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

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.