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Research Papers

A Modified Storen-Rice Bifurcation Analysis of Sheet Metal Forming Limit Diagrams

[+] Author and Article Information
A. Jaamialahmadi

Department of Mechanical Engineering,  Ferdowsi University of Mashhad, 91775-1111, Mashhad, Iranjaami-a@um.ac.ir

M. Kadkhodayan1

Department of Mechanical Engineering,  Ferdowsi University of Mashhad, 91775-1111, Mashhad, Irankadkhoda@um.ac.ir

1

Corresponding author.

J. Appl. Mech 79(6), 061004 (Sep 17, 2012) (10 pages) doi:10.1115/1.4005538 History: Received August 04, 2009; Revised April 04, 2011; Posted January 30, 2012; Published September 17, 2012; Online September 17, 2012

Bifurcation analysis is a theoretical prediction approach to measure the FLD when the localized neck causes development of vertex on subsequent yield surface as was adopted by Storen-Rice. Some analyses lead to solutions for special cases such as zero and minimum extension. They offer an equation which needs to be optimized with respect to the minimum limit strain versus neck orientation for the whole domain of FLD. Moreover, the previous reported results for the left-hand side of FLD are not quite satisfactory. In this paper, a re-investigation into bifurcation analysis adopted by S-R lead to modified equations which significantly improved FLD and could be respected as a more general approach to find FLD theoretically. The derivation and optimization procedure of equations are indicated and discussed in detail. The predicted limit strains are studied for different work hardening coefficients and compared with Storen-Rice, Zhu and some experimental data and the obtained results show more agreement. Furthermore, the present restrictions and the required conditions for validation of the Zhu approach are fully discussed.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

A sheet with a localized necking and related coordinate system

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Figure 2

Predicted limit strains for localized neck orientations for the directions of zero extension condition on left hand side and parallel to minor strain or minimum extension condition at right hand side of FLD for different values of N

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Figure 3

A comparison between the experimental and analytical prediction of FLD for a few typical materials; (a) Hecker experimental data for Al with N = 0.245 [30], (b) AA6111 with N = 0.26 [23], (c) A1100 with N = 0.27 [24], (d) AA6111-T4 with N = 0.23 [31]

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Figure 4

The variation of limit strain for different N values at the left-hand side of FLD, a comparison between the current results and the Zhu results (minimum and zero extension depending on N to be greater or lesser than 0.33), (a) N = 0.2, (b) N = 0.3, (c) N = 0.33, (d) N = 0.4

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