Modelling of Drawing

  • Claudio R. Böer
  • Nuno M. R. S. Rebelo
  • Hans A. B. Rydstad
  • Günther Schröder
Part of the MRE Materials Research and Engineering book series (MATERIALS)


In an attempt to reduce costs, increasing attention is being paid to the drawing of section rods from round bar in a minimum possible number of steps. However, a direct theoretical approach to this problem has been only partially attempted in the past [6.1] due to the difficulty in applying simple techniques to represent the deformation pattern even in the relatively simple section analyzed in this chapter. The analysis of the deformation process from a round bar to a square rod with different corner radii was chosen as a first step towards the study of more complicated shape drawing [6.2, 6.3].


Flow Line Corner Radius Finite Element Approach Initial Billet Drawing Stress 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols


Constant shear factor at the die-workpiece interface


die surface area


geometrical parameter (2 ≤ n ≤ ∞)


deviatoric stress tensors


inlet cross-sectional area


outlet cross-sectional area

\(\left. {\begin{array}{*{20}{c}}{{v_1},{v_2},{v_3}} \\ {or} \\ {{{\dot u}_1},{{\dot u}_2},{{\dot u}_3}} \end{array}} \right\}\)

velocity field


volum under deformation


tangential velocity difference

αS, αC

die angles


reduction of area

\({\dot \varepsilon _{ik}}\)

strain rate components

\(\bar \sigma\)

effective stress


flow stress of the material


axial drawing stress


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References Chapter 6

  1. [6.1]
    Basily B.B., Sansome D.H., Some Theoretical Considera-tions for the Direct Drawing of Section Rod from Round Bar, Int. J. mech. Sci., 18 (1976) 201.CrossRefGoogle Scholar
  2. [6.2]
    Boër C.R., Avitzur W.R., Schneider W.R., Eliasson B., An Upper-Bound Approach for the Direct Drawing of Square Rod from Round Bar, Proceedings 20th MTDR Conference (1979) 149–156.Google Scholar
  3. [6.3]
    Hoshino S., Gunasekera J.S., An Upper-Bound Solution for the Extrusion of Square Section from Round Bar Through Converging Dies, Proceedings 21st MTDR Conference (1980) 97–105.Google Scholar
  4. [6.4]
    Avitzur B., Metal Forming: Processes and Analysis,McGraw-Hill, New York (1968).Google Scholar
  5. [6.5]
    Johnson W., Mellor P.B., Engineering Plasticity, Van No strand Reinhold, London (1973).Google Scholar
  6. [6.6]
    Wistreich J.G., Investigation of the Mechanics of Wire Drawing, Proc. Inst. Mech. Engrs. (London), 169 (1955) 659.Google Scholar
  7. [6.7]
    Webster W., Davis R., Finite Element Analysis of Round to-Square Extrusion Processes, Manufacturing Engineering Transactions, Proceeding NAMRC (1978).Google Scholar
  8. [6.8]
    Zienkiewicz O.C., The Finite Element Method in Engine ering Science, London: McGraw-Hill (1971).Google Scholar
  9. [6.9]
    Drucker D.C., Prager W., Greenberg H.J., Quarterly of Applied Mathematics, 9 (1952) 381–389.Google Scholar
  10. [6.10]
    Chacour S., Transactions of the ASME, Journal of Basic Engineering (1972) 71–77.Google Scholar
  11. [6.11]
    Kudo H., International Journal of Mechanical Science, 1 (1960) 57–83.CrossRefGoogle Scholar
  12. [6.12]
    Kobayashi S., Transactions of the ASME, Journal of. Engineering for Industry, 86, Series B, 2 (May 1964) 122–126.Google Scholar
  13. [6.13]
    Lee C.H., Altan T., American Society of Mechanical Engineers (1971).Google Scholar
  14. [6.14]
    Nagpal V., Transactions of the ASME, Journal of Engineering for Industry, 96 (1974) 1197–1201.CrossRefGoogle Scholar
  15. [6.15]
    Wilde Douglass J., Beightler Charles S., Foundations of Optimization, Englewood Cliffs, New Jersey: Prentice Hall, Inc. (1967).Google Scholar
  16. [6.16]
    Pun L., New York: Introduction to Optimization Practice, John Wilex & Sons, Inc. (1969).Google Scholar
  17. [6.17]
    Wilde Douglass J., Optimum Seeking Methods, Englewood Cliffs, New Jersey: Prentice Hall, Inc. (1964).Google Scholar
  18. [6.18]
    Fletcher R., Optimization, New York: Academic Press (1969).Google Scholar
  19. [6.19]
    Cooper L., Steinber D., Method of Optimization, Philadelphia, Penn.,: W.B. Sounders Company (1970).Google Scholar
  20. [6.20]
    Rosen J.B., Journal of the Society for Industrial and Applied Mathematics, 8 (1960) 181–217.CrossRefGoogle Scholar
  21. [6.21]
    Olmsted John M.H., Advanced Calculus, New York: Appleton-Century-Crofts, Inc. (1961).Google Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1986

Authors and Affiliations

  • Claudio R. Böer
    • 1
  • Nuno M. R. S. Rebelo
    • 2
  • Hans A. B. Rydstad
    • 1
  • Günther Schröder
    • 1
  1. 1.Research CenterBBC Brown, Bovery & Company, LimitedBadenSwitzerland
  2. 2.MARC Analysis Research Corp.Palo AltoUSA

Personalised recommendations