Research Article | OPEN ACCESS
Analyses of Plane-strain Compression Using the Upper Bound Method
Mahir Es-Saheb, Ali Al-Witry and Abdulmohsen Albedah
Department of Mechanical Engineering, College of Engineering, King Saud
University, P.O. Box 800, Riyadh 11241, Saudi Arabia
Research Journal of Applied Sciences, Engineering and Technology 2013 5:761-767
Received: August 07, 2012 | Accepted: September 03, 2012 | Published: June 25, 2013
Abstract
Traditional upper bound analyses for plane-strain compression leads to low load prediction values, for a large ratio range of contact Length (L) to thickness (h). These predicted load values are based on deformation fields consisted of rigid regions separated by planes upon which discrete shear occurs. In this study, the relatively simple deformation fields consisted of odd number of triangles such like, 1, 3 and 5, are used. A general minimum solution for this class of upper bounds is derived and found to occur when the base of the center triangle (w) [= 2L/ (n+1)], where n is an odd integer ≥3. Consequently, whether still lower values would occur with this class of field when the ratio(R), of the field triangles side lengths is varied, has been systematically investigated. Thus, the upper bound loads are calculated over a wide range of the ratio (R) and the deformation field parameters. These parameters include the thickness (h) the contact Length (L) and the base of the center triangle (w). It is found that, all the minimum load values occur at unity R ratio and the minimum values of h, L and w. The minimum values obtained for hopt, Lopt and wopt are 1.466, 3.266 and 2.0 units, respectively. Also, the corresponding overall minimum optimal upper bound value found is P/2k = 1.93.
Keywords:
Fields, metal forming, plane-strain compression, plasticity, upper bound method,
Competing interests
The authors have no competing interests.
Open Access Policy
This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Copyright
The authors have no competing interests.
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ISSN (Online): 2040-7467
ISSN (Print): 2040-7459 |
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