An analysis of the axisymmetric compression of viscous materials

The axisymmetric compression of a cylinder and ring of a viscous power-law material is studied. It is assumed that the friction stress attains its maximum value at sliding. However, an analysis of such a friction law has shown that the sliding condition contradicts other equations. Therefore, this friction law leads to the sticking condition and, thus, to the kinematic boundary conditions at the friction surface. In this case, there is a class of metal-forming processes for which an upper bound on the force required to deform the specimen of a viscous power-law material can be obtained. Numerical results are given for the axisymmetric compression of a cylinder and ring.