Finite difference method for analysis of open-die forging of sintered cylindrical billets

In this paper, an analysis of the upsetting of axisymmetric cylindrical billets of porous materials is made on the basis of plasticity theory. A newly established yield function for porous materials based on Shima and Oyane is used to simulate the open die forging of porous billets, taking into account the current state of porosity at each stage of deformation. The proposed theoretical model combined with the concepts of the slab method and a finite difference solution, provides with a valuable design tool allowing for a more precise evaluation of the process loading and the shape changes of the porous billets obtained during upsetting. The variation of radial distribution of radial stress (σr), normal pressure (p), porosity (f), radial strain (εr), mean strain and Poisson’s ratio for various value of initial porosity (f0) is predicted. It is observed that with an increase in initial porosity, the normal pressure, the radial stress, Poisson ratio, and the radial strain are decreased. The current porosity (f) variation in the radial direction seems to be negligible but it increases with increasing initial porosity. It is of interest to note that for a given initial porosity, the radial stress and the pressure attain their maximum values at r = 0 (at center).