Necking in extrusion film casting: numerical predictions of the maxwell model and comparison with experiments - Pol, Harshawardhan V.; Thete, Sumeet S. (Journal of Macromolecular Science Part B-Physics, 2016)
The role of viscoelasticity in determining the extent of necking of a web of molten polymer extruded in an isothermal steady state extrusion film casting (EFC) process is considered. Following a brief review of experimental and theoretical efforts on this problem, analytical and numerical solutions to a well-established model for extrusion film casting using the Maxwell constitutive equation is presented. The extent of film necking was found to either increase or decrease with draw ratio (DR) depending on the Deborah number (De). The locus of points on the draw ratio-Deborah number diagram at which the draw ratio dependence of the necking width inverts was calculated and compared with the locus that separates the unattainable regime from the experimentally accessible regime. Predicted trends were found to be in qualitative agreement with experimental data for various polyethylene grades.

New insights into the use of multi-mode phenomenological constitutive equations to model extrusion film casting process - Thete, Sumeet S.; Doshi, Pankaj; Pol, Harshawardhan V. (Journal of Plastic Film & Sheeting, 2017)
This article is concerned with the effect of the individual viscoelastic relaxation modes of a polymer melt on its behavior in polymer melt extrusion film casting process. We compare the predicted versus experimentally obtained film necking or neck-in profile as a function of draw ratio. The predicted necking profile was obtained using well-established one-dimensional isothermal flow kinematics and consisted of using two different phenomenological constitutive equations, upper convected Maxwell and Phan-Thien-Tanner, with a discrete spectrum of relaxation times. The numerical simulations, containing the two different phenomenological constitutive equations, provided an insight into the effect of the slow and the fast relaxing modes on the stresses, strains, and strain/extensional rates that develop in the molten polymer film as it is stretched from the die exit to the chill-roll. The slow relaxing modes follow trends that are directly proportional to strain (similar to Hookean solids), whereas the fast relaxing modes follow trends that are directly proportional to the stretch rate (in accordance with Newton's law of viscosity). Comparing the numerical predictions with the experiments showed that predictions using the upper convected Maxwell constitutive equation best described the long-chain branched polymers (like low-density polyethylene, which shows extensional strain hardening) in the extrusion film casting process. On the other hand, predictions using the Phan-Thien-Tanner constitutive equation best described the linear polymers (like linear low-density polyethylene, which does not show noticeable extensional strain hardening) in the extrusion film casting process.