Bifurcation behavior of cylindrical pressure vessels simultaneously loaded by internal pressure and axial tension is investigated theoretically and numerically with emphasis on the transition between diffuse bulging and necking modes of bifurcation. It is illustrated that in very long cylinders, bifurcation occurs always instantly once instability is reached, resulting in catastrophic failure under all loading conditions. For short cylinders, both axisynunetric necking and bulging occur after the peak load, as steady deformation continues under falling loads before the occurrence of bifurcation. The delay is more obvious in shorter cylinders as axisymmetric bifurcation is delayed under some loading conditions so much that it does not occur, even after extremely large steady deformation under decreasing loads. A transition line, defined for any specified cylinder diameter-ratio, separates bulging and necking modes of bifurcation for all associated slenderness ratios. The delay of bifurcation after instability decreases significantly when a cylinder is loaded along the transition line, diminishes for thin walled cylinders, as localized necking occurs almost instantly, once the instability condition has been reached, leading to catastrophic failure. The style of bifurcation limit curves of thick-walled cylinders is generally similar to that of thin-walled cylinders. However, bifurcation of short thick cylinders is delayed noticeably, even when loaded along the transition line. Transition lines are defined and presented for cylinders with different diameter ratios. Axisymmetric bulging and necking bifurcation limits are displayed in correlation with the corresponding transition lines. The theoretical analysis is based on the continuum theory, takes into account large elastic plastic deformation and non-linear material hardening. The theoretical solution is validated by comparing the theoretical results with FEA simulation results using independent commercial software. The findings provide a clear mapping of the loading conditions, which should be avoided in order to delay or prevent catastrophic failure when pressurized cylinders are accidentally overloaded.
