Analyses of Axisymmetric Drawing-Bulging Forming Process of Sheet Metal Using Parametric and Direct Integral Methods

For the forming problems of axisymmetric curved parts, it is generally believed that the flat-bottom region of the forming part is in an equibiaxial tensile stress state when an axisymmetric flat-bottom punch is used for bulging or drawing-bulging forming processes. However, this view lacked in-depth analysis and mathematical proof. In this research, under the assumptions of Kirchhoff’s membrane theory, the proportional loading condition and transversely anisotropic material model, mathematical proof is provided based on parametric equations and finite element simulations and experiments are carried out to verify that the flat-bottom region of the forming part is in an equibiaxial tensile stress state when an axisymmetric flat-bottom punch is used. On this basis, the direct integral method is supplemented and improved. The strain distributions of the conical parts in the flange, die arc, side wall, punch arc and bottom regions are obtained by the improved integral method. The theoretical results are compared with and validated by those obtained by the finite element method and experiment. This research is helpful to the prediction of strain distribution in axisymmetric sheet forming.