| Popis: |
The main issue for fulfilling a correct and reliable simulation of a plastic deformation process is the identification of strain, strain rate and stress fields. The definition of these aspects can also permit to state the heat developed by the plastic deformation, which is a ruling factor for the micro-structural evolution of the formed materials. On the other hand, in a lot of plastic deformation technologies, the only physical condition certainly known is the velocity assumed by the material on some boundaries (i.e. inlet and outlet velocity of the material during rolling, extrusion, wiredrawing etc.). The use of Navier-Stokes’ equations can appear unusual in the study of the mechanical behaviour of solid materials, but this is due to the fact that the plastic deformation phenomena are usually treated starting from the dynamic point of view and rarely starting from a kinematic point of view. On the other hand, the plastic deformation is related to the slip on some activated lattice systems, where the resolved shear stress becomes greater than the critical one needed for permitting the slip to take place; the slip velocities are related to the deformation and to its rate (through a time integration). The activation of some systems by the application of a stress field causes the transmission of the forces to the adjacent systems, which can assume a particular movement velocity. The transmission of the motion among the sliding systems is ruled by the viscosity of the transmitting mean (i.e. the bulk plastically deformed material). Actually, on the basis of its physical definition, the viscosity points out the relation between an applied shear stress and the gradient of the velocities transmitted among the layers parallel to the direction of the applied shear stress. So, when a velocity is imposed on a mass of plastically deformed metal, it can be transmitted to the adjacent regions as a function of the particular viscosity of the worked material, in a way mainly dependent on the temperature. Thus the velocity field, which characterizes the plastic deformation of the metal, can be calculated starting from the imposition of the correct kinematic boundary conditions. When the velocities are imposed on the boundary, the viscosity of the metal rules their transmission to the inner volumes of the metals. It is impressive and worth noting the analogy between the well known velocity profile of a liquid flowing on a plane and the morphology of the plastic flow deformation line observed in the immediately sub-surface layers of a metal which underwent a wear process featured by the plastic deformation. The difference in the movement entities between the liquid and the solid case is due to the different order of magnitude of the viscosity interesting the liquid phase and the solid one. |
