Collapse analysis of the squaring circular tube using finite element method

Abstract

The circular tube squaring process is examined by a three-dimensional elastic-plastic finite element method, which is based on Prandtl-Reuss flow rule and Hill’s yield criterion, associating with an updated Lagrangian formulation. The high nonlinearity of the process due to the geometric changes, the inelastic constitutive behavior, and the boundary conditions being varied with deformation is taken into account in an incremental manner. In terms of the contact boundary, a modified Coulomb friction mode is specially considered. A weighting factor rmin is employed to limit the step size of loading increment to linear relation. The simulated geometry of squaring clearly demonstrates the tube squaring process till unloading. The squaring defects of formation, both collapse and asymmetry, are reported herein. Accordingly, the effects of various parameters, such as geometric ratio R/t, strain hardening exponent n, friction coefficient μ, and the length of tube L, on the occurrence of collapse (collapse ratio C/t, Cm/t, δ1/t, δ2/t, a measurement of the extent of collapse) and the extent of asymmetry (deviation ratio C1/C2) in the tube squaring process are discussed and interpreted in the simulation. The simulation clearly demonstrates the efficiency of the model simulating the tube squaring process. Mainly, it is expected that the formation of a square tube for industrial use without collapse will be found during the design stage, before beginning trials. The present work may be expected to improve the understanding of the formation of square tubes.