Age dependent modes of extensional necking instability in soft glassy materials

TL;DR

This study investigates how the age of soft glassy materials influences the mode of necking instability during extensional stretching, revealing age-dependent transition from liquid-like to solid-like failure modes.

Contribution

It introduces a combined numerical and analytical approach to demonstrate how sample age determines the necking mode in soft glassy materials, linking it to elastic and plastic stress components.

Findings

Young samples exhibit gradual, liquid-like necking.

Older samples fail rapidly via a solid-like mode.

The solid-like mode parallels the Considère mode in elastic solids.

Abstract

We study the instability to necking of an initially cylindrical filament of soft glassy material subject to extensional stretching. By numerical simulation of the soft glassy rheology model and a simplified fluidity model, and by analytical predictions within a highly generic toy description, we show that the mode of instability is set by the age of the sample relative to the inverse of the applied extensional strain rate. Young samples neck gradually via a liquid-like mode, the onset of which is determined by both the elastic loading and plastic relaxation terms in the stress constitutive equation. Older samples fail at smaller draw ratios via a more rapid mode, the onset of which is determined only by the solid-like elastic loading terms (though plastic effects arise later, once appreciable necking develops). We show this solid-like mode to be the counterpart, for elastoplastic materials, of the Consid\`ere mode of necking in strain-rate-independent solids.