The steady axisymmetric flow of ideally plastic materials in a conical channel

The problem of the asymmetric flow of an ideally plastic medium is formulated within the framework of the von Mises model and the total plasticity condition, using the invariant condition of compatibility for the deviator component of the stress tensor. Flow in a converging conical channel, on the boundary of which the shear stresses are specified, is considered. First-order differential equations are obtained, describing the shear-stress distribution in the moving medium, one of which corresponds to the von Mises model, and the other to the total plasticity condition. It is established from an analysis of the solution in the neighbourhood of singular points, that the minus sign in front of the radical in these equations corresponds to positive shear stresses and vice versa. The problem of the shear stresses reaching a maximum value on the specified boundary surface of the channel is investigated. The aperture angle of the channel, beginning from which this value is reached, is determined. It is established that the value of the angle, following from the total plasticity condition, somewhat exceeds its value obtained within the framework of the von Mises model. (C) 2010 Elsevier Ltd. All rights reserved.