As expected, it is observed that the necessary loads for the simulated direct extrusion processes are greater than the ones required for indirect extrusion under the same friction conditions. This is due to the contact of the billet with the container before being extruded through the extrusion die. In direct extrusion, the material is displaced by the punch along the container and it is affected by the friction with the container walls. In indirect extrusion this does not occur, as it can be observed in Figure 2; therefore, in comparison with direct extrusion, friction at the container walls, Fc, is negligible and the necessary force to run the process is lower. By comparing the load results of direct and indirect processes, it can also be identified the contribution of friction at the die, Fdie, to the friction load. The maximum friction load contribution due to the die-billet contact in cup extrusion is much higher than in the case of solid extrusion. On the contrary, the maximum friction load contribution due to the container wall is much higher in the case of solid extrusion than in cup extrusion. Required loads for the same extrusion ratio are higher in cup extrusion processes than in solid extrusion ones. Thus, the analysis performed allows the estimation of the maximum effect of friction in the four extrusion processes, and to clearly identify the contributions of friction at the container walls and the extrusion die. In future works this analysis will be extended to more complex geometries of the extrudates and to the extrusion of advanced materials such as high strength steels whose formability is poor compared to other metallic alloys. This will lead to broaden the application field of extrusion processes and to investigate their limitations in order to improve their performance in future industrial scenarios. Acknowledgements This work has been financially supported by the funds provided through the Annual Grant Call of the E.T.S.I.I. of UNED of reference 2014-ICF04. References [1] G.W. Rowe, Principles of Industrial-Metalworking Processes, Edward Arnold, London, 1977. [2] M.P. Groover, Fundamentals of modern manufacturing , fourth ed., John Wiley & Sons, Hoboken, New Jersey, 2010. [3] L. Butnar, N. Pop, H. Cioban (2009). Researches Concerning Friction Influence on Material Flow in Inverse Extrusion of Toothed Gears, Annals of DAAAM for 2009 & Proceedings of the 20th International DAAAM Symposium, 25-28th November 2009, Vienna, Austria, ISSN 1726-9679, ISBN 978-3-901509-70-4, Katalinic, B. (Ed.), pp. 0797-0798, Published by DAAAM International Vienna, Vienna. [4] N. Ghiban, G. Chelu, N. Serban, B. Ghiban (2008). 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Bakhshi-Jooybari, A theoretical and experimental study of friction in metal forming by the use of the forward extrusion process, Journal of Materials Processing Technology 125–126 (2002) 369-374. [8] Q. Zang, M. Arentoft, S. Bruschi, L. Dubar, E. Felder, Measurement of friction in a cold extrusion operation: study by numerical simulation of four friction tests, Proceedings of the 11th ESAFORM 2008 conference on material forming, 23-25 April, 2008, Lyon, France. [9] M. Kunogi, A New Method of Cold Extrusion. Journal of the Scientific Research Institute 50 (1956) 215–246. [10] A.T. Male, M.G. Cockcroft, A Method for the Determination of the Coefficient of Friction of Metals under Condition of Bulk Plastic Deformation, Journal of the Institute of Metals 93 (1965) 38–46. [11] T. Schrader, M. Shirgaokar, T. Altan, A critical evaluation of the double cup extrusion test for selection of cold forging lubricants, Journal of Materials Processing Technology 189 (2007) 36-44. [12] S.-H. 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Ghiban, F. - D. Dumitru, N. Ghiban, R. Saban, A. Semenescu, M. Marin (2010). Consideration Regarding Die Design for Equal Channel Angular Extrusion, Annals of DAAAM for 2010 & Proceedings of the 21st International DAAAM Symposium, 20-23rd October 2010, Zadar, Croatia, ISSN 1726-9679, ISBN 978-3-901509-73-5, Katalinic, B. (Ed.), pp. 0189-0190, Published by DAAAM International Vienna, Vienna. [18] B.P.P.A. Gouveia, J.M.C. Rodrigues, N. Bay, P.A.F. Martins, Finite-element modelling of cold forward extrusion, Journal of Materials Processing Technology 94 (1999) 85-93. [19] T. Altan, S.-I. Oh, H.L. Gegel, Metal forming: fundamentals and applications, ASM International, Ohio, 1983. [20] B. Avitzur, Metal forming: processes and analysis, Robert E. Krieger Publishing Company, Huntington, New York, 1979. [21] W. Johnson, The pressure for the cold extrusion of lubricated rod through square dies of moderate reduction at slow speeds, Journal of the Institute of Metals 85 (1956-1957) 403-408.
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