Abstract: Stretch forming process usually consists of multiple passes and each pass consists of multiple reductions , so it is time-consuming to run simulations of the process by using the conventional finite element method (FEM). This problem is an obstacle to the use of FE simulations in optimal design of stretch forming process. In order to improve the computational efficiency of the FE simulations, a rigid-end degree-of-freedom (DOF) reduction method is presented based on the characteristic of local deformation of billet. In this method, through transformation of the FE equilibrium equations, the number of DOFs of each rigid end and the order of the equilibrium equations are reduced. An algorithm to select the rigid-end DOFs is proposed and an important parameter of the algorithm is suggested through numerical tests. The presented method is applied into a self-developed three-dimensional thermo-mechanical coupling rigid-viscoplastic FE program. A stretch pass of an octagonal cross-section billet is simulated by using this method and by using the conventional FEM. The load during the stretch process and the equivalent strain and temperature distribution after the pass are predicted. The computation time by using this method is compared with that by using the conventional FEM. The effectiveness of this method is verified by the computational results.

Key words: Degree of freedom, Finite element, Rigid end, Stretch forging