# An upper bound solution for the spread extrusion of elliptical sections

## Abstract

The three dimensional problem of extrusion of elliptical sections with side material flow or spread has been formulated using the upper bound theory. The shape of the die for such a process is such that it could allow the material to flow sideways as well as in the forward direction. When flat faced dies are used a deforming region is developed with dead metal zones. Therefore this deforming region has been represented in the formulation based on the definitions of streamlines and stream surfaces. A generalized kinematically admissible velocity field was then derived for this formulation and strain rate components obtained for the upper bound solution. The general formulation for the deforming region and the velocity and strain rate fields allow for the optimization of the upper bound solution so that the nearest geometry of the deforming region and dead metal zone to the actual one was obtained.Using this geometry a die with similar surfaces to those of the dead metal zone is designed having converging and diverging surfaces to lead the material flow. The analysis was also carried out for this die and results were obtained showing a reduction in the extrusion pressure compared to the flat faced die.more »

- Authors:

- Mechanical Engineering Department, University College of Engineering, University of Tehran, Kargar Shomali St., PO Box 14395-515, Tehran (Iran, Islamic Republic of)

- Publication Date:

- OSTI Identifier:
- 21057066

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 907; Journal Issue: 1; Conference: 10. ESAFORM conference on material forming, Zaragoza (Spain), 18-20 Apr 2007; Other Information: DOI: 10.1063/1.2729581; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; ALLOYS; DEFORMATION; EXTRUSION; FRICTION; OPTIMIZATION; STRAIN RATE; SURFACES; THREE-DIMENSIONAL CALCULATIONS; VELOCITY; ZONES

### Citation Formats

```
Abrinia, K., and Makaremi, M.
```*An upper bound solution for the spread extrusion of elliptical sections*. United States: N. p., 2007.
Web. doi:10.1063/1.2729581.

```
Abrinia, K., & Makaremi, M.
```*An upper bound solution for the spread extrusion of elliptical sections*. United States. doi:10.1063/1.2729581.

```
Abrinia, K., and Makaremi, M. Sat .
"An upper bound solution for the spread extrusion of elliptical sections". United States.
doi:10.1063/1.2729581.
```

```
@article{osti_21057066,
```

title = {An upper bound solution for the spread extrusion of elliptical sections},

author = {Abrinia, K. and Makaremi, M.},

abstractNote = {The three dimensional problem of extrusion of elliptical sections with side material flow or spread has been formulated using the upper bound theory. The shape of the die for such a process is such that it could allow the material to flow sideways as well as in the forward direction. When flat faced dies are used a deforming region is developed with dead metal zones. Therefore this deforming region has been represented in the formulation based on the definitions of streamlines and stream surfaces. A generalized kinematically admissible velocity field was then derived for this formulation and strain rate components obtained for the upper bound solution. The general formulation for the deforming region and the velocity and strain rate fields allow for the optimization of the upper bound solution so that the nearest geometry of the deforming region and dead metal zone to the actual one was obtained.Using this geometry a die with similar surfaces to those of the dead metal zone is designed having converging and diverging surfaces to lead the material flow. The analysis was also carried out for this die and results were obtained showing a reduction in the extrusion pressure compared to the flat faced die. Effects of reduction of area, shape complexity, spread ratio and friction on the extrusion process were also investigated.},

doi = {10.1063/1.2729581},

journal = {AIP Conference Proceedings},

number = 1,

volume = 907,

place = {United States},

year = {Sat Apr 07 00:00:00 EDT 2007},

month = {Sat Apr 07 00:00:00 EDT 2007}

}