Experimental and theoretical study of constant curvature multi-square punch forming process of strips under follower load

During the multi-square punch forming (MSPF) process of hull plate in shipbuilding industry, the springback occurs after unloading due to the elastic deformation energy stored in the plate, which makes the one-step forming difficult to achieve. This paper aims to uncover the physical mechanism of the elasto-plastic deformation and the springback characteristics in the MSPF process and derive appropriate mathematical interpretations. A series of strip-forming tests were carried out by using the three-dimensional computational numerical control (CNC) hull plate forming machine. Besides, by considering the follower load with moving boundary condition in the forming process, theoretical equations are derived to analyse the forming mechanism and springback characteristics of the strip, and their accuracy is demonstrated through the comparison with experimental data. Through the proposed formula, the strip's profile under different loadings in the forming process can be properly described, which provides the characteristic range of the strip (e.g. the strip's thickness) which can be formed on a specific MSPF machine. Parametric studies indicate that the springback ratio of the strip increases with the increase of the strip's thickness and the tool curvature.