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.

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 Central Bursting Defects in Plane Strain Drawing and Extrusion

1986 ◽  
Vol 108 (4) ◽  
pp. 317-321 ◽  
Author(s):  
B. Avitzur ◽  
J. C. Choi
Keyword(s):  
Plane Strain ◽  
Upper Bound ◽  
The Other ◽  
Major Conclusion ◽  
Upper Bound Theorem ◽  
Other Hand ◽  
Identical Manner ◽  
Bound Theorem ◽  
Inclined Angle ◽  
Proportional Flow

Based on the upper-bound theorem in limit analysis, the central bursting defect in plane strain drawing and extrusion is analyzed by comparing the proportional flow with the central bursting flow for the metal with voids at the center. A criterion for the unique conditions that promote this defect has been derived. The metal with voids may flow in the identical manner to that of solid strip with no voids to form a sound flow, deterring central bursting. A solid strip, on the other hand, or a material with voids, may flow in a manner so as to produce central bursting defects. A major conclusion of the study is that, for a range of combinations of inclined angle of the die, reduction, and friction, central bursting is expected whether or not the material originally had any voids. On the other hand, central bursting can be prevented even if the original rod contains small-size voids.

An Upper Bound Approach of Ring Compression Test Solutions

2014 ◽  
Vol 797 ◽  
pp. 93-98 ◽  
Author(s):  
F. Martín ◽  
Lorenzo Sevilla ◽  
Miguel Ángel Sebastián ◽  
Ana M. Camacho
Keyword(s):  
Plane Strain ◽  
Compression Test ◽  
Upper Bound ◽  
Ring Compression Test ◽  
Upper Bound Theorem ◽  
Strain Behavior ◽  
Ring Compression ◽  
Simplifying Assumptions ◽  
Bound Theorem ◽  
New Perspective

The forging processes have usually been studied by analytical methods under simplifying assumptions such as the consideration of plane strain. Present work this study is approached from Upper Bound Theorem using the Triangular Rigid Zones model from a new approach, that is, through the analysis of Ring Compression Test, axisymmetric element under its canonical geometry ensures a similar aforementioned plane strain behavior. A new perspective of calculating the so-called neutral plane (defined by the radius at which the material flows in opposite directions), which is the basis element in solving the problem is proposed.

Upper-Bound Solutions to Tube Extrusion Problems Through Curved Dies

1972 ◽  
Vol 94 (4) ◽  
pp. 1108-1111 ◽  
Author(s):  
K. T. Chang ◽  
J. C. Choi
Keyword(s):  
Upper Bound ◽  
Cone Angle ◽  
Incompressible Material ◽  
Velocity Fields ◽  
Die Geometry ◽  
Tube Extrusion

Velocity fields of tube extrusion problems through curved dies are presented for an incompressible material. These velocity fields are also applicable to conical and square-cornered dies. Thus, in principle, upper bound solutions for tube extrusion problems through arbitrarily shaped dies are obtained. As an illustration, tube extrusion processes through conical dies of small cone angle have been treated. Effect of die geometry and friction is presented graphically.

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.

scholarly journals An Upper Bound Solution for the Compression of an Orthotropic Cylinder

Materials ◽  
2021 ◽  
Vol 14 (18) ◽  
pp. 5253
Author(s):  
Lihui Lang ◽  
Sergei Alexandrov ◽  
Yun-Che Wang
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Yield Criterion ◽  
Limit Load ◽  
Compression Force ◽  
Orthotropic Cylinder ◽  
Upper Bound Theorem ◽  
Admissible Velocity ◽  
Bound Theorem ◽  
Quick Estimate

The upper bound theorem is used in conjunction with Hill’s quadratic yield criterion for determining the force required to upset a solid cylinder. The kinematically admissible velocity field accounts for the singular behavior of the real velocity field in the vicinity of the friction surface if the maximum friction law is adopted. The regime of sticking is also taken into consideration. The effect of this regime on the upper bound limit load is revealed. In particular, the kinematically admissible velocity field that includes the regime of sticking may result in a lower upper bound than that with no sticking. The boundary value problem is classified by a great number of geometric and material parameters. Therefore, a systematic parametric analysis of the effect of these parameters on the compression force is practically impossible. An advantage of the solution found is that it provides a quick estimate of this force for any given set of parameters.

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.

Selection of the Optimal Distribution for the Upper Bound Theorem in Indentation Processes

2014 ◽  
Vol 797 ◽  
pp. 117-122 ◽  
Author(s):  
Carolina Bermudo ◽  
F. Martín ◽  
Lorenzo Sevilla
Keyword(s):  
Upper Bound ◽  
Geometric Distribution ◽  
Optimal Choice ◽  
Optimal Distribution ◽  
Upper Bound Theorem ◽  
Modular Model ◽  
Bound Theorem ◽  
Rigid Zones ◽  
Dimensionless Relation ◽  
Selection Of

It has been established, in previous studies, the best adaptation and solution for the implementation of the modular model, being the current choice based on the minimization of the p/2k dimensionless relation obtained for each one of the model, analyzed under the same boundary conditions and efforts. Among the different cases covered, this paper shows the study for the optimal choice of the geometric distribution of zones. The Upper Bound Theorem (UBT) by its Triangular Rigid Zones (TRZ) consideration, under modular distribution, is applied to indentation processes. To extend the application of the model, cases of different thicknesses are considered

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