Post-critical plastic deformation of biaxially stretched sheets

Petryk, H.; Thermann, K.

doi:10.1016/0020-7683(95)00061-e

Cited by 15 publications

(5 citation statements)

References 13 publications

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“…Accordingly, the results of the current study are not intended to be compared with sheet necking analyses and the associated FLDs, and whenever such a comparison is attempted, it should only be considered qualitatively. Note, however, that some contributions have investigated the three-dimensional effects on necking instabilities (e.g., Needleman and Tvergaard, 1977;Tvergaard, 1993;Petryk and Thermann, 1996;Benallal, 1998;Ito et al, 2000); while clarified the conditions of validity of the plane stress approximations in sheet necking analysis. In virtue of the 'intrinsic' nature of the adopted 'material' instability concept, viewed as an instability in the constitutive description, a more consistent use is proposed, which consists in setting the limits to achievable ductility of metals.…”

Section: Introductionmentioning

confidence: 99%

Ductility limit prediction using a GTN damage model coupled with localization bifurcation analysis

Mansouri

Chalal

Abed‐Meraim

2014

Mechanics of Materials

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Because the localization of deformation into narrow planar bands is often precursor to material failure, several approaches have been proposed to predict this phenomenon. In this paper, the Gurson–Tvergaard– Needleman (GTN) elastic–plastic–damage model for ductile materials is considered. A large-strain version of this constitutive model is coupled with the Rice localization criterion, which is based on bifurcation theory, to investigate strain localization. The resulting loss of ellipticity condition is then used to determine ellipticiy loss diagrams (ELDs) associated with strain paths that are those typically applied to metals under biaxial stretching. A sensitivity analysis is conducted with respect to the model parameters on a representative selection of ductile materials. The analysis shows that the damage parameters have a significant impact on the predicted ELDs, which confirms the predominant role of damage-induced softening in triggering plastic flow localization with the adopted constitutive description combined with the bifurcation approach. As a consequence of this high sensitivity, it appears that the proper identification of damage parameters is a key issue for accurate plastic flow localization predictions using the GTN model coupled with bifurcation theory. The effect of the dense matrix hardening parameters on the strain localization predictions of the voided aggregate, although found much smaller in the whole, is more noticeable for the plane strain tension loading path or, more generally, when the critical hardening modulus required for localization is not strongly negative.International audienceBecause the localization of deformation into narrow planar bands is often precursor to material failure, several approaches have been proposed to predict this phenomenon. In this paper, the Gurson–Tvergaard– Needleman (GTN) elastic–plastic–damage model for ductile materials is considered. A large-strain version of this constitutive model is coupled with the Rice localization criterion, which is based on bifurcation theory, to investigate strain localization. The resulting loss of ellipticity condition is then used to determine ellipticiy loss diagrams (ELDs) associated with strain paths that are those typically applied to metals under biaxial stretching. A sensitivity analysis is conducted with respect to the model parameters on a representative selection of ductile materials. The analysis shows that the damage parameters have a significant impact on the predicted ELDs, which confirms the predominant role of damage-induced softening in triggering plastic flow localization with the adopted constitutive description combined with the bifurcation approach. As a consequence of this high sensitivity, it appears that the proper identification of damage parameters is a key issue for accurate plastic flow localization predictions using the GTN model coupled with bifurcation theory. The effect of the dense matrix hardening parameters on the strain localization predictions of the voided aggregate, although found m...

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Section: Introductionmentioning

confidence: 99%

Ductility limit prediction using a GTN damage model coupled with localization bifurcation analysis

Mansouri

Chalal

Abed‐Meraim

2014

Mechanics of Materials

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“…However, it is quite common both for plane strain loadings, e.g. Hill and Hutchinson (1975), Needleman (1979), Hutchinson and Tvergaard (1981), Steinmann et al (1994) and for the analysis of thin sheets in plane stress, Hill (1952), Thomas (1961), StoÈ ren and Rice (1975), Petryk and Thermann (1996). The solution for strain localization obtained in this paper is therefore, in the ®rst place, a generalization of earlier solutions that assume elastic isotropy and coaxiality of plastic properties, e.g.…”

Section: Introductionmentioning

confidence: 99%

Localization of deformation in plane elastic–plastic solids with anisotropic elasticity

Bigoni

Loret

Radi

2000

Journal of the Mechanics and Physics of Solids

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“…These models are generally based on the coupling between a localization criterion used to predict the onset of localized necking and a constitutive model describing the evolution of the mechanical fields. Among the most known localization criteria used in the literature, one can quote the initial imperfection approach, which was developed initially by Marciniak and Kuczynski [ 3 ], the bifurcation theory initiated by Rice in [ 4 , 5 ], and the energy criterion of instability of a deformation process formulated by Petryk et al [ 6 , 7 , 8 ]. Despite its large popularity, the initial imperfection approach has a main drawback: the over-sensitivity of its predictions (in terms of limit strain) to the amount of initial imperfection (which may be viewed as a nonphysical parameter).…”

Section: Introductionmentioning

confidence: 99%

Influence of the Non-Schmid Effects on the Ductility Limit of Polycrystalline Sheet Metals

Bettaieb

Abed‐Meraim

2018

Materials

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The yield criterion in rate-independent single crystal plasticity is most often defined by the classical Schmid law. However, various experimental studies have shown that the plastic flow of several single crystals (especially with Body Centered Cubic crystallographic structure) often exhibits some non-Schmid effects. The main objective of the current contribution is to study the impact of these non-Schmid effects on the ductility limit of polycrystalline sheet metals. To this end, the Taylor multiscale scheme is used to determine the mechanical behavior of a volume element that is assumed to be representative of the sheet metal. The mechanical behavior of the single crystals is described by a finite strain rate-independent constitutive theory, where some non-Schmid effects are accounted for in the modeling of the plastic flow. The bifurcation theory is coupled with the Taylor multiscale scheme to predict the onset of localized necking in the polycrystalline aggregate. The impact of the considered non-Schmid effects on both the single crystal behavior and the polycrystal behavior is carefully analyzed. It is shown, in particular, that non-Schmid effects tend to precipitate the occurrence of localized necking in polycrystalline aggregates and they slightly influence the orientation of the localization band.

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Post-critical plastic deformation of biaxially stretched sheets

Cited by 15 publications

References 13 publications

Ductility limit prediction using a GTN damage model coupled with localization bifurcation analysis

Ductility limit prediction using a GTN damage model coupled with localization bifurcation analysis

Localization of deformation in plane elastic–plastic solids with anisotropic elasticity

Influence of the Non-Schmid Effects on the Ductility Limit of Polycrystalline Sheet Metals

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