Application of equations of the plasticity theory in the processes of prosessing porous body pressure

Abstract

In the article the results of the application of the equations of the plasticity theory in the processes of processing of the powder body pressure such as a porous sleeve were presented. The mathematical model describing the plastic behavior of a porous body is preferred. For this purpose, the hypothesis on the use of the Beltram plastic flow in the construction of a model of the plastic behavior of the porous body was used, diagrams of tangential and normal stresses and the contact surface of the body were constructed. On the basis of the Beltram hypothesis, the plasticity condition in which, the three-dimensional space of principal stresses, the equation is an ellipsoid. An equation of plastic friction of a porous powder body during re-compaction is obtained. In the case when the components of the stress deviator are known, when using certain boundary conditions, it becomes possible to find the components of the stress tensors. Testing of the processes of deformation of a porous body was carried out on cylindrical powder samples with dimensions D´H - 10´10 mm. after primary pressing, their relative density was
r = 0.68. As a result of the experimental tests of repeated pressing of the sleeve, a graph of the dependence of the yield strength of the iron-based material on the relative density of the sleeve was built, which is in good agreement with the calculated data. Further tests carried out on the porous bushings are further compacted by pulling. The zones of plastic deformation in the powder sleeve are determined. Diagrams of normal σr and tangential τ_rx stresses of the tangent to the contact surface along the r = const line are constructed. The proposed method for determining the stresses and plastic behavior of iron-based porous powder bushings can be used for other stationary methods of deformation of powder materials (rolling, extrusion, drawing, etc.)