Rubber materials are made of two networks, chemical and filler networks. The networks are characterized usually by overall network density estimated at equilibrium condition. However, rubbers are used in nonlinear conditions where the filler network may change from the one at equilibrium. We need additional information on the filler network. Hence, differential dynamic modulus (DDM) in large compression (eϭϪ0.1) and recovery (eϭ0) were measured for the samples filled with carbon blacks (CB) having different primary particle sizes. The change in EЈ for unfilled sample was reversible in large compression followed by recovery, while those for filled samples were irreversible, showing change in filler network in large deformation. The differences in DDM at the recovered and the initial states were compared for characterization of the filler network. The difference for the sample filled with smaller CB was larger than the one with larger CB. The results show that the rubber filled with CB having smaller particle size makes weaker filler network. In addition, we observed the restoration behavior of the filler network structure. Recovery of filler network ruptured due to large compression and recovery in shape was attained at a time scale depending on particle size. The characteristic time was found to increase with increase in the CB particle size. It was concluded that the restoration process of CB filler network is based on diffusion of CB aggregate.
Correspondence between nonlinear viscoelastic properties and change in various networks in carbon black (CB) filled, uncured SBRs has been studied by using combined measurements of relaxation modulus, differential dynamic modulus, and volume resisitivity in wide range of filler concentrations at various shear strains. Volume resistivity at no deformation showed step-off like change which can be explained by the percolation theory. This indicates formation of contact filler network at high filler loading. In addition, change in volume resistivity showed clear correspondence with linear-nonlinear transition in viscoelasticity. By the use of simple three-network model, contributions of contact filler, bridged filler, and entanglement networks to relaxation modulus were estimated. It was found that contact filler and bridged filler networks were dominant at lower and at higher filler concentrations, respectively. It was proposed, furthermore, that differential dynamic modulus can be used as the probes for changes in contact filler and bridged filler networks, respectively.
The two-dimensional contact pressure distribution of a running radial tire under load is a fundamental property of the tire structure. The two-dimensional contact pressure distribution in the static case and the one-dimensional contact pressure distribution in the dynamic case were previously analyzed for a spring bedded ring model consisting of a composite belt ring and a spring system for the sidewall and the tread rubber. In this paper, a Voigt-type viscoelastic spring system is assumed for the sidewall and the tread rubber. We analyzed the dynamic deformation of the belt ring in a steady state, and obtained the two-dimensional dynamic contact pressure distribution at speeds up to approximately 60 km/h. The predicted contact pressure distribution for a model with appropriate values for the damping coefficient of each constituent rubber is shown to be in good agreement with experimental results. It is a characteristic feature that increasing velocity yields an increase in the pressure at the leading edge of the crown centerline in the contact area and at the trailing edge of the shoulder line.
The contact deformation of a radial tire with a camber angle, has been an important problem closely related to the cornering characteristics of radial tires. The analysis of this problem has been considered to be so difficult mathematically in describing the asymmetric deformation of a radial tire contacting with the roadway, that few papers have been published. In this paper, we present an analytical approach to this problem by using a spring bedded ring model consisting of sidewall spring systems in the radial, the lateral, and the circumferential directions and a spring bed of the tread rubber, together with a ring strip of the composite belt. Analytical solutions for each belt deformation in the contact and the contact-free regions are connected by appropriate boundary conditions at both ends. Galerkin's method is used for solving the additional deflection function defined in the contact region. This function plays an important role in determining the contact pressure distribution. Numerical calculations and experiments are conducted for a radial tire of 175SR14. Good agreement between the predicted and the measured results was obtained for two dimensional contact pressure distribution and the camber thrust characterized by the camber angle.
Uncured, filled rubbers show remarkable nonlinear viscoelasticity as well as cured, filled rubbers. The nonlinearity may come from change in entanglement and filler network structures. Many people use dynamic modulus to characterize rubber materials. However, dynamic modulus cannot be defined at large strain. Hence we must study a viscoelastic function to be defined at large strain. In addition, we need other information to separate the effects of the change in entanglement and filler network structures on nonlinear viscoelasticity. In this work, we have measured simultaneously relaxation modulus G(γ,t) and electrical resistivity ρ(γ,t) for carbon black (CB)-filled, uncured styrene-butadiene copolymers (SBRs) at wide range of strains. Electrical resistivity at equilibrium, ρ(0,t), showed step-like change at the CB loading between 20 and 35 phr, indicating threshold for filler network formation should exist in the range of values in CB loading. Both G(γ,t) and ρ(γ,t) for the samples having CB loading to be higher than the threshold showed nonlinearity at the strain larger than shear strain γ=0.1, indicating rupture in filler network at large strain.
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