Large strain time-dependent behavior of filled elastomers

The stress-strain behavior of elastomeric materials is known to be rate-dep endent and to exhibit hysteresis upon cyclic loading. Although these featur es of the rubbery constitutive response are well-recognized and important t o its function, few models attempt to quantify these aspects of response. E xperiments have acted to isolate the time-dependent and long term equilibri um 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 be havior of elastomers where the behavior is decomposed into an equilibrium m olecular network acting in parallel with a rate-dependent network (cf. loc. cit.). In this paper, the Bergstrom and Boyce constitutive model is extend ed to specifically account for the effect of filler particles such as carbo n black on the time-dependent, hysteretic stress-strain behavior. The influ ence of filler particles is found to be well-modeled by amplification of sc alar equivalent values of the stretch and the shear stress thus providing e ffective measures of matrix stretch and matrix shear stress. The amplificat ion factor is dependent on the volume fraction and distribution of filler p articles; three-dimensional stochastic micromechanical models are presented and verify the proposed amplification of stretch and stress. A direct comp arison between the new model and experimental data for two series of filled elastomers (a chloroprene rubber series and a natural rubber series) indic ates that the new model framework successfully captures the observed behavi or. The success of the model implies that the effects of filler particles o n the equilibrium, rate and hysteresis behavior of elastomers mainly requir es a treatment of the composite nature of the microstructure and not micro- level concepts such as alteration of mobility or effective crosslinking den sity of the elastomeric phase of the material. (C) 2000 Elsevier Science Lt d. All rights reserved.