Geodesic
An optimal die profile for plane strain drawing of sheets
Matematičeskoe modelirovanie, Tome 30 (2018) no. 7, pp. 3-15.

Voir la notice de l'article provenant de la source Math-Net.Ru

The ideal flow theory is used to determine an optimal die profile for drawing and extrusion of sheets under plane strain conditions. The solution is based on the theory of characteristics. In contrast to available solutions based on the ideal flow theory, it is assumed that a portion of the die is prescribed. The solution reduces to evaluating ordinary integrals. As an example, a die profile is found assuming that a portion of this profile is given and is a circular arc.
Keywords: ideal flow, method of characteristics, drawing
Mots-clés : optimal die profile. 
@article{MM_2018_30_7_a0,
     author = {E. A. Lyamina and O. V. Novozhilova},
     title = {An optimal die profile for plane strain drawing of sheets},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--15},
     publisher = {mathdoc},
     volume = {30},
     number = {7},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2018_30_7_a0/}
}
TY  - JOUR
AU  - E. A. Lyamina
AU  - O. V. Novozhilova
TI  - An optimal die profile for plane strain drawing of sheets
JO  - Matematičeskoe modelirovanie
PY  - 2018
SP  - 3
EP  - 15
VL  - 30
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2018_30_7_a0/
LA  - ru
ID  - MM_2018_30_7_a0
ER  - 
%0 Journal Article
%A E. A. Lyamina
%A O. V. Novozhilova
%T An optimal die profile for plane strain drawing of sheets
%J Matematičeskoe modelirovanie
%D 2018
%P 3-15
%V 30
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2018_30_7_a0/
%G ru
%F MM_2018_30_7_a0
E. A. Lyamina; O. V. Novozhilova. An optimal die profile for plane strain drawing of sheets. Matematičeskoe modelirovanie, Tome 30 (2018) no. 7, pp. 3-15. http://geodesic.mathdoc.fr/item/MM_2018_30_7_a0/

[1] N. Zabaras, S. Ganapathysubramanian, Q. Li, “A continuum sensitivity method for the design of multi-stage metal forming processes”, Int. J. Mech. Sci., 45:2 (2003), 325–358 | DOI | Zbl

[2] A.I. Oleinikov, S.N. Korobeinikov, K.S. Bormotin, “Vliianie tipa konechno-elementnogo predstavleniia pri modelirovanii formoobrazovaniia panelei iz uprugoplasticheskogo materiala”, Vychisl. Mekh. Sploshnykh Sred, 1:2 (2008), 63–73

[3] C.J. Cawthorn, E.G. Loukaides, J.M. Allwood, “Comparison of analytical models for sheet rolling”, Proc. Eng., 81 (2014), 2451–2456 | DOI

[4] K. Chung, S. Alexandrov, “Ideal flow in plasticity”, Appl. Mech. Rev., 60:6 (2007), 316–335 | DOI

[5] R. Hill, “Ideal forming operations for perfectly plastic solids”, J. Mech. Phys. Solids, 15 (1967), 223–227 | DOI

[6] S.E. Aleksandrov, “Ploskie ustanovivshiesia idealnye techeniia v teorii plastichnosti”, Izv. RAN MTT, 2000, no. 2, 136–141

[7] O. Richmond, S. Alexandrov, “Nonsteady planar ideal plastic flow: general and special analytical solutions”, J. Mech. Phys. Solids, 48:8 (2000), 1735–1759 | DOI | MR | Zbl

[8] O. Richmond, M.L. Devenpeck, “A die profile for maximum efficiency in strip drawing”, Proc. 4th. U.S. Natl. Congr. Appl. Mech., v. 2, ed. R. M. Rosenberg, ASME, NY., 1962, 1053–1057

[9] O. Richmond, “Theory of streamlined dies for drawing and extrusion”, Mechanics of the solid state, eds. F.P.J. Rimrott, J. Schwaighofer, University of Toronto Press, Toronto, 1968, 154–167

[10] M.L. Devenpeck, O. Richmond, “Strip-drawing experiments with a sigmoidal die profile”, ASME J. Eng. Ind., 87:4 (1965), 425–428 | DOI

[11] O. Richmond, H.L. Morrison, “Streamlined wire drawing dies of minimum length”, J. Mech. Phys. Solids, 15 (1967), 195–203 | DOI

[12] R. Khill, The Mathematical Theory of Plasticity, University Press, Oxford, 1998, IX, 355 pp. | MR

[13] S. Alexandrov, Y. Mustafa, E. Lyamina, “Steady planar ideal flow of anisotropic materials”, Meccanica, 51:9 (2016), 2235–2241 | DOI | MR | Zbl