Structural composite laminate materials with low dielectric loss: Theoretical model towards dielectric characterization

HAL Id: hal-02971767

https://hal.archives-ouvertes.fr/hal-02971767

Submitted on 19 Oct 2020

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Structural composite laminate materials with low dielectric loss: Theoretical model towards dielectric

characterization

Maëlle Sergolle, Xavier Castel, Mohamed Himdi, Philippe Besnier, Patrick Parneix

To cite this version:

Maëlle Sergolle, Xavier Castel, Mohamed Himdi, Philippe Besnier, Patrick Parneix. Structural com- posite laminate materials with low dielectric loss: Theoretical model towards dielectric characteriza- tion. Composites Part C: Open Access, Elsevier, 2020, 3, pp.100050. �10.1016/j.jcomc.2020.100050�.

�hal-02971767�

ContentslistsavailableatScienceDirect

Composites Part C: Open Access

journalhomepage:www.elsevier.com/locate/jcomc

Structural composite laminate materials with low dielectric loss:

Theoretical model towards dielectric characterization

Maëlle Sergolle

, Xavier Castel

, Mohamed Himdi

, Philippe Besnier

, Patrick Parneix

aUniv Rennes, INSA Rennes, CNRS, IETR-UMR 6164, F-35000 Rennes, France

bNaval Group, Technocampus Océan, 44340 Bouguenais, France

a r t i c le i n f o

Keywords:

Composite materials Dielectric characterization Maxwell-Garnett model Microwaves

a b s t r a ct

Organicmatrixcompositematerialsexhibithighmechanicalpropertiesassociatedwithlightweight.Theyalso providetheabilitytoembedradiofrequencyfeatures,suchasmicrowaveantennas,forsmartload-bearingstruc- turesofvariousmeansoftransport.Antennasimplementationintocompositepanelsrequireselectricallyconduc- tivefabricsfortheradiatingelements,feedinglinesandgroundplanesembeddedintothestructuraldielectric compositematerialswithlowlossatmicrowaves.Accordingly,thepresentstudyinvestigatestheassessmentof thedielectriccharacteristics,namelytherelativepermittivity𝜀randthelosstangenttan𝛿ofcompositelaminate materialsmadeofE-glass,S2-glassandquartzfabricsinfusedwithepoxy,polyesterandurethaneacrylatether- mosettingresins.Therelateddielectriccharacteristics,measuredintwooperatingbands,namely100MHzto 1GHzand18–26GHz,arecomparedwiththetheoreticalvaluescomputedfromthe2DMaxwell-Garnettmodel thatwehaveadaptedtolaminatecompositematerials.Mechanicalcharacteristicsofsuchcompositelaminate materialsarealsoinvestigated.Eventually,thequartz/urethaneacrylatelaminateishighlightedasalowloss compositematerial,highlysuitableforthefabricationofantennasoperatingatmicrowaves.

1. Introduction

Organicmatrixcompositematerialsareincreasinglyusedintrans- port area. These materials are mainlymade of reinforcement fibers infused with thermosetting resins. They enable the fabrication of lightweightandmechanicallyresistantstructuralpanels.Moreover,they promoteembeddedelectronicapplications.ThevastareaofMultifunc- tionalStructures(MFS)[1]showstheinterestofcombiningthefunc- tionalcapabilities of oneor more subsystemswiththat of theload- bearingstructure,therebyreducingthemassandvolumeofthetotal system[2].Amongcleanenergyproductionstructures[3],integrated electronics[4]andsmartstructures[5],compositepanelsforradiofre- quencycommunicationshaveaprominentplaceinsuchmultifunctional structurefield.

Antennasimplementationintoload-bearingcompositepanelsis a majoraspectof thesmartcompositematerialsdevelopment.Various studies have already developed this innovative concept. Kim et al.

[6]fabricatedamultibandaero-vehiclesmartskinantenna (MASSA) madeofasinglehoneycombincludingtheradiatingelementstacked betweentwostructuralcompositefacesheets.Thisantennacanbein- tegratedin theairplaneload-bearingstructure andoperates closeto 300MHz.Manac’hetal.[7]demonstratedsimilarmicrowaveperfor- mancebetweenapurecompositelaminateantennaandacopperone

∗Correspondingauthor.

E-mailaddress:[email protected](M.Sergolle).

operatingbothinthe600MHzto2.1GHzfrequencyband.Youetal.

builtconformalload-bearingantennastructures(CLAS)byintegrating slots[8]andradiatingpatches[5]betweentwolayersofhoneycomb.

Thefirststructureresonatesat5.3GHzandthesecondoneoperatesat 12.2GHz.Intheseworks,atwofoldstudywascarriedout,(i)onthecon- ductivefabricstominimizetheohmiclossandtheskindepthloss[7], and(ii)onthedielectricmaterialstominimizethedielectricloss[5,6,8].

Themainobjectiveofsuchstudiesaimstodevelopembeddedcommu- nicatingsystemswithoptimalradiofrequencyefficiencyatmicrowaves.

Thepresentstudyfocuseswiththeframeworkofthecase(ii),namely thedielectriclossreductionof thedielectriccompositematerials. To date,thefibersreinforceddielectriclaminatesusedforantennaappli- cationsarebasedonthetwosomeformedbyE-glass/polyester[7],E- glass/vinylester[9,10],E-glass/epoxy[5,11,12],orS-glass/epoxy[13], asdisplayedinTable1.Therelativepermittivityofsuchcompositelam- inatesremainscloseto𝜀r≈4andthelosstangenttan𝛿higherthan0.01, relativelyhighvaluesforapplicationsatmicrowaves.

Thepresentpaperinvestigatestheoreticallyandexperimentallyvar- iousdielectriccompositelaminatesmadeofglass fabricsandorganic thermosettingresins,thatmaybeusedasload-bearingcompositepan- elswithlowdielectriclossforantennasubstrateand/orradomeappli- cations.Afterthedescriptionofthedielectricandmechanicalcharacter- izationtechniques,theglassfabricsused(namelyE-glass,S2-glassand

https://doi.org/10.1016/j.jcomc.2020.100050

Received10June2020;Receivedinrevisedform28September2020;Accepted29September2020

2666-6820/© 2020TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense (http://creativecommons.org/licenses/by-nc-nd/4.0/)

M. Sergolle, X. Castel, M. Himdi et al. Composites Part C: Open Access 3 (2020) 100050

Table1

Dielectriccharacteristicsofthefibersreinforceddielectriclaminatesusedforantennaapplications.

Composite laminate materials L -band S -band X -band V -band

E-glass/Polyester [7] 𝜀 r= 4.5; tan 𝛿= 0.01 @ 1 GHz / / /

E-glass/Vinylester [ 9 , 10 ] 𝜀 r= 4.5; tan 𝛿≈0.015 @ 1.5 GHz / / /

E-glass/Epoxy [ 5 , 11 , 12 ] / 𝜀 r= 4.0; tan 𝛿= 0.03 @ 2.5 GHz 𝜀 r= 4.0; tan 𝛿= 0.03 @ 12 GHz 𝜀 r= 4.6; tan 𝛿= 0.035

@ 50-75 GHz

S-glass/Epoxy [13] / / 𝜀 r= 4.3; tan 𝛿= 0.02 @ 10 GHz /

Fig.1. Complexdielectriccharacterizationbyimpedancemeasurement.

fusedquartzfibers)andthethermosettingresinsused(namelyepoxy, polyesterandurethaneacrylate)aredescribed,aswellastheimplemen- tationprocess.Then,atwo-dimensionalMaxwell-Garnettmodelispre- sentedanddevelopedforourspecificcompositelaminatestocompute theirdielectriccharacteristics(relativepermittivity𝜀randlosstangent tan𝛿).Thedielectricmeasurementsarecarriedoutovertwofrequency bands(100MHzto1GHzand18–26GHz).Theoreticalandexperimen- talresultsarethencomparedanddiscussed.Themechanicalcharacter- izationofthecompositelaminates,throughtensiletests,completesthe study.Finally,conclusionsaredrawn.

2. Characterizationtechniques 2.1. Dielectriccharacterization

Relativepermittivity𝜀r=𝜀’_randlosstangenttan𝛿=𝜀”_r/𝜀’_raredis- playedfromthecomplexdielectricpermittivityexpression𝜀^∗=𝜀’_r – j 𝜀”_r . 𝜀^∗ is retrieved from two separate techniques, namely the impedancemeasurementandthefree-spacemeasurement.Foreachtype ofcompositelaminates,threedifferentsamplesmachinedfromthesame laminateareassessed.

2.1.1. Impedancemeasurement

Theimpedancemeasurement(Fig.1)retrieves𝜀r andtan𝛿values from100MHzto1GHz.Animpedanceanalyzerisconnectedtoamea- surementhead.Themeasurementheadacts asacapacitorof7mm- diameter.Priortomeasurements,astandardcalibrationwascarriedout throughanopen(non-contactcapacitorplates),short(face-to-facecon- tactcapacitorplates),andload(25mm×25mm×0.8mmTeflon^○R samplewith𝜀r=2.08overtheentirefrequencyband)sequentialsteps.

Thesamplesurfaceshavetobesmoothtopreventanyairgapbetween thesamplefaceandtherelatedcapacitorplate(whichwouldcausearti- facts).Themeasurementuncertaintiesareprovidedbythemeasurement accuracyoftheapparatus,asgivenbythesupplier[14].

2.1.2. Free-spacemeasurement

Thefree-space measurement(Fig.2)retrieves 𝜀r andtan𝛿 values from18to26GHz.Thistechniqueis basedonthesignalprocessing ofreflection/transmissionelectromagneticplanewavesilluminatingthe sampleundertest.Atransmittinghornantenna,connectedtoanetwork analyzer,radiatesanelectromagneticfieldwhichisfocusedasa(locally) planewaveonthesamplebytheuseoftwosuccessivereflectivemirrors.

Fig.2. Complexdielectriccharacterizationbyfree-spacemeasurement.

Theincidentplanewavesundergoreflectionandtransmissionthrough thesampleundertestaccordingtoitsdielectricproperties.Thesecond hornreceivestheoutgoingelectromagneticwavesaftertheirreflection ontotwo newsuccessivemirrors.Prior tomeasurements,calibration wasalsocarriedoutthroughastandardthru(nosample),reflect(metal plate),load(150mm×150mm×6.7mmTeflon^○Rsamplewith𝜀r=2.09 overtheentirefrequencyband)sequentialsteps.Forthistechnique,the measurementuncertaintiesaremostlyrelatedtothesamplethickness spreading.Asamesampleofcompositelaminatematerialfabricatedby thevacuuminfusionprocessmayexhibitathicknessvariationofabout

±0.2mmon150mm×150mmsamplearea.Duetothisuncertainty, resultsoffreespacemeasurementexhibitarelativepermittivityvaria- tionof8%andalosstangentvariationof11%at18GHz.

2.2. Mechanicalcharacterizationbytensiletests

Toevaluatethemechanicalcharacteristicsof thecompositelami- natematerials,tensiletestswereperformeduptothesamplerupture, accordingtothemechanicalstandard[15].ALloydInstrumentstesting machine(LR50KPlus)wasusedwithaconstantdisplacementrateof 2mm/minappliedon25mm-widthand250mm-lengthsamples.Re- sultingforcewasmeasuredwitha50kN-forcesensorandsampleelon- gationwasmeasuredthroughthevariationofarandomspecklepattern appliedoneachsamplesurfaceandmonitoredbyacamera.Therelated strain,definedas(L-L₀)/L₀whereListhelengthofthesampleduring thetestandL₀istheinitiallengthofthesample,wascomputedwiththe DigitalImageCorrelation(DIC)method[16].Theresultingtensileelas- ticmodulus(Youngmodulus)wasretrievedbetween100and200MPa (curveslope).Thebehaviorofeach typeof compositelaminateswas averagedfrom5samplesmeasurements.

3. Fabrics,thermosettingresinsandtheirimplementation 3.1. Reinforcementfibersandtherelatedfabrics

Amongthefamiliesofinorganicreinforcementfibersandtherelated fabrics,fibersofE-glass,S2-glassandfusedquartz(commonlyknown as“quartz”)wereselectedhereaccordingtotheirattractivedielectric characteristicsandtheircommonuseinthefieldofcompositemate- rials. E-glass fibers arethemost popularreinforcements used in the transportationarea.Theyaremainlymadeofsilica(55%wt.SiO₂)and

Table2

Dielectriccharacteristics(𝜀f;tan𝛿f)at100MHzand1GHzof theselectedreinforcementfibers,estimatedfrom[18].

Fibers 𝜀 f tan 𝛿f

100 MHz 1 GHz 100 MHz 1 GHz Quartz 3.7 3.7 1.0 ×10 ⁻⁴ 1.1 ×10 ⁻⁴ S2-glass 5.3 5.3 2.0 ×10 ⁻³ 2.5 ×10 ⁻³ E-glass 6.4 6.4 3.0 ×10 ⁻³ 3.1 ×10 ⁻³

calciumoxide(19%wt.CaO).Theremaining26%wt.arecomposedof othersoxides,mainlyAl₂O₃,B₂O₃andMgO.S2-glasscontainsahigh contentofsilica (65%wt.),alumina(25%wt. Al₂O₃)andmagnesium oxide(10%wt.MgO),andisknownforitslowerrelativepermittivity (Table2)anditsgoodmechanicalstrength[17].Quartzfiber,madeof 99.99%wt.puresilica,exhibitshightemperatureresistanceaswellas lowdielectriccharacteristicsvalues(Table2,[18]).Therelativepermit- tivity𝜀fandlosstangenttan𝛿fofthethreetypesoffibersaredisplayed inTable2.

Inthisstudy, aquadriaxialfabricof E-glassfibers (2.8 yarns/cm inthewarpdirectionwithanareadensityequalto618g/m²,refer- enceQX618from Sicomin,France), aplainweave of S2-glassfibers (2.1yarns/cminthewarpdirectionwithanareadensityof516g/m², reference 6000 from CTMI, France) and a 4H-satinof quartzfibers (11yarns/cminthewarpdirectionwithanareadensityof180g/m², reference5903fromCTMI,France)wereused.Thequadriaxialweave isastackoffourlayersofunidirectionalyarns:afirstlayerorientedat +45° tothewarpdirection,asecondlayerorientedat90°,athirdlayer orientedat−45° andthetoplayerparalleltothewarpdirection(0°).The plainweavecorrespondstoaperiodicinterlacingofyarns,alternatively oneover,oneunder.Finally,4H-satin(four-harnesssatin)isathreeby oneinterlacingpattern.Accordingtothesupplierdata,theYoungmod- ulusoftheE-glassandofthequartzfibersisequalto72GPa,andthat oftheS2-glassfibersisequalto87GPa.Literaturereportsanelongation atbreakof4.5–5%forE-glassfibers[18],5.4–5.8%forS2-glassfibers [18]and8.7%forquartzfibers[19].

3.2. Thermosettingresins

Inordertoinfusethepreviousreinforcementfabricstofabricatethe compositelaminatematerials,threetypesofthermosettingresinswere selectedinthepresentstudy:thepolyester,theepoxyandtheurethane acrylateresins.

Polyesteristhecheapestthermosettingresinandthemostusedin thefieldofcompositematerials,mainlyinthefabricationofmainstream ships,carsandindustrialparts.Itisproducedbyacondensationreac- tionbetweenaglycolandanunsaturateddibasicacid.Thepolyester resinpolymerizesafteraddingacatalyst(anorganicperoxide)anda cobaltaccelerator[17].Inthisstudy,thepolyesterresinusedisapre- acceleratedNorester^○R823(NordComposites,France)andwascatalyzed with2%wt.ofcatalyst(PMECfromNordComposites,France).Theresin waspolymerizedfirstatroomtemperaturefor24h,andthenwascured at40°Cfor16h.

Epoxyisa two-componentresin.This thermosettingresinis well knowntoachievehighmechanicalandtemperatureresistanceperfor- manceofcompositelaminatesforhighvalue-addedproductsinvarious meansoftransport:ships,vehiclesandaircraft[17].Inthisstudy,epoxy resin(SR8100fromSicomin,France),afteraddinghardener(SD8824 fromSicomin,France)witha27:100(v/v) ratio,waspolymerizedat roomtemperaturefor24h,followedbyacuringstepat80°Cfor6h.

Urethaneacrylateresinismadeofamonomercontainingurethane groupswith chain extenders.This resin is mainlyused in the auto- motivesector,forthebumpersfabricationforexample.Inthisstudy, aspolyesterresin,theurethaneacrylateresin(Crestapol^○R 1261from ScottBader,UK),afteraddingfirst2%wt.ofcobaltaccelerator(NL49P

Table3

Measureddielectriccharacteristics(𝜀m;tan𝛿m)at100MHzand1GHz oftheselectedthermosettingresins(retrievedfromimpedancemea- surement)

Resin

𝜀 m( ± 0.5) tan 𝛿m( ± 0.5 ×10 ⁻³) 100 MHz 1 GHz 100 MHz 1 GHz Urethane acrylate 2.7 2.7 5 ×10 ⁻³ 5 ×10 ⁻³ Polyester 2.7 2.6 1.4 ×10 ⁻² 1.1 ×10 ⁻² Epoxy 3.3 3.1 3.0 ×10 ⁻² 2.5 ×10 ⁻²

Fig.3.Compositelaminatematerialduringitsfabricationbyvacuuminfusion process.

fromAkzoNobelFunctionalChemicals,Netherlands)andthen2%wt.of specificcatalyst(Trigonox239fromAkzoNobelFunctionalChemicals, Netherlands),waspolymerizedatroomtemperaturefor24h,followed byacuringstepat40°Cfor16h.

Thethreethermosettingresinsusedinthisstudyareinfusionresins.

Furthermoreatroomtemperature,theseresinsareglassypolymers.Ac- cordingtothesupplierdata,theYoungmodulusofthepolyester,epoxy andurethaneacrylateresinsisequalto3GPa,2.4GPaand3.6GPa, respectively.

Thesingleresinswerecastinsiliconmoldsandcuredfortherelevant time.Impedancemeasurementson2-mmthicksampleswerecarriedout (Table3).Urethaneacrylateresinexhibitsthelowestvaluesofdielectric characteristicsinthe100MHzto1GHzfrequencyrange:𝜀m=2.7±0.5 andtan𝛿m=5.0×10⁻³±0.5×10⁻³.

3.3. Fabricationofthecompositelaminatematerials

Samplesfabricationwasdonebystandardvacuuminfusionprocess, widely usedin industrialenvironment.Itconsistsininfusingafabric byathermosettingresinundervacuum.Inthisway,dryfabricswere stackedontoawaxedglassslab.Placedundervacuum(−0.6bar)with aplasticbagasshowninFig.3,fabricswereinfusedjointlywiththe liquidthermosettingresin.After24hofpolymerizationatroomtem- peraturefollowedbythesuitablecuringstep,thecompositelaminate materialswerecuttotherequiredsizestoundergothedielectricchar- acterizations(25mm×25mm×2mmfortheimpedancemeasurement;

150mm×150mm×2mmforthefree-spacemeasurement)andthe mechanicalcharacterizations(250mm×25mm×2mm).

ThefibervolumefractionV_fofeachsamplewascomputedasfol- lows:

𝑉_𝑓= 𝑛×𝑚_𝑜𝑓

𝜌×ℎ (1)

wherenisthenumberofpliesofthedryreinforcementfabrics,m_ofisthe areadensityofthedryfabrics(kg/m²),𝜌fistheglassfibervolumeden- sity(kg/m³),andhisthemeasuredthicknessofthecompositelaminate sample(m).

Nineseparatecompositelaminates(Table4)werefabricatedandin- vestigatedhere,eachmadeofspecificreinforcementfabrics(E-glass,S2-

M. Sergolle, X. Castel, M. Himdi et al. Composites Part C: Open Access 3 (2020) 100050

Table4

FibervolumefractionV_fofthefabricatedcompositelaminatematerialscom- putedfromEq.(1)with𝜌quartz=2200kg/m³and𝜌E-glass=𝜌S2-glass=2600kg/m³, nisthenumberofpliesofthereinforcementfabricineachlaminate,andhis thethicknessofthecompositelaminatesample.

Composite laminate materials n h ± 0.2 (mm) V _f(%)

Quartz / Epoxy 12 2.3 42

Quartz / Polyester 12 2.4 42

Quartz / Urethane acrylate 12 2.4 41

S2-glass / Epoxy 5 2.1 46

S2-glass / Polyester 5 2.3 44

S2-glass / Urethane acrylate 5 2.3 43

E-glass / Epoxy 5 2.7 45

E-glass / Polyester 5 2.6 46

E-glass / Urethane acrylate 5 2.7 45

glassandquartz)infusedwithaspecificthermosettingresin(polyester, epoxyandurethaneacrylate).

4. Mixingrulesinthe100MHzto1GHzfrequencyrange

Sincethelastcentury,researchersdeveloptheoreticalmodels,called effectivemediumapproximations(EMA),topredictandcomputetheo- reticallythemacroscopicrelativepermittivity𝜀effofcompositemateri- alsmadeofahostmedium(characterizedbytherelativepermittivity 𝜀handvolumefractionV_h)andinclusions(characterizedbytherelative permittivity𝜀iandvolumefractionV_i=1–V_h).

4.1. Mixingruleswithoutloss

From the Maxwell equations, Maxwell-Garnett built a theory of homogenization[20]basedon amedium containingsphericalinclu- sions,stillwidelyusedtoday[21–23].Basedonthistheory,athree- dimensionalmixingrulewasdevelopedtocomputetheeffectiveper- mittivity(orthe macroscopicrelative permittivity)of thecomposite mediumaccordingtotherelativepermittivityofeachcomponentand itsrelatedvolumefraction[24],asfollows:

𝜀𝑒𝑓𝑓=𝜀ℎ+3𝑉𝑖𝜀ℎ 𝜀_𝑖−𝜀_ℎ 𝜀_𝑖+2𝜀_ℎ−𝑉_𝑖(

𝜀_𝑖−𝜀_ℎ) (2)

Fromatheoreticalpointofview,Bruggemansolvedtheproblemof non-symmetryoftheMaxwell-Garnettmixingrule(theresultsdiffered when𝜀iandV_iweresubstitutedby𝜀handV_h)[25].Otherstudiesleaded toaneffectiverelativepermittivityvaluecoveredbylowerandupper boundstotakeintoaccountthephasedistributioninfluence[26],or arelativepermittivityvaluedependinguponthefibersdirectioninre- lationwiththatoftheappliedelectricfield[27–29].Nevertheless,all thepreviousmodelsconsideredthecompositemediaaslosslessmate- rials.Accordingly,thepresentstudyadaptsaMaxwell-Garnettmodel consideringcompositemediawithdielectricloss.

4.2. 2DMaxwell-Garnettmodelofcompositematerialswithdielectricloss

SihvoladevelopedaMaxwell-Garnettmixingrulewhichcomputed thecomplexdielectricpermittivity𝜀^∗=𝜀r –j𝜀”_rofcompositemedia withoutneglectingtheloss,wheretheinclusiondimensionsremained largecomparedwiththemoleculardimensions[30].Inthecaseoffiber reinforcedcompositelaminates,thisconditionisobviouslycompletely fulfilled.Moreoverthefiberswereconsideredastwo-dimensionalin- clusions,asdonebyBalandKotharitopredicttherelativepermittivity ofnon-infusedpolyethylenefabrics[28].Accordingtotheseconsider- ations,theMaxwell-Garnettmodelwas extendedtotwo-dimensional compositemedia,namelythecompositelaminatematerials,wherethe fibersofthereinforcementfabricswereconsideredas2Dcylinderdi- electricinclusionsembeddedintoadielectric matrix.Becauseof the dielectricnatureofthe2Dcylinderfiberinclusionsandofthematrix

[31],weassumethatthecomplexpermittivity𝜀^∗compofthecomposite laminatematerialscanbeexpressedasfollows[32]:

𝜀^∗_{𝑐𝑜𝑚𝑝}=𝜀^∗_𝑚+2𝑉_𝑓𝜀^∗_𝑚 𝜀^∗_𝑓−𝜀^∗_𝑚 𝜀^∗_𝑓+𝜀^∗_𝑚−𝑉_𝑓(

𝜀^∗_𝑓−𝜀^∗_𝑚) (3)

where𝜀^∗misthecomplexpermittivityoftheresinhostmedium,𝜀^∗fis thecomplex permittivityofthefibers(2Dinclusions),V_f isthefiber volumefraction,andV_m=1–V_fisthematrixvolumefractioninthe compositelaminatematerial.Eq.(3)compliestheboundaryconditions, namely𝜀^∗comp=𝜀^∗mwhenV_f=0and𝜀^∗comp=𝜀^∗fwhenV_f=1.Itis worthnotingthatporosity(with𝜀^∗air=1)intothecompositelaminate samplesisneglected,whichisclosetorealitywhenthevacuuminfusion processisimplementedtofabricatesuchsamples.Moreoverthemodel describedaboveremainssuitableifthewavelengthoftheelectromag- neticfieldusedtocharacterizethecompositematerialislargeenoughin comparisonwiththedispersionanddimensionsoftheinclusions.These conditionsthenenablethemodellingofthediffusioneffectsascoming fromanequivalenthomogeneousmaterial.At3GHz,theworkingwave- lengthoftheelectromagneticfieldequals10cm.Thebiggestfabricyarn usedis0.5cm-wide(S2-glass– 2.1yarns/cm)witharepeatweaveunit of 1cm-wide. Thereforetoconsiderthecompositelaminatematerial asahomogeneousmaterialforanelectromagneticpointofview,the presentmodelisnolongersuitablebeyondthe3GHzlimit-frequency.

Accordingly,themixingrulehasbeenappliedinthe100MHzto1GHz frequencyrange.

4.3. Applicationofthe2DMaxwell-Garnettmodeltothecomposite laminatematerials

The2DMaxwell-Garnettmodelwasusedtocomputethecomplex dielectricpermittivity𝜀^∗comp(Eq.(3))ofthecompositelaminatemateri- alsfromthecomplexdielectricpermittivityvaluesofthereinforcement fibers𝜀^∗f(Table2)andofthesinglethermosettingresins𝜀^∗m(Table3), andbytakingintoaccountthefibervolumefractionV_finthecompos- itelaminatesamples(Table4).ResultsaredisplayedinTable5atboth endsofthestudiedfrequencyband,namely100MHzand1GHz.

Ontheonehand,therelativepermittivityvaluesofthesinglether- mosettingresinsrangefrom2.6–2.7(polyesterandurethaneacrylate resins)to3.1–3.3(epoxyresin)inthe100MHzto1GHzfrequencyband, inducinganamplitudedeviationΔ𝜀m=0.6at100MHzandΔ𝜀m=0.5 at1GHz(Table3).Fortherelativepermittivityvaluesofthereinforce- mentfibers,theyrangefrom3.7(quartzfibers)to6.4(E-glassfibers)in theworkingfrequencyband,inducinghighervaluesandlargerampli- tudedeviation(Δ𝜀f=2.7)(Table2).Accordinglythecomputedrelative permittivityvalues𝜀rcompofthecompositelaminatematerialsarecon- trolledbythetypeofreinforcementfibersusedandtheycanbegrouped inthreefamilieswhatevertheworkingfrequency(Table5):theE-glass fiberreinforcedlaminateswith𝜀rcomprangingfrom3.9to4.5;theS2- glassfiberreinforcedlaminateswith𝜀rcomprangingfrom3.5to4.1;and thequartzfiberreinforcedlaminateswith𝜀r comprangingfrom3.0to 3.5.Withineachfamily,thecompositelaminateswithepoxyresinhost mediumalwaysexhibittherelativehigher𝜀rcompvalueswhiletheones withpolyesterandurethaneacrylatehostmediaareclosetogether(in agreementwiththeirrelated𝜀mvalues).

Ontheotherhand,losstangenttan𝛿mvaluesofthesinglethermoset- tingresinsrangefrom5×10⁻³(urethaneacrylate)to25–30×10⁻³ (epoxy)witharatioequalto6(Table3)andthoseofthereinforcement fibers from0.1×10⁻³ (quartz)to3×10⁻³(E-glass,Table2)in the 100MHzto1GHzfrequencyband.Despitetheratiovariationofthere- inforcementfibertan𝛿fvalues,losstangentofthecompositelaminates iscontrolledbythetypeofthethermosettingresinusedduetotheirrel- ativehighvalues,andcanalsobegroupedinthreefamilies(Table5):

laminateswithepoxyhostmedium(tan𝛿comphigherthan10⁻²);lami- nateswithpolyesterhostmedium(6×10⁻³<tan𝛿comp<10⁻²);and laminates with urethane acrylate host medium (tan𝛿comp lower than 5×10⁻³).Foreachfamily,thetheoreticallosstangentvaluesincrease

Table5

Theoreticalcomplexpermittivity𝜀^∗compandlosstangenttan𝛿compofthecompositelaminatematerialscomputedfromthe2DMaxwell-Garnettmodelat100MHz and1GHz.

100 MHz Quartz S2-glass E-glass

Epoxy 𝜀 ^∗comp 3.48 –j 6.0 ×10 ⁻² 4.11 –j 7.2 ×10 ⁻² 4.43 –j 8.3 ×10 ⁻²

tan 𝛿comp 17.2 ×10 ⁻³ 17.4 ×10 ⁻³ 18.6 ×10 ⁻³

Polyester 𝜀 ^∗comp 3.09 –j 2.0 ×10 ⁻² 3.62 –j 3.2 ×10 ⁻² 3.96 –j 3.7 ×10 ⁻²

tan 𝛿comp 8.1 ×10 ⁻³ 8.9 ×10 ⁻³ 9.4 ×10 ⁻³

Urethane

acrylate 𝜀 ^∗comp 3.10 –j 1.0 ×10 ⁻² 3.61 –j 1.4 ×10 ⁻² 3.94 –j 1.7 ×10 ⁻²

tan 𝛿comp 3.1 ×10 ⁻³ 3.9 ×10 ⁻³ 4.3 ×10 ⁻³

1 GHz Quartz S2-glass E-glass

Epoxy 𝜀 ^∗comp 3.36 –j 2.5 ×10 ⁻² 3.97 –j 5.9 ×10 ⁻² 4.27 –j 6.7 ×10 ⁻²

tan 𝛿comp 14.3 ×10 ⁻³ 14.9 ×10 ⁻³ 15.8 ×10 ⁻³

Polyester 𝜀 ^∗comp 3.04 –j 2.0 ×10 ⁻² 3.55 –j 2.7 ×10 ⁻² 3.88 –j 3.1 ×10 ⁻²

tan 𝛿comp 6.6 ×10 ⁻³ 7.7 ×10 ⁻³ 7.9 ×10 ⁻³

Urethane acrylate

𝜀 ^∗comp 3.07 –j 0.9 ×10 ⁻² 3.57 –j 1.4 ×10 ⁻² 3.90 –j 1.7 ×10 ⁻²

tan 𝛿comp 3.1 ×10 ⁻³ 4.0 ×10 ⁻³ 4.3 ×10 ⁻³

Fig.4. 100MHzto1GHzfrequencyvariationsoftherelativepermittivity𝜀rcomp(a)andlosstangenttan𝛿comp(b)ofthecompositelaminatesamplesmeasuredby impedancetechnique.

slightlyaccordingtothetypeoffibers(inagreementwiththeirrelated losstangentvalues),butwithoutreallyaffectingtheirrelatedabsolute value.

5. Characterizationsofthecompositelaminatesamples 5.1. Dielectriccharacterizations

5.1.1. Impedancemeasurement

Impedancemeasurementfrom 100MHzto1GHzwasperformed ontheninestudiedcompositelaminatesamples(E-glass,S2-glass,and quartzfibers,infusedonebyonewithepoxy,polyesterandurethane acrylatethermosettingresins).Fig.4presents(𝜀r comp;tan𝛿comp)vari- ationsversusfrequencyofthecompositelaminatesamples.𝜀^∗compand tan𝛿compat100MHzand1GHzaregiveninTable7.Asexpected,therel- ativepermittivity𝜀rcompmeasurementidentifiesthreecompositelami- natefamilies,namelytheE-glassreinforcedlaminateswiththehighest 𝜀rcompvalues(𝜀rcomp≈4.1–4.4),theS2-glassreinforcedlaminateswith themiddle𝜀rcompvalues(𝜀rcomp≈3.6–3.7),andthequartzreinforced laminateswiththelowest 𝜀r comp values (𝜀r comp ≈ 3.1–3.2)in good agreementwiththetheoreticalbehaviorresultingfromthe2DMaxwell- Garnettmodelapplication.Therelativepermittivityvaluesslightlyde- creasefrom100MHzto1GHz,asexpectedforstandarddielectricma- terials[33].

Focusingonthedielectricloss,Fig.4.bpresentsarelativelymoder- atevariationoftan𝛿compversusfrequencyforallthesamples;itmaybe assumedasaconstantforpracticalapplications.Thecompositelaminate samplesinfusedwithepoxyresinexhibitsalwaysthehighestlossvalues (tan𝛿comphigherthan10⁻² overthefrequency band).E-glassandS2- glass/polyesterlaminatesamplesshowhigherlossthanthatoflaminates infusedwithurethaneacrylateresin.Losstangentofquartz/polyester laminates remainsclose tothat of theE-glassandS2-glass/urethane acrylatelaminates.Accordingly,combinationofmiddlelossreinforce- mentfiberswithalowlossthermosettingresinissimilartothecombi- nationoflowlossreinforcementfiberswithmiddlelossthermosetting resin.Therefore,thecombinationoflowlossreinforcementfiberswitha lowlossthermosettingresin,namelyquartz/urethaneacrylatelaminate sample,mustexhibitthelowestdielectriclossovertheentirefrequency band:tan𝛿comp=2.8×10⁻³at100MHzandtan𝛿comp=3.1×10⁻³at 1GHz.

5.1.2. Free-spacemeasurement

The dielectric characterizations weresupplemented byfree-space measurementfrom18to26GHzonthesamecompositelaminatesam- ples(Fig.5).

Asatlowerfrequencies(100MHzto1GHz),theresultsfromfree- spacemeasurementspecifythreecompositelaminatefamilies,regard- lessoftheresinsused:theE-glassfiberreinforcedlaminateswith𝜀rcomp

rangingfrom4.3to5.0;theS2-glassfiberreinforcedlaminateswith

M. Sergolle, X. Castel, M. Himdi et al. Composites Part C: Open Access 3 (2020) 100050

Fig.5.18-26GHzfrequencyvariationsoftherelativepermittivity𝜀rcomp(a)andlosstangenttan𝛿comp(b)ofthecompositelaminatesamplesmeasuredbyfree-space technique.

Table6

Youngmodulus(GPa)ofthecompositelaminatematerials.

Young modulus Quartz S2-glass E-glass Epoxy 18.1 ± 0.7 21.1 ± 0.9 12.9 ± 1.2 Polyester 17.4 ± 0.5 20.6 ± 0.7 12.4 ± 0.4 Urethane acrylate 16.5 ± 0.5 19.5 ± 0.5 12.1 ± 1.1

𝜀rcomprangingfrom3.6to4.0;andthequartzfiberreinforcedlaminates with𝜀rcomprangingfrom3.1to3.4.Comparisonoftheabsoluterela- tivepermittivityvaluesfromfree-spacemeasurementwiththosefrom impedancemeasurementexhibitsanincreasing𝜀rcompvaluefrom1GHz to18GHz.Thisincreaseisascribedtotheownuncertaintiesofthetwo separatetechniquesusedtocharacterizethesamplesintwodifferentfre- quencybands.Asareminder,theimpedancemeasurementisbasedona capacitivemethodwhilefree-spacemeasurementisbasedonanelectro- magneticreflection/transmissionwavesmethod.Nevertheless,theex- pecteddecreaseof𝜀rcompvaluesisnoticedfrom18GHzto26GHz.

Focusing now on the loss tangent variations versus frequency, tan𝛿compvaluesexhibitingbytheninesamplesarelesssplitfromeach otherthanatlowerfrequencies.However,thesametrendsareobserved:

first,thedirectimpactoftheresintypeonthedielectriclossofthecom- positelaminates,andsecond,theslightinfluenceofthereinforcement fiberstypeontheirdielectricloss.Accordingly,E-glass/epoxylaminates exhibitthehighestdielectriclosswithtan𝛿comphigherthan2×10⁻² overtheentire18–26GHzfrequencybandwhilequartz/urethaneacry- latelaminatesexhibitoncemorethelowestdielectriclosswithtan𝛿comp

lowerthan8×10^-3.

5.2. Mechanicalcharacterization

Thestress-straincurves(Fig.6)highlightapureelasticbehaviorof theninecompositelaminates.Moreovertheuseofquartzfiberreinforce- mentshowsanincreaseoftheelongationatbreak(upto3.6%),while thecompositelaminatesreinforcedwithS2-glassandE-glassfibersex- hibitasimilar elongationatbreak(closeto2.7%).This resultisex- plainedbytheintrinsicelongationatbreakofthepureglassfibers(asa reminder,8.7%forquartzfibers,5.4–5.8%forS2-glassfibersand4.5–

5%forE-glassfibers). Regardingthestiffnessof thesamplesstudied (Table6),thecompositelaminatesreinforcedwithS2-glassfibersex- hibitaYoungmoduluscloseto20GPa,thosereinforcedwithquartz fiberscloseto17GPa,andthosereinforcedwithE-glassfiberscloseto

Fig.6. Stress-straincurvesofthecompositelaminatesamplesmeasuredfrom tensiletest.

12GPa.Itisworthnotingthat,eventhoughepoxyresinprovidesaslight increaseinstiffnessofthecompositelaminates,theimpactoftheresin usedisnotrelevantontheirabsoluteYoungmodulusvalue.Thisresult stemsfromthesimilarmechanicalcharacteristicsofthepureresinsused (asareminder,Youngmodulusequals2.4GPaforepoxyresin,3GPa forpolyesterresinand3.6GPaforurethaneacrylateresin).

6. Comparisonofthe2DMaxwell-Garnettmodelwiththe microwavemeasurements

(𝜀rcomp;tan𝛿comp)valuesretrievedfromimpedancemeasurementare comparedwiththosecomputedfromEq.(3)ofthetailored2DMaxwell- Garnettmodelat100MHzand1GHz(Table7).Theoretical𝜀rcompval- uesalwaysfitwiththemeasuredonesintheuncertaintyrangeofmea- surement.Thetheoreticaltan𝛿compvaluesoftenexhibitslightlyhigher levelsthanthemeasuredones.Nevertheless,theoreticalandmeasured values remain very close toeach other. Therefore,theproposed 2D Maxwell-Garnettmodelprovidesfair(𝜀rcomp;tan𝛿comp)theoreticalval- ues ofthelowlosscompositelaminatematerials,conditionallyupon theelectromagneticwavelengthusedislarge enoughcomparedwith thedispersionanddimensionscalesofthereinforcementfibers.

Table7

Comparisonofthecomputedandmeasured(𝜀rcomp;tan𝛿comp)dielectriccharacteristicsofthecompositelaminatematerialsat100MHzand1GHz.

Composite laminate materials Theoretical 𝜀 _rcomp Measured 𝜀 _rcomp Theoretical tan 𝛿_comp Measured tan 𝛿_comp 100 MHz

Quartz / Epoxy 3.48 3.2 ± 0.5 17.2 × 10 ⁻³ 14.0 ×10 ⁻³± 0.5 ×10 ⁻³

Quartz / Polyester 3.09 3.2 ± 0.5 8.1 × 10 ⁻³ 6.4 ×10 ⁻³± 0.5 ×10 ⁻³

Quartz / Urethane acrylate 3.10 3.1 ± 0.5 3.1 × 10 ⁻³ 2.8 ×10 ⁻³± 0.5 ×10 ⁻³

S2-glass / Epoxy 4.11 3.7 ± 0.5 17.4 × 10 ⁻³ 13.7 ×10 ⁻³± 0.5 ×10 ⁻³

S2-glass / Polyester 3.62 3.6 ± 0.5 8.9 × 10 ⁻³ 7.6 ×10 ⁻³± 0.5 ×10 ⁻³

S2-glass / Urethane acrylate 3.61 3.7 ± 0.5 3.9 × 10 ⁻³ 4.8 ×10 ⁻³± 0.5 ×10 ⁻³

E-glass / Epoxy 4.43 4.2 ± 0.6 18.6 × 10 ⁻³ 14.6 ×10 ⁻³± 0.5 ×10 ⁻³

E-glass / Polyester 3.96 4.4 ± 0.6 9.4 × 10 ⁻³ 8.4 ×10 ⁻³± 0.5 ×10 ⁻³

E-glass / Urethane acrylate 3.94 4.3 ± 0.6 4.3 × 10 ⁻³ 5.0 ×10 ⁻³± 0.5 ×10 ⁻³

1 GHz

Quartz / Epoxy 3.36 3.1 ± 0.5 14.3 × 10 ⁻³ 11.1 ×10 ⁻³± 0.5 ×10 ⁻³

Quartz / Polyester 3.04 3.1 ± 0.5 6.6 × 10 ⁻³ 5.2 ×10 ⁻³± 0.5 ×10 ⁻³

Quartz / Urethane acrylate 3.07 3.1 ± 0.5 3.1 × 10 ⁻³ 3.1 ×10 ⁻³± 0.5 ×10 ⁻³

S2-glass / Epoxy 3.97 3.6 ± 0.5 14.9 × 10 ⁻³ 12.3 ×10 ⁻³± 0.5 ×10 ⁻³

S2-glass / Polyester 3.55 3.6 ± 0.5 7.7 × 10 ⁻³ 7.6 ×10 ⁻³± 0.5 ×10 ⁻³

S2-glass / Urethane acrylate 3.57 3.6 ± 0.5 4.0 × 10 ⁻³ 6.6 ×10 ⁻³± 0.5 ×10 ⁻³

E-glass / Epoxy 4.27 4.1 ± 0.6 15.8 × 10 ⁻³ 12.9 ×10 ⁻³± 0.5 ×10 ⁻³

E-glass / Polyester 3.88 4.3 ± 0.6 7.9 × 10 ⁻³ 8.0 ×10 ⁻³± 0.5 ×10 ⁻³

E-glass / Urethane acrylate 3.90 4.2 ± 0.6 4.3 × 10 ⁻³ 5.7 ×10 ⁻³± 0.5 ×10 ⁻³

Boththeoreticalandexperimentalinvestigationsdemonstratethat thereinforcementfibers typeimpactstherelativepermittivity ofthe compositelaminatematerials,andtheorganicresintypeimpactstheir dielectricloss.Inthatway,thequartz/urethaneacrylatecompositelami- nateexhibitsthemostattractivedielectriccharacteristicsformicrowave applications,namelylowrelativepermittivityvalue(𝜀rcomp=3.1±0.5) andverylowlossvalue(tan𝛿comp≈2.9×10⁻³±0.5×10⁻³)inthe 100MHzto1GHzfrequencyband.Thiscompositelaminatecanthere- forebeusedasradomeand/ordielectricsubstrateforantennaapplica- tions.

Todate,cyanateesterresinwasthemostattractiveresinintheaero- nauticalareadue toitshighdielectric andmechanical performance.

This resin is an epoxy-like processing, but more difficult to imple- ment due to its strong exothermic behavior, high vacuumwith ad- ditionallyautoclave processing andhighcuring temperature(higher than200°C)requirements.Recentopenliteratureprovidesthemea- sureddielectriccharacteristicsofquartz/cyanateestercompositelam- inatematerialsat300MHz(𝜀rcomp=3.42andtan𝛿comp=5.8×10⁻³ [34]).Thequartz/urethaneacrylatecompositelaminatesstudiedhere exhibithigherdielectricperformanceatthesameoperatingfrequency:

𝜀rcomp=3.1andtan𝛿comp≈2.8×10⁻³.Athigheroperatingfrequency, astudypresents thequartz/cyanate estercompositelaminatesasthe combinationprovidingthelowestlossachievablefromcommercialoff- the-shelfaerospacematerialswithtan𝛿comp=3×10^-3at10GHz[13]. Forcomparison,ourquartz/urethaneacrylatecompositelaminatesex- hibitalossvaluetan𝛿comp= 6×10⁻³at18 GHz,demonstratingthe relevanceofsuchcompositematerialsoverawideoperatingfrequency band,from100MHzupto26GHz.

7. Conclusions

Dielectriccharacteristics, namely relative permittivity 𝜀rcomp and losstangenttan𝛿comp,of low losscompositelaminate materialswere theoretically and experimentally studied at microwaves. The two- dimensionalMaxwell-Garnettmixingruledevelopedforsuchamate- rialprovidesfair(𝜀rcomp;tan𝛿comp)theoreticalvalues,whichfitstrongly withthemeasuredonesinthe100MHzto1GHzfrequencyband(in theuncertaintyrangeof measurement).Mechanical characteristicsof thecompositelaminateswerealsomeasuredthroughtensiletests.

This study highlighted the quartz fabric/urethane acrylate type resin composite laminate materials which exhibit (𝜀r comp = 3.1;

tan𝛿comp=3.1×10⁻³)and(𝜀r comp=3.2;tan𝛿comp =6×10⁻³)mea-

suredvaluesat1GHzand18GHz,respectively.Suchcompositelami- natematerialsarethereforerelevantforlowlossload-bearingantenna compositestructuresformicrowaveapplications,indirectcompetition withthequartzfabric/cyanateestertyperesincompositelaminates.In- deed,thiswell-knowncompositematerialremainsmoreexpensiveand difficulttoimplement.Urethaneacrylatecouldthereforebeconsidered asthepromisingthermosettingresinforsubstratesand/orradomesof antennasembeddedintoload-bearingcompositepanels.

DeclarationofCompetingInterest

Theauthorsdeclarethattheyhavenoknowncompetingfinancial interestsorpersonalrelationshipsthatcouldhaveappearedtoinfluence theworkreportedinthispaper.

Funding

This workwas supportedinpartbytheDGA,in partbytheRé- gions Pays-de-la-LoireandBretagne, inpartbytheDépartement des Côtesd’Armor,theSaint-BrieucArmorAgglomération,andtheLannion- TrégorCommunauté,throughtheFUI’23STARCOMproject.Thiswork wasalsosupportedinpartbytheEuropeanUnionthroughtheEuropean RegionalDevelopmentFund,inpartbytheMinistryofHigherEduca- tionandResearch,inpartbytheRégionBretagne,andinpartbythe DépartementdesCôtesd’ArmorandSaint-BrieucArmorAgglomération, throughtheCPERProjects2015-2020MATECOMandSOPHIE/STIC&

Ondes.

Acknowledgements

TheauthorswarmlyacknowledgeF.BoutetfromIETRandIDCom- positeteamfortheirtechnicalsupports.

References

[1] A.D.B.L. Ferreira, P.R.O. Nóvoa, A.T. Marques, Multifunctional mate- rial systems: a state-of-the-art review, Compos. Struct. 151 (2016) 3–35 https://doi.org/10.1016/j.compstruct.2016.01.028 .

[2] K.K. Sairajan, G.S. Aglietti, K.M. Mani, A review of multifunctional struc- ture technology for aerospace applications, Acta Astronaut. 120 (2016) 30–42 https://doi.org/10.1016/j.actaastro.2015.11.024 .

[3] T. Pereira, Z. Guo, S. Nieh, J. Arias, H.T. Hahn, Embedding thin-film lithium en- ergy cells in structural composites, Compos. Sci. Technol. 68 (2008) 1935–1941 https://doi.org/10.1016/j.compscitech.2008.02.019 .