Micromechanics of Internal Friction of Filler Reinforced Elastomers

Lorenz, H.; Meier, Jens; Klüppel, Manfred

doi:10.1007/978-3-642-10657-6_2

Cited by 11 publications

(17 citation statements)

References 16 publications

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“…A proper physical treatment of the set phenomena requires a time dependent formulation of the model which is a task of future work. Empirically, a separate dependence of s set on maximum deformation and the distance of the temperature T from the glass transition temperature T g of the elastomer has been found (Lorenz et al, 2010) s set ¼ s set,0…”

Section: Parameter Evaluationmentioning

confidence: 99%

“…When the load is released, broken clusters can re-aggregate. The cyclic breakage and re-aggregation of the damaged bonds, which form relatively soft clusters, causes the observed hysteresis and the pronounced energy dissipation with increasing amplitude of deformation (Klüppel and Schramm, 2000;Klüppel and Meier, 2001;Klüppel, 2003;Klüppel et al, 2005;Lorenz et al, 2010). A related phenomenological model to explain the Mullins effect and viscoelastic behaviour of filled rubbers has recently been proposed by Svistkov et al (2008), which refers to a similar structural-cluster mechanics.…”

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confidence: 91%

“…In order to relate material parameters of rubber and filler to those of the vulcanised material, we use a microstructure-based approach where material parameters are physical quantities, instead of mere fit parameters. On this basis, an extension of the DFM with respect to time and temperature-dependence (Klüppel et al, 2005;Lorenz et al, 2010) is possible in a much more focused way, as compared with phenomenological models. In order to transform the microstructure-based relations into solvable equations, the considerations so far have been limited to special deformation modes, i.e.…”

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confidence: 99%

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Microstructure-based modelling of arbitrary deformation histories of filler-reinforced elastomers

Lorenz

Klüppel

2012

Journal of the Mechanics and Physics of Solids

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Section: Parameter Evaluationmentioning

confidence: 99%

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confidence: 91%

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confidence: 99%

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Microstructure-based modelling of arbitrary deformation histories of filler-reinforced elastomers

Lorenz

Klüppel

2012

Journal of the Mechanics and Physics of Solids

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“…The origin of the strong inelasticity of filled elastomers was identified in a dynamic breakdown and re-aggregation of filler-filler bonds. The mechanism of cyclic breakage and re-aggregation of filler clusters, which has been successfully applied [18][19][20] in the past for explaining stress-softening and hysteresis, can be summarized in the following way.…”

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confidence: 99%

Microstructure‐based modelling and FE implementation of filler‐induced stress softening and hysteresis of reinforced rubbers

2012

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Reinforcement of rubber by nanoscopic fillers induces strong nonlinear mechanical effects such as stress softening and hysteresis. The proposed model aims to describe these effects on a micromechanical level in order to predict the stress-strain behaviour of a rubber compound. The material parameters can be obtained by fitting stress-strain tests. These quantities have a clear defined physical meaning. The previously introduced "dynamic flocculation model" was extended for general deformation histories. Stress softening is modelled by hydrodynamic reinforcement of rubber elasticity due to strain amplification by stiff filler clusters. Under stress these clusters can break and become softer, leading to a decreasing strain amplification factor. Hysteresis is attributed to cyclic breakdown and re-aggregation of damaged clusters. When stressstrain cycles are not closed, not all of these clusters are broken at the turning points. For the resulting "inner cycles" additional elastic stress contributions of clusters are taken into account. The uniaxial model has been generalized for threedimensional stress states using the concept of representative directions. The resulting 3D-model was implemented into a Finite Element code, and an example simulation is shown. Good agreement between measurement and simulation is obtained for uniaxial inner cycles, while the 3D-generalization simulates the behaviour closer to the experiment than the original model. IntroductionReinforcement of elastomers is essential for their application. Without nanoscopic filler additives such as carbon black or silica, rubber products as e.g. tires or seals would rupture or wear off very rapidly. Besides making the elastomer stiffer and tougher, the incorporation of fillers leads to a non-linear dynamic-mechanical response. An example is the Payne effect: the amplitude dependence of the dynamic moduli [1-3]. With increasing strain amplitude an increasing loss angle and a decreasing storage modulus are seen. The drop will be even more pronounced at higher amount of filler in the elastomer. We point out that the uniaxial stress-strain cycles and hysteresis of filler-reinforced rubbers are indeed strongly non-linear effects also at small strain amplitudes. The apparent linear behavior that is observed during standard dynamic mechanical testing even up to 100% strain amplitude and more is only a special case found in simple shear experiments. This is also called the "harmonic paradox" of the Payne effect [4,5] since an almost linear viscoelastic stress-strain behavior is observed also at large strain amplitudes. Because of the pronounced decrease of the storage modulus with increasing amplitudes, one would rather expect non-linear viscoelastic stress-strain behavior and no neat sinusoidal response as at low amplitude. One reason being that an ideal Gaussian statistics of polymer networks with constant volume (Neo-Hook model), which approximately applies up to moderate strain, leads to a linear relation between shear stress and strain, τ = Gγ, though the ...

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“…The price for violating the energy balance condition due to overestimation of the strain amplification factor is however high. One unavoidably confronts a number of mathematical problems, among them difficulties with keeping the condition of constant volume in the case of incompressible rubbers and a need to exchange original matrix parameters for example cross‐linking and entanglement densities on some effective fitting parameters . The latter modification contradicts the very principle of hydrodynamic amplification concept, namely prediction of composite properties from the matrix values, as well as recent findings showing that the density of crosslinks and entanglements is not changed by the presence of filler particles …”

Section: Amplification Approaches Existing In Literaturementioning

confidence: 99%

Non‐Linear Viscoelasticity of Filled Polymer Melts: Stress and Strain Amplification Approach

Domurath

Saphiannikova

Heinrich

2014

Macromolecular Symposia

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Summary The aim of the present study is to develop an analytical stress and strain amplification approach (SSAA) for description of non‐linear mechanical response in polymer melts containing spherical hard inclusions in a non‐dilute regime. The main presumption of this approach is that non‐aggregating filler particles reinforce a polymer matrix purely hydrodynamically. The SSAA is verified by comparison with two other approaches existing in literature, when only stress or strain is amplified, and selected experimental results.

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Micromechanics of Internal Friction of Filler Reinforced Elastomers

Cited by 11 publications

References 16 publications

Microstructure-based modelling of arbitrary deformation histories of filler-reinforced elastomers

Microstructure-based modelling of arbitrary deformation histories of filler-reinforced elastomers

Microstructure‐based modelling and FE implementation of filler‐induced stress softening and hysteresis of reinforced rubbers

Non‐Linear Viscoelasticity of Filled Polymer Melts: Stress and Strain Amplification Approach

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