Streamlined wire drawing dies of minimum length

Richmond, O.; Morrison, H. L.

doi:10.1016/0022-5096(67)90032-4

Cited by 85 publications

(27 citation statements)

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“…In addition to the equations for stresses which have been reduced to (10) and (11), we should satisfy the following kinematic equations: the incompressibility equation and the condition that n is an eigenvector of the strain rate tensor (the associated flow rule). The former equation is…”

Section: _0 [Lnmentioning

confidence: 99%

“…A theory for steady planar flow based on streamline coordinates was developed by Alexandrov [9]. Ideal axisymmetric steady flows for Tresca solids were calculated by Richmond [4] and Richmond and Morrison [10] for the cases of wire drawing and extrusion, again using the method of characteristics. Chung and Richmond [11] and colleagues have determined many solutions for ideal membrane forming mostly using the Mises model, and including anisotropic modifications.…”

Section: Introductionmentioning

confidence: 99%

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The theory of general and ideal plastic deformations of Treasca solids

Richmond

Alexandrov

2002

Acta Mechanica

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Summary. Ideal plastic deformations have been defined elsewhere as solenoidal smooth deformations in which an eigenvector field associated everywhere with the greatest (major) principal rate of deformation is fixed in the material. For the rigid/perfectly plastic Tresca solid, which satisfies the Tresca yield condition and its associated normality flow rule, it is always possible to find an equilibrium stress field which is compatible with an ideal deformation. Under such conditions all material elements undergo paths of minimum plastic work, a condition which is believed to be advantageous for metalforming processes. Thus, ideal deformation theory has been used as the basis of a procedure for the direct preliminary design of such processes.The present work is focused on three-dimensional deformations where none of the components of principal strain rate vanishes and where the Tresca model is particularly useful. First the general nonsteady three-dimensional equations are derived in a special Lagrangian coordinate system. Then new results involving this coordinate system are obtained for nonsteady axisymmetric ideal deformations. Finally, similar ideas are applied to steady three-dimensional and axisymmetric deformations. In these cases, however, the special coordinate system is not Lagrangian, but is associated with streamlines.

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Section: _0 [Lnmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The theory of general and ideal plastic deformations of Treasca solids

Richmond

Alexandrov

2002

Acta Mechanica

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“…Early work on this, however, was limited to two-dimensional steady flow of rigid-perfect plastic solids (Richmond and Devenpeck, 1962;Richmond and Morrison, 1967;Richmond, 1968). Hill (1967), who proposed the name ideal flow, generalized the effort to three-dimensional steady flow.…”

Section: Introductionmentioning

confidence: 98%

Non-steady plane-strain ideal plastic flow

Chung

Lee

Richmond³

et al. 2005

International Journal of Plasticity

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“…Most early attempts to describe three-dimensional plastic flow were concerned, in fact, with conditions of axial symmetry [14], although no distinction was made between tri-axial and bi-axial strain. Neither was any attempt made to identify different mechanisms of plastic flow or the manner in which such mechanisms might be reflected in the form of the yield curve of the solid concerned.…”

Section: Introductionmentioning

confidence: 99%

Tri-axial deformation of a plastic-rigid solid

Bish¹

2011

Acta Mech

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The paper deals with the deformation of an ideal plastic solid that is initially rigid, i.e., elastic deformations are neglected. In addition, the solid flows by means of the mechanism of extended slip, for which the rotation-rate vector field remains continuous and the strain-rate tensor is solenoidal. The Tresca yield criterion applies to such a solid and with an associated flow-rule is represented in a manner that includes both bi-axial and tri-axial states of strain. Two new theorems are proved, and a second-order partial differential equation is derived for the first invariant of the stress tensor (hydrostatic pressure); the analogue of a similar published equation for the bi-axial strain case. To illustrate the methodology, the above theory is applied to the tri-axial problem of a thick metal plate clamped round a circle and deflected by means of pressure. It is shown, from the exact solution, that the errors due to the use of the approximate membrane formula for a clamped thin plate are small, even for a 6 mm thick plate clamped on a circle 100 mm in diameter. Surprisingly, there is an initial thickening of the plate and it is shown that, regardless of the plate thickness, the pressure passes through a maximum at a deflection equal to 1/ √ 3 of the radius of the clamping circle.

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Streamlined wire drawing dies of minimum length

Cited by 85 publications

References 1 publication

The theory of general and ideal plastic deformations of Treasca solids

The theory of general and ideal plastic deformations of Treasca solids

Non-steady plane-strain ideal plastic flow

Tri-axial deformation of a plastic-rigid solid

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