Finite Element Modelling of the Mechanical Behaviour of Graphene Nanocomposites Aerospace ...

112 Pages·2016·3.43 MB·English

by  Andre C. Marta

Finite Element Modelling of the Mechanical Behaviour of
Graphene Nanocomposites
Jorge Miguel Grossinho Araújo
Thesis to obtain the Master of Science Degree in
Aerospace Engineering
Supervisor: Prof. Nuno Miguel Rosa Pereira Silvestre
Examination Committee
Chairperson: Prof. Fernando José Parracho Lau
Supervisor: Prof. Nuno Miguel Rosa Pereira Silvestre
Member of the Committee: Prof. José Arnaldo Pereira Leite Miranda Guedes
December 2016
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Acknowledgments
First of all, the aspiration of doing my master degree dissertation on such remarkable theme began
some years ago, when I intended to perform a simple but encouraging presentation on nanomaterials
formyhigh-schoolcolleagues. Forgivingmethatopportunityandalltheneededsupporttoaccomplish
myobjective,IwouldliketoexpressmyenormousgratitudewithProf. NunoSilvestre.
Tomyfamily,mymotherAlice,myfatherJorgeandmysisterAnaFilipa,therearenotenoughwords
thatmayappearwrittenheretorevealmygreatestjoyingivingthemthissoexpecteddayintheirlives,
aswellonmyown.
For accompanying me throughout the entire master course, I would like also to manifest all my
appreciation for having such faithful friends, Miguel Dias, Nuno Martins, David Palma and Joa˜o Silva,
who started by my side the shortest but yet challenging journey of our academic lives. Certainly, I will
remember forever all the good conversations and all the late-night dinners, but most important is the
satisfactionIhavebysharingthosemomentswithsuchpartners.
For all the days that I was less patient or fewer present, for all the love that I was given, for never
havingrefusedtohearmylongspeechesaboutnanomaterialsandfiniteelements,andforbeingalways
there when I mostly needed, to my cherished girlfriend Rafaela Albino, my sincere apologies and my
biggestthankyouIcouldfitintotwowords.
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Resumo
Ografenoe´ ummaterialdeu´ltimagerac¸a˜o,conhecidopelassuaspropriedadesmecaˆnicas,te´rmicas,
o´ticaseele´tricasu´nicas. Porestaraza˜o,ascomunidadeste´cnicaecient´ıficateˆmvindoaexplorarasua
imensida˜o de aplicac¸o˜es nas u´ltimas de´cadas. Presentemente, o excelente comportamento mecaˆnico
do grafeno tem-no levado a ser empregue em materiais compo´sitos com uma nota´vel capacidade de
otimizac¸a˜o. Nesta dissertac¸a˜o, e´ desenvolvida uma ana´lise de elementos finitos composta em dois
n´ıveis para estudar o comportamento de materiais compo´sitos reforc¸ados com grafeno. Inicialmente,
as propriedades mecaˆnicas da folha de grafeno sa˜o extra´ıdas atrave´s de um modelo de elementos
finitos que simula a sua estrutura ato´mica, e onde as ligac¸o˜es covalentes sa˜o consideradas como el-
ementos estruturais. Em seguida, a representac¸a˜o ato´mica do grafeno e´ inserida num meio ela´stico
(matriz)representadonumelementodevolumeadequadoparaextrairosmo´dulosela´sticosdomaterial
nanocompo´sito. A u´ltima parte do documento investiga as consequeˆncias no comportamento ela´stico
do nanocompo´sito quando sa˜o introduzidos defeitos ato´micos no grafeno. A abordagem apresentada
e´ capaz de reproduzir as propriedades ela´sticas do grafeno em concordaˆncia com outras metodolo-
gias,revelandoqueocomportamentoortotro´picoprevistoanteriormenteda´ lugaraisotropiaemfolhas
quadradasdemaioresdimenso˜es. Adicionalmente,omodelorepresentativodonanocompo´sitomostra
queoaumentodaotimizac¸a˜omecaˆnicae´ conseguidoquandoe´ consideradaumamaioradereˆnciaen-
treografenoeamatrizenvolvente. Porfim,foiidentificadoqueografenocomumbaixograudedefeitos
e´ capazdemanteroseuelevadoefeitocomoreforc¸oemnanocompo´sitos.
Palavras-chave:
Elementos Finitos, Grafeno, Nanocompo´sito, Propriedades Mecaˆnicas,
DefeitosAto´micos
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Abstract
Graphene is a state-of-art material, known by its unique mechanical, thermal, optical and electrical
properties. For this reason, the technical and scientific communities have been exploring its immensity
of applications in the last few decades. Presently, the excellent mechanical behaviour of graphene has
leading it to be employed in composite materials with notable capability of improvement. In this disser-
tation, a two-level finite element analysis is developed to address the behaviour of composite material
reinforcedwithgraphene. First,themechanicalpropertiesofpristinegrapheneareextractedthrougha
refined finite element model that simulates its nanostructure, and where covalent bonds are regarded
as structural elements. Then, the atomistic representation of graphene is assembled into a suitable
representativevolumeelementtoextracttheelasticmoduliofnanocompositematerial. Thefinalpartof
this document investigates the effects in the elastic behaviour of nanocomposite when atomic defects
areintroducedingraphene. Thepresentapproachisabletoreproducetheelasticpropertiesofpristine
graphene in agreement with other methodologies, revealing also that orthotropic behaviour earlier pre-
dicted gives rise to isotropy for square sheets with larger dimensions. Additionally, the representative
modelofnanocompositeshowsthatincreasingmechanicalenhancementisachievedwhenhigheradhe-
sionisconsideredbetweengrapheneandsurroundingmatrix. Ultimately,itwasidentifiedthatgraphene
withlowdefectcontentiscapabletomaintainitssuperiorreinforcingeffectinnanocomposites.
Keywords:
Finite Elements, Graphene, Nanocomposite, Mechanical Properties, Atomic De-
fects
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Contents
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Resumo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
ListofTables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
ListofFigures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix
1 Introduction 1
1.1 Grapheneanditsapplications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 ScopeandObjectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 OrganizationofContents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 MechanicalBehaviourofGrapheneanditsNanocomposites–LiteratureReview 7
2.1 PristineGraphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 GrapheneNanocomposites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 Graphene-basedPolymerNanocomposites . . . . . . . . . . . . . . . . . . . . . . 12
2.2.2 Graphene-basedMetalNanocomposites . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.3 Structure-PropertyRelations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 StructuralDefectsinGraphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3 FiniteElementModellingofGrapheneandGraphene-basedNanocomposite 25
3.1 ProblemDefinition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1.1 ForceField,CovalentandNon-CovalentBondsinGraphene . . . . . . . . . . . . 25
3.1.2 MatrixandInterface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1.3 StructuralDefects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 PristineGrapheneFiniteElementAnalysis. . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2.1 ModelDescription . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2.2 BoundaryandDisplacementConditions . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 NanocompositeFiniteElementAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3.1 ModelDescription . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3.2 BoundaryandDisplacementConditions . . . . . . . . . . . . . . . . . . . . . . . . 42
4 Results 47
4.1 ElasticPropertiesofPristineGraphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
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4.1.1 PresentationofResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.1.2 CalculationofElasticProperties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.1.3 ModelValidationandDiscussionofResults . . . . . . . . . . . . . . . . . . . . . . 52
4.2 ElasticBehaviourofGraphene-basedNanocomposite . . . . . . . . . . . . . . . . . . . . 59
4.2.1 PresentationofResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2.2 CalculationofElasticProperties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.2.3 ModelValidationandDiscussionofResults . . . . . . . . . . . . . . . . . . . . . . 64
5 InfluenceofDefectiveGrapheneinNanocomposites 69
5.1 ModelDescription . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.2 ParametricStudyonDefectCoverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.3 DiscussionofResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6 ConclusionsandFutureWork 77
Bibliography 81
A Single-PhaseMaterials 91
A.1 Interrelationsamongthe2Dand3Delasticmoduli . . . . . . . . . . . . . . . . . . . . . . 91
A.2 Two-dimensionalityelasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
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