Bulge formation and necking in a polymer tube under dynamic expansion

Bulging and necking in long thin polymer tubes subjected to increasing internal pressure are analysed numerically. The polymer is characterized by a finite strain elastic-viscoplastic constitutive relation and the calculations are carried out using a dynamic finite element program. Two types of imposed loading are prescribed: (i) a pressure that increases linearly with time and (ii) a change in enclosed volume that increases linearly with time. For both loading conditions, an axisymmetric bulge develops on the tube followed by necking in the bulge. The necks propagate in both the circumferential and the axial directions. Multiple necks form at locations given by the thin points associated with the wave number of the prescribed initial thickness imperfection. When a change in enclosed volume is prescribed, the pressure reaches a maximum, decreases and then stays approximately constant. One neck eventually becomes dominant in that it propagates further along the tube axis than any of the other necks.