An approximate load estimation method for three dimensional metal forming problems

Slip line field solutions have been presented only for plane strain and axisymmetric problems in the literature. In fact due to the very nature of the differential equations for the slip line field theory, it has never been possible to apply the theory to three dimensional problems. In this paper a three dimensional solution is presented for metal forming processes using an approximate load estimation method based on the slip line field theory. This has been done by extending the axisymmetric solution and modifying it in order to apply it to the three dimensional case. Using the idea of stream lines and stream surfaces, the deforming region has been defined. A generic stream surface was developed which was a ruled surface with a three dimensional shape. The slip line field theory could only be applied to flat surfaces in the case of axisymmetric problem. Here using some assumptions an approximate load estimation method was developed so that it was applied to the three dimensional stream surfaces and hence to the deforming region under considerations. This method was applied to the forward extrusion of elliptical sections from round billets. Experiments were also carried out by authors to verify the theory. The results obtained from the new formulations were compared to the results obtained from other analytical, numerical and experimental methods. It was shown that there exist good agreements between these results.