Viscoelastic Properties of a Styrene-Butadiene Vulcanizate in Large Biaxial and Simple Tensile Deformations

Abstract

Biaxial tensile tests were made by stretching thin-wall cylindrical specimens in the axial direction and controlling the internal pressure to maintain constant the initial outside diameter; this procedure gives essentially pure shear. From −40 to 20°C, stress-relaxation data were obtained at axial extension ratios, λ1, up to about 2.5; relaxation data in simple uniaxial tension at −20°C were also obtained. From 25 to 90°C tests were made at constant extension rates between 0.0031 and 3.1 min−1 in both biaxial and simple tension. The data is biaxial tension conform to equations of the form: σ1(λ1,i,T)=4G(t,T)Γ1(λ1) and σ2=2G(t,T)Γ2(λ1), where σ1 and σ2 are the axial and circumferential stresses and G(t,T) is the time- and temperature-dependent stress-relaxation modulus in shear; Γ1(λ1) and Γ2(λ1) are functions only of λ1 that approach the Cauchy strain at sufficiently small deformations. From this behavior, observed over a time-temperature range within which the modulus varies about 1.5-fold, it follows that (1/G)(∂W/∂I1)≡W1/G and (1/G)(∂W/∂I2)≡W2/G are time and temperature independent, where W is the “strain energy” and I1 and I2 are strain invariants. (For pure shear, I1=I2=λ12+λ2−2+1.) The data show that W2/G is a decreasing function of the deformation and that W1/G is sensibly constant for I1<5.3, i.e., λ1<2; at larger deformations W1/G appears to decrease somewhat. Subject to the assumption that W1 is independent of I2, or equivalently that W2 is independent of I1, a calculation of simple tensile behavior gave results in reasonable agreement with experimental data. Under the conditions that W1/G remains constant, the strain energy is represented closely by: W=G[0.3125(I1−3)+0.5625 ln (I2/3)]. A representation of data by the product of a time- and temperature-dependent modulus and a deformation function is strictly valid only when W2/W1 is independent of time and temperature; the limitations of this method are briefly considered.