Rigid-plastic finite element analysis of three-dimensional forging with curved dies

Abstract

The prediction of metal flow, forging load and distributions of strain ans stress in the forging processes is very important. It provides necessary information and guidelines for the effective design and manufacture of the forging dies. It is desirable to develop a computer simulation code in order to predict such information more realistically. In the present work, a three-dimensional finite element formulation is presented on the basis of rigid-plastic material model by considering the work-hardening effect. The discretization is made with 8-node hexahedral isoparametric elements and 6-node triangular prismatic elements. A finite element code has been developed, where the three-dimensional cold forging processes with arbitrarily curved die geometries can be analyzed. A systematic method to generate an initial velocity field is proposed by assuming a linear viscous material. The effectiveness of the proposed initial guess generation scheme is shown for the analysis of some forging processes with complicated die geometry. In order to impose velocity boundary conditions on arbitrarily curved die surfaces, an effective method is suggested by using the skew boundary condition. The description of the die surface is made easily by employing the parametric form. The treatment of the frictional boundary condition on curved three-dimensional surfaces is formulated for 4-node rectangular patches and 3-node triangular ones which are generated from the 8-node hexahedral solid elements and 6-node triangular prismatic elements, respctively. In order to treat the contact problem, an iterative method is used by checking the contact condition during the iterations of the finite element procedures. The position and the velocity of sliding nodes and the penetrating nodes are adjusted so that they satisfy the contact condition during the iterations. Furthermore, a three-dimensional remeshing technique is proposed by introducing a modular concept. The computational region is di...