Research Papers

Die Profile Optimization of Rectangular Cross Section Extrusion in Plane Strain Condition Using Upper Bound Analysis Method and Simulated Annealing Algorithm

[+] Author and Article Information
Hamed Farzad

Department of Materials Science
and Engineering,
School of Engineering,
Shiraz University,
Shiraz 71946-84334, Iran
e-mail: hamed.farzad@outlook.com

Ramin Ebrahimi

Department of Materials Science and Engineering,
School of Engineering,
Shiraz University,
Shiraz 71946-84334, Iran
e-mail: ebrahimy@shirazu.ac.ir

1Corresponding author.

Manuscript received March 17, 2016; final manuscript received July 15, 2016; published online September 6, 2016. Assoc. Editor: Gracious Ngaile.

J. Manuf. Sci. Eng 139(2), 021006 (Sep 06, 2016) (11 pages) Paper No: MANU-16-1170; doi: 10.1115/1.4034336 History: Received March 17, 2016; Revised July 15, 2016

Extrusion die profile has a significant role on material flow characteristics, product microstructure, die life, and required load. Nowadays, economic requirements and effort to improve and homogenize metallurgical product properties have compelled the researchers to modify the conventional constant angle extrusion dies by employing streamlined die profiles. In the present research work, an optimum plane strain extrusion profile has been presented through implementation of upper bound analysis and Bezier curve in a simulated annealing (SA) algorithm to minimize the process force and its redundant work. The effect of material properties, friction conditions, reduction of area, and cross-sectional ratio on the optimum die profile is considered. The results of finite-element simulation proved that utilizing the optimum curved die instead of the constant angle die is superior regarding the decrease of the maximum required force, 10.5%, and the product inhomogeneity factor (IF), 50%. In addition, based on stress analysis of die/work piece interfaces, it is expected that the die life of optimal curved dies be longer than that of the optimum constant angle dies. Also, it has been demonstrated that the material work hardening characteristics does not have remarkable effect on the optimum curved die profile.

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Fig. 3

Schematic illustration of two consecutive elements and their appropriate coordinates. O1 is the appropriate coordinate origin of the second element.

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Fig. 2

Schematic illustration of the first cylindrical element and its constant angle, α0

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Fig. 1

Three-dimensional schematic diagram of plane strain extrusion through dies of any shape. Z direction is parallel to the billet's width.

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Fig. 4

True stress–plastic strain curve of AA1050 alloy

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Fig. 5

Degeneracy of Eq. (21) versus decreasing i parameter

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Fig. 6

Flowchart of the computational algorithm

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Fig. 7

Optimized die shape by the algorithm and its fitted polynomial curve

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Fig. 8

Load–displacement curves for extrusion through the optimum curved and constant angle die in the case of 80% reduction of area

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Fig. 9

Strain distribution developed on (a) the optimum curved die product and (b) the optimum constant angle die product

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Fig. 12

Effect of friction on the optimum die profile in the case of 80% reduction of area and optimized for AA1050 alloy's work hardening characteristics

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Fig. 13

Effect of width per initial thickness on the optimum curved die profile

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Fig. 14

Effect of material work hardening characteristics on the optimum die profile (m=0.1, W/t0=3, reductionof area=80%)

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Fig. 10

The normal stresses acting on the optimum dies along the (a) upper/lower and (b) lateral die–specimen interfaces, in the case of 80% reduction of area which calculated numerically

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Fig. 11

Comparison between the optimum curved profiles represented for different area reductions



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