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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.
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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.
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32 ◾ Composite Materials: Design and Applications
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.
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Ply Properties ◾ 33
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.
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34 ◾ Composite Materials: Design and Applications
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).
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Ply Properties ◾ 35
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
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36 ◾ Composite Materials: Design and Applications
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
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Ply Properties ◾ 37
◾ 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
� ���������������� ����������������
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38 ◾ Composite Materials: Design and Applications
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
Ply Properties ◾ 39
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
40 ◾ Composite Materials: Design and Applications
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
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Ply Properties ◾ 41
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
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42 ◾ Composite Materials: Design and Applications
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.
Copyrighted Material – Taylor & Francis
Ply Properties ◾ 43
◾ 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.
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44 ◾ Composite Materials: Design and Applications
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
Specific mass, ρ (kg/m3) 1,900 1,330 1,450
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
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Ply Properties ◾ 45
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� .
Copyrighted Material – Taylor & Francis
46 ◾ Composite Materials: Design and Applications
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.
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Ply Properties ◾ 47
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.
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48 ◾ Composite Materials: Design and Applications
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.
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Ply Properties ◾ 49
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.
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50 ◾ Composite Materials: Design and Applications
◾ 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).
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Ply Properties ◾ 51
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).
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52 ◾ Composite Materials: Design and Applications
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
Specific mass, ρ (kg/m3) 2,300 3,100 2,700
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.
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Ply Properties ◾ 53
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.
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54 ◾ Composite Materials: Design and Applications
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.
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Ply Properties ◾ 55
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–
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56 ◾ Composite Materials: Design and Applications
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
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Ply Properties ◾ 57
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.
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58 ◾ Composite Materials: Design and Applications
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.
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Ply Properties ◾ 59
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.
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60 ◾ Composite Materials: Design and Applications
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.
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Ply Properties ◾ 61
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.
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62 ◾ Composite Materials: Design and Applications
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
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Ply Properties ◾ 63
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
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64 ◾ Composite Materials: Design and Applications
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
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Ply Properties ◾ 65
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.
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66 ◾ Composite Materials: Design and Applications
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.
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Ply Properties ◾ 67
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.
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