A Theoretical Analysis of the External Tube Inversion Process in the Thin- Walled Circular Tubes

External inversion of thin-walled tubes using a die is used for manufacturing double-walled parts that are difficult to manufacture by any other technique. In this study, the external inversion process in the thin-walled circular tubes is investigated, theoretically and experimentally. The theoretical relationship is obtained, based on the energy method. Several deformation mechanisms are assumed in the theoretical model: bending around circular hinge line, bending in normal to meridian direction and circumferential expansion. A total inversion process in the circular metal tubes is divided to three different stages versus the inversion angle: 0≤θ≤π, π ≤θ≤2π and after θ=2π. In each stage, the total dissipated energy is calculated. The different strain components are calculated and based on the principle of energy conservation; some theoretical relations are derived to predict the instantaneous inversion force. Some circular brazen tubes are used in the external inversion tests under axial loading and the diagram of axial load-displacement is sketched. The theoretical relations can predict the variations of the axial load during the inversion process in the circular tubes with a good agreement.

Keywords:

Axial load , Circular tube , Energy absorption , External tube inversion , Thin-walled