Simulation of the linear rheological behavior of silica-filled, star-shaped SBR compounds

Pole, Sandeep S.; Isayev, A. I.

doi:10.1007/s00397-017-1049-5

Cited by 5 publications

(12 citation statements)

References 20 publications

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“…An extensive investigation on the effect of various model parameters on rheological behavior of compounds was conducted in our previous study 27 . Based on this investigation, model parameters for the relaxation modes of the SBR gum,

η_{k}^{m}

and

θ_{k}^{m}

, were found by fitting the Leonov model to measured values of G ′ and G ′′ vs. frequency to the following equations:

G^{' m} = \sum_{k = 1}^{N} \frac{η_{k}^{m}}{θ_{k}^{m}} ([], \frac{{(ω θ_{k}^{m})}^{2}}{1 + {((), ω θ_{k}^{m})}^{2}}),

G^{'' m} = m_{0} ω + \sum_{k = 1}^{N} \frac{η_{k}^{m}}{θ_{k}^{m}} ([], \frac{((), ω θ_{k}^{m})}{1 + {((), ω θ_{k}^{m})}^{2}}),

where ω is the frequency.…”

Section: Methodsmentioning

confidence: 99%

“…These equations are similar to those of the generalized Maxwell model, excluding the term of m 0 ω in Equation ). In our previous study 27 we measured G ′ and G ′′ as functions of frequency for the SBR gum at a linear strain amplitude and fit them to the Leonov model. Nine relaxation modes were found sufficient to obtain a good fitting.…”

Section: Methodsmentioning

confidence: 99%

“…Several researchers have investigated the relaxation behavior of uncured rubber compounds filled with carbon black and silica. Relaxation after a step shear strain has been investigated 16–28 . Stress relaxation tests have also been conducted in extension, 29,30 compression, 29 and after cessation of steady shear flow 17,28,31,32 .…”

Section: Introductionmentioning

confidence: 99%

“…Stress relaxation tests have also been conducted in extension, 29,30 compression, 29 and after cessation of steady shear flow 17,28,31,32 . While most of this research has focused on carbon black‐filled elastomers, some of it has focused on silica‐filled compounds, 19,21,26–30,32 and some of this research has specifically studied SBR/silica systems 21,26–28,30 …”

Section: Introductionmentioning

confidence: 99%

“…Although the stress relaxation behavior of SBR containing silica has been previously studied, the emphasis has generally been on linear SBR using a single silica grade. We have recently carried out theoretical and experimental research on the linear rheology of compounds of star‐shaped SBR filled with silica of various surface areas 27 . Accordingly, the present study is directed at expanding our previous novel research by assessing the influence of surface area of silica on the nonlinear stress relaxation behavior of compounds of star‐shaped SBR containing silica after a step shear strain.…”

Section: Introductionmentioning

confidence: 99%

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The nonlinear stress relaxation behavior after a step shear of star‐shaped styrene‐butadiene rubber filled with precipitated silica: Experiment and simulation

Pole

Isayev

2020

J of Applied Polymer Sci

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The nonlinear stress relaxation behavior after a step shear strain of star‐shaped SSBR/silica compounds containing 21 vol% filler of various surface areas was measured and simulated using constitutive equations. A styrene‐butadiene rubber (SBR) gum and SBR filled with silica having BET surface areas of 55, 135, 160, and 195 m2/g were used. Relaxation modulus behavior of the filled compounds was found to be dependent on surface area. Specifically, stress relaxation tests indicated that an increase in surface area led to increase in values of relaxation moduli in both the linear and nonlinear regimes. The time‐dependent relaxation modulus exhibited a plateau at long times of relaxation in compounds containing silica of high surface area. Additionally, good time‐strain superpositions were achieved for all samples at intermediate times of relaxation, and the strain‐dependent damping function decreased with filler surface area. The constitutive equations proposed by Leonov and Simhambhatla and Leonov, modified to include multimodal relaxation of the particle network, were used to predict the time evolution of the relaxation modulus in the nonlinear regime for all samples. The simulations provided good results for the SBR gum for all tested strain levels. Also, in the compounds filled with silica, both models satisfactorily described the experimental observation in the nonlinear regime at low strain levels. However, at higher strain levels, due to a possible slip effect, the simulations overpredicted measured values of the relaxation moduli, thus leading to only qualitative predictions of the observed behavior. It is also possible that neither model accurately captured the floc rupture kinetics of these complex rubber compounds.

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η_{k}^{m}

and

θ_{k}^{m}

, were found by fitting the Leonov model to measured values of G ′ and G ′′ vs. frequency to the following equations:

G^{' m} = \sum_{k = 1}^{N} \frac{η_{k}^{m}}{θ_{k}^{m}} ([], \frac{{(ω θ_{k}^{m})}^{2}}{1 + {((), ω θ_{k}^{m})}^{2}}),

G^{'' m} = m_{0} ω + \sum_{k = 1}^{N} \frac{η_{k}^{m}}{θ_{k}^{m}} ([], \frac{((), ω θ_{k}^{m})}{1 + {((), ω θ_{k}^{m})}^{2}}),

where ω is the frequency.…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The nonlinear stress relaxation behavior after a step shear of star‐shaped styrene‐butadiene rubber filled with precipitated silica: Experiment and simulation

Pole

Isayev

2020

J of Applied Polymer Sci

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Correlations in rheological behavior between large amplitude oscillatory shear and steady shear flow of silica‐filled star‐shaped styrene‐butadiene rubber compounds: Experiment and simulation

Pole

Isayev

2021

J of Applied Polymer Sci

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The large amplitude oscillatory shear (LAOS) and steady shear behavior of star‐shaped SSBR/silica 60 phr (21 vol%) compounds with various filler surface areas was measured and simulated. An SBR gum and SBR compounds containing four different silicas with surface areas of 55, 135, 160, and 195 m2/g were utilized. Rheological behavior indicated clear correlation with surface area. LAOS tests showed an increase in dynamic moduli, shear stress, and higher order harmonic contributions with surface area. Elastic and viscous Lissajous figures showed significant distortion at intermediate and higher strain amplitudes. Additionally, ratios of third and fifth order stress harmonics to the first stress harmonic (I3/1 and I5/1, respectively) showed a ''bump'' at intermediate strain amplitudes for the three highest surface area compounds. With regards to steady shear, all materials showed strong shear thinning behavior, and an increase in shear viscosity with surface area. The Cox‐Merz rule was shown to be valid for the SBR gum but not for the filled compounds. However, the complex viscosity as a function of shear rate amplitude at various frequencies at high strain amplitudes and the steady shear viscosity as a function of shear rate coincided. This correlation, referred to as the Philippoff approach, has important ramifications for the rubber industry, providing quick data for predicting processing behavior. The Simhambhatla‐Leonov model was successfully employed to simulate rheological behavior for the SBR gum and the lowest surface area silica compound, but the model yielded mixed results for the higher surface area silica compounds.

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Liquids

Malkin

Isayev

2022

Rheology

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Simulation of the linear rheological behavior of silica-filled, star-shaped SBR compounds

Cited by 5 publications

References 20 publications

The nonlinear stress relaxation behavior after a step shear of star‐shaped styrene‐butadiene rubber filled with precipitated silica: Experiment and simulation

The nonlinear stress relaxation behavior after a step shear of star‐shaped styrene‐butadiene rubber filled with precipitated silica: Experiment and simulation

Correlations in rheological behavior between large amplitude oscillatory shear and steady shear flow of silica‐filled star‐shaped styrene‐butadiene rubber compounds: Experiment and simulation

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