Nonlinear Viscoelastic Response of Amorphous Elastomers to Constant Strain Rates

Tensile stress-strain curves determined at constant strain rates are nonlinear because relaxation of stress generally occurs during a test and also because of inherent nonlinear effects. To develop a method for determining the conditions under which time and nonlinear effects are separable, consideration was first given to a linear viscoelastic material. It was shown that stress-strain curves determined at different strain rates superpose to yield a single curve on a plot of log σ(ε, t)/ε vs. log t, where σ(ε, t) is the stress, a function of the strain ε and the time t; by definition t equals ε/ε where ε is the strain rate. The quantity σ(ε, t)/ε was called the constant-strain rate modulus F(t) which is related exactly to the stress-relaxation modulus E(t) by the equation E(t)=F(t)(1+m) where m=d log F(t)/d log t. For amorphous elastomers tested in tensions over a wide range of strain, it was proposed that stress-strain curves determined at constant strain rates can be represented by F(t)=g(ε)σ(ε,t)/ε where g(ε) is a function only of strain and approaches unity as the strain goes to zero. To test this equation, an analysis was made of stress-strain curves of an SBR gum vulcanizate measured to rupture at numerous strain rates at 10 temperatures between −42.8 and 93.3° C. From − 34.4 to 93.3° C, g (ε) was found to be independent of both time and temperature, but at −42.8° C for strains greater than about unity, g(ε) was found to be different. The functional form of g(ε) was compared with that predicted by three different analytical expressions for representing stress-strain data. To show further the advantages of F(t) for representing stress-strain data determined at different strain rates and temperatures, previously published data on the NBS polyisobutylene were presented on a plot of log F(t)298/T vs. log t/aT. From the composite curve, E(t) was calculated and found to be in close agreement with published data.