Simulation and comparison of the results of the exact analytical solution of the boundary problem of a flow in a thin layer with experimental data

The approach under study is important for practical application, since is the basis of many basic plastic deformation operations associated with plastic flow in a thin layer of material deformed by rolls (longitudinal rolling, rolling) or dies (volumetric and sheet stamping), which are described by spatial mathematical models with a variety of parameters that determine the rheology of the material. Pressures are created on the contact surfaces of the processing material with the tool, which exceed the shear characteristics of the material by an order of magnitude, so that, in the initial approximation, it is possible to use the model of a hydrodynamic fluid to describe the properties of the material of the plastic layer [1, 2, 3]. As was shown earlier, sliding is observed almost along the entire contact surface, in which the contact surfaces coincide with the sliding surfaces, and the specific friction forces on them are maximum [4] and equal to the shear yield strength of the material [5, 6]. It should be noted another feature of the course of these processes, which determines the requirements for the accuracy of the final forging. It is clear that high contact pressures cause normal elastic displacements of the working surfaces of the tool, commensurate with the thickness of the plastic layer [7, 8]. We consider a plastic layer in the wedge-shaped region, composed of materials with different mechanical characteristics. the layer spreads freely between the rigid rough slabs converging in parallel. The layer under the action in the direction of the thickness of the distributed load from the side of the tool flows freely in the direction of the radii.