In this study, the interdependence between temperatures and metal flow during upset forging of rings has been investigated. An improved upper-bound analysis has been developed to predict metal flow and temperatures during ring compression. The metal flow and temperatures are considered to influence each other and are estimated at small discrete steps of deformation. Good correlation was found between predicted profiles of the bulged ring surfaces and the experimental results. The analysis and the experimental data show the effects of (a) friction on temperatures, (b) time of contact between the ring and the dies on temperatures and metal flow, and (c) ram speed upon metal flow and temperature. The simulation of the ring test, presented in this paper, is expected to allow a more precise interpretation of experimental results obtained in ring compression tests, especially in warm and hot deformation ranges.

An approach for selecting general kinematically admissible velocity fields for an incompressible material from assumed shape of streamlines is outlined. Velocity field and generalized boundaries of plastic zone are obtained for axisymmetric extrusion of a rod through arbitrarily shaped die. For special case of conical die, the velocity field reduces to that presented by Stepanskii and Avitzur. General velocity field and boundary of dead zone, if assumed, for the problem of axisymmetric forging of cylindrical work-pieces are obtained. Other problems which can be treated are briefly discussed.

The use of “dual-stream functions” in analyzing some three-dimensional metal-forming processes is demonstrated in this paper. The problems discussed are open-die forging of blocks, rolling of a rectangular bar with spread, piercing by elliptic and rectangular punches, and extrusion of a rectangular shape. For these forming processes, kinematically admissible velocity fields are selected using characteristics of the two stream functions. Approximate upper-bound solutions of the forming processes can be obtained from the proposed velocity fields.

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A general kinematically admissible velocity field applicable to forging of a rectangular strip of a incompressible material is presented. Generalized shape of any dead zone, if assumed, can be obtained in terms of process parameters from this velocity field. Two different upper bound solutions for average forging pressure are obtained from simple velocity fields which are special cases of proposed general velocity field. Numerical results of the solutions show improvement over previous upper bound solutions published in literature over a certain range of process parameters.