A Semianalytical Model for the Determination of Bistability and Curvature of Metallic Cylindrical Shells

Abstract

Bistable metal shells with a fully closed unfolded geometry are of great interest as lightweight construction parts which could be transported without housing and unfolded at the construction place. In order to achieve the effect of bistability in metallic shells, residual stresses with a specific distribution along the shell thickness are necessary. These residual stresses can be introduced in bending processes. The tools with specific bending radii are used to influence the curvature of the shell in the different stable states and thus determine whether a completely closed profile can be achieved. In addition to the forming process, the shell thickness and the shell material have an effect on the achievable geometries and stability. In order to manufacture bistable metallic cylindrical shells from different materials and shell thicknesses, it is necessary to be able to determine a promising process sequence and corresponding bending radii in advance. For this reason, this article presents a semianalytical model for the calculation of bistability and final curvatures. This model is applied to an incremental die-bending process using two bending operations with bending radii of 6 to 12 mm and a 0.2 mm thick steel shell of grade 1.1274 (AISI 1095). The calculation results show that bistability cannot be reached for all combinations of the two bending radii. Moreover, the model indicates that a bistable and fully closed shell is only achieved for a bending radii combination of R1 = 6 mm and R2 = 6 mm. With the aim of model verification, experiments with a closed-die incremental bending tool were performed. Calculated and experimental results show good correlation regarding bistability and curvature. In addition, X-ray diffraction measurement of the residual stresses shows a good qualitative agreement regarding the calculated and experimental results.