On the predictive/fitting capabilities of the advanced differential constitutive equations for linear polyethylene melts

The role of the Gordon–Schowalter derivative term in the constitutive models—improved flexibility of the modified XPP model

“…They also documented the deviation between shear ηγ ð Þ and complex |η*(ω)| viscosities for LDPE materials (the Cox-Merz rule states η * ω ð Þ j j ¼ ηγ ð Þ) but not for HDPE and LLDPE materials. In contrast to these results, Pivokonsky et al [7,8] presented that the CoxMerz rule was satisfied for branched polyethylene (LDPE), and for HDPE and LLDPE, this rule does not seem to be valid. The complex viscosity was always higher than the shear viscosity for both HDPE and LLDPE materials.…”

“…The GS derivative term in the constitutive models immensely improves the ability to fit shear thinning with almost no impact on elongation characteristics (see e.g., [6][7][8]). However, the usage of this term is accompanied by spurious oscillations in transient shear characteristics [1,[7][8][9].…”

“…However, the usage of this term is accompanied by spurious oscillations in transient shear characteristics [1,[7][8][9]. Vlassopoulos and Hatzikiriakos [9] pointed out that the presence of more than one oscillation in shear characteristics has not been observed experimentally; instead, an undershoot followed by a steady value is usually observed, which justifies the usage of the GS derivative term.…”

A simple phenomenological non-Newtonian fluid model

“…To test the proposed model, strain rate dependent steady shear and uniaxial extensional viscosities were taken from the open literature [11,12] for three different polymer melts (highly branched LDPE Escorene LD165 BW1, slightly branched mLLDPE Exact 0201 and linear HDPE Tipelin FS 450-26). These polymers were chosen mainly because they are very well characterized and their Theological properties have already been modeled by advanced differential parameters.…”

“…The main weakness of generalized Newtonian law model, in which the stress tensor is directly proportional to the deformation rate tensor through r] (IID, IIID), is its incapability to correctly represent the flow behavior in extensional flows, especially in plane flows, where the third invariant of deformation rate tensor IIID is 0. In order to overcome this problem, new definition of the non-Newtonian fluid viscosity is proposed here and tested for three different polymer melts (highly branched LDPE, slightly branched mLLDPE and linear HDPE) whose rheological characteristics were taken from the open literature [11,12].…”