Since general forging processes, especially precision closed-die forging processes, involve dies with complex geometries, three-dimensional forging simulations require the flexibility and robustness to handle the complex die geometry. Also, in three-dimensional finite element analysis of forging processes, large mesh layouts are needed for improved solution accuracy. This results in increased computation time and memory requirements, which still remain major problems for effective three-dimensional metal forming analyses. Thus, the present study consists of two major parts. First, a contact treatment algorithm for three-dimensional thermo-rigid-viscoplastic finite element analysis was proposed to improve accuracy and stability of contact treatment for general closed-die forging simulations. Second, in order to increase computational efficiency a parallel computation technique was adopted into the thermo-rigid-viscoplastic approach based on the domain decomposition algorithm and conjugate gradient solving technique.
For successful forging simulations, contact nodes must be prevented from penetrating into the complex three-dimensional complex die geometries. Thus, in the proposed contact treatment algorithm, time increments for updating were determined by the minimum time duration for free boundary node to touch the die surfaces. Also, in the proposed contact algorithm, contact nodes at the interfaces between several dies or at the edges of die surfaces, regions susceptible to nodal penetration are fixed in multiple directions to prevent penetration. Based on the contact algorithm, three dimensional contact treatment modules for die surfaces modeled by Ferguson surface patch and triangular meshes were developed. Also, considering the geometrical symmetry, the developed contact module was expended to the shape rolling analyses. Using the developed programs, a closed-die upsetting, aluminum swash plate forming process, and shape rolling process of bars and H-beam were simulated and the results showed that the simulation can be carried out to achieve complete filling without any occurrence of die penetration.
As mentioned earlier, the second part of this study is concerned with the parallel computation of the thermo-rigid-viscoplastic approach to reduce computation time and memory requirements. The domain decomposition algorithm and conjugate gradient iterative solver were used for parallelization. To improve the convergence characteristics of the conjugate gradient solver, a preconditioning technique for the thermo-rigid-viscoplastic approach was proposed and applied. In the proposed technique, the block Jacobi is applied to the interior degree of freedoms while the Jacobi preconditioner is applied to the interface degree of freedoms of each sub-domain. Using the proposed parallelization and preconditioning techniques, a thermo-rigid-viscoplastic finite element program for parallel computation of three-dimensional forging simulations was developed. To investigate the efficiency of the proposed parallel algorithm, simple upsetting simulations of cubic and brick type workpiece were carried out. From the simulation results, it was found that the proposed preconditioning technique is more efficient compared to both the conjugate gradient and the Jacobi preconditioned conjugate gradient solving techniques. To apply the proposed preconditioning technique to more complex forging simulations, swash plate forging was simulated using the developed parallelized program. In this case, the efficiency of the proposed preconditioning technique was poor compared with the previous results for upsetting. This is due to reduction of convergence efficiency influenced by the effect of complex flow characteristics. Thus, to improve the efficiency of the proposed parallel computing algorithm, consideration of flow patterns must be included and more optimal domain decomposition algorithm is needed.
