MODELAGEM ANALÍTICA DA EXTRUSÃO EM CANAIS EQUIANGULARES
ANALYTICAL MODELLING OF THE EQUAL CHANNEL ANGULAR EXTRUSION
Medeiros, Neil de; Moreira, Luciano Pessanha; Lins, Jefferson Fabricio C.; Gouvêa, Jayme Pereira de
http://dx.doi.org/10.4322/tmm.00502006
Tecnol. Metal. Mater., vol.5, n2, p.94-99, 2008
Resumo
Neste trabalho, é proposta uma extensão para materiais com encruamento das soluções analíticas reportadas na literatura para o processo de extrusão em canais equiangulares (ECEA), com base no método do limite superior (MLS). O encruamento não-linear do material e o comportamento em atrito são considerados em conjunto com diferentes raios de adoçamento situados na interseção dos canais. A dependência da pressão de extrusão e as deformações plásticas equivalentes obtidas para um único passe são analisadas em função do fator de atrito e dos raios de adoçamento. O estudo analítico conduzido mostra que a condição mais severa é obtida quando ambos os raios de adoçamento são nulos. Entretanto, verifica-se que elevados níveis de deformação podem ser alcançados a partir de combinações dos raios interno e externo de adoçamento em conjunto com reduções de pressão. Este resultado é interessante visto que as desvantagens de aumentos de cargas podem ser minimizadas em rotas de processamento de múltiplos passes adotando-se diferentes geometrias para a matriz.
Palavras-chave
Extrusão, Modelagem, Atrito, Deformação plástica
Abstract
In this work, an extension of the equal-channel angular extrusion (ECAE) process upper bound analytical solutions reported in the literature for work-hardening materials is proposed. The material nonlinear work-hardening and friction behavior are taken into account together with different fillet radii located at the die intersection channels. The dependence of the ECAE pressure and the equivalent plastic strains obtained for a single pass are analyzed as a function of the friction factor and the die fillet radii. The analytical study performed shows that the most severe condition is achieved when either die fillet are equal to zero. However, it is verified that high strain levels could be achieved by combining the inner and outer die fillet radii with reducing pressing pressure values. This result is very interesting since the disadvantages related to the increasing loads needed for multi-pass ECAE processing routes could be minimized by adopting different die geometries.
Keywords
Extrusion, Modelling, Friction, Plastic strain
Referências
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2 SEGAL, V.M. Materials processing by simple shear. Materials Science and Engineering A, v. 197, n. 2, p. 157-64, Sept.1995.
3 VALIEV, R.Z.; LANGDON, T.G. Principles of equal-channel angular pressing as a processing tool for grain refinement. Progress in Materials Science, v. 51, n. 7, p. 881-981, Feb. 2006.
4 SEGAL, V.M. Engineering and commercialization of equal channel angular extrusion (ECAE). Materials Science and Engineering A, v. 386, n.1-2, p. 269-76, Nov. 2004.
5 IWAHASHI, Y.; WANG, J.; HORITA, Z.; NEMOTO, M.; LANGDON, T.G. Principle of equal-channel angular pressing for the processing of ultra-fine grained materials. Scripta Materialia, v. 35, n. 2, p. 143-6, Oct. 1996.
6 ALKORTA, J.; SEVILLANO, J.G. A comparison of FEM and upper-bound type analysis of equal-channel angular pressing (ECAP). Journal of Materials Processing Technology, v. 141, n. 3, p.313-8, Nov. 2003.
7 PÉREZ, C.J.L. Upper bound analysis and FEM simulation of equal fillet radii angular pressing. Modelling and Simulation in Materials Science and Engineering, v. 12, n. 2, p. 205-14, Jan. 2004.
8 EIVANI, A.R., KARIMI TAHERI, A. An upper bound solution of ECAE process with outer curved corner. Journal of Materials Processing Technology, v. 182, n. 1-3, p. 555-63, Feb. 2007.
9 KOBAYASHI, S.; OH, S.I.; ALTAN, T. Metal forming and the finite-element method. New York: Oxford University Press, 1989.
10 PÉREZ, C.J.L. On the correct selection of the channel die in ECAP processes. Scripta Materialia, v. 50, n. 3, p. 387-93, Feb. 2004.
11 AVITZUR, B. Metal forming: processes and analysis. New Delhi: Mc Graw-Hill, 1968.
12 MOREIRA, L.P., ROMÃO, E.C., FERRON, G., VIEIRA, L.C.A., SAMPAIO, A.P., Cyclic bending and stationary drawing deformation of metal sheets: experiments and associated numerical simulations. AIP Conference Proceedings, v. 778, n.1, p. 667-72, Ago. 2005.
13 PÉREZ, C.J.L., LURI, R. Study of the ECAE process by the upper bound method considering the correct die design. Mechanics of Materials, v. 40, p. 617-28, Feb. 2008.
14 LURI, R., PÉREZ, C.J.L., LEÓN, J. A new configuration for equal channel angular extrusion dies. Journal of Manufacturing Science and Engineering, v. 128, p. 860-5, Nov. 2006.
15 WAGONER, R.H., CHENOT, J.-L. Fundamentals of Metal Forming. New York: John Wiley & Sons, 1997.
2 SEGAL, V.M. Materials processing by simple shear. Materials Science and Engineering A, v. 197, n. 2, p. 157-64, Sept.1995.
3 VALIEV, R.Z.; LANGDON, T.G. Principles of equal-channel angular pressing as a processing tool for grain refinement. Progress in Materials Science, v. 51, n. 7, p. 881-981, Feb. 2006.
4 SEGAL, V.M. Engineering and commercialization of equal channel angular extrusion (ECAE). Materials Science and Engineering A, v. 386, n.1-2, p. 269-76, Nov. 2004.
5 IWAHASHI, Y.; WANG, J.; HORITA, Z.; NEMOTO, M.; LANGDON, T.G. Principle of equal-channel angular pressing for the processing of ultra-fine grained materials. Scripta Materialia, v. 35, n. 2, p. 143-6, Oct. 1996.
6 ALKORTA, J.; SEVILLANO, J.G. A comparison of FEM and upper-bound type analysis of equal-channel angular pressing (ECAP). Journal of Materials Processing Technology, v. 141, n. 3, p.313-8, Nov. 2003.
7 PÉREZ, C.J.L. Upper bound analysis and FEM simulation of equal fillet radii angular pressing. Modelling and Simulation in Materials Science and Engineering, v. 12, n. 2, p. 205-14, Jan. 2004.
8 EIVANI, A.R., KARIMI TAHERI, A. An upper bound solution of ECAE process with outer curved corner. Journal of Materials Processing Technology, v. 182, n. 1-3, p. 555-63, Feb. 2007.
9 KOBAYASHI, S.; OH, S.I.; ALTAN, T. Metal forming and the finite-element method. New York: Oxford University Press, 1989.
10 PÉREZ, C.J.L. On the correct selection of the channel die in ECAP processes. Scripta Materialia, v. 50, n. 3, p. 387-93, Feb. 2004.
11 AVITZUR, B. Metal forming: processes and analysis. New Delhi: Mc Graw-Hill, 1968.
12 MOREIRA, L.P., ROMÃO, E.C., FERRON, G., VIEIRA, L.C.A., SAMPAIO, A.P., Cyclic bending and stationary drawing deformation of metal sheets: experiments and associated numerical simulations. AIP Conference Proceedings, v. 778, n.1, p. 667-72, Ago. 2005.
13 PÉREZ, C.J.L., LURI, R. Study of the ECAE process by the upper bound method considering the correct die design. Mechanics of Materials, v. 40, p. 617-28, Feb. 2008.
14 LURI, R., PÉREZ, C.J.L., LEÓN, J. A new configuration for equal channel angular extrusion dies. Journal of Manufacturing Science and Engineering, v. 128, p. 860-5, Nov. 2006.
15 WAGONER, R.H., CHENOT, J.-L. Fundamentals of Metal Forming. New York: John Wiley & Sons, 1997.
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