Non-axisymmetric buckling behaviour of elastic-plastic circular tubes subjected to a nosing operation

Theoretical investigations have been carried out to predict the non-axisymmetric buckling seen in the throat of circular elastic-plastic tubes subjected to a nosing operation along a frictionless conically shaped die. The buckling points and associated modes are determined by Hill's bifurcation theory in conjunction with a non-axisymmetric buckling mode. The results show that increasing the die semi-angle and the tube thickness or decreasing the material work-hardening rate are always beneficial to improve the buckling limit. The associated critical buckling mode number generally decreases as the tube thickness increases and does not depend drastically on the die semiangle nor on the hardening rate. The effect of the average r value is substantial and the buckling limit is improved when the r value reduces. Part of the present results predict well the results observed in existing experimental work.