Aluminum foam-polymer hybrid structures (APM aluminum foam)

15 Pages·2008·2.55 MB·English

InternationalJournalofSolidsandStructures45(2008)5627–5641
ContentslistsavailableatScienceDirect
International Journal of Solids and Structures
journal homepage: www.elsevier.com/locate/ijsolstr
Aluminum foam-polymer hybrid structures (APM aluminum foam)
in compression testing
Karsten Stöbenera,*, Dirk Lehmhusa, Massimiliano Avalleb, Lorenzo Peronib, Matthias Bussea
aFraunhoferIFAM,ManufacturingandAdvancedMaterials,WienerStraße12,28359Bremen,Germany
bPolitecnicodiTorino,DipartimentodiMeccanica(MechanicsDepartment),CorsoDucadegliAbruzzi,24,10129Torino,Italy
a r t i c l e i n f o a b s t r a c t
Articlehistory: TheAdvancedPoreMorphology(APM)process,anewmethodforproductionofaluminum
Received 30October2007 foam-polymerhybridmaterials,isdescribed.Smallvolumealuminumfoamspheresare
Receivedinrevisedform27May2008 producedfirstandthenadhesivelyjoinedinaseparateprocesssteptorealizeanAPMfoam
Availableonline21June2008
part.Detailedinformationonmechanicalpropertiesofthisnewhybridmaterialisgiven.
Results ofuniaxial and hydrostatic compression testsare summarized andevaluated to
showhowtypicalparameterscharacterizingmaterialandprocesssuchasspatialarrange-
Keywords:
ment,sizeanddensityofthefoamelementsinfluencetheglobalproperties.Twolevelsof
Aluminumfoam
the hierarchical architecture of the material are evaluated—namely the individual foam
Mechanicalproperties
spheresandthehybridstructure.Variationofadhesivesandadhesivecoatingthickness
Uniaxialcompression
Hydrostaticcompression usedinbondingthespheresinconjunctionwithstudyofunbondedspecimensprovides
Deformationbehavior additionalinsightintheinfluenceofthisbond.Firstestimatesondensitydependenceof
Metalfoam-polymerhybridmaterial mechanical properties are derived from the experimental data. Distinctive differences
betweenAPMandconventionalaluminumfoamsarequalitativelyexplained.Throughout
thestudy,AlSi7 aluminumfoam producedfromchemically identicalprecursor material
according to the powder metallurgical FOAMINAL(cid:2) process is included as reference
material.
(cid:3)2008ElsevierLtd.Allrightsreserved.
1. Introduction
Duetotheiruniquepropertycombinationoflowdensity,competitiveweightspecificmechanicalpropertiesandhigh
energyabsorptioncapability,aluminumfoamscan,e.g.,beappliedinautomotivestructurestoimprovetheircrashworthi-
ness(RauschandStöbener,2006).Amongthedrawbacksoftoday’spreferredproductionmethod,thepowdermetallurgical
Fraunhoferprocess(FOAMINAL(cid:2)),whichisbasedonaprecursormaterialincorporatingafoamingagent(Baumeister,1990),
arerelativelyhighproductioncostsas wellasacertainscatterinmaterialproperties.Thelatterisinducedbystochastic
influencesontheproductionprocesswhicharereflectedinthefinalporestructure,affectingcharacteristicssuchaspore
sizedistribution,cellwallshapeordegreeofcellwallcracking,whichinturnimpingeonmechanicalresponse(Andrews
etal.,1999;MarkakiandClyne,2001;Issenetal.,2005).Theprecursormaterialisexpandedinmouldswhichshapethe
developing,liquidfoambylimitingitsgrowth.Duringcoolingthefoamretainsitsshapeuntilsolidandmaythusbeused
withoutsignificantpost-processing(netshapemanufacturingtechnology).Inthisprocesschaintheuseoffoamingmoulds
increasesproductioncostsandlimitsflexibility,sincedesignevolutionsrequiringchangesinfoampartgeometrycallfora
newfoamingmould,oranadaptationoftheexistingone.
* Correspondingauthor.
E-mailaddress:[email protected](K.Stöbener).
0020-7683/$-seefrontmatter(cid:3)2008ElsevierLtd.Allrightsreserved.
doi:10.1016/j.ijsolstr.2008.06.007
5628 K.Stöbeneretal./InternationalJournalofSolidsandStructures45(2008)5627–5641
WiththeAdvancedPoreMorphology(APM)approach,anewprocessroutehasbeendevelopedwhichallowsforproduc-
tionofaluminumfoam-polymerhybridswithoutaneedforfoamingmoulds(Stöbeneretal.,2005).Thesehybridsconsistof
numeroussmallvolumealuminumfoamelementswithsphericalgeometry(volume<1cm3).Suchfoamelementscanbe
expandedonaflatsurface.Surfacetensionthendrawstheliquidfoamintoasphericalshape.Duetothissimplegeometry
thefoamexpansionprocessiswellcontrollable.Asaresult,highreproducibilityoffoamdensityandhomogeneityofpore
structureisachieved.Coatedwithathermoplasticpolymer/adhesive,whichisnon-tackyatroomtemperature,foamele-
mentscandirectlybepouredintoahollowstructure(e.g.,automotiveA-pillar,sill,etc.).Oncetheadhesivecoatingisacti-
vated (molten/cured) by low temperature heating (usually below 200(cid:4)C), the polymer turns liquid and neighboring
elementsmergeatcontactpoints.Inasimilarway,adherenceoftheliquidpolymertotheinnersurfaceofthesurrounding
structureisachieved.Aftercoolingdowntoroomtemperature,thesolidifiedpolymerformsjointsbondingthefoamele-
mentstoeachotherandtotheinnersurfaceoftheshellstructure(Fig.1,middleandright).Asaconsequenceofthissim-
plifiedprocess,productionmaybeautomated,andflexibilityinmanufacturingofaluminumfoampartsisgreatlyincreased.
Bothaspectscontributetoasignificantcostreductionpotentialinaluminumfoamapplication.
2. Objectives
Forapplicationinenergyabsorptionthedeformationbehaviorofthenewlydevelopedaluminumfoam-polymerhybrids
needstobeunderstood.Toprovidefundamentalknowledgeofthiskindistheprimaryobjectiveofthepresentstudy.
Tothisend,experimentalresultshavebeengatheredontwodifferentlevelsofgeometricalscale,i.e.thelevelsofthe
individual foam spheres and of APM hybrid material samples. Uniaxial and hydrostatic testing of selected aluminum
foam-polymerhybridsamplesshallprovideafirstinsightintotheroleofthefollowingparameters:
(cid:2) foamelementvolume/diameter
(cid:2) foamelementdensity
(cid:2) typeandthicknessofpolymer/adhesivecoating
Acomparisonoftestresultswiththedeformationpatternofconventionallyproducedaluminumfoamsismeanttoshow
ifandhowtheelementalbuild-upofAPMfoamsgovernstherespectiveresponseofthismaterial.
3. Samplesandexperiments
3.1. Samples
3.1.1. Aluminumfoamelements
Thematrix alloyof allinvestigatedsampleswas AlSi7.Starting frompowders, compaction wasdone accordingtothe
CONFORM(cid:2)process,aspecificpowderrollingmethod,toachieveagastightandexpandableprecursormaterialwire.Foa-
mabilitywasensuredbyadditionofafoamingagent(0.5wt%TiH )totheinitialpowdermixture.Theprecursormaterial
2
wascutintosmallvolumegranules,whichwerefinallyexpandedintosphericalfoamelementsbyheatingabovetheirmelt-
ingpoint(approximately700(cid:4)Cfor3–5min.)inacontinuousbeltfurnace.Theelementgeometryisnotperfectlyspherical
sincegravityforcesdeformtheliquidaluminumfoam(situatedontheflatfurnacebeltsurface)resultinginanellipticcross
section(Fig.2).Semi-majoraxis(paralleltobeltsurface)isbetween14.2%and20.4%largerthansemi-minoraxis(perpen-
diculartobeltsurface).Averagediameteroftheinvestigatedfoamelementswasbetweenapprox.5and15mm.
Fig.1. Aluminumfoamelementsofapproximately10mmdiameter(left),foamelementsandfilledstructure(middle)andcrosssectionofautomotive
transversecontrolarmwithaluminumfoam-polymerhybridcore(right).
K.Stöbeneretal./InternationalJournalofSolidsandStructures45(2008)5627–5641 5629
Fig.2. Crosssectionsofaluminumfoamelementsofdifferentsizesbutsimilaroveralldensity.
Fig.2furtherillustratesthattheporesizeandmorphologydoesnotdependsignificantlyontheelementvolume.Small
volumeelementsthereforecontainfewerporesthanlargervolumeelements.
3.1.2. Adhesivesandgenerationofaluminumfoam-polymerhybrids
Tojointhefoamelementstoeachotherandthustoachievethedesiredaluminumfoam-polymerhybridmaterialtwo
typesofadhesivewereemployed:
Polyamide12(short:PA)isathermoplasticpolymerused,e.g.,asanti-corrosioncoatingonmetalcomponents.Itisaduc-
tilematerialwith49MPatensilestrengthand311%elongationatbreak.Mechanicalpropertiesundercompressiveloadwere
notavailabletotheauthors.PA12meltsat176(cid:4)Candwetsaluminumsurfaceswell(Degussa,2004).
AralditeAT1-1(short:EP)isasinglecomponentthermoplasticreactionadhesive(epoxy)usedforstructuralbonding.It
exhibits34MPatensiletransverseresistanceand68MPaelasticcompressionlimit.MeltingofAralditeAT1-1isinitiatedat
70(cid:4)C,whilecuringstartsat120(cid:4)C,followingwhichthematerialremainsthermallystableupto180(cid:4)C(Vantico,2001).
Forcoating,foamelementswereheatedwellabovethemeltingpointoftheemployedadhesiveandpouredintoafluid-
izedbedofadhesivepowder(fluidizedbycompressedairsupply).Oncethepolymerparticlesmakecontactwiththehot
foamelementsurface,theymeltandbuildupasurfacefilm.Thecoatingthicknesscanbeadjustedviathefoamelement
temperaturepriortoenteringthepowderbed.CoatingwiththePAadhesivewasdoneinthreedifferentthicknesses,but
maintaining a constant ratio between coating thickness b and foam element diameter D (b/D=5(cid:3)10(cid:4)3; 15(cid:3)10(cid:4)3 and
29(cid:3)10(cid:4)3).WiththeEPadhesiveonecoatingthickness(b/D=10(cid:3)10(cid:4)3)hasbeenrealized.
Forproductionofthealuminumfoam-polymerhybrids,coatedfoamelementswerepouredintocylindricalmoulds.The
randomelementarrangementwasdensifiedbymeansofvibration.Bysubsequentheatingtoapproximately180(cid:4)Cthecoat-
ingwasmoltenandcured(thelatteronlyinthecaseofEP).Theliquidpolymercoatingsmergeatcontactpointsbetween
neighboringfoamelements,finallyconstitutingsolidpolymerjointsbetweenfoamelements.Adhesiontothemouldsurface
was inhibited using PTFE foil. Activation of the adhesive results in a further densification of the random foam element
arrangementuptoalevelof10%,dependingonthecoatingthickness.Thiseffectcanbeexplainedbyassumingthatunder
theinfluenceofgravitytheliquidpolymercoatingisdisplacedatcontactpointsbetweenneighboringfoamspheres.The
effectivefoamelementdiameterthusdecreasestothelevelassociatedwiththeuncoatedfoamelements,leadingtotheob-
servedvolumereduction.Inthecourseofthisprocess,newdisplacementpathsmaybeopenedforarearrangementofthe
spheres,adevelopmentwhichwillonceagainleadtohigherpackingdensity.
Accordingtothismethodsamplesformechanicaltestingwereproducedfromadhesivecoatedaluminumfoamelements
withdiametersofapproximately5,7,10and15mm.Acircularaluminumextrusionprofilehasbeenemployedasmouldto
shapethealuminumfoam-polymerhybridsamplesincylindricalgeometry(diameter=50mm)duringtheadhesivebond-
ingprocessingstep.Contactandadhesivebondingoffoamelementstotheinnersurfaceoftheprofilehasbeeninhibitedby
athinPTFEfoil.Sampleswerefinallycuttolengthsof75mmforuniaxialand50mmforhydrostatictesting.
3.1.3. Referencesamples
Asreferencematerial,conventionalFraunhofertypeAlSi7foam(Fig.3)sampleswereproducedfromprecursormaterial
identicalinchemicalcompositiontothatusedinthemakingofsmallvolumealuminumfoamelements.Compactionwas
basedoncoldisostaticpressingandsubsequenthotextrusionofthepowdermixture(FOAMINAL(cid:2)process).Thesamples
tested were cubic with dimensions of 41(cid:3)41(cid:3)41mm3 for uniaxial compression and cylindrical with 41mm diameter
at41mmheightforhydrostatictesting.Theywerecutfromlargersamplesinordertoremovetheclosedskinusuallydevel-
opedinthiskindoffoamduringexpansionandincontactwiththemould.Adetailedreviewofanextendedtestprogram
performedonconventionalaluminumfoamsamplesofthiskindhasbeenprovidedbyAvalle(Avalleetal.,2004).
3.2. Testprocedures
3.2.1. Uniaxialcompressiontesting
Singlefoamelementsaswellasadhesivelybondedaluminumfoam-polymerhybridsamplesweretestedinauniversal
testingmachine(ZwickA1472)betweentwoflatandparallelplates.Inasecondtestseriesloosefoamelements(bulk)and
adhesivelybondedaluminumfoam-polymerhybridsamplesweresubjectedtoconfinedcompressioninacylindricaldie.
Testingsamplesinacloseddiealmostcompletelyinhibitstransversestrainingmorecomparabletofoamapplicationascore
inshellstructures.Thealuminumfoam-polymerhybridsamplesdiameterwasapproximately0.1–0.2mmsmallerthanthe
5630 K.Stöbeneretal./InternationalJournalofSolidsandStructures45(2008)5627–5641
Fig.3. Referencematerial:FOAMINAL(cid:2)aluminumfoam(closedcellporosity,closedsurfaceskin).
innerdiameterofthetestdie.Thisminimumspacefortransversestraining(max.0.4%)mustbetakenintoaccountwhen
interpreting test results from confined compression. Initial modulus and yielding are mainly affected by this transverse
straining.Consequently,theinitialmodulushasnotbeenanalyzed.Foranalysisofthetransitionfromquasi-elastictoplastic
deformation(yielding)sampletransversestrainingneedstobeconsidered.Inallconfinedcompressiontests,theinnerdie
andstampsurfaceswerecoatedwithhighpressureresistantlubricant.Remainingforcesfromfrictionbetweensampleand
die,aswellasbetweenstampanddie,caninprincipleaffecttheexperimentalmeasurementsandcannotbeextracted,since
noexactvaluesofeitherfrictioncoefficientsorPoisson’sratioofthealuminumfoam-polymerhybridsamplematerialare
available.Effectsofthiskindwillbediscussedqualitativelyintheresultssection(chapter4).
3.2.2. Hydrostaticcompressiontesting
Hydrostaticcompressiontestswereperformedonlyonselectedsampletypeswithfoamelementdiametersof7and(pre-
dominantly)10mm.
Thetestswereexecutedbymeansofacustommadetestchamberconsistingofasteeltube(140mmexternaldiameter,
90mminternaldiameter)closedbyacoupleofflangesfastenedbyaseriesofbolts(Fig.4).Thechamberisfilledwitha
nearlyincompressiblefluid,namelywaterwithaddedethyleneglycol.Pressureisgeneratedbytherelativemovementof
tworodsconnectedtoageneralpurposehydraulictestingmachine(DARTECHA100,with100kNmaximumload,0.1m/s
maximum speed, 100mm travel). The rods, one fixed, the other sliding into the chamber, pass through sealed holes in
thetestchamberflanges.Thepressure, whichisalsothehydrostaticstressappliedtothesample,isindirectlymeasured
bymeansofthemachineloadcell.Somedirectmeasurementsofthepressureinsidethechamberwerealsoperformed:since
lowfrictionsealsareadopted,thedifferencesobservedincomparisontotheindirectmeasurementswerenegligible.There-
fore,inthepresenttestsonlyindirectmeasurementswereused.Thevolumetricstrainisrelatedtothestrokeoftherodinto
thechamber.Tocompensatefortheremaining,thoughverylow,compressibilityofthefluid,correctioncurveshavebeen
measuredandaccountedforinallsubsequentmeasurements.
Toexertahydrostaticstressonthesampletheloadingfluidmustbecompletelyseparatedfromit.Otherwisetheindi-
vidualspheres,orthebasematerialitselfinthecaseofopencells,ratherthanthefoamwillbeloadedinhydrostaticcom-
pression.TheseparationwaspracticallyobtainedusingastrongPVCsheathinternallyandanexternallatexpouch.ThePVC
jacketwasnecessarytoavoidtearingofthelatexpouch.
Fig.5showsafoamsamplebeforeinsertionintothechamber,andtwo(onePAandoneEPbonded)samplesafterthetest.
Asimplevisualexaminationrevealstheinhomogeneousdeformationofthesamplecausedbythespecimengeometryand,
toalesserextentinthiscase,materialanisotropy.
4. Results
4.1. Unconfineduniaxialcompression
4.1.1. Aluminumfoamelements—experimentalresults
Individualaluminumfoamelementsdifferfromsamplesusuallytestedinbeingofsphericalorellipsoidalgeometry.The
contactareabetweenelementandstampsdependsonsampledeformation.Fig.6depictsafoamelement(D=10mm)at
K.Stöbeneretal./InternationalJournalofSolidsandStructures45(2008)5627–5641 5631
Fig.4. Testchamberforhydrostatictests:(a)schematicrepresentationofthesystem(left);(b)thetestchambermountedontheDARTECHA100testing
machine(right).
Fig.5. (a)Analuminumfoam-polymerhybridsamplejustbeforeinsertioninthehydrostaticloadingchamber(left);(bandc)APMfoamsampleafterthe
hydrostatictest(middle:D=10mm,Polyamide12,b/D=29(cid:3)10(cid:4)3,0.41g/cm3;right:D=10mm,AralditeAT1-1,b/D=10(cid:3)10(cid:4)3,0.41g/cm3).
variousglobalcompressionstates(inthefollowing,globalcompressionorglobalcompressivestrainaredefinedasstamp
deflectionrelatedtosemi-minoraxisoftheellipticalcrosssectionparalleltoloadingdirection).Thestampsflattenthefor-
mer,nearsphericalshape.At60%globalcompressioncrackingoftheformerlyclosedsurfaceskinisvisible.Occurrenceof
similareffectsatlowerstrainlevelsispossible,butcannotbedirectlyobservedowingtothedeformedgeometry.
Associatedforce-compressivestraincurvesareshowninFig.7,wheredifferentaluminumfoamdensitiesandelement
diametersarecontrasted.Naturally,higherdensityincreasestheforcelevelatconstantelementvolume.Largerfoamele-
mentvolumealsoresultedinincreaseddeformationresistanceandforcelevels.
5632 K.Stöbeneretal./InternationalJournalofSolidsandStructures45(2008)5627–5641
Fig.6. Compressionstatesofasinglealuminumfoamelement(D=10mm)inuniaxialcompression.
Obviously,thecrosssectioninthedirectionofloadingisnon-uniform.Deformationislikelytostartatthecontactpoints
betweenloadingplatesandspecimen,i.e.,foamsphere.Theelementisthenprogressivelycompressed,withplasticstraining
occurringprimarilyinthemomentarilysmallestcrosssectionalarea.Fig.6perfectlyreflectsthispattern:Theinitialellipsoid
iseffectivelyflattenedfrombothloadintroductionpointstowardsthecentreplane.Severalotheraspectsaresuperimposed
tothisgeneralbehavior.Actinginpartagainstthedescribedcourseofeventsisstrainhardening,sinceitservestostrengthen
thoseareaswithinthefoamwhichsufferthehighestlevelsofdeformation.Besides,likeconventionalaluminumfoams,the
foamspheresarecharacterizedbyaclosedouterskin,whichconstitutesadensitygradientfromcoretosurface.Anaddi-
tionalstructuralresistancefromthisskinisexpectedbutcannotbequantifiedduetoirregularshapeandinteractionwith
thecellularstructureintheelementvolume.
Anaverageglobalcompressivestressintheplateauregion(betweenapprox.20%and40%globalcompressivestrain)is
estimatedbyrelatingcompressiveforcestothecontactareabetweendeformedfoamelementandstamp(Fig.8).Thiscon-
tactareaisestimatedfromthebaseareaofthedeformedellipsoidsegment.Comparisonwithexperimentallydetermined
contact areas has proved sufficient accuracy of this area approximation. Average compressive stress values determine a
power law dependency on the relative foam density r (eq. 1; C=material constant, n(cid:5)1.5) as developed by Ashby
rel
et al. (2000) for conventional closed cell aluminum foams. A significant influence of the foam element volume/diameter
onthestresslevelisnotsubstantiated.Averageglobalcompressivestressesaremarginallylowerthanthoseoflargervolume
butequaldensityaluminumfoam(FOAMINAL(cid:2))samples.Thisminordiscrepancyisnotattributedtoelementvolumeor
geometry.Itisconsideredmorelikely,thattheaccuracyofthechosenstressapproximationislimited.
r¼C(cid:3)qn ð1Þ
rel
4.1.2. Aluminumfoam-polymerhybridmaterials—experimentalresults
TestingofAPMfoamsunderuniaxialloadsbetweentwoparallelloadplatesgivesafirstinsightintothebasicdeformation
mechanismsofthishybridmaterialandconfirmsamajorroleforallcomponentsofthehybrid.Adhesivejointsbetween
foamelementsturnedouttobeofprimaryimportancefortheoveralldeformationpattern,whereasfoamelementvolume
anddensityhadnoinfluenceinthisrespect.PAbondedsampleswithhighestpolymercoatingthickness(b/D=29(cid:3)10(cid:4)3)
deformedasacontinuum(Fig.9).
1800
0.60 g/cm3
1600 0.70 g/cm3
0.80 g/cm3
1400
N]
e [ 1200
c D = 15 mm
r
o
e f 1000
v
ssi 800
e
r
p
m 600
o D = 10 mm
C
400
200 D = 5 mm
0
0 10 20 30 40 50 60
Global compressive strain [%]
Fig.7. Compressiveforcevs.globalcompressivestrainofdifferentaluminumfoamelementsinuniaxialcompression.
K.Stöbeneretal./InternationalJournalofSolidsandStructures45(2008)5627–5641 5633
9
n) D = 5 mm
pr. stress [MPa]obal compr. strai 5678 DDAAAppp ==ppp rrr11ooo05xxx ...mm DDDmm === 11 505 mmmmmm
mgl
co% 4 Approximation:
al 40
glob% - 3 D = 5 mm: σ=67.25×ρr1e,7l854
r. 20 D = 10 mm: σ=42.00×ρ1,4317
vew. 2 rel
Aet D = 15 mm: σ=54.59×ρ1,6276
(b 1 rel
0
0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30
Relative density
Fig.8. Averageglobalcompressivestressvs.relativedensitydeterminedfromuniaxialtestingoffoamelementswithdifferentvolumes/diametersand
powerlawequationsaslinearapproximation.
AreductionofthePAcoatingthickness(b/D=5(cid:3)103andb/D=15(cid:3)10(cid:4)3)weakenedthejointsbetweenthefoamele-
ments,resultingindisintegrationofthehybridstructureatlowglobalstrainlevels(Fig.10,left).Inthisfailuremode,the
separationplanesliewithinthepolymerandthusbetweenfoamelements.Bondingfoamelementsviathealternativeepoxy
resin(AralditeAT1-1)leadstoathirddeformationpattern.Thesamplevolumeisfirstcompressedasacontinuum.Starting
atapproximately35–40%globalstrain,macroscopiccrackingoccurs.Inthiscase,thepolymericjointisstrongerthanthe
aluminumfoam:Cracksrunthroughthefoamelementvolume(Fig.10,right).
Fig.11displayscompressivestressvs.globalcompressivestraingraphsoftworepresentativesampleswhichdidnotdis-
integrateduringcompression.Aninfluenceoftheadhesivetypeand/orcoatingthicknessonthestresslevelisdistinguish-
ableandmatchesqualitativelytherelativetensilestrengthoftheadhesivesasspecifiedbythesuppliers(seechapter3.1.2).
ForEPbondedsamples,localcrackingofaluminumfoamelementsstartedatapproximately35–40%.Thus,globalcompres-
sivestraincausedalossindeformationresistanceresultinginadecreasingnominalstresslevel.
Comparedtotheplasticresponse,elasticpropertiesevenofconventionalaluminumfoamsaredifficulttoestablish,since
theinitialslopeofthestress–straincurveinuniaxialcompressionofaluminumfoamsisnottrulyofelasticnature(Ashby
etal.,2000).Itisknown,forexample,thatclosedcellfoamsshowdirectplasticdeformationintheporestructureatdefects,
irregularlyshapedpores,etc.(Huschkaetal.,1997;Simanciketal.,1997;DegischerandKottar,1999).Ashbyetal.(2000)
thereforerecommenddeterminingthestiffness(Young’smodulus)fromtheslopeofanunloadingcurve.Infollowingthis
procedure, aluminum foam-polymer hybrid samples were unloaded at defined compression states (5%, 10%, 20%, 30%,
40%and50%)duringuniaxialcompressionbetweentwoflatplates.Fig.12displaysaveragestiffnessintermsofanelastic
modulusdeterminedbetween5%and30%globalcompressivestrainonsamplesthatdidneitherdisintegratenorcrack.All
thesevaluesareapproximatelyoneorderofmagnitudehigherthantheinitialslopesoftheassociatedexperimentalstress–
strain curves. Type of coating, coating thickness and sample density are the main influencing factors. Increasing coating
thicknessorfoamelementdensityresultedinastiffnessincrease.Incontrast,thevolume/diameteroftheemployedfoam
elements did not show a direct influence. Stiffness also increased with accumulated sample compression (>30%). Results
Fig.9. PAbondedAPMfoams(b/D=29(cid:3)10(cid:4)3)duringuniaxialcompression(nominalengineeringcompressivestrainchosenasstrainmeasure).
5634 K.Stöbeneretal./InternationalJournalofSolidsandStructures45(2008)5627–5641
Fig.10. Failureofadhesivebonding(left;PA;b/D=5(cid:3)10(cid:4)3andb/D=15(cid:3)10(cid:4)3)andrupturewithinthealuminumfoamelementvolume(right;EP,b/
D=10(cid:3)10(cid:4)3).
24
Polyamide 12; b/D = 29 x 10-3; 0.43 g/cm³ D = 10 mm
22
Araldite AT 1-1; b/D = 10 x 10-3; 0.40 g/cm³
20
a]
P 18
M
s [ 16
s
e 14
r
st
e 12
v
si 10
s
re 8
p
m
6
o
C
4
2
0
0 10 20 30 40 50 60
Global compressive strain [%]
Fig.11. Compressivestressvs.globalcompressivestrainresponseofselectedsamplesinuniaxialcompression.
gatheredatthisandhigherlevelsofdeformationhavenotbeenconsideredforcalculationofaveragestiffnessvaluessince
here the characteristic inner sample structure and specifically the fraction of interconnected porosity between foam ele-
mentsisalmostcompletelydensified.Experimentsofthiskindhavebeenperformedonconventionalaluminumfoamsof
thesamematrixalloyinthepast(Avalleetal.,2004).Fromthese,theelasticmoduluscanbeestimatedtobe1595MPa
foradensityof0.4g/cm3and3589MPaat0.6g/cm3assumingascalingofstiffnesswiththesquareofdensity,ashasbeen
suggestedbyGibsonandAshby(GibsonandAshby,1997).Usingthesamedependencyondensitysquared,thetangentmod-
ulusormaximumslopeofthestress–straincurveintheelasto-plasticregionturnsouttoliebetween266and597MPafor
conventionalaluminumfoaminthesamedensityrange.Onaverage,weightspecificstiffnessofthesefoamsisthusatleast
twiceashighasthatofAPMmaterialswhenlookingatresultsgainedfromunloading/reloadingcycles.Anexplanationmay
oncemorebebasedontheelementalbuild-upofthehybridmaterialandtheconsequentialprogressivedeformationofthe
individualfoamspheres.Thefactassuchisputintoperspective,though,bytheexceedinglyhighscatterofdataobservedin
thestiffnessevaluationofconventionalaluminumfoams.
4.2. Confineduniaxialcompression
Furtherinvestigationsofthedeformationbehaviorofaluminumfoam-polymerhybridshavebeenconductedundercon-
ditionsofconfinedcompression.Thesampleswereuniaxiallycompressedinaclosedcylindricalsteeldiebetweentwosteel
stamps.Thisexperimentalconfigurationallowedforadditionaltestingofpurealuminumfoamelementbulkswithoutadhe-
sivebonding,sincethedieenclosedthesamplevolumecompletely.Samples(notbondedandadhesivelybondedfoamele-
ments)werepreparedfromfoamelementswithdiameters5,10and15mm.Forsamplesmadefromlargerelements(10and
15mm) the cylindrical test cavity (diameter=50mm, height=75mm) was only coarsely filled and random element
K.Stöbeneretal./InternationalJournalofSolidsandStructures45(2008)5627–5641 5635
1400
D = 5 mm
n)
ai D = 10 mm
str 1200 D = 15 mm
Pa]ompr. 1000
Mc
ness [global 800
stiff0% 600
ge o 3
ra% t 400
Avew. 5 3m 3m 3m 3m 3m 3m 3m 3m 3m
bet 200 g/c g/c g/c g/c g/c g/c g/c g/c g/c
et. 49 44 38 59 54 49 44 41 34
d 0. 0. 0. 0. 0. 0. 0. 0. 0.
( 0
Polyamide 12; 29 x10-3 Polyamide 12; 29 x10-3 Araldite AT 1-1; 10 x10-3
Polymer type and b/D-ratio
Fig.12. Averagestiffnessofaluminumfoam-polymerhybridsamples,determinedfromunloadingcurvesatdefinedlevelsofglobalcompressivestrain.
arrangementmighthavebeendisturbedbyfringeeffects.However,nosignificanteffectofthefoamelementdiameter/vol-
umeontheresultsofconfineduniaxialcompressiontestinghasbeenobservedinthepresentstudy.
Foamelementbulksrespondedtoconfineduniaxialcompressionwithanalmostlinearstressincrease,whichchangesat
approximately40–50%compressiontoexponentiallyincreasing(Fig.12).Anexpectedinitialstiffness(elasticdeformation
mode)couldnotbeidentified.Thebulkoffoamelementsseemtodeformplasticallybeginningwithinitialloading.
Aninadequatecompactionofthefoamelementbulkpriortotestingisonepotentialreasonfortheobservedstress–strain
response.Uniaxialloadingwouldresultindensificationoftheelementpackingandoverlapwithelasticdeformationofthe
foamelements.Bothprocessesrunparallelleadingtotheobservedlinearglobalstress–strainresponse.
Assuminganadequateelementcompaction(sinceallelementbulkshavebeencompactedbymeansofvibrationinthe
diepriortotesting)analternativeexplanationfortheobservedstress–strainresponseisdeveloped.Sphericalfoamelements
areinpointcontacttotheirclosestneighborswithverysmallinitialcontactarea.Globalloadingoftheelementbulkgen-
eratescomparablyhighstressesinthecontactareas.Naturally,theelementvolumeunderneaththecontactareaisfirstelas-
ticallydeformed.Theinnerstructureofafoamelement(Fig.2)indicatesthatstiffnessandyieldstrengthofthethinelement
surfaceskinandinnercellwalls(underneath)shouldbecomparablylow.Inthemeasuredglobalstress–strainresponseof
thenotbondedfoamelementbulktheelasticdeformationmodemightnotbeidentifiableinthestress–straincurvaturedue
toitsverysmallextent.Further,(elasticorplastic)deformationofelementsopensdegreesoffreedomforrearrangementand
densificationofpacking.Thisprocessalsoimpactsontheglobalstress–straincurvatureandimpedesidentificationofthe
elasticdeformationmode.
The performed confined compression of loose foam element bulks has high analogy to metal powder compaction in
closedcylindricaldies.Inbothcasesrandomarrangementsofsphericalparticles/elementsaresubjectedtoconfineduniaxial
compression. Fleck (Fleck, 1995) as well as Heylinger and McMeeking (Heylinger and McMeeking, 2001) investigated
mechanicsofrandommetalpowderparticlearrangementsinconfineduniaxialcompression.Neglectingfriction(between
sampleanddie)andassumingidealplasticdeformationbehaviorofthemetalpowderparticles(noelasticdeformation)fi-
nallydeliveredalinearglobalstressincreaseasafirstapproximation.Thisresultisingoodagreementwithconfinedfoam
elementbulkcompressionresultsofthisstudy,themoresosincemetalfoamdeformationbehaviorclearlyresemblesthe
ideal plasticapproximation as longas thedensification regionisnotreached(see Fig. 18). This,however,isnotthecase
for the present material up to strain levels between 40% and 50%. The assumption that the elastic deformation mode of
notbondedfoamelementbulksistoosmalltobeclearlyidentifiedintheglobalstress–straincurvatureisunderlined.
Irrespectiveofthereasonforthelinearstress–strainresponseofnotbondedfoamelementbulkstoconfineduniaxial
compressiontheprimarygoalofthistestconfigurationwasthecomparisonofmechanicalbehaviorofnotbondedandof
adhesivelybondedsamplesundersimilartestconditions.Eveninthecaseelementswerecompactedinadequatelythiscon-
ditionappliedtonotbondedandadhesivelybondedsamplesinthesamewaysinceprocessingandtestinghasbeenidentical
inallcases.Practically,thismeansthatacomparisonamongexperimentsofthistypeisvalid.
Adhesivebondingoffoamelementsledtoadistinctchangeintheglobalstress–strainresponsetoconfineduniaxialcom-
pression(Fig.13).Aninitialquasi-elasticdeformationmodeisfollowedbyplasticdeformationwitharathersmoothtran-
sitionbetweenbothmodes.Adhesivelybondedfoamelementsarefixedintheirpositionandcannotrearrange.Contactto
neighboringspheresisassociatedwithadefinedareaand,e.g.,controlledbythecoatingthickness.Thecoatingitselfiscon-
5636 K.Stöbeneretal./InternationalJournalofSolidsandStructures45(2008)5627–5641
24
Polyamide 12; b/D = 29 x 10-3; 0.44 g/cm³
22
Araldite AT 1-1; b/D = 10 x 10-3; 0.41 g/cm³
20 Polyamide 12; b/D = 15 x 10-3; 0.38 g/cm³
a] 18 Polyamide 12; b/D = 5 x 10-3; 0.35 g/cm³
P
M 16 not bonded; 0.35 g/cm³
s [
s 14
e
r
st 12
e
v 10
si
es 8
r
p
m 6
o
C 4
2
D = 10 mm
0
0 10 20 30 40 50 60
Global compressive strain [%]
Fig.13. Compressivestressvs.globalcompressivestraininconfineduniaxialcompressionofloosefoamelementsanddifferenttypesofaluminumfoam-
polymerhybrids.
tinuousandenvelopestheneighboringspheresaswellasthejoint.Shearstressesperpendiculartothenormalofthesep-
arationplanecanthusbetransmittedfromspheretospherethroughthisplane.Keepingfrictionoutofconsideration,thisis
notpossibleamongloosespheres.Undercompressiveloadsboththepolymerjointandtheadjacentaluminumfoamspheres
arefirstdeformedquasi-elastically.Localizedplasticdeformationintheporestructureofthealuminumfoamispossiblebut
notdominant;hencetheterm‘‘quasi-elasticbehavior”isused.Thesameholdstruefortheinitiationofplasticyieldatcon-
tactpointsasdescribedabove.Withincreasingcompressiveforce,theelasticdeformationlimitofthepolymerjointandthe
aluminumfoamisreached.Plasticdeformationinbothcomponentsdominatesthestress–strainresponsefromthispoint
onwardsandresultsinaslowerstressincrease.Fig.12furthersubstantiatesthatthetypeofadhesiveandthecoatingthick-
nessinfluencethestresslevelincompressivetesting.Withincreasingbondstrength,i.e.,withincreasingcoatingthickness,
higherdeformationresistanceisobserved.Atthesametime,thegeneralshapeofthestress–straincurveapproachesthatof
conventionalaluminumfoamsinshowingacleardistinctionbetweenthequasi-elasticandsubsequentfailuremodes.Be-
yondthistransition,stress–straincurvesofloosefoamelementsandjoinedaluminumfoam-polymerhybridsamplesdevel-
opqualitativelysimilarinplasticdeformation.Adhesivebondingoffoamelementsraisesthedeformationresistanceand,
thus,thestresslevelbutdoesnotchangegeneralplasticdeformationmechanismssignificantly.
Theprecisepointoftransitionfromquasi-elastictoplasticdeformationisdifficulttoquantify,theprocessbeinggradual.
Linearapproximationofquasi-elasticandplasticregionsofthestress–straincurvaturedeliversapointofintersectionde-
scribedbytheelasticcompressionlimite andstressr (Fig.14).Asboundariesforinterpolation,0.5%to2.0%(quasi-elastic)
P P
and10%to30%globalcompressivestrainwereselected.
Aquantitativeevaluationofbothcharacteristics(e ;r )aswellasweightspecificenergyabsorptionrevealsadepen-
P P
dencyprimarilyonsampledensity.Furtherinfluenceisattributabletotypeandthicknessofthepolymercoating.Highest
valuesofr ande areobservedforsampleshavinggreatestdensityandcoatingthickness(Figs.15,16).ForthePAbonded
P P
sampleswithab/D-ratioof29(cid:3)10(cid:4)3,theexperimentsallowdirectcomparisonofdifferentspheresizes.Forthestrainmea-
sure,theissueisunresolved,whilestresslevelsseemtobehigherinsamplesbuiltupfromsmallerelements.However,due
tothescatterofdata,whichismuchhigheramongthestresscomparedtostrainvalues,noclearstatementcanbederived.
Densityscalingisalsomoreevidentamongstrainvalues.Altogether,aluminumfoam-polymerhybridsshowcompression
propertiesanddensitydependencesimilartoclosedcellaluminumfoams(Ashbyetal.,2000).Opposingr valuestosim-
P
ilarlyderivedstrengthvaluesofconventionalaluminumfoambasedonthesamematrixalloyyieldssimilarresultsasinthe
caseofelasticproperties:Theconventionalfoamoutperformsthehybridmaterialinabsolutefigures.Themargin,however,
isnegligibleforlowdensities,withacompressivestrengthof3.9MParecordedforadensityof0.4g/cm3and9.0MPaat
0.6g/cm3(Avalleetal.,2004).ThelatterexceedstheAPMfoamvaluebyafactoroflessthan1.4.
Intermsofweightspecificenergyabsorption,PAbondedsampleswithhighestfoamdensityandpolymercoatingthick-
nessyieldbestperformancewithinthistestseries.Basedontheassumptionthatinfluenceoftheelementsizemaybene-
glected,Fig.17showsdependenceoftheamountofenergyabsorbedfromthedensity.Forreasonsofclarity,linearfitcurves
havebeenprovidedforthevariousdatasets.Inthisdiagram,verticaltranslationsofcurvesdenotetheinfluenceoftheadhe-
sive,whiletheinclinationismainlyduetothedensitydependenceofaluminumfoamstrength.ComparisonofPAbonded
samplesshowsthatacertaincoatingthicknessisneededtoheightenenergyabsorptionlevels.Thesteepergradientfound
forPAbondedsampleswithab/D-ratioof29(cid:3)10(cid:4)3isprobablyaconsequenceofthelargerdensityrangecoveredbythese
specimens,whichleadstoamoreobviousexpressionofthepowerlawlinkingfoamstrengthtodensity.Theexampleofthe