Tool/workpiece interface stresses in simple upsetting

When analysing the stress distribution at the tool/workpiece interface in simple upsetting, it is conventional to assume either Amonton's friction law or the law of constant friction stress. Neither of these two laws, however, is valid generally. Furthermore, the friction stress is assumed to jump discontinuously at the centre, which assumption has been proven, experimentally, to be incorrect.

In this paper considerations are made of these two objections.A combination of a lower-bound analysis using the slab method with an axi-symmetric upper-bound analysis is found to be satisfactory when studying disk forging. The slab method combined with a general friction model developed by Wanheim and Bay, is used to estimate the local normal stress and frictional stress.

A central region of sticking where the friction stress varies linearly with the radius is introduced into this analysis. The radius of the sticking region is found by an upper-bound analysis using the distribution of friction stress obtained by the slab method. It is shown that a sticking region is always present except in the case of zero friction, which explains experimental observations showing that the value of the friction stress increases linearly with the radius in the centre region.

The calculated distribution of normal stress is compared with experimental measurements obtained using a special pressure sensor mounted in the lower anvil. The agreement between the results of theory and experiment is good.