Fracture Mechanics and Statistical Mechanics of Reinforced Elastomeric Blends PDF
Preview Fracture Mechanics and Statistical Mechanics of Reinforced Elastomeric Blends
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 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. 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Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) 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
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