A Novel Method for Determining the Rheological Parameters in the Wagner Constitutive Equation, for Modelling the Transient Extensional Viscosity of a LLDPE.
Mark Welsh, Sati N. Bhattacharya
Rheoloy and Materials Processing Centre, School of Civil and Chemical Engineering, RMIT
Australia
Keywords: Modelling, Extensional, Rheology
One popular constitutive equation used to predict the response of a molten polymer in extension is the Wagner modification of the K-BKZ type equation. To improve the prediction of the visco-elastic response of molten linear low density polyethylene in extensional flow using this equation, a new method of determining the constitutive equations parameters using a limited number of extensional stress relaxation experiments was developed. The method involves elongating the sample to a predetermined strain and measuring the stress decay (stress relaxation after step extensional strain). This work on uniaxial extensional rheology was performed using the extensional rheometer at RMIT. Stress relaxation after step extensional strain over Hencky strains ranging from 0.1 to 4.5, and Transient Extensional Viscosity tests at 130 °C for a Linear Low Density Polyethylene were studied. By the application of extensional strain through both the linear and non-linear visco-elastic region it was possible to generate a series of relaxation moduli that are parallel, thus fulfilling the requirement of time-strain separability required by the Wagner equation. From these moduli the Wagner damping function was determined, along with the linear visco-elastic relaxation spectrum determined by extensional stress relaxation. The transient uniaxial extensional viscosity at strain rates of 1, 0.1 and 0.01 1/s was then predicted using the Wagner Equation using the parameters determined by the aforementioned method. The Transient Extensional Viscosity predictions for the Linear Low Density Polyethylene were excellent when compared to both data from RMIT and results from laboratories overseas. The difference between Extensional Relaxation Modulus and linear relaxation modulus determined from shear experiments are explained by non-instantaneous application of extensional strain.