The shaping of a circular tube into a symmetric square-tube by finite-element modeling

The squaring processes to shape the circular tube into a symmetric square-tube are examined by an incremental elasto-plastic finite-element method based on an updated Lagrangian formulation. The highly non-linear problems due to the geometric changes, the inelastic constitutive behavior and the boundary conditions varied with deformation are taken into account in an incremental manner. On 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 geometries of squaring could clearly demonstrate the squaring processes until unloading. The formation of squaring defects that are classified as two kinds of collapse, modes I and II, are reported herein. Accordingly, the effects of various parameters of process, such as geometric ratio R/t, strain hardening exponent n and friction coefficient μ, on the occurrence of collapse (collapse ratio C/t a measurement of the extent of collapse) for the squaring process are discussed and interpreted in a theoretical manner. Therefore, this modeling can be used for judging whether a symmetric square-tube can be shaped successfully. The present work may be expected to improve the understanding of the formation of the symmetric square-tube.