FRACTURETOUGHNESSCHARACTERIZATIONOF
THERMOSETTINGPOLYMERSYSTEMSREINFORCEDBY
GRAPHENENANOPLATELETS
By
AbdulrahmanAlfadhli
ATHESIS
Submittedto
MichiganStateUniversity
inpartialentoftherequirements
forthedegreeof
MechanicalEngineering|MasterofScience
2020
ABSTRACT
FRACTURETOUGHNESSCHARACTERIZATIONOFTHERMOSETTING
POLYMERSYSTEMSREINFORCEDBYGRAPHENENANOPLATELETS
By
AbdulrahmanAlfadhli
Theinterlaminarfracturetoughnessisacriticalpropertyforthedamagetolerance,im-
pactresistance,anddelaminationofer-reinforcedpolymer(FRP)composites.Toenhance
thisproperty,variousstrategieshavebeenexplored,fromintroducingthroughthethickness
reinforcement,strengtheningtheer-matrixinterface,toimprovingthefracturetoughness
ofthematrixresins.ThisresearchexaminestheofGrapheneNanoplatelet(xGnP)
onthefracturetoughnessofepoxyresinscommonlyusedinFRPs.Twoepoxysystemswere
examined:EPON862andSC-15.xGnPwasaddedintotheepoxyresinsattwoweightfrac-
tions:0.1wt%and0.5wt%.Thefracturetoughnessofthereinforcedresinswasinvestigated
withthecompacttension(CT)experiment.ItwasobservedthatxGnPresultedinagreater
enhancementinthefracturetoughnessofEPON862thanthatofSC-15.ForEPON862,
the
G
IC
valuehadanimprovementof87%and156%forthereinforced0.1wt%and0.5wt%,
respectively.ForSC-15,theimprovementwas21%and14%forthereinforced0.1wt%and
0.5wt%,respectively.SC-15isalreadyrubbertoughened.Forcomparisonpurpose,EPON
862wasalsoreinforcedwithnano-silicaparticles.At0.1wt%and0.5wt%,theimprovement
in
G
IC
was49%and87%,respectively.Insummary,addingxGnPcantlyimprove
thefracturetoughnessofarelativelybrittleepoxysystem.Atalowconcentration,xGnPis
muchmoretthannano-silicaintermsofimprovingthefracturetoughness.Finally,
infractureexperiment,themethodofintroducingpre-crackwasfoundtohaveat
onthemeasuredfracturetoughnessvalue.
ACKNOWLEDGMENTS
IwouldliketoexpressmydeepestappreciationtomyadvisorDr.XinranXiaoforher
support,encouragement,andguidanceduringmygraduatestudy.Theprofessorhastaught
mehowtoreviewliteraturepapersandhowtoformaresearchplan.Withoutherassistance,
Iwouldneverbeabletoaccomplishthisthesis.Dr.Xiaowasalwaysavailableandwilling
togiveaboveandbeyondtohelpmewiththeresearch.Ialsowouldliketoacknowledge
Dr.ShiwangChengforhiscontribution.Hiscontributionbyprovidingthematerialwith
thenanoadditiveswasprecious.IamthankfultoDr.PatrickKwonforacceptingtobe
amemberofthemasterthesiscommittee.Iamalsogratefultoallmycolleaguesfortheir
continuoussupportandhelp,includingSakibIqbal,ShutianYan,RoyalIhuaenyi,JieFu,
andRuTao.
Iwanttoshowgratitudetomyparents,whotoraiseandeducateme.Without
theirinspiration,guidance,andsupport,ImightnotbethepersonIamtoday.Iamdeeply
thankfultomywifeforhercontinuoussupportandencouragement.Withouther,Iwould
neverbeabletocontinuemygraduatestudies.Iappreciatemybrothers,sisters,andfriends
fortheirgreatmotivation.Finally,IwouldliketothanktheKingdomofSaudiArabiaand
TheIslamicUniversityofMadinahforthefellowshiptopursuemyhighereducation.
iii
TABLEOFCONTENTS
LISTOFTABLES
....................................
vi
LISTOFFIGURES
...................................
vii
KEYTOSYMBOLS
..................................
x
Chapter1IntroductionandLiteratureReview
................
1
1.1ThesisOrganization................................1
1.2Introduction....................................2
1.3Graphene-basedNanocomposites........................3
1.3.1TougheningMechanisms.........................5
1.3.2Dispersionof.........................6
1.4FractureMechanics................................7
1.4.1TypesofFracture.............................8
1.4.2Modesoffracture.............................9
1.4.3Linear-ElasticFractureMechanics(LEFM)...............9
1.4.3.1EnergyBalanceCriteria...............10
1.4.3.2StressIntensityFactor(K)...................11
1.4.3.3RelationshipBetweenEnergyReleaseRateandStressInten-
sityFactor...........................13
1.4.4Elastic-PlasticFractureMechanics(EPFM)..............13
1.4.4.1Cracktipopeningdisplacement(CTOD)...........13
1.4.4.2J-integral............................14
Chapter2FractureToughnessExperiment
...................
15
2.1TestingStandardsandCalculations.......................15
2.2MaterialsandMethods..............................18
2.2.1CuringCycleandSpecimenPreparation................19
2.3ExperimentSetup.................................22
2.4DataAcquisition.................................24
Chapter3ResultsandDissection
.........................
26
3.1tPre-crackingProceduresandtheir..............26
3.2FracturetoughnessResults............................30
3.2.1EPON862.................................30
3.2.2SC-15...................................33
3.3StressDistributionandPlasticityCorrection..................35
3.3.1CreagerandParis(1967)'sEstimation.................43
3.3.2StressDistributionfortSamples'Loading...........44
3.3.3PlasticZoneShape............................45
iv
Chapter4Conclusion
................................
48
4.1SummaryandConclusion............................48
4.2FutureWork....................................49
APPENDIX
........................................
50
BIBLIOGRAPHY
....................................
54
v
LISTOFTABLES
Table3.1:Comparisonbetweentwoentpre-crackingmethodsonEPON862's
fracturetoughness...............................28
Table3.2:Comparisonbetweentwotpre-crackingmethodsonSC-15'sfrac-
turetoughness.................................28
Table3.3:
K
IC
(
MPa:
p
m
)averagesofEPON862withxGnP.............31
Table3.4:
G
IC
(
J=m
2
)averagesofEPON862withxGnP...............31
Table3.5:
K
IC
(
MPa:
p
m
)averagesofEPON862withNano-silica..........32
Table3.6:
G
IC
(
J=m
2
)averagesofEPON862withNano-silica............32
Table3.7:
K
IC
(
MPa:
p
m
)averagesofSC-15withxGnP...............35
Table3.8:
G
IC
(
J=m
2
)averagesofSC-15withxGnP..................35
Table3.9:MechanicalPropertyofSC-15baseline....................38
Table3.10:ThethreeexamplesamplesofSC-15with0.5wt%xGnP...........39
TableA.1:SC-15Samples-baseline............................51
TableA.2:SC-15Samples-0.1wt%xGnP.........................51
TableA.3:SC-15Samples-0.5wt%xGnP.........................51
TableA.4:EPON862Samples-baseline.........................52
TableA.5:EPON862Samples-0.1wt%xGnP......................52
TableA.6:EPON862Samples-0.5wt%xGnP......................52
TableA.7:EPON862Samples-0.1wt%Nano-Silica...................52
TableA.8:EPON862Samples-0.5wt%Nano-Silica...................53
vi
LISTOFFIGURES
Figure1.1:Mode-Iinterlaminarfracturetoughnessofcomposites
G
c
IC
andmode-I
matrixtoughness
G
m
IC
forconventionalcomposites[1]............3
Figure1.2:Mapsoftmechanicalpropertiesfornanocompositeswithrespect
toparticleloading:(a)Fracturetoughnessmap.(b)map.(c)
Ultimatetensilestrengthmap.Obtainedfrom[2]..............4
Figure1.3:Modesoffracture:ModeIOpening,ModeIIIn-planeshear,ModeIII
Out-of-planeshare,Drawingobtainedfrom[3]...............9
Figure1.4:Anwideplatewithathroughthicknessellipsecracksubjectedto
remotetensilestress,Drawingobtainedfrom[4]...............11
Figure1.5:Polarcoordinatesofthestressesaheadofthecracktip.Drawingobtained
from[4].....................................12
Figure2.1:TheASTMD5045standard[5]:(a)Specimen(b)Load
vsloadingpointdisplacementcurve.....................16
Figure2.2:Solventevaporationprocess..........................20
Figure2.3:Sample'sdesignandsiliconmolds:(a)Thedesignthestainlesssteelproto-
typein(mm)followingthestandards[5].(b)Thestainlesssteelprototype
andthesiliconmold..............................21
Figure2.4:Aftercompletingthecuringcycle:(a)Samplesliftinsidetheopendoor
oventocooldownafterthecuringcycle.(b)Samplesareready
tobecarefullyextractedfromthemolds...................21
Figure2.5:SC-15samples,fromright:baseline,0.1wt%,then0.5wt%ofxGnP....22
Figure2.6:EPON862samples:(a)0.1wt%,0.5wt%ofnano-silica.(b)0.1wt%,0.5wt%
ofxGnP.(c)Baseline.............................22
Figure2.7:Theexperimentsetupwithcameraandlightsource............23
Figure2.8:Samplesarrangementbeforeattachingtothetensilegrip:(a)Frontview.
(b)Sideview..................................24
vii
Figure2.9:Theexperiment'sstagesuntilthefracture:(a)Thesecondstillimage.
(b)Themiddleofthetest.(c)Themomentbeforethefracture.(d)The
momentafterthefracture...........................25
Figure3.1:Thetwomethodsofpre-cracking:(a)Pressingtherazorintothenotch.
(b)Slidingtherazoronthenotch......................27
Figure3.2:Thestrainofthepressedsample:(a)Beforeinsertingtheblade.(b)

x
afterinsertingtheblade.(c)

y
afterinsertingtheblade........29
Figure3.3:LoadvsLoading-pointdisplacementofEPON862withxGnP.......30
Figure3.4:
K
IC
and
G
IC
ofEPON862withxGnP....................31
Figure3.5:ComparisonbetweenEPON862withxGnPandEPON862withNano-
Silicaforentweightfractions......................32
Figure3.6:LoadvsLoading-pointdisplacementofSC-15withxGnP.........33
Figure3.7:
K
IC
and
G
IC
ofSC-15withxGnP......................34
Figure3.8:Thestressnearthecracktip......................35
Figure3.9:First-orderandsecond-orderestimatesofplasticzonesize(
r
y
and
r
p
,
respectively).Thecross-hatchedarearepresentstheloadthatmustbe
redistributed,resultinginalargerplasticzone.Obtainedfrom[6].....37
Figure3.10:Thespecimen'snormalstress
˙
y
distributionalongthecrackpath
justbeforethefracture............................40
Figure3.11:Thesecondspecimen'snormalstress
˙
y
distributionalongthecrackpath
justbeforethefracture............................40
Figure3.12:Thethirdspecimen'snormalstress
˙
y
distributionalongthecrackpath
justbeforethefracture............................41
Figure3.13:LoadvsCTODforthethreesamples.....................42
Figure3.14:ComparisonbetweenIrwin'smoandCreagerandParis'sesti-
mation.....................................44
Figure3.15:Thenormalstress
˙
y
distributionalongthecrackpathfortloading.45
Figure3.16:TheplasticzoneshapeestimationfromtheelasticsolutionforModeI.
Obtainedfrom[6]...............................46
viii
Figure3.17:TheestressfromaelementanalysisVstheplasticzone
estimation[6]..................................46
Figure3.18:Straindistributionofy-direction.......................47
FigureA.1:Compacttensionspecimen..................51
FigureA.2:Microscopicimageofacracktipmadebyrazorsliding...........53
FigureA.3:Microscopicimageofacracktipmadebyrazorpressing..........53
ix
KEYTOSYMBOLS
FRPFiber-reinforcedPolymer
xGnPGraphenenanoplatele
CNTsCarbonnanotubes
K
IC
ModeICriticalStressIntensityFactor
G
IC
ModeICriticalStrainEnergyReleaseRate
CTODCrackTipOpeningDisplacement
JJ-integral
LEFMLinearElasticFractureMechanic
EPFMElastic-PlasticFractureMechanics
TTemperature
T
g
GlassTransitionTemperature
SSYSmallScaleYielding
EDMElectricalDischargeMachining
CTCompactTension
SENBSingleEdgeNotchedBend
PLoad
BThickness
WWidth
aCrackLength
DICDigitalImageCorrelation
FEAFiniteElementAnalysis
SEMTheStandardErroroftheMean
x
Chapter1:
IntroductionandLiteratureReview
1.1
ThesisOrganization
Thisthesisisstructuredasfollows:
Chapter1
reviewstherelationshipbetweenthefracturetoughnessofthematrixand
theinterlaminarfracturetoughnessoftheer-reinforcedpolymer.Thischapteroverviews
theliteratureonthemechanicalofaddingrstoepoxyresins.Thereasons
forchoosingthegraphenenanoplateletsasanadditivearediscussed.Sincethefocusison
thefracturetoughnessproperty,fracturemechanicsandfracturetoughnessareexplainedin
thischapter.
Chapter2
discussesthemethodologyofthestudy,fromidentifyingthestandards,
preparingthematerial,tomanufacturingthespecimens.Thetestingprocedureandthe
dataacquisitionmethodaredescribed.
Chapter3
reportstheofbothepoxysystemsandevaluatestheof
addingnanoadditives.Thelastpartofthischapterpresentsanalyticalsolutionsforthestress
distributionalongthecrackpathandthecrack-tipplasticity.Furthermore,acomparison
betweentheanalyticalsolutionsandtheexperimentalanalysisispresented.
Chapter4
summarizesandconcludesthethesisinadditiontorecommendingfuture
work.
1
1.2
Introduction
Theinterlaminarfracturetoughnessisakeypropertyforthedamagetoleranceandimpact
resistanceofber-reinforcedpolymer(FRP)composites[7{10].Toimprovethisproperty,
variousstrategieshavebeenexplored,fromintroducingthroughthethicknessreinforcement,
increasingtheer/matrixinterfacestrength,toenhancingthetoughnessofthematrix
resins.Eachmethodhasledtosomeimprovement,buttheproblemisfarfrombeingsolved.
Thisthesisfocusesoninvestigatingtheenforcementofthematrixbygraphenenanoplatelets
asthecorrelationbetweencomposites'andmatrices'fracturetoughnessisevident.
Thematrixtoughnessisoneofthedominantfactorsdeterminingtheinterlaminarfracture
toughnessofcompositesduototheinteractionbetweenthenanoparticlesandthereinforcing
[1,10,11].Toimprovethematrixresintoughness,variousstrategieshavebeende-
veloped,includingrubbertoughenedthermosetresinsandthermoplasticresins.Thematrix
tougheningisgaugedbythe
G
c
IC
/
G
m
IC
ratio,i.e.TheMode-Iinterlaminarfracture
toughnessofthecompositeovertheMode-Ifracturetoughnessofthematrixresin.Improv-
ingthematrixtoughnessisparticulartforbrittleresinsystems.Ageneraltrendis
G
c
IC
/
G
m
IC
>
1forbrittlematriceswhen
G
m
IC
<
500
J=m
2
,and
G
c
IC
/
G
m
IC
<
1fortoughmatrices
when
G
m
IC
>
500
J=m
2
inconventionaler-reinforcedpolymers(FRP)s,asshowninFigure
1.1.Itwasfoundthatthehigheramountofnanoparticlesdispersedintotheresin,thelower
matrixtoughening
G
c
IC
/
G
m
IC
observed[11].
2
Figure1.1:Mode-Iinterlaminarfracturetoughnessofcomposites
G
c
IC
andmode-Imatrixtoughness
G
m
IC
for
conventionalcomposites[1].
1.3
Graphene-basedNanocomposites
Thefracturetoughnessandstrengtharetwofundamentalpropertiesforstructuralmaterial.
Usually,theyarenotcompatible.Theimprovementofoneisoftenattheexpenseoftheother.
Theemergingnanocompositehaschangedthisperspective.Withtheadditionofnano-sized
polymerscanbetougher,stronger,andwithaddedmulti-functionality.Amongthem,
grapheneappearstohavethehighesteatthelowloadingregion.
Itisnotasimpletasktocomparetheoftduetothediversity
inmaterialssource,thewiderangeofdispersionmethods,andthesizesoftheseBy
compilingdatafromhundredsofresearchpapersonepoxy-basednanocomposites,Domun
etal.[2]generatedasetofmapsthatcomparetheeoffourtypesofnanoparticles
onfracturetoughness,andstrength,asshowninFigure1.2.Inthesemaps,The
propertiesaregivenastheratiototheneatepoxy,andthedatapointsabove1.0lineindicate
apositiveTheFigurescomparetheofnanoparticles/epoxynanocompos-
ites(withCarbonnanotubes,graphene,nanoclayandnanosilicon)withrespecttoparticle
loadingweightfraction[2].
3
Figure1.2:Mapsoftmechanicalpropertiesfornanocompositeswithrespecttoparticleloading:(a)
Fracturetoughnessmap.(b)map.(c)Ultimatetensilestrengthmap.Obtainedfrom[2].
4
Figures1.2showsthatthegrapheneisaclearwinnerintheregionoflowweightfraction
upto0.5wt%.Grapheneconsistentlyout-performedcarbonnanotubes(CNTs),nanoclay
andnanosilicainallthreeproperties.Thistheearlierofetal.[12]
thatatalowconcentrationof0.1wt%,graphenenanoplatelet(GNP)/epoxyoutperformed
SWCNT/epoxyandMWCNT/epoxynanocompositesbyatmarginintensilemod-
ulus,strength,Mode-Ifracturetoughness,andfatiguecrackingresistance.
1.3.1
TougheningMechanisms
Theremarkabletougheningofhasbeenattributedtoadditionaltoughening
mechanismsbroughtuponbythese[11].For0-Dand1-Dtheseincludegreater
energyabsorptionfromresindebondingand/ornanotubepull-outduetothe
extraordinarilylargeinterfacearea,reducedplasticzoneduetoincreasedmatrixyieldstress,
andhighererinterfacialstrength.Innanoclaycomposites,itwasobservedthat
theplateletsproducenanovoids/cracksandpromoteshearyieldingofthematrixatthecrack
tip.
ThemechanicsofgraphenenanocompositeshavebeendiscussedbyYoungetal.[13].
Inagraphenesheet,thecarbonatomsareheldtogetherby
sp
2
bonds,whichrenderthe
graphenewithultra-highin-planestrength,andconductivity.Thebondsbetween
sheetlayersareweakvanderWaalsforces.Theinterfacialshearstrengthbetweenthe
graphenesheetswasfoundtobeattheorderof1MPa.Forin-planemodulusofelasticity,
Leeatal.[14]measurementforthemonolayergraphenemembranewasabout1TPa.How
thisuniquestructurelinkstoitsreinforcinginnanoandmultiscalecompositesisyet
tobeunderstood.Theabovesuggestthatfurtherresearchisneededtoexplorethe
potentialofusinggraphene-moresinsinimprovingtheinterlaminarfracturetoughness
5
andimpactresistanceofstructuralcomposites.
1.3.2
Dispersionof
Oneofthemostcriticalstepsinpreparinghigh-qualitygraphene-basedepoxycomposites
isthemethodofnano-graphenedispersion.Improperdistributionofthegrapheneintothe
epoxymaycauseissuessuchasvoidformation,tcuringoftheepoxy,viscosity
buildupoftheepoxy,andshearthinning[15].Theoptimalmethodofgraphenedisper-
sionwillhelptogethighermechanicalbondingbetweentheepoxyandthenano-graphene
platelets(NGP)andenhancematerialperformance[15].
Solutionmixingandhighshearmixingaretwoofthemostcommonlyusedmethodsfor
dispersingnano-grapheneplatelets(NGP)intothepolymer[15].Solutionmixingusesthe
sonicationprocesstodispersetheNGPsintoaproperorganicsolventwingbyaddingthe
epoxyandthenevaporatethesolvent[16,17].Highshearmixingmechanicallydistribute
theNGPsintothepolymer[18,19].Kumar[18]usedonlyahighshearmixerat2000rpmto
dispersetheNGPsintotheepoxyfollowingnotesfromtheNGPmanufacturer,andreported
gooddispersionqualityandrandomorientation.However,athigherweightfraction,some
agglomerationofthegrapheneplateletshaveoccurred.Kumarin2018[19],followingYang's
paper[20]suggestions,hydrogenpassivatedtheNGPsusing5%H2/N2mixturetoimprove
dispersionoftheplateletsthenusedahighshearmixertodisperseHP-NGPsintothe
epoxy.Kumarusinganopticalmicroscopecomparedpassivatedandnon-passivatedNGPs
compositesandshowedthebofthehydrogenpassivationonthedispersionofthe
NGPs.
[16]dispersedGPLintoacetoneusinghighamplitudeultrasonicthenaddedthe
epoxywingthesameprocedure.Theacetonelaterwasremovedthroughheatingthemix-
6
ture.Wajid[17]preparedthegraphene-basedepoxycompositesusingtwotechniques:solu-
tionprocessingandfreeze-dryingandcomparedbetweenthem.Wajidforthemethod
usedDMFasasolventforPVP-stabilizedgraphenebeforeaddingtheepoxy.DMFwascho-
senbecausetheyfoundittobethebestcompatibilitywiththeirepoxyresin.Afteradding
theepoxy,thesolutionwastipsonicatedtoensuretheuniformdispersionofthegraphene
\lessagglomeration".Then,theDMFwasevaporatedbyheatingthemixturewhilemag-
neticallymixthesolutiontoensuretheuniformdistributionoftheepoxyinthemixture.To
ensuretheeliminationoftheremainingsolvent,thesolutionwasplacedinavacuumovenat
asptemperaturefor14h.Theothermethodisfreeze-drying.Thepolymer-stabilized
grapheneinwaterwerefreeze-driedusingaVitrisBenchtopFreezeDryerthroughout48h
toobtainadarkgraycoloredpowder.Thefreeze-driedPVP-stabilizedgraphenewasredis-
persedintheresinbystirringandsonicatingfor30min.Thehardenerwasaddedtothe
graphene/resinmixtureandwascuredunderthesameconditionsasthesolutionprocessing
method.Wajid[17]concludesthatthesolutionprocessingmethodresultsinreliabledis-
persionqualitybutfromresidualsolventathigh-grapheneconcentrations,unlikethe
solvent-freetechnique,freeze-drymixing,thatavoidsthisproblem.
1.4
FractureMechanics
Itisoftenassumedduringthedesignprocessthatthematerialisisotropicandwless.
However,thisisalmostimpossibletoachieve,asmicrostructureandotherscalesdefects
areusuallyinevitableduringthemanufacturingprocess.Iftheexistenceofcracksisnot
takenintoaccountduringdesign,thesewscancausesevereconsequences.Thesedefects
canleadtoacompletefailureofthesystemeventhoughthetotalstressiswaybelowthe
7
ultimatetensilestrengthofthematerial.Manyaccidentsoccurredinhistoryduetoalack
ofconsiderationoffracturemechanics,whichisthetheoreticalexplanationofthecracks'
behaviorinmaterials.Iftheconceptoffracturemechanicsisappropriatelyapplied,mostof
theseincidentscouldbeavoided.
Fracturetoughnessisthestudyofthematerial'sresistancetocrackpropagationand
describedbyseveralparameters;stressintensityfactor(K),energyreleaserate(G),J-integral
(J),andcracktipopeningdisplacement(CTOD).Tensileproperties,crackgeometry,and
temperaturearefactorsthefracturetoughnessofthematerial.Epoxyresinscan
fractureeitherinthelinearelasticornonlinearelastic-plasticregimes.Therearetwomain
approachestodescribethefracturemechanics;LinearElasticFractureMechanics(LEFM)
andElastic-PlasticFractureMechanics(EPFM).Epoxiesoftenobey(LEFM)whentheyare
wellbelowtheirglasstransitiontemperature
T
g
andobey(EPFM)whentheyarenearand
abovetheir
T
g
.
1.4.1
TypesofFracture.
Therearemainlytwotypesoffracture:brittlefractureandductilefracture.Brittlefracture
correspondstothesuddenandrapidcrackpropagationunderstress,wherethematerial
exhibitedlittleornoplasticdeformationpriortofailure.Consequently,arelativelysmall
amountofenergyisrequiredtocompletethefracture.Ontheotherhand,ductilefracture
occurswhenthecrackhasasubstantialplasticdeformationbeforeseparation,andthis
usuallytakeslongertimeandrequiredmoreenergy[4].
8
Figure1.3:Modesoffracture:ModeIOpening,ModeIIIn-planeshear,ModeIIIOut-of-planeshare,
Drawingobtainedfrom[3].
1.4.2
Modesoffracture
TherearethreebasicmodesoffractureindicatedinFigure1.3.Inarealsituation,materials
andcrackscouldexperienceacombinationoftwoorallthreestyles.ModeIhastheload
perpendiculartothecracksurface,andthismoderequireslowloadandenergytopropagate
thecrackcomparedtotheothertwomodes.ModeIloadingisthemostcommonmodeused
forfracturetoughnesscharacterization.ModeIIloadingexperiencesin-planeshearingstress
andModeIIIexperiencesout-of-planeshearingstress.
1.4.3
Linear-ElasticFractureMechanics(LEFM)
Linearelasticfracturemechanics(LEFM)isatheorybasedonGcriteriaanddescribes
theexperiencedstressatcrackswithintheyieldlimit.Thistheorydescribesthedeformation
intheelasticregionformaterialsthatobeyHooke'slawoflinearelasticity.However,small
scaleyielding(SSY)mostlyoccurs,anditisgenerallyneglectable.LEFMhastwoparameters
forthefracturetoughness:Energyreleaserate(G)andStressintensityfactor(K).
9
1.4.3.1
EnergyBalanceCriteria
AnEnglishaeronauticalengineerA.A.inthe1920s[21]hasledoneofthewell-known
earlyadvancesoffracturemechanicswherehestudiedbrittlefractureonglass.Followingthe
principleofthelawofthermodynamics,theassumptionwasthattheoverallenergyex-
periencedbythecrackwouldbeinequilibriumwiththeloadappliedtothecrack.Therefore,
thereisnochangeintotalenergyunderequilibriumuntilthecrackhitsthecriticalstageand
startgrowing.Whenthecrackprogresses,itreleasesenergy,sotheenergythatisapplied
tothecrackandtheenergyreceivedbythecrackisnolongerinequilibrium,andthere
willbeanetdecreaseofenergy.Forthecracktoexpand,theremustbeenoughpotential
energytosurmountthesurfaceenergy.Foranwideplatewithathrough-thickness
cracksubjectedtotensilestressin-planestressconditionasshowninFigure1.4,The
energybalanceforgrowthinthecrackarea
dA
isexpressedinequilibriumconditionsasin
Eq.1.1.Whereisthepotentialenergysuppliedbytheinternalstrainenergyandexternal
stress,and
W
s
istheworkneededtocreatenewsurfaces.AfterdevelopmentbyG
(1921)basedontheanalysisofInglis[22],thefracturestress,
˙
f
isobtainedasinEq.1.2for
isotropiclinearelasticmaterialswhere

s
isthesurfaceenergyofthematerial.
d

dA
+
dW
s
dA
=0(1.1)
˙
f
=
r
2

s
E
ˇa
(1.2)
In1956,Irwin[23]introducedafractureenergysolutionthatisbasicallysimilartoGrif-
concept,exceptthatIrwin'sapproachisinshapemorepracticaltoaddressengineering
10
Figure1.4:Anwideplatewithathroughthicknessellipsecracksubjectedtoremotetensilestress,
Drawingobtainedfrom[4].
challenges.Irwindetheenergyreleaserate
G
whichisthemeasurementoftheavailable
energyforacrackextension,astherateofchangeinpotentialenergywiththecrackarea.
Irwin[23]describesthereleasedenergyduotothecrackinitiationsinEq.1.3.Whereis
thepotentialenergyofthecrack,whichisalsoknownasthecrackextensionforce,andAis
thecrackarea.
G
=

d

dA
(1.3)
1.4.3.2
StressIntensityFactor(K)
Westergaard[24],Irwin[25],etal.arethetodriveexpressionsdescribingthestress
nearthecracktipforacrackedbodywithexternalforceconsideringtheisotropicbehavior
oflinearelasticmaterials.Therstorderstresscouldbeinalinearisotropic
material,settingthecracktipastheoriginofthepolarcoordinateaxis,asshowninFigure
1.5andexpressedinEq.1.4.Where
˙
ij
isthestresstensor,
K
isthestressintensityfactor,
11
Figure1.5:Polarcoordinatesofthestressesaheadofthecracktip.Drawingobtainedfrom[4].
and
f
ij
isadimensionlessfunction,while
r
and

arepolarthecoordinates.
˙
ij
=

K
p
2
ˇr

f
ij
(

)+

(1.4)
StressintensityfactorKisaparameterintroducedbyIrwin[25]usedinLEFMtopredict
thestressstatenearthecracktip.Asubscriptisassignedtothestressintensityfactorto
denotetheloadingmode,thatis,
K
I
,
K
II
,or
K
III
.Eq.1.5istodetermine
K
I
ofthe
stressesinthevicinityofthecracktip.Where
Y
isadimensionlessfactordependsoncrack
geometryandloadingcondition,
˙
istheappliedload,and
a
isthecracklength.
Y
inthe
caseoffracturetoughnesstestdescribedasafunctionofcracktowidthratio
a=W
asin
Eq.1.6.
K
I
=
Y˙
p
ˇa
(1.5)
K
I
=
P
B
p
W
f

a
W

(1.6)
12
1.4.3.3
RelationshipBetweenEnergyReleaseRateandStressIntensityFactor
Energyreleaserate
G
andStressintensityfactor
K
aretwotparametersdescribing
cracks.
G
isaparameterbasedonthestrainenergy,and
K
isbasedonthestressnearthe
cracktip.ConsideringthetwoEquationsin1.7,arelationshipbetweenthetwoparameters
canbedescribedforplanestrainconditionsasinEq.1.8.
G
=
ˇ˙
2
a
E
K
I
=
˙
p
ˇa
(1.7)
G
=
K
2

1

v
2

E
(1.8)
1.4.4
Elastic-PlasticFractureMechanics(EPFM)
Theprevioustwoparameters,theenergyreleaserateandstressintensityfactordon'tde-
scribethematerialthatexhibitingatplasticdeformationatthecracktipand
woulddeformplasticallyafterreachingthemaximumstress.Twonewparameterswould
beintroducedforthistypeofmaterials:Cracktipopeningdisplacement(CTOD)andJ-
integral.
1.4.4.1
Cracktipopeningdisplacement(CTOD)
AfracturecriterionknownascracktipopeningdisplacementwasintroducedbyWells[26]
thatmeasuresthephysicalopeningofthecracktip.CTODisthedistanceoftheopening
ofaninitialcracktiptothepointofstableorunstablecrackextensioninatypicalfracture
toughnesstestspecimen.Themaximumcracktipopeningduetocleavagecrackingorplastic
failureistheCTOD.Materialsthatshowingelastic-plasticbehaviorbeforefracturewould
13
experienceplasticdeformationatthecracktip.
1.4.4.2
J-integral
Rice[27]proposedtheJ-integralenergyapproach,whichisbasedonthedensityofthestrain
energyaroundthecracktip.J-integraldescribestheindependentcrackpathofstrainenergy
releaserate,applicabletobothlinearandnonlinearelasticmaterial.TheJ-integralwould
haveaconstantvaluecharacterizingthestressandstraininthevicinityofthecrack
tip.InLEFM,
G
isassumedtobetheavailableenergytoextendthecrack,whichisequalto
J.However,foranelastic-plasticmaterial,partoftheenergyisusedinplasticdeformation
asthecrackpropagates.
14
Chapter2:
FractureToughnessExperiment
Themethodologyofthisstudyisdescribedinthischapterasfollows.Sincethebaseof
thisthesisisthefractureexperiment,thesectionidenthestandardsthatwere
adaptedfortesting,fromdesigningthesamples,performingthetest,tocalculatingthe
properties.Preparingthematerialandmanufacturingthespecimenstookadecentamount
ofthechapterduetoitstroleinresults.Beforemovingontothenextchapter
thatdiscussingtheresults,detailedinformationwasincludedaboutthetestingprocedure
anddataacquisition.
2.1
TestingStandardsandCalculations
ThemodeIplanestrainfracturetoughnesstestforplasticmaterialsfollowsTheASTM
D5045standardtodeterminethecriticalstressintensityfactor
K
IC
,andtheenergyperunit
areaofcracksurfaceorcriticalstrainenergyreleaserate
G
IC
.ASTME399formetallic
materialswithbrittlefractureisusedformoredetailsandrequirements.Thestandard
permitstwotspecimenshapes:singleedgenotchedbend(SENB)andcompact
tension(CT)showninFigure2.1(a).Thecompacttension(CT)
hasbeenselectedforthisresearch.Thestandardindicatesthatthreemeasurementsare
necessaryfor
K
IC
and
G
IC
calculations:thethicknessB,thecracklengtha,andthewidth
W.Therecommendedtestingconditionforthetemperatureis23

C,andthecross-head
displacementratetobe(10mm/min).Theloadingtimesshouldn'tbelessthan1msbecause
theriskofdynamiccausingerrors.Thestandardrequiresatleastthreereplicate
testsforeachmaterialconditionandaccurateintegrationoftheloadversaloadingpoint
15
Figure2.1:TheASTMD5045standard[5]:(a)Specimen(b)Loadvsloadingpointdis-
placementcurve.
displacement,whichisusedtodetermineaccurateresultsofcriticalstrainenergyrelease
rate
G
IC
.Theidealcaseofthetestisalineardiagramwithasuddendropoftheloadat
theinstantofcrackinitiation[5].
Forpre-cracking,thestandardASTMD5045recommendsthenaturalcracktobemade
bysawingortappingafreshrazorblade.Thelengthofthepre-crackshouldbeatleast
twicelongerthanthewidthofthesawed-inslotorthetipradiusofthemachinednotch.If
thepre-crackcannotbegeneratedbytappingtherazorbecauseofthematerialbrittleness,
slidingtherazorbladeacrossthemachinedgrooveistheotheroption.Pressingtherazorinto
themachinedgrooveshouldbeavoidedforductilematerialsbecauseoftheriskofinducing
residualstressesatthecracktipthatmightpromotehigher
K
IC
and
G
IC
values.
IntheloadvsloadingpointdisplacementcurveshowninFigure2.1(b).AB'isasketched
linewith5%lessslopethantheABline,andthecorrespondingpinttotheintersection
betweenthelineAB'andtheload-displacementcurveis
P
Q
.If
P
max
isbetweenABand
AB',itwouldbecalled
P
Q
,andwillbeusedtocalculate
K
Q
.Ifnot,
P
Q
willbeused.
16
Moreover,if
P
max
=P
Q
islessthan1.1,then
P
Q
isvaluedtobeused;otherwise,thetest
wouldbeinvalid.
K
Q
,whichissofaraconditionalfracturetoughnessuntilpassthevalidity
Eq.2.2,canbecalculatedusingEq.2.1.WhereBandWarethethicknessandthewidth,
respectively,and
f
(
x
)isadimensionlessfactorthatdependsontheratio
x
=
a=W
.
K
Q
becomes
K
IC
whenitpassesthevchickofsizecriteriainEq.2.2where
K
Q
isthe
conditional
K
IC
,and
˙
y
istheyieldstressofthepolymer.Thisrelationshipwillensurethat
thicknessBisenoughtoconsidertheproblemfollowingtheplanestraincondition.The
term(
W

a
)istoensurepreventingplasticityintheligamentwhiletheothersideofthe
equationisrepresentingthesmallsizeoftheprocesszone,thattheinitialassumptionof
LEFMisbasedon.
K
Q
=
 
P
Q
BW
1
2
!
f
(
x
)(2.1)
f
(
x
)=
(2+
x
)(0
:
886+4
:
64
x

13
:
32
x
2
+14
:
72
x
2

5
:
6
x
4
)
(1

x
)
3
2
B;a;
(
W

a
)
>
2
:
5

K
Q
˙
y

2
(2.2)
Forcalculatinganaccuratecriticalstrainenergyreleaserate
G
IC
,acorrectiontotheload-
displacementcurveisrequiredduotopinpenetration.Thatinvolvesloadinganunnotched
CTsampletothepointthattheregularspecimenwouldfailthensubtractstheresulting
areaunderthecurvefromtheonesobtainedfromthenotchedsamples.Thecorrected
newenergyisrepresentingtherequiredenergyforthefractureaftersubtractingthepin
penetrationEq.2.3isusedtocalculate
G
IC
,where
U
isthecorrectedcriticalenergy
ortheareaundertheload-displacementcurve,and
;
isadimensionlessfactorthatdepends
17
ontheratio
x
=
a=W
.
G
IC
=
U
(
BW
;
)
(2.3)
;
=
(1
:
9118+19
:
118
x

2
:
5122
x
2

23
:
226
x
3
+20
:
54
x
4
)(1

x
)
(1
:
9118

5
:
0244
x

69
:
678
x
2
+82
:
16
x
3
)(1

x
)+2(1
:
9118+19
:
118
x

2
:
5122
x
2

23
:
226
x
3
+20
:
54
x
4
)
2.2
MaterialsandMethods
Twothermosetepoxyresinshavebeencharacterizedforfracturetoughnessinthisthe-
sis:SC-15andEPON862.SC-15,alow-viscosity,rubbertoughenedepoxycuredwith
aCycloaliphaticamine,wasobtainedfromAppliedPoleramic(Benicia,CA).EPON862
(di-glycidyletherofbisphenol-Fepoxy(DGEBF))anditscuringagent`W'(DETDA(di-
ethyltoluenediamine))wereobtainedfromMiller-StephensonChemicalCo.Thenanopar-
ticlesthatwereusedinthisstudyareGraphenenanoplateletsandnano-silica.Graphene
Nanoplatelets(xGnP)areuniquenanoparticlesconsistingofshortstacksofgraphene.xGnP
gradeCparticlesobtainedfromXGSciences,consistofaggregatesofsub-micronplatelets
thathaveaparticlediameteroflessthan2micronsandatypicalparticlethicknessofafew
nanometerswithaveragesurfaceareasof750
m
2
=g
[28].Thenano-silicaparticles(MEK-
AC-5140)withanaveragediameterof80
nm
wereobtainedfromNissanChemicalAmerican
Corporation.Dr.ShiwangCheng,afacultymemberoftheChemicalengineeringandmate-
rialssciencedepartmentofMSU,suppliedtheparticlesandpreparedtheepoxieswiththe
nanoadditive.xGnPweredispersedintoEPON862andSC-15in0.1wt%and0.5wt%while
thenano-silicaparticlesweredispersedonlyinEPON862in0.1wt%and0.5wt%.Thedis-
persionmethodisanessentialstepforgettingthemostmechanicalbondingandenhancing
themechanicalperformance.tdispersionmethodswerereviewedinsection1.3.2.
18
xGnPweredirectlydispersedinTetrahydrofuran(THF)ataconcentrationof0.1wt%.The
Graphene/THFsuspensionwasfurtherdispersedwith1-hoursonicationbeforedispersing
intoEPON862andSC-15.TheNano-silicaparticles(MEK-AC-5140)wereprecipitated
intoHexaneandresuspendedintoTetrahydrofuran(THF)uptoaconcentrationof10wt%
beforedispersingintotheEPON862.AftertheepoxiesbeingdeliveredbyDr.Cheng,we
stillhaveonemoresteptopreparethemformanufacturing,whichissolventevaporation.
Forepoxiespreparedwiththenanoparticles,fullevaporationofthesolventisneeded
beforestartingtomixtheepoxieswiththecuringagents.Otherwise,amassivereduction
inthemechanicalpropertieswilloccur.Therearemultiplemethodstoevaporatesolvents,
dependingontheamountofsolventandequipmentavailability.Inoursituation,avacuum
chamberwasusedtoreducetheboilingtemperatureofthesolvent;however,itwasfoundto
beinadequate.Subsequently,aheatingsourcewasusedtoreduceviscosityandtomakeit
easierforthesolventtobereleased,Figure2.2.Forthelaststageoftheevaporation,stirring
theepoxieswereneededtoensuretheremovalofallunwantedsolvent.Allthesestepswere
weightmonitoredbyweightingthemixturetogettingridofallthesolvent.These
stepstookanaverageofsixdays.
2.2.1
CuringCycleandSpecimenPreparation
Themixingweightratiooftheepoxiestocuringagentsis100:30forSC-15and100:26.4
forEPON862,asrecommendedbythemanufacturer.Themixtureofthetwosystemswas
degassedusingaregularvacuumchambertoremovethebubblescreatedduringthestirring
process.Ittook25mintoremoveallbubblesinSC-15.ForEPON862,additionalheating
isrequiredsinceEPON862hasahigherviscositycomparedtoSC-15.Afterdegassing,the
resinswerepouredintothepreheatedsiliconmolds.Thesiliconmoldsweremadewitha
19
Figure2.2:Solventevaporationprocess.
stainlesssteelprototype,whichwasmachinedusingElectricalDischargingMachine(EDM),
asshowninFigure2.3.
Afterpouringthemixture,thesiliconmoldswereplacedintoanovenandsubjectedto
acurecyclewingliterature[18,29]andconsideringmanufacturerrecommendations.For
SC-15,thesampleswerecuredat60

Cfor4hoursandthenpost-curedat121

Cforother
3hours.ForEPON862,thecyclehastworamps:theonefor30minfrom90

Cto
121

C,thenmaintainingat121

Cfor2h.Thesecondrampisforanother30minfrom
121

Cto177

Candthenmaintainsthetempat177

Cforanother2h.Afterthecuring
cyclethemoldswerecooledtoroomtemperature,andthesampleswerereadyto
betested,seeFigure2.4.
AsshowninFigures2.5and2.6,theoriginalcolorofEPON862samplesisyellow
20
Figure2.3:Sample'sdesignandsiliconmolds:(a)Thedesignthestainlesssteelprototype
in(mm)following
thestandards[5].(b)Thestainlesssteelprototype
andthesiliconmold.Figure2.4:Aftercompletingthecuringcycle:(a)Samplesliftinsidetheopendooroventocooldownafter
thecuringcycle.(b)Samplesarereadytobecarefullyextractedfromthemolds.
21andtransparent,whereasSC-15samplesarewhiteandopaque.Afteradding0.1wt%of
xGnP,theEPON862samplesturnedinblackwhiletheSC-15samplesbecamedarkgray.
With0.5wt%ofxGnP,EPON862stayedblackandtheSC-15changedtofullyblack.For
EPON862sampleswith0.1wt%and0.5wt%ofnano-silica,thesampleslostitstransparent
gradually.Fordigitalimagecorrelation(DIC)measurement,allsampleshavebeenpainted
withwhiteandthenblackspraypainttocreatespecklesonsurface.
Figure2.5:SC-15samples,fromright:baseline,0.1wt%,then0.5wt%ofxGnP.
Figure2.6:EPON862samples:(a)0.1wt%,0.5wt%ofnano-silica.(b)0.1wt%,0.5wt%ofxGnP.(c)Baseline.
2.3
ExperimentSetup
ForthefracturetoughnessModeIexperiment,ASTMstandardD5045[5]hasbeenfollowed.
TheexperimentswereperformedusingtheMTSInsightElectromechanicaltestframewith
10KNloadingunit,asshowninFigure2.7.Tocapturetheimagesduringexperimentfor
DICmeasurement,aStingraycamerawithimagepre-processingbyAlliedVisionwasused.
22
Figure2.7:Theexperimentsetupwithcameraandlightsource.
Theimageswererecordedatarateof20imagespersecondtomatchthemachine'ssampling
rateof20Hz.Thetestsrunningtimewereabout3to5.5secondsdependingonthematerial
andtheamountofneededforfracturewithcross-headspeed10
mm=min
.Duo
tothesmallsizeoftheCTspecimenusedinthiswork,insteadofusingstandardcompact
tension(CT)analternativeloadingmethodwasdevelopedasshowninFigure2.8.A
5mmhollowtensionpinandatoughcopperaluminumwirewereusedtolinkthespecimens
tothetestingmachineusingtheregulartensilegrip.Additionalattentionwaspaidto
thesamples'alignmentforeverytrialtoensurehavingtheloadperpendiculartothecrack
surface.Thedimensions,theinitialandcracklengthofthesamplesweremeasured
perASTMstandardD5045.Afterperformingthetestandobtainingdataandimages,DIC
analysiswasperformedandtheresultwillbediscussedinchapter3.
23
Figure2.8:Samplesarrangementbeforeattachingtothetensilegrip:(a)Frontview.(b)Sideview.
2.4
DataAcquisition
DICisanon-contactopticaltechniqueforthemeasurementofdeformation,and
strainonthesurfaceofmaterialsandstructures.Itcanbeusedinbothstaticanddynamic
conditions,anditsapplicationsrangefrommicrosizetestingtolargestructures.Inme-
chanicaltestingsuchastensile,torsion,bending,andfracturetesting,DIChasbeenused
toreplacestraingaugeandextensometermeasurement.
DICanalysiswasperformedusingGOMsoftware.ThefourimagesinFigure2.9show
thetypicaldeformationprocessofaCTspecimeninfracturetesting.Usinganoptical
extensometerinGOM,thedisplacementattheloadingpointwasmeasured.The
load-displacementcurvewasthenusedtocalculatetheenergyreleaserates.Thismethodis
moreaccuratethanthedisplacementrecordedbythecross-headdisplacementofthetesting
machine.AnothermeasurementwastheCracktipopeningdisplacement(CTOP).CTOPisa
fracturecriterionassociatedwithEPFM.Itisalsohelpfulforrecordingthesmallplasticityat
thecracktip.Thepositionswheretheloading-pointdisplacementandCTODweremeasured
wereindictedinFigure2.9.TheDICdisplacementresolutionis
˘
0
:
002
mm
,andtheDIC
strainresolutionis
˘
0
:
1%.
24
Figure2.9:Theexperiment'sstagesuntilthefracture:(a)Thesecondstillimage.(b)Themiddleofthe
test.(c)Themomentbeforethefracture.(d)Themomentafterthefracture.
25
Chapter3:
ResultsandDissection
Inthischapter,theofpre-crackingmethodwasexaminedusingtheresultsofEBON
862specimens.Thentheexperimentalresultsoffracturetoughnessoftwoepoxieswiththe
nano-additivesarepresented.Inthelastsection,thecracktipplasticzoneswereanalyzed,
andtheresultswerecomparedwiththeexperimentalobservations.
3.1
tPre-crackingProceduresandtheir
Thepurposeofpre-crackingistointroduceaninitialcracksimilartothatnaturallyproduced
duringcrackpropagationprocess.Themeasuredfracturetoughnessdependsonthewayhow
theinitialcrackisintroduced.Toinvestigatetheofinitialcrack,McAninch[29]
createdthecrackbyseveralmethods,suchasinsertingttypesofthininto
polymersamplesbeforecuring;scoringthesampleswithathindouble-edgedrazorblade;
andusingthicksingle-edgedrazortomake\instantlypropagated"cracks,i.e.anaturalcrack
propagatedaftertherazortip.Itwasfoundthat,unlikeinstantlypropagatedcracks,the
specimenswithinitialcrackbyrazorscoringorinsertingthinyieldedhigherfracture
toughnessvalues.McAninch'sstudyraisestheofhavingasharpcrackinfracture
toughnessmeasurement.
ASTMD5045standardrecommendsapre-crackingprocedureusingarazor.Tocreate
apre-crackinanotchedspecimen,itsuggeststhatonecaneithertapetherazorbyhand
orapplyaslidingmotion.Inthiswork,bothmethodshavebeentried.However,tapingby
handwasnotttointroduceaninitialcrack.Toincreasetheload,amechanicalvise
wasemployedtopressthebladeintothenotch,asshowninFigure3.1(a).Ontheother
26
Figure3.1:Thetwomethodsofpre-cracking:(a)Pressingtherazorintothenotch.(b)Slidingtherazoron
thenotch.
hand,themethodofapplyingaslidingmotionwassuccessfultogenerateaninitialcrack.
ThismethodisshowninFigure3.1(b).
Table3.1presentsthefracturetoughnessvaluesmeasuredwiththreeEPON862baseline
specimens:onewiththeinitialcrackgeneratedbypressingtherazorintothenotch,andthe
othertwowiththeinitialcrackgeneratedbyslidingmotion.The
K
IC
valueofthespecimen
pre-crackedbyforcingtherazorintothesampleis
ˇ
1
:
99
MPa:
p
m
,andfor
G
IC
is
ˇ
1397
J=m
2
.Thetwospecimenspre-crackedbyslidingtherazoryieldedlowerfracturetoughness.
Themeasuredvalueswere
ˇ
1
:
25
MPa:
p
m
and
ˇ
0
:
75
MPa:
p
m
in
K
IC
,and
ˇ
623
J=m
2
and
ˇ
201
J=m
2
in
G
IC
.Theresultsshowthatpre-crackmadebypressingtherazorledtoa
muchhighermeasuredfracturetoughnessthanthatmadebyslidingmotion.Furthermore,
EPON862baselinematerialappearedtobeverysensitivetothepre-crackingprocess.Even
forthespecimenspre-crackedwiththesameslidingmotion,themeasuredfracturetoughness
wasquitet.
27
Table3.1:Comparisonbetweentwotpre-crackingmethodsonEPON862'sfracturetoughness
K
IC
(
MPa:
p
m
)
G
IC
(
J=m
2
)
Sliding0.75201
Sliding1.25623
Pressing1.991397
Table3.2comparesthefracturetoughnessvaluesmeasuredwithtwoSC-15baseline
specimens.Again,thepre-crackintroducedbypressingtherazoryieldedahigherfracture
toughnessvaluethantheonewithslidingmotion.Itwassuspectedthatpre-crackingby
pressingtherazormayintroducelocalcompressiveresidualstressesatthecrack-tip.To
examinethisDICwasusedtomeasurethestrainbeforeandafterthepre-
crackingprocedurebypressingtherazor.Figure3.2presentstheDICresultsforaEPON
862baselinespecimeninthisprocess.Asshown,pre-crackingleftacompressiveresidual
strainatthecracktip.Themeasuredmaximum

x
strainvaluewas-6.672%.Witha
compressiveresidualstressnormaltothecracksurface,theforcerequiredforMode-Itype
crackpropagationwouldbehigher.Thisexampleshowsthatthemeasuredhigherfracture
toughnessusingspecimenspre-crackedbypressingtherazoristheartifactofimproperpre-
crackingmethod.ItisnotedthatthefracturetoughnessmeasurementforSC-15appeared
tobelesssensitivetothepre-crackingmethodascomparedthattoEPON862.Thiscan
beattributedtothefactthatSC-15neatresinisrubbertoughened.Itisnotasbrittleas
EPON862neatresin.Indeed,thexGnPandtheNano-silicamoEPON862resins
werelesssensitivetopre-crackingprocess,astobediscussedinthenextsection.
Table3.2:Comparisonbetweentwotpre-crackingmethodsonSC-15'sfracturetoughness
K
IC
(
MPa:
p
m
)
G
IC
(
J=m
2
)
Sliding1.547965
Pressing2.121550
28
Figure3.2:Thestrainofthepressedsample:(a)Beforeinsertingtheblade.(b)
xafterinsertingthe
blade.(c)
yafterinsertingtheblade.
293.2
FracturetoughnessResults
TheMode-IfracturetoughnessoftheEPON862andSC-15baselineresinsandthenano
additivemotworesinswasmeasuredfollowingASTMD5045standardusingCTspec-
imenspre-crackedbyusingarazorwithslidingmotion.Thecriticalstressintensityfactor
K
IC
andthecriticalenergyreleaserates
G
IC
weredetermined.
3.2.1
EPON862
Figure3.3comparesthetypicalload-displacementcurvesofEPON862baselineandEPON
862with0.1and0.5weightfractions(wt%)ofxGnP.Ascanbeseen,addingxGnPincreased
theslopoftheload-displacementcurvesandthemaximumload.However,itdidnotchange
theshapeofthecurve.Allsamplesexhibitedalinearcurveuptofailure,indicatingbrittle
fracture.Therefore,themaximumloadswereusedtocalculatethefracturetoughnessvalue.
Figure3.3:LoadvsLoading-pointdisplacementofEPON862withxGnP.
30
Figure3.4andTables3.3,3.4comparethefracturetoughnessvaluesofEPON862resins.
Thebaselinesamplesweresensitivetothepre-crackingandthereforethescatterinmeasured
fracturetoughnessvalueswashigh.Thisisshownbytherelativelyhighstandarddeviation
(SD)andthestandarderrorofthemean(SEM)values.xGnPmoEPON862showed
muchsmallerscatterinfracturetoughnessmeasurement.Adding0.1wt%ofxGnPresulted
animprovementin
K
IC
by
˘
44.87%and
G
IC
by
˘
87.38%.Adding0.5wt%ofxGnPfurther
improved
K
IC
by
˘
70%,and
G
IC
by
˘
156.6%.
Figure3.4:
K
IC
and
G
IC
ofEPON862withxGnP.
Table3.3:
K
IC
(
MPa:
p
m
)averagesofEPON862withxGnP
K
IC
SDSEMImprovementNo.S
Baseline1.0063

0.27

0.095-8
0.1wt%1.4578

0.05

0.02344.87%5
0.5wt%1.7114

0.09

0.03970%5
Table3.4:
G
IC
(
J=m
2
)averagesofEPON862withxGnP
G
IC
SDSEMImprovementNo.S
Baseline412

221

78-8
0.1wt%772

70

3187.38%5
0.5wt%1058

44

20156.59%5
31
ToexaminethereinforcingoftnanoEPON862hasalsobeenmodi-
withnano-silica.TheresultsareshowinFigure3.5andTables3.5,3.6.Adding0.1wt%
nano-silica,theimprovementto
K
IC
was
˘
30.76%and
G
IC
˘
48.85%.With0.5wt%of
nano-silica,
K
IC
wasincreasedby
˘
43.697%,and
G
IC
by
˘
86.52%.Comparingwiththe
resultsofxGnP,theimprovementwithnano-silicawasaboutahalfofthevalueofthatwith
xGnP,asshownbyFigure3.5.TheresultsshowthatxGnPisamoretadditiveto
EPON862thannano-silica.
Figure3.5:ComparisonbetweenEPON862withxGnPandEPON862withNano-Silicafortweight
fractions.
Table3.5:
K
IC
(
MPa:
p
m
)averagesofEPON862withNano-silica
K
IC
SDSEMImprovementNo.S
Baseline1.0063

0.27

0.095-8
0.1wt%1.3154

0.07

0.03830.76%4
0.5wt%1.4456

0.06

0.03134.69%4
Table3.6:
G
IC
(
J=m
2
)averagesofEPON862withNano-silica
G
IC
SDSEMImprovementNo.S
Baseline412

221

78-8
0.1wt%613

79

3948.58%4
0.5wt%769

102

5186.52%4
32
3.2.2
SC-15
ForSC-15,theresultsshowedaslightimprovementinboththestressintensityfactor
K
IC
andstrainenergyreleaserate
G
IC
whenadding0.1wt%ofxGnP.However,theenhancement
startedtodiminishforhaving0.5wt%ofthesameparticles.
Figure3.6:LoadvsLoading-pointdisplacementofSC-15withxGnP.
Figure3.6comparesthetypicalload-displacementcurvesofSC-15baselineresinand
SC-15mowithxGnP.Allthreetypesofsamplesdisplayedabrittlefracture.SC-15
with0.1wt%showedaslightlyhighermaximumload.However,thecurveforSC-15with
0.5wt%xGnPdisplayedaslopeevenlowerthanthebaseline,indicatingalowerof
thisspecimen.ACTspecimencanhaveloweraseachspecimenmayhaveaunique
initialcracklength.ToprecludethistheinitialcracklengthsofallCTspecimens
wereexaminedtoensurethattheload-displacementcurvesofthreetypesofSC-15samples
werecomparedusingthespecimenswithsimilarinitialcracklength.Itwasfoundthatthe
slopesfortheload-displacementcurvesofSC-15with0.5wt%xGnPwereconsistentlylower
33
thanthetwoothertypesofSC-15samples.Thiscouldbecausedbyresidualsolventinthis
typeofsamples.Whensolventisnotremovedcompletely,thenanoadditivemoepoxy
resincanbehavesofterthanthebaselineresin.Therefore,thedatawithSC-15with0.5wt%
xGnPpresentedhereshouldbetreatedwithcaution.
Figure3.7andTables3.7,3.8comparethefracturetoughnessofSC-15baselineresinand
SC-15with0.1Wt%,0.5wt%xGnP.UnlikethecaseofbrittleEPON862baselinesample,
SC-15baselinesampleswerenotsensitivetothepre-cracking.Adding0.1wt%ofxGnP
resultinanimprovementof
K
IC
by
˘
8.81%and
G
IC
by
˘
21%.SC-15with0.5wt%of
xGnPresultedmuchsmallerimprovementinfracturetoughness.
K
IC
improvedby
˘
2.63%
andthe
G
IC
increasedby
˘
14.6%.Thislimitedenhancementinthefracturetoughnessmay
beattributedtothefactthatSC-15isalreadyrubbertoughened.Ontheotherhand,the
resultforSC-15with0.5wt%ofxGnPpresentedheremaynottherealtrend.As
statedpreviously,itispossiblethatthesolventwasnotremovedcompletelyinthistypeof
material.
Figure3.7:
K
IC
and
G
IC
ofSC-15withxGnP.
34
Table3.7:
K
IC
(
MPa:
p
m
)averagesofSC-15withxGnP
K
IC
SDSEMImprovementNo.S
Baseline1.5476

0.03

0.015-5
0.1wt%1.6840

0.05

0.0208.81%7
0.5wt%1.5884

0.06

0.0242.63%7
Table3.8:
G
IC
(
J=m
2
)averagesofSC-15withxGnP
G
IC
SDSEMImprovementNo.S
Baseline965

46

20-5
0.1wt%1168

115

4321%7
0.5wt%1106

83

3114.6%7
3.3
StressDistributionandPlasticityCorrection
Thecracktipstressisaclassicproblemoffracturemechanics.Foracentercrackin
anlargeplatesubjectedtobiaxialloading,theLEFMsolutionforelasticstresses
nearthecrack-tiphasbeenprovidedbyWestergaard[24].ForMode-Iloading
˙
x
=
K
p
2
ˇr

cos

2

1

sin

2
sin
3

2

˙
y
=
K
p
2
ˇr

cos

2

1+sin

2
sin
3

2

˝
xy
=
K
p
2
ˇr

sin

2
cos

2
cos
3

2

(3.1)
WhereKistheMode-Istressintensityfactor,risthedistancetothecracktip,

istheangle
tothex-axismeasuredatthecracktip,asshowninFigure3.8.
Figure3.8:Thestresseldnearthecracktip.
35
AlimitationofLEFMisthestresssingularityatthecrack-tip.InEq3.1,whenr
approachestozero,the
˙
x
and
˙
y
stresscomponentsbecomeInreality,aplasticity
regionwilldevelopnearthecracktipwheneverthestressexceedstheyieldstrengthofthe
materialasthecracktipradiusmustbe[6,30,31].SimplecorrectiontoLEFM,suchas
theIrwinapproachareavailablewhenmoderatecracktipyieldingoccurs[6],Forsubstantial
yielding,otherparameterssuchJ-integralforthenonlinearmaterialbehaviormustbetaken
intoaccount.Thecrack-tipplasticsizecanbeestimatedbytwomethods:theIrwinapproach
andthestripyieldmodel[6].TheIrwinapproachusestheelasticstressanalysistoestimate
theelastic-plasticboundary.Notethatthetermplasticzoneusuallyreferredtometals,but
itisusedheretodescribetheinelasticcracktipbehavior[6].Theestimationoftheplastic
zonelengthbeginsbycalculatingthenormalelasticstress
˙
y
directlyaheadofthecrack
along

=0.Astheapproximation,theboundarybetweenelasticandplasticzone
occurswhentheelasticstressessatisfyayieldcriterioninEq.3.2.
˙
y
=
K
p
2
ˇr
y
=
˙
ys
(3.2)
Forplanestressconditions,yieldingoccurswhen
˙
y
=
˙
ys
.Solvingfor
r
y
givesarst-
orderestimateofplasticzonesizeasexpressedinEq3.3.
r
y
ˇ
1
2
ˇ
K
2
˙
2
ys
(planestress)(3.3a)
r
y
ˇ
1
6
ˇ
K
2
˙
2
ys
(planestrain)(3.3b)
ThisprocessisillustratedinFigure3.9.Whenyieldingoccurs,stressesmustberedis-
tributedtosatisfytheequilibrium.Forplanestrainconditions,yieldingissuppressedbythe
36
Figure3.9:First-orderandsecond-orderestimatesofplasticzonesize(
r
y
and
r
p
,respectively).Thecross-
hatchedarearepresentstheloadthatmustberedistributed,resultinginalargerplasticzone.Obtained
from[6].
triaxialstressstate,andtheIrwinplasticzonecorrectionisreducedbyafactorof3asin
Eq3.3b[6].However,specimensalwaysfollowplanestressconditionsatthesurfacesince
thereisno
˙
z
constrainthedeformationinthethrough-thicknessdirection.
FollowingIrwin'sapproach,
˙
y
stressdistributionalongthecracksurfaceforseveralCT
specimenshasbeencalculated.First,theelasticstresswascalculatedusingEq.3.1.Next,the
orderplasticzonesizewasestimatedusingEq.3.3a.The
˙
y
stressdistributionwasthen
shiftedtotheappropriateposition.Asdiscussedearlier,DICwasusedinfracturetesting
tomonitorthedisplacementandstrainUsingDICresults,thestressdistributions
nearthecrack-tipcanbevInthiswork,thestressjustbeforefracturewas
examined.
FromtheDICimagescapturedjustbeforethefracture,thethreestraincomponents
inthefrontofthecrackpathweredetermined.
˙
y
stressalongthesamepathwasdetermined
using3DHooke'slaw.Ifthevon-Misestressvalueatapointexceedstheyieldstrength,it
isassumedtofallintotheplasticzoneandsubsequentlythestressvalueisreducedtothe
valueoftheyieldstrength.ThemechanicalpropertiesoftheSC-15islistedinTable3.9.
37
Table3.9:MechanicalPropertyofSC-15baseline.
Young'smodulus(E)YieldStrength(
˙
ys
)Poisson'sratio(
v
)
2.5
GPa
60
MPa
0.33
Thevon-MisesstressiscalculatedbyEq.3.4where
˙
1
,
˙
2
,and
˙
3
aretheprincipalstresses
and
˙
v
isthevon-Misesstress.Theassumptionisthatthematerialstartyieldingwhenthe
von-Misesstressreachestheyieldstrength
˙
ys
.
˙
v
=
1
p
2
h
(
˙
1

˙
2
)
2
+(
˙
1

˙
3
)
2
+(
˙
2

˙
3
)
2
i
1
2
(3.4)
ThreeSC-15specimenswith0.5wt%xGnPwereexaminedaslistedinTable3.10.The
proceduretocalculatetheexperimental
˙
y
stressdistributionandtheexperimentalplastic
zoneisillustratedusingspecimen1.FromDIC,thestraincomponentswererecordedfor
eachpointnearthecrack-tipalongthecrackpathwith

=0.Forexample,thestrain
componentsofthepointare

x
=-0.4259%,

y
=3.008%,

z
=-2.482%,and

xy
ˇ
0%.The
correspondingstresseswerecalculatedusing3DHooke'slawandthestresscomponents
werefoundtobe
˙
x
=-9.86MPa,
˙
y
=56.42MPa.Then,thevon-Misesstress
˙
v
inEq.3.4
wascalculatedfromtheprincipalstressesofthestresscomponents,andit'sfoundtobe
˙
v
=61.9MPa.Thatmeansthispointfallintotheplasticzone.Forthesecondpoint,the
correspondingstresseswere
˙
x
=-11.09MPa,
˙
y
=53.64MPa.ThevonMisesstressis
˙
v
=60MPa=
˙
ys
.Thispointwassetastheelasticitylimitsincetheestressreaches
theyieldstrengthandthepreviouspointwerereducedtothislimit,asshowninFigure
3.10.Fromthislimit,thecorrespondinglengthfromthecracktipwassetastheestimated
experimentalplasticzone,anditisfoundtobe24

mforthissample.
ThisprocesswasrepeatedforallDICpointsnearthecrackusingExcel,andthecurves
of
˙
y
wereplotted.Forthesecondandthethirdspecimen,thesameprocesswaspreformed.
38
Table3.10:ThethreeexamplesamplesofSC-15with0.5wt%xGnP.
Specimen1Specimen2Specimen3
Pre-crackingmethodSlidingSlidingOneroundsliding
WidthW(
mm
)24.223.9223.8
Cracklengtha(
mm
)11.4811.1311.06
ThicknessB(
mm
)6.045.96.12
Criticaldisplacement(
mm
)0.330.390.48
P
Q
(
N
)161159228
K
IC
(
MPa:
p
m
)1.5381.5452.1
G
IC
(
J=m
2
)94611011835
First-orderplasticzone
r
y
(

m)104105195
Second-orderplasticzone
r
p
(

m)208210390
Experimentalplasticzone(

m)24196311
Theestimationoftheexperimentalplasticzonewasfoundtobe196

mand311

mforthe
secondandthirdspecimenrespectively.
Figure3.10forthesampleandFigure3.11forsecondsampleshowsthetheoretical
andtheexperimentalstressforthenormaly-direction.Basedoneachsampleparameters,
theelasticstressdistributionwasdrawnusingEq.3.1forbothsamples.UsingEq.3.3b,the
plasticzone
r
y
wasfoundtobe34.87

mforthesampleand35.20

mfor
thesecondonewhilethesecond-orderofplasticzonesaredoubletheBasedonthat,a
newlinehasbeenplacedfortheredistributedstress,consideringtheplasticzone.
Thetwosampleshaveafractureloadabout160Nandtheir
K
IC
valueswerevery
close.However,thecriticalloadingpointdisplacement(u)andcriticalstrainenergyrelease
rate(
G
IC
)valuesweret.Thesamplehasacriticaldisplacementof0.33mm
and
G
IC
of946
J=m
2
whilethesecondonehasacriticaldisplacementof0.39mmand
G
IC
1101
J=m
2
.Thesamplefracturedasitreachedtheyieldstrengthofthematerialwitha
plasticzonemuchsmallerthantheIrwinplasticzoneestimation,whilethesecondsample
crackedwithaplasticzonequitesimilartotheIrwinplasticzoneestimation.
39
Figure3.10:Thespecimen'snormalstress
˙
y
distributionalongthecrackpathjustbeforethefracture.
Figure3.11:Thesecondspecimen'snormalstress
˙
y
distributionalongthecrackpathjustbeforethe
fracture.
40
ThethirdsampleinTable3.10andFigure3.12thatwasnotcorrectlypre-cracked
recordedahighercriticalloadabout228N,higher
K
IC
about2.1
MPa:
p
m
,andahigher
G
IC
about1835
J=m
2
.Thetheoreticalsolutionofthestressdistributionalsocomparedto
theexperimentalstressforthenormaly-direction,asitcanbeseeninFigure3.12.The
samplefracturedasitreachedtheyieldstrengthofthematerialwithaplasticzonelessthan
theIrwinplasticzoneestimationby25%.
Figure3.12:Thethirdspecimen'snormalstress
˙
y
distributionalongthecrackpathjustbeforethefracture.
Thetypical(loading-pointdisplacementversaloading)'scurves,thatusedfordetermining
theenergyneededforthefracture,arenotgivinganyinductionofplasticityatthecracktip.
Allcurvesshowlinerrelationshipuntilthefractureoccurs.However,thecracktipopening
displacement(CTOD)isfoundtothisifthesamplehasaplasticityregionaround
thecracktipandhowfar.Forthethreesamplesdiscussedearlier,anopticalextensometer
isusedtoobtaintheCTODandthebetweenthesesamplesbecameclear.As
41
showninFigure3.13,thesampleappearedtohaveaverysmallplasticzonewhilethe
thirdsamplehasthemost.Thismethodofanalysistiatedbetweentheandthe
secondsampleintermofplasticzonewhereasaccordingtotheLEFMtheoriesthevalues
wereveryclose.CTODisassociatedwiththeElastic-PlasticFractureMechanicsEPFM;
however,itisevidentthatthismeasurementisalsorelevanttotheLEFMespeciallyunder
theplanestrainconditionsbecauseofthesmallplasticzonearoundthecracktip.
Figure3.13:LoadvsCTODforthethreesamples.
42
3.3.1
CreagerandParis(1967)'sEstimation
ThestressEquations3.1andCreagerandParis[32]Equations3.5arethetwosets
ofequationsdescribingtheelasticstressnearthecracktip.CreagerandParis(1967)
Equations3.5hastheWestergaardpartofthesolutionplusconsideringtheblunting
WithCreagerandParis'sEquations3.5,wehaveastressdistributionconsidering
thecracktipradiuswhilewithEquations3.1,Irwinmowasneededtolimitthe
y.StressEquations3.1estimatesthat
˙
y
equals
˙
x
foraverysharpcracktip;
however,thatisn'tsuitableforarealmaterial.Instead,CreagerandParis(1967)looked
atthesolutionfromatperspectivebystatingthatthecracktipinactualmaterial
wouldbeblunt,andthetipwouldhavearadius(
ˆ
).Sothatthe
˙
x
startsfrom0atthe
cracktipandthenreachesthemaximumvalueatashortdistance.
˙
x
=
K
p
2
ˇr

cos

2

1

sin

2
sin
3

2

+
K
p
2
ˇr
ˆ
2
r


cos
3

2

˙
y
=
K
p
2
ˇr

cos

2

1+sin

2
sin
3

2

+
K
p
2
ˇr
ˆ
2
r

cos
3

2

˝
xy
=
K
p
2
ˇr

sin

2
cos

2
cos
3

2

+
K
p
2
ˇr
ˆ
2
r


sin
3

2

(3.5)
AcomparisonbetweenthetwotheorieshasbeenmadeinFigure3.14.Itcanbesaidthat
CreagerandParis'sestimationfor
˙
y
isclosetotheIrwin'smothatconsidersthe
plastictothepointoftheestimatedmaximumstress.Afterthat,theydisagreesince
CreagerandParissolutiondoesn'tconsiderplasticity.For
˙
x
,theconsiderationofblunting
isneededsincetheexperimentaldataof
˙
x
iswaybellow
˙
y
.Forcalculating
˙
y
and
˙
x
,CreagerandParis(1967)Equations3.5hasbeenusedat

=0and(
r
)startsfrom
ˆ
2
accordingtothetheory.Foroursamples,thecracktipradiuswasmeasuredusingadigital
43
microscopeandthevaluewasfoundtobeabout60

m.
Figure3.14:ComparisonbetweenIrwin'smoandCreagerandParis'sestimation.
3.3.2
StressDistributionfortSamples'Loading
Theexperimentalstressdistributionalongthecrackpathhasbeenstudiedfort
loadinguntilthefracture,asshowninFigure3.15.Itisobvioushowthestressstartsto
concentratenearthecracktipwhileloadingthespacemanuntilthefractureoccurred.Duo
tothewaythatthecompacttensionsamplesareloaded,acompressivestressisrecorded
after9
mm
fromthecracktip,whichalsoincreaseswhileloadingthesample.158Nisthe
peakloadbeforethefracture.
44
Figure3.15:Thenormalstress
˙
y
distributionalongthecrackpathfortloading.
3.3.3
PlasticZoneShape
Toestimatetheplasticzoneforallangles,anappropriateyieldcriterionhastobeappliedto
theelasticstressEquations3.1.ConsideringthevonMisescriterion3.4where
˙
v
isthe
vonMisesstress,and
˙
1
,
˙
2
,and
˙
3
arethethreeprincipalnormalstress.BasedontheVon
Misescriterion,yieldingoccurswhen
˙
v
=
˙
ys
andtheprincipalstressescanbeobtainedfrom
Mohr'scirclerelationship.Then,bysubstitutingtheModeIstressintotheprincipal
stressesandthenintotheVonMisesEquation3.4,solvingfor
r
y
willresultintheestimate
ofModeIplasticzoneradiusasafunctionof(

)Equation3.6.
r
y
(

)=
1
4
ˇ

K
I
˙
ys

2

1+cos

+
3
2
sin
2


(3.6)
Figure3.16showstheterenceinsizeandshapeoftheplasticzonesbetween
theplanestressandplanestrainconditions.TheestimatesofModeIplasticzoneradius
45
asafunctionof(

)andshowninFigure3.16arenotfullycorrectbecausetheyarebased
onthepurelyelasticanalysis,andtheredistributionofthestresshasnotbeentakeninto
account.EventheIrwinplasticitycorrectionisnottotallycorrect[6,33].Figure3.17
showsacomparisonbetweentheplanestrainplasticzoneshapeestimatedfromEq.3.6with
theelastic-plasticcracktipstressobtainedfromelementsimulation,wheren
characterizesthestrainhardeningrateofmaterial,and

isadimensionlessfactor.The
stressdistributionassociatedwiththesimulationseemstobetiltedtothesidealittlefrom
theplasticzoneshapeestimatedfromtheequation.
Figure3.16:TheplasticzoneshapeestimationfromtheelasticsolutionforModeI.Obtainedfrom[6].
Figure3.17:TheestressfromaelementanalysisVstheplasticzoneestimation[6].
46
Digitalimagecorrelation(DIC)allowsustovisualizethestraindistributionaroundthe
crack,whichwillgiveanideaofwhatshapethestrainandstressaredistributed.Asitcan
beseeninFigure3.18,thenormalstraininthey-directionarealsotiltedtotheopposite
sideofthecrack,whichmatchestheeelementanalysisoftheestressinFigure
3.17.Asdiscussedbefore,theestimationoftheplasticshapewasnottotallycorrectbecause
itwasbasedonanelasticanalysis.
Figure3.18:Straindistributionofy-direction.
47
Chapter4:
Conclusion
4.1
SummaryandConclusion
ThisresearchinvestigatedtheofGrapheneNanoplatelet(xGnP)onthefracture
toughnessofEPON862andSC-15.Intwoweightratios,thexGnPwasdispersedintothe
twoepoxyresins:0.1wt%and0.5wt%.Forthesakeofcomparison,nano-silicaparticles
wereaddedtoEBPN862.Thefracturetoughnessofthebaselineandreinforcedresinswas
investigatedwiththecompacttension(CT)experiment.
ItwasobservedthatxGnPresultedinagreaterimprovementinthefracturetoughness
ofEPON862thanthatofSC-15.ForEPON862,the
G
IC
valuewas412,772,1058
J=m
2
forthebaseline,0.1wt%and0.5wt%reinforced,respectively,representinganimprovement
of87%and156%.The
K
IC
valuewas1.0,1.45,1.71
MPa:
p
m
forthebaseline,0.1wt%and
0.5wt%reinforced,respectively,representinganimprovementof45%and70%.ForSC-15,
the
G
IC
valuewas965,1168,1106
J=m
2
forthebaseline,0.1wt%and0.5wt%reinforced,
representinganimprovementof21%and14%.TheKICvaluewas1.54,1.68,1.58
MPa:
p
m
forthebaseline,0.1wt%and0.5wt%reinforced,representinganimprovementof8.8%and
2.6%.TheadditionofxGnPledtomarginalimprovementat0.1wt%.Thisstartedto
diminishat0.5wt%.ThentofxGnPbetweenthetwoepoxiesisassumedtobe
becauseSC-15isalreadyrubbertoughened.Forcomparison,EPON862wasalsoreinforced
with80
nm
diameternano-silicaparticles.At0.1wt%and0.5wt%,theimprovementin
G
IC
was49%and87%,respectivelyandtheimprovementin
K
IC
was30%and34%.Itcanbe
saidthatnano-silicaimprovedthe
G
IC
by
˘
50%and
K
IC
by
˘
64%oftheenhancement
obtainedbyaddingxGnPforbothweightfractions.
48
Toconclude,addingxGnPwillgreatlyincreasethefracturetoughnessofafairlybrittle
epoxysystem.xGnPisfoundtobemuchmoretthannano-silicaatalowconcen-
tration.Themethodofintroducingthepre-crackwasfoundtohaveamajorimpactonthe
measurementoffracturetoughnessvalueincompacttension(CT)experiments.Theresid-
ualstrainresultingfrompre-crackingprocedurewereanalyzedusingtheDigitalImage
Correlation(DIC)method,andthecorrespondingresidualstresswerecalculated.It
wasobservedthatthepre-crackingprocedurethatleaveshighcompressiveresidualstresses
atthecracktipresultinanincreasedfracturetoughnessvalue.
4.2
FutureWork
Thefollowingimportantstepwouldbefractography,whichisthemicroscopicobservation
ofthefracturesurfaces,forinterpretingthefracturemechanismsthatoccurredinthetested
specimen.Thenextmilestonewouldbetestingtheenforcedepoxieswither-reinforced
polymer(FRP)compositesalongwithemployingothercompositeenforcementmethods
suchasaquasi-three-dimensional(Q3D)braideder.Theinvestigationcouldinclude
quantifyingtheenhancementcausedbythetwomethodstoMode-IandMode-IIinterlaminar
fracturetoughnessandimpactresistance.
49
APPENDIX
50
FigureA.1:Compacttensionspecimenation.
TableA.1:SC-15Samples-baseline.
Sample1Sample2Sample3Sample4Sample5
W(
mm
)23.9524.092423.9824.03
a(
mm
)11.1511.1711.1311.1611.12
B(
mm
)6.256.356.245.885.9
P
Q
(
N
)176173173156166
K
IC
(
MPa:
p
m
)1.591.521.551.491.56
G
IC
(
J=m
2
)9921023984894930
TableA.2:SC-15Samples-0.1wt%xGnP.
Sample1Sample2Sample3Sample4Sample5Sample6Sample7
W(
mm
)2423.6524.3423.7823.7423.8523.83
a(
mm
)11.1211.09511.18411.10411.1061.1141.109
B(
mm
)66.216.295.845.825.655.45
P
Q
(
N
)173196184174172159162
K
IC
(
MPa:
p
m
)1.631.771.741.681.671.601.68
G
IC
(
J=m
2
)1144138211761097101310871276
TableA.3:SC-15Samples-0.5wt%xGnP.
Sample1Sample2Sample3Sample4Sample5Sample6Sample7
W(
mm
)2423.923.823.923.9224.223.7
a(
mm
)11.3811.3311.1511.1511.13111.4811.06
B(
mm
)6.156.156.056.25.96.045.83
P
Q
(
N
)170181169180158161153
K
IC
(
MPa:
p
m
)1.5161.711.591.641.541.531.55
G
IC
(
J=m
2
)117511781194110911019461037
51
TableA.4:EPON862Samples-baseline.
Sample1Sample2Sample3Sample4Sample5Sample6Sample7Sample8
W(
mm
)2424.0524242424.0524.124
a(
mm
)1111.211.511.0311.11.1051.10611.5
B(
mm
)5.9565.86.476.036.76.176.03
P
Q
(
N
)92816414314214714872
K
IC
(
MPa:
p
m
)0.850.760.651.221.311.211.310.7
G
IC
(
J=m
2
)254197169481651631729183
TableA.5:EPON862Samples-0.1wt%xGnP.
Sample1Sample2Sample3Sample4Sample5
W(
mm
)24.052424.0824.1524.4
a(
mm
)11.2111.2411.2811.3511.3
B(
mm
)5.835.65.75.645.7
P
Q
(
N
)148146147138159
K
IC
(
MPa:
p
m
)1.431.471.441.41.54
G
IC
(
J=m
2
)994821719666862
TableA.6:EPON862Samples-0.5wt%xGnP.
Sample1Sample2Sample3Sample4Sample5
W(
mm
)24.324.224.224.5524.2
a(
mm
)11.6411.511.5911.8311.59
B(
mm
)5.956.146.26.066.1
P
Q
(
N
)189177190170185
K
IC
(
MPa:
p
m
)1.851.661.781.641.62
G
IC
(
J=m
2
)1121104110949951038
TableA.7:EPON862Samples-0.1wt%Nano-Silica.
Sample1Sample2Sample3Sample4Sample5
W(
mm
)24.224.224.3924.1424.1
a(
mm
)11.3911.411.1811.2411.21
B(
mm
)6.146.176.066.16.2
P
Q
(
N
)146128140154145
K
IC
(
MPa:
p
m
)1.351.181.311.411.31
G
IC
(
J=m
2
)742536600659530
52
TableA.8:EPON862Samples-0.5wt%Nano-Silica.
Sample1Sample2Sample3Sample4
W(
mm
)24.0924.324.5824.6
a(
mm
)11.4511.521211.51
B(
mm
)5.825.855.365.61
P
Q
(
N
)135152130151
K
IC
(
MPa:
p
m
)1.341.481.441.50
G
IC
(
J=m
2
)635727798914
FigureA.2:Microscopicimageofacracktipmadebyrazorsliding.
FigureA.3:Microscopicimageofacracktipmadebyrazorpressing.
53
BIBLIOGRAPHY
54
BIBLIOGRAPHY
[1]
D.L.Hunston,R.J.Moulton,N.J.Johnston,andW.Bascom,\Matrixresin
incompositedelamination:modeifractureaspects,"in
Toughenedcomposites
,ASTM
International,1987.
[2]
N.Domun,H.Hadavinia,T.Zhang,T.Sainsbury,G.Liaghat,andS.Vahid,\Improving
thefracturetoughnessandthestrengthofepoxyusingnanomaterials{areviewofthe
currentstatus,"
Nanoscale
,vol.7,no.23,pp.10294{10329,2015.
[3]
E.Preiˇ,\Fracturetoughnessoffreestandingmetallicthinstudiedbybulgetest-
ing,"2018.
[4]
T.L.AndersonandT.L.Anderson,
Fracturemechanics:fundamentalsandapplications
.
CRCpress,2005.
[5]
ASTMInternational,\D5045-14StandardTestMethodsforPlane-StrainFracture
ToughnessandStrainEnergyReleaseRateofPlasticMaterials,"standard,ASTM
International,WestConshohocken,PA,2014.
[6]
T.L.Anderson,
Fracturemechanics:fundamentalsandapplications
.CRCpress,2017.
[7]
W.J.CantwellandJ.Morton,\Theimpactresistanceofcompositematerials|are-
view,"
composites
,vol.22,no.5,pp.347{362,1991.
[8]
M.RichardsonandM.Wisheart,\Reviewoflow-velocityimpactpropertiesofcomposite
materials,"
CompositesPartA:AppliedScienceandManufacturing
,vol.27,no.12,
pp.1123{1131,1996.
[9]
N.SelaandO.Ishai,\Interlaminarfracturetoughnessandtougheningoflaminated
compositematerials:areview,"
Composites
,vol.20,no.5,pp.423{435,1989.
[10]
V.Dikshit,S.K.Bhudolia,andS.C.Joshi,\Multiscalepolymercomposites:Areview
oftheinterlaminarfracturetoughnessimprovement,"
Fibers
,vol.5,no.4,p.38,2017.
[11]
Y.Tang,L.Ye,Z.Zhang,andK.Friedrich,\Interlaminarfracturetoughnessand
caistrengthofre-reinforcedcompositeswithnanoparticles{areview,"
Composites
ScienceandTechnology
,vol.86,pp.26{37,2013.
[12]
M.A.J.Z.Wang,H.Song,Z.-Z.Yu,andN.Koratkar,\Enhanced
mechanicalpropertiesofnanocompositesatlowgraphenecontent,"
ACSnano
,vol.3,
no.12,pp.3884{3890,2009.
55
[13]
R.J.Young,I.A.Kinloch,L.Gong,andK.S.Novoselov,\Themechanicsofgraphene
nanocomposites:areview,"
CompositesScienceandTechnology
,vol.72,no.12,
pp.1459{1476,2012.
[14]
C.Lee,X.Wei,J.W.Kysar,andJ.Hone,\Measurementoftheelasticpropertiesand
intrinsicstrengthofmonolayergraphene,"
science
,vol.321,no.5887,pp.385{388,2008.
[15]
A.Kumar,
Multiscalecharacterizationandmodelingofprogressivefailureinnano-
graphenereinforcedcarbon/epoxycomposites
.PhDthesis,UniversityofAlabamaLi-
braries,2016.
[16]
M.A.\Graphene-basedcompositematerials,"
RensselaerPolytechnicInstitute:
Troy,NY,USA
,2011.
[17]
A.S.Wajid,H.T.Ahmed,S.Das,F.Irin,A.F.Jankowski,andM.J.Green,\High-
performancepristinegraphene/epoxycompositeswithenhancedmechanicalandelectri-
calproperties,"
MacromolecularMaterialsandengineering
,vol.298,no.3,pp.339{347,
2013.
[18]
A.Kumar,S.Li,S.Roy,J.A.King,andG.M.Odegard,\Fracturepropertiesof
nanographenereinforcedepon862thermosetpolymersystem,"
CompositesScienceand
Technology
,vol.114,pp.87{93,2015.
[19]
A.KumarandS.Roy,\Characterizationofmixedmodefracturepropertiesof
nanographenereinforcedepoxyandmodeidelaminationofitscarbonercompos-
ite,"
CompositesPartB:Engineering
,vol.134,pp.98{105,2018.
[20]
Y.Yang,W.Rigdon,X.Huang,andX.Li,\Enhancinggraphenereinforcingpotential
incompositesbyhydrogenpassivationinduceddispersion,"
reports
,vol.3,
p.2086,2013.
[21]
A.A.\Vi.thephenomenaofruptureandwinsolids,"
Philosophicaltrans-
actionsoftheroyalsocietyoflondon.SeriesA,containingpapersofamathematicalor
physicalcharacter
,vol.221,no.582-593,pp.163{198,1921.
[22]
C.E.Inglis,\Stressesinaplateduetothepresenceofcracksandsharpcorners,"
Trans
InstNavalArchit
,vol.55,pp.219{241,1913.
[23]
G.R.Irwin,\Onsetoffastcrackpropagationinhighstrengthsteelandaluminum
alloys,"tech.rep.,NavalResearchLabWashingtonDC,1956.
[24]
H.M.Westergaard,\Bearingpressuresandcracks,"
TransAIME,J.Appl.Mech.
,vol.6,
pp.49{53,1939.
56
[25]
G.R.Irwin,\Analysisofstressesandstrainsneartheendofacracktransversinga
plate,"
Trans.ASME,Ser.E,J.Appl.Mech.
,vol.24,pp.361{364,1957.
[26]
A.Wells,\Unstablecrackpropagationinmetals:cleavageandfastfracture,"in
Pro-
ceedingsofthecrackpropagationsymposium
,vol.1,1961.
[27]
J.R.Rice,\Apathindependentintegralandtheapproximateanalysisofstraincon-
centrationbynotchesandcracks,"1968.
[28]
X.G.Sciences,\(xGnP)GrapheneNanoplatelets-GradeC."
https://xgsciences.com/product/xgnp/,April2020.
[29]
I.M.McAninch,J.J.LaScala,G.R.Palmese,andE.J.Robinette,\Thininitiation
ofcracksforfracturetoughnessmeasurementsinepoxyresins,"
JournalofApplied
PolymerScience
,vol.134,no.1,2017.
[30]
G.E.DieterandD.Bacon,
Mechanicalmetallurgy
,vol.3.McGraw-hillNewYork,1986.
[31]
R.W.HertzbergandF.E.Hauser,
Deformationandfracturemechanicsofengineering
materials
.1977.
[32]
M.CreagerandP.C.Paris,\Elasticequationsforbluntcrackswithreferenceto
stresscorrosioncracking,"
Internationaljournaloffracturemechanics
,vol.3,no.4,
pp.247{252,1967.
[33]
P.KumarandK.Prashant,
Elementsoffracturemechanics
.TataMcGraw-HillEduca-
tion,2009.
57