Constitutive equations for modelling of polymeric materials and rubbers

Abstract

Extrusion of polymeric materials can be made more efficient by modelling with computational techniques. Material-dependent data obtained through a constitutive equation is required to close the fluid dynamic equations. The paper outlines constitutive equations developed for non-Newtonian behaviour and details the choice that is required to obtain a constitutive equation that encapsulates actual material behaviour. 

Constitutive relations for the extrusion of siloxane gum and silicone rubber

“…The constitutive equations available have been reviewed5 and a detailed study of the rheological data4 has resulted in the following equations being used to simulate the silicone materials. Of the generalised Newtonian fluid (GNF) models the Yasuda model of Eqn (1) was chosen to simulate the purely viscous behaviour of the silicones: where η is the shear viscosity at 0 and infinite shear, λ N is the invert of the shear rate, n is the non‐Newtonian power‐law index, a is the Carreau index and II D is the second invariant viscosity function.…”

“…Of these the White–Metzner model (eqn [34] in Ref. 5) was able to describe the shear behaviour but underestimated die swell downstream of the extrusion. The Giesekus model (eqn [32] in Ref.…”

“…The Giesekus model (eqn [32] in Ref. 5) was unable to simultaneously fit the shear‐thinning shear viscosity and the tension‐thinning extensional viscosity. The Phan Thien–Tanner (PTT) model, with multiple relaxation modes could handle both shear and extensional viscosity data.…”

“…Of the integral viscoelastic models, the Papanastasiou–Scriven–Macosko (PSM) form of the Kaye–Bernstein–Kearsley–Zapas (KBKZ) equation (eqn (75) in Ref. 5) which was developed for the silicone gum material, gave an improved fit of data over other models such as the Wagner equation in the linear regime and at higher strains. The modification of the KBKZ model proposed by Luo and Tanner7 (eqn [77] in Ref.…”

“…The modification of the KBKZ model proposed by Luo and Tanner7 (eqn [77] in Ref. 5) enabled the second normal stress to be investigated which is important as it affects swelling behaviour 8. The modelling of die swell was possible using the irreversible form of the PSM equation (eqn [79] in Ref.…”