Towards a universal shear correction factor in filament stretching rheometry

Abstract

Filament stretching rheometry is a prominent experimental method to determine rheological properties in extensional flow whereby the separating plates determine the extension rate. In literature, several correction factors that can compensate for the errors introduced by the shear contribution near the plates have been introduced and validated in the linear viscoelastic regime. In this work, a systematic analysis is conducted to determine if a material-independent correction factor can be found for non-linear viscoelastic polymers. To this end, a finite element model is presented to describe the flow and resulting stresses in the filament stretching rheometer. The model incorporates non-linear viscoelasticity and a radius-based controller for the plate speed is added to mimic the typical extensional flow in filament stretching rheometry. The model is validated by comparing force simulations with analytical solutions. The effects of the end-plates on the extensional flow and resulting force measurements are investigated, and a modification of the shear correction factor is proposed for the non-linear viscoelastic flow regime. This shows good agreement with simulations performed at multiple initial aspect ratios and strain rates and is shown to be valid for a range of polymers with non-linear rheological behaviour.

Fiber-Induced Crystallization in Elongational Flows

“…Using a full slip boundary condition, the flow type is predominantly extension along the complete lateral surface of the fiber, similar to the simulation results without the fiber inclusion. , Only at the tip of the fiber a slight appearance of shear flow is present. The size of the shear area remains constant throughout the elongation of the filament.…”

“…The material, rheological, and experimental parameters used for the simulation are given in Table . Here, the viscosity is obtained by taking the shear viscosity at an effective shear rate of 3 ε̇ for the iPP 1 material used in the work of Roozemond et al at a temperature of 160 °C . The obtained value is then shifted to a temperature of 133 °C using the Arrhenius equation …”

“…The work of van Berlo et al , is followed for applying the mesh movement and remeshing and projection procedure in the numerical simulation. − Here, a detailed explanation of the finite element model can be found. Analogously, the controller of the radius, which is added to ensure the radius decreases exponentially such that the strain rate is constant, is adopted from the work of Román Marín et al The domain Ω is discretized using triangular, isoparametric, P 2 –P 1 (Taylor-Hood) elements for the interpolation of the velocity and pressure.…”