The load analysis of the plane—strain forging processes using the upper-bound stream-function elemental technique

1995 ◽  
Vol 47 (3-4) ◽  
pp. 345-359 ◽  
Author(s):  
J.P. Wang ◽  
Y.T. Lin
Keyword(s):  
Plane Strain ◽  
Stream Function ◽  
Upper Bound ◽  
Load Analysis

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.

Analysis of plane-strain rotational compression using the upper-bound method

1989 ◽  
Vol 19 (2) ◽  
pp. 211-222 ◽  
Author(s):  
K.H. Na ◽  
N.S. Cho
Keyword(s):  
Plane Strain ◽  
Upper Bound ◽  
Upper Bound Method

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.

Mechanical Solutions for Hot Forward Extrusion under Plane Strain Conditions by upper Bound Method

2008 ◽  
pp. 201-208
Author(s):  
R. Domingo ◽  
A.M. Camacho ◽  
E.M. Rubio Alvir ◽  
M.A. Sebastián Pérez
Keyword(s):  
Plane Strain ◽  
Upper Bound ◽  
Upper Bound Method ◽  
Forward Extrusion

A general upper-bound formulation of stream function of upset forging of ring using a variational approach

2010 ◽  
Vol 172 (1) ◽  
pp. 55-67 ◽  
Author(s):  
Wei-Ching Yeh ◽  
Ming-Chang Wu ◽  
Jia-Jyun Hong
Keyword(s):  
Stream Function ◽  
Upper Bound ◽  
Variational Approach ◽  
Upset Forging

Plane Strain Compression of Rigid-Perfectly Plastic Strip Between Parallel Dies With Slipping Friction

1979 ◽  
Vol 46 (2) ◽  
pp. 317-321 ◽  
Author(s):  
N. S. Das ◽  
J. Banerjee ◽  
I. F. Collins
Keyword(s):  
Yield Stress ◽  
Plane Strain ◽  
Upper Bound ◽  
Metal Interface ◽  
Plastic Strip ◽  
Perfectly Plastic ◽  
Slipping Friction ◽  
Computer Calculations ◽  
Linear Integral ◽  
Linear Integral Equations

This paper presents the results of computer calculations of a class of slipline solutions for compression between parallel dies with slipping friction at the die-metal interface such that the frictional shear traction is a constant proportion of the yield stress. The slipline fields considered here have previously only been suggested qualitatively. The fields are of “indirect type”, requiring the solution of linear integral equations. They have been analyzed and computed here using the recently developed matrix operator procedure. The numerical results obtained are compared with those obtained from approximate upper bound and other “technological” theories.

Mechanical Solutions for Hot Forward Extrusion under Plane Strain Conditions by upper Bound Method

2008 ◽  
Vol 367 ◽  
pp. 201-208 ◽  
Author(s):  
Rosario Domingo ◽  
A.M. Camacho ◽  
E.M. Rubio Alvir ◽  
M.A. Sebastián
Keyword(s):  
Plane Strain ◽  
Upper Bound ◽  
Analytical Methods ◽  
Mechanical Parameters ◽  
Upper Bound Method ◽  
Zone Length ◽  
Forward Extrusion ◽  
Dead Metal Zone ◽  
Fractional Reduction ◽  
The Dead

This paper present a study focused on hot forward extrusion by upper bound method. In particular, hot forward extrusion of plates through square face dies under plane strain conditions. Slater defines the models used for large fractional reduction. Different models have been taken in account; they are dissimilar in relation to the dead metal zone (if covers or not the entire die face, partially or totally). Triangular rigid patterns of velocity discontinuities have been validated by analytical methods and a range of use for the selected configurations has been established. This methodology has been applied to other process with good results. Thus, the mechanical parameters analysed are fractional reduction, dead metal zone, length die and friction. Finally the calculation of the energy has been achieved by upper bound method. The results allow researching an optimisation of use of upper bound method in hot forward extrusion.

An upper bound on the performance of plane strain mixers

1978 ◽  
Vol 18 (9) ◽  
pp. 738-740 ◽  
Author(s):  
Lewis Erwin
Keyword(s):  
Plane Strain ◽  
Upper Bound

Limit Analysis of Flow Through Inclined Converging Planes

1980 ◽  
Vol 102 (2) ◽  
pp. 109-117 ◽  
Author(s):  
M. Kiuchi ◽  
B. Avitzur
Keyword(s):  
Lower Bound ◽  
Plane Strain ◽  
Upper Bound ◽  
Limit Analysis ◽  
Velocity Fields ◽  
The Body ◽  
Design Flow ◽  
Upper And Lower Bounds ◽  
Lower Upper ◽  
Flow Through

A variety of mathematical models may be used to analyze plastic deformation during a metal-forming process. One of these methods—limit analysis—places the estimate of required power between an upper bound and a lower bound. The upper- and lower-bound analysis are designed so that the actual power or forming stress requirement is less than that predicted by the upper bound and greater than that predicted by the lower bound. Finding a lower upper-bound and a higher lower-bound reduces the uncertainty of the actual power requirement. Upper and lower bounds will permit the determination of such quantities as required forces, limitations on the process, optimal die design, flow patterns, and prediction and prevention of defects. Fundamental to the development of both upper-bound and lower-bound solutions is the division of the body into zones. For each of the zones there is written either a velocity field (upper bound) or a stress field (lower bound). A better choice of zones and fields brings the calculated values closer to actual values. In the present work, both upper- and lower-bound solutions are presented for plane-strain flow through inclined converging dies. For the upper bound, trapezoidal velocity fields, uni-triangular velocity fields, and multi-triangular velocity fields have been dealt with and the solutions compared to previously published work on cylindrical velocity fields. It was found that in different domains of the various combinations of the process parameters, different patterns of flow (cylindrical, triangular, etc.) provide lower upper-bound solutions. The lower-bound solution for plane-strain flow through inclined converging planes is newly developed.

Sign in / Sign up

Export Citation Format

Share Document