Limit Analysis of Flow Through Inclined Converging Planes

[+] Author and Article Information
M. Kiuchi

Institute of Industrial Science, University of Tokyo, Tokyo, Japan

B. Avitzur

Institute for Metal Forming, Department of Metallurgy and Material Engineering, Lehigh University, Bethlehem, Pa.

J. Eng. Ind 102(2), 109-117 (May 01, 1980) (9 pages) doi:10.1115/1.3183841 History: Received August 09, 1979; Online July 30, 2009


A variety of mathematical models may be used to analyze plastic deformation during a metal-forming process. One of these methods—limit analysis—places the estimate of required power between an upper bound and a lower bound. The upper- and lower-bound analysis are designed so that the actual power or forming stress requirement is less than that predicted by the upper bound and greater than that predicted by the lower bound. Finding a lower upper-bound and a higher lower-bound reduces the uncertainty of the actual power requirement. Upper and lower bounds will permit the determination of such quantities as required forces, limitations on the process, optimal die design, flow patterns, and prediction and prevention of defects. Fundamental to the development of both upper-bound and lower-bound solutions is the division of the body into zones. For each of the zones there is written either a velocity field (upper bound) or a stress field (lower bound). A better choice of zones and fields brings the calculated values closer to actual values. In the present work, both upper- and lower-bound solutions are presented for plane-strain flow through inclined converging dies. For the upper bound, trapezoidal velocity fields, uni-triangular velocity fields, and multi-triangular velocity fields have been dealt with and the solutions compared to previously published work on cylindrical velocity fields. It was found that in different domains of the various combinations of the process parameters, different patterns of flow (cylindrical, triangular, etc.) provide lower upper-bound solutions. The lower-bound solution for plane-strain flow through inclined converging planes is newly developed.

Copyright © 1980 by ASME
Your Session has timed out. Please sign back in to continue.





Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In