Shear bands in polymer tubes under internal pressure

Abstract

The extensive emergence and frequent interaction of shear bands play a pivotal role in the behavior of ductile polymers under large deformations. This paper employs the finite element method to analyze the emergence and evolution of shear bands in polymer tubes under internal pressure. Assuming the tube is sufficiently long, plane strain conditions prevail in the axial direction. The behavior of polymers is represented by the classical elastic-viscoplastic constitutive model, which incorporates influences of pressure, strain rate and temperature on yielding and encompasses intrinsic softening and consequent orientation hardening. Simulations indicate that shear bands initially propagate in a spiral pattern, followed by widening, multiplication, and annihilation indications. These phenomena collectively contribute to the onset and expansion of necks. The competition between the propagation and multiplication of shear bands governs the unpredictability in the initiation sites of necking. Particular attention is paid to four interesting interactions between shear bands (i.e., “detour”, bifurcation, obstruction, “repulsion”) and their genesis mechanisms. The effects of material parameters, initial geometric imperfections, specimen thickness and loading method are systematically discussed. It is demonstrated that intrinsic softening facilitates the emergence and propagation of bands, while orientation hardening contributes to the widening of bands and the expansion of necks. The synergistic effect of intrinsic softening and orientational hardening modulates shear bands’ morphology, multiplication, competition and interaction. The initial imperfection wave number significantly affects the number of shear bands. Periodic symmetric imperfections result in a comparable number of clockwise and counterclockwise shear bands, followed by necks propagating bi-directionally along the specimen. Conversely, periodic asymmetric imperfections induce a unidirectional spiral configuration of shear bands, followed by necks propagating unidirectionally along the specimen. Compared with experiments, it is demonstrated that the constitutive model can qualitatively depict the onset and propagation of necks. The multiplication, bifurcation, “detour”, and obstruction of shear bands frequently observed in experiments can also be predicted well qualitatively.