Criteria for extensional necking instability in complex fluids and soft solids. Part I: imposed Hencky strain rate protocol

Abstract

We study the necking dynamics of a filament of complex fluid or soft solid in uniaxial tensile stretching at constant imposed Hencky strain rate $\dot{\epsilon }$, by means of linear stability analysis and nonlinear (slender filament) simulations. We demonstrate necking to be an intrinsic flow instability that arises as an inevitable consequence of the constitutive behaviour of essentially any material (with a possible rare exception, which we outline). We derive criteria for the onset of necking that are reportable simply in terms of characteristic signatures in the shapes of the experimentally measured rheological response functions, and should therefore apply universally to all materials. As evidence of their generality, we numerically show them to hold in six popular constitutive models of polymers and soft glasses. Two distinct modes of necking instability are predicted. The first is relatively gentle, and sets in when the tensile stress signal first curves down as a function of the time $t$ (or accumulated strain $\epsilon =\dot{\epsilon }t$) since the inception of the flow. The second is more violent, and sets in when a carefully defined `elastic derivative' of the tensile force first slopes down as a function of $t$ (or $\dot{\epsilon }$). In the limit of fast flow $\dot{\epsilon }\tau \to \infty$, where $\tau$ is the material's characteristic stress relaxation time, this second mode reduces to the Considére criterion for necking in solids. However we show that the Considére criterion fails to correctly predict the onset of necking in any viscoelastic regime of finite imposed $\dot{\epsilon }\tau$. Finally, we elucidate the way these modes of instability manifest themselves in entangled linear polymers, wormlike micelles and branched polymers. We demonstrate four distinct regimes as a function of imposed strain rate, consistent with experimental master curves.

Manuscript with 30 pages and 11 figures

References in corpus (6)

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• Fractures in complex fluids: the case of transient networks
• Dynamics of Large-Scale Plastic Deformation and the Necking Instability in Amorphous Solids
• Tensorial Constitutive Models for Disordered Foams, Dense Emulsions, and other Soft Nonergodic Materials
• Age dependent modes of extensional necking instability in soft glassy materials
• Criteria for extensional necking instability in complex fluids and soft solids. Part II imposed tensile stress and force protocols

Cited by in corpus (4)

• 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
• Necking instabilities in elasto-viscoplastic materials
• A Linear Time-Variant Rheological Model for Frictional Aging, Stress Relaxation, and Creep