Research Papers

An Investigation Into the Prediction of Forming Limit Diagrams for Normal Anisotropic Material Based on Bifurcation Analysis

[+] Author and Article Information
A. Jaamialahmadi

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

M. Kadkhodayan

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

J. Appl. Mech 78(3), 031006 (Feb 07, 2011) (10 pages) doi:10.1115/1.4003351 History: Received September 30, 2009; Revised April 28, 2010; Posted January 04, 2011; Published February 07, 2011; Online February 07, 2011

In this paper, formula derivation for bifurcation analysis based on a constitutive model including Hill 48 yield criterion with normal anisotropy of a pointed vertex on subsequent yield loci to predict the entire forming limit diagram (FLD) is carried out. Proportional loading, total deformation theory of plasticity, and power law relation are assumed. Predicted limit strains for Hill’s zero and minimum extension of localized neck orientation is derived. The dominancy of zero extension and minimum extension on the left-hand side of FLDs for different work hardening components and r-values are investigated in detail. An implicit four order rational function equation for major strain, which preferred that the orientation of neck correspond to minimum value of limit strain, is found by a developed optimization method. Optimized predicted limit strains for typical work hardening components and different r-values are obtained and discussed. Limit strains vary directly on the left and reversely on the right-hand side of FLD when r-value increases. Comparison between the predicted and experimental results exhibits a better agreement compared with those from the isotropic material. In addition, on the left-hand side, the resulted prediction limit strains represent a full dependency to assumed yield criterion. A comparison between the current work and Chow et al. results are performed and discussed in detail.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

A sheet with a localized necking and related coordinate system

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Figure 2

The dependency of localized neck orientation on r-values for a typical N on the left-hand side

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Figure 3

A comparison between the predicted limit strains for Hill’s zero extension condition on the left-hand side, minimum extension condition on the right-hand side, and optimized localized neck orientations for typical values of N and r

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Figure 4

The variation of limit strains with respect to r-value for two typical magnitudes of work hardening components

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Figure 5

A comparison between the experimental and analytical predictions of FLD for two aluminum and one stainless steel types of materials: (a) Al 1100 with N=0.26 and r=0.78(26), (b) Al 5182 with N=0.21 and r=0.93(26), and (c) AISI 304 with N=0.47 and r=1.075(27)

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Figure 6

A comparison of replotted FLD of Al 2028 for various orders of Hosford yield criterion based on Chow (20) results with the current work: (a) isotropic materials and (b) magnified of (a)



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