Rigid-plastic finite element analysis of three-dimensional forming with recurrent boundary conditions

Abstract

An effective and accurate method of analysis of forging processes is essential to the design of optimized dies as well as to the production of net-shape products. CAD/CAM/CAE involving FEM has been extensively applied to various metal forming areas with the fast development of computers, in order to make effective approaches to the die design and the die manufacturing for more accurate products of high quality. Up to date many useful schemes for analysis of three-dimensional metal forming have been developed and applied to practical problems. However, in the case of problems with recurrent shapes and without explicitly prescribed boundary conditions which mainly arise from recurrent loading condition or recurrence of shape, no effective method has been thus far proposed for analysis of metal forming problems. In the present work, so-called recurrent boundary condition is systematically formulated in the three-dimensional rigid-plastic finite element method so as to treat readily and efficiently the problems in which the geometric shape for consideration is not symmetric in the ordinary sense and is only recurrent. In order to show the validity and effectiveness of the introduced method, computations have been carried out for some metal forming examples having recurrent geometry. Analysis of torsion, one of important mechanical tests, has been carried out mainly concerning the comparison with the conventional methods in computational time and accuracy. Helical extrusion of a clover section has been analyzed with a full region as well as with a minimum region using recurrent boundary conditions as a region of analysis. Comparisons of deformed configuration and effective strain of a section have been made between two cases. The computational results have shown that there is no appreciable difference at all between two cases and thus computation can be effectively carried out using recurrent boundary conditions and it can be extended to other processes with twiste...