Journal ArticleDOI
On discontinuous plastic states, with special reference to localized necking in thin sheets
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In this article, the authors investigated the permitted discontinuities of stress, velocity, and surface slope in a plastic-rigid sheet deformed in its plane, and the necessary restrictions on the stress-state and rate of workhardening were obtained for any yield function and plastic potential.Abstract:
Permissible discontinuities of stress, velocity, and surface slope are investigated in a plastic-rigid sheet deformed in its plane. One such discontinuity of velocity is shown to be the mathematical idealization of localized necking; the necessary restrictions on the stress-state and rate of workhardening are obtained for any yield function and plastic potential. The results are illustrated by an examination of the modes of necking in notched tension strips. The constraint factors at the yield point are obtained for notches with wedge-shaped or circular roots.read more
Citations
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Necking and radial cracking around perforations in thin sheets at normal incidence
TL;DR: In this paper, the formation of multiple necks and cracks around perforations in ductile materials is investigated, and expressions for the number of plane-strain radial necks formed by conical penetrators (with or without starter holes in the flat target), and also by round-ended projectiles into flat targets having starter holes or, in plain targets with no starter holes, after fracture of the initial circumferential neck has detached a circular cap of material (discing).
Journal ArticleDOI
Ellipticity loss analysis for tangent moduli deduced from a large strain elastic–plastic self-consistent model
Gérald Franz,Farid Abed-Meraim,Jean-Paul Lorrain,Tarak Ben Zineb,Xavier Lemoine,Marcel Berveiller +5 more
TL;DR: In this article, the impact of microstructures and deformation mechanisms on the ductility of polycrystalline aggregates was investigated by applying the criterion first proposed by Rice to elastic-plastic tangent moduli derived from a large strain micromechanical model combined with a self-consistent scale-transition technique.
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An experimental and theoretical study on the prediction of forming limit diagrams using new BBC yield criteria and M–K analysis
TL;DR: Banabic et al. as mentioned in this paper developed a comprehensive study on the prediction of forming limit diagrams (FLDs) for an AA3003-O aluminium alloy, and an out-of-plane formability test was performed based on the technique proposed by Ozturk and Lee.
Journal ArticleDOI
Folding and necking across the scales: a review of theoretical andexperimental results and their applications
TL;DR: A review of theoretical and experimental results on folding and necking, including the lithospheric scale, can be found in this article, together with a short historical overview of research.
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Finite element modeling simulation of in-plane forming limit diagrams of sheets containing finite defects
K. Narasimhan,Robert H. Wagoner +1 more
TL;DR: In this article, the authors used the Marciniak-kuczynski (M-K) results of finite element modeling (FEM) to predict forming limit diagrams (FLDs) of thin sheets based on two-dimensional (2-D) finite thickness defects.
References
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Book
The mathematical theory of plasticity
TL;DR: In this paper, the solution of two-dimensional non-steady motion problems in two dimensions is studied. But the solution is not a solution to the problem in three dimensions.
Journal ArticleDOI
XLVI. A theory of the plastic distortion of a polycrystalline aggregate under combined stresses.
J.F.W. Bishop,Rodney Hill +1 more
TL;DR: In this paper, a general relationship between stress and plastic strain in polycrystalline aggregate is derived for any metal in which individual crystals deform by slipping over preferred planes under a critical shear stress.
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CXXVIII. A theoretical derivation of the plastic properties of a polycrystalline face-centred metal
J.F.W. Bishop,Rodney Hill +1 more
TL;DR: In this paper, it was shown that the work-hardness of an isotropic aggregate of face-centred cubic crystals is a function only of the total plastic work if the grains hardened equally.
Journal ArticleDOI
Extended limit design theorems for continuous media
TL;DR: In this paper, the safe loads for a Prandtl-Reuss material subject to surface tractions or displacements which increase in ratio are extended to any perfectly plastic material and any history of loading.