3.1 isotropy and anisotropy - Routledge · 2017. 7. 15. · 34 Composite Materials: Design and Applications 3.2.1 Fiber Mass Fraction Fiber mass fraction is defined as M f = Mass

$Page 1: 3.1 isotropy and anisotropy - Routledge · 2017. 7. 15. · 34 Composite Materials: Design and Applications 3.2.1 Fiber Mass Fraction Fiber mass fraction is defined as M f = Mass$
29

Chapter 3

Ply Properties

It isessentialforthedesignertoknowpreciselyandunderstandthegeometricandmechanicalcharacteristicsofamixtureofreinforcementandmatrixaftercuring,whichisthebasicstructureofcompositeparts.Thedescriptionofthesefeaturesisthefocusofthischapter.

3.1 isotropy and anisotropyWhenstudyingthebehaviorofelasticbodiesundermechanicalloading(theoryofelasticity),thefollowingbasicpropertiesarehighlighted,bymeansofconsiderationsandtoolsthatarenotneces-sarilycomplicated:

◾ Anelasticbodysubjecttostressdeformsinareversiblemanner.◾ Ateachpointwithinthebody,theprincipal.planes.aretheplanesontowhichonlynormal.stressacts.

◾ Thenormal.directions.totheseplanesarecalledtheprincipal.stress.directions.◾ Insideofthebody,asmallsphere.ofmaterialsurroundingapointbecomesanellipsoid.afterloading.

Thespatialpositionoftheellipsoidrelativetothedirectionsofprincipalstressenablestodeterminewhetherthematerialunderstudyisisotropicoranisotropic.Figure3.1illustratesthisphenomenon.

Aneasywaytoseetheeffectsofanisotropyonthedeformationofasampleconsistsinloadingaplateofanisotropicmaterialinitsownplane.Figure3.2illustratesthedeformationsunderload,respectively,ofanisotropicandanisotropicplate.Inthelattercase,theobliquelinesonFigure3.2representthereinforcementfibers.Itshouldberecalledthatalongitudinalloadingappliedtotheisotropicplatecreatesanextensioninthelongitudinaldirectionandacontractioninthetrans-versedirection.AsseenonFigure3.2,thesameloadingappliedtoananisotropicplatecreatesanangulardistortion,in.addition.totheclassicallongitudinalextensionandtransversalcontraction.

Copyrighted Material – Taylor & Francis

30 ◾ Composite Materials: Design and Applications

Application of stress

Before stress application

σzσz

σx σxσy σy

M

Isotropic material: the axesof the ellipsoid coincide with

the principal stress axes

Anisotropic material: the axesof the ellipsoid are different

from the principal stress axes

Figure 3.1 Schematic of deformation.

Isotropic material Anisotropic material

Figure 3.2 isotropic and anisotropic plate: Comparison of deformation.


Ply Properties ◾ 31

Inthesimplecaseofplanestress,asonthepreviousexample,someelasticcoefficientsallowtolinkthestresscomponentstothedeformationsthattheyinduce.Thecorrespondingrelationsaretheso-calledbehaviorrelations,aswrittenhereafter.

3.1.1 Isotropic MaterialsThefollowingrelationsarevalidforamaterialthatiselasticandisotropic.

Thestress–strainrelationcanbewritten(seeFigure3.3)inmatrixformas*

z

y

x

*Intheseequations,εx, εy,andγxyarealsothesmallstrains(twonormalstrainsandadistortion)thatareobtainedinaclassicalmannerfromthedisplacementsuxanduyasεx=∂ux/∂x;εy=∂uy/∂y;γxy=∂ux/∂y+∂uy/∂x.

Dimensions1×1

y

y

σy

σx

x

x

τxy

xy

y

x

σx σyvx= –E E

σy σxvy= –E E

xyτxyG=

Figure 3.3 Stress–strain behavior in an isotropic material.



εεγ

σστ

x

y

xy

x

y

xy

EvE E

G

=

−

−

10

10

0 01

vE

Wecannotethreeelasticconstants:E,v,G.Thereisarelationamongthemas

G

Ev

=+2 1( )

Theearlierrelationshowsthatamaterialthatisisotropicandelasticcanbecharacterizedbyonlytwoindependentelasticconstants:E andv.

3.1.2 Anisotropic MaterialThematrixequationforanisotropicmaterial(seeFigure3.4)is

εεγ

x

y

xy

x

yx

y

xy

x y

xy

E

v

E

v

E E

G

=

−

−

10

10

0 01

σστ

x

y

xy

Wecannoteanapparentasymmetryofthematrixofelasticcoefficientsearlierandfiveelasticconstants:

◾ Twomoduliofelasticity:Ex andEy◾ TwoPoissoncoefficients:vyx andvxy◾ Oneshearmodulus:Gxy

Infact,thismatrixissymmetric,*andthereareonlyfourindependentelasticconstants†:Ex,Ey,Gxy,andvyx(orvxy).Thefifthelasticconstantcanbeobtainedfromtheothersusingthesymmetryrelation

v v

EE

xy yxx

y

=

*Toobtainmoredevelopmentaboutthispoint,refertoSections9.2and18.2.† RefertoSection13.2.



3.2 Characteristics of the Reinforcement–Matrix MixtureThe termply is commonlyused todescribe the semifinishedproduct reinforcement.+.resin,whichpresentsasaquasi2Dthinlayer.*Thiscanbe

◾ Alayerofunidirectionalfibersinamatrix◾ Alayerofwovenfabricinamatrix◾ Alayerofmatinamatrix

TheseareexaminedinmoredetailinSections3.3through3.5.

* Thisconditioningisavailableas.isonthemarket.Itiscalledprepreg.ItisalsothecaseoftheSMC.Inadditiontothistypeofconditioning,nonpreformedmixturesofshortfibersandresincanalsobefound.TheyarecalledpremixorBMC.SeeSection2.3.

yσy

σx

x

x

y

z

Dimensions1×1

y

x

y

τxy

xy

x

σx σyvyxx = –Ex Ey

ExEyσy σxvxyy= –

xyτxyGxy

=

Figure 3.4 deformation in an anisotropic material.



3.2.1 Fiber Mass FractionFibermassfractionisdefinedas

Mf =

Mass of fibers

Total mass

andthematrixmassfractionissuchas

Mm =

Mass of matrix

Total mass

fromwhich

Mm=1−Mf

3.2.2 Fiber Volume FractionFibervolumefractionisdefinedas

Vf =

Volume of fiber

Total volume

Asaresult,thevolumefractionofmatrixisgivenas

Vm =

Volume of matrix

Total volume

fromwhich*

V Vm f= −1

Notethatmassfractioncanbeobtainedfromvolumefractionandviceversa.Ifρf andρm arethespecificmassofthefiberandmatrix,respectively,wehave

V

M

M MM

V

V Vf

f

f

f

f

m

m

ff f

f m mf

=+

=+

ρ ρρ ρ

ρ ρ

Dependingon themethodof fabrication, thecommonfibervolume fractionsareas shown inTable3.1.

* Infact,thereinforcement/matrixmixturealsoincludesasmallvolumeofvoidsnotoccupiedbythematrix,characterizingacertainporosityofthecomposite.ItwouldthusbemorelogicaltowriteV V Vm f p+ + = 1,inwhichVpdenotestheporosity.volume.fraction,withVp � 1(seeSection18.11).



3.2.3 Mass Density of a PlyThemassdensityofaplycanbecalculatedas

ρ =

Total mass

Total volume

whichcanalsobeexpandedas

ρ = +Mass of fiber

Total volume

Mass of matrix

Total volume

=Volume of fiiber

Total volume

Volume of matrix

Total volumeρ ρf + m

or

ρ ρ ρ= +f f m mV V

3.2.4 Ply ThicknessTheplythicknessisdefinedstartingfromtheweightperunitareaoffiberorgrammagewrittenasmof .Theplythickness,denotedash,isthensuchthat

h

mof

f

× = ××

1 2( )m Total volume= Total volumeFiber volume ρ

or

h

m

Vof

f f

=ρ

Onecanalsoexpressthethicknessintermsofmassfractionoffibersratherthanintermsofvol-umefraction:

h m

M

Mof

f m

f

f

= +

1 1 1

ρ ρ−

Table3.2showsafewexamplesofplythicknesses.

table 3.1 Common Fiber volume Fractions in different Processes

Molding Process Fiber Volume Fraction (%)

Contact molding 30

Compression molding 40

Filament winding 60–85

Vacuum molding 50–80



3.3 Unidirectional Ply3.3.1 Elastic ModulusThemechanicalcharacteristicsofthefiber/matrixmixturecanbeestimatedfromthecharacter-isticsofeachoftheconstituents.Theliteratureprovidesanumberoftheoreticalorsemiempiricalrelations,whoseresultsdonotalwaysagreewiththevaluesderivedfromtests.Oneofthereasonsisthatthefibersthemselvesshowamoreorlesspronouncedanisotropy.Thus,forexample,lowvaluesof the longitudinalmodulusofelasticity in the transversedirectionofbothKevlarandcarbonfibers*canbeseeninTable3.3.Theglassfiberappearsisotropic.

Withdefinitionsandwritingconventionsinthepreviousparagraph,wecanretainthefollow-ingexpressionstocharacterizetheunidirectionalply(reinforcement+matrix):

◾ Elastic.modulus.along.the.fiber.direction, Eℓ

Afairlyaccuratevalueisgivenby†

E E V E Vf f m m� = +

or

E E V E Vf f m f� = + −( )1

Inpractice,thismodulusdependsessentiallyonthe longitudinalmodulusofthefiberEfbecauseE Em f� (asEm resin/Ef glass≃6%).

◾ Elastic.modulus.in.the.transverse.direction.to.the.fiber.axis,.Et

Inthefollowingequation,Eft representstheelasticmodulus.ofthefiberinthedirectionthatisperpendiculartothefiberasindicatedinTable3.3:

E E VEE

Vt mf

m

ftf

= − +

1

1( )

* This isdue to the stretchingof the carbon andKevlarfibersduring fabrication.Thisorients the chainsofmolecules.

† Chapter10detailsthecalculationleadingtotheseestimationsofthemoduliEℓ,Et,Gℓt,andvℓt.

table 3.2 Ply thickness of Some Common Composites

Mf (%) H (mm)

E glass 34 0.125

R glass 68 0.175

Kevlar® 65 0.13

HR Carbon 68 0.13



◾ Shear.modulus,.Gℓt:Anorderofmagnitudeofthismodulus(difficulttoestimatebycalcula-tion)isgivenbythefollowingexpressioninwhichGfℓt representstheshearmodulusofthefiberasshowninTable3.3:

G G VGG

Vt mf

m

t

f

f

�

�

= − +

1

1( )

◾ Poisson. coefficient,.vℓt: ThePoisson coefficient represents the contraction in the trans-versedirectiont whenaply issubjectedtotensile loading inthe longitudinaldirectionℓ(see Figure3.5):

v v V v Vt f f m m� = +

◾ Modulus.along.any.direction:Itispossibletoevaluateelasticandshearmodulusalonganydirectionwithin theplane (ℓ, t).*The longitudinalmodulusalongdirectionx,calledEx, ispresentedinthefollowingequationwherec =cosθands =sin θ(seeFigure3.6).Itshouldbenotedthatthismoduledecreasesrapidlywhenxdepartsfromthefiberdirection(asθincreases):

EcE

sE

c sG

vE

x

t t

t

=+ + −

1

21

2

4 42 2

� �

�

�

* ThecalculationofthesemoduliisshownindetailinChapter11.

table 3.3 Fiber elastic Modulus

Glass E Kevlar Carbon HR Carbon HM

t

ℓ Fiber longitudinal modulus in ℓ direction, Efℓ (MPa)

74,000 130,000 230,000 390,000

Fiber transverse modulus in t direction, Eft (MPa)

74,000 5,400 15,000 6,000

Fiber shear modulus, Gfℓt (MPa)

30,000 12,000 50,000 20,000

Fiber Poisson ratio, vfℓt

0.25 0.4 0.3 0.35

isotropic anisotropic

� ��



3.3.2 Ultimate Strength of a PlyThe curves inFigure 3.7 show the significant difference in failure behavior between classicalmetallicmaterial and theunidirectionalplies.Suchdifference canbe summarized in the fewpointslistedhere:

◾ Alackofplasticdeformationintheunidirectionalply—thisisadisadvantage.◾ Ahighultimatetensilestressfortheunidirectional—thisisanadvantage.◾ Animportantelasticdeformationoftheunidirectional,whichcanconstituteanadvantageor adisadvantagedependingon the applications—for example, this is an advantage forsprings,bows,orpoles.

0° 90°θ

θ

Et

Ex

Eℓ

ℓ

x

Figure 3.6 off-axis modulus.

Fibers

Matrix

ℓ (longitudinaldirection)

ℓ

z

t (transverse direction)

t

WeftWarp

(a) (b)

Figure 3.5 orientations in composite layers: (a) unidirectional ply and (b) unidirectional fabric. Copyrighted Material – Taylor & Francis


Whenthefibersbreakbeforethematrixduringloadingalongthefiberdirection,weobtainthefollowingforthecomposite:

σ σ� rupture rupture= + −

f f f

m

f

V VEE

( )1

orapproximately,

σ σ� rupture rupture≈ ×f fV

Theultimate.strength.along.any.direction*isgivenbythefollowingrelationwhere(seeFigure3.8)

σℓrupture isthefracturestrengthinthedirectionofthefibersσtrupture isthefracturestrengthtransversetothedirectionofthefibersτℓtrupture istheshearstrengthintheplane(ℓ, t)oftheply

σ

σ σ τ σ

x

t t

c srupture

rupture rupture rupture ruptu

=

+ + −

1

1 14

2

4

2 2� � � rre2

2 2

c s

withc =cosθ;s =sinθ

3.3.3 ExamplesTable3.4givesthepropertiesofthefiber/epoxyunidirectionalplyat60%fibervolumefraction.†

The compression strength along the fiber direction is smaller than the tensile strengthalongthesamedirectionduetothemicrobucklingphenomenonofthefibersinthematrix(see Section12.1.4andFigure14.5).

*DetailedcalculationisshowninSection14.3.† ThevaluesassignedinTable3.4canvarysignificantlydependingonthemanufacturingprocess.

Load Load

Rupture

Rupture

Metal Unidirectional

Elongation Elongation

(a) (b)

Figure 3.7 Loading curves of (a) metal and (b) unidirectional composite.Copyrighted Material – Taylor & Francis


θ

θ0° 90°

σ x ru

ptur

e

σℓ rupture

σt rupture

ℓ

x

Figure 3.8 off-axis rupture strength.

table 3.4 Properties of Fiber/epoxy Plies

ℓ

t

Vf = 0.6

Glass Kevlar Carbon

Specific mass, ρ (kg/m3) 2,080 1,350 1,530

Longitudinal tensile strength, σ� rupturetensile (MPa) 1,250 1,410 1,270

Longitudinal compressive strength, σ� rupturecompr (MPa) 600 280 1,130

Transverse tensile strength, σt rupttensile

ure (MPa) 35 28 42

Transverse compressive strength, σt ruptcompr

ure (MPa) 141 141 141

In-plane shear strength, τ�t rupture (MPa) 63 45 63

Interlaminar shear strength, τ�z rupture = τtz rupture (MPa) 80 60 90

Longitudinal elastic modulus, Eℓ (MPa) 45,000 85,000 134,000

Transverse elastic modulus, Et (MPa) 12,000 5,600 7,000

Shear modulus, Gℓt (MPa) 4,500 2,100 4,200

Poisson ratio, vℓt 0.3 0.34 0.25

Longitudinal coefficient of thermal expansion at 20°C, αℓ (°C−1)

0.4–0.7 × 10−5 −0.4 × 10−5 −0.12 × 10−5

Transverse coefficient of thermal expansion at 20°C, αt (°C−1)

1.6–2.0 × 10−5 5.8 × 10−5 3.4 × 10−5



3.3.4 Examples of High-Performance Unidirectional PliesTheunidirectionals inTable3.5haveVf =50%boronfibers.Theboron/aluminumcompositementionedearlierbelongstothegroupofmetalmatrixcomposites(seeSection3.7);amongthese,onecanfindthefollowing:

◾ Forfibers,thesecanbe− Glass− Siliconcarbide− Aluminum− Otherceramics

◾ Formatrices,thesecanbe− Magnesiumanditsalloys− Aluminum− Ceramics

3.4 Woven Ply3.4.1 Forms of Woven FabricsThewoven fabricsare formedbyfibersarrangedalong twomutuallyperpendiculardirections:oneiscalledthewarpdirection(thelengthdirectionoftherollofwovenfabric)andtheotheriscalledtheweftdirection.Thefibersarewoventogether,whichmeansthattheweftyarnspassoverandundercertainwarpyarns,followingapredeterminedpattern.Thewayinwhichthewarpyarnsandtheweftyarnscrosseachotherdefinesthetypeofweaveofthefabric.TheweavesinFigure 3.9areinascendingorderfortheirabilitytodrapecomplexsurfaces,fortheirstrength,fortheirrigidity,andfortheircost.

table 3.5 Properties of Unidirectional Plies Made of Boron Fibers

ℓ

t

Vf = 0.5

Boron/Epoxy Boron/Aluminum

Specific mass, ρ (kg/m3) 1,950 2,650

Longitudinal tensile strength, σ� rupttensile

ure (MPa) 1,400 1,400

Longitudinal compressive strength, σ� ruptcompr

ure (MPa) 2,600 3,000

Transverse tensile strength, σt rupttensile

ure (MPa) 80 120

Longitudinal elastic modulus, Eℓ (MPa) 210,000 220,000

Transverse elastic modulus, Et (MPa) 12,000 140,000

Shear modulus, Gℓt (MPa) 7,500

Longitudinal coefficient of thermal expansion at 20°C, αℓ (°C−1) 0.5 × 10−5 0.65 × 10−5



Figure3.9ashowsaplain.weave.fabric.whereeachweftyarnpassesalternativelyoverandunderthesuccessivewarpyarns.Figure3.9bshowsatwill.weave.fabric.Here,aweftyarnfloatsoverawarpyarn(1)andunderthetwothatfollow(2,3);inthenextpass,theshuttleoftheloompassesunderwarpyarns1and2andoverthethirdone.ReferringtoFigure3.9b,weseehowtheshuttleshiftsduringsubsequentpassages.Atwillordiagonaleffectisthenformedonthefabricface.Thisisthesimplesttwillthatcanbemade,so-called3-harnesstwill.Figure3.9cshowsasatin.weavefabric:eachweftyarnfloatsoverfourwarpyarnsbeforegoingunderthefifthone.Forthisreason,itiscalleda5-harness.satin.

Forapproximatevaluesof the fabricelasticproperties (about15%),onecanconsider themtoconsistoftwounidirectionalpliescrossingat90°angle.Thefollowingnotationscanbeused:

e isthetotallayerthicknessn1isthenumberofwarpyarnspermetern2isthenumberofweftyarnspermeterk

nn n

=+

1

1 2

Vf isthevolumefractionoffibers

Wecandeducethethicknessoftheequivalentunidirectionalplies(seeFigure3.10)as

e e

nn n

k ewarp = ×+

= ×1

1 2

e e

nn n

k eweft1 2

+

= × = − ×2 1( )

3.4.2 Elastic Modulus of Fabric LayerInordertoobtainestimatedvalues,thetwo layersofreinforcementcanbetaken intoaccounteitherseparatelyortogether.

◾ Separately:Thefabriclayerisreplacedbytwounidirectionalpliescrossedat90°,withthefollowingthicknesses:

ewarp=k × e ; eweft = (1−k)× e

TheaveragefibervolumefractionVfbeingknown,thenthemechanicalpropertiesEℓ,Et,Gℓt,andvℓtofthesepliescanbedetermined(seeSection3.3.1).

Warp

(a) (b) (c)

Weft

Figure 3.9 Forms of woven fabrics: (a) plain weave, (b) twill weave, and (c) satin weave.



◾ Together:Thefabriclayerisreplacedbyonesingleanisotropicplywiththicknesse.x-direction beingthewarpdirectionandy theweftdirection(seeFigure3.9),wehavethenapproximately*

E k E k E

E k E k E

G G

k kEE

x t

y t

xy t

xyt

t

≈ × + ×

≈ × + ×

=

≈+ −

�

�

�

�

�

( )

( )

( )

1

1

−

−

ν ν

1

Notes◾ Thestiffnessobtainedwithawovenfabricislessthanwhatwouldbeobservedbysuperim-posingtwocrosspliesofunidirectionals.Thisisduetothecurvatureofthefibersduringtheweavingoperation(seeFigure3.11).Thiscurvaturemakesthewovenfabricmoredeformablethanthetwocrossplieswhensubjecttothesameloading.(Thereexistfabricsthatareofhigh.moduluswheretheunidirectionallayersarenotconnectedwitheachotherbyweaving.Theunidirectionalpliesareheldtogetherbystitchingfinethreadsofglassorpolymer.)

◾ Thefabricplyshowsanuppertensilestrengthanda lowercompressivestrength,ascom-paredwiththecorrespondingstrengthsobtainedwhensuperposingtwocross plies.†

3.4.3 Examples of Balanced Fabric/EpoxyThefabricissaidtobebalancedwhenthereareasmanywarpasweftyarns,madeinthesamemate-rial.Therefore,thewarpandweftdirectionsplayequivalentroleswithregardtothermomechanicalcharacteristics.ThecorrespondingpliesaredescribedinTable3.6withanepoxyresinmatrix.

*Forthecalculationofthesecharacteristics,see Section12.1.2andalsoSection19.12.† Compare,forexample,thetensileandcompressivestrengthsinTable3.6.ComparethesevaluesalsoonTables5.1,5.6,and5.11ofSection5.4byselectingproportionsof50%at0°and50%at90°.

e

z

Warp

Weft

y

x

Figure 3.10 notations for a fabric layer.



Woven reinforcement

Matrix Warp Weft

Crossed unidirectional reinforcement

Figure 3.11 Cross section of a layer with fibers crossed at 90°.

table 3.6 Properties of Balanced Fabric/epoxy Composites

x

E Glass Kevlar Carbon

Fiber volume fraction, Vf (%) 50 50 45


Tensile strength along x or y: σx rupturetensile = σy rupture

tensile (MPa) 400 500 420

Compressive strength along x or y: σx rupturecomp = σy rupture

comp (MPa) 390 170 360

In-plane shear strength, τxy rupture (MPa) 150 55

Elastic modulus, Ex = Ey (MPa) 20,000 22,000 54,000

Shear modulus, Gxy (MPa) 2,850 4,000

Poisson coefficient, vxy 0.13 0.045

Coefficient of thermal expansion, αx = αy (°C−1) −0.2 × 10−5 0.05 × 10−5

Elongation at break, A (%) 2.1 1.0

Price (relative value) 1 4.2 7.3



3.5 Mats and Reinforced Matrices3.5.1 MatsMatsaremadeofcutfibers(fiberlengthsbetween5and10cm)orofcontinuousfibersmakingabidimensionallayer.Matsareisotropicwithintheirplane(x,y).Theycanthereforebecharacter-izedbytwoelasticconstantsonly,asspecifiedinSection3.1.

IfEℓ andEt aretheelasticmoduli(longitudinalandtransversedirections,respectively)oftheunidirectionalplywhichwouldhavethesamevolumefractionVfofreinforcementasthatofthematply,wehavethen

E E E

GE

v

v

tmat

matmat

mat

mat

≈ +

≈+

≈

38

58

2 1

0 3

�

( )

.

Forexample,matswithcutfibersmadeofglass/epoxyhavethefollowingcharacteristics:

Fiber volume fraction, Vf (%) 28

Specific mass, ρ (kg/m3) 1,800

Elastic modulus, E (MPa) 14,000

Tensile fracture strength, σrupturetensile (MPa) 140

Heat capacity, c (J/g × °C) 1.15

Coefficient of thermal conductivity, λ (W/m × °C) 0.25

Linear coefficient of thermal expansion, α (°C−1) 2.2 × 10−5

3.5.2 Example: A Summary of Glass/Epoxy LayersFigures3.12and3.13summarizethemainfeaturesofthedifferenttypesofplies(unidirectional,fabric,mat)whenthefibervolumefractionVfvaries.

3.5.3 Microspherical FillersMicrosphericalfillersarereinforcementsassociatedwithpolymermatrices(seeFigure3.14).Thesefillersaremadeofsolidorhollowmicroballsofglass,carbon,orpolystyrenewithdiametersbetween10and150μm.

◾ ThefillervolumefractionVfcanreachupto50%.◾ ThefillerpropertiesaresuchthatE Ef m� .



Defining

K

Ev

vv

V

Vm

m

m

m

f

f

=−( )

+ −+

−( )

3 1 2

1 311 1

thecomposite(matrix+filler)isisotropic,withtheelasticconstantsE,G,andvgivenbythefollowingrelations:

EKG

K G

GE

v

vv

V

V

v

m

m

m

m

f

f

≈+

≈+( )

+ −−

−( )

≈

93

2 11

152

14 5 1

12

33 23K GK G−+

70,000

60,000

50,000

40,000

E (balanced fabric)

Eℓ (“E” glass roving)

Eℓ (“R” glass roving)

E (mat) Et

30,000

Mod

ulus

of e

last

icity

(MPa

)

20,000

10,000

010% 20% 30% 40% 50%

Fiber volume fraction, Vf

60% 70% 80%

Figure 3.12 elastic modulus of glass/epoxy layers.



2250

2000

1750

1500

1250

1000

Tens

ile st

reng

th (M

Pa)

750

500

250

010% 20% 30% 40%

Fiber volume fraction, Vf

σrupture(mat)

σrupture(balanced fabric)

σℓ rupture

σℓ rupture(glass roving “E”)

σℓ rupture(glass roving “R”)

(Unidirectionalfabric)

50% 60% 70% 80%

Figure 3.13 tensile strength of glass/epoxy layers.

Hollow microspheres

Inert gas(expanded by

heating)

20–100 μm

≈1 μm

Figure 3.14 Spherical fillers.



3.5.4 Other Classical ReinforcementsOnemayalsousereinforcementsintheformofmilledfibers,flakes(seeFigure3.15),orpowdersmadeofanyofthefollowingmaterials:

◾ Glass◾ Mica(L≈100μm)◾ Talc(L≈10μm)◾ Graphite◾ Somemetals◾ Alumina

Example:Themicaflakeswhenembedded inaresinwithafiberreinforcement.TheyadoptageometriclayeredconfigurationasshowninFigure3.16.Itcanbeobservedthefollowingimpacts:

◾ First,anincreaseinthevalueoftheresin’smodulusas*

E

Ln u

uE V E V u

Le

GE

VV

m mm

m

= −+( )

× + = ×1

1mica mica

mica

micawhere

*Formoredetails,seeRiley(1990),whichislistedintheBibliographyattheendofthebook.

L

e

Figure 3.15 Form of flakes.

Mica �ake

Unidirectional

100 μm

Figure 3.16 Mica flake arrangement.



Inwhichtheaveragepropertiesofmicaare

Emica 000 MPa= 170, and ρmica3kg/m= 2 800,

◾ Second,adelayinthemicrocrackingofresin(seeFigure3.17).Itisalsonoteworthythatthisremarkablepropertyoccurswhen,intheabsenceofclassicalmacroscopicreinforcements,thedimensionsof thepreviouslymentionedfillersdecrease.We then getwhat is callednanocomposites.TheircasewillbeexaminedinmoredetailinSection3.8.

3.6 Multidimensional Fabrics3.6.1 Example: A Four-Dimensional Architecture

of Carbon Reinforcement*ThereinforcementisassembledaccordingtopresetdirectionsinspaceasseeninFigure3.18.Thefibervolumefractionisontheorderof30%.Thematrixcomestofillthevoidsbetweenthefibers.†

Thekeyadvantagesofthesetypesofcompositesareasfollows:

◾ Theadditionalconnection(comparedtobidimensionalplies)increasesthedamagetoleranceversusimpact(resistancetodelamination).

◾ Mechanical resistance ismaintained—and even improved—athigh temperatures (up to3000°Cforcarbon–carbon).

*ProductofformerEuropean.Propulsion.Company,todaySAFRAN.Group(FRA).† SeeSection2.2.4.

Fiber Fiber

Matrix microcracksFlake Resin(a) (b)

Figure 3.17 Cross section (a) with and (b) without mica flakes.

Cube

Pultrudedcarbon sticks;

1–3 mmdiameter

(carbon/epoxy; Vf = 60%)

Figure 3.18 Four-dimensional architecture.



◾ Thecoefficientofthermalexpansionremainslow.◾ Thesetypesofcompositesarethermalshockresistant.◾ Thethermalconductivityofcarbon–carbonishigh.◾ Thedensityislow.◾ Theradioelectricalwavestraveleasilythroughthesilica/silicacomposites.

3.6.2 Example: Three-Dimensional Carbon/Carbon ComponentsTable3.7givesthecharacteristicsoftwocompositesmadeoftridimensionalcarbon/carbon.ThemechanicalpropertiesarethesamefollowinganydirectiondenotedasℓonthefigureinTable3.7.Therefore,thecompositeisreferredastransversely.isotropic.*

3.7 Metal Matrix Composites3.7.1 Some ExamplesThisareaincludes,indevelopmentorinservice,anumberofproductsconsistingofthefollowing:

◾ Matrices:aluminum,magnesium,andtitanium(seealsoSections7.4and7.5.4)◾ Fibrousreinforcements:aramid,carbon,boron,andsiliconcarbide(SiC)◾ Example:. Aluminum-reinforced aramid (ARALL) and aluminum-reinforced glass(GLARE).†Thekeyadvantageisbetterimpactdamagetolerancebecauseof(a) Betterresistancetofailureduetothinmetalliclayers(b)Better resistance against the crackpropagation from one layer to the other (see

Figure3.19)◾ Example:.Short.silicon.carbide.fibers.(whiskers)/aluminum

This is called an incompatible composite because of the large differences between thethermomechanicalpropertiesoftheconstituents.Thisleadstohighstressconcentrationsaswellasdebondingbetweenthefibersandthematrix(seeFigure3.20).Thesetypesofcom-positesareinterestingforhigh-temperatureapplications.InFigure3.20,thediameterofthewhiskerisabout20μmandtheslendernessratioL/ϕ≈5.ThefibervolumefractionisaboutV f ≈ 30%.

◾ Example:.Boron/aluminum Thesetypesofcompositesareusedinaerospaceapplications(seeSection7.5.4).Themanu-

facturingtechnologytoobtainthesematerialsissummarizedinFigure3.21.Suchcom-positesallowhighoperatingtemperatures,intheorderof300°Cforservicetemperature,whilepreservingsignificantmechanicalproperties(seeSection1.6forthepropertiesofboron).

* ThisnotionisshownindetailinSection13.2.† AKZO.Fibers/DELFT.University(Holland).®Structural.LaminatesCompany.NewKensington(USA).



table 3.7 Properties of 3d Carbon/Carbon

z

ℓ

ℓℓ Aerolor ® 41a Septcarb® 4b

Specific mass, ρ (kg/m3) 1,700–2,000 1,500–2,000

Longitudinal tensile strength, σ� rupturetensile (MPa) 40–100 95 and increasing, up to 2,000°C

Longitudinal compressive strength, σ� rupturecompr (MPa) 80–200 65

Tensile strength in the z direction, σz rupturetensile (MPa) >10 3

Compressive strength in the z direction, σz rupture

compr (MPa)80–200 120

Shear strength in (ℓ, z) plane, τ�z rupture (MPa) 20–40 10

Longitudinal elastic modulus, Eℓ (MPa) 30,000 16,000

Elastic modulus, Ez (MPa) 5,000

Shear modulus, Gℓz (MPa) 2,200

Shear modulus, Gℓℓ (MPa) 5,700

Poisson ratio, vzℓ 0.17

Poisson ratio, vℓℓ 0.035

Thermal expansion coefficient, αℓ (°C−1)

At 1000°C 0.7 × 10−6 3 × 10−6

At 2500°C 3 × 10−6 4 × 10−6

Thermal expansion coefficient, αz (°C−1)

At 1000°C 6 × 10−6 7 × 10−6

At 2500°C 6 × 10−6 9 × 10−6

Coefficient of thermal conductivity, λ (W/m × °C)

300

a Aerolor® is a product of Mersen Group, the former Carbone Lorraine Company (FRA).b Product of former european Propulsion Company, today SaFRan Group (FRA).



3.7.2 Unidirectional Fibers/Aluminum MatrixThe following table. shows the characteristicsof someunidirectional reinforcements associatedwithanaluminummatrixA96061(6061):

HR Carbon Alumina Silicon Carbide

Fiber volume fraction, Vf (%) 50 50 50


Longitudinal tensile strength, σ� rupturetensile (MPa) 800 550 1,400

Longitudinal compressive strength, σ� rupturecompr (MPa) 600 3,100 3,000

Longitudinal elastic modulus, Eℓ (MPa) 200,000 190,000 140,000

Unidirectionals: Aramid/epoxy (ARALL) e= 0.2 mme= 0.25 mmGlass/epoxy (GLARE)

e

Aluminum (2024-T3)

Bonded stack

0.2 mm

Figure 3.19 Layers of aRaLL and GLaRe.

L

Figure 3.20 SiC whisker.

Boron �bers Aluminum powder

Aluminum sheets

Recure by diusionunder pressure

Boron/aluminum laminateT= 600°C, p= 300 bar

Figure 3.21 Boron/aluminum composite.



3.8 Biocomposite Materials3.8.1 Natural Plant Fibers

3.8.1.1 Natural Fibers

Thesearederivedfromplantsandfromanimalsandhavelongbeenwoven,knitted,orbraidedtomaketextiles.Theywereusedalsointhepastforthereinforcementofmatrices(cobforbuilding,cotton/phenolic,hemp/phenolicfortechnicalparts).

Today,becauseofthesignificanceoftheenvironmentalimpacts,thedevelopmentofcompos-itereinforcedwithnaturalfibersisrapidlyemerging.

Thevegetablefiberstaketheformofbundlesoftensofelementaryfibers(20–50)bondedwithtackysubstances.Thedegummingofthesebundlesisnecessarytoreleasebasicfibers.Thesefibersarecomposedlargelyofcellulosefibrils.Thefibrilsfollowhelicalcurvesaroundtheaxisofthefiber,withahelixangleofafewdegreescalledthemicrofibrillarangle.Thecellulosehasanalmostcrystallinestructure.Itslongitudinalmodulusofelasticityis135,000MPa,comparedwiththatofthe“R”glass(86,000MPa).Itthusappearspossibletoobtainmechanicalperformancescomparabletotheseofglass.

3.8.1.2 Pros

◾ Theyarebiodegradable.◾ Theyareneutralwithrespecttoemissionsofcarbondioxide.◾ Theyhavealowenergycost(however,fiberprocessingrequiresalotofwater,anditisapollutingindustry).

◾ Theyarelight,andmanyofthemhaveinterestingvaluesofspecificmodulescombinedwithexcellentdampingandshock-resistantproperties.

◾ Some,suchasflaxandhemp,arenativeplants.Thisensuresthesupplyandoffersasignifi-cantandvaluableperspectiveforagriculturalindustry.

3.8.1.3 Cons

Theuseofnaturalfibersrequiresprerequisitesolutionsforthefollowingproblems:

◾ Whileconventionalfibershavewell-controlledreproduciblecharacteristics,thequalityofnaturalfibersdependsontheenvironmentinwhichtheyareproduced:theseason,wheretheywereplantedandharvested,characteristicsofthesoilonwhichtheyhavegrown,orlocationfromwhichtheyoriginateintheplant(peripheralpartorinternalpartofthestem,leaf,etc.).Allthesecausethedisadvantageofadispersionofcharacteristics:varyingdiam-eteralongfibers,variouslengthsanddegreesofpolymerization,andshapedefectscausedoramplifiedbythehandlingandimplementation.

◾ Naturalfibersarehydrophilic.Thepossibilityofmoistureabsorptionforcompositesrein-forcedbythesefibersisthuslarge(upto8%or10%),accompaniedbyadegradationofthefiberleadingtoareductioninperformancesofthematerialovertime.

◾ Naturalfibersarenotresistanttohightemperatures.Theylosetheirstiffnessto160°Canddegradeatatemperatureofapproximately200°C.Applicationswiththermoplasticmatri-cesthusexcludetheuseofhigh-performancetypessuchasPEEKresins(seeSection1.6).

◾ Thetensilestrengthisnotveryhigh.Theycanbeusedforrigidpartsratherthanresistant.◾ Theriskofmicrobialcontaminationmustbetakenintoaccount.



3.8.1.4 Examples

◾ Flax.fibers Theyaretakenfromtheplantontheoutskirtsofthestem.Afterselection,cleaning,and

separation,thefiberlooksgenerallylikeasix-sidedpolygonalcylinderwithfacesremarkablysmooth.Itiscomposedofahemicellulosematrix,oflignin,withareinforcementofcellulosefibrils incrystallineform(Vf ≈ 70%)thatareorientedatamicrofibrillarangleabout10°withtheaxisofthefiber.

◾ Hemp.fibers Thegrowing(cultivation)ofthehemprequiresneitherpesticidesnorherbicides.Theaverage

fiberyieldisabout250kg/ha.Thefiber,composedofabundleofafewtensofelementaryfibers,islocatedontheouterperipheryofthestemtoensurestructuralstiffnessofthelatter.

Table3.8showsthecharacteristicsofsomenaturalfibersusedasreinforcements.Thesignificantvariationsforasametypeoffibersshouldbenoted,duetothereportedparametersearlierincom-binationwiththespecifictreatmentreceived.

Note:FailurevaluesonindustrialrovingsaremuchlowerthaninTable3.8.For example,afailurevaluetothetuneof60MPafortheflax(upto85MPaonrovings)and35MPaforhemp.

3.8.2 Natural Vegetable Fiber–Reinforced Composites

3.8.2.1 Mechanical Properties

Themechanicalpropertiesofthistypeofcompositedependonthevolumefractionoffibers,ori-entationofthesefibers,andqualityofbondingbetweenfiberandmatrix.Itsohappensthatthecelluloseisscarcelycompatiblewiththepolymermatrices.Fortechnical.fibers,therefore,apriorsurfacetreatmentisaclearneedinviewofimprovingthefiber–matrixlinkage:

◾ Forflaxfibers:combinationwithpolyesterandepoxyresins◾ Forhempfibers:combinationwithpolyurethaneandPVCresins

Theflaxandhempcanbeusedastechnical.fibersintheformofunidirectional,wovenreinforce-ment,mat(nonwoven),andshortfibers(compound).

◾ Example:Characteristics.of.aPultrudedUnidirectional.Flax/Polyester

Fiber Volume Fraction, Vf (%) Density, ρ (kg/m3)

Tensile Longitudinal

Elastic Modulus, E (MPa)

Coefficient of Thermal

Conductivity, λ (W/m × °C)

Flax/unsaturated polyester resin

60 1,400 35,000 0.3

3.8.2.2 Biodegradable Matrices

After manufacturing, it becomes impossible for a composite to dissociate reinforcement andmatrix.Soforacompleterecycling,theuseofnaturalfibersaspartofacompositerespectfuloftheenvironmentmustbeassociatedwithabiodegradablematrix,thatistosayabiopolymer.



tabl

e 3.

8 C

hara

cter

isti

cs o

f Som

e n

atur

al F

iber

s U

sed

as R

einf

orce

men

ts

Nat

ure

of th

e Fi

ber

Fl

axH

emp

Sisa

lJu

teC

otto

nSi

lk T

hrea

dSp

ider

Thr

ead

Dia

met

erϕ

(μm

)4–

77; A

vera

ge: 1

910

–51

50–4

005–

200

12–2

5

Fib

er le

ngt

h(m

m)

Ave

rage

: 33

5–55

0.8–

8;

Ave

rage

: 3

2–5

2–40

Frac

tio

n fi

ber

vo

lum

e o

f ce

llulo

se

Vf (

%)

64–7

173

–78

67–7

861

–71

90

Mic

rofi

bri

llar

angl

eD

egre

e (°

)10

620

8

Den

sity

ρ (k

g/m

3 )1,

400–

1,54

01,

070–

1,48

01,

330–

1,45

01,

370–

1,46

01,

500–

1,60

0

Lon

gitu

din

al

mo

du

lus

of

elas

tici

ty

E (M

Pa)

12,0

00–8

5,00

030

,000

–70,

000

9,00

0–38

,000

10,0

00–3

0,00

05,

500–

13,0

005,

000–

16,0

007,

000

Ten

sile

st

ren

gth

σ ru

ptu

re (M

Pa)

600–

2,00

038

0–90

035

0–70

038

3–80

028

7–59

720

0–65

060

0

Elo

nga

tio

n a

t b

reak

A (%

)1–

41.

6–2.

72–

141.

5–2

3–10

15–1

830

Mo

istu

re

rega

in(%

)7

811

128–

25Copyrighted Material – Taylor & Francis


Someexamplesofbiopolymers(biodegradableresins)todayareasfollows:

◾ Biopolyethylenehighdensity(HDPE)◾ Biodegradablepolyester:polycaprolactone(PCL)◾ Biodegradablepolyester:polylacticacid(PLA)◾ Thermoplasticstarchderived:Mater-bi®◾ Example:.Biodegradable.Composite.Hemp/Resin

Table3.9showsthemechanicalcharacteristicsoftheresinsgivenearlier,pureandreinforcedbyshorthempfibers.

3.8.3 Manufacturing Processes*

3.8.3.1 With Thermosetting Resins

◾ Contactmolding(polyester)◾ SMC(flax/polyester)◾ Compressionmolding(cotton/polyester)◾ Filamentwinding(jute/polyester)◾ Pultrusion(jute/vinylester)◾ RTM(hemp/phenolicresin)

*Forthemeaningofacronyms,seeSections1.2.2,2.3.1,andTable1.4.

table 3.9 Mechanical Characteristics of Biodegradable Composite Hemp/Resin

Biodegradable Composite

Tensile Longitudinal Elastic Modulus Tensile Strength

Volume fraction of hemp

(short fibers), Vf

Vf = 0% (Pure resin)

E (MPa)

Vf = 30% Multiplication

factor

Vf = 0% (Pure resin) σrupture (MPa)

Vf = 30% Multiplication

factor

Resin

HDPE 750 ×2.8 22 ×1.13

Biodegradable polyester: PCL

375 ×5.7 17 ×1.43

Biodegradable polyester: PLA

3250 ×2.3 70 ×1.06

Thermoplastic starch derived: Mater-bi®

225 ×7.7 12 ×1.83



3.8.3.2 With Thermoplastic Resins

◾ Injectionmolding(hemp/acrylonitrile-butadiene-styrene[ABS]resin)◾ Pultrusion(flax/PPresin),TRE(flax/PEresin)◾ Extrusion(hemp/polyvinylchloride[PVC]resin)◾ Examples

− Nonwoven mats(50%ofhempfiber+50%ofpolymerfiber):theyaremadeupbytheneedlingofnonwovenlapsandarethenthermoformed.

− Compoundsreinforcedwithhempfiber(30%ofhempfibers+70%ofpolymer):theyareusedininjectionmolding.

Therearenumerousapplications in theareasofbuilding, infrastructure, furniture,navigation,sportsandrecreation,andespeciallyintheautomotiveindustry(seeChapter8).

3.9 nanocomposite MaterialsThesetermsrefertocompositematerialswithpolymermatricesforthemost;theyaremechani-callymoreresistantthanthematrixbutofferothersignificantbenefitsintermsofresistancetofire,electrical,optical,andsurfaceproperties.

3.9.1 NanoreinforcementAmaterialiscallednanocompositewhenatleastoneofthedimensionsofthereinforcementislessthan100nm:itisthencallednanoreinforcement.

3.9.1.1 Nanoreinforcement Shapes

Figure3.22illustratesthetypicalgeometricalshapesofnanoreinforcements.Usingthetermnanocomposite.materialtodescribeanyadditionofadjuvantsinapoly-

mershouldbeavoided,althoughsomemaybeofnanosize.Infact,inananocomposite,theassociationmatrix+nanoreinforcementisspecific:theinterestistomakethebestofatomsofthenanoparticles.

For example, consider a compact spherical cluster of atoms, of radius r, as described inFigure 3.23.Thesurface/volumeratioofthiscluster is( )4 4 3 32 3π πr r r)/( / /= .Weseethereforethatthis ratioincreaseswhentheclustersizedecreases,whichmeansthatanincreasingnumberofatomsoftheclusterareexposedtotheexternalenvironment.Thus,whenthesizeoftheclusterisoftheorderofthenanometer,thenumberofclusteratomsexposedexceeds90%.

Itthencomestotakefulladvantageoftheconnectionofthisavailableatomsurfacewithamatrix,polymer,forexample.WecanseeinFigure3.24thatthequalityofthisbondingischar-acterizedbyadegreeofdispersionof thenanoreinforcements.When thisdispersionbecomescomplete, the interactions at the atomic level become more complex than for the interfacesmatrix–reinforcementofconventionalcomposites.Suchamechanismcansignificantlyimprovesomeofthepropertiesofthecreatedproducts.

Althoughwearemostinterestedinstructuralapplicationsofnanocompositematerials,wewillalsoconsidertheothertypesofapplications,importantanddiverse.



3.9.1.2 Properties of Nanoreinforcements

◾ Grains.or.nanoparticles Theyareoftenofsphericalshape(solidorhollowspheres)ofafewnanometersto100nmin

diameter. Theuseofsuchparticles isnotrecent.Asoldnanoparticlescanbeconsideredsilica,

carbonblack,andnanocalciumcarbonate,which isaclassicalmineral filler inmanyapplications, where it is often associated with PVC matrix.This allows to increasethe modulus of elasticity, the flexural strength, and to strengthen the dimensional

100 nm

100 nm

(a) (b)

100 nm

(c)

Figure 3.22 Geometrical shapes of nanoreinforcements: (a) grain (nanoparticle), (b) tube (nanowire or nanofiber), and (c) lamellae or layer (nanoplatelet).

Nanoparticle

Atoms

Figure 3.23 Spherical cluster of atoms.



stability.Thechemicalcompoundsavailabletodayleadingtonanoparticlesarenumer-ous (about 150) and are involved in a broad variety of applications.As seen beforeconcerningtheadvantagesofexpositionofthenanoparticleatomstotheexternalenvi-ronment,itisofinteresttobeabletodefineanouter.mean.surface.area.of.nanopar-ticlesexpressed inm2/g.Toevaluatesuchasurface,oneofthetechniquesconsistsofmeasuringaspecificsurfaceareareferredasB.E.T.*SomeofthesemeasurementvaluesaregiveninTable 3.10.

◾ Lamellae.or.nanosheet.or.nanoplatelet− Silicates: They include nanosheets of clay, nanosheets ofmica (aluminum silicate,potassium silicate) having the form of lamellae of a few nanometers in thickness,witharatioinbothothersdirectionsgreaterthan25.Forexample,themostusedisthemontmorillonite, a lamellar aluminosilicate characterized by nanometer-sizedthickness.

− Graphene:Consistingofcarbonatoms,itistheuniquecaseof2Dcrystal.Itsatomsarearrangedinhexagonslikeahoneycombandformaplanarmoleculeofthethicknessofasinglecarbonatom,thatis,0.1nm.Asanexample,whensheetsarestackedoneontopoftheother,weobtainthegraphiteofapencillead.Figure3.25showsagraphenesheet.Theavailableprocessingmethodsprovidestacksofsheets, forexample, from

*B.E.T.istheacronymofBrunauer–Emmett–Tellersurfacecharacterization(1938).

Polymer+

Nanoreinforcement

Complete dispersion:nanocomposite material

Partial dispersion:classical composite material

Figure 3.24 dispersion of nanoreinforcement.



two to several tensof sheets. It isworthnoting that theabsenceofdefectson thesheetofthecrystalmakesthelatterthemostresistantofallmaterials,ascanbeseeninTable3.11.

◾ Nanotubes,nanowires,.nanofibers− Nanotubes:Theyincludecarbon,alumina,clay,andtungstendisulfide.Thepresenceofcarbonnanotubesimproves• Theelectricalandthermalconductivity• Themechanicalproperties• ThethermalwithstandandthefireresistanceFigure3.26showsthestructureofasingle-wallcarbonnanotube.

− Nanowires:Carbidesilicon,siliconnitride,andcarbon.− Nanofibers:Polyester,siliconwithdiameter<100mmandslenderness(length-to-diameterratio)�/φ >100,andfibrousclays.

table 3.10 Some values of B.e.t.-Specific Surface area

Nanoparticle B.E.T.-Specific

Surface Area (m2/g) Average Grain

Size (nm)

Carbon black 24

Carbon particles 60–100 45

Titanium silicate 95 20

Titanium dioxide 50–250 6–30

Alumina silicate 215

Alumina 20–70 7–13

Tin–silver alloy 5 <150

Calcium carbonate >25 80–100

20,000–30,000 nm

Graphene sheet �ickness = 0.1 nm

20–30 nm

Figure 3.25 Graphene sheet.



Afewgeometricalcharacteristicsofnanofiberscanbefoundinthefollowing:

Diameter (nm) Length (μm)B.E.T.-Specific

Surface Area (m2/g)

Aluminum nanofiber 10 160

Single-wall carbon nanotube 1–2 1–1000 1000

Multiwall carbon nanotube 8–50 1–1000

High-strength carbon fiber (HR) (see Section 1.6)

7000

Table3.12comparesthemechanicalandthermalpropertiesofcarbonnanotubestoothertypesofreinforcementsalreadycitedinSection1.6.

3.9.2 Nanocomposite MaterialNanocompositematerialswithpolymericmatrices(thermoplastics,thermosets,andelastomers)arereinforcedbysmallamountsofnanoparticles(lessthan5%bymass)havingahighshapefac-tor�/h > 300.TheoptimuminteractionbetweenpolymermatrixandnanoparticlesmayresultinanincreaseofmechanicalpropertiessimilartowhatonewouldobservewithamasscontentMf10timeshigherwithconventionalfillerssuchastalcormica,asshownintheTable3.13.

Today,thepolymermatrixnanocompositesarethemostcommonbecausetheirmanufactur-ingprocessesareunderbettercontrol.Afewexamplesofapplicationsinuseorindevelopmentareshownhereafter.

table 3.11 Some Mechanical Properties of nanosheets

B.E.T.-Specific Surface

Area (m2/g)

Longitudinal Modulus of Elasticity (in the Plane of

Sheet), E (MPa)

Shear Modulus (in the Plane of

Sheet), G (MPa)

Poisson Ratio, v

Tensile Strength,

σrupture (MPa)

Elongation at Break, A (%)

Aluminosilicate (montmorillonite)

800

Graphene sheet 2,600 1,000,000 40,000 0.16 130,000 20

Stack of graphene sheets (<5)

640 500,000 100,000

Figure 3.26 Carbon nanotube.



3.9.3 Mechanical Applications

3.9.3.1 Improvement in Mechanical Properties

Theseincludestiffness,mechanicalstrength,abrasionresistance,andimpactstrength.

◾ Sincealongtimeago,thegumofthetiresisstrengthenedbytheadditionofblackcarbonandformorethan15yearsbytheadditionofnanoparticlesofsilicaSiO2,about2kgpertire:whatisknownasgreen.tire.

◾ Aircraftparts(secondarystructure).. Example:ThefighteraircraftF-35.Lightning.IILockheed Martin(USA)useswingtips

ofepoxyresinreinforcedbycarbonnanotubes(pricedividedby10comparedtothatoftheoriginalcarbonfiberreinforcement).

◾ Electric conductors are made of extra reinforced materials for nondestructive coils,allowingtheproductionofhigh-pulsedmagneticfieldscloseto100Teslaandoflongduration.TheLorentz forcesonelectricconductorsgeneratemechanicalstresses,able

table 3.12 Comparative Mechanical and thermal Properties of Carbon nanotubes

Density, ρ (kg/m3)

Longitudinal Modulus of Elasticity, E (MPa)

Poisson Ratio, v

Tensile Strength,

σrupture

(MPa)

Elongation at Break, A (%)

Coefficient of Thermal

Conductivity 20°C,

λ (W/m × °C)Price

($/kg)

Single-wall carbon nanotube

1,300–2,000 1,000,000 0.25 100,000 10 2,000 200–300

Multiwall carbon nanotube

700,000 100,000 2,000 200–300

High-strength carbon fiber (HR)

1,750 230,000 0.3 3,200 1.3 200 60–200

High-modulus carbon fiber (HM)

1,800 390,000 0.35 2,500 0.6 200

Glass (R) 2,500 86,000 0.2 3,200 4 1 14

Glass (E) 2,600 74,000 0.25 2,500 3.5 1 3

Kevlar® 49 1,450 130,000 0.4 2,900 2.3 70

Steels 7,800 205,000 0.3 400–1,600 1.8–10

Copper 8,800 125,000 0.3 200–500 380



toleadtoyieldingoreventoruptureofthecoils.Nanocompositeconductorsmadeofniobium nanofilamentswith coppermatrix have a highmechanical resistance, highelectricalconductivity,andaverygooddeformability:σrupture 900 MPa=1 at77Kforanelectricalconductorof5mm2sectionthatcontains30%ofniobiumdistributedintheformof52millionof140nmdiameterfibers.Thisstrengthvaluerevealsasignificantdifferencecomparedtotheresultsofthe lawofmixtures(seeSection3.3.2),whichisduetothenanosizeoffibers.

◾ Aeronauticalpanelsreinforcedcarbon:Inadditiontotheenhancementofmechanicalprop-ertiessuchastheimprovementofimpactresistance,thedispersionofcarbonnanotubesinapolymermatrixallowsthatalowcurrentappliedheatsthenanotubes.Thisisallowingtheuseofathermographiccameratodetectadefect.

◾ Theintroductionofcarbonnanotubesinanadhesiveprovidesmonitoringofconductioninthenanocompositematerial.Todothis,theprincipleofpercolation isinvolved.Themate-rialisdefinedstatisticallyasasystemconsistingofanetworkofalargenumberofobjects

table 3.13 Comparative Mechanical Properties of nanocomposites

Volume Fraction of Nanoreinforcement,

Vf (%)

Mass Fraction of Nanoreinforcement,

Mf (%)

Increase in Longitudinal Modulus of Elasticity,

E (%)

Increase in Tensile

Strength, σrupture (%)

Increase in Elongation at Break,

A(%) (%)

Nanosheets aluminosilicate/polyamide matrix

2–5 70 (at 23°C); 220 (at 120°C)

40 (at 23°C); 20 (at 120°C)

Nanosheets aluminosilicate/polypropylene matrix

2.5

6

60

80

Nanosheets aluminosilicate/poly (methyl) methacrylate matrix

2.5

5

40

38

0

0

Nanosheets aluminosilicate/polyethylene matrix

3 14 0 35

Carbon nanotubes/epoxy matrix

4

0.1

100

3

50

14

Nanofeuillets graphene/epoxy matrix

0.1 30 40



thatcanbelinkedtogether.Theconductanceiseitherpossibleorimpossibledependingonthenumberofobjectsandconnections:Thereisaprecisetransitionthreshold(orpercolationthreshold)betweenthosetworegimes.

◾ Todetectexcessivedeformationofwindturbineblades,sensorslocatedinsensitiveregionsusethesameresinasthatoftheblade,withadditionofcarbonnanotubes.Thecontinuityofthedeformablenetworkofnanotubesprovidesaconductancesensitivetodeformation,analogueofapiezoresistiveproperty.

◾ Improvementofthemechanicalresistanceofbondedjointsisachievedbydispersingnano-particlesofaluminainepoxyresins.

◾ Improvementofthemechanicalresistanceofceramicsisobtainedbydispersionofnanoren-forts:Theybecomestrongerandmoreductilethantraditionalceramics.

3.9.3.2 Further Examples of Nonmechanical Applications

◾ Asnoted earlier,onemay improve. the.electrical. conductivityof amatrix. Insertionofcarbonnanotubescan render itconductive.Anotherexampleof itsapplication isasfollows:

− Electrostaticpaint:Dissipationofstaticelectricityofsomeequipment.◾ Improvement.of.coating.propertiesusingdispersionofcarbonnanotubes:

− Coatingsabsorbingradarwaves(stealthtechnology).◾ Improvement.of.chemical.properties:Dyeaffinity.◾ Improvement.of.thermal.propertiessuchasthermalconductivity,heatresistance,orfireresistance(fireproofquality):Incaseoffire,theintroductionofnanosheetsofclayinapoly-mermatrixdecreasestherateofheatreleaseandreducesthespeedofpropagationofthefire.

◾ Improved.barrier.properties:Abilitytoretainsomemolecules(liquidsorgases)byaddingsmallamountsofclayinthestartingmaterial:

− Reductioninthepermeabilityoffilmcoatingforfoodpackaging− Coatingoftennisballs

◾ Improvement.of.optical.propertiessuchaslightabsorptioncapacity,fluorescentemission,andtransparency:Nanoparticleintroductionprovidesnanocompositepolymer/mineralfill-ers,whicharetransparenttovisiblelight.Thiseliminatesthelightscatteringandcanalsobringnewpropertiestothethusachievedtransparentmaterial:

− Theinclusionofclayinthermoplasticfilmsincreasestheirtransparency.− Luminescentnanoparticlesareusedintheproductionofcertaintypesofscreen.− Metallicpigmentsaddedinpaintsorinpottery(isquitewellknownfromancienttimes).

◾ Improvement.of.the.UV.resistance:Nanoparticlesoftitaniumandzincoxidesareusedasanti-UVadditivesbecausetheyhavealargeabsorptionrangeoftheUVspectrumwithoutaffectingthetransparencyfromthepolymermatrix.

◾ Titaniumdioxideisalsousedforthemanufactureofself-cleaning.surfaces.

3.9.4 Manufacturing of Nanocomposite MaterialsWhilemanufacturingananocompositematerial,itisessentialtoensureahomogeneousdis-tributionofthenanoparticlesinthematerial,thatis,toavoidparticlestocongregateinclus-ters,whichwouldresultinlossofalltheexpectedproperties.Manufacturingtechniquesvary



dependingonthenatureofthematrix(polymer,ceramic,metal)andonthatofnanorenforts.Thefollowingcanthusbefound:

◾ Directmixtureofnanoreinforcementswiththestartingmaterialthathasbeenmelted inadvance(exsitumanufacturing)

◾ Theincorporationofnanoparticlesinamatrixthathasbeenprealablydissolvedinasolvent◾ Directgrowthofthenanoreinforcementswithinthematrixbychemicalreactions(insitumanufacturing)

Forpolymericmatrices,themanufacturingprocessesrequireactionatthelevelofthepolymer/nanoparticleinterfacestoensurethedispersionofnanoparticles:graftingofcompoundsontothesurfaceof thenanoparticles; introductionof ions, so-calledorganophilic; and introductionofgraftpolymers.Nanocompositeswithpolymermatricesaremarketedas semifinishedproductscallednanocomposite.compounds.Theycanbeformedasclassicalcompositecompounds(seeChapter2).Thepartsareobtainedbyinjection,extrusion,andblowmolding.

Note:.Toxicity.of.nanocomposite.materials

Thenanometricsizeofreinforcementsprovidesthemtheabilityto◾ Reachthedeepramificationsoftherespiratorytract(seeFigure3.27)◾ Crossbiologicalbarriers,suchascellmembranes◾ Increasethereactivityofsomeusuallyinertmaterials,whichcanthusbecomechemicallyactive

Numerousstudiesareunderwayinordertoassessrelevantphysicochemicalfactors(chemical,size,surface,shape,potentialcontaminants,etc.)andcontroltherisks.

0.001μm

nm 0.1

Molecules Virus

Tobacco smoke

Combustion

Nanoparticles

1 10 100 1000

0.01 0.1 1

Figure 3.27 Sizes of particles.



3.10 testsTherelationscitedontheprevioussectionsinordertoevaluateelasticmoduliandPoissoncoef-ficientsofcompositesallowobtainingonlyanorderofmagnitudeforthesemechanicalproper-ties.Someoftheserelationsarenotquitereliable,particularlyfortheshearmodulus.Also,thesepropertiesareverysensitivetothefabricationconditions.Itisthereforeessentialforthedesignofficetohaveaccesstotheresultsprovidedbythesuppliersconcerningthereinforcementsandthematricesorevenbettertotheresultsobtainedaftercarryingoutlaboratorytests,whichprovidemoduli,Poissonratios,andfracturestrengthvalues.

Typicaltestsarestandardized:tensiletest,bendingtest,sheartest,shocktest,etc.

◾ Example:.Tensile.test Thetensiletest(ASTMD3039,NFT51-034)onthespecimeninFigure3.28,instrumented

withelectricalstraingauges,allowsthemeasurementofthestrengthandtheelongationatbreak.◾ Example:.Delamination.test

Thetest(NFT57-104) isperformedwithaspecimenhavinga lowslenderness,that is,ashortbeam,workinginbending(seeFigure3.29).Thebreakageiscausedbydelaminationundertheeffectofbendingstressesandparticularlyofinterlaminarshearstresses.Onecanthusobtaintheinterlaminarshearstrength.*

* Thisisbyusingasimplifiedformulawhoseprecisionisinsufficientinviewofthecomplexityoftheactualstateofstressesduetothepresenceofconcentratedforcesthatarecloselyspaced.

b

y

e

x

e ≥ 2 mmb ≥ 10 mmℓ ≥ 200 mm

ℓ

Traction grips

Bonded tabs of duralumin

Figure 3.28 tensile test.

e

5e Shear stresses

Figure 3.29 Short beam shear test.



Furthertestingisveryusefulforthemanufactureofperformantcomposites.Thisisthecaseinparticular forthecontroloffibervolumecontent inthematrix.Indeed,duringthephaseof polymerizationunder pressure of afiber/resin composite (seeChapter 2), the resinflowsinanabsorbent fabric invaryingamountsdependingontheadoptedworkingpressurecyclecomparedtothetemperaturecycleovertime.ThefibervolumefractionVf variesaccordingly,aswellasthedimensionalcharacteristicsofthepart(thickness).Toavoidtheseleaksofresin,one isbroughttoassessbymeansoftestingtheoptimumpoint intimeforpressurizationoftheinstallation.Thisisdonebymeasuringtheevolutionovertimeofthebendingstiffnessofasample(seeFigure3.30).

Sti�nessTemperature

135°C

180°C

Optimal periodto apply pressure Time

Figure 3.30 Stiffness evolution during curing.


Documents

3.1 isotropy and anisotropy - Routledge · 2017. 7. 15. · 34 Composite Materials: Design and Applications 3.2.1 Fiber Mass Fraction Fiber mass fraction is defined as M f = Mass