Challenges in Mechanics of Time-Dependent Materials, Volume 2: Proceedings of the 2018 Annual Conference on Experimental and Applied Mechanics

111 Pages·2019·8.92 MB·English

by  Alex Arzoumanidis, Meredith Silberstein, Alireza Amirkhizi

Conference Proceedings of the Society for Experimental Mechanics Series
Alex Arzoumanidis · Meredith Silberstein
Alireza Amirkhizi Editors
Challenges in
Mechanics of
Time-Dependent
Materials, Volume 2
Proceedings of the 2018 Annual Conference on
Experimental and Applied Mechanics
Conference Proceedings of the Society for Experimental Mechanics Series
SeriesEditor
KristinB.Zimmerman,Ph.D.
SocietyforExperimentalMechanics,Inc.,
Bethel,CT,USA
Moreinformationaboutthisseriesathttp://www.springer.com/series/8922
(cid:129) (cid:129)
Alex Arzoumanidis Meredith Silberstein Alireza Amirkhizi
Editors
Challenges in Mechanics of
Time-Dependent Materials, Volume 2
Proceedings of the 2018 Annual Conference on Experimental
and Applied Mechanics
Editors
AlexArzoumanidis MeredithSilberstein
Psylotech DepartmentofMechanicalandAerospaceEngineering
Evanston,IL,USA CornellUniversity
Ithaca,NY,USA
AlirezaAmirkhizi
DepartmentofMechanicalEngineering
UniversityofMassachusetts,Lowell
Lowell,MA,USA
ISSN2191-5644 ISSN2191-5652 (electronic)
ConferenceProceedingsoftheSocietyforExperimentalMechanicsSeries
ISBN978-3-319-95052-5 ISBN978-3-319-95053-2 (eBook)
https://doi.org/10.1007/978-3-319-95053-2
LibraryofCongressControlNumber:2016949637
©TheSocietyforExperimentalMechanics,Inc.2019
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Preface
ChallengesinMechanicsofTime-DependentMaterialsrepresentsoneofeightvolumesoftechnicalpaperspresentedatthe
2018 SEM Annual Conference & Exposition on Experimental and Applied Mechanics organized by the Society for
Experimental Mechanics in Greenville, SC, June 4–7, 2018. The complete proceedings also include volumes on Dynamic
BehaviorofMaterials;AdvancementofOpticalMethods&DigitalImageCorrelationinExperimentalMechanics;Mechan-
ics of Biological Systems & Micro-and Nanomechanics; Mechanics of Composite, Hybrid & Multifunctional Materials;
Fracture, Fatigue, Failure and Damage Evolution; Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Tech-
niquesandInverseProblems;andMechanicsofAdditiveandAdvancedManufacturing.
Each collection presents early findings from experimental and computational investigations on an important area within
ExperimentalMechanics,theMechanicsofTime-DependentMaterialsbeingoneoftheseareas.
Thistrackwas organized toaddressconstitutive,time (or rate)-dependent constitutive,andfracture/failurebehaviorofa
broad range of materials systems, including prominent research in progress in both experimental and applied mechanics.
PapersconcentratingonbothmodelingandexperimentalaspectsofTime-DependentMaterialsareincluded.
Thetrackorganizersthankthepresenters,authors,andsessionchairsfortheirparticipationandcontributiontothistrack.
ThesupportandassistancefromtheSEMstaffarealsogreatlyappreciated.
Evanston,IL,USA AlexArzoumanidis
Ithaca,NY,USA MeredithSilberstein
Lowell,MA,USA AlirezaAmirkhizi
v
Contents
1 ModifiedHyper-ViscoelasticConstitutiveModelforElastomericMaterials. . . . . . . . . . . . . . . . . . . . . . . . 1
KarenHarbanandMarkTuttle
2 TemperatureDependenceofStatisticalStaticStrengthsforUnidirectionalCFRPwithVarious
CarbonFibers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
YasushiMiyanoandMasayukiNakada
3 Time-TemperatureMechanicalResponseofaPVADualCross-LinkSelf-HealingHydrogel. . . . . . . . . . . 23
MincongLiu,JingyiGuo,Chung-YuenHui,andAlanT.Zehnder
4 DissipativeDamageTheoryforStronglyTime-DependentCompositeMaterials. . . . . . . . . . . . . . . . . . . . 29
R.B.HallandR.A.Brockman
5 UnderstandingCreep-FatigueInteractioninFe-25Ni-20Cr(wt%)AusteniticStainlessSteel. . . . . . . . . . . 33
N.Kumar,A.Alomari,andK.L.Murty
6 TheDevelopmentofTimeDependentConstitutiveLawsofJujubeFlesh. . . . . . . . . . . . . . . . . . . . . . . . . . 39
Q.T.PhamandN.-S.Liou
7 Time-TemperatureDependentCreepandRecoveryBehaviourofMWCNTs-Polypropylene
Nanocomposites. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
VivekKhare,DavidKumar,G.M.Kamath,andSudhirKamle
8 ComparisonofPorcineBrainTissuewithPotentialSurrogateMaterialsUnderQuasi-static
CompressionandDynamicMechanicalAnalysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
D.Singh,S.Boakye-Yiadom,andD.S.Cronin
9 ModelingofCavitationErosionResistanceinPolymericMaterialsBasedonStrainAccumulation. . . . . . 61
VahidrezaAlizadehandAlirezaAmirkhizi
10 ExperimentalInvestigationofDynamicStrainAgingin304LStainlessSteel. . . . . . . . . . . . . . . . . . . . . . . 65
BonnieR.Antoun,ColemanAlleman,andKelseyDeLaTrinidad
11 ACaseStudytoEvaluateLiveLoadDistributionsforPre-stressedRCBridge. . . . . . . . . . . . . . . . . . . . . 73
AbbasAllawi,MohannadAl-Sherrawi,MohannedAlGharawi,andAymanEl-Zohairy
12 ExperimentalInvestigationofSegmentalPost-tensionedGirders. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
AbbasAllawi,MohannadAl-Sherrawi,BasimAL-Bayati,MohannedAlGharawi,andAymanEl-Zohairy
13 ExperimentalandNumericalEvaluationsofLiveLoadDistributionsofSteel-Concrete
CompositeBridge. . . .. . . . . . . .. . . . . . . .. . . . . . .. . . . . . . .. . . . . . . .. . . . . . .. . . . . . . .. . . . . . . .. . 95
AbbasAllawi,AmjadAlBayati,MohannedAlGharawi,andAymanEl-Zohairy
14 StrainRateDependentFEMofLaserShockInducedResidualStress. . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
ColinC.Engebretsen,AnthonyPalazotto,andKristinaLanger
vii
Chapter 1
fi
Modi ed Hyper-Viscoelastic Constitutive Model
for Elastomeric Materials
KarenHarbanandMarkTuttle
Abstract Elastomers constitute an essential group of materials that are widely used in the automotive, aerospace industry,
biomedical, microfluidic and signal processing applications. Elastomeric materials undergo large deformations without
fracture and exhibit time dependency under a prescribed displacement or load. Characterization of elastomeric materials
can be challenging, hence the use of a proper constitutive model that captures the behavior of elastomeric materials is
essential.Experimentaldataobtainedfromsimpleuniaxialtensiontestsandcreeptestsperformedatvariousconstantstress
levels using dog bone samples were used to approximate hyperelasticity and the time-dependent responses of the material
respectively. The experimental results suggested that the instantaneous strains were largely responsible for the nonlinear
behavior of the material. Thus, a rheological hyper-viscoelastic constitutive model consisting of a nonlinear spring, which
wouldcapturethenonlinearinstantaneousstrains,andatwoparameterKelvin-Voightmodel,whichwouldmodelthelinear
time-dependentstrainresponses,wasdeveloped.TheMooney-Rivlinmodel,aclassicphenomenologicalhyperelasticmodel,
was used to represent the nonlinear spring. The resulting hyper-visco constitutive model, which obeys the Boltzmann’s
superpositionprinciple,wasusedfornumericalpredictionsoftime-dependentbehaviorofthismaterialinacommercialfinite
element software (Abaqus). The creep deformations predicted using this approach demonstrated good consistency with
experimentalresultsovertheappliedrangeofstressesandthedurationoftimemeasurements.
Keywords Elastomers·Hyperelastic·Viscoelastic·Pronyseries·Finiteelementmethod
1.1 Introduction
Elastomers constitute an essential group of materials that are widely used in the automotive, aerospace industry and more
recentlyinbiomedical[1–3],microfluidic[4,5],andsignalprocessing[2,6]applications.Elastomericmaterialsaretypically
lightly cross-linked polymers that canundergo large deformationswithoutfractureanddisplaytime-dependent viscoelastic
behavior. The nonlinear elastic behavior of elastomers under prescribed displacement or load can be modelled using the
classicalGaussianstatistictheory,macromolecularnetworktheory,orcontinuummechanicsasdiscussedbythepioneersof
hyperelastic constitutive models, Treolar [7], Rivlin [8], Boyce and Arruda [9]. On the other hand, the time-dependent
behavior of elastomers (i.e., viscoelasticity that comprises and combines both the elastic and viscoelastic behavior) can be
characterizedbymeansofcreepcomplianceorrelaxationmodulus.
Hyperelastic constitutive laws, which account for the large nonlinear elastic material behavior associated large shape
changes, are used to model materials that exhibit high strains without failure. Hyperelastic constitutive models are derived
fromastrainenergydensityintermsofprincipalstretches[10].Thestretch(orthestretchratio),λisdefinedastheratioofthe
lengthofadeformedlineelementtothelengthofthecorrespondingundeformedlineelementandtheprincipalstretchesare
the associated stretches of a material that undergoes deformation in three mutually orthogonal directions. The process of
findinghyperelasticparametersofamaterialrequiresrelevantexperimentaltest(s)followedbymathematicallydescribingthe
physicalbehaviorofthetestresults.
Viscoelasticity [11] is a mechanical behavior of polymers describes the time-dependent response to an applied stress or
strain.Incontratstothebehaviorofelasticsolidssuchasmetalsandceramics,whichatlowstrainsobeystheprinciplesof
K.Harban(*)·M.Tuttle
DepartmentofMechanicalEngineering,UniversityofWashington,Seattle,WA,USA
e-mail:[email protected]
©TheSocietyforExperimentalMechanics,Inc.2019 1
A.Arzoumanidisetal.(eds.),ChallengesinMechanicsofTime-DependentMaterials,Volume2,ConferenceProceedings
oftheSocietyforExperimentalMechanicsSeries,https://doi.org/10.1007/978-3-319-95053-2_1
2 K.HarbanandM.Tuttle
Hooke’sLaw[12],thestressandstrainbehaviorofpolymersmaybehighlytimedependent.Attemperatureswellbelowthe
glasstransitiontemperatureandhighratesofstrain,polymersbehaveinanelasticmanner,whileathightemperaturesandlow
ratesofstrain,polymersbehaveinaviscousmanner.Hence,polymersaredescribedasviscoelasticmaterials,astheyexhibit
both elastic and viscous behaviors. Relevant tests (i.e. creep or relaxation) are needed to characterize the viscoelastic time-
dependentbehaviorthroughformulation ofamathematicalmodel.Themostpopularmathematical form ofthisbehavioris
givenbythePronySeries[13].Themathematicalbackgroundofhyperelasticityandviscoelasticityofelastomericmaterials
arebrieflydiscussedinthefollowingsections.
1.2 Theoretical Background
Theprocedureofderivingthehyperelasticconstitutivemodelsbeginswithfirstdefiningthestrainenergydensityasafunction
of the deformation gradient tensor, specifically the Cauchy-green deformation tensor. Then, computing the invariants
generally the principal stretches or strain invariants of the Left Cauchy-green deformation tensor and finally obtaining the
stressesbydifferentiatingthestrainenergydensityfunctionwithrespecttotheinvariants.Notethattheconceptof“stretch”
differsfromthedefinitionof“engineeringstrain”,wherethelatterisdefinedastheratioofthechangeinlengthofadeformed
line element to the undeformed length. A strain energy density is a scalar valued function that represents the strain energy
density of a material as a function of the deformation gradient. The strain energy density can be expressed in terms of the
deformation gradient (F ), the invariants of the strain tensor (I , I , I ) or in terms of the principal stretches (λ , λ , λ )
ij 1 2 3 1 2 3
[14]. Since this research involves the study of elastomeric materials (rubbers) the assumption of incompressibility can be
adaptedtosimplifythestrainenergyfunction.Ifthematerialisincompressible,itfollowsthattheJacobianofthedeformation
tensorisequalto1andtheproductoftheprincipalstretchesisequalto1whichmeansthethirdprincipalstretch,λ canbe
3
representedintermsofthefirstandsecondprincipalstretches,λ ,λ .Onlyafewhyperelasticmodelsthatarebuilt-inthefinite
1 2
elementsoftwarepackageusedinthisstudyarediscussedinthissection.
1.2.1 Polynomial Model
Thegeneralformofapolynomialmodelisgivenas:
Xm Xn
W ¼ C ðI (cid:2)3ÞiðI (cid:2)3Þj ð1:1Þ
ij 1 2
i¼0 j¼0
whereC isthematerialconstants.Followingtheassumptionofincompressibility,thethirdinvariantI isassumedtobezero.
ij 3
Thesecondorderpolynomialmodelisderivedfromthisstrainenergydensityexpressionfollowingm¼n¼2and1(cid:3)(i+j)(cid:3)2,
expressedas:
W ¼C ðI (cid:2)3ÞþC ðI (cid:2)3ÞþC ðI (cid:2)3ÞðI (cid:2)3ÞþC ðI (cid:2)3Þ2þC ðI (cid:2)3Þ2 ð1:2Þ
10 1 01 2 11 1 2 02 2 20 1
1.2.2 Mooney-Rivlin Model
TheMooney-Rivlinmodelisaclassicphenomenologicalmodelwhichisbasedonstraininvariant[15].Thegeneralizedstrain
energydensityoftheMooney-Rivlinmodelisexpressedas:
W ¼C ðI (cid:2)3ÞþC ðI (cid:2)3Þ ð1:3Þ
10 1 01 2
whereC arematerialconstantsderivedfromthegeneralpolynomialmodelinwhichm¼n¼1and(i+j)¼1.
ij
1 ModifiedHyper-ViscoelasticConstitutiveModelforElastomericMaterials 3
1.2.3 Ogden Model
The Ogden model is another classic phenomenological model. Ogden [16] proposed an invariant function based model
comprisingalinearcombinationofstraininvariantsandprinciplestretchessubjectedtoincompressibility.Thestrainenergy
densityfunctionoftheOgdenmodelisexpressedas:
XN 2μ (cid:2) (cid:3)
W ¼ i λ(cid:2)αi þλ(cid:2)αi þλ(cid:2)αi (cid:2)3 ð1:4Þ
α2 1 2 3
i¼1 i
whereλ aredeviatoricprincipalstretchandα,μ arematerialconstants.Inthisstudy,wehaveassumedN¼2.
i i i
1.2.4 Neo-Hookean Model
ThismodelwasderivedfrommolecularchainstatisticsandisthesimplestformoftheMooney-Rivlinmodelbasedonlyon
twomaterialparameters[17].Thestrainenergydensityisexpressedas:
W ¼C ðI (cid:2)3Þ ð1:5Þ
10 1
This equation islinear in the first invariant, I which limits theability of accurately capturing large non-linear strains of
1
elastomers.Apartfromthatthestrainenergydensityexpressionisnotdependentonthesecondinvariant,I whichmayresult
2
ininaccuratestresspredictionsforabiaxialstateofstress.
Theinvariantsinthestrainenergydensityfunctionsexpressedarerelatedtotheprincipalstretchesasfollows:
I ¼λ 2þλ 2þλ 2
1 1 2 3
I ¼λ 2λ 2þλ 2λ 2þλ 2λ 2 ð1:6Þ
2 1 3 2 3 1 2
I ¼λ 2λ 2λ 2
3 1 2 3
wherestretch,λcanbeexpressedintermsofengineeringstrains,bytheexpressionλ¼1+e.Agoodhyper-elasticmodelis
onethathasagoodcomparisonwithexperimentalresultsforanystressstatewithagivensetofmaterialpropertiesandone
that gives stable results for all loadings. Uniaixal tension test were performed in this study to obtain hyperelastic material
parameters. For a uniaxial tension test, the uniaxial stretch in the first principal direction can be expressed in terms of
engineeringstrainsλ ¼λ ¼1+e,andtheothertwoprincipalstretchdirectionscanbeexpressedas:
1 uniaxial
1
λ ¼λ ¼pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1:7Þ
2 3 λ
uniaxial
Thecorrespondingstrainenergydensityexpressioncanbeobtainedby:
ð
λðIÞ(cid:2)1
WðIÞ¼ σðεÞdε ð1:8Þ
0
whereεandσarethenominalstrainandstressinuniaxialtensiontest.Toaccountforlinearviscoelasticityinthismaterial,a
suitablehyperelasticconstitutivemodelshouldbecoupledwiththeviscoelasticmodel.
1.2.5 Linear Viscoelasticity
Theconstitutiveequationforlinearviscoelasticmaterialcanbeexpressedas:
ð
t
_
εðtÞ¼ Jðt(cid:2)τÞε(cid:4)ðτÞdτ ð1:9Þ
0