Fate of a bulge in an inflated hyperleastic tube: theory and experiment

TL;DR

This study investigates the behavior and failure modes of inflated hyperelastic tubes, combining theoretical analysis and experiments to understand how boundary conditions and initial tension influence bulge propagation, buckling, and rupture.

Contribution

The paper extends bulge formation and buckling theories to realistic boundary conditions and experimentally verifies the critical failure maps for inflated hyperelastic tubes.

Findings

Buckling acts as a protective mechanism against rupture.

Failure maps accurately predict bulge and rupture behavior.

Boundary conditions significantly influence bulge evolution.

Abstract

Mechanical instability in a pre-tensioned finite hyperelastic tube subjected to a slowly increasing internal pressure produces a spatially localized bulge at a critical pressure. The subsequent fate of the bulge, under continued inflation, is critically governed by the end-conditions, and the initial tension in the tube. In a tube with one end fixed and a dead weight attached to the other freely moving end, the bulge propagates axially at low initial tension, growing in length and the tube relaxes by extension. Rupture occurs when the tension is high. In contrast, the bulge formed in a tube, initially stretched and held fixed at both its ends can buckle or rupture, depending on the amount of initial tension. Experiments on inflated latex rubber tubes are presented for different initial tensions and boundary conditions. Failure maps in the stretch parameter space and in stretch-tension space are constructed, by extending the theories for bulge formation and buckling analyses to the experimentally relevant boundary conditions. The fate of the bulge according to the failure maps deduced from the theory is verified; the underlying assumptions are critically assessed. It is concluded that buckling provides an alternate route to relieve the stress built up during inflation. Hence buckling, when it occurs, is a protective fail safe mechanism against the rupture of a bulge in an inflated elastic tube.