Generalization of the Prandtl solution to the case of axisymmetric deformation of materials obeying the double shear model

Abstract

A semianalytic solution of the problem on the compression of an annular layer of a plastic material obeying the double shear model on a cylindrical mandrel is obtained. The approximate statement of boundary conditions, which cannot be satisfied exactly in the framework of the constructed solution, is based on the same assumptions as the statement of the classical plasticity problem of compression of a material layer between rough plates (Prandtl’s problem). It is assumed that the maximum friction law is satisfied on the inner surface of the layer. The solution is singular near this surface. The strain rate intensity factor is calculated, and its dependence on the process and material parameters is shown.