Criterion for extensional necking instability in polymeric fluids

Abstract

We study the linear instability with respect to necking of a filament of polymeric fluid undergoing uniaxial extension. Contrary to the widely discussed Considere criterion, we find the onset of instability to relate closely to the onset of downward curvature in the time (and so strain) evolution of the zz component of the molecular strain, for extension along the z axis. In establishing this result numerically across five of the most widely used models of polymer rheology, and by analytical calculation, we argue it to apply generically. Particularly emphasized is the importance of polymer chain stretching in partially mitigating necking. We comment finally on the relationship between necking and the shape of the underlying steady state constitutive curve for homogeneous extension.

4 pages, 4 figures

References in corpus (2)

• Recent experimental probes of shear banding
• Dynamics of Large-Scale Plastic Deformation and the Necking Instability in Amorphous Solids

Cited by in corpus (9)

• Shear Banding of Complex Fluids
• Perspectives on the viscoelasticity and flow behavior of entangled linear and branched polymers
• Fractures in complex fluids: the case of transient networks
• Triggers and signatures of shear banding in steady and time-dependent flows
• Criteria for extensional necking instability in complex fluids and soft solids. Part I: imposed Hencky strain rate protocol
• Criteria for extensional necking instability in complex fluids and soft solids. Part II imposed tensile stress and force protocols
• Necking after extensional filament stretching of complex fluids and soft solids
• Elastic instability behind brittle fracture
• Necking instabilities in elasto-viscoplastic materials