New instability model leading the wrinkling at the positive-curvature arc part during the tube hydro-forging process

The tube hydroforging process (THFG) is an advanced technology for manufacturing tubular components with complex cross-sections. The positive-curvature arc is one of the most fundamental and difficult-to-form features of complex cross-sections. However, its wrinkling mechanism in the THFG process cannot be explained by the existing theory. This restricts the application of the technology. First, because of the bending deformation caused by the excessive circumferential force, compression instability occurs at the positive-curvature arc part. This results in wrinkling similar to that in the conventional linear part. In addition, owing to the existence of the positive-curvature arc, the circumferential force produces a component force along the vertical direction that causes rigid displacement of the materials. This yields another new instability model: motion instability. The corresponding critical pressures for the two instability models were determined by adopting static method and energy methods respectively. Theoretically, motion instability is dominant in the early stages of compression, whereas compression instability is dominant in the subsequent stages. However, considering actual production, the correlations between the critical pressures of the different parts were compared. The wrinkling of the linear part inhibits the occurrence of compression instability in the positive-curvature arc. Thus, wrinkling of the arc can be caused only by motion instability. Therefore, the critical pressure for motion instability is defined as the critical pressure required for the positive-curvature arc. In addition, a forming window that considers the critical pressure of each part was established successfully.