Modeling techniques in metal forming: upsetting of a forged plastic ring
Numerical studies of a plastic ring in axial compression were made using the method of finite element. Standard rings with geometry 6:3:2 (outside diameter:inside diameter:height) were compressed to 8% and 16% deformations with sticking friction for both loaded and unloaded situations;An elastic-plastic finite element program was developed incorporating several different modeling considerations. Special attentions were paid to elastic unloading, modified von Mises yield criterion and large deformation in order to simulate a corresponding plastic model of material 'Rigid Laminac' correctly;The material 'Rigid Laminac' has a higher elastic strain than ordinary metal such as aluminum, hence has larger elastic recovery upon unloading, which leads to the need for elastic unloading modeling. The material also follows a pressure-dependent modified von Mises yield criterion where yield strength is different in compression from that in tension. A nonassociated plasticity model was chosen to satisfy the requirement of incompressibility. The Updated Lagrangian Method was used for modeling large deformation where Jaumann rate of Kirchhoff stress was used in the constitutive equations. The initial load method was used throughout the analysis with a modified Aitken's accelerator to accelerate convergence;Results of the finite element analysis, such as propagation of yield zones, distribution of strains and change of geometry etc. were compared with photoplastic experiments as well as other numerical and analytical solutions. Contour plots whenever possible were drawn to make detailed whole field comparisons. Differences and similarities of comparisons were discussed. The general pattern of results agrees well between finite element and experimental solutions.