A critical analysis of the viscoelastic mechanical response of elastomers
Elastomers or rubber-like polymers are known to exhibit rich nonlinear and rate dependent mechanical response. When compounded with particulate fillers, their mechanical properties are reinforced and additional nonlinear effects such as the Payne effect (softening of the modulus with strain amplitude) and the Mullins effect (stress softening observed at large strains on subsequent deformation cycles) occur. It is generally assumed that elastomer response could be modeled as a sum of elastic (possibly with damage) and viscoelastic contributions. However, due to lack of a comprehensive experimental data set obtained for a single material, this constitutive assumption has not yet been critically examined for its ability to describe the full range of response features of this class of materials. To bridge that gap, an extensive set of linear and nonlinear mechanical experiments, including stress-strain behavior, stress relaxation and creep/recovery, was carried out on unfilled and carbon black (CB) filled lightly cross-linked Styrene-Butadiene Rubber (SBR) under a wide range of temperatures and deformation rates. The key findings were: ^ Linear deformations: ^ (i) For unfilled systems ^ The linear viscoelastic response of a series of unfilled elastomers with varying degree of cross-linking was studied. Unexpectedly, to achieve time-temperature superposition (TTS) in the uncross-linked and lightly cross-linked SBR systems, a non-standard vertical shifting was required in a relatively narrow temperature region where the shift factor was not proportional to temperature in contrast to the predictions of standard elasticity theory. This unusual temperature dependence of the shear modulus disappeared with increase in degree of cross-linking in the unfilled SBR. In case of the Polybutadiene and EPDM elastomers the temperature dependence was observed to be standard. The anomalous behavior specific to SBR elastomers was explained on the basis of the formation of micro-heterogeneities (phenyl ring stacks). ^ (ii) Filled systems ^ With careful measurements in the linear viscoelastic regime of filled elastomers, TTS was demonstrated to be valid for filled elastomers which has until now been a controversial topic in the literature owing to insufficient sensitivity of dynamic measurements at very low strains. This was established for all types of CB with the exception of the highest structure/ highest surface area CB. From the TTS it was found that the glass transition behavior as manifested in the horizontal shift factor aT is not affected by the presence of filler. The departure of the temperature dependence of the modulus from the predictions of standard elasticity theory in a narrow temperature range was also observed for filled and lightly cross-linked SBR, where the deviation increased with filler structure/surface area. ^ Nonlinear deformations: ^ Nonlinear mechanical experiments, including stress-strain behavior, stress relaxation and creep/recovery were conducted on an unfilled lightly cross-linked SBR. The viscoelastic relaxation modulus obtained for the same material from the linear viscoelastic measurements was used to describe the behavior in the nonlinear regime for validating the class of the additive constitutive models. The limitations of the additive model were clearly revealed. Specifically, the rate dependence and the hysteresis could not be simultaneously described even under moderate deformations. This is a first demonstration that some essential physics is not captured by the additive model even for the unfilled elastomers. ^ However, this study was able to show that from an engineering perspective the additive model did provide a fair description of the nonlinear response at close to ambient temperatures usually encountered during the service life of rubber components.^
James M. Caruthers, Purdue University.