A theory of necking in semi-crystalline polymers

Abstract

Necking or cold drawing is a smoothed jump in cross-sectional area of long and thin bars (filaments or films) propagating with a constant speed. The necks in polymers, first observed about seventy years ago, are now commonly used in modern processing of polymer films and fibers. Yet till recently there was a lack in fundamental understanding of necking mechanism(s). For semi-crystalline polymers with co-existing amorphous and crystalline phases, recent experiments revealed that such a mechanism is related to unfolding crystalline blocks. Using this idea, this paper develops a theoretical model and includes it in a general continuum framework. Additionally, the paper explains the "forced" (reversible) elasticity observed in slowly propagating polymeric necks, and also briefly analyses the viscoelastic effects and dissipative heat generation when polymer necks propagate fast enough.

On line interferometric investigation of the neck propagation phenomena of stretched polypropylene fibre

“…As reported by Leonov [8], Barenblatt was the first who tried to develop a theory for neck propagation along polymeric bars. Barenblatt treated it as an eigen value problem for a nonlinear second order ordinary differential equation; the eigen value being the speed of neck propagation [8].…”

Kinematic study of necking in a semi-crystalline polymer through 3D Digital Image Correlation

“…The availability of full-field measurements should allow substantial progress in discriminating between efficient numerical methods coupled to behavioral models (see Muhammad and Jar, 2013 for an application concerning necking in HDPE material). It would obviously help in validating or challenging theories of necking based directly on the kinematic of plastic instabilities such those put forward by Leonov (2002), where basic considerations are introduced in terms of strain energy functions for both amorphous and crystalline phases.…”

A hybrid model of rubber elasticity in simple extension

“…It should be mentioned that the modification (ii) could contradict the experimental data where the opposite effects, unfolding the folded polymer crystals under stretching, were reported (e.g. see [19,20] and references there).…”