2013-influence of adhesive thickness on high velocity impact performance of ceramicmetal composite...

International Journal of Adhesion & Adhesives 41 (2013) 186–197

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International Journal of Adhesion & Adhesives

0143-74

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Influence of adhesive thickness on high velocity impact performance ofceramic/metal composite targets

Amar Prakash, J. Rajasankar n, N. Anandavalli, Mohit Verma, Nagesh R. Iyer

CSIR-Structural Engineering Research Centre, Taramani, Chennai 600 113, India

a r t i c l e i n f o

Article history:

Accepted 14 November 2012Influence of adhesive thickness on high velocity impact (HVI) performance of ceramic (Al2O3-99.5)/

aluminium (Al5083 H116) composite targets is critically examined in this paper through numerical
Available online 21 November 2012
Keywords:

Ceramic/aluminium composite target

High velocity impact

Adhesive bond

Depth of penetration

Shear strain

96/$ - see front matter & 2012 Elsevier Ltd. A

x.doi.org/10.1016/j.ijadhadh.2012.11.008

esponding author. Tel.: þ91 44 22549208; fa

ail address: [email protected] (J. Rajasankar)

a b s t r a c t

investigations. Detailed parametric studies are carried out by choosing a practical problem and for a

range of adhesive thickness between 0.1 mm and 1.5 mm. Studies are focussed on normal impact of the

composite target by ogive nosed projectile with a velocity of 830 m/s. Numerical simulation is carried

out by adopting the Lagrangian approach and an axisymmetric finite element model. Impact responses

are compared in relative terms among different cases of analysis to highlight the role played by

adhesive thickness. Various response parameters such as shear strain developed at the interface of

adhesive layer, target deformation, energy transformation, depth of penetration and deflection profile

of back plate are considered in the investigations. These response parameters are observed to be

influenced to different degree by the adhesive thickness. In particular, the depth of projectile

penetration into the aluminium back plate is found to have non-monotonic variation with the

thickness of adhesive layer.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

During high velocity impact (HVI) on ceramic/metal compositetargets, kinetic energy of the projectile is dissipated throughshattering and erosion of projectile, fracturing of the ceramictiles, plastic deformation of back plate and heat. Energy transferfrom projectile to target is realised by generation and travel ofshock waves from front to rear face of the target. Transmission ofenergy due to travel of shock waves in target materials and thenreflection from free surfaces or material interfaces depends on thetype and thickness of adhesive used for bonding besides thecharacteristics of adherend materials [1,2].

Zaera et al. [3] have studied the effect of adhesive layerthickness on response of ceramic/metal armours to impact byshort and sharp nosed projectile. Two different types of adhesives,namely, epoxy resin and polyurethane of different thicknesses inthe range 0.5–1.5 mm were used in the study. Based on theresponses, it was reported that thicker adhesive layer inducesdeformation over a larger area of the metal back plate which ismeant to absorb most of the kinetic energy of projectile andresults in early shattering of the ceramic tile. As a consequence, akey recommendation was made to avoid more than the required

ll rights reserved.

x: þ91 44 22541508.

.

thickness of adhesive, particularly for thicker ceramic tiles, todelay the fragmentation. Another important finding in a targetwith an array of front tiles was that the adhesive betweenadjacent tiles acts as cushion during an impact and suppressespropagation of the impact effect.

Based on tests, Kaufmann et al. [4] concluded that non-oxideceramic tiles such as silicon carbide and boron carbide exhibitrelatively better impact performance compared to ceramic tilescontaining oxide component. Lopez-Puente et al. [1] have eval-uated the impact performance of alumina/aluminium armoursconsisting of 0.1–1.1 mm thick adhesive layer and concluded that,for the chosen target configuration, 0.3 mm thick adhesive layerresults in better performance.

Studies have been carried out to identify the role of adhesiveductility on the impact performance of composite targets [5,6]. Ithas been suggested that the performance of such targets can besignificantly improved by using chemically-altered adhesives thatare made ductile with mixing of suitable additives. Vaidya et al.[7] have investigated adhesive bonded joints in structures sub-jected to in-plane and out-of-plane impact loads and reportedthat normal load results in higher peel stress concentration in theadhesive layer as compared to in-plane loading. Through numer-ical analysis conducted to understand dynamic fracture of theadhesive layer, it has become clear that strain rate in the adhesivelayer can be several order higher than that in the parts attached toit [8,9,10].

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E1>E2

E2

P

E1

P

Fig. 1. Generation of interface shear due to mismatch in the elastic constants of

bonded adherends.

Adherend 1

Adhesive

Adherend 2

P

P

P

P

P

P

Fig. 2. Typical failure modes in adhesive bonds.

A. Prakash et al. / International Journal of Adhesion & Adhesives 41 (2013) 186–197 187

Ubeyli et al. [2] have experimentally investigated the effect ofdifferent types of adhesives on the performance of Al2O3/Al2024laminated composite armours against 7.62 AP bullets. The mea-sured responses have been used to show that polyurethaneadhesive enhances the resistance of ceramic tiles to spallingcompared to epoxy adhesive. Goglio and Rossetto [11] haveexperimentally studied the behaviour of epoxy (Hysol 3425)adhesive joints. Several values of lap length, adhesive andadherend thicknesses were considered and tested till failure ofjoint under different peel and shear stress combinations. Throughinstrumented impact tests, it has been reported that the jointexhibits higher strength for dynamic loading and minimumrequired thickness of adhesive layer. Gefu et al. [12] have pointedout that the interfacial strength of the adhesive layer decreaseswith increase in the thickness of the adhesive layer over the range0.1–1.0 mm.

The literature review indicates that adhesive bond plays anactive role in the performance of the ceramic/metal compositetargets to impact loads. Critical studies [1,3] have examined theimpact performance of composite targets mainly in terms ofdepth of penetration of projectile into the back plate. In thepresent paper, adhesive effect is studied based on additionalresponses, such as shear strain at the interface layer or energytransfer during an impact, which govern the failure mode of thetargets. Thus, the present study differs from others by attemptingto generate more information about the role of adhesive on theperformance of ceramic/metal composite targets.

Impact studies are carried out on Al2O3/Al5083 H116 compo-site targets. Extensive numerical experiments are carried out tohighlight the role played by the adhesive thickness based on finiteelement method using the AUTODYN software. An exampleproblem consisting of single tile composite target is chosen forthe numerical studies. The parameters of the problem are care-fully chosen to be within the practical range such that it ispossible to make relative comparison among the responses ofdifferent cases. The studies are confined to normal impact of thecomposite targets by ogive nosed projectile at a velocity of 830 m/s.A 2-D axisymmetric finite element model of the target andprojectile is developed following the well-known Lagrangianapproach. Number of finite element analysis of the problem iscarried out by varying only the adhesive thickness in the rangebetween 0.1 mm and 1.5 mm. Impact responses such as shearstrain at the interface adhesive layer, target deformation, energytransformation, depth of penetration and deflection profile of backplate are captured and compared in relative terms to provide ameasure of the influence of adhesive thickness. For the chosenproblem, the response parameters are noticed to be affected bydifferent degree due to variation in adhesive thickness. Further, thedepth of penetration is observed to exhibit non-monotonic varia-tion with the thickness of adhesive layer.

2. Adhesion mechanism

Behaviour of joints connecting similar materials (whether theybe metals, ceramics, composites or plastics) and dissimilar mate-rials (steel bonded to copper, metal bonded to rubber or ceramic,or a metallic contact to a semiconductor) can be different. In thecase of dissimilar materials, the engineering compatibility ofthese materials is critical to their performance. Mismatch of theelastic modulus is a common form of engineering incompatibilitywhich leads to stress concentrations and stress discontinuities atthe bonded interface between the two different materials (Fig. 1).The adherend with stiffer material restricts the lateral contractionof the other adherend. This induces shear stress at the interfacewhich may eventually contribute significantly to debonding of

adherends [13]. Joints may fail either cohesively at the adhesiveinterface or within the adherends or in a mode which is combina-tion of the above (Fig. 2). The failure of the bond may be brittle ormay involve considerable plastic flow, accompanied by thenucleation, growth and coalescence of cavitation. Many adhesivesare elastomeric, exhibiting a very large and reversible elasticcompliance [14].

Thickness of adhesive in a joint plays critical role to determinethe performance of composite panels for low as well as high rateof loading [15]. Most designs expect uniform adhesive layerthickness, although this is not always optimal. Slightly thickeradhesive layers in high stress or strain regions can relieve stressconcentrations. However, excessively thick bonds are to beavoided as they normally result in reduction of strength. Theoptimal thickness of adhesive layer depends on a number offactors like type of adhesive, material and thickness of adherends,impedance ratio between adhesive and adherends, etc. [16].

Number of interesting investigations have been reported todetermine the influence of adhesive thickness on impact resistance

A. Prakash et al. / International Journal of Adhesion & Adhesives 41 (2013) 186–197188

of composite targets, for example, analytical models [17,18], finiteelement simulation [19,20,21] and laboratory experiments [22,23].The investigations cover wide range of adhesive thickness from0.09 mm to 2 mm. A classical elastic analysis leads to a conclusionthat bond strength increases with the adhesive thickness, whereasexperimental results are found to show exactly opposite trend.Various theories have been proposed to explain this contradictorybehaviour. Adams and Peppiatt [24] have found that the jointstrength decrease with increase in adhesive thickness due to sizeeffect as thick adhesive layer is likely to contain more defects suchas voids and microcracks. Crocombe [25] has explained that as theadhesive gets thicker, the plastic spreading of the adhesive alongthe overlap occurs more rapidly. In spite of conducting extensiveresearch, the effect of adhesive thickness on the impact perfor-mance of single-lap or double-lap adhesive joints in compositetargets is still not understood clearly. In this background, theproposed investigations are designed to generate more informationwhich will help in better understanding of the effect of adhesive onimpact performance of the composite target. Responses obtainedfrom numerical experiments are compared in systematic mannerand in relative terms to highlight the role played by adhesive onimpact resistance of the composite target.

3. Numerical investigations

Numerical investigations are carried out by analysing a single tileceramic/aluminium composite target for impact by ogive nosedprojectile. The values of parameters that define the target andprojectile are decided by referring to standard literature [1] andpartly based on authors’ experience in conducting similarstudies [26].

3.1. Problem description

The composite target is made up of 8 mm thick ceramic(Al2O3-99.5) front tile and 25 mm thick aluminium back plate

Fig. 3. Arrangement of composite target and projectile.

Table 1Mechanical properties of target and projectile materials.

Properties Target

Alumina Al2O3-99.5 Aluminium allo

Shear modulus (GPa) 135 26.9

Density (g/cc) 3.80 2.70

Bulk modulus (GPa) 200 58.3

Yield strength (MPa) 190 167

(Al5083 H116). Both the tile and the plate are of same size100 mm�100 mm (Fig. 3). The thickness ratio of ductile backplate to the ceramic tile is decided to be about 3 based on thefindings of Lee and Yoo [27] and Lopez-Puente et al. [1].A 7.62 mm calibre 34 mm long ogive nosed steel projectile havinga mass of 10.3 g is considered for the present study. The projectileis assumed to impact the target in normal direction at a constantvelocity of 830 m/s. Influence of adhesive thickness on the impactresponses of the target is proposed to be studied in detail.Accordingly, seven cases with epoxy adhesive layer thickness as0.1, 0.3, 0.5, 0.7, 1.0, 1.2 and 1.5 mm are intended to be solved.Standard mechanical properties of the projectile and targetmaterials are presented in Table 1.

3.2. Finite element model

Numerical analysis is carried out by using the advancedanalysis software AUTODYN [28] which has special features tomodel the nonlinear transient dynamic phenomena like highvelocity impact and blast. The objective of the present study istowards understanding the effect of thickness of the adhesive onhigh velocity impact performance of ceramic/metal compositetargets. Two-dimensional axisymmetric finite element model ofthe target and projectile has been developed based on theLagrangian approach for solution. The Finite element model isgenerated separately for each case of analysis by taking care ofthe adhesive layer thickness. It is ensured that the modelcorresponding to various cases of analysis differ by only thethickness of adhesive layer and the approximate extent of highlystressed zones. While developing the mesh, smooth variation ofelement size has been ensured such that the highly distorted zonecontains finer elements as shown for a typical analysis case inFig. 4. The outer edge of the target is fixed by applying suitableboundary conditions (Fig. 4). The finite element mesh for theadhesive layer is decided at by taking its thickness into consid-eration. Two layers of finite element have been used in caseswhere the adhesive thickness is less than 0.5 mm. The 1.5 mmthick adhesive layer has been modelled with 5 finite elementlayers. On the same lines, 1.0 or 1.2 mm thick adhesive layer hasbeen modelled with 2 finite element layers while 3 finite elementlayers are used for 0.7 mm thick adhesive. The model with 3 finiteelement layers for 0.7 mm thick adhesive is shown in Fig. 4.Continuity between different layers of the target is modelledusing node to node contact to maintain strain compatibility at theinterface. In order to capture the response under shock wavepropagation, gauge points are provided at sufficiently closeinterval at critical locations in the finite element model as shownin Fig. 5. The distribution of monitoring gauges is given in Table 2.

3.3. Material model

The specific constitutive models of the target and projectilematerials and the values of their parameters are selected from thebuilt-in material library of AUTODYN software. The materials are

Projectile steel 4340

y Al5083 H116 Adhesive epoxy

1.6 81.8

1.186 7.86

7.46 159

45 792

Projectile Targetpanel

Fig. 4. Finite element mesh.

Fig. 5. Distribution of gauge points.

Table 2Distribution of gauge points in the FE model.

Gauge point number Location in Model

1, 2 and 3 Projectile

4, 8 and 12 Front face of ceramic tile

5, 9 and 13 Ceramic tile-adhesive interface

6, 10 and 14 Adhesive-aluminium plate interface

7, 11, 15–23 Rear face of aluminium plate


defined in terms of equation of state, erosion criteria besidesstrength and failure models.

3.3.1. Projectile

For steel projectile, the strength and failure model proposed byJohnson–Cook is employed. This model is capable of reproducingthe strength behaviour of steel under large strains, high strainrates and high temperature. Apart from this, linear equation ofstate is adopted to consider the initial elastic behaviour of steelunder shock loads. More details about the material description interms of the parameters and their values are given in Appendix A.

3.3.2. Target

By treating the ceramic tile as brittle material, the constitutivebehaviour model proposed by Johnson and Holmquist (JH) [29] is

adopted in the present study. Both strength and failure behaviourof ceramic are modelled using the JH model. While using themodel, the strength of ceramic is described as a smoothly varyingfunction of intact strength, fractured strength, strain rate anddamage. The model is combined with polynomial equation ofstate in the present study.

Johnson–Cook strength model is used for modelling thebehaviour of ductile aluminium back plate. The von Mises stressis used as criterion to identify yielding of aluminium and thematerial failure is identified through a threshold value of hydro-dynamic tensile force (Pmin). The model is used along with amatching hydrodynamic tensile limit for the material. This modelpresents an advantage by requiring only few basic inputs aboutthe material and allows smooth progress in numerical calcula-tions with consideration of tensile wave propagation. The linearequation of state is adopted to describe the behaviour of alumi-nium back plate. Appendix A provides the complete informationabout the material models used to describe the behaviour ofceramic and aluminium.

3.3.3. Epoxy resin

Cowper–Symonds strength model is used for defining thebehaviour of epoxy adhesive under impact conditions. The shockequation of state is adopted. Hydrodynamic tensile force (Pmin) isused as criterion to identify material failure. This model is alsoapplicable in sub grids other than shell provided a constanthydrodynamic tensile limit is specified. Care has been taken inchoosing the values for this limit. The selected model requiresonly few parameters and allows numerical calculations to pro-ceed continuously by accounting for tensile wave propagation.Additional details about the material description of the epoxyresin is included in Appendix A.

3.3.4. Erosion criteria

The present study is carried out based on analysis usingLagrangian grid. During the high velocity impact analysis, theLagrangian cells near the contact point can usually get distortedbeyond acceptable limits and affect the progress of the numericalcalculation. Conventionally, the numerical difficulty is overcomeby removing such highly distorted finite elements from thecalculations, i.e., artificially eroding such distorted elements [1].The element removal process is done automatically by checkingthe instantaneous geometric strain values in the analysis againstthe pre-defined values. The values of geometric strain used for thedifferent materials are presented in Table 3. The mass of suchremoved elements is distributed equally to the corner nodes of

Table 3Percentage geometric strain.

Target Steel 4340 Projectile

Ceramic (Al2O3-99.5) Aluminium alloy Epoxy resin

200 200 150 210

Fig. 6. Variation in velocity of the projectile at near front tip (gauge point 3).

Fig. 7. Variation in velocity of the projectile at rear end (gauge point 1).


the discarded element. By doing so, the inertia and spatialcontinuity of inertia are conserved in the finite element mesh.However, the internal energy of the material corresponding to theremoved element is lost in the analysis. Any free node that arisesdue to the removal of elements is treated as slave nodes.

3.4. Results and discussions

The results obtained from the present numerical investigationsfor different cases of analysis are discussed here.

3.4.1. Deceleration of projectile

The variation in projectile velocity monitored at gauge points 1(rear end) and 3 (near front tip) for different adhesive thickness isplotted in Figs. 6 and 7, respectively. Both these figures showcontinuous decrease in the projectile velocity from the instant ofestablishing contact with the composite target. In general sense,the velocity curves corresponding to front tip show a linear trendwhile those corresponding to rear end show a parabolic trend.These figures also indicate that the duration of impact is margin-ally less than 0.1 ms after which the system reaches steady stateequilibrium. This has been taken into consideration while subse-quently plotting the variation of other responses. The plotsgenerally indicate that the thickness of adhesive induces oscilla-tion in velocity of the projectile in the later part of the impactduration.

The velocities corresponding to different cases are found todiffer by a maximum of about 10% (at rear end). The figures alsodepict the expected trend that the rear end comes to rest beforethe front tip portion. The velocity profile at rear end of theprojectile (Fig. 7) indicate almost no reduction in projectilevelocity for an initial duration of about 10 ms. This can beexplained by the expected delay in the arrival of stress waves tothe rear end of the projectile.

3.4.2. Transverse displacement in target

During impact the target material is subjected to thrustinstantaneously in the direction of projectile movement. This will

induce deformation in target and projectile along transversedirection also, mostly of negligible magnitude due to inertiaeffects. The transverse displacement in target recorded at thegauge points 9 and 10 for the case of adhesive thickness 0.1 mmand 1.5 mm are plotted in Fig. 8(a) and (b), respectively. Asthese adhesive thicknesses represent extreme conditions, theseare chosen as representative cases for critical study. Sinceseparate gauge points are marked in the front interface (withceramic tile) as well as rear interface (with aluminium plate) ofthe adhesive, it is possible to separately plot the interfacemovement.

The variation of displacement plotted in Fig. 8 is found toexhibit transient movement with mild oscillation. Besides this,both the plots show a characteristic out of phase movement of theparticipating boundaries at about 0.05 ms which is also seen tohave correlation with the time at which the projectile loses itsentire kinetic energy according to Fig. 7. The end of impactprocess is also denoted by 0.05 ms while the subsequentresponses of the target and projectile can be seen as similar tofree vibration of the panel. As the chosen gauge points areseparated by only 10 mm from the impact location, there is astrong possibility for the material at the gauge locations mighthave been damaged at 0.05 ms due to impact and in such case, thedisplacement recorded beyond this time represent spuriousvalues. Among the two cases studied, the front and rear interfacesof the target are found to have a maximum relative movement ofabout 0.35 mm in the transverse direction for 0.1 mm adhesivethickness at about 0.05 mm. Such instantaneous variation oftransverse displacement at the interface induces transverse shearstresses in adhesive layer and could influence target failureinitiated by loss of adhesion. Further it can be seen that theadhesive layer introduces damping effect as the maximumtransverse displacement for the case of 1.5 mm thick adhesive isonly 30% of that for 0.1 mm thick adhesive layer.

3.4.3. Interface stresses

In the ceramic based composite panels, shock waves (i.e.compressive stress waves) propagate in both in planar directionas well as along the thickness. When these compressive stresswaves reach the back surface of ceramic tiles, which are in thecontact with the adhesive layer, a fraction of incident energy gettransmitted into the adhesive and a part gets reflected back. Thishappens due to the mismatch of mechanical impedances in alayered structure and induces tensile stresses in ceramic tile. Asceramic is known to be weak under tensile loading as comparedto its compressive resistance, failure initiates where the tensilestress exceeds a critical value.

Fig. 8. Variation of transverse displacement at interface near centre of panel.

Fig. 9. Comparison of von Mises stress at 5 mm away on front interface from

centre of impact.

Fig. 10. Comparison of von Mises stress at 5 mm away on rear interface from

centre of impact.

Fig. 11. Comparison of von Mises stress at 10 mm on front interface away from

centre of impact.

Fig. 12. Comparison of von Mises stress at 10 mm away on rear interface away

from centre of impact.


For selected cases of adhesive thicknesses, the variation of vonMises stresses at 5 mm away from the impact location with timeis compared in Fig. 9 for the front interface and in Fig. 10 for therear interface. A characteristic difference in the variation patterncan be observed between the front and rear interfaces. In the caseof front interface, severe oscillations are observed during theentire duration of observation whereas in the rear interface, arelatively stabilised response is observed. In the rear interface, thestress values are found to increase monotonically for an initialduration of about 0.01 ms which is contrary to the observedbehaviour in front interface. In the case of front interface, themaximum stress value among all the cases is found to varyapproximately between 0.55 GPa (1.5 mm thick adhesive) and

0.7 GPa (1.0 mm thick adhesive). This clearly represents a randomvariation among the analysed cases. On the other hand, in the rearinterface, the maximum stress value is found to vary approxi-mately between 0.40 GPa (0.7 mm thick adhesive) and 0.5 GPa(1.5 mm thick adhesive).

The variation of von Mises stresses at 10 mm away from theimpact location with time is compared in Fig. 11 for the frontinterface and in Fig. 12 for the rear interface. These figures show asimilar trend as observed in the response at 5.0 mm from theimpact location but with a slight shift in the time scale. In the caseof front interface, the maximum stress value among all the casesis found to vary approximately between 1.4 GPa (0.7 mm thickadhesive) and 2.10 GPa (1.5 mm thick adhesive). In the rearinterface, the maximum stress value is found to vary approxi-mately between 0.25 GPa (0.7 mm thick adhesive) and 0.30 GPa(1.0 mm thick adhesive). For most of the duration of observation,

Fig. 15. Variation of internal pressure in projectile.


the von Mises stresses values show considerable oscillation for allthe cases studied.

3.4.4. Shear strain at interface

In ceramic/aluminium composite targets, due to differentialtransverse movement of the interface, shear strains and stressesdevelop which eventually results in fracture of the target, ifprincipal stress exceeds the tensile strength of adhesive. Thetransverse velocities obtained at the companion gauge pointsare used to compute the shear strain rate, _e, Zaera et al. [3]

_e ¼ vce�val

hadð1Þ

where vce is the transverse velocity in the ceramic tile, val is thetransverse velocity in aluminium alloy at the same section and had

is the thickness of adhesive layer.In the present case, gauge points 5, 9 and 13 form companion

to 6, 10 and 14 as these points lie at the same distance from thepoint of impact but on the front and rear face of the adhesivelayer. The computed shear strain rates corresponding to the7 different adhesive thickness values are plotted in Fig. 13. Itcan be easily noticed from Fig. 13 that the rate of shear straininduced at the interface is inversely proportional to the thicknessof adhesive layer.

3.4.5. Depth of penetration

The registered depth of penetration into back plate for variouscases of analyses is compared in Fig. 14(a). As a representativecase, the penetration profile of the projectile into the compositetarget for the 0.5 mm thick adhesive case is shown in Fig. 14(b).Following the convention in evaluating the depth of penetration[30], the crater depth in the aluminium back plate is consideredas the depth of penetration in the present study. It can be clearlyseen that the depth of penetration varies from a minimum of

Fig. 13. Shear strain rate at the interface for different adhesive thickness.

Fig. 14. Depth of penetration

about 3 mm (0.7 mm thick adhesive) to 5 mm (1.0 mm thickadhesive) among the various cases of analysis. In general, nodirect relation could be established between depth of penetrationand adhesive thickness. Hence, it can be inferred that impactperformance of the ceramic/metal composite target exhibits anon-monotonic response which further may be affected by theratio between the thickness of front tile and back plate besidesthe type and thickness of adhesive.

3.4.6. Projectile response

As the depth of penetration of the projectile is recorded to beleast for 0.7 mm adhesive thickness, it is proposed to carry outdetailed investigations on the projectile responses for this case. Ascan be seen from Figs. 6 and 7, the projectile velocity varies by amaximum of about 10% between the locations of gauge points1 and 3. This differential velocity within projectile could lead to

in aluminium back plate.

Fig. 16. Variation of von Mises stress in projectile.


buildup of instantaneous pressure within the projectile. There-fore, it is proposed to probe the details on pressure and stressesgenerated within the projectile during the impact.

The variation of internal pressure and von Mises stress in theprojectile is plotted, respectively, in Figs. 15 and 16. From Fig. 15, itcan be seen that the maximum pressure recorded at gauge point 3,which is near the tip of the projectile, is about 4.5 GPa. Themaximum pressure at the adjacent gauge point 2 is found to dropto less than 2.0 GPa. The large variation observed over the length ofthe projectile confirms the validity of the model to capture thetypical response in a high velocity impact phenomenon. With regardto the von Mises stress variation plotted in Fig. 16, linear trend can benoticed up to a peak value of about 0.7 GPa (roughly the yieldstrength of the projectile material) followed by a softening trend forshort duration and subsequently hardening response to reach amaxium value of about 1.25 GPa. The peak value of von Mises stressat gauge points 2 and 3 in projectile is almost same as can be seenfrom Fig. 16. However, the peak value is registered first at gaugepoint 2 and subsequently at gauge point 3. The time lag is estimatedto be about 55 ms from Fig. 16. This is as per expected trend since theshock wave generated from the projectile tip due to impact willreach the gauge point 3 before reaching the location of gauge point 2.

Fig. 17. Variation of transverse velocity of projectile.

Initial shape

Fig. 18. Deformatio

At the tail end of the projectile (gauge point 1), the von Mises stressis recorded to be less than the yield strength of the material whichmeans that the material still remains in elastic state. Based on thisobservation, it can be inferred that the projectile has plasticized onlypartially in the front portion while the tail end still remains elastic.

The variation of transverse velocity (perpendicular to thedirection of projectile movement) recorded at the three gaugepoints on the projectile is plotted in Fig. 17. The transversevelocity in the projectile is the manifestation of plastic flow inthe material. In exact terms, the plastic deformation at the tip ofthe projectile results in material flow in transverse direction withvelocity of about 35 m/s. The negligible transverse velocityrecorded at the remaining two gauge points confirms that thematerial at these locations has not reached the yield state.

The intial shape of projectile along with the deformed shapeafter impact is shown in Fig. 18. The final shape of the projectileshows severe deformation of the front tip with mushroom effectdue to plasticisation of material. The figure also gives informationabout the estimated damage in the projectile according to whichonly the front half of the projectile has non-zero damage whilethe rear portion remains elastic with only negligible level ofdamage. The projectile length is found to have reduced to about20 mm at the end of impact, i.e., at 60 ms which corresponds tothe dissipation of entire kinetic energy of projectile.

The internal flow of material as a result of impact has beencaptured from the velocity vector plot of target and projectile at60 ms. Such a plot is shown in Fig. 19 which indicates complexmovements of the particles near the impact location and uniformmaterial flow along the direction of impact in the aluminium backplate. The vector lines approximately indicating bulb shape seenin the back plate are indication of outward material flow due tovery high compressive stresses generated due to impact. Simi-larly, the almost flat lines seen in the back plate near the adhesiveinterface are an indication of tensile stresses developed there. Inaddition to this, it can be clearly inferred from the plot that theceramic tile flows against the impact direction due to extensivebreaking and separation. This response is seen to be only verylocal to the exact point of impact. The material state at the end of

Final shape after 60 µs

n of projectile.

Fig. 19. Plot of velocity vector in target and projectile.

Fig. 20. Plot of material state in target and projectile.

Fig. 21. Variation of kinetic and internal energies in projectile and target

materials.


impact duration is plotted in Fig. 20 which confirms severeerosion in the ceramic tile and the aluminium back plate whichis again very local to the exact point of impact. Further, inaccordance with the material data defined in the solution of theproblem, material states has been distinguished as elastic, plasticand damaged, etc. The material information provided in Figs. 19and 20 correlates well in terms of their impact behaviour.

3.4.7. Energy transformation

Before impact, the projectile possesses kinetic energy of theorder of 3.5 kJ. Due to impact, the kinetic energy is transformedmainly as internal energy in projectile and target materials.

The extent of such transformation is governed by the presenceof hard ceramic tile at the front face of target and ductilealuminium plate at the back. Variation of kinetic and internalenergies in the target and projectile materials is plotted sepa-rately in Fig. 21 for the case of 0.5 mm thick adhesive layer. Thefigure shows the variation in only those materials that containssubstantial portion of energy. By applying this criterion, kineticenergy variation in only the projectile material and internalenergy variation in the target materials except epoxy are qualifiedto be plotted. As per Fig. 21, nearly 35% of kinetic energy of theprojectile is used up as its internal energy for deformation. Therecould be significant variation in the internal energy absorbed bythe projectile. The main contribution factor for the projectileconsuming large quantity of its kinetic energy is a clear designstrategy to ensure effective HVI performance of such structures.The ceramic tile is responsible for offering resistance to theprogressive movement of projectile. As a result of this, theceramic tile is broken and shattered into pieces. According toFig. 21, breaking of the ceramic tile consumes about 24% of thekinetic energy present with the projectile. Of the remainingkinetic energy present with the projectile, about 12% is absorbedby the aluminium back plate by the way of global deformation,

Fig. 22. Deflection profile of back plate.

Table A1Description of the material models of target and projectile.

Material name—alumina

Equation of State PolynomialReference density (g/cm3) 3.80

Bulk Modulus A1 (kPa) 2.0�108

Parameter A2 (kPa) 0.0

Parameter A3 (kPa) 0.0

Parameter B0 0.0

Parameter B1 0.0

Parameter T1 (kPa) 2.00�108

Parameter T2 (kPa) 0.0

Reference temperature (K) 293.0

Specific heat (J/kg K) 0.0

Thermal conductivity (J/mK s) 0.0

Strength Johnson–HolmquistShear modulus (kPa) 1.35�108

Model type Continuous (JH2)

Hugoniot elastic limit (kPa) 5.90�106

Intact Strength Constant A 0.989

Intact strength exponent N 0.376

Strain rate constant C 0.0

Fractured strength constant B 0.77

Fractured strength exponent M 1.0

Max. fracture strength ratio 0.5

Failure Johnson–HolmquistHydro-tensile limit (kPa) �1.50�105

Model type Continuous (JH2)

Damage constant, D1 0.01


Bulking constant, beta 1.0

Damage type Gradual (JH2)

Tensile failure (Pmin) Hydro

Erosion Geometric strainErosion Strain 2.0

Type of geometric strain Instantaneous

Material name—aluminium alloy

Equation of state LinearReference density (g/cm3) 2.7

Bulk modulus (kPa) 5.83�107

Referencetemperature (K) 2.93�102

Specific heat (J/kg K) 9.10�102


Strength Johnson–CookShear modulus (kPa) 2.69�107

5


local compression and penetration. The remaining energy can beaccounted by miscellaneous factors such as the energy absorbedby epoxy resin, loss of energy due to heat, etc. which may not beuseful in an analysis of this nature. Nevertheless, such minorsplit-up in the energy transformation can also be obtained bysuitable means.

3.4.8. Deflection profile of target

Deflection profile (or bulge thickness) of the rear face of backplate is a measure of the energy absorbed by the back plate of thecomposite target. The profile is calculated by finding out thetranslational shift of rear face with respect to a fixed reference(that is fixed edge which is 50 mm away from the impactlocation) in the direction of impact. The calculated deflectionprofile of rear face of back plate for various thickness of adhesiveis shown in Fig. 22. Among the various cases analysed, the bulgethickness at centre is found to vary approximately between 0.5and 0.65 mm. The profile curves corresponding to some of thecases are found to intersect each other thus indicating that acomplex relation between the thickness of adhesive, the area andprofile of the deformation zone. However, in general, it can benoted that the radius of influence is more for thicker adhesivelayer. This can be interpreted that the zone of plastic deformationenlarges with the increase in thickness of adhesive layer.

Yield stress (kPa) 1.67�10

Hardening constant (kPa) 5.96�105

Hardening exponent 0.551

Strain rate constant 0.001

Thermal softening exponent 0.859

Melting temperature (K) 0.0893

Ref. strain rate (/s) 1.0

Strain rate correction 1st order

Failure Hydro(Pmin)Hydro-tensile limit (kPa) �1.50�106

Reheal Yes

Crack softening No

Stochastic failure No

Erosion Geometric strainErosion strain 2.0


Material name—epoxy

Equation of state Shock

4. Summary and conclusions

Influence of the adhesive layer thickness on the high velocityimpact performance of ceramic/aluminium composite target isstudied in this paper through a detailed numerical investigationusing the AUTODYN software. Various response characteristicslike energy transformation, shear strain development at interface,deformation of target and projectile, depth of penetration anddeflection of back plate for different adhesive (epoxy resin)thickness in the range of 0.1–1.5 mm thickness have been studied.It has been shown that the adhesive layer plays a significant rolein the impact performance and, therefore, a thorough investiga-tion is required while deciding the thickness of adhesive layer inthe impact resistant targets. Based on the present numericalinvestigation following specific conclusions are drawn:

Reference density (g/cm3) 1.19

Gruneisen coefficient 1.13
i. Parameter C1 (m/s) 2730
Parameter S1 1.49

Parameter quadratic S2 (s/m) 0.0

Relative volume, VE/V0 0.0

Relative volume, VB/V0 0.0

Parameter C2 (m/s) 0.0

Parameter S2 0.0

Interface adhesive layer thickness affects the impact perfor-mance of ceramic/metal composite targets. The responses ofcomposite panels under high velocity impact like shear strainrate, depth of penetration and back plate deformation, etc.are found to be influenced to different degree by adhesivethickness. It is difficult to generalise these effects based onlyon the present investigation as there are many other

Table A1 (continued )

Material name—epoxy




Strength Cowper–SymondsShear modulus (kPa) 1.6�106


Hardening constant, B (kPa) 0.0

Hardening exponent, n 0.0

Strain rate constant, D 0.0

Strain rate exponent, q 0.0


Failure Hydro (Pmin)Hydro tensile limit (kPa) �1.50�105

Reheal Yes

Crack softening No

Stochastic failure No



Material name—steel

Equation of state LinearReference density (g/cm3) 7.86

Bulk modulus (kPa) 1.59�108




Strength Johnson–CookShear modulus (kPa) 7.70�107


Hardening constant (kPa) 5.10�105

Hardening exponent 0.26

Strain Rate constant 0.0140

Thermal softening exponent 1.03

Melting temperature (K) 1790.0



Failure Johnson–CookDamage constant, D1 0.05


Damage constant, D3 �2.12



Melting temperature (K) 1790





probable parameters like ratio of ceramic tile to aluminiumplate, type of adhesive, material composition of projectileand target and shape of projectile tip involved in animpact event.

ii.
Depth of penetration due to projectile impact is found toexhibit non-monotonic variation with adhesive layerthickness.
iii.
Relative transverse displacement between the ceramic tileand aluminium plate results as transient response of shearstress at the interface. Shear strain rate obtained at theinterface indicate a pattern such that it is inversely propor-tional to the thickness of adhesive layer.
iv.
The transverse displacement at interface is found to bereduced by about 80% for 1.5 mm thick adhesive layer whencompared with that of 0.1 mm thick layer.
v.
Radius of influence for plastic deformation is found to bemore for the case of thicker adhesive layer. It can be inferredfrom this that the zone of plastic deformation increases withthickness of adhesive layer.
vi.
The analysis was found to capture the transformation ofkinetic energy of projectile into strain (internal) energy anddeformation of both projectile and target.
vii.
In view of the non-monotonic nature of the critical impactresponses with the adhesive thickness, a thorough numericalinvestigation with selected range of values should be carriedout to understand the impact behaviour of ceramic/alumi-nium composite targets. The results of such investigationscan be judiciously used to arrive at optimum designs of suchtargets for a given threat and checks can be made byconducting limited number of experiments.
Acknowledgements

The assistance rendered by the post graduate student Mr. H.Manigandan in carrying out some of the numerical simulations isduly acknowledged. The authors thank Mr. K. Chandrasekaran, pro-ject assistant for his help in documentation.

This paper is being published with the kind permission of theDirector, CSIR-SERC, Chennai.

Appendix A. Description of the material models of target andprojectile

See Table A1.

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