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A level set method for simulating wrinkling of extruded viscoelastic sheets
Author(s) -
Kabanemi Kalonji K.,
Marcotte JeanPhilippe
Publication year - 2020
Publication title -
polymer engineering and science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.503
H-Index - 111
eISSN - 1548-2634
pISSN - 0032-3888
DOI - 10.1002/pen.25409
Subject(s) - materials science , extrusion , viscoelasticity , composite material , die (integrated circuit) , die swell , weissenberg number , newtonian fluid , finite element method , mechanics , structural engineering , physics , engineering , nanotechnology
When a polymer is extruded freely from a rectangular die of large cross‐sectional aspect ratio, wrinkles are observed. While not present in extruded Newtonian materials, such wrinkles develop in extruded viscoelastic sheets and are understood as an elastic stress‐driven instability. The present study is devoted in developing a transient finite element method, which combines the matrix‐logarithm‐based formulation of the conformation tensor and the single‐phase level set method, for simulating wrinkles that form during sheet extrusion of viscoelastic fluids. Numerical analyses of sheet extrusion were conducted over a wide range of flow rate and width‐to‐thickness ratio of the die exit cross section, χ , to determine critical conditions for the onset of wrinkling of extruded sheets. For large aspect ratios, that is, χ >> 1 , wrinkles develop at moderate extrusion flow rate, corresponding to a Weissenberg number of about 29. Calculations based on Rayleigh's energy method show that the critical compressive stress, σ c , for the onset of wrinkling of an elastic sheet scales like σ c ~1/ χ 2 , with a significant drop for χ >> 1 . As next to the die exit lip, compressive normal stresses are induced in the extruded sheet, wrinkling will take place for large χ ( σ c being small), in accordance with numerical predictions.