Analysis of Stress Relaxation of Reinforced Rubber Vulcanizates under Large Deformations with a Series-Expanded Constitutive Equation

Abstract

A constitutive model is developed by assuming a Maxwellian relaxation for the relaxation function ψ_A, ψ_B, ψ_C of the coefficients in the constitutive equation f(t)={A(t)+B(t)/α+C(t)α²}×(α-1/α²), where f denotes the tension based on the cross-sectional area, α denotes the extension ratio and the coefficients A(t), B(t), C(t) are given as A(t)=A_D-∫^t₀ψ_A(t-τ)dτ, B(t)=B₀-∫^t₀ψ(t-τ)dτ, C(t)=C₀-∫^t₀ψc(t-τ)dτ, where A₀, B₀, C₀ are the coefficients at t=0. The above equation was derived as one of the approximation equations of the expansion type from the constitutive equation for Green-Rivlin viscoelastic bodies. An experimental equation, f₀=Kf_∞, is also introduced into the equation, where f₀,f_∞, are respectively the initial tension and the relaxed equilibrium tension during stress relaxation of carbon black filled rubber; and K is a constant almost independent of the kinds of black fillers, of concentration, and of extension ratio. Stress relaxation data for HAF black filled SBR under large deformations are compared with the equation obtained.