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The Scientific World Journal
Volume 2014, Article ID 189070, 7 pages
Research Article

An Accurate Upper Bound Solution for Plane Strain Extrusion through a Wedge-Shaped Die

1A. Yu. Ishlinskii Institute for Problems in Mechanics, Russian Academy of Sciences, 101-1 Prospect Vernadskogo, Moscow 119526, Russia
2Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Johor Darul Ta’zim, Malaysia
3Department of Mechanical and Electro-Mechanical Engineering, National Sun Yat-sen University, Kaohsiung 804, Taiwan

Received 19 February 2014; Revised 28 May 2014; Accepted 11 June 2014; Published 29 June 2014

Academic Editor: Guangxiong Chen

Copyright © 2014 Sergei Alexandrov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An upper bound method for the process of plane strain extrusion through a wedge-shaped die is derived. A technique for constructing a kinematically admissible velocity field satisfying the exact asymptotic singular behavior of real velocity fields in the vicinity of maximum friction surfaces (the friction stress at sliding is equal to the shear yield stress on such surfaces) is described. Two specific upper bound solutions are found using the method derived. The solutions are compared to an accurate slip-line solution and it is shown that the accuracy of the new method is very high.