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    Forming Limit Analysis of Sheet Metals Based on a Generalized Deformation Theory

    Source: Journal of Engineering Materials and Technology:;2003:;volume( 125 ):;issue: 003::page 260
    Author:
    C. L. Chow
    ,
    S. J. Hu
    ,
    M. Jie
    DOI: 10.1115/1.1586938
    Publisher: 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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      Forming Limit Analysis of Sheet Metals Based on a Generalized Deformation Theory

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    http://yetl.yabesh.ir/yetl1/handle/yetl/128476
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    contributor authorC. L. Chow
    contributor authorS. J. Hu
    contributor authorM. Jie
    date accessioned2017-05-09T00:10:21Z
    date available2017-05-09T00:10:21Z
    date copyrightJuly, 2003
    date issued2003
    identifier issn0094-4289
    identifier otherJEMTA8-27049#260_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/128476
    description abstractThis 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).
    publisherThe American Society of Mechanical Engineers (ASME)
    titleForming Limit Analysis of Sheet Metals Based on a Generalized Deformation Theory
    typeJournal Paper
    journal volume125
    journal issue3
    journal titleJournal of Engineering Materials and Technology
    identifier doi10.1115/1.1586938
    journal fristpage260
    journal lastpage265
    identifier eissn1528-8889
    keywordsPlasticity
    keywordsDeformation
    keywordsSheet metal
    keywordsNecking
    keywordsStress
    keywordsWork hardening
    keywordsBifurcation AND Anisotropy
    treeJournal of Engineering Materials and Technology:;2003:;volume( 125 ):;issue: 003
    contenttypeFulltext
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