On the Solution of Three-Dimensional Metal-Forming Processes

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Abstract
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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