied load F and the confin-ing pressure sc, i.e. s � s0(F)¡sc. We proceed in two steps by firstcalculating the relation between n and s and then relate s0 to F. Toobtain the relation n(s) consider an infinite elastic plate withYoung's modulus E under plane stress conditions subjected to aremote radial tensile stress s as shown in Fig. 9. A star-crack with nradial cracks each of length a0 is assumed to exist at the centre ofthe plate with an angle 2p/n between each crack, as sketched inFig. 9. Westmann [26] and Williams [27] give the mode I energyrelease rate at the tip of each crack as

GI D 4psE

a0n¡1n2 : ð4:1Þ

TaggedPAt incipient fracture, the applied energy release rate GIDGIc,where GIc is the mode I toughness and the number n � 2 of propagat-ing cracks is then obtained from Eq. (4.1) as

n¼2psa0EGIc

1þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� EGIc

pa0s

s" #: ð4:2Þ

Fig. 8. (a) Comparison between measurements and predictions of the number of radial cracks in the quasi-statically indented granite tiles as a function of the indentation force F.Results are shown for the three confining pressures sc investigated here. (b) The biaxial stress s0 generated by the indentation force F calibrated from the scD0 measurements.The inset compares this calibration curve to the predictions of s0 based on the elastic analysis of Eq. (4.6).

Fig. 9. Sketch of a star crack comprising n radial arms of length a0 in a plate subjectedto a remote radial stress s.

130 E.G. Pickering et al. / International Journal of Impact Engineering 110 (2016) 123�137

TaggedPRecall that a0 is representative of the size of inherent criticalflaws in the material and thus it is reasonable to assume that thetensile strength ST is related to the toughness via

ST ¼ffiffiffiffiffiffiffiffiffiEGIc

pa0

s; ð4:3Þ

and Eq. (4.2) then simplifies to

nD2s

ST

� �2

1Cffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1¡ ST

s

� �2s2

435: ð4:4Þ

TaggedPSubstituting s � s0(F)¡sc, the relation between number ofradial cracks, applied load F and sc is given as

nD2s0¡sc

ST

� �2

1Cffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1¡ ST

s0¡sc

� �2s2

435: ð4:5Þ

TaggedPIt now remains to specify s0(F). This typically requires a non-lin-ear finite element calculation for a ceramic plate on an elastic foun-dation with the damage in the ceramic modelled using anappropriate ceramic constitutive model; see for example Gambleet al. [22] who performed such an analysis using the Deshpande andEvans [28] constitutive model. Such an analysis is beyond the scopeof this study and instead here we determine s0(F) by fitting to the

TaggedPscD0 data in Fig. 8a as follows. With scD0 we have the measured nfor three values of F as seen in Fig. 8a. Then using STD16.8 MPa(Table 1) we obtain the relation s0(F) for the three values of F usingEq. (4.5). This inferred relation is plotted in Fig. 8b along with a bestfit linear relation through the three data points. This linear relation-ship is then used as the required s0(F) and the predictions of n(F) areincluded in Fig. 8a for the three values of sc investigated here. Ofcourse, the model fits the scD0 data (as the s0(F) was generated byfitting to this data) but good agreement between predictions andmeasurements is also seen for the other two values of sc confirmingthe fidelity of the analysis.

TaggedPWe note in passing that an analytical s0(F) relation can beobtained by assuming that the granite plate is completely elastic. Inthis regard, consider a large elastic plate of thickness h with Young'smodulus E and Poisson's ratio n on a semi-infinite elastic foundationwith Young's modulus and Poisson's ratio Es and ns, respectively. Theplate is subjected to a normal point force F on the front surface. TheWestergaard [29] solution to this problem gives the maximum ten-sile hoop stress s0Dsuu occurring on the rear surface of the plateimmediately under the point of load application as

s0

F=h2 D0:275 1Cnð Þ log10 98:65 1Cnsð Þ EEs

� �2=3 1¡n21¡n2s

� �1=3" #ð4:6Þ

TaggedPPredictions using Eq. (4.6) with ED10.2 GPa (Table 1), nD0.18and steel parameters EsD210 GPa as well as nsD0.3 are included inthe inset in Fig. 8b for the hD10 mm granite tile. It is clear that Eq.(4.6) significantly overestimates s0 compared to that inferred above.This is because there is significant damage in the granite tiles due tocomminution and radial cracking. This damage relaxes the stressesand thus a purely elastic analysis as in Eq. (4.6) overestimates s0.

TaggedPIt is worth emphasizing here that the Westergaard solution hasbeen successfully used in the literature to predict the impactresponse of fine-grained ceramics such as alumina [5,30]. We pro-ceed to understand the differences between those studies and theresponse of the model ceramic (i.e. granite) considered. Comptonet al. [30] only observed micro-cracking (communition) in aluminaat the highest impact velocities, with lattice plasticity and conecracking being the operative failure modes at lower velocities. Thisimplied that at lower velocities the response of alumina is not signif-icantly affected by damage and thus the elastic Westergaard solution

Fig. 10. (a) Images showing the front surfaces of the Corian�tiles after quasi-static indentation testing. Nine images are shown corresponding to the different combinations of the

indentation force F and confining stress sc. (b) Magnified views of the impression of the indenter on the Corian�tiles at three smaller quasi-static indentation loads F with scD0.

In both (a) and (b), the cracks are highlighted with a red coloured epoxy. (For interpretation of the references to colour in this figure legend, the reader is referred to the web ver-sion of this article.)

E.G. Pickering et al. / International Journal of Impact Engineering 110 (2016) 123�137 131

TaggedPprovided a good approximation to the stress state. However, in thegranite micro-cracking occurred even at the lowest impact velocitiesthereby invalidating the elastic assumption in the Westergaard solu-tion. To understand why micro-cracking occurs at low impact veloci-ties in granite, consider the ductility parameter D DKIc=sY

ffiffiffiffiffiffiffipd

pintroduced by Horii and Nemat-Nasser [31], where d is the grainsize. With dD300 mm and 3 mm for granite and alumina, respec-tively we have DD0.02 for granite and DD0.21 for alumina. Thisclearly shows that granite is significantly more brittle compared toalumina with cracking being favoured compared to plasticity. Thisenhanced propensity for micro-cracking results in the Westergaardelastic solution not providing a good estimate of the stress statewithin the granite even at the low impact velocities. We note thatenhanced micro-cracking with increasing grain size has also beenreported for alumina [32] and we would anticipate the Westergaardsolution to be insufficient to predict the impact responses of theselarge grained alumina systems as well.

TaggedP4.1.2. Indentation of the Corian� tilesTaggedPA matrix of images (in sc¡F space) showing the damage on the

front face of the Corian� tiles at the same values of sc and F as forthe granite tiles in Fig. 6a is presented in Fig. 10a. The deformationand fracture modes for the Corian� are very different compared tothe granite. To explain these differences first consider the scD0case. For FD19 kN nearly no cracking is observed on the length scaleof Fig. 10a. To better visualise the deformation we include in Fig. 10bmagnified views of the impression left by the indenter at three loadsFD5 kN, 10 kN and 15 kN for the scD0 case. At FD5 kN, only theresulting impression due to the plastic deformation caused by thehemispherical indenter is observed with no cracking. For F � 10 kN,small radial cracks are seen to emanate from the edge of theindented region. These cracks are shallow and there is no visibledamage on the rear surface. With increasing F, the plastic impressionmade in the Corian� by the indenter increased in size as do the radial

TaggedPcracks that are now visible at the scale of Fig. 10a. However, thesecracks are again shallow with no damage seen on the rear face. Thepicture remained essentially unchanged for the larger values of sc

with neither the plastic impression made by the indenter nor theshallow radial cracks emanating from the edge of the indented zonebeing affected by sc over the range of sc values investigated here.

TaggedPThus, in contrast to the granite no comminution or radial crack-ing was observed, with the response limited to plastic deformationunder the indenter and shallow radial cracks emanating from theedge of the indented zone. These differences are understood asfollows:

�

TaggedP(i) The high toughness of the Corian (Table 1) prevents extensive

cracking and comminution. The shallow radial cracks resultfrom tensile stresses associated with the indentation field [33]exceeding the tensile strength of the Corian� at the edge of theindented zone.

TaggedP(ii)

The applied load F is expected to generate tensile bendingstresses as in the case of the granite tiles. However, the tensilestrength of Corian� is high with ST � 66 MPa (Table 1) and thetensile bending stresses generated over the range of F valuesinvestigated here were unable to drive the extension of radialcracks: Eq. (4.5) predicts that radial cracking cannot occurwhen s0¡sc <ST.

TaggedPThe use of higher indentation loads would enable the generationof larger tensile bending stresses. However, the relatively low hard-ness (Table 1) of the Corian� implies that the indentation depthsbecome large and approach the order of the tile thickness for F >

48 kN. In other words, the plastic collapse mode of the tiles requiresless stress than the radial cracking mode due to the combination ofhigher fracture toughness and relatively low hardness of Corian�.

Fig. 11. Images showing the (a) front and (b) rear surfaces of the granite tiles after impact testing. The cracks are highlighted with a red coloured epoxy and images are shown ineach case for different combinations of the impact velocity v0 and confining stress sc. (For interpretation of the references to colour in this figure legend, the reader is referred tothe web version of this article.)

132 E.G. Pickering et al. / International Journal of Impact Engineering 110 (2016) 123�137

Fig. 12. Images of central sections through the (a-b) granite and (c-d) Corian�tiles after impact testing. The cracks are highlighted with a red coloured epoxy and images are

shown in each case for different combinations of the impact velocity v0 and confining stress sc. (For interpretation of the references to colour in this figure legend, the reader isreferred to the web version of this article.)

6 The shear modulus of anomalous glasses like fused silica increases with increas-ing temperature and Chaudhri [34] has reported that impact does not result in multi-ple cone cracks but rather a dominant cone crack whose subtended angle decreaseswith increasing vo.

E.G. Pickering et al. / International Journal of Impact Engineering 110 (2016) 123�137 133

4.2. Dynamic impact response

TaggedPTo investigate the fracture response to impact, granite andCorian� tiles were mounted in the loading frame to apply the confin-ing pressure and then impacted by 12.5mm diameter spherical ballsmade of AISI 52100 grade 28 steel. The loading frame was mountedonto a rigid angle steel structure, the design of which added no addi-tional support behind the backing plate of the loading frame. The 8 gballs impacted the plates centrally and normally as sketched inFig. 5c. The balls were fired from a gas gun with a barrel of innerdiameter slightly greater than 12.5mm, negating the need for asabot. The velocity of balls was measured via laser gates mounted onthe muzzle of the gas gun. The transient response of the front face ofthe tiles during impact was recorded via high-speed photographyusing a Phantom v12 digital camera with an inter-frame time of33 ms and exposure time of 0.3 ms. Each sample was impacted atfour velocities v0 in the range 50¡120 ms-1 for up to five confiningstresses 0 � sc � 5.6 MPa. Similar to the quasi-static tests, the tileswere constrained post-impact by tightening the steel confining striparound the perimeter of the tiles (Fig. 5a) prior to removal from theconfining frame. These constrained tiles were then mounted in col-oured epoxy as in the static tests.

TaggedP4.2.1. Impact of granite tilesTaggedPA matrix of images (in sc¡v0 space) of the front and rear faces of

the impacted granite tiles is shown in Fig. 11a and b, respectively.Three types of cracking patterns are observed: (i) comminution atthe impact site; (ii) radial cracks on the front and rear surfaces and(iii) circumferential cracks mainly (but not exclusively) on the rear

TaggedPface. For a given confinement level sc, the number of radial and cir-cumferential cracks as well as the size of the comminuted zoneincreased with increasing impact velocity v0. However for a given v0,whilst the appearance of the discrete cracks decreased with increas-ing sc, the comminuted zone was relatively unaffected. This is verysimilar to the static indentation case with the impact velocity v0playing a similar role to that of the indentation force F.

TaggedPA series of images (in v0¡sc space) of central sections throughthe granite tiles (analogous to the images in Fig. 7) is included inFig. 12a and b for scD0 (and four impact velocities) andv0D120 ms-1 (and five values of sc), respectively. First consider thescD0 case shown in Fig. 12a. There is clear evidence of cone crack-ing in all cases for scD0 with the circumferential cracks seen onthe front and rear surfaces (Fig. 11) corresponding to the tops andbases of the conical frusta of these cracks, respectively. Withincreasing vo, multiple cone cracks are observed consistent withthe findings of Chaudhri [34] for “normal” glasses (e.g. glasses suchas soda-lime whose shear modulus decreases with increasing tem-perature)6. Now consider the effect of sc, as shown in Fig. 12b.With increasing confinement the number of cone cracks is observedto decrease, whilst the depth of the crater due to comminution isseen to increase. At the highest value of sc there is no clear evi-dence of cone cracking but rather a series of distributed lateralcracks distributed approximately parallel to the surfaces of the tiles

Fig. 13. A montage of high-speed photographs showing the impact of the steel ball on the granite tile with scD0 at (a) v0D100 ms-1 and (b) v0D120 ms-1, and (c) with scD1.4MPa and v0D100 ms-1. Here time tD0 corresponds to the instant the ball impacts the tile.

134 E.G. Pickering et al. / International Journal of Impact Engineering 110 (2016) 123�137

TaggedPare observed [33]. Lateral cracks are typically a result of tensileresidual stresses due to plastic indentation fields as discussed byChen et al. [35]. We argue that the increased confinementreduces the propensity for cracking in granite resulting in plasticdeformation immediately under the impact site. This plasticdeformation results in lateral cracking as the impacting steel ballrebounds and unloads the tile. The observations here are thussuggestive of reduced cracking and enhanced plastic deformationof the granite at high confining pressures consistent with mostconstitutive models for ceramics [36].

TaggedPA montage of high-speed photographs showing the impact of thesteel ball on the unconfined (scD0) the granite tile at v0D100 ms-1

and 120 ms-1 are included in Fig. 13a and b, respectively, with timetD0 corresponding to the instant the ball impacts the tile. Localizedfragmentation immediately under the impact site leading to “ejecta”is seen in both cases. The ejecta was observed to be more extensivefor the higher velocity impact. Moreover, the appearance of radialcracks for t > 33 ms suggests that flexural waves that cause tensilestresses on the front face of the tile develop relatively early in theloading. A similar montage of high-speed images for a granite tileconfined with scD1.4 MPa and impacted at v0D100 ms-1 isincluded in Fig. 13c. For this case, radial cracking was not observedon the front face over the time period shown in Fig. 13c. The reducedradial cracking seemed to result in the formation of more ejecta;compare the images for scD0 and 1.4 MPa for v0D100 ms-1 inFig. 13a and c, respectively. This suggests a larger loss of

TaggedPmaterial due to comminution with increasing confinement and con-sistent with the observation of larger craters with increasing sc

(Fig. 12b).

TaggedP4.2.2. Impact of Corian� tilesTaggedPPost-impact images (in sc¡v0 space) of the front and rear surfa-

ces of the Corian� tiles are included in Fig. 14a and b, respectively.While no significant radial cracking was observed under quasi-staticindentation, clear radial cracking is now observed on both faces withthe number of cracks increasing with increasing vo and decreasingconfinement sc. These radial cracks on the front face emanate fromthe edge of the indented region but originate from the centre of thetile on the rear surface. Recall that under quasi-static indentation,the indentation due to plastic deformation approached the tile thick-ness prior to the onset of radial cracking, i.e. the loads required toinitiate radial cracking could not be attained. However, the yieldstrength of Corian� increases significantly with increasing strainrate (Fig. 4b). This results in large contact forces but relatively smalllevels of plastic deformation for the dynamic impact case as seen inFig. 14a. These contact forces induce tensile bending stresses suchthat s0 > ST and thus cause radial cracks. Since the contact forces Fincrease with vo, the number of radial cracks also increases with voas predicted by Eq. (4.5). Similarly, increasing sc reduces the numberof radial cracks due to the decrease in the effective tensile stressesthat open these cracks as discussed in Section 4.1.1 and predicted byEq. (4.5).

Fig. 14. Images showing (a) the front and (b) rear surfaces of the Corian�tiles after impact testing. The cracks are highlighted with a red coloured epoxy and images are shown in

each case for different combinations of the impact velocity v0 and confining stress sc. (For interpretation of the references to colour in this figure legend, the reader is referred tothe web version of this article.)

E.G. Pickering et al. / International Journal of Impact Engineering 110 (2016) 123�137 135

136 E.G. Pickering et al. / International Journal of Impact Engineering 110 (2016) 123�137

TaggedPA matrix of images (in v0¡sc space) of central sections throughthe Corian� tiles is included in Fig. 12c and d. There is no evidence ofcone cracking, lateral cracking or comminution over the entire rangeof parameters that were investigated. Rather the only evidence ofdamage on these central sections was the radial cracks that intersectthe sectioned plane.

TaggedPThus, even though there is a significant change in the fracturemodes from quasi-static to dynamic indentation of the Corian�, dif-ferences between the granite and Corian� persist. These are mainlyrelated to the fact that the granite is more susceptible to crackingresulting in comminution, radial cracking, cone cracking and lateralcracking while the Corian� shows more plastic deformation andexhibits only radial cracks. With only the cracking modes sensitiveto confinement, the sensitivity of the granite to confinement ishigher than the Corian� under both static and dynamic loading.

5. Concluding summary

TaggedPWe first reported a scoping study showing the effect on ballisticperformance of encasing alumina ceramic and TiC/Ni cermet tileswithin a metal-matrix composite. This study indicated that increas-ing the thickness of the casing significantly enhanced the perfor-mance of the alumina tiles by reducing both radial cracking and thesize of the impact crater. However, the casing thickness has a rela-tively minor effect on the cermet tiles, with only small reductions inthe number of radial cracks observed. Based on this scoping study itwas hypothesized that confinement has a smaller effect on cermetscompared to ceramics.

TaggedPTo test this hypothesis, we report a detailed experimental inves-tigation on the effect of confining pressure on the static and dynamicindentation performance of granite and Corian� which serve as amodel ceramic and cermet, respectively. These materials resembleengineering ceramics and cermets in terms of their microstructureand have an appropriate contrast in hardness and toughness. Impor-tantly, the relatively low hardness and tensile strength of both thesematerials allows for confining pressures that have a significant effecton their response to be applied within a standard laboratory setting.

TaggedPUnder quasi-static indentation, comminution and radial crackingare the two observed deformation/fracture modes in the granitetiles, with radial cracking decreasing with increasing confining pres-sure for the same applied indentation load. The radial cracking wascaused by tensile bending stresses, and the number of radial crackswas reasonably well predicted by a model based on a pressurisedstar-crack. By contrast, the quasi-static indentation of the Corian�

results in plastic indentation and small shallow radial cracks. Thesedeformation and cracking modes were negligibly affected by theapplication of a confining pressure.

TaggedPDynamic loading experiments were conducted by impacting 8 gsteel balls on these tiles over a velocity range of 50¡120 ms-1. Thegranite tiles now exhibited cone and lateral cracking modes in addi-tion to the modes observed under quasi-static loading. The conicaland radial cracks were suppressed by increasing the confining pres-sure, but this resulted in the appearance of the lateral cracks. Thissuggests that increasing confining pressure resulted in increasedplastic deformation at the impact site with the residual stressesassociated with this plastic deformation resulting in lateral cracking.By contrast, the strain rate sensitivity of the yield strength of theCorian� reduced the level of plastic indentation under dynamic load-ing and promoted the formation of radial cracks. The number ofthese radial cracks decreased with increasing confinement. No lat-eral cracks, cone cracks or comminution was observed in theCorian�.

TaggedPThe study on the model ceramics and cermets has confirmed thata confining pressure significantly reduces cracking in ceramics buthas a less significant effect on cermets as suggested by the scopingstudy on the alumina and TiC/Ni systems. Since confinement

TaggedPsystems add considerable weight to ceramic-based ballistic protec-tion systems, this study suggests that the use of cermets couldreduce the need for confinement and thereby reduce the overallweight of some ballistic protection systems.

Acknowledgements

TaggedPThe work was supported by Office of Naval Research GrantsN00014-09-1-0573 and N00014-14-1-0641 (Program manager Dr.David Shifler) as well as by the Defense Advanced Research ProjectsAgency (DARPA) under grant number W91CRB-11-1-0005 (Programmanager Dr. J. Goldwasser).

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