(A) rigid-plastic finite element alalysis of sheet metal forming considering contact and friction

Abstract

Process modelling of sheet metal forming with contact is carried out by using the rigid-plastic finite element method based on the membrane theory. The sheet materials are assumed to possess normal anisotropy and to obey Hill``s new yield criterion and its associated flow rule. A variational formulation is derived for the incremental analysis of the nonsteady large deformation of normal anisotropic rigid-plastic sheet metal obeying Hill``s new yield criterion. Geometric nonlinearity is incorporated by using the convected coordinate system and by introducing the asumption about the deformation path. Using the natural convected coordinate system, the numerical efficiency is improved. The corresponding finite element equations are found from the variational equation in order to analyze the sheet metal forming processes. In order to show the validity of the present formulation, hydrostatic bulging of circular and elliptic diaphragms are analyzed. The computational results are shown to be in good agreement with the existing theoretical and experimental results. A systematic method of initial guess generation is devised by using the nonlinear elastic finite element method combined with the proposed contact treatment. An improved method of contact treatment is developed in which skew boundary condition is successively used during iteration. A simple but effective contact algorithm to decide the proper contact region is also suggested. In order to verify the validity of the developed method, axisymmetric stretching is analyzed and compared with the available axisymmetric FEM results. As three-dimensional applications, stretching of a square sheet and deep drawing of a square cup from a circular blank are analyzed. The supporting experiments are also che computational results are compared with the experiments. The comparison shows that the computed results by the proposed method are generally in good agreement with the experiments. It is shown that the present method ca...