Plastic Flow through Taper Dies: A Threedimensional Analysis
The plastic flow of metal in the extrusion process is
an important factor in controlling the mechanical properties of the
extruded products. It is, however, difficult to predict the metal flow
in three dimensional extrusions of sections due to the involvement of
re-entrant corners. The present study is to find an upper bound
solution for the extrusion of triangular sectioned through taper dies
from round sectioned billet. A discontinuous kinematically
admissible velocity field (KAVF) is proposed. From the proposed
KAVF, the upper bound solution on non-dimensional extrusion
pressure is determined with respect to the chosen process parameters.
The theoretical results are compared with experimental results to
check the validity of the proposed velocity field. An extrusion setup
is designed and fabricated for the said purpose, and all extrusions are
carried out using circular billets. Experiments are carried out with
commercially available lead at room temperature.
[1] Basily, B.B. & Sansome, D.H. 1976, "Some theoretical considerations
for the direct drawing of section rod from round bar", International
Journal of Mechanical Sciences, vol. 18, no. 4, pp. 201-208.
[2] Gatto, F. & Giarda, A. 1981, "The characteristics of the threedimensional
analysis of plastic deformation according to the SERR
method", International Journal of Mechanical Sciences, vol. 23, no. 3,
pp. 129-148.
[3] Kar, P.K. & Das, N.S. 1997, "Upper bound analysis of extrusion of Isection
bars from square/rectangular billets through square dies",
International Journal of Mechanical Sciences, vol. 39, no. 8, pp. 925-
934.
[4] Nagpal, V. & Altan, T. 1975, "Analysis Of The Three-Dimensional
Metal Flow In Extrusion Of Shapes With The Use Of Dual Stream
Functions.", Proc. Third N.Am. Met. Res. Conf., Pittsburgh,
Pennsylvenia,,pp 26-40.
[5] Sahoo, S K and kar, P K, 2000, Round-to-Square Extrusion Through
Taper Die: A Three-dimensional Analysis. Manufacturing Technology
Proc. of 19th AIMDT Conf.
[6] Sahoo, S.K., Kar, P.K. & Singh, K.C. 1999, "Numerical application of
the upper-bound technique for round-to-hexagon extrusion through
linearly converging dies", Journal of Materials Processing Technology,
vol. 91, no. 1, pp. 105-110.
[7] Sahoo, S.K. 2003, "An analysis of plastic flow through polygonal
linearly converging dies: As applied to forward metal extrusion", Journal
of Materials Processing Technology, vol. 132, no. 1-3, pp. 286-292.
[8] Sahoo, R.K., Kar, P.K. & Sahoo, S.K. 2003, "3D upper-bound modeling
for round-to-triangle section extrusion using the SERR technique",
Journal of Materials Processing Technology, vol. 138, no. 1-3, pp. 499-
504.
[9] Sahoo, R.K., Samantaray, P.R., Sahoo, S.K., Sahoo, B. & Kar, P.K.
2009, "Round-to-channel section extrusion through linearly converging
die: A three-dimensional analysis", International Journal of Advanced
Manufacturing Technology, vol. 41, no. 7-8, pp. 677-683.
[10] Sahoo, S.K., Sahoo, B., Patra, L.N., Paltasingh, U.C. & Samantaray, P.R.
2010, "Three-dimensional analysis of round-to-angle section extrusion
through straight converging die", International Journal of Advanced
Manufacturing Technology, vol. 49, no. 5-8, pp. 505-512.
[1] Basily, B.B. & Sansome, D.H. 1976, "Some theoretical considerations
for the direct drawing of section rod from round bar", International
Journal of Mechanical Sciences, vol. 18, no. 4, pp. 201-208.
[2] Gatto, F. & Giarda, A. 1981, "The characteristics of the threedimensional
analysis of plastic deformation according to the SERR
method", International Journal of Mechanical Sciences, vol. 23, no. 3,
pp. 129-148.
[3] Kar, P.K. & Das, N.S. 1997, "Upper bound analysis of extrusion of Isection
bars from square/rectangular billets through square dies",
International Journal of Mechanical Sciences, vol. 39, no. 8, pp. 925-
934.
[4] Nagpal, V. & Altan, T. 1975, "Analysis Of The Three-Dimensional
Metal Flow In Extrusion Of Shapes With The Use Of Dual Stream
Functions.", Proc. Third N.Am. Met. Res. Conf., Pittsburgh,
Pennsylvenia,,pp 26-40.
[5] Sahoo, S K and kar, P K, 2000, Round-to-Square Extrusion Through
Taper Die: A Three-dimensional Analysis. Manufacturing Technology
Proc. of 19th AIMDT Conf.
[6] Sahoo, S.K., Kar, P.K. & Singh, K.C. 1999, "Numerical application of
the upper-bound technique for round-to-hexagon extrusion through
linearly converging dies", Journal of Materials Processing Technology,
vol. 91, no. 1, pp. 105-110.
[7] Sahoo, S.K. 2003, "An analysis of plastic flow through polygonal
linearly converging dies: As applied to forward metal extrusion", Journal
of Materials Processing Technology, vol. 132, no. 1-3, pp. 286-292.
[8] Sahoo, R.K., Kar, P.K. & Sahoo, S.K. 2003, "3D upper-bound modeling
for round-to-triangle section extrusion using the SERR technique",
Journal of Materials Processing Technology, vol. 138, no. 1-3, pp. 499-
504.
[9] Sahoo, R.K., Samantaray, P.R., Sahoo, S.K., Sahoo, B. & Kar, P.K.
2009, "Round-to-channel section extrusion through linearly converging
die: A three-dimensional analysis", International Journal of Advanced
Manufacturing Technology, vol. 41, no. 7-8, pp. 677-683.
[10] Sahoo, S.K., Sahoo, B., Patra, L.N., Paltasingh, U.C. & Samantaray, P.R.
2010, "Three-dimensional analysis of round-to-angle section extrusion
through straight converging die", International Journal of Advanced
Manufacturing Technology, vol. 49, no. 5-8, pp. 505-512.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:58895", author = "Laxmi Narayan Patra and Susanta Kumar Sahoo and Mithun KumarMurmu", title = "Plastic Flow through Taper Dies: A Threedimensional Analysis", abstract = "The plastic flow of metal in the extrusion process is
an important factor in controlling the mechanical properties of the
extruded products. It is, however, difficult to predict the metal flow
in three dimensional extrusions of sections due to the involvement of
re-entrant corners. The present study is to find an upper bound
solution for the extrusion of triangular sectioned through taper dies
from round sectioned billet. A discontinuous kinematically
admissible velocity field (KAVF) is proposed. From the proposed
KAVF, the upper bound solution on non-dimensional extrusion
pressure is determined with respect to the chosen process parameters.
The theoretical results are compared with experimental results to
check the validity of the proposed velocity field. An extrusion setup
is designed and fabricated for the said purpose, and all extrusions are
carried out using circular billets. Experiments are carried out with
commercially available lead at room temperature.", keywords = "Extrusion, Kinematically admissibly velocity fieldSpatial Elementary Rigid Region (SERR), Upper Bound Analysis", volume = "5", number = "2", pages = "387-6", }