Simulation of plastic deformations in metal rolling

Mathematical simulation of plastic deformations in rolling of porous materials involves a consequent combination of the general energy relationship in plasticity and the variation inequality expressing the principle of minimum of entire deformation energy. A real deformation state in a plastic zone beneath rolls and corresponding kinematic and dynamic conditions on the contact surface are considered as a limited one for the consequent approximate deformation states and found out by the method of approximated approach. Any realization of this kind of method on personal computers requires a rational construction of a kinematic admissible velocity field in the spatial domain on plastic flow. Using the ordinary propositions and assumptions it became possible to construct one of the simple spatial kinematic admissible velocity field in the plastic zone beneath rolls. On the base of a big amount of experimental data a new hypothesis and analytic function describing the density distribution along the plastic zone during the rolling process have been proposed. On the base of the consequent approach in which the general energetic relationship and the variation inequality are interrelated it has been able to find out the geometric, kinematic and dynamic characteristics of plastic deformation states in rolling of porous materials.