Non-Axisymmetric Bifurcation Analysis of Elastic-Plastic Thin Circular Tubes Subjected to Forming with Axisymmetric Die

Abstract

Non-axisymmetric buckling phenomenon seen during the nosing, sinking, and drawing of elastic-plastic thin circular tubes is investigated theoretically based upon Hill's bifurcation theory in conjunction with finite element approximation. The influence of the thickness of the tube to the initial mean radius ratio, the die semi-angle, the sinking zone and the exit radius, and the material properties including the transversely anisotropy of the tube on the buckling limit is investigated. It is revealed that the buckling limit is postponed when the thickness and the die semi-angle increase but conversely decreases as the yield stress σ_y, the hardening exponent n, and the average γ-value γ-<aν> increase Further, the existence of the sinking zone and the exit radius is found to have a suppressive effect on the critical drawing ratio.