Numerical Predictions Of Transient And Steady Rheometric Functions Of Polyethylene Melts Through A Spectral Tensorial Constitutive Equation.

Abstract

At present, one can find in the literature a high number of constitutive equations in order to quantify,
with varying precision, the stress tensor of viscoelastic materials through rheometric measurements.
These equations may be basically classified as integral and differential models. Also, these models
may be expressed through the addition of several stress modes by using a spectrum of relaxation
times, which is obtained from linear viscoelastic properties of materials, tested in the mechanical
spectrometer. Therefore, the choice of a tensorial constitutive equation to predict computationally
complex flow kinematics in the processing operations of materials is a rather difficult task with this
wide menu. This undesired situation occurs mainly when one needs a rather complete set of
rheometric functions characterizing the material under consideration. In this work we explore the
capability of the spectral Phan-Thien and Tanner model to characterize transient and steady shear and
elongational rheometric functions of linear and branched, and low and high density polyethylene
melts, involving different microstructures. For these specific purposes, precise numerical programs are
carried out to consider different mechanical histories involving experimental data already reported in
the literature. A discussion concerning the prediction quality of the rheological model proposed is
presented and some physical aspects involving requirements for further research are provided.