Inelastic effects in tube inflation: non-axisymmetric bulge instability and propagation in polyethylene tubes

Abstract

When an elastic tube such as a rubber hose is inflated, it may sometimes show a bulge instability wherein a portion of the tube inflates much more than the rest. We show that low density polyethylene tubes show an entirely different bulge instability: first an axisymmetric bulge grows gradually, followed by rapid non-axisymmetric bulge growth into a hemispherical “bubble” prior to rupture. The pressure reaches a maximum just before the axisymmetric bulge starts growing and then decreases steeply but continuously once the bulge grows non-axisymmetrically. These behaviors are distinct from rubber tubes in which bulges are always axisymmetric, and the pressure reduces discontinuously when the bulge initiates. An approximate thin-shell model is constructed to explain bulge initiation in terms of the two chief phenomena at play: geometric effects (inflation increases the tube diameter and reduces the wall thickness), and constitutive behavior (tube wall yields at some pressure). The growth of the hemispherical bubble is attributed to the strong strain hardening of polyethylene at high strain. Finally, we show that limiting the growth of the non-axisymmetric bulge using an external constraint forces it to propagate axially—the first reported example of a non-axisymmetric propagation instability in tube inflation.