Determination of the stress state and the force of deformation of ball-shaped billets in a closed matrix

At the present stage of development of science and technology, the problem of improving the quality of metal products by integrating methods of severe plastic deformation into existing technological processes is urgent. Intense plastic deformation makes it possible to obtain nanostructured metallic materials with improved quality and an attractive set of properties due to the saturation of the metal with nanoscale defects. Spherical billets with two ends along the edges are a common form of metal products. For the manufacture of such metal products, the effect of mutual influence of all-round compression and ECAP pressing in a device for the implementation of equal-channel angular pressing in a closed matrix was used. The purpose of this study is to develop a theoretical approach to determining the stress state and deformation force of spherical blanks in a closed matrix. To achieve this goal, an integrated approach was used to determine the stress state and deformation force by the method of slip lines and computer simulation in the Deform-3D software package. Analysis of the results of the stress state of the workpieces obtained by the slip line method showed that a uniform stress state is formed with a predominance of the maximum compressive stresses. The combination of the latter with angular metal extrusion into the lateral channels of the matrix predicts the production of workpieces with sub-ultrafine-grained and/or nanostructure. By the method of joint solution of differential equations of equilibrium and plasticity conditions, as well as computer modeling, the deforming force of the blanks at the final stage of deformation, when the metal flows out into the lateral channels of the matrix, is determined. The analysis of the obtained results shows that the value of the deformation force obtained by the two methods is comparable with a difference of up to 2 %, which confirms the correctness of the obtained values.