FEM analysis of mechanism of free deformation under dieless constraint in axial compressive forming process of tube

The axial compression of a thin-walled tube over a simple radiused die can make the tube invert to form a complicated part that is difficult to be manufactured by any other technique. However, the behavior of the free deformation under dieless constraint existing in the process has an essential effect on the degree of precision of the product obtained by the process and the advantages of the process. This paper explores the mechanism of the free deformation on the basis of the development of a rigid-plastic FEM. It is found from the results obtained that: (1) for a given t0/d0 or rρ/t0, the free deformation behavior of the tube under dieless constraint depends mainly on the value of rρ/d0 and little on the properties of the tube material and the friction condition, which, however, have a significant influence on the deforming force; (2) before reaching steady-state, the radius of curvature at each point in the free deformation zone may be different from that at the other points, and it changes continuously with time; (3) the free deformation zone relative to the die fillet decreases with increasing rρ/d0, and there is a critical parameter k for a given t0/d0 or rρ/t0, such that when rρ/d0>k, the free deformation will go within a circle with the same radius as the die; correspondingly, the relative gap Δ/2rρ of the double-walled tube obtained decreases with increasing rρ/d0, and when rρ/d0>k, then Δ/2rρ<1; contrarily, the free deformation will then extend beyond the circle, and Δ/2rρ>1. The achievements of this research may serve as a significant guide to the practice of the relevant processes.