An optimal die profile for plane strain drawing of sheets

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, optimal die profile

Received

25.09.2018

Publication date

27.09.2018

Number of characters

488

Cite Download pdf To download PDF you should sign in

GOST	- , An optimal die profile for plane strain drawing of sheets // Matematicheskoe modelirovanie – 2018. – V. 30. – Number 7 C. 3-15 [Electronic resource]. URL: http://ras.jes.su/mmod/s207987840000027-8-1-en (circulation date: 04.12.2023). DOI: 10.31857/S023408790000572-3
MLA	-, -., , "An optimal die profile for plane strain drawing of sheets." Matematicheskoe modelirovanie 30.7 (2018):3-15. DOI: 10.31857/S023408790000572-3
APA	- , (2018). An optimal die profile for plane strain drawing of sheets. Matematicheskoe modelirovanie 30(7), pp.3-15 DOI: 10.31857/S023408790000572-3

Размещенный ниже текст является ознакомительной версией и может не соответствовать печатной

Readers community rating: votes 0

1. N. Zabaras, S. Ganapathysubramanian, Q. Li. A continuum sensitivity method for the design of multi-stage metal forming processes // Int. J. Mech. Sci., 2003, v.45, №2, p.325-358.

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., 2008, t.1, №2, s.63-73.

3. C.J. Cawthorn, E.G. Loukaides, J.M. Allwood. Comparison of analytical models for sheet rolling // Proc. Eng., 2014, v.81, p.2451–2456.

4. K. Chung, S.Alexandrov. Ideal flow in plasticity // Appl. Mech. Rev., 2007, v.60, №6, p.316-335.

5. R. Hill. Ideal forming operations for perfectly plastic solids // J. Mech. Phys. Solids, 1967, v.15, p.223-227.

6. S.E. Aleksandrov. Ploskie ustanovivshiesia idealnye techeniia v teorii plastichnosti // Izv. RAN MTT, 2000, №2, s.136-141.

7. O. Richmond, S. Alexandrov. Nonsteady planar ideal plastic flow: general and special analytical solutions // J. Mech. Phys. Solids., 2000, v.48, №8, p.1735-1759.

8. O. Richmond, M.L. Devenpeck. A die profile for maximum efficiency in strip drawing. – NY.: ASME, 1962, Proc. 4th. U.S. Natl. Congr. Appl. Mech., v.2, RM Rosenberg (ed), p.1053-1057.

9. O. Richmond, Theory of streamlined dies for drawing and extrusion. - Toronto: University of Toronto Press, 1968, Mechanics of the solid state, FPJ Rimrott and J Schwaighofer (eds), p.154-167.

10. M.L. Devenpeck, O. Richmond. Strip – drawing experiments with a sigmoidal die profile // ASME J. Eng. Ind., 1965, v.87, №4, p.425-428.

11. O. Richmond, H.L. Morrison. Streamlined wire drawing dies of minimum length // J.Mech. Phys. Solids, 1967, v.15, p.195-203.

12. R. Khill. The Mathematical Theory of Plasticity. Oxford: University Press, 1998, IX, 355p.

13. S. Alexandrov, Y. Mustafa, E. Lyamina. Steady planar ideal flow of anisotropic materials // Meccanica, 2016, v.51, №9, p.2235-2241.