The Considere condition and rapid stretching of linear and branched polymer melts

We analyze the onset of ''necking'' and subsequent filament failure during the transient uniaxial elongation of viscoelastic fluid samples in extensio nal rheometers. In the limit of rapid elongation (such that no molecular re laxation occurs), the external work applied is all stored elastically and t he Considere criterion originally developed in solid mechanics can be used to quantitatively predict the critical Hencky strain to failure. By compari ng the predictions of the Doi-Edwards model for linear homopolymer melts wi th those of the "Pom-Pom" model recently proposed by McLeish and Larson [J. Rheol. 42, 81-110 (1998)] for prototypical branched melts we show that the critical strain to failure in rapid elongation of a rubbery material is in timately linked to the molecular topology of the chain, especially the degr ee of chain branching. The onset of necking instability is monotonically sh ifted to larger Hencky strains as the number of branches is increased. Nume rical computations at finite Deborah numbers also show that there is an opt imal range of deformation rates over which homogeneous extensions can be ma intained to large strain. We also consider other rapid homogeneous stretchi ng deformations, such as biaxial and planar stretching, and show that the d egree of stabilization afforded by inclusion of material with long-chain br anching is a sensitive function of the imposed mode of deformation. (C) 199 9 The Society of Rheology. [S0148-6055(99)00105-4].