A kinematically admissible velocity field is proposed on the basis of the concept of flow function for both plane strain and axisymmetric upsettings with an arbitrary shaped punch. An upper bound solution is numerically obtained from the velocity field for the case of axisymmetric upsetting with a conical punch. The effect of workhardening and free surface bulging is taken into account.
The numerical result is compared with the experiments for upsetting Al-2024 with conical punches of various angles under different friction conditions. The theoretical predictions are shown to be in good agreement with the experimental observations, especially when the range of punch angle is within ±10˚. It is also shown that the friction condition has a negligible affect on the forging load, but considerably influences the strain distribution.
