Matiukhin A. Modeling of processes of plastic forming of thick-walled hollow bodies of rotation with use of harmonic functions.

The object of Study is the process of plastic deformation in non-homogeneous axisymmetric stress-strain state bodies. The subject of Research is the inhomogeneous stress-strain state bodies under Axially Symmetric loading conditions. The purpose of research is to develop a mathematical model based on a closed solution of the problem of plasticity theory under axisymmetric loading to ensure the accuracy and reliability of results in conditions of non-uniform plastic deformation. Research methods: theoretical analysis of the stress-strain state of the metal is based on the method of harmonic functions Dual-zone and single-band deformation zone, the boundary conditions were investigated by experimentally rainfall thick-walled annular workpiece on the press. The problems are compared with experimental and theoretical data of other authors to assess the reliability of the results of solving. Received result: are mathematical model of hardening plastic medium in terms of axisymmetric stress state, which allows you to take into account both the technological parameters of plastic deformation (coefficient of friction, form factor, internal and external overpressure) and kinematical parameters of the deformation zone (strain rate, degree of deformation and the temperature ). The solution of applied problems of plasticity theory to determine the normal and shear stresses, both in contact and in the volume of a deformable billet, with one-and two-band flow of the metal are supplied. The Study of the finite element method, based on ANSYS / LS-DYNA software, was done. Methods of solving axisymmetric problem of the theory of plasticity with draft hollow cylindrical products were introduced at JSC "Motor Sich"