A New Upper-Bound Method for Analysis of Some Steady-State Plastic Deformation Processes

1969 ◽  
Vol 91 (3) ◽  
pp. 731-741 ◽  
Author(s):  
E. R. Lambert ◽  
H. S. Mehta ◽  
S. Kobayashi
Keyword(s):  
Plastic Deformation ◽  
Steady State ◽  
Plane Strain ◽  
Velocity Component ◽  
Velocity Fields ◽  
Flow Lines ◽  
Upper Bound Method ◽  
Admissible Velocity ◽  
Tube Extrusion ◽  
Deformation Processes

A method of obtaining admissible velocity fields without velocity discontinuities is described, and applied to plane-strain extrusion, tube extrusion, and axisymmetric piercing. In plane-strain extrusion, the flow lines, grid distortions, and extrusion pressures were obtained and the values were compared with those found in previous solutions. For tube extrusion and axisymmetric piercing, the solutions are presented as examples in terms of flow lines and velocity component distributions; these solutions await experimental confirmation.

Upper Bound Solutions to Plane-Strain Extrusion Problems

1970 ◽  
Vol 92 (1) ◽  
pp. 158-164 ◽  
Author(s):  
P. C. T. Chen
Keyword(s):  
Plane Strain ◽  
Upper Bound ◽  
Material Properties ◽  
Incompressible Material ◽  
Velocity Fields ◽  
Deformation Pattern ◽  
Upper Bound Theorem ◽  
Admissible Velocity ◽  
Die Geometry ◽  
Bound Theorem

A method for selecting admissible velocity fields is presented for incompressible material. As illustrations, extrusion processes through three basic types of curved dies have been treated: cosine, elliptic, and hyperbolic. Upper-bound theorem is used in obtaining mean extrusion pressures and also in choosing the most suitable deformation pattern for extrusion through square dies. Effects of die geometry, friction, and material properties are discussed.

Direct Upper Bound Solution to Rectangular-to-Polygonal Extrusion Through Square Die

1999 ◽  
Vol 121 (2) ◽  
pp. 195-201 ◽  
Author(s):  
S. K. Sahoo ◽  
P. K. Kar ◽  
K. C. Singh
Keyword(s):  
Steady State ◽  
Velocity Field ◽  
Upper Bound ◽  
Velocity Fields ◽  
Extrusion Pressure ◽  
Admissible Velocity ◽  
Bound Solution ◽  
Upper Bound Solution ◽  
Aspect Ratios

This paper is concerned with an attempt to find an upper bound solution for the problems of steady-state extrusion of asymmetric polygonal section bars through rough square dies. A class of kinematically admissible velocity fields is examined, reformulating the SERR technique, to get the velocity field that gives the lowest upper bound. This velocity field is utilized to compute the non-dimensional average extrusion pressure at various area reductions for different billet aspect ratios.

Analysis of Tube Extrusion

1970 ◽  
Vol 92 (2) ◽  
pp. 403-410 ◽  
Author(s):  
H. S. Mehta ◽  
A. H. Shabaik ◽  
Shiro Kobayashi
Keyword(s):  
Velocity Field ◽  
Velocity Fields ◽  
The Other ◽  
Stress Distributions ◽  
Pure Lead ◽  
Admissible Velocity ◽  
Tube Extrusion ◽  
Commercially Pure ◽  
Superplastic Alloy ◽  
Good Agreement

Two solutions for the detailed mechanics of tube extrusion are presented. One is based on the theoretical velocity field, and the other on the flow field observed experimentally. The theoretical solution makes use of admissible velocity fields containing no velocity discontinuities. Experimental flow patterns are obtained for commercially pure lead and a superplastic alloy of the eutectic of lead and tin. The two solutions are compared in terms of velocity components, grid distortions, and strain and stress distributions, and very good agreement between the two solutions is revealed.

A Generalized Velocity Field for Plane Strain Extrusion Through Arbitrarily Curved Dies

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
H. Haghighat ◽  
P. Amjadian
Keyword(s):  
Finite Element ◽  
Velocity Field ◽  
Angular Velocity ◽  
Plane Strain ◽  
Upper Bound ◽  
Velocity Fields ◽  
Finite Element Code ◽  
Admissible Velocity ◽  
Paper Plane ◽  
Good Agreement

In this paper, plane strain extrusion through arbitrarily curved dies is investigated analytically, numerically, and experimentally. Two kinematically admissible velocity fields based on assuming proportional angles, angular velocity field, and proportional distances from the midline in the deformation zone, sine velocity field, are developed for use in upper bound models. The relative average extrusion pressures for the two velocity fields are compared to each other and also with the velocity field of a reference for extrusion through a curved die. The results demonstrate that the angular velocity field is the best. Then, by using the developed analytical model, optimum die lengths which minimize the extrusion loads are determined for a streamlined die and also for a wedge shaped die. The corresponding results for those two die shapes are also determined by using the finite element code and by doing some experiments and are compared with upper bound results. These comparisons show a good agreement.

Research of stamping of unequal channel bars. Part 4. Deformed state of the workpiece when extruding channels. 2. Deformations under the punch end

2021 ◽  
pp. 53-57
Author(s):  
A.L. Vorontsov
Keyword(s):  
Plastic Deformation ◽  
Plane Strain ◽  
Deformation Zone ◽  
Plastic Deformation Zone ◽  
Die Forging ◽  
Deformed State

Determination of the deformed state of the workpiece at free extrusion of channels is considered. Formulas are obtained for determining the accumulated deformations at a given point of the plastic deformation zone and extruded walls of the product for any punch working stroke. Keywords: die forging, extrusion, misalignment, punch, matrix, plane strain, accumulated deformations, hardening. [email protected]

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