Predictive/fitting capabilities of differential constitutive models for polymer melts—reduction of nonlinear parameters in the eXtended Pom-Pom model

Viscoelastic Property of an LDPE Melt in Triangular- and Trapezoidal-Loop Shear Experiment

The time-dependent viscoelastic behaviors of a low-density polyethylene melt (LDPE) in a triangular- and trapezoidal-loop shear experiment reported previously are described here by an integral-type Rivlin–Sawyers (RS) constitutive equation. The linear viscoelasticity of the melt was obtained through a dynamic frequency sweep experiment at a small strain and fitted by a relaxation spectrum. The nonlinear viscoelasticity was characterized by viscosity. All the experimental viscoelastic behaviors of the melt can be divided into two types in terms of the predictions of the RS model: (1) predictable time-dependent viscoelastic behaviors at low shear rates or during short-term shear, and (2) unpredictable shear weakening behavior occurring at the high shear rate of 3–5 s⁻¹ during long-term shear with the characteristic time interval of about 40–100 s. The influence of experimental error caused possibly by inhomogeneous samples on the viscoelasticity of the melt was analyzed, and the large relative error in the experiment is about 10–30%.

Two Ways to Examine Differential Constitutive Equations: Initiated on Steady or Initiated on Unsteady (LAOS) Shear Characteristics

The exponential Phan–Tien and Tanner (PTT), Giesekus, Leonov, and modified extended Pom–Pom (mXPP) differential constitutive models are evaluated in two ways: with regard to steady shear characteristics and with regard to large amplitude oscillatory shear characteristics of a solution of poly(ethylene oxide) in dimethyl sulfoxide. Efficiency of the models with nonlinear parameters optimized with respect to steady shear measurements is evaluated by their ability to describe large amplitude oscillatory shear (LAOS) characteristics. The reciprocal problem is also analyzed: The nonlinear parameters are optimized with respect to the LAOS measurements, and the models are confronted with the steady shear characteristics. In this case, optimization is based on the LAOS measurements and equal emphasis is placed on both real and imaginary parts of the stress amplitude. The results show that the chosen models are not adequately able to fit the LAOS characteristics if the optimization of nonlinear parameters is based on steady shear measurements. It follows that the optimization of nonlinear parameters is much more responsible if it is carried out with respect to the LAOS data. In this case, when the optimized parameters are used for a description of steady shear characteristics, efficiency of the individual models as documented differs.