Forming Limit Analysis of Sheet Metals Based on a Generalized Deformation TheorySource: Journal of Engineering Materials and Technology:;2003:;volume( 125 ):;issue: 003::page 260DOI: 10.1115/1.1586938Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: This paper presents the development of a generalized method to predict forming limits of sheet metals. The vertex theory, which was developed by Stören and Rice (1975) and recently simplified by Zhu, Weinmann and Chandra (2001), is employed in the analysis to characterize the localized necking (or localized bifurcation) mechanism in elastoplastic materials. The plastic anisotropy of materials is considered. A generalized deformation theory of plasticity is proposed. The theory considers Hosford’s high-order yield criterion (1979), Hill’s quadratic yield criterion and the von Mises yield criterion. For the von Mises yield criterion, the generalized deformation theory reduces to the conventional deformation theory of plasticity, i.e., the J2-theory. Under proportional loading condition, the direction of localized band is known to vary with the loading path at the negative strain ratio region or the left hand side (LHS) of forming limit diagrams (FLDs). On the other hand, the localized band is assumed to be always perpendicular to the major strain at the positive strain ratio region or the right hand side (RHS) of FLDs. Analytical expressions for critical tangential modulus are derived for both LHS and RHS of FLDs. For a given strain hardening rule, the limit strains can be calculated and consequently the FLD is determined. Especially, when assuming power-law strain hardening, the limit strains can be explicitly given on both sides of FLD. Whatever form of a yield criterion is adopted, the LHS of the FLD always coincides with that given by Hill’s zero-extension criterion. However, at the RHS of FLD, the forming limit depends largely on the order of a chosen yield function. Typically, a higher order yield function leads to a lower limit strain. The theoretical result of this study is compared with those reported by earlier researchers for Al 2028 and Al 6111-T4 (Grafand Hosford, 1993; Chow et al., 1997).
keyword(s): Plasticity , Deformation , Sheet metal , Necking , Stress , Work hardening , Bifurcation AND Anisotropy ,
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contributor author | C. L. Chow | |
contributor author | S. J. Hu | |
contributor author | M. Jie | |
date accessioned | 2017-05-09T00:10:21Z | |
date available | 2017-05-09T00:10:21Z | |
date copyright | July, 2003 | |
date issued | 2003 | |
identifier issn | 0094-4289 | |
identifier other | JEMTA8-27049#260_1.pdf | |
identifier uri | http://yetl.yabesh.ir/yetl/handle/yetl/128476 | |
description abstract | This paper presents the development of a generalized method to predict forming limits of sheet metals. The vertex theory, which was developed by Stören and Rice (1975) and recently simplified by Zhu, Weinmann and Chandra (2001), is employed in the analysis to characterize the localized necking (or localized bifurcation) mechanism in elastoplastic materials. The plastic anisotropy of materials is considered. A generalized deformation theory of plasticity is proposed. The theory considers Hosford’s high-order yield criterion (1979), Hill’s quadratic yield criterion and the von Mises yield criterion. For the von Mises yield criterion, the generalized deformation theory reduces to the conventional deformation theory of plasticity, i.e., the J2-theory. Under proportional loading condition, the direction of localized band is known to vary with the loading path at the negative strain ratio region or the left hand side (LHS) of forming limit diagrams (FLDs). On the other hand, the localized band is assumed to be always perpendicular to the major strain at the positive strain ratio region or the right hand side (RHS) of FLDs. Analytical expressions for critical tangential modulus are derived for both LHS and RHS of FLDs. For a given strain hardening rule, the limit strains can be calculated and consequently the FLD is determined. Especially, when assuming power-law strain hardening, the limit strains can be explicitly given on both sides of FLD. Whatever form of a yield criterion is adopted, the LHS of the FLD always coincides with that given by Hill’s zero-extension criterion. However, at the RHS of FLD, the forming limit depends largely on the order of a chosen yield function. Typically, a higher order yield function leads to a lower limit strain. The theoretical result of this study is compared with those reported by earlier researchers for Al 2028 and Al 6111-T4 (Grafand Hosford, 1993; Chow et al., 1997). | |
publisher | The American Society of Mechanical Engineers (ASME) | |
title | Forming Limit Analysis of Sheet Metals Based on a Generalized Deformation Theory | |
type | Journal Paper | |
journal volume | 125 | |
journal issue | 3 | |
journal title | Journal of Engineering Materials and Technology | |
identifier doi | 10.1115/1.1586938 | |
journal fristpage | 260 | |
journal lastpage | 265 | |
identifier eissn | 1528-8889 | |
keywords | Plasticity | |
keywords | Deformation | |
keywords | Sheet metal | |
keywords | Necking | |
keywords | Stress | |
keywords | Work hardening | |
keywords | Bifurcation AND Anisotropy | |
tree | Journal of Engineering Materials and Technology:;2003:;volume( 125 ):;issue: 003 | |
contenttype | Fulltext |