Limit strains in the processes of stretch-forming sheet metal

doi:10.1016/0020-7403(67)90066-5

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Limit strains in the processes of stretch-forming sheet metal

Journal Article•DOI•

Limit strains in the processes of stretch-forming sheet metal

01 Sep 1967-International Journal of Mechanical Sciences (Pergamon)-Vol. 9, Iss: 9, pp 609-620

TL;DR: In this paper, a theoretical analysis of the process of the generation of the groove based on anisotropic plasticity theory is presented, and the system of equations derived was solved numerically with the aid of a computer, which enabled the limiting strain of the sheet metal to be determined as a function of the material.

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About: This article is published in International Journal of Mechanical Sciences.The article was published on 1967-09-01. It has received 1814 citations till now. The article focuses on the topics: Forming limit diagram & Groove (music).

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Book Chapter•DOI•

Material Failure by Void Growth to Coalescence

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Viggo Tvergaard¹•Institutions (1)

Technical University of Denmark¹

01 Jan 1989-Advances in Applied Mechanics

TL;DR: In this paper, a convected coordinate formulation of the field equations is used to describe the material failure by coalescence of microscopic voids, and a detailed micromechanical study of shear band bifurcation that accounts for the interaction between neighboring voids and the strongly nonhomogeneous stress distributions around each void has been carried out, and also elaborated in this chapter.

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Abstract: Publisher Summary This chapter describes the material failure by coalescence of microscopic voids. The voids nucleate mainly at second phase particles, by decohesion of the particle-matrix interface or by particle fracture, and subsequently the voids grow because of plastic straining of the surrounding material. The growth of voids to coalescence by plastic yielding of the surrounding material involves so large geometry changes that finite strain formulations of the field equations are a necessary tool. A convected coordinate formulation of the governing equations is used. Convected coordinates are introduced, which serve as particle labels. The convected coordinate net can be visualized as being inscribed on the body in the reference state and deforming with the material. It is found that after nucleation, cavities elongate along the major tensile axis and that two neighboring cavities coalesce when their length has grown to the order of magnitude of their spacing. This local failure occurs by the development of slip planes between the cavities or simply necking of the ligament. A detailed micromechanical study of shear band bifurcation that accounts for the interaction between neighboring voids and the strongly nonhomogeneous stress distributions around each void has been carried out, and are also elaborated in this chapter.

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938 citations

Journal Article•DOI•

Modification of the Gurson Model for shear failure

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Ken Nahshon¹, John W. Hutchinson¹•Institutions (1)

Harvard University¹

01 Jan 2008-European Journal of Mechanics A-solids

TL;DR: In this paper, an extension of the Gurson model is proposed that incorporates damage growth under low triaxiality straining for shear-dominated states, which can be used to characterize important growth and coalescence features.

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Abstract: Recent experimental evidence points to limitations in characterizing the critical strain in ductile fracture solely on the basis of stress triaxiality A second measure of stress state, such as the Lode parameter, is required to discriminate between axisymmetric and shear-dominated stress states This is brought into the sharpest relief by the fact that many structural metals have a fracture strain in shear, at zero stress triaxiality, that can be well below fracture strains under axisymmetric stressing at significantly higher triaxiality Moreover, recent theoretical studies of void growth reveal that triaxiality alone is insufficient to characterize important growth and coalescence features As currently formulated, the Gurson Model of metal plasticity predicts no damage change with strain under zero mean stress, except when voids are nucleated Consequently, the model excludes shear softening due to void distortion and inter-void linking As it stands, the model effectively excludes the possibility of shear localization and fracture under conditions of low triaxiality if void nucleation is not invoked In this paper, an extension of the Gurson model is proposed that incorporates damage growth under low triaxiality straining for shear-dominated states The extension retains the isotropy of the original Gurson Model by making use of the third invariant of stress to distinguish shear dominated states The importance of the extension is illustrated by a study of shear localization over the complete range of applied stress states, clarifying recently reported experimental trends The extension opens the possibility for computational fracture approaches based on the Gurson Model to be extended to shear-dominated failures such as projectile penetration and shear-off phenomena under impulsive loadings

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921 citations

Cites methods from "Limit strains in the processes of s..."

...The approach is a rigorous finite strain analysis that follows earlier localization studies first employed by Marciniak and Kuczynski (1967) to study localization in thin sheets under plane stress and laid out within a three-dimensional, finite strain setting by Rice (1977). This approach has been employed by several authors including Saje et al. (1982), Pan et al....
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...The approach is a rigorous finite strain analysis that follows earlier localization studies first employed by Marciniak and Kuczynski (1967) to study localization in thin sheets under plane stress and laid out within a three-dimensional, finite strain setting by Rice (1977). This approach has been employed by several authors including Saje et al. (1982), Pan et al. (1983), and Mear and Hutchinson (1985). The following development closely follows Rice’s (1977) treatment as detailed by Mear and Hutchinson (1985). The formulation requires consideration of only two states, those inside and outside the band, as the material in each region is initially uniform but with differing initial damage states....
[...]
...The approach is a rigorous finite strain analysis that follows earlier localization studies first employed by Marciniak and Kuczynski (1967) to study localization in thin sheets under plane stress and laid out within a three-dimensional, finite strain setting by Rice (1977)....
[...]
...The approach is a rigorous finite strain analysis that follows earlier localization studies first employed by Marciniak and Kuczynski (1967) to study localization in thin sheets under plane stress and laid out within a three-dimensional, finite strain setting by Rice (1977). This approach has been employed by several authors including Saje et al....
[...]
...The approach is a rigorous finite strain analysis that follows earlier localization studies first employed by Marciniak and Kuczynski (1967) to study localization in thin sheets under plane stress and laid out within a three-dimensional, finite strain setting by Rice (1977). This approach has been employed by several authors including Saje et al. (1982), Pan et al. (1983), and Mear and Hutchinson (1985)....
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Journal Article•DOI•

Localized necking in thin sheets

[...]

Sigurd Støren¹, James R. Rice¹•Institutions (1)

Brown University¹

01 Dec 1975-Journal of The Mechanics and Physics of Solids

TL;DR: Using a simplified constitutive model of a pointed vertex on subsequent yield loci, the onset of localized necking under biaxial stretching has been predicted and this result supports the hypothesis of vertex-formation on the yield locus under continued plastic flow.

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Abstract: B y using a simplified constitutive model of a pointed vertex on subsequent yield loci, namely, such that the equations of deformation-theory of rigid-plastic solids apply for fully-active stress increments, the onset of localized necking under biaxial stretching has been predicted. The predictions agree reasonably well with reported experimental observations. Since localized necking under biaxial stretching of a uniform and homogeneous sheet is impossible when flow theories of plasticity with smooth yield-loci are used, this result supports the hypothesis of vertex-formation on the yield locus under continued plastic flow. The implications of this conclusion with respect to the study of the inception of ductile fracture in solids, viewed as a material instability, may be far-reaching. Still, explanations based on a smooth yield-locus but small initial inhomogeneities cannot be ruled out, and both initial imperfections and yield-vertex effects may contribute in general to localization instabilities.

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816 citations

Cites background from "Limit strains in the processes of s..."

...MARCINIAK and KUCZYNSKI (1967) made an attempt to resolve this ‘paradox’ by assuming pre-existing inhomogeneities in the sheet....
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...…development of a neck, and certainly when the problem is analyzed on the basis of the rigid-plastic isotropic-hardening material model, with a smooth yield-locus at the applied stress-point, no neck can be predicted for p > 0 without the assumption of imperfections (MARCINIAK and KUCZYNSKI, 1967)....
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Journal Article•DOI•

Influence of the plastic properties of a material on the forming limit diagram for sheet metal in tension

[...]

Zdzisław Marciniak¹, Kazimierz Kuczyński¹, Tadeusz Pokora¹•Institutions (1)

Warsaw University of Technology¹

01 Oct 1973-International Journal of Mechanical Sciences

TL;DR: In this article, the formation of a groove, which appears before fracture in sheet metal subject to tension, is presented, and is based on the assumption of initial nonhomogeneity of the material in order to facilitate the determination of the limit strain.

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435 citations

Journal Article•DOI•

New ductile fracture criterion for prediction of fracture forming limit diagrams of sheet metals

[...]

Yanshan Lou¹, Hoon Huh¹, S. J. Lim¹, Keunhwan Pack¹•Institutions (1)

KAIST¹

01 Dec 2012-International Journal of Solids and Structures

TL;DR: In this paper, a new ductile fracture criterion is proposed to model fracture behavior of sheet metals for nucleation, growth and shear coalescence of voids during plastic deformation.

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388 citations

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References

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Journal Article•DOI•

Plastic instability under plane stress

[...]

H.W. Swift¹•Institutions (1)

University of Sheffield¹

01 Oct 1952-Journal of The Mechanics and Physics of Solids

TL;DR: In this paper, conditions for instability of plastic strain under plane stress for a material conforming to the Mises-Hencky yield condition and strain-hardening according to a unique relationship between root-mean-square values of shear stress (q) and incremental strain (δψ).

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Abstract: This paper examines the conditions for instability of plastic strain under plane stress for a material conforming to the Mises-Hencky yield condition and strain-hardening according to a unique relationship between root-mean-square values of shear stress (q) and incremental strain (δψ). If, under fixed loading conditions, the material undergoes a strain increment which is consistent with the applied stress system, the conditions are stable or unstable according as the increment in representative yield stress is greater or less than the increment in representative induced stress. The strain at which instability arises is found in terms of the biaxial stress ratio p2/p1 under different conditions of applied loading, and the effect is demonstrated of strain-hardening according to an empirical relation of the type q = c (a + ψ)n. The analysis is also applied to certain cases of non-uniform stress distribution. In the case of the hydrostatic bulge results are obtained showing a critical thinning ranging from 26 per cent for a non-hardening material to about 45 per cent for typical strain-hardening materials, values in general agreement with experimental data. Conditions over the punch head in the pressing of a cylindrical shell are discussed but computations are not attempted.

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1,604 citations

Journal Article•DOI•

C. A theory of the plastic bulging of a metal diaphragm by lateral pressure

[...]

R. Hill

01 Jan 1950-Philosophical Magazine Series 1

TL;DR: In this article, explicit formulae are obtained for the stresses in a metal diaphragm which is bulged plastically by lateral pressure, and the predicted influence of work-hardening on the shape of the profile, and on the relation between polar strain and curvature, agree well with experimental data.

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Abstract: Summary Explicit formulae are obtained for the stresses in a metal diaphragm which is bulged plastically by lateral pressure. The predicted influence of work-hardening on the shape of the profile, and on the relation between polar strain and curvature, agrees well with experimental data. A simple expression is developed for the instability strain.

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262 citations