Fracture Mechanics and Statistical Mechanics of Reinforced Elastomeric Blends

310 Pages·2013·22.551 MB·English

by  Jaroslaw Paturej, Andrey Milchev (auth.), Wolfgang Grellmann, Gert Heinrich, Michael Kaliske, Manfred Klüppel, Konrad Schneider, Thomas Vilgis (eds.)

Lecture Notes in Applied and Computational Mechanics 70
Wolfgang Grellmann · Gert Heinrich
Michael Kaliske · Manfred Klüppel
Konrad Schneider · Thomas Vilgis Editors
Fracture Mechanics
and Statistical Mechanics
of Reinforced Elastomeric
Blends
Lecture Notes in Applied and Computational
Mechanics
Volume 70
SeriesEditors
F.Pfeiffer,Garching,Germany
P.Wriggers,Hannover,Germany
Forfurthervolumes:
http://www.springer.com/series/4623
·
Wolfgang Grellmann Gert Heinrich
·
Michael Kaliske Manfred Klüppel
·
Konrad Schneider Thomas Vilgis
Editors
Fracture Mechanics
and Statistical Mechanics
of Reinforced Elastomeric
Blends
ABC
Editors
WolfgangGrellmann ManfredKlüppel
ZentrumfürIngenieurwissenschaften DeutschesInstitutfür
Martin-Luther-UniversitätHalle-Wittenberg Kautschuktechnologiee.V.
Halle(Saale) Hannover
Germany Germany
GertHeinrich KonradSchneider
Leibniz-InstitutfürPolymerforschung Leibniz-InstitutfürPolymerforschung
Dresdene.V. Dresdene.V.
Dresden Dresden
Germany Germany
MichaelKaliske ThomasVilgis
InstituteforStructuralAnalysis Max-Planck-InstituteforPolymerResearch
TechnischeUniversitätDresden Mainz
Dresden Germany
Germany
ISSN1613-7736 ISSN1860-0816 (electronic)
ISBN978-3-642-37909-3 ISBN978-3-642-37910-9 (eBook)
DOI10.1007/978-3-642-37910-9
SpringerHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2013935633
(cid:2)c Springer-VerlagBerlinHeidelberg2013
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Preface
Fracturemechanicsandfatiguebehaviourofelastomersareofgreattechnical
importance for rubber parts. Durability is essential for the development of
tailor made rubber materials for high performance elastomeric products like
tires, conveyor belts, seals, air springs, dampers and other components. In
spiteofrecentprogress,morescientificandtechnologicalpotentialforfurther
developmentoffracturemechanicalmodelsandtestingconceptsofreinforced
elastomers can be identified, especially if considering the strongly nonlinear
viscoelastic material behaviour.
For manyyears,effortfora quantitativecharacterizationandphysicalun-
derstanding of crack propagation and tear resistance in viscoelastic solids
has been undertaken. Most of the work is based on the fundamental ap-
proaches of Rivlin and Thomas. The main focus of our work lies in a better
understanding of fatigue crack propagation under dynamical loading condi-
tions and a more fundamental, physicallymotivated predictionofservice life
properties of rubber parts, which is based on micro-mechanical mechanisms
of crack initiation and propagation in elastomeric materials. At present, it
is still not exactly known how these processes start and how they proceed
under dynamic loading conditions.
Thepresentbookgivessomenewinsightsintothefieldoffracturemechan-
ics of rubber and approaches the rupture phenomenon by different methods
ranging from molecular to macroscopic length and time scales. In particu-
lar,adetailedanalysisofstructure-propertyrelationshipsoffilledelastomers
and of multi-phase elastomeric blends is presented with respect to dynamic
crackpropagation,stress-strainbehaviourandmicro-mechanicalmechanisms
ofreinforcementbyfillerslikecarbonblack.Byapplyingsuitabletesting,ana-
lyticalandnumericalmethods,themorphologicstructureofthefillernetwork
and the phase morphology of heterogeneous elastomeric blends are charac-
terized on microscopic and mesoscopic length scales. Fracture mechanical
investigations on crack propagation under harmonic pulsed deformation are
carriedoutbymeansofanautomaticcrackpropagationmeasurementdevice
– the Tear Fatigue Analyser (TFA). Further, the influence of“confinement”
VI Preface
on the interfacial glass dynamics of polymer chains within nano-scaled filler
structures is investigated in order to obtain a deeper understanding of the
polymer-filler and filler-filler interaction. On the structural level, numerical
investigationsbasedonphysicalpropertieshavebeencarriedoutusingnewly
developed methods.
In Chapter1,some elementarystatements basedonstatisticalphysicsap-
proaches are presented. When a material breaks at the crack tip, individual
moleculesrupture.Thisphenomenoniseasilyunderstoodwhencracktipsare
consideredindetail.Rightatthetip,polymerchainsbecomehighlystretched
andorientedbeforetheyrupture.Inconsequence,theirlocalhighdeformation
ratioimplicates a complete changeoftheir polymerdynamics. Incontrastto
low stretching ratios, when the polymer motion is easily described by linear
Rousedynamics, itchangesto highly nonlinearcharacteristicswhichneedto
be the starting point for more refined theories of individual chain rupturing.
The strongnonlinearcharacterofthe theoryimplies involvednumericalsim-
ulations,whichareabletoexplainthelimitsofelementarylinearizedtheories
also proposed in this chapter. The ideas are discussed at higher dimensional
networks,mainlytwo-dimensionalcross-linkedpolymersystems,whichallow
adetailedanalysisoftherupturephenomenaasafunctionofthedeformation
modes.
In Chapter 2, synchrotronwide-angle X-ray diffraction is described which
was employed to follow the strain-induced crystallization in natural rubber
on previously inaccessibly short time scales during dynamic cyclic loading
and during step-like loading. Strain-induced crystallization is a fascinating
phenomenon that enhances the mechanical properties of some elastomers,
most prominently of natural rubber. The tear fatigue resistance is consider-
ablyelevated,givingnaturalrubberasignificantedgeoversyntheticrubbers.
Thankstothe WAXDanalysis,new structure-propertyrelationships,linking
the kinetics of strain-induced crystallization to the tear fatigue behaviour,
couldbe established.Furthermore,scatteringmethods wereappliedto study
cavitations and filler orientation.
Chapter 3 describes the development of new micro-mechanical concepts
of fracture mechanics of filled rubbers and demonstrates their validation by
experimental data. These concepts are based on the well established Dy-
namicFlocculationModelforrubberreinforcementwhichitselfcombinesthe
well founded tube model of rubber elasticity with specific and detailed fea-
tures of the morphology and micro-mechanics of the used filler systems. In
particular, it is demonstrated that the characteristics of the filler network
are closely related to the fracture mechanical properties of filled elastomers.
Micro-mechanical material parameters for various elastomeric materials are
evaluated by fitting quasi-static stress-strain cycles to the Dynamic Floc-
culation Model. This allows for a quantitative description of stress softening
effectsandfillerinducedhysteresisintheareaclosetothecracktipbyapply-
ing numerical simulationswith the Finite ElementMethod(FEM). Thereby,
theinfluencesoftheclusterstructureandthestrengthoffiller-fillerbondson
Preface VII
the deformationbehaviourclosetothe cracktipandthe fracturemechanical
properties are demonstrated.
Linking macroscopicand mesoscopic aspects of crack propagationis topic
of Chapter 4. Combining experiments and numerical simulations based on a
global energy balance, the influences of particular dissipative processes such
as viscoelasticityand deformation-inducedchanges of filler structures on the
tearing energy are investigated. The process of material degradation in the
immediate vicinity of the crack front is driven by the rupture of polymer
chain segments and by the interaction of resulting defects with the crack
front. Characteristic length scales of the fracture process can be estimated
from a statistical analysis of fracture surface topography by means of deter-
miningcharacteristicself-affineroughnessexponents.Alsononlocalmodeling
ofthe materialdegradationdue toruptureofpolymerchainsegmentswithin
the fracture process zone is presented in Chapter 4 taking into account the
overloadingofchainsbothinthefullystretchedstateandduetofastloading.
Characteristic properties like finite deformations, nonlinear elasticity, and
localdamageaswellasrate-dependentandrate-independentdissipativeprop-
erties of filled elastomers are considered for a realistic representation of the
material response within numerical finite element simulations in Chapter 5.
Material models formulated on the macroscale are developed which repre-
sent finite viscoelasticity and endochronic elastoplasticity of the undamaged
continuum. Failure of rubber material is addressed by a micro-continuum-
mechanical model. Crack sensitivity of the material is investigated by the
so-called material force method where material forces are employed for the
computation of fracture mechanical parameters of dissipative rubber mate-
rial. Arbitrarycrack growthis modelled onthe structuralscale by the use of
cohesive elements in combination with an adaptive implementationstrategy.
Several examples show the numerically simulated crack propagation in rub-
ber specimens under considerationofdifferent fracturecriteriaas well as the
durability analysis of different tire structures.
Chapter6containsexperimentalresultsofvariousmechanicalandfracture
mechanicalinvestigationsofdifferentelastomericmaterials.Furthermore,re-
sults of structural investigations and of micro-fractographical investigations
are reported. The fracture mechanics investigations contribute to a further
development of the experimental methods in the range of quasi-static and
impact-like loading. Especially the performance of impact tests with varia-
tionofthetesttemperatureandasubsequentfracturemechanicalanalysisis
a new field in polymer diagnostics. The results show the strong influence of
the test temperature on the fracture behavior of filler-reinforced elastomeric
materials. The further methodical development of the quasi-static test con-
tributes to the understanding of stable crack initiation and propagation be-
havior. The experimental results allow for a structure-related discussion of
the mechanical and fracture mechanical properties, which is an important
factor in material development.
VIII Preface
Chapter7describesanew methodfortheanalysisofdynamiccrackprop-
agation in filled rubber by simultaneous tensile and pure shear mode test-
ing. This method is based upon the mechanical redevelopmentof the testing
machine TFA and its subsequent equipment with new hardware and, addi-
tionally, a camera system for continuously recording of the crack length. It
is shown how tearing energy and crack growthrate depend on the test spec-
imen’s geometries and crack length. Moreover, the importance of a defined
and reproducible notching of elastomeric specimens is also demonstrated in
this chapter.
Allpresentedcontributionsandresultsinthisbookaretheoutcomeofthe
researchunit FOR 597 funded by the German Research Foundation (DFG).
This support is gratefully acknowledged.
Contents
Rupture Dynamics of Macromolecules ....................... 1
Jaroslaw Paturej, Andrey Milchev, Vakhtang G. Rostiashvili,
Thomas A. Vilgis
In-Situ Structural Characterization of Rubber during
Deformation and Fracture ................................... 43
Karsten Bru¨ning, Konrad Schneider, Gert Heinrich
Morphology and Micro-mechanics of Filled Elastomer
Blends: Impact on Dynamic Crack Propagation.............. 81
Hagen Lorenz, Dagmar Steinhauser, Manfred Klu¨ppel
Linking Mesoscopic and Macroscopic Aspects of Crack
Propagation in Elastomers................................... 129
Thomas Horst, Gert Heinrich, Martin Schneider, Annegret Schulze,
Mirko Rennert
Macroscopical Modeling and Numerical Simulation
for the Characterization of Crack and Durability Properties
of Particle-Reinforced Elastomers............................ 167
Ronny Behnke, Hu¨snu¨ Dal, Gordon Geißler, Bastian N¨aser,
Christiane Netzker, Michael Kaliske
Technical Material Diagnostics – Fracture Mechanics
of Filled Elastomer Blends................................... 227
Wolfgang Grellmann, Katrin Reincke
Analysis of Dynamic Crack Propagation in Elastomers
by Simultaneous Tensile- and Pure-Shear-Mode Testing ..... 269
Radek Stoˇcek, Gert Heinrich, Michael Gehde, Reinhard Kipscholl
Author Index................................................ 303
Rupture Dynamics of Macromolecules
JaroslawPaturej1,AndreyMilchev2,VakhtangG.Rostiashvili3,
andThomasA.Vilgis3
1 InstituteofPhysics,UniveristyofSzczecin,Wielkopolska15,70-451Szczecin,Poland
[email protected]
2 InstituteforPhysicalChemistry,BulgarianAcademyofSciences,Akad.G.Bonchev11,
1113Sofia,Bulgaria
3 MaxPlanckInstituteforPolymerResearch,Ackermannweg10,55128Mainz,Germany
Abstract. Inaseriesofstudiesweconsiderthebreakageofapolymerchainofseg-
ments,coupledbyanharmonicbondsunderappliedtensionalforceorsubjecttorise
intemperature.Thechaindynamicsattheonsetoffractureisstudiedbymeansof
MolecularDynamicssimulationandalsousinganalyticconsiderations.Adeeperin-
sightintothechangesinpolymerrelaxationdynamicswhenbondinganharmonicity
istakenintoaccount,thatis,beyondthelimitsoftheconventionalRousemodelde-
scription,isgainedbycomparinganalyticresultsfromtheGaussianSelf-Consistent
approachtodataderivedfromMonteCarloandMolecularDynamicssimulations.
Simulationresultsonpolymerchainruptureareconfrontedwiththepredictionsof
Kramers-Langertheory.Twocasesareinvestigated:a)thermallyinducedfractureof
unstrainedchain,andb)ruptureofachainundertensilestress.Casesofbothunder-
andoverdampeddynamicsareexplored.Therecentlyexperimentallyobservedand
intensivelystudiedcaseofcovalentbondscissionin“bottle-brush”macromolecules
adsorbedonahardsurfaceismodeledandcomprehensivelyinvestigatedwithregard
totensionaccumulationandbreakdownkinetics.Eventuallywereportonourlatest
studiesoftheforce-inducedruptureandthermaldegradationof2D(graphene-like)
networks,focusingonthecreationandproliferationofcracksduringfailure.
1 Introduction
Materialsfailurehasbeensincealongtimethestandardmethodinmaterialstesting.
Well knownfromsolid state crystallinematerialsit hasbeen realizedhow macro-
scopic materials properties related to failure such as crack propagation, breaking
strains,yieldstressesarerelatedtocrystallinestructures,concentrationsalloysand
otherlocallattice properties.Thisknowledgewasthen used to designmetallic al-
loys or differentsteels by variation of the carbon content and differentquenching
temperatures.
In soft materials, especially in polymers similar methods are of wide empiric
use. The relation between macroscopic failure and molecular propertiesis clearly
W.Grellmannetal.(Eds.):FractureMechanics&StatisticalMech.,LNACM70,pp.1–42.
DOI:10.1007/978-3-642-37910-9_1 (cid:2)c Springer-VerlagBerlinHeidelberg2013