InternationalJournalofImpactEngineering34(2007)11191146Experimentalinvestigationofenergy-absorptioncharacteristicsofcomponentsofsandwichstructuresS.Nemat-Nasser,W.J.Kang,J.D.McGee,W.-G.Guo,J.B.IsaacsCenterofExcellenceforAdvancedMaterials,DepartmentofMechanicalandAerospaceEngineering,UniversityofCalifornia,SanDiego,LaJolla,CA92093-0416,USAReceived7July2004;receivedinrevisedform5May2006;accepted17May2006Availableonline28September2006AbstractTwo series of experiments are performed to investigate the dynamic response of various essential components of a classof sandwich structures, under high-rate inertial loads. One consists of dynamic inertia tests and the other involves dynamicimpacttests.AsplitHopkinsonbarapparatusismodiedandusedfortheseexperiments.First, theenergy-absorbingcharacteristicsof theplatematerial inasandwichstructureareinvestigatedusingnoveldynamicinertiatests,paralleledbydetailednite-elementsimulations.Theloadingconditionsinthiscasearesimilartothose in high-rate pressure loading situations, and hence more closely simulate potential blast effects on structures. PlatesmadeofDH-36navalstructuralsteelareusedinthedynamicinertiatests.Theplatessubjectedtoinertialoadingshowmembranedeformationbehavior,butasthedeectionorthicknessincreases,thebendingdeformationneartheclampedjointbecomessignicant.Second, the dynamic behavior of the core material in a sandwich structure is studied through dynamic impact(compression) tests, using high-speed photography. In addition, both the quasi-static and dynamic response of the materialisquantiedusinghydraulictestingmachinesandtheHopkinson-bartechniques.Aluminumfoamasacorematerialisused in these experiments. Aluminum foam is a lightweight material with excellent plastic energy absorbing characteristics.The experimental results show a localized deformation in the metal foam specimens, at suitably high impact velocities. Thesimulationresultscorrelatewellwiththetestresultsintheoverallbehaviorofthemetalfoamspecimens.Withthesetwoexperimental methods, thedynamicbehaviorofsandwichstructuresunderhigh-rateinertial loadingconditions can be examined minimizing the need for direct pressure-induced impulse experiments. Each series ofexperimentsisrelativelysimpleandcanbeperformedseparatelytostudythecomplexbehaviorofsandwichpanelsinsimpleandwell-controlledtests. Thevalidityof separateperformancetest is shownbyaniteelement analysis withaluminumfoamcoresandwichspecimensubjectedtoblastloading.r 2006PublishedbyElsevierLtd.Keywords:Energyabsorption;Sandwichstructures;Experiments;Blastloading;ModelingARTICLEINPRESSwww.elsevier.com/locate/ijimpeng0734-743X/$ - seefrontmatter r 2006PublishedbyElsevierLtd.doi:10.1016/j.ijimpeng.2006.05.007Correspondingauthor.Tel.:+1 858 534 4914;fax:+1 858 534 2727.E-mailaddress:sia@ucsd.edu(S.Nemat-Nasser).1. IntroductionSandwichstructuresconsistingoftwoplatesseparatedbymetal foam, havebeenconsideredaspotentialcandidates to mitigate impulsive (short duration) loads. Their optimal design, subject to ease of manufacturingand eld implementation,cost, and weight constraints, has been a subject of current interest [1]. Some recentinvestigations suggest excellent energy-absorbing characteristics under high-velocity impact loadingconditions [2]. The inner and outer plates, as well as the core material and their dimensions and morphology,maybeadjustedtosuitspecicapplications.Impulsive loads are usually characterized by a pressure eld that decays with time. The impulse duration isoftenveryshort comparedwiththe time-characteristics of the deformationresponse of most structures.Therefore, when a pressure-impulse load is imposed on a sandwich structure, the load may be represented byassigninganappropriateinitial velocityeldtotheouterhullplate.Thekineticenergyoftheouterplateisabsorbed during the deformation of the sandwich structure. To enhance energy absorption, it is important toselectoptimalmaterialsunderagivensetofdesignconstraints.Thebehaviorof clampedcircular platessubjectedtouniformlydistributedblastloadshasbeenintensivelystudied and three failure modes are theoretically analyzed [3]. Experimental techniques have also beendevelopedtoexaminethreefailuremodesastheimpulseincreaseslargeinelasticmode, tearingmodeandtransverseshearfailuremode[4,5].In this paper, we report the results of our experimental investigation of the dynamic response of a sandwichstructure to impulsive loads. The structure has a metal foam core and metal outer and inner hull plates that aremadeofthenavalstructuralsteel,DH-36.Thissteelshowsgoodductilityandplasticityatlowtemperaturesandhighstrainrates, without displaying any noticeable damage andmicro-cracking. At relatively hightemperatures and low strain rates, its strength is not very sensitive to the temperature. The material has goodweldability,anditsmicro-structuralevolutiondoesnotseemtobeverysensitivetothechangesinthestrainrateandtemperature;see[6].Forthecorematerial, weconsideraluminumfoamwhichislightweightandpotentiallyattractiveforitsenergy-absorbing characteristics. It has been used in various energy-absorbing structural designs, as well as fornoiseandheatprotection.Varioustechniqueshavebeendevelopedtomanufacturemetal foams[7].Liquidmetal can be foamed directly by injecting gas or gas-releasing blowing agents, or by producing supersaturatedmetal gas solutions. Indirect methods include investment casting or melting of powder compacts whichcontainablowingagent. If inert gas is entrappedinpowder compacts, asubsequent heat treatment canproducecellularmetalseveninthesolidstate.Thesameholdsforvarioussinteringmethods,metalpowderslurry foaming, or extrusion and sintering of polymer/powder mixtures. The idea of using aluminum foam tomitigate blastloadingis brieymentionedinthedesignhandbook formetalfoams[8]and tworeports[9,10]on full-scale explosion tests used to investigate the behavior of aluminum foam panels under blast conditions.Theyshowthatsurfaceeffectsduetothepanel deformationandfracture, control theenergyandimpulsetransfer.Wereport heretheresults of twoseries of experiments that areperformedtoinvestigatethedynamicresponseofsandwichstructuresunderhigh-rateinertial loads. Oneconsistsofdynamicinertiaexperimentsand the other involves dynamic impact experiments. A split Hopkinson bar apparatus is modied and used forthese experiments. Our results show that the dynamic response of each component of a sandwich structure canbestudiedandcharacterizedindependently.First,westudytheenergy-absorbingcharacteristicsoftheplatematerialinasandwichstructure,usingthedynamicinertiatests,paralleledbydetailednite-elementsimulations.Theloadingconditionsinthiscasearesimilar to those in high-rate pressure impulse situations. Plates made of DH-36 naval structural steel are used inthedynamic inertiatests. Thespecimen underinertialoadingshowsamembranedeformationbehaviorat lowdeections. From experiments and nite-element simulations, it is also found that, as the deection increases, thebendingeffectsbecomeimportantandcannotbeignoredinthedesignofsuchstructuralsystems.Second, thedynamicbehavior of thecorematerial inasandwichstructureis studiedthroughdynamicimpact (compression) tests and nite-element simulations. Aluminum foam is used as a core material in theseexperiments. Aluminumfoamis alightweight material that is consideredtohaveexcellent plasticenergyabsorbing characteristics. The experimental results show a localized deformation in the metal foam specimensARTICLEINPRESSS.Nemat-Nasseretal./InternationalJournalofImpactEngineering34(2007)11191146 1120at suitablyhighimpact velocities. Thesimulationresults correlatewell withthetest results intheoverallbehaviorofthemetalfoamspecimens.Third, the dynamic behavior of sandwich panels composed of DH-36 plate and aluminum foam is analyzedbynite-elementsimulations.Ablastloadingconditionisimposedtothemodel.Explosionenergyisalmostabsorbed by front plate and core. If we effectively design the sandwich panel, back plate could be safe duringblastloading.Thesimulationresultsshowthedeformedshapeoftheplateissimilartothatobtainedfromdynamicinertiatest.Withthesetwoexperimentalmethods,thedynamicbehaviorofsandwichstructuresunderhigh-rateinertialloading conditions can be examined, minimizing the need for direct pressure-induced impulse experiments whicharecostlyandrequirehighlyspecializedfacilitiesandexpertise.Inourapproach,eachseriesofexperimentsisrelatively simple and can be performed separately to study thecomplex behavior of sandwich panelsby simpleand well-controlled tests. Based on this kind of test, it is possible to optimize the material and conguration ofthesandwichstructuresinordertomaximizetheirenergy-absorptioncapacityunderimpulsiveloads.2. Dynamicinertiaexperimentsofplatesandnite-elementsimulations2.1. DynamicinertiaexperimentsFig. 1shows theexperimental setup. Acircular (DH-36steel) plate of uniform(denotedas type-I) orvariable(denotedastype-II)thickness,havingacircularrim,isboltedtoa3-incylindrical(7075aluminum)tubeof3-inouterand2.5-ininnerdiameter.Itispropelledbyagasgunatacontrolledvelocitytowardsanimpedance-matched, 12-inlongincidenttubeofthesamematerial andcrosssection, restingagainsta3-inHopkinson bar. Upon impact, an elastic compressive wave is produced in both tubes, and within a short timeinterval(aboutseveralhundredsmicroseconds),thetubewiththeattachedplatecomestorest,allowingtheunsupportedpart of theplatetodeformunderitsowninertiaforce. Thedeformationmodeis similar toARTICLEINPRESS(a)(b)TYPE II TYPE IStriker tube( 7075 Al )Incidenttube(7075 Al )Circular platespecimen(DH-36 steel )Incident Baro=3inchi=2.5inchL1=3inch L2=12inchInitial Velocity(30 ~ 60 m/sec)Fig. 1. Schematicdiagramof theexperimental setupforinertiatest platesinasandwichstructure: (a) test setup; (b) plategeometryspecimens.S.Nemat-Nasseretal./InternationalJournalofImpactEngineering34(2007)11191146 1121the one that results from a short-duration pressure impulse which would impart an initial velocity to the plate.Theactualimpactvelocityismeasured,usingvelocitysensors.Anumber of tests were performed at various velocities, using plates of different thicknesses. TheexperimentalconditionsandthecorrespondingresultsaresummarizedinTable1.Intests7and8atype-IIspecimen are used. The impact velocity is varied from about 32 to 60 m/s, and the thickness of the plates variesfromabout0.8to2 mm. Fig. 2ashowsadeformedplate, andFig. 2bsummarizestheobservedpermanentdeection (measuredat thecenteroftheplates)perunit platethickness,asa functionoftheimpactvelocity.At the same impact velocity, both the kinetic energy and the strength of the specimen increase as the thicknessincreases. Themembranestiffnessvarieslinearlywiththeplatethicknesswhilethebendingstiffnessrelateslinearlytothesquareof thethickness. At lowvelocities, thedeectionis small andhencethemembranedeformation is dominant, while the bending effect becomes signicant at high impact velocities which producelargebendingdeformations.Theplasticworkinthemembranedeformationismuchlargerthanthatofthebendingdeformation,whenthedeectionissmall.Therefore,theenergyabsorbedbythespecimensplasticdeformationhasalinearrelationwiththethicknessatlowvelocities. Thismeansthatforthesameimpactvelocity,asthethicknessofthespecimenincreases,thekineticenergythatisconvertedintothedeformationenergy increases linearly with the thickness. However, as the deection increases, the bending mode begins todominatethedeformation. Inthisregime, theenergy-absorbingabilityandthepermanentdeectionoftheplate is a complex function of its thickness, as is shown in what follows. In Fig. 2, the experimental results forthetype-IIplatesaregiven.2.2. ComparisonbetweensimulationandexperimentalresultsThe inertiaexperiments are simulatedusingthe LS-DYNA[11] nite-element code. The nite-elementmodelisshowninFig.3.Theplateandbothtubesarediscretizedusingsolidelements,anda1/4symmetricmodel is analyzed. In the simulation, it is assumed that the plate is perfectly xed to the striker tube along itsboundary, andnoresidual stressesareconsidered. Acompletesurface-to-surfacecontactovertheinterfacebetweenthestrikertubeandtheincidenttubeisassumed.Sincetheplateandthestrikertubearejoinedbybolts, there is some exible interaction between the plate and the striker tube. This interaction is notconsideredinthesimulation.Thestrikerandincidenttubesareconsideredtobeelastic.Fortheplates,thephysicallybasedconstitutivemodelproposedbyNemat-NasserandGuo[6]isused.Thismodelisbasedontheconceptofdislocationkinetics, andextensiveexperimental dataoverabroadrangeofstrainratesandtemperatures. Eq. (1)givestheeffectivestressasafunctionoftheeffectivestrain, effectivestrainrate, andtemperature for DH-36structural steel. InFig. 4, the correspondingstressstraincurves are plottedforvariousindicatedstrainratesatroomtemperature.t 750g1=41500 1 6:6 105Tlng

2 1010" #1=28