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Woodhead Publishing Series in Composites
Science and Engineering
Stability and Vibrations of
Thin-Walled Composite
Structures
Edited by
Haim Abramovich
Technion, I.I.T., Haifa, Israel
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List of contributors
HaimAbramovich Technion, I.I.T., Haifa, Israel
MarianoArbelo ITA,AeronauticsInstituteofTechnology,S~aoJosédosCampos,
Brazil
Jan Błachut The University ofLiverpool, Liverpool,UnitedKingdom
Saullo G.P. Castro Embraer,S~aoJosé dosCampos,Brazil
F(cid:2)abioRibeiro Soaresda Cunha Embraer, S~ao José dos Campos, Brazil
Richard Degenhardt German Aerospace Center (DLR), Institute for Composite
Structures and Adaptive Systems, Braunschweig, Germany; PFH, Private University
of Applied Sciences G€ottingen, Composite EngineeringCampusStade, Germany
Michele D’Ottavio UPL, Université Paris Nanterre, Ville d’Avray, France
FiorenzoA. Fazzolari University ofCambridge, Cambridge, United Kingdom
Christian Hu€hne German Aerospace Center (DLR), Institute for Composite
Structures and Adaptive Systems, Braunschweig,Germany
Eelco Jansen Leibniz Universit€at Hannover, Hannover, Germany
K. Kalnins Riga Technical University, Riga,Latvia
Steffen Niemann German Aerospace Center (DLR), Institute for Composite
Structures and Adaptive Systems, Braunschweig,Germany
Adrian Orifici RMIT University, Melbourne, VIC, Australia
Olivier Polit UPL, Université Paris Nanterre,Ville d’Avray, France
TanvirRahman DIANA FEA BV,Delft, Netherlands
Khakimova Regina INVENTGmbH, Braunschweig, Germany
Ronald Wagner German Aerospace Center (DLR), Institute for Composite Struc-
tures and Adaptive Systems,Braunschweig,Germany
A. Wieder Griphus e Aerospace Engineering and Manufacturing Ltd., Tel Aviv,
Israel
1
Introduction to composite
materials
Haim Abramovich
Technion, I.I.T., Haifa, Israel
1.1 Introduction
1.1.1 General introduction
Oneofthedefinitionsforacompositematerial,madeoftwoconstituents,oneisfiber
(thereinforcement)andtheotherisglue(thematrix),statesthatacombinationofthe
twomaterialswouldresultinpropertiesbetterthanthoseoftheindividualcomponents
when they are used alone. The main advantages of composite materials over other
existingmaterials,suchasmetalorplastics,aretheirhighstrengthandstiffness,com-
binedwithlowdensity,allowingforweightreductioninthefinishedpart.Thevarious
types of composites are usually referred in the literature, as a block diagram, as
depicted in Fig. 1.1. In this chapter, when we are discussing a composite material,
werestrictourselvestocontinuousfibers(reinforcements)beingembeddedinthema-
trix in theform of an adequateglue.
Examples of such continuous reinforcements include unidirectional, woven cloth,
and helical winding (see Fig. 1.2). Continuous-fiber composites are often made into
laminates by stacking single sheets of continuous fibers in different orientations to
obtain the desired strength and stiffness properties with fiber volumes as high as
60%e70%.Fibersproducehigh-strengthcompositesbecauseoftheirsmalldiameter;
Composites
Particle - Fiber -
Structural
reinforced reinforced
Large Dispersion Continuous Discontinuous
Laminates Sandwich
particles strengthened (aligned) (short)
Randomly
Aligned
oriented
Figure1.1 Typicalcompositematerials.
StabilityandVibrationsofThin-WalledCompositeStructures.http://dx.doi.org/10.1016/B978-0-08-100410-4.00001-6
Copyright©2017ElsevierLtd.Allrightsreserved.
2 StabilityandVibrationsofThin-WalledCompositeStructures
(a) (b) (c)
0° 0° / 90° ±30°
Figure1.2 Typicalcompositematerials:(a)unidirectionalfiber,(b)wovencloth(two
directions),and(c)filamentwinding.
theycontainfarfewerdefects(normallysurfacedefects)comparedtothematerialpro-
ducedin bulk. In addition, because oftheirsmall diameter the fibers areflexible and
suitable for complicated manufacturing processes, such as small radii or weaving.
Materials such as glass, graphite, carbon, and aramid are used to produce fibers (see
typical properties in Table 1.1). The present usage of composite materials is mainly
drivenby theaerospacesector,with alarge percentageofthe modern airplane struc-
tures, such as Boeing 787 or Airbus A380 (see Fig. 1.3), being manufactured from
carbon,glass,andaramidfibers.Themainmaterialforthematrixisapolymer,which
haslowstrengthandstiffness.Themainfunctionsofthematrixaretokeepthefibersin
properorientationandspacingandtoprotectthefiberfromabrasionandtheenviron-
ment.Inpolymermatrixcomposites,thegoodandstrongbondbetweenthematrixand
thereinforcementallowsthematrixtotransmittheoutsideloadsfromthematrixtothe
fibersthroughshearloadingattheinterface.Two typesofpolymermatricesareavail-
able: thermosets and thermoplastics. A thermoset starts as a low-viscosity resin that
reacts and cures during processing, forming a solid. A thermoplastic is a high-
viscosity resin that is processed by heating it above its melting temperature. Because
athermosetresinsetsupandcuresduringprocessing,itcannotbereprocessedbyreheat-
ing. A thermoplastic can be reheated above its melting temperature for additional
processing.
1.2 Unidirectional composites
Unidirectionalcompositesareusuallycomposedoftwoconstituents,thefiberandthe
matrix(whichistheglueholdingthetwocomponentstogether).Basedontheruleof
mixtures,onecancalculatethepropertiesoftheunidirectionallayerbasedontheprop-
ertiesofthefibersandthematrixandtheirvolumefracture.Theassumptiontobemade
whenapplyingtheruleofmixturesisthatthetwoconstituentsarebondedtogetherand
theybehavelikeasinglebody.Thelongitudinalmodulus(orthemajormodulus),E ,
11
of thelayer can bewritten as
E11 ¼EfVf þEmVm (1.1)
Introductiontocompositematerials 3
Table1.1 Typical properties of mostly used reinforced continuous
fibers
Young’s Tensile
Density, Typicalfiber modulus, strength
Material Tradename r(kg/m2) diameter(mm) E(GPa) (GPa)
a-Al O (aluminum FP(US) 3960 20 385 1.8
2 3
oxide)
Al O þSiO þB O Nextel480 3050 11 224 2.3
2 3 2 2 3
(mullite) (USA)
Al O þSiO Altex(Japan) 3300 10e15 210 2.0
2 3 2
(alumina-silica)
Boron(CVDaon VMC(Japan) 2600 140 410 4.0
tungsten)
Carbon(PANb T300(Japan) 1800 7 230 3.5
precursor)
Carbon(PANb T800(Japan) 1800 5.5 295 5.6
precursor)
Carbon(pitchc ThornelP755 2060 10 517 2.1
precursor) (USA)
SiC(þO)(silicon Nicalon(Japan) 2600 15 190 2.5e3.3
carbide)
SiC(lowO)(silicon Hi-Nicalon 2740 14 270 2.8
carbide) (Japan)
SiC(þOþTi) Tyranno(Japan) 2400 9 200 2.8
(siliconcarbide)
SiC(monofilament; Sigma 3100 100 400 3.5
siliconcarbide)
E-glass(silica) 2500 10 70 1.5e2.0
E-glass(silica) 2500 10 70 1.5e2.0
Quartz(silica) 2200 3e15 80 3.5
Aromaticpolyamide Kevlar49 1500 12 130 3.6
(USA)
Polyethylene Spectra1000 970 38 175 3.0
(UHMW)d (USA)
High-carbonsteel E.g.,Pianowire 7800 250 210 2.8
Continued
4 StabilityandVibrationsofThin-WalledCompositeStructures
Table1.1 Continued
Young’s Tensile
Density, Typicalfiber modulus, strength
Material Tradename r(kg/m2) diameter(mm) E(GPa) (GPa)
Aluminum Electricalwire 2680 1670 75 0.27
Titanium Wire 4700 250 115 0.434
aCVD,chemicalvapordeposition.
bPAN,polyacrylonitrile.About90%ofthecarbonfiberproducedworldwidearemadefromPAN.
cPitchisaviscoelasticmaterialthatiscomposedofaromatichydrocarbons.Pitchisproducedbythedistillationofcarbon-based
materials,suchasplants,crudeoil,andcoal.
dUHMW¼ultra-high-molecular-weightpolyethylene(orpolyethene,themostcommonplasticproducedintheworld)isasubsetofthe
thermoplasticpolyethylene.
FromB.Harris,EngineeringCompositeMaterials,TheInstituteofMaterials,London,UK,1999,193p.andR.M.Jones,Mechanicsof
CompositeMaterials,seconded.,Taylor&Francis,Philadelphia,PA19106,USA,1999,519p.
whereEfandEmarethelongitudinalmoduliforthefibersandthematrix,respectively,
and Vfand Vm aretheirrespective volume fractions.1
The majorPoisson’s coefficient, y , isgiven by
12
y12 ¼yfVf þymVm (1.2)
whereyfandymarethelongitudinalmoduliforthefibersandthematrix,respectively.
TheminorPoisson’scoefficient,y ,willbecalculatedtobe
21
y y E
12 ¼ 21 0y ¼y 22 (1.3)
E E 21 12E
11 22 11
The transverse modulus (or theminor modulus),E , ofthe layer isgiven as
22
E122 ¼VEff þVEmm 0E22 ¼VfEEmEmþVm ¼VfEEmþEðm1(cid:2)VfÞ (1.4)
f f
The shear modulus of thelayer, G , isgiven as
12
G112 ¼GVff þGVmm 0G12 ¼VfGGGmmþVm ¼VfGGmþGðm1(cid:2)VfÞ (1.5)
f f
1 NotethatVf þVm¼1.
Introductiontocompositematerials 5
Boeing 787 “dreamliner” composite structure
(a)
Materials used in 787 body
Fiberglass Carbon laminate composite Total materials used
Aluminum Carbon sandwich composite By weight
Aluminum/steel/titanium Other
Steel 5% Composites
10% 50%
Titanium
15%
Aluminum
20%
By comparison, the 777 uses 12 percent
composites and 50 percent aluminum.
(b)
Model aeroplane
A380 composite components
Outer wing
Carbon fiber Wing box Allerons Vertical Tail cone
Aramid fiber stabiliser
Horizontal
Glass fiber Flap-track stabiliser
Hybrid (carbon + glass) fairings outer boxes
Outer flap
Fixed leading-edge Keel beam
upper and lower panels
Pressure
bulkhead
Belly fairing
skins Over wing
panel Trailing-edge upper
and lower panels
and shroud-box
Spoilers
Radome
Main and centre
landing-gear doors
Nose landing- Main landing-gear
gear doors Central leg-fairing door Pylon
torsion box fairings
Nacelle
cowlings
Figure1.3 Usageofcompositematerialsinaerospacestructures:(a)Boeing787and(b)Airbus
A380.
(a)BoeingIndustryand(b)AirbusIndustrie.
whereGfand Gmare theshear moduli for the fibers andthe matrix, respectively.
To assess and compare the differences between the properties of the fiber and the
matrix, thereader isreferred toTable 1.2 .
AsdescribedinRef.[1]thesimplemicromechanicsmodelusedintheruleofmix-
turespredictswellthevaluesofthefourvariables,E ,E ,G ,andy ,ascompared
11 22 12 12
to experimentalvalues, ascan be seen inTable 1.3.
1.3 Properties of a single ply
Aplyhastwomajordimensionsandanotherdimension,i.e.,thethickness,thatisvery
small when compared to the two major ones. Therefore, the 3D presentation of an
6 StabilityandVibrationsofThin-WalledCompositeStructures
Table1.2 Typical properties of T300 carbon fibers and 914 epoxy
resin
Property T300carbonfibers 914epoxyresinmatrix
Young’smodulus,E(GPa) 220 3.3
Shearmodulus,G(GPa) 25 1.2
Poisson’sratio,y 0.15 0.37
FromB.Harris,EngineeringCompositeMaterials,TheInstituteofMaterials,London,UK,1999,193p.
Table1.3 Predictions of unidirectional composite properties by the
simple micromechanics model
Predictedvalues Experimentalvalues
Equations Relationship [moduliin(GPa)] [moduliin(GPa)]
1.1 E11¼EfVfþEm 124.7 125.0
(1(cid:2)Vf)
1.4 1 ¼Vf þð1(cid:2)VfÞ 7.4 9.1
E E E
22 f m
1.5 1 ¼Vf þð1(cid:2)VfÞ 2.6 5.0
G G G
12 f m
1.2 y12¼yfVfþym 0.25 0.34
(1(cid:2)Vf)
AdaptedfromB.Harris,EngineeringCompositeMaterials,TheInstituteofMaterials,London,UK,1999,193p.
orthotropicmaterialwillbesimplifiedtoa2Dpresentation(planestress)byassuming
thats ¼0(seeRefs.[1,2]).Thisleadstoareducedcompliancematrixfortheplyin
33
the form
2 3
1 n
6 (cid:2) 21 0 7
8 9 6 E E 78 9
>><ε11>>= 66 1 2 77>><s11>>=
6 7
>>:ε22>>;¼6666(cid:2)nE112 E12 0 7777>>:s22>>; (1.6)
g 6 7 s
12 4 1 5 12
0 0
G
12
Thethirdequationforthestraininthethicknessdirection,ε ,thatisseldomused
33
has thefollowing form
g g
ε ¼(cid:2) 13s (cid:2) 23s (1.7)
33 E 11 E 22
1 2
