Experimental characterization and modeling of the non-linear mechanical behavior of unfilled and carbon black filled styrene-butadiene rubber
The stress-strain response of unfilled crosslinked elastomers subjected to loading/unloading deformation histories displays non-linear elastic and viscoelastic characteristics. In addition, filled elastomers exhibit a number of peculiar features referred to as the Mullins effect, including (i) a large stress-softening as the sample is deformed to the same strain in second and subsequent deformation cycles, (ii) a much larger hysteresis in the first deformation cycle as compared to an unfilled elastomer, (iii) a dramatic drop in stress at the point where the loading is reversed and, (iv) complete recovery of the virgin sample-like behavior when strain in second cycle exceeds the previous maximum strain. Developing a constitutive model to describe all of these effects has proven to be a major challenge. One important reason for this has been a dearth of experimental data performed on a single well-characterized unfilled and filled system where the potentially relevant parameters that control the mechanical behavior were systematically varied. A comprehensive data set has been obtained for both linear and non-linear mechanical experiments, including non-linear constant strain rate uniaxial deformation and non-linear creep/recovery for a wide range of temperatures, extension rates and stretch ratios on a styrene butadiene rubber (SBR) cured with dicumyl peroxide. The data set was analyzed using a series of non-linear viscoelastic constitutive models that employs an additive combination of hyperelastic and quasi-linear viscoelastic contributions; surprisingly the standard theory is unable to describe the data. Specifically, the standard theory predicts stiffer than experimentally observed response in constant strain rate experiments and softer than observed response in creep experiments. This indicates towards additional physical processes occurring in the material not accounted for by the standard viscoelastic constitutive models. The mechanical behavior of carbon black filled crosslinked SBR systems were studied in order to determine the effects of the amount, dispersion and properties, the particle size, surface area, structure, of the carbon black on the stress-strain response of filled elastomers (i.e. Mullins effect), at various stretch ratios, temperatures and deformation rates. The traditional model for Mullins effect advanced in the literature has been a "damage" mechanism, where the stress-softening is postulated to be a due to the breakage of either filler-rubber bonds or filler-filler contacts. The experimental data conclusively shows that damage models are inconsistent; specifically, they cannot account for the dramatic drop in stress occurring at load reversal. In order to account for the stress drop on load reversal, a new physical mechanism is proposed for filled elastomers based on the idea that the material undergoes a jamming/unjamming transition in the course of deformation. From this perspective, the virgin material being pulled for the first time is in a jammed state, and the reversal of load leads to unjamming which persists until the previous maximum deformation is exceeded. All the experimental findings are consistent with this mechanism, including stress relaxation, cyclic deformation, dependence on carbon black properties and effect of the stretch ratio. A simple phenomenological model based on the jamming/"unjamming" picture is developed. The jamming in the material is taken into account via introduction of two internal variables, one of them a structure variable which captures the memory of the deformation history. The evolution of the structure variable is governed by a relaxation equation which is highly asymmetric such that the rate of change of the structure variable depends on whether the system is being loaded or unloaded. This phenomenological model captures for the first time all the qualitative features of the Mullins effect.
Caruthers, Purdue University.
Polymer chemistry|Chemical engineering
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