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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Conditions for the localization of deformation in pressure-sensitive dilatant materials
John W. Rudnicki,James R. Rice +1 more
TL;DR: In this paper, the authors investigated the hypothesis that localization of deformation into a shear band may be considered a result of an instability in the constitutive description of homogeneous deformation.
Journal ArticleDOI
Overview no. 42 Texture development and strain hardening in rate dependent polycrystals
R.J. Asaro,Alan Needleman +1 more
TL;DR: In this article, a rate dependent constitutive model is developed for polycrystals subjected to arbitrarily large strains, and the model is used to predict deformation textures and large-strain strain hardening behavior following various stressstrain histories for single phase f.c. aggregates that deform by crystallographic slip.
Journal ArticleDOI
Localized necking in thin sheets
Sigurd Støren,James R. Rice +1 more
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.
Journal ArticleDOI
Plastic stress and strain fields at a crack tip
TL;DR: In this article, the dominant singularity governing the plastic behavior at a crack tip is analyzed for conditions of plane stress and plane strain for cracks in both far tensile and far shear fields.
Journal ArticleDOI
Plastic stress-strain matrix and its application for the solution of elastic-plastic problems by the finite element method
TL;DR: In this paper, a finite element approach is proposed for the solution of the continuum elastic-plastic problems by means of a plastic stress-strain matrix which is derivable by inverting the Prandtl-Reuss equations in plasticity theory.
References
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Journal ArticleDOI
LXXXVIII. On the state of stress in a plastic-rigid body at the yield point
TL;DR: In this paper, it is shown that part of the plastic zone at the yield point, where deformation occurs, depends only on the current surface tractions and not on the previous loading programme.
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XXX. A note on estimating yield-point loads in a plastic-rigid body
TL;DR: In this paper, bounds are obtained for the error committed when any approximate theory of plasticity is used to estimate yield-point loads, and it is shown that, if the Mises yield function and potential are used to approximate the Taylor-Quinney data for copper, the error is less than 1% for a wide variety of loading programs.
Journal ArticleDOI
L. On the significance of the limit load theorems for an elastic-plastic body
TL;DR: The limit load theorems of Drucker, Greenberg, and Prager as discussed by the authors for an elastic-plastic material flowing under constant surface tractions are contrasted with the theory of the yield of a plastic-rigid body.
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The method of characteristics applied to problems of steady motion in plane plastic stress
TL;DR: In this paper, the methods presented above have been applied to more complicated frames and readily give the required solutions for collapse design under constant or varying loads, for all three types of design, since it will be found that a large proportion of the inequalities generated become redundant and can be ignored.