General Kinematically Admissible Velocity Fields for Some Axisymmetric Metal Forming Problems

1974 ◽  
Vol 96 (4) ◽  
pp. 1197-1201 ◽  
Author(s):  
V. Nagpal
Keyword(s):  
Velocity Field ◽  
Plastic Zone ◽  
Metal Forming ◽  
Dead Zone ◽  
Incompressible Material ◽  
Velocity Fields ◽  
Admissible Velocity ◽  
Conical Die ◽  
General Velocity ◽  
Special Case

An approach for selecting general kinematically admissible velocity fields for an incompressible material from assumed shape of streamlines is outlined. Velocity field and generalized boundaries of plastic zone are obtained for axisymmetric extrusion of a rod through arbitrarily shaped die. For special case of conical die, the velocity field reduces to that presented by Stepanskii and Avitzur. General velocity field and boundary of dead zone, if assumed, for the problem of axisymmetric forging of cylindrical work-pieces are obtained. Other problems which can be treated are briefly discussed.

Plane Strain Forging—A Lower Upper Bound Approach

1975 ◽  
Vol 97 (1) ◽  
pp. 119-124 ◽  
Author(s):  
V. Nagpal ◽  
W. R. Clough
Keyword(s):  
Velocity Field ◽  
Process Parameters ◽  
Upper Bound ◽  
Dead Zone ◽  
Incompressible Material ◽  
Velocity Fields ◽  
Admissible Velocity ◽  
Special Cases ◽  
Rectangular Strip ◽  
General Velocity

A general kinematically admissible velocity field applicable to forging of a rectangular strip of a incompressible material is presented. Generalized shape of any dead zone, if assumed, can be obtained in terms of process parameters from this velocity field. Two different upper bound solutions for average forging pressure are obtained from simple velocity fields which are special cases of proposed general velocity field. Numerical results of the solutions show improvement over previous upper bound solutions published in literature over a certain range of process parameters.

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.

A General Velocity Field for Shape Rolling of a V-Sectioned Sheet

1999 ◽  
Vol 122 (1) ◽  
pp. 227-234 ◽  
Author(s):  
Yeong-Maw Hwang ◽  
Hung-Jiun Lin ◽  
J. R. Chen
Keyword(s):  
Plastic Deformation ◽  
Velocity Field ◽  
Rolled Product ◽  
Deformation Behavior ◽  
Thickness Reduction ◽  
Shape Rolling ◽  
Admissible Velocity ◽  
Plastic Deformation Behavior ◽  
Roll Gap ◽  
General Velocity

A general kinematically admissible velocity field has been proposed in this work to examine the plastic deformation behavior of the sheet at the roll gap during shape rolling of a V-sectioned sheet. This velocity field is employed to examine the geometry of the rolled product, which are effected by various rolling conditions such as the sizes of the raw sheet and the vacancy, thickness reduction, etc. Furthermore, experiments on cold shape rolling of aluminum sheet have also been conducted. The rolling forces and the shape of the rolled product were measured to compare with the analytical values. Through the comparisons between them, the validity of this newly proposed velocity field was verified. [S1087-1357(00)71301-3]

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.

An Arbitrarily Inclined Triangular UBET Element and Its Application to Combined Forging

1985 ◽  
Vol 107 (2) ◽  
pp. 134-140 ◽  
Author(s):  
D. Y. Yang ◽  
J. H. Kim ◽  
C. K. Lim
Keyword(s):  
Velocity Field ◽  
Room Temperature ◽  
Field Experiments ◽  
Velocity Fields ◽  
Admissible Velocity ◽  
Forming Load ◽  
Theoretical Predictions ◽  
Triangular Elements ◽  
Al 2024 ◽  
Good Agreement

A kinematically admissible velocity field is derived for a proposed arbitrarily inclined triangular UBET element. The method is applied to combined forging to show the flexibility of application. From the derived velocity fields upper-bound loads on the punch and deformed configurations are determined by optimizing some given parameters related with geometry and velocity field. Experiments on combined forging are carried out with annealed Al-2024 billets at room temperature for several punch shapes. The theoretical predictions both in the forming load and deformed configuration are in good agreement with the experimental results. It is shown that arbitrarily inclined triangular elements proposed in this work can effectively be used for the prediction of the forming load and deformation in combined forging and can be applied to other forming processes with flexibility.

An Upper Bound Solution for a Two-Layer Cylinder Subject to Compression and Twist

2007 ◽  
Vol 345-346 ◽  
pp. 37-40 ◽  
Author(s):  
Gow Yi Tzou ◽  
Sergei Alexandrov
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Additional Condition ◽  
Velocity Fields ◽  
Upper Bound Theorem ◽  
Predictive Capacity ◽  
Admissible Velocity ◽  
Bound Solution ◽  
Bound Theorem ◽  
Formal Requirements

The choice of a kinematically admissible velocity field has a great effect on the predictive capacity of upper bound solutions. It is always advantageous, in addition to the formal requirements of the upper bound theorem, to select a class of velocity fields satisfying some additional conditions that follow from the exact formulation of the problem. In the case of maximum friction law, such an additional condition is that the real velocity field is singular in the vicinity of the friction surface. In the present paper this additional condition is incorporated in the class of kinematically admissible velocity fields chosen for a theoretical analysis of two - layer cylinders subject to compression and twist. An effect of the angular velocity of the die on process parameters is emphasized and discussed.

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.

On the Solution of Three-Dimensional Metal-Forming Processes

1977 ◽  
Vol 99 (3) ◽  
pp. 624-629 ◽  
Author(s):  
V. Nagpal
Keyword(s):  
Upper Bound ◽  
Metal Forming ◽  
Three Dimensional ◽  
Velocity Fields ◽  
Rectangular Shape ◽  
Admissible Velocity ◽  
Die Forging ◽  
Stream Functions ◽  
Open Die Forging

The use of “dual-stream functions” in analyzing some three-dimensional metal-forming processes is demonstrated in this paper. The problems discussed are open-die forging of blocks, rolling of a rectangular bar with spread, piercing by elliptic and rectangular punches, and extrusion of a rectangular shape. For these forming processes, kinematically admissible velocity fields are selected using characteristics of the two stream functions. Approximate upper-bound solutions of the forming processes can be obtained from the proposed velocity fields.

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.

Velocity Field in Direct, Indirect and Friction Assisted Extrusion of Al

2013 ◽  
Vol 554-557 ◽  
pp. 776-786 ◽  
Author(s):  
Sepinood Torabzadeh Khorasani ◽  
Henry Valberg
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Velocity Field ◽  
Velocity Fields ◽  
Al Alloys ◽  
Low Friction ◽  
Element Analysis ◽  
Admissible Velocity ◽  
Deform 2D ◽  
Good Agreement

This study investigates the velocity fields that are descriptive for the forward, backward and friction assisted extrusion of axisymmetric rods. The Avitzur theory was used to calculate the velocity field and strain rate in extrusion of Al alloys. Several simulations have also been performed by using finite element analysis (FEA) with DEFORM 2D, in order to find the admissible velocity field for different conditions of friction including high and low friction. The results from FEA and theory of axisymmetric extrusion are compared to see if there is good agreement. The correlation between the data obtained by theory and FEA is discussed.

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