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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Journal ArticleDOI
The forming limit diagram of ferritic stainless steel sheets: Experiments and modeling
TL;DR: In this paper, the forming limit diagrams (FLDs) of two ferritic stainless steel sheets of thicknesses 1 and 0.1mm were determined experimentally using the modified Marciniak test and the conventional ASTM standard test.
Journal ArticleDOI
Hardening laws, surface roughness and biaxial tensile limit strains of sheet aluminium alloys
TL;DR: In this article, the role of hardening laws and surface roughness in the prediction of biaxial tensile limit strains of two A1 alloy sheet materials with different strain hardening characteristics was assessed.
Journal ArticleDOI
A theory of the tensile and compressive textures of face-centred cubic metals
TL;DR: In this article, the possible rotations of a representative set of grains due to a small increment of strain are computed and a hypothesis is advanced to account for the different textures observed under similar straining conditions by metals of the same lattice.
Journal ArticleDOI
Effect of Grain anisotropy on limit strains in biaxial stretching: part i. influence of sheet thickness and grain size in weakly textured sheets
TL;DR: In this article, the authors investigated the role of the plastic anistropy of individual grains of the primary phase in the formation of inhomogeneous deformation in biaxial stretching.
Book ChapterDOI
Bifurcation and Instability of Non-Associative Elastoplastic Solids
TL;DR: In this paper, global and local uniqueness and stability criteria for elastoplastic solids with non-associative flow rules are presented, where Hill's general theory is developed in the form generalized by Raniecki to nonassociativity.
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.
Journal ArticleDOI
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.