Shear-dependent relaxation spectrum: Conversion from viscosity to stress relaxation after cessation of steady-state flow for polyethylene melts

Abstract

Interrelations were established, in a limited range of shear rate γ, among the non-Newtonian shear stress relaxation following cessation of steady-state flow σ(γ, t), the steady-flow viscosity η(γ), and the dynamic viscosity η(ω) or the storage modulus G′(ω) for three linear polyethylene melts (190°C). The data for these melts were obtained using the Weissenberg rheogoniometer and the Instron rheometer. Agreement between the experimental σ(γ, t) and those calculated from the relaxation spectrum H(ln τ) was good and involved no coordinate shift. The calculated values were obtained through the relation

where θ = γτ/2, τ is the relaxation time, ω is the radian frequency, h(θ) = (2/π)[cot⁻¹ θ + θ(1 - θ²)/(1 + θ²)²], andg(θ) = (2/π) [cot⁻¹ θ + θ)/(1 + θ²)]. The relaxation spectrum was obtained either from the linear viscoelastic data [η(ω)] using the iterative method of Roesler and Twyman or from the nonlinear steady-flow viscosity using the iterative procedure based on the equation