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Vol. 46 No. 2 (2021)
Original articles

On “Generalized Upper Bound” method and its application to some plane strain compression and extrusion problems

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  • Nitai S. Das,
  • Hillol Joardar,
  • Matruprasad Rout,
  • Bikash C. Behera,
  • Kalipada Maity
Nitai S. Das
Department of Mechanical Engineering, C. V. Raman Global University, Bhubaneswar, India
Hillol Joardar
Department of Mechanical Engineering, C. V. Raman Global University, Bhubaneswar, India
Matruprasad Rout
Department of Mechanical Engineering, National Institute of Technology Tiruchirappalli, Trichy, India
Bikash C. Behera
Department of Mechanical Engineering, C. V. Raman Global University, Bhubaneswar, India
Kalipada Maity
Department of Mechanical Engineering, National Institute of Technology Rourkela, Odisha, India
DOI: https://doi.org/10.24867/ATM-2021-2-002

Published 2021-12-01

abstract views: 15 // Full text article (PDF): 21


Keywords

  • Coulomb friction,
  • Upper bound,
  • Plain strain,
  • stream function compression,
  • extrusion,
  • Finite element modelling
    • ...More
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How to Cite

[1]
N. S. Das, H. Joardar, M. Rout, B. C. Behera, and K. Maity, “On ‘Generalized Upper Bound’ method and its application to some plane strain compression and extrusion problems”, Adv Techn Mat, vol. 46, no. 2, pp. 7–18, Dec. 2021.
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This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

This paper outlines the salient features of the “generalized upper bound” technique and uses it to derive upper bounds for plane strain compression and extrusion of metals in the presence of Coulomb friction (τ = µp). For compression the velocity field is established by reformulating the same proposed earlier by Lee and Altan so as to be compatible with the interface Coulomb friction condition. For extrusion, the upper bound velocity field is derived from a stream function for flow through a smooth die of wedge angle (α+λ) where, α is the semi-wedge angle of the rough die, and λ is the friction angle (tanλ = µ). Analysis for this case is also presented assuming the flow to be radial. The analytical results are compared with those obtained from, the slip-line field and finite element analyses and from the rigid triangle velocity fields. These are also validated by some e experimental results available in literature.

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