Riemann's Method in Modelling of Powder Metallurgy Processes

The method of moving coordinates is widely used for determining characteristic nets and, as a result, stress fields in plane strain problems of classical plasticity of rigid plastic material obeying a pressure-independent yield criterion. A great number of boundary value problems related to metal forming processes have been solved by this method. In particular, the method is efficient for constructing the characteristic net in the vicinity of a traction free surface. However, many materials reveal pressure-dependency of the yield criterion, for example materials used in powder metallurgy. The present paper extends the method of moving coordinates to plastically compressible materials that obeys a singular yield criterion and its associated flow rule. This criterion generalizes Tresca's yield criterion. The general problem of determining the state of stress in plane strain deformation is reduced to the equation of telegraphy in characteristic coordinates. This equation can be solved by the method of Riemann. Then, the mapping between the characteristic and Cartesian coordinates is given by simple algebra.