Stress Relaxation and Differential Dynamic Modulus of Carbon Black-Filled Styrene-Butadiene Rubber in Large Shearing Deformations
Authors: Isono Yoshinobu , Ferry John D. 
Published: February 2011

Abstract
Combined measurements of shear stress relaxation and differential dynamic storage and loss shear moduli G′ and G″ have been made on styrene-butadiene rubber (type 1502) containing 50 phr N299 carbon black and 10 phr Sundex 790 oil, both cured and uncured, and compared with similar measurements on the cured and uncured gum rubber. The range of temperature was −22.5° to 63°C, and of static shear strain 0.01 to 0.40; the maximum oscillatory shear strain was about 0.005 and the frequency was usually 0.64 Hz. Dynamic measurements of G′ and G″ with no superposed static strain and stress relaxation measurements at small strains on the filled samples could be reduced by frequency-temperature superposition with αT shift factors that were somewhat larger than those that applied to the raw or crosslinked gum. At about 0.6 Hz, the filler increased the storage modulus by about a factor of 5 for the cured sample and about 10 for the uncured; the moduli for the cured and uncured filled samples were almost identical. The order of rates of relaxation was unfilled uncured &gt; filled uncured &gt; filled cured &gt; unfilled cured. At small static strains, the stress relaxation of the filled samples (both uncured and cured) was substantial, but the differential dynamic moduli G′ and G″ remained nearly equal to their values with zero static strain throughout the relaxation process. With increasing static strain γ, the strain-dependent relaxation modulus G(γ;t) decreased by as much as a factor of 3 for the filled, cured sample and 4 for the filled, uncured sample. The modulus G(γ;t) could not be factored into a strain-dependent and a time-dependent function. During stress relaxation of the filled samples (both cured and uncured) at large strains, the differential storage modulus G′(ω,γ;t) experienced a drop followed by slow recovery toward its initial value at 25°C; the loss modulus G″(ω,γ;t) was unchanged. For the filled, cured sample, complete recovery to the initial value G′(ω,0) (where 0 refers to zero static strain) was accomplished by removing the shearing stress and heating for one day at 63° followed by return of the temperature to 25°C. The results are interpreted in terms of a structure which combines a crosslinked (or, in the case of uncured, an entangled) polymer network and a network of carbon black particles. At small strains, stress relaxation is thought to be accomplished primarily by rearrangements of carbon particles and/or polymer molecules bridging them, without structural damage in the sense that the rearranged structure has the same properties as the original. These rearrangements are impeded by crosslinking in the cured vis-a-vis the uncured filled rubber. The kinetics of rearrangement may be governed by configurational changes of the polymer molecules since the temperature shift factors do not differ greatly from those for the gum rubber. At large strains, the particle network can be damaged but can regain its structure by a healing process which is accelerated at higher temperatures. The conclusions apply to the particular compound studied here and not necessarily to other rubber-black compounds, which according to the literature show great diversity of properties.