Viscoelasticity carbon black-filled rubber

When a sinusoidal strain is imposed on a linear viscoelastic material, e.g., unfilled rubbers, a sinusoidal stress response will result and the dynamic mechanical properties depend only upon temperature and frequency, independent of the type of deformation (constant strain, constant stress, or constant energy). However, the situation changes in the case of filled rubbers. In the following, we mainly discuss carbon black filled rubbers because carbon black is the most widespread filler in rubber products, as for example, automotive tires and vibration mounts. The presence of carbon black filler introduces, in addition, a dependence of the dynamic mechanical properties upon dynamic strain amplitude. This is the reason why carbon black filled rubbers are considered as nonlinear viscoelastic materials. The term non-linear viscoelasticity will be discussed later in more detail. 

The effect of amplitude-dependence of the dynamic viscoelastic properties of carbon black filled rubbers has been known for some 50 years, but was brought into clear focus by the work of Payne in the 1960s [1-7]. Therefore, this effect is often referred as the Payne-effect. It has been also investigated intensively by... 

Linear (Small Strain) Viscoelasticity of Carbon Black Filled Rubbers... 

It has been remarked that time (frequency) - temperature reduced data on carbon black filled rubbers exhibit increased scatter compared to similar data on unfilled polymers. Payne (102) ascribes this to the effects of secondary aggregation. Possibly related to this are the recent observations of Adicoff and Lepie (174) who show that the WLF shift factors of filled rubbers giving the best fit are slightly different for the storage and loss moduli and that they are dependent on strain. Use of different shift factors for the various viscoelastic functions is not justified theoretically and choice of a single, mean ar-funetion is preferred as an approximation. The result, of course, is increased scatter of the experimental points of the master curve. This effect is small for carbon black... 

The non linear viscoelasticity of various particles filled rubber is addressed in range of studies. It is found that the carbon black filled-elastomer exhibit quasi-static and dynamic response of nonlinearity. Hartmann reported a state of stress which is the superposition of a time independent, long-term, response (hyperelastic) and a time dependent, short-term, response in carbon black filled-rubber when loaded with time-dependent external forces. The short term stresses were larger than the long term hyperelastic ones. The authors had done a comparative study for the non linear viscoelastic models undergoing relaxation, creep and hysteresis tests [20-22]. For reproducible and accurate viscoelastic parameters an experimental procedure is developed using an ad hoc nonlinear optimization algorithm. 

The main aspects of the nonlinear theory of elasticity are presented. As nonlinear elasticity, and, in particular, hyperelasticity, is such a useful tool in the description of the behavior of carbon black-filled rubber undergoing quasi-static loadings, the main methodologies for describing the behavior of materials subjected to large strains are introduced. Some of the results herein presented will be apphed to nonlinear viscoelastic constitutive models and discussed in subsequent review. 

It has long been reported in literature [18, 19] that (carbon black) filled compounds are yield stress materials, i.e., when plotted versus the shear stress, the shear viscosity appears bounded by a critical shear stress Oc so that below it, no flow occurs (in other words, the viscosity goes to infinity as the shear stress decreases towards Oc). The right graph in Fig. 4 shows indeed that the shear viscosity q(o) increases, as the shear stress decreases, but one would hardly derive a bounding critical shear stress from such data. In other terms, that filled rubber compounds are essentially nonlinear viscoelastic materials is experimentally well demonstrated but that they are yield stress materials might be considered as a controversial subject. 

There is much more to tell about the rheology of filled melts, but space limitations preclude further discussion here. The interested reader is directed to the articles by Khan and Prud homme (1987), Metzner (1985), amd White (1982), the book by Han (1981), and references therein. Viscoelastic theories for filled melts, especially for rubbers containing carbon black, can be found in Montes and White (1993), Witten et al. (1993), and references therein. 

The effect of filler structure on the rubber properties of filled rubber has been explained by the occlusion of rubber by filler aggregates (45). When stmctin-ed carbon blacks are dispersed in rubber, the polymer portion filling the internal void of the carbon black aggregates, or the polymer portion located within the irregular contours of the aggregates, is imable to participate fully in the macrodeformation. The partial immobilization in the form of occluded rubber causes this portion of rubber to behave like the filler rather than like the polymer matrix. As a result of this phenomenon, the effective volume of the filler, with regard to the stress-strain behavior and viscoelastic properties of the filled rubber, is increased considerably. 

It has been shown that the viscoelastic losses of OH-terminated poly(dimethyl-siloxane), crosslinked with tetra-functional silicates, decreases with increased crosslink density. Furthermore, identical results were obtained when the polymer was crosslinked with y-irradiation, in bulk and in solution this indicates that there is no significant change in the number of interchain entanglements, and these are responsible for the observed losses. Vulcanization studies of poly(di-methylsiloxane)s, y-irradiated up to 500 Mrad, have shown linear correlation of the crosslink density with swelling, indentation and extension behaviour up to 160 Mrad, and exponentially for higher doses. Basic principles for the thermal stabilization of silicone rubbers, filled with carbon blacks and silica, have been discussed and a tentative stabilization mechanism put forward. ... 

The viscoelastic analysis for DMA requires that the sample be in the linear viscoelastic range. In practice, this means that the strain/stress behavior is independent of the strain/stress level. Unmodified polymers, such as PMMA and PC, which are amorphous, are not likely to exhibit strain-dependent behavior as long as the strain amplitude is kept below about 0.3%. However, certain filled materials, especially carbon black or sUica-filled rubbers, may... 

Nakajima, N., Bowerman, H.H. and Collins, E.A. (1978) Nonlinear viscoelastic behavior of butadiene-acryloiutrile copolymers filled with carbon black, Rubber Chem. Tech., 51,322-34. 

This paper describes the effect of velocity and temperature on the friction coefficient of both filled and unfilled rubber vulcanizates sliding on smooth ice. It has been shown that the mechanism of the friction of rubber on ice is the same as that on other smooth surfaces under similar low sliding speed conditions and that the maximum friction coefficients are similar. The Williams Landel and Ferry equation is used to superpose curves of the velocity dependence of the friction coefficient at different temperatures to produce a master curve and therefore to demonstrate the viscoelastic nature of the frictional mechanism. The frictional behaviour depends on the condition of the ice track and a tentative explanation for this observation is suggested. The frictional properties of vulcanizates containing various amounts of a reinforcing carbon black filler have been studied. 

Using the mixing method described in the previous paper in this series, which produces reproducible data, the authors investigated each factor that affects the black incorporation time. Various carbon blacks, oil-extended rubber and oil were used as the materials in the tests. The mixing conditions used were the rotational speed, rotational ratio of the rotor, fill factor and ram pressure. The authors studied the effect of these factors on the black incorporation time by the new theory based on static electricity phenomena and rabber viscoelasticity. 7 refs. Articles from this journal can be requested for translation by subscribers to the Rapra produced International Polymer Science and Technology. 

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