Large strain time-dependent behavior of filled elastomers

The stress-strain behavior of elastomeric materials is known to be rate-dependent and to exhibit hysteresis upon cyclic loading. Although these features of the rubbery constitutive response are well-recognized and important to its function, few models attempt to quantify these aspects of response. Experiments have acted to isolate the time-dependent and long term equilibrium components of the stress-strain behavior (Bergstrom, J.S., Boyce, M.C., 1998. J. Mech. Phys. Solids 46, 931-954). These data formed the foundation of a constitutive model for the time-dependent, hysteretic stress-strain behavior of elastomers where the behavior is decomposed into an equilibrium molecular network acting in parallel with a rate-dependent network (cf. loc. cit.). In this paper, the Bergstrom and Boyce constitutive model is extended to specifically account for the effect of filler particles such as carbon black on the time-dependent, hysteretic stress-strain behavior. The influence of filler particles is found to be well-modeled by amplification of scalar equivalent values of the stretch and the shear stress thus providing effective measures of matrix stretch and matrix shear stress. The amplification factor is dependent on the volume fraction and distribution of filler particles; three-dimensional stochastic micromechanical models are presented and verify the proposed amplification of stretch and stress. A direct comparison between the new model and experimental data for two series of filled elastomers (a chloroprene rubber series and a natural rubber series) indicates that the new model framework successfully captures the observed behavior. The success of the model implies that the effects of filler particles on the equilibrium, rate and hysteresis behavior of elastomers mainly requires a treatment of the composite nature of the microstructure and not micro-level concepts such as alteration of mobility or effective crosslinking density of the elastomeric phase of the material. (C) 2000 Elsevier Science Ltd. All rights reserved.