  In this paper, the influence of non-Newtonian material properties on the draw
resonance instability in film casting is investigated. Viscoelastic models of
infinite width film casting are derived systematically following an asymptotic
expansion and using two well-known constitutive equations: the Giesekus model
and the simplified Phan-Thien/Tanner~(PTT) model. Based on a steady state
analysis, a numerical boundary condition for the inlet stresses is formulated,
which suppresses the unknown deformation history of the die flow. The critical
draw ratio in dependence of both the Deborah number and the nonlinear
parameters is calculated by means of linear stability analysis. For both
models, the most unstable instability mode may switch under variation of the
control parameters, leading to a non-continuous change in the oscillation
frequency at criticality. The effective elongational viscosity, which depends
exclusively on the local Weissenberg number, is analyzed and identified as
crucial quantity as long as the Deborah number is not too high. This is
demonstrated by using a generalized Newtonian fluid model to approximate the
PTT model. Based on such a generalized Newtonian fluid model, the effects of
strain hardening and strain thinning are finally explored, revealing two
opposing mechanisms underlying the non-Newtonian stability behavior.
