Об одном подходе к аналитическому решению задачи экструзии труб при наличии внутреннего высокого давления

Abstract

Based on the assumption that external v p and internal r p pressures acting on the pipe are equal: the circumferential stress of the pipe is determined. Simplified plasticity condition is obtained and the stress-strain state of the pipe is investigated by the analytical method. The problem of extrusion of pipes loaded with internal high pressure is firstly completely solved in the case of the presence of friction, and then by a fairly simplified method in the absence of friction. This is due to the fact that in the main case, in the denominator of the formula for determining the Ϭm meridional stress, there is a coefficient, that takes into account friction, and in the case of k = 0 it is impossible to immediately determine the corresponding formula for the case in the absence of friction. To implement this process, the formula of the meridional stress was transformed to obtain an exponential function and its representation in the form of a series. Dimensionless meridional, circumferential and average stresses are determined, depending on the degree of pipe deformation, which makes it possible to use the formulas of the deformation theory of plasticity of porous materials to study the process of compaction of the pipe material. Numerical calculations are carried out in the MS EXCEL software environment for various coefficients of friction at 10% of the initial porosity of the material. To obtain a fully compacted material of a sintered pipe, the process of extrusion of the pipe with various dimensions is modeled in a corresponding conical die.