An Upper Bound Solution for Upsetting of Two-Layer Cylinder

Abstract

An upper bound solution for axisymmetric upsetting of two-layer cylinder made of rigid perfectly plastic materials is provided. An important feature of the solution is that the kinematically admissible velocity field, in addition to the necessary requirements of the upper bound theorem, satisfies the frictional boundary condition in stresses, the maximum friction law. The latter is archived by introducing a singular velocity field such that the equivalent strain rate approaches infinity at the friction surface. The dependence of the upper bound limit load on geometric parameters and the ratio of the yield stresses of the two materials is analyzed. The solution can be used in industrial applications for evaluating the load required to deform two-layer cylinders.