Simulation of Elastic Rupture in Extension of Entangled Monodisperse Polymer Melts

We use a Lagrangian finite element method to simulate experiments on continued and interrupted extensions of a highly entangled monodisperse polymer melt. It is demonstrated that delayed sample necking or rupture may be explained in terms of the original Doi-Edwards model augmented by the mechanism of chain stretching alone.

Figure 1

Data from (17, Fig. 1) fitted to the BSW spectrum. Only the 12 lower frequency data points were included in the fit, since the glassy part of the BSW model was omitted.

Figure 2

The sequence to the left shows a typical necking of the sample during relaxation. The top figure shows the filament prior to deformation. The second is immediately after cessation of extension. The next two figures show the ongoing filament necking where ${ϵ}_N=1.597$ and $\dot{ϵ}=0.8{\mathrm{s}}^{-1}$. The coloring is a measure of relative internal pressure ($\mathrm{\text{red}}=\mathrm{\text{high}}$, $\mathrm{\text{blue}}=\mathrm{\text{low}}$). The two bottom figures show a zoom-in on the necking zone—notice the smooth element to element transition except at the contact point.

Figure 3

Simulation of 250 k SBR filament necking after interrupted extension. Right: Local strain rate at the thinnest place as function of time after imposition of strains 0.804–1.597. Left: Time to necking as function of imposed Hencky strain compared to data by 4. No delayed necking is observed after imposed Hencky strains $\le 0.60$.