Rheological Modeling of Polymer Melts

Transient Rheological Modeling of Polymer Melts

Capillary and parallel plate rheological characterization was conducted for a low density polyethylene. In contrast with conventional rheological analysis, steady conditions were not assumed. Transient data, with time steps between 0.0001 and 0.2 s, were analyzed with a non-linear, viscoelastic constitutive model in which the relaxation time was modeled as a function of the applied stress. The fit model explained more than 99% of the observed transient variation in the capillary and parallel plate rheometers. The model coefficients for the capillary and parallel plate were compared directly to conventional linear viscoelastic analysis of the same parallel plate data. The results indicate that the described constitutive transient rheological modeling of polymer melts closely predicts the observed viscoelastic behavior of the polymer melt tested in the parallel plate rheometer.

Furthermore, the results indicate that the relaxation spectrum modeled with the transient analysis of the capillary rheological data correlate closely to the results predicted by the same transient analysis of parallel plate rheological data. The conclusion is that described constitutive modeling describes the viscoelastic behavior in both capillary and parallel plate rheometers. Moreover, the analysis and results suggest that the viscoelastic behavior of the polymer melt is a significant factor during the rheological characterization and the modeling of the transient response should be taken into consideration during rheological analysis to provide high fidelity models.

Transient Modeling of Viscosity

Towards a Unified Theory of Fluids

This research is investigating a simple but non-linear and as yet unexplored constitutive model for viscoelastic relaxation to explain the non-Newtonian behavior of polymers as well as their creep and stress relaxation phenomena. Inspired by Maxwell’s observation that the observed relaxation time is a function of the applied stress, the research will implement a corotational Maxwell model with the relaxation time described as a power law or reciprocal function of the stress. The main research tasks are:

  1. the theoretical modeling of the creep, viscosity, and associated flows according to the proposed corotational model, including implementation of both time-temperature and time-stress superposition to model the relaxation response of the polymer as a function of the material pseudo time at varying material temperatures and stresses; 
  2. numerical simulation of axisymmetric geometries including non-isothermal and non-isobaric effects for the modeling of capillary, parallel plate, and polymer processing applications; 
  3. validation of the proposed constitutive models with performance assessed by the consistency of the model coefficients fit to data from capillary rheometer and parallel plate rheometers, as well as the accuracy of extrudate swelling predictions for different die geometries, material systems, and processing conditions; and, 
  4. dissemination via a scalable web fitting service for implementation in commercial simulations.

The Intellectual Merit arises from the modeling and characterization of highly transient polymer melts, which has been identified as a barrier to high fidelity simulations. The research will specifically test the hypotheses that (1) the behavior of shear thinning fluids exhibiting a Newtonian viscosity transitioning at a critical shear stress to a power-law regime can be explained by the fluid’s relaxation time behavior as a function of the applied stress; (2) the viscous and viscoelastic behavior of fluids can be predicted from the derived constitutive model with temperature dependent material modulus data through the use of time-stress superposition; (3) this model unifies the solid-like and fluid-like responses of polymer melts over a broad time-temperature domain to significantly improve simulation fidelity in polymer processing with an application to extrudate swelling and draw down. The intellectual merit of the proposed research is further enhanced by the possibility that the proposed theory of stress-time superposition may be extensible beyond polymer melts to molten metals, biological materials, and other composites that are currently of interest in large amplitude oscillatory shear (LAOS) flow. 

The Broader Impacts are far reaching and widespread across rheology, simulation, and product development, including: (1) Capillary viscosity, when characterized, relies on a small set of potentially erroneous "steady state" data while discarding the majority of the "transient" data; the proposed research will provide higher fidelity rheological models for analysis and design by modeling the transient effects. (2) The applied system identification techniques will allow the acquisition of steady state viscosity, modulus, and relaxation spectrum (and thus storage/loss moduli) from capillary rheometers without the need for additional instrumentation; the new methods will greatly expand the universe of materials described by viscoelastic model coefficients and with it the usefulness of advanced simulations. (3) The described techniques will be very broadly disseminated through a scalable web-fitting service with open source releases of the implemented models and rheological fitting routines while creating a clearinghouse for on-line rheological analysis as well as a repository of characterized materials data and constitutive model coefficients. The proposed model has the potential to significantly improve accuracy of viscoelastic behavior prediction, which is a major source of error in current polymer processing applications.

Observed creep behavior, and the behavior predicted with a proposed three coefficient constitutive model

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