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.

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.

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.

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.

Radial Flow Velocity Field for Predicting Upper-Bound Solutions for Plane Strain Extrusion

1968 ◽  
Vol 90 (1) ◽  
pp. 45-50
Author(s):  
R. G. Fenton
Keyword(s):  
Velocity Field ◽  
Flow Field ◽  
Flow Velocity ◽  
Plane Strain ◽  
Upper Bound ◽  
Radial Flow ◽  
Flow Velocity Field ◽  
Wide Range ◽  
Ram Pressure ◽  
Considerable Range

The upper bound of the average ram pressure, based on an assumed radial flow velocity field, is derived for plane strain extrusion. Ram pressures are calculated for a complete range of reduction ratios and die angles, considering a wide range of frictional conditions. Results are compared with upper-bound ram pressures obtained by considering velocity fields other than the radial flow field, and it is shown that for a considerable range of reduction ratios and die angles, the radial flow field yields better upper bounds for the average ram pressure.

Solutions for Non-Newtonian Flow Into Elliptical Openings

1991 ◽  
Vol 58 (3) ◽  
pp. 820-824 ◽  
Author(s):  
A. Bogobowicz ◽  
L. Rothenburg ◽  
M. B. Dusseault
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Steady State ◽  
Hydrostatic Pressure ◽  
Velocity Field ◽  
Velocity Fields ◽  
Newtonian Flow ◽  
Element Analysis ◽  
Elliptical Opening ◽  
Elliptical Coordinates

A semi-analytical solution for plane velocity fields describing steady-state incompressible flow of nonlinearly viscous fluid into an elliptical opening is presented. The flow is driven by hydrostatic pressure applied at infinity. The solution is obtained by minimizing the rate of energy dissipation on a sufficiently flexible incompressible velocity field in elliptical coordinates. The medium is described by a power creep law and solutions are obtained for a range of exponents and ellipse eccentricites. The obtained solutions compare favorably with results of finite element analysis.

LOAD-CARRYING CAPACITIES FOR CIRCULAR METAL FOAM CORE SANDWICH PANELS AT LARGE DEFLECTION

2008 ◽  
Vol 22 (31n32) ◽  
pp. 6218-6223 ◽  
Author(s):  
W. HOU ◽  
Z. WANG ◽  
L. ZHAO ◽  
G. LU ◽  
D. SHU
Keyword(s):  
Finite Element ◽  
Velocity Field ◽  
Large Deflection ◽  
Metal Foam ◽  
Yield Criterion ◽  
Metallic Foam ◽  
Foam Core ◽  
Element Simulation ◽  
Load Carrying ◽  
Good Agreement

This paper is concerned with the load-carrying capacities of a circular sandwich panel with metallic foam core subjected to quasi-static pressure loading. The analysis is performed with a newly developed yield criterion for the sandwich cross section. The large deflection response is estimated by assuming a velocity field, which is defined based on the initial velocity field and the boundary condition. A finite element simulation has been performed to validate the analytical solution for the simply supported cases. Good agreement is found between the theoretical and finite element predictions for the load-deflection response.

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