Visco-elasticity under large, uniform deformations of rubber-like polymers in the transition range

Abstract

The relaxation moduli of crosslinked polymers as a function of the main elongation ratios have been calculated on the basis of a non-Gaussian sub-chains model. The effect of a mobility reduction of the sub-chains as a result of elongation has been examined on freely jointed chain models and those having a weak correlation in orientationally adjacent chain units. The movements are thought to be instant rotations by 180° of an adjacent chain unit pair. The effect of a chain rigidity increase in the case of the freely jointed chain model in fully compensated by a reduction in movement as regards the relaxation time, while the existence of a correlation reduces the latter. A reduction of the sub-chain movements due to elongation makes stronger the dependence of the relaxation functions only on the elongation ratio. The simple elongations, uniform expansion, pure shear at constant rate of natural deformations, and also pure shear at constant rate, were examined for constant relaxation times. The finite extensibility of the chains results in a typical increase of the viscous stress in the network and the appearance of normal viscous stresses in simple shear.