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.

本文研究了非牛顿材料特性对薄膜浇铸中拉延共振不稳定性的影响。通过渐近扩展并使用两个著名的本构方程，即Giesekus模型和简化的Phan–Thien / Tanner（PTT）模型，系统地导出了无限宽膜流延的粘弹性模型。在稳态分析的基础上，制定了入口应力的数值边界条件，从而抑制了模流未知的变形历史。通过线性稳定性分析计算与Deborah数和非线性参数相关的临界拉伸比。对于这两种模型，最不稳定的不稳定模式可能会在控制参数变化的情况下切换，导致临界频率下振荡频率的不连续变化。只要Deborah值不太高，就将有效伸长粘度（仅取决于局部Weissenberg数）进行分析并确定为关键量。通过使用广义牛顿流体模型来近似PTT模型可以证明这一点。在这种广义牛顿流体模型的基础上，最后探索了应变硬化和应变稀化的影响，揭示了非牛顿稳定性行为的两个相反的机制。通过使用广义牛顿流体模型来近似PTT模型可以证明这一点。在这种广义牛顿流体模型的基础上，最后探索了应变硬化和应变稀化的影响，揭示了非牛顿稳定性行为的两个相反的机制。通过使用广义牛顿流体模型来近似PTT模型可以证明这一点。在这种广义牛顿流体模型的基础上，最后探索了应变硬化和应变稀化的影响，揭示了非牛顿稳定性行为的两个相反的机制。