# Deformation of Rectangular Billets Between Dies with Unparallel Grooves

## Abstract

Deformation of rectangular billets between grooved dies takes place in an extrusion forging mode in which the billet material is simultaneously forced into the die cavity and expand laterally. This process is similar to the initial stages of the closed-die forging. The understanding of the material flow patterns and the prediction of the forming load in such deformation process is important both for the die design and the product quality control.

The deformation of rectangular billets between parallel grooves has been previously investigated by the authors. By assuming the existence of three distinct deformation modes, an analytical solution was presented using an upper bound approach, which can successfully predict the forging load as well as the deformed profiles. It was found that the deformation patterns in such process depends not only on the relative widths of die grooves, but also on the relative geometry of the die and the billet.

In this paper, experimental and analytical investigations have been performed on the deformation of rectangular billets between dies with unparallel grooves. Three combinations of dies with different angles of unparallelness were used to deform the lead billets and the theoretical results have been obtained by choosing an “average groove width” and dealing the problem as one involving dies with parallel grooves.

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## References

- 1.E.G. Thomsen, C.T. Yang and S. Kobayashi (1965) Mechanics of Plastic Deformation in Metal forming, Macmillan, New York.Google Scholar
- 2.W. Johnson and P.B. Mellor (1986) Engineering Plasticity, Ellis Horwood Limited, England.Google Scholar
- 3.S.C. Jain, A.N. Bramley, G.H. Lee and Kobayashi, S. (1970) Theory and Experiment in Extrusion Forging,
*Proc. Eleventh Int. MATADOR conf.*Google Scholar - 4.H. Kudo (1960) An Upper-Bound Approach to Plane-Strain Forging and Extrusion-I,
*Int. J. Mech. Sci*, 229, 366CrossRefGoogle Scholar - 5.A. Pomp, T. Muenker and W. Lueg (1938),
*Mitt. K. Wil. Inst. Eisen*, 20, 265Google Scholar - 6.Y. Saida, C.H. Lee and S. Kobayashi (1970) Some Aspects of Friction in Forging Problems,
*II Inter-American Conf. on Materials Technology*, Mexico CityGoogle Scholar - 7.J.A. Newnham and G.W. Rowe (1973) An Analysis of Compound Flow of Metal in a Simple Extrusion/Forging Process,
*J. Ints. of Metals*, 101, 1–9Google Scholar - 8.M.S.J. Hashmi and F.B. Flemz (1986) Axisymmetric Extrusion Forging: Effect of Material Property and Product Geometry,
*Int. J. Mach. Tool Des. Res.*, 26, No. 2, pp. 157–170CrossRefGoogle Scholar - 9.M.S.J. Hashmi (1986) Double-sided Extrusion Forging of Cylindrical Billets,
*Proc. Fifth Polytechnic Symposium on Manufacturing Engineering*, Brighton, Unite KingdomGoogle Scholar - 10.M.S.J. Hashmi (1990) Theory and Experiment on Plane Strain Deformation of Rectangular Billets between Flat and Grooved Platens,
*J. Material Proc. Tech.*, 24, pp. 13–22CrossRefGoogle Scholar - 11.W. Hu and M.S.J. Hashmi (1990) Effect of Material Property on Plane Strain Deformation of Rectangular Billets Between Grooved Platens,
*Proc. Sixth NCPR*, Glasgow, U.K.Google Scholar - 12.W. Hu, P. Liu and M.S.J. Hashmi (1991) Extrusion Forging of Rectangular Billets between Unparallelly Grooved Dies,
*Proc. Seventh NCPR*, Hatfield, U.K.Google Scholar - 13.W. Hu, P. Liu and M.S.J. Hashmi (1991) Effect of Lubrication and Forming Speed in Plane Strain Extrusion Forging of Rectangular Billets,
*Proc. Eleventh Int. Conf. Prod. Res.*, Hefei, ChinaGoogle Scholar