An Upper Bound Solution for Upsetting of Anisotropic Hollow Cylinders

The paper concerns with an effect of plastic anisotropy on the load required to deform hollow cylinders between two parallel, rough dies. It is assumed that the material obeys Hill’s quadratic yield criterion and its associated flow rule. The friction stress is supposed to be proportional to the corresponding shear yield stress, including the maximum friction law as a special case. The kinematically admissible velocity field is chosen such that the stress field following from the associated flow rule satisfies the boundary condition at the plane of symmetry. Moreover, this velocity field is singular in the vicinity of the friction surface. Therefore, in the case of the maximum friction law the friction law is satisfied, again if the associated flow rule is combined with the velocity field. A significant effect of plastic anisotropy on the limit load is illustrated.