Engineering5(2024)1159–1170Contents lists available at ScienceDirectEngineeringResearch
4DPrinting—Article
PreliminaryInvestigationoftheReversible4DPrintingofaDual-LayerComponent
AmeliaYilinLeea,?,JiaAna,CheeKaiChuaa,b,?,YiZhangaabSingaporeCentrefor3DPrinting,SchoolofMechanicalandAerospaceEngineering,NanyangTechnologicalUniversity,Singapore639798,SingaporeEngineeringProductDevelopment,SingaporeUniversityofTechnologyandDesign,Singapore487372,Singaporearticleinfoabstract
Therapiddevelopmentofadditivemanufacturingandadvancesinshapememorymaterialshavefueledtheprogressoffour-dimensional(4D)printing.Withincreasingimprovementsindesign,reversible4Dprinting—ortwo-way4Dprinting—hasbeenproventobefeasible.Thistechnologywillfullyeliminatetheneedforhumaninterference,astheprogrammingiscompletelydrivenbyexternalstimuli,whichallows4D-printedpartstobeactuatedinmultiplecycles.Thisstudyproposesanewreversible4Dprint-ingactuationmethod.Theswellingofanelastomerandheatareusedintheprogrammingstage,andheatisusedintherecoverystage.Themainfocusofthisstudyisontheself-actuatedprogrammingstep.Toattaincontroloverthebending,asimplepredictivemodelhasbeendevelopedtostudythedegreeofcur-vature.Theparameters,temperature,andelastomerthicknesshavealsobeenstudiedinordertogainabetterunderstandingofhowwellthemodelpredictsthecurvature.Thisunderstandingofthecurvaturewillprovideagreatdegreeofcontroloverthereversible4D-printedstructure.ó2024THEAUTHORS.PublishedbyElsevierLTDonbehalfofChineseAcademyofEngineeringandHigherEducationPressLimitedCompany.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Articlehistory:Received31January2024Revised9May2024Accepted29May2024Availableonline29September2024Keywords:4DprintingAdditivemanufacturingShapememorypolymerReversible4DprintingTwo-way4DprintingElastomerswelling1.IntroductionThedevelopmentofnewtechniquesandmaterialsinthethree-dimensional(3D)printingofpolymershasfueledthegrowthofthefour-dimensional(4D)printingofpolymers[1,2],whichisother-wiseknownasthe3Dprintingofshapememorypolymers(SMPs)[3].In4Dprinting,printedobjectscanbeprogrammedtocarryoutshapechangesinresponsetoenvironmentalfactors[4].However,4Dprintingisstillinitsearlystageofdevelopment.IncomparisonwiththeconventionalmanufacturingofSMPs,the4Dprintingofpolymersstillfallsbehind.Onemajordifferenceisthelackofreversibility[5].Reversibilityisusuallyreferredtoas‘‘two-waymemory”becauseitgivesthematerialtwopermanentshapes[6].Mostcurrent4Dprintingdemonstrationsrequirereprogram-mingaftereachrecovery.Reversibilityenablesrepeatedactuationandeliminatestheneedforreprogramming,whichisusuallytime-andlabor-consumingandmightlackprecisionineachreprogram-mingcycle.ReversibilitywillallowtheuseofSMPsinapplicationswithcomplexgeometryandelaboratedesigns.Fig.1depictsthe?Correspondingauthors.E-mailaddresses:ylee057@e.ntu.edu.sg(A.Y.Lee),cheekai_chua@sutd.edu.sg(C.K.Chua).effectsofirreversible(one-way)shapememoryandreversible(two-way)shapememorywithheatingandcoolingasthestimuli[5].Inrecentyears,successfulbreakthroughshaveoccurredinreversible4Dprinting.Whilethemajorityofthisworkhasbeeninthe?eldofhydrogels,therearesomeexamplesofpolymercom-posites.Severalmechanismshavebeenutilizedtoprogram4D-printedhydrogels.Na?cyetal.[7]developedanextrudedhydrogelcompositehingethatenablesreversibleactuation.Theyusedtem-peratureandhydrationasthestimulitocarryoutshapesetting.Suetal.[8]usedtwodifferentsolvents,acetoneandwater,astherespectivestimuli.Theprintingwascarriedoutintwostepsbyprintingtheactiveareasandpassiveareasseparately.ThebendingbehavioroftheprintedpartswasexplainedbyTimoshenkotheory,whichinvolvesanisotropicexpansionofthebilayerstructure.Whiletheabovetwomethodswereprintedwithbio-extrusion,reversible4Dprintingwasalsoattemptedwithdigitallightprint-ingthatofferedafasterprintingspeed.Huangetal.[9]printedahydrogelwithactivesectionscontainingionicpotassium3-sulfopropylmethacrylate(PSPMA)inordertoattainlargerswellingcontrast.Liketheabovementionedstudies,twosolventswereusedastherespectivestimuliforactuation:0.1moláLà1NaClandwater.Asimilartestwascarriedoutwithawax-basedSMPinorderto1160A.Y.Leeetal./Engineering5(2024)1159–1170Fig.1.Processchainsofshapememoryeffects.(a)Irreversible(one-way)shapememoryeffect;(b)reversible(two-way)shapememoryeffect.demonstratethattheconceptwasfeasibleinvariousmaterials.Oneofthelimitationsofthisconceptisthatahydrogellacksmechanicalstrength.Thus,theresultsofthisstudyaremoresuit-ableforbiomedicalapplicationsandlesslikelytobeusedforload-bearingapplications.Otherstudieshaveemployedmaterialswithstrongermechan-icalproperties,suchasthestudiesbyMaoetal.[10]andUlaetal.[11].Maoetal.utilizedthemulti-materialinkjetprinterObjet260Connex(StratasysLtd.,USA)toprintthreelayers,eachwithafunc-tionforactuationineithershapesettingorrecovery.Thiscompos-itewasabletocompensateforthehydrogel’slackofmechanicalstrengthwiththestrengthoftheSMPsection.However,thestrengthwasstillrelativelylowduetotheuseofahydrogel.Ulaetal.[11]usedaliquidcrystalelastomer(LCE),whichisknowntohavereversibleshapememoryproperties.ThehingeswereprintedusingObjet260Connex,andthenDuPontTMME603silverink(silverconductor,DuPontdeNemours,Inc.,USA)wasdirectlywrittenontotheelastomerichinge.Next,theresearchersfabri-catedtheLCEwithnormalcuringoverthesilverink.WhentheLCEstripswereactivatedbyJouleheatingoftheconductivewireunderagivencurrent,thestripbent.Whenthecurrentwasremoved,thestripcooledandstraightened.Thegreatestissuewiththisstudywasthatthedevicelostitsself-actuationcapabilityduetotheuseofcurrent.TheprogrammingstageofmostshapememorycompositesrequiresmechanicalloadingtoinducestressontheSMPinordertoachieveshape?xing.Asimilarconceptisusedinthepresentstudy.However,insteadofmechanicalloading,anenvironmentalstimulusisused.Thedifferenceinthisworkisthatthecomponentonlycomprisestwolayers,whichissimilartothedualcomponentmechanism(DCM)thatisusedinone-wayshapememory.TheDCMusuallyhastwoormorecomponentswithahard/softseg-mentstructureoranelasticmatrix/transitioninclusion[12].Thesoftsegmentorelasticmatrixisrelativelyelasticsothatitcanstoreelasticenergyduringprogramming.Thehardsegmentiscon-sideredtobethetransitioncomponent,andhasastiffnessthatchangesuponheating.Thetransitioncomponentpreventsshaperecoveryatlowtemperaturesduetoitshigherstiffnessatlowtemperatures.Reheatingthecomponentwillsoftenthetransitioncomponenttoremovetheconstraints,andthestoredelasticenergyisactivatedtoreturnthepolymertoitsoriginalshape[13].InDCM,mechanicalstressisinducedonacompositeofmatrixand?berabovetheglasstransitiontemperature;thecom-positeisthencooledtoallowshape?xity.Inthisstudy,weusedastimulus—insteadoftheexternalmechanicalforceappliedmanu-allythatiscommonlyusedinone-way4Dprinting—toinduceastressontheshapememorypolymerthatissimilartothatofthe?bersinDCM.InthestudiesbyMaoetal.[10]andNa?cyetal.[7],themainfunctionofthehydrogelprimarilyoccursintheprogrammingstep,whereitswellsandinducesstressthatresultsinbendingwhenthecomponentisheated.However,weseektoachievethisswellingbyothermeans.Inthisstudy,thatfunctionisperformedbytheelas-tomericmatrix.Elastomersaregenerallycapableofabsorbingalargequantityoforganicliquids[14].Inthelasttwodecades,elas-tomershavebeenusedinthedrillingofdif?cultoilandgaswells[15,16].Some?uidsthathavebeentestedwithelastomersincludetolueneandethanol[17,18].Graham’slawofeffusionstatesthatthelowerthemolecularweight,thefasterthediffusion[19].Therefore,thislawsuggeststhatlowmolecularalcoholswellingisaplausiblesolutiontoattainswelling,althoughitisimportantforthestructureoftheelastomertohavefunctionalgroupsthatattractalcoholgroups.Elastomersarelooselycrosslinked,andthushavemorefreevolumethanotherpolymers[20];thisaidsintherateofswelling.Theelastomerhasdualfunctionsinthissetupusedinthisstudy.Intheprogrammingstep,itswellsandinducesinternalstress;intherecoverystep,itconvertsthestoredpotentialenergyintoelasticenergyandpullsthecomponentbacktothepermanentshape.Asonelessmaterialisused,thenumberoflay-erscanbereducedtojusttwo.Inthiswork,thestimulususedisethanol,whichisabletoswelltheelastomer;theswellingoftheelastomercomponentisthenutilizedtoinducestressonthetran-sitionmaterialduetostraindiscrepancy.Oncethe3Dstructureisheatedabovetheglasstransitiontemperature(Tg),theinducedstressonthetransitionmaterialisreleasedtochangetheshapeoftheprintedparts;thisgivesrisetothe?rstshapechange.WhileA.Y.Leeetal./Engineering5(2024)1159–11701161itislikelythatastraindifferencemaybecausedbythemismatchinthermalcoef?cient,Dingetal.[21]reportedthatwhentheyheatedthebilayerofatransitionmaterialandanelastomerforamodestdeformation,thethermalstrainwaslessthan1%fromroomtemperaturetoupto70°C.Therefore,thermalstrainisassumedtobenegligibleinthisstudy.Sincetherecoverystephasbeenwidelystudied—asitisthesameasthatinheat-inducedone-wayshapememory—thispaperfocusesontheself-actuatedprogrammingstep.Inordertoachievebettercontroloftheshapechange,theswellingbehavioroftheelastomermustbeunderstoodsothattheparametersoftheswellingcanbecon-trolled.Asimplepredictivemodelisdevelopedsothatthedegreeofcurvaturecanbestudied.Thisunderstandingofthecurvaturewillprovideagreatdegreeofcontroloverthereversible4D-printedstructure.2.3.Swellingtestsoftheelastomer2.3.1.LinearswellingThreesetsofathinbeamofTangoBlackPluswiththedimen-sions2mm?2mm?5cmwereprinted.ThebeamlengthsweremeasuredandrecordedwithaVerniercaliper;thebeamswerethensoakedinethanolfor24h.Afterthebeamswereremovedfromtheethanol,the?nallengthofthethinbeamwasmeasuredandrecordedwithaVerniercaliper.2.3.2.VolumetricswellingTwosetsofdifferentshapeswereprintedofTangoBlackPlusandVeroWhitePlus:acubewithsidesof5.84cm,andablockwiththedimensions5cm?5cm?8cm.Thesedimensionswereusedtomaintainanapproximatetotalvolumeof200cm3.Twodifferentshapeswereusedtoinvestigatewhethertheelastomeralsoswelledisotopically.Thedrymassofthesampleswas?rstweighedusingaMettlerToledoXS204analyticalbalanceandrecordedasmd.Thesampleswerethenplacedinethanolfor24hattempera-turesof25,30,40,50,and60°C.Thesampleswereremovedandweighedagain.Thewetmasswasrecordedasmw.Thevolumewascalculatedusingtheformulav?aemdàmwT=eqoàqlT,wherea?0:99985,qlisthedensityoftheliquidsubstance,andqoisthedensityofair[23].2.4.TensiletestofVeroWhitePlusandTangoBlackPlusBothmaterials—thatis,VeroWhitePlusandTangoBlackPlus—weretestedwiththeShimadzuUniversalTesterAGS-Xseriesat10kNwiththeteststructurecompliantwithASTMD638andASTMD412,respectively.Thesampleswereloadedat10mmáminà1.Bothmaterialsweretestedat25and60°Cwiththreereplicates.Thesampleswerestabilizedatthetemperaturefor30minbeforetensiletestingwascarriedout.2.5.ReversibilitycycleThereversibilityofthebilayerwasachievedbytwostimuli—ethanolandheat—intheprogrammingstagetocauseashapechangefrompermanentshape1topermanentshape2,asshowninFig.2.Then,intherecoverystage,heatstimuluswasappliedtoenableashapechangefrompermanentshape2backtoperma-nentshape1.Adual-layeredstripmeasuring4cmby1cmwithathicknessof1.5mmofTangoBlackPlusand1.5mmofVeroWhite-Pluswasprinted.Thestripwasplacedinabeakerofethanolwithinawaterbathat25°Cfor1h.Theelastomericmaterial2.Materialsandmethods2.1.MaterialsAllthesampleswerefabricatedusinganObjet500Connex3polyjetprinter(Stratasys,Ltd.,USA).Inthecurrentprintingsystem,allmaterialsweresuppliedbyStratasys.ThematerialsusedinthepresentresearchwerebasedontwomaterialsprovidedbyStratasys:VeroWhitePlusandTangoBlackPlus(productcodesfromStratasys).VeroWhitePlusisahardandrigidmaterialatroomtem-peraturewithaglasstransitiontemperatureof58°C,whereasTangoBlackPlusissoftandrubberyatroomtemperaturewithaglasstransitiontemperatureofà10°C[22].TheTangoBlackPlusliquidresincomprisesurethaneacrylateoligomer,exo-1,7,7-trimethylbicyclo[2.2.1]hept-2-ylacrylate,methacrylateoligomer,poly-urethaneresin,andaphotoinitiator.TheVeroWhitePlusliquidresinconsistsofisobornylacrylate,acrylicmonomer,urethaneacrylate,epoxyacrylate,acrylicmonomer,acrylicoligomer,andaphotoinitiator.Thesolventusedwas99%ethanol,obtainedfromA.P.C.ChemicalIndustries,Inc.,USA.2.2.PrintingparametersThematerialswereprintedwithanObjet500Connex3polyjetprinterusingtheDigitalMaterialmodeataresolutionof300dpiáinà1(1in=2.54cm)alongthexandyaxes.Allpartswereprintedat100lmáminà1withalayerthicknessof30lmandupto85lmforthexandyaxes.Theresinswerecuredbyultraviolet(UV)lightwithintheprinter.Fig.2.Thetwomainstagesofthereversiblecycle:programmingandrecovery.Intheprogrammingstage,therearethreesteps.Step1:The?rstpermanentshapeisexposedtoethanol.Step2:Thecomponentisremovedfromethanolandheatedat60°Cinwatertoallowthesecondpermanentshapetoform.Step3:Thecomponentiscooledtoallowthecomponentto?xinthesecondpermanentshape.Intherecoverystage,therearetwosteps.Step4:Thecomponentislefttodry.Step5:Thecomponentisheatedtorecovertothe?rstpermanentshape.1162A.Y.Leeetal./Engineering5(2024)1159–1170(TangoBlackPlus)swelledandincreasedinvolume.Stressbuiltupasthetransitionmaterial(VeroWhitePlus)didnotswell.Thestripwasthenremovedtostoptheswellingandplacedinanotherwaterbathat60°Cfor5min.Thestripwasthenremovedandplacedinicewaterforapproximately1min.Thestripwaslefttodryfor3hinordertoremovetheethanolwithintheelastomer.Tocarryouttherecoverystep,thestripwasonceagainplacedinthe60°Cwaterbath.2.6.Curvatureofbilayerstrip2.6.1.PredictivemathematicalmodelBecausetherecoverystep,whichlastsfromStep4toStep5(Fig.2),hasbeenwidelystudiedinone-way4Dprintingactuatedbyheat,ourfocusisontheshape-settingstep,whichcomprisesSteps1and2.Amodelisessentialtopredictthecurvaturethatcanbeobtainedinshapesetting.ApredictivemathematicalmodelwasobtainedbyimprovisingontheFlory–Rehnerequation,thePeppasmodel,andthemechan-icsofcomposites.TheswellingoftheelastomercanbedescribedandpredictedwiththePeppasmodel.TheswellingrateoftheequilibriumisdeterminedbytheFlory–Rehnerequation[24].lne1àv2Ttv2tvv2V1v1=32?àqMc2e1Twherev2isthepolymervolumefraction,vistheFlory–Hugginsinteractionparameter,qisthedensityofthepolymer,V1isthemolarvolumeofthesolvent,andMcisthemeanmolecularweightofthechainsbetweeneachsuccessivecrosslink.vFromtheFlory–Rehnerequation,thepolymervolumefraction2canbefound.Theequilibriumvolumeisgivenasfollows:V1V?v12e2TwhereVisthedryvolumeoftheelastomerandV1istheequilib-riumvolumeoftheswollenelastomer.TheswellingcontentS1,whichisalsoknownastheratioofswellingagenttothedryvolumeofelastomer,isfoundusingthefollowingequation:SV1?1àVVe3TTodeterminetheswellingcontentatvarioustimepoints,twomodelsareusedseparately,aseachhasitsownlimitations.Forshortdiffusiontimes,wherethefractionofswellingcontentSt=S1<0:6,thePeppasmodelwillbeused.Thismodelisdescribedbyapowerlaw:St=S1?ktne4TwhereStistheswellingcontentattimet,kisaconstantthatchangesaccordingtothenetworkandgeometricstructure,andnisthediffusionexponentialofthesolvent.TheconstantscanbeobtainedbysolvingFick’ssecondlawofdiffusion[25],whichisgivenasfollows:@c@??@c??@t?@x@xe5Twherecistheconcentrationofthesolventandxisthedistance(Fig.3).Fordiffusionintoaslabofthickness2h,theconcentrationctatanypointwithinthe?lmattimetcanbefoundbythefollowing:c\t4X1eà1TnàDe2nt#????c?1àexp1T2p2t1p2?cose2nt1Tpxn?02nt14h2he6TFig.3.Illustrationoftheeffectsofelongationoftheelastomerwhenunbondedandbondedtothetransitionmaterial.Whenbonded,themismatchinstrainresultsincurvature.ByintegratingEq.(6),thefollowingequationcanbeobtained:M\De2nt1T2p2#tM1?1àX18àte2nt1T2e7Tn?0p2exp4h2whereMtisthemolecularweightattimetandM1istheequilib-riummolecularweight.Forshorttimes,Eq.(7)isreducedtobesomewhatsimilartothePeppasmodel[26]inEq.(4),M????nt2DM1?hptne8TTherefore,theconstantkis2eD=pTn=h.ThemassdiffusivityDisgovernedbyanexponentialequationthatistemperature????Tdependent:D?DàEa0expRTe9TwhereD0isthemaximaldiffusioncoef?cientandEaistheactivationenergyfordiffusion.CombiningEq.(9)withPeppas’model,thefollowingequationsareobtained:S????????nt2D0tS?hpexpEa1RTe10TForthe4D-printedcomponent,theswellableelastomerononlyonesideoftheslaballowssolventtodiffusein;therefore,thewholeequationisdividedbytwoforthecomponent.S1??D??????ntp0tEaS1?hexpeRTe11Twhereheisthethicknessoftheelastomer.To?ndtheswellingcontentthatispresentintheelastomeratagiventime,temperature,andthickness,thefollowingequationisused:Vt?StVtVe12TwhereVtisthevolumeattimet.Assumingthattheswellingisisotropic,thelinearswellingratioattimetwillbe??kV??1t3t1T1t??eSt3Ve13TThestrainexwillbeex?ktà1e14TTherefore,A.Y.Leeetal./Engineering5(2024)1159–11701163e???S1??D??????n??10tE3xhexpaepRTt1à1e15TConsideringthatthetwolayersoftransitionmaterialandelas-tomerarenotbonded,theswellingoftheelastomerwillbringaboutanincreaseinstrainthatdoesnotexistforthetransitionmaterial.Whentheyarebonded,themismatchinstrainwillresultinstressthatwillforcethetransitionmaterialtobend.However,themechanicalstrengthofthetransitionmaterialishighatroomtemperature.Thebendingforcethatiscreatedisinsuf?cienttocausealargebending(Fig.3).Therefore,thetransitioncomponentisheatedaboveitsglasstransitiontemperature.Now,thestiffnessofthetransitionmaterialdecreases,enablingthecomponenttobendfurther.Thisstructureisconsideredtobeadual-layercom-posite,andthecurvatureiscalculatedusingthemechanicsofcom-posites.Thedifferenceinstrainduetothedifferenceinthermalexpansioncoef?cientisassumedtobenegligible[21].Tosimplifythemechanicalmodel,itisassumedthattherearetwolaminatesinthemodel.Inthemechanicsofacomposite,theplanesectionsnormaltothelongitudinalaxisremainplaneandnormalduringbending.Hence,etzT/àr/zx?err/?re16Twhereexisthestrainalongthexaxis,ristheradiusofcurvatureoftheneutralsurfaceduringbending,/istheangleofthebentmate-rial,andzisthefurthestdistancefromtheneutralsurfacede?nedbythexyplane,whichistheneutralaxisofthebilayer.zistakentobethefurthestdistance,astheelasticmodulusoftheelastomertendstobemuchlowerthanthatofthetransitionmaterial.Todeterminetheneutralaxisofthebilayer,itis?rstnecessarytodeterminetheratiooftheelasticmodulusofVeroWhitePlustotheelasticmodulusofTangoBlackPlus:ratio?ETEee17TwhereETistheelasticmodulusofthetransitionmaterialat60°C,andEeistheelasticmodulusoftheelastomerat60°C.ThebilayerisshowninFig.4.Theactualarea(Aa)ofthecross-sectionisgivenasfollows:Aa?whe18TUsingthesmallerelasticmodulusasabase,theareaoftheelas-tomer(Ae)willbe:Ae?wehee19TAssumingthebendingoccurredasthoughitisahomogeneousmaterial,thedifferenceintheelasticmodulusisconsideredandthecentroidaxisforthetransitionmaterialmustbenormalized;hence,itisnecessarytofactorintheratiooftheelasticmodulusofthetransitionmaterialtotheelasticmodulusoftheelastomertothearea:AETT?wThTEee20Twherewandhrefertowidthandheight,respectively.ThesubscriptTanderefertotransitionmaterialandelasomer,respectively.Fig.4.Height(h)andwidth(w)ofthebilayer.Theneutralaxis(na)fortherespectivematerialsisasfollows:naT?hhTet2e21Tnaee?h2e22TTheneutralaxisofthebilayer,z,willbe:z?naTATtnaeAeATtAee23Tz?naTwThTeET=EeTtnaewehewThTeET=EeTtwehee24TTheequationobtainedisasfollows:(j???1S1??Dt??????n??1)03zhexpEaepRTt1à1e25T(j???wThTeET=EeTtweheS????????n??1)1D0t3naTwThTeET=EeTtnaewehehexpEaepRTt1à1e26Twherejisthecurvature.2.6.2.MeasurementofcurvatureDual-layercomponentsofTangoBlackPlusandVeroWhitePluswithalengthof4cm,widthof1cm,varyingthicknessof1.5,2,2.5,3,and3.5mmofTangoBlackPlus,andstandardthicknessof1.5mmofVeroWhitePluswereprintedandsoakedinthefourdif-ferenttemperaturesof25,35,45,and55°Cfor60min.Next,thecomponentswereheatedtoabove60°C(whichisabovetheTgofVeroWhitePlus)inwaterfor1mintoallowtheVeroWhitePlustobeheatedpastitsTg.Thecomponentswerequicklyremovedandplacedincoldwaterat10°Cinordertorapidlycoolthecom-ponent.Thesampleswerethenremovedandplacedongridpaper.ThecurvaturesweredeterminedbymeasuringthechordlengthandchordheightwithaVerniercaliper.Similarly,dual-layercomponentsofTangoBlackPlusandVero-WhitePluswithalengthof4cm,widthof1cm,varyingthicknessof1.5,2,2.5,3,and3.5mmofVeroWhitePlus,andstandardthick-nessof1.5mmofTangoBlackPluswereprintedandsoakedinthefourdifferenttemperaturesof25,35,45and55°Cfor60min.Theradiusisgivenasfollows:22R?dt4hc8hce27TwhereRistheradiusofcurvature,hcisthechordheight,anddisthechordlength(Fig.5).Fig.5.Measurementsoftheradius.