An efficient method for accounting the strength-differential effect and Coulomb friction in upper bound solutions of plasticity

The upper bound method is widely used to estimate the load required to deform the material in metal forming processes. However, most solutions are for the von Mises or Tresca yield criteria. It may be explained by the simplicity with which the plastic work rate is expressed in terms of the strain rate invariants when these criteria are adopted. Therefore, it is more convenient to formulate the constitutive equations using the work function. If necessary, the latter can usually be chosen to closely approximate available yield criteria. The strength-differential effect is an important property of some materials whose plastic yielding is independent of the state of hydrostatic stress. In this paper, a recently proposed work function appropriate for such materials is combined with the upper bound technique. As an example, the upsetting of a cylinder, which is sometimes used as a friction test, is analyzed. Coulomb’s friction law is assumed between the plates and the cylinder, which requires a non-conventional formulation of the upper bound theorem. The solution is compared to that for the von Mises yield criterion. It is shown that neglecting the strength-differential effect in the material model can affect the interpretation of the friction test.