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

Abstract

We analyze the onset of 'necking' and subsequent filament failure during the transient uniaxial elongation of viscoelastic fluid samples in extensional rheometers. In the limit of rapid elongation (such that no molecular relaxation occurs) the external work applied is all stored elastically and the Considère criterion originally developed in solid mechanics can be used to quantitatively predict the critical Hencky strain to failure. By comparing the predictions of the Doi-Edwards model for linear homopolymer melts with those of the 'Pom-Pom' model recently proposed by McLeish & Larson (J. Rheol. 42,(1998) p.81-110) for prototypical branched melts we show that the critical strain to failure in rapid elongation of a rubbery material is intimately linked to the molecular topology of the chain, especially the degree of chain branching. The onset of necking instability is monotonically shifted to larger Hencky strains as the number of branches is increased. Numerical computations at finite Deborah numbers also show that there is an optimal range of deformation rates over which homogeneous extensions can be maintained to large strain. We also consider other rapid homogeneous stretching deformations, such as biaxial and planar stretching, and show that the degree of stabilization afforded by inclusion of material with long-chain branching is a sensitive function of the imposed mode of deformation.

Effect of nonlinear viscoelastic properties on tack

“…McKinley and Hassager [29]. Thus the maximum Hencky strain at failure is strongly dependent on the velocity V, but may show a constant regime at rapid stretching rates.…”

“…In any case, one should note [29] that increasing the velocity should lead to a higher ε f , whereas above a certain velocity, ε f decreases again to a constant level.…”

Spontaneous Breakup of Extended Monodisperse Polymer Melts

“…Here the transition from viscoelastic to viscous behavior, controlled by the relaxation time, stabilizes the sample. It is of interest to notice that the theoretical ideal lower limit for the occurrence of the necking, the elastic Considere criteria, is at a real strain of 0 ¼ 0:86 [19], corresponding to a set strain of _ N;0 ¼ 0:96. Both the experiments and the computations show the break much earlier than this, as a consequence of the nonideal conditions.…”

Large amplitude oscillatory shear flow of gluten dough: A model power-law gel

“…The FENE network over-predicts the magnitude of the strain-hardening growth in the normal stress difference that occurs just before the sample ruptures, while the modified network model gives more reasonable stress growth functions. The fact that the point of rupture occurs extremely close to the finite extensibility plateau should not be surprising, since the mass rupturing of network junctions dramatically reduces the rate of stress growth in the system and can lead to tearing or necking as implied in the Considère criterion [Considère (1885); Pearson and Connelly (1982); McKinley and Hassager (1999); Ng et al (2006)]. …”