Accumulation of Second-Order Strain in Workhardening Media

  • A. M. Freudenthal
  • Maria Ronay
Conference paper
Part of the IUTAM Symposia book series (IUTAM)


Observations of accumulating axial extension produced by cyclic torsion of cylindrical bars and tubes of some workhardening metals are presented. The phenomenon is interpreted as an irreversible second order effect arising from the quadratic term in the constitutive equation of such media required by the condition of tensorial invariance.


Shear Strain Axial Strain Cyclic Creep Axial Extension Axial Elongation 
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  1. [1]
    Taylor, G. I., and H. Quinney: Phil. Trans. Roy. Soc. London A230, 323–362 (1939).ADSCrossRefGoogle Scholar
  2. [1]
    Hsu, T. C.: J. Basic Engng, T.ans. Am. Soc. Mech. Engrs (Ser. D) SS, 61–70 (1966).Google Scholar
  3. [1]
    Feigen, M.: Proc. Second U.S. Congress Appt Mech. 1954. pp. 469–476. New York: Am. Soc. Mech. Engng 1955.Google Scholar
  4. [2]
    Mandel, J., P. Habib, and H. D. Bui: Proc. Fourth Internat. Congres Rheology, 1963, 3, 97–117. New York: Interscience. 1965.Google Scholar
  5. [3a]
    Ivey, H.: J. Mech. Engng Sci., 3, 15–31 (1961).CrossRefGoogle Scholar
  6. [3b]
    Nagiidi, P. M., F. ESSENBURG, and W. J. KORFF: J. Appl. Mech. 25, 201–209 (1958).Google Scholar
  7. [4]
    Swift, H. W.: Engineering 1947, 253–257.Google Scholar
  8. [5]
    L’hermmite, R., and G. DAWANCE: Circul. Inst. Tech. Batiment, Serie G, No. 16 (1947).Google Scholar
  9. [6a]
    Bendler, H. M., and W. A. WOOD: Trans. Met. Soc. AIME 224, 18 (1962).Google Scholar
  10. [6b]
    Wood, W. A., and S. Mck. COUSLAND: Inst. Conf. Creep (London) 1, Paper 3–25 (1963).Google Scholar
  11. [6.
    c] Moyar, G. J., and C. M. SINCLAIR: Inst. Conf. Creep (London) 1, Paper 2–47 (1963).Google Scholar
  12. [7]
    Benham, P. P.: Int. J. Mech. Sci. 7, 81–86 (1965).CrossRefGoogle Scholar
  13. [8]
    Coffin, L. F.: J. Basic Engng, Trans. Am. Soc. Mech. Engrs (Ser. D) 82, 671 to 682 (1960).Google Scholar
  14. [9]
    Feltner, C. E.: Acta Met. 11, 817 (1963).CrossRefGoogle Scholar
  15. [10]
    Kadashevicii, I. I. and V. V. Novoznmov• Prikl. Math. Mech. 22, 78–89’ (1958).Google Scholar
  16. [11]
    Freudential, A. M., and M. RONAY: Proc. Roy. Soc. (London) A 292, 14–50 (1966).ADSCrossRefGoogle Scholar
  17. [12]
    Poynting, J. H.: Proc. Roy. Soc. (London) A S2, 564–559 (1909); A 86,. 534–561 (1912).Google Scholar
  18. [13]
    Weissenberg, K.: Nature 159, 310–311 (1947).ADSCrossRefGoogle Scholar
  19. [14]
    Reiner, M.: Amer. J. Math. 67, 350–362 (1945).MathSciNetMATHCrossRefGoogle Scholar
  20. [15]
    Reiner, M.: Amer. J. Math. 70, 433–446 (1948).MathSciNetMATHCrossRefGoogle Scholar
  21. [16]
    Reiner, M., and D. ABIR: Proc. IUTAM Symp. on Second-Order Effects,. Haifa 1962. New York-London: Pergamon Press. 1964.Google Scholar
  22. [17]
    Lodge, A. S.: Elastic Fluids. New York: Academic Press. 1964.Google Scholar
  23. [18]
    Ronay, M.: British J. Appl. Phys. 16, 727 (1965).Google Scholar
  24. [19]
    Prager, W.: J. Appl. Phys. 16, 837–840. (1945)MathSciNetADSCrossRefGoogle Scholar
  25. [20]
    Handeltiman, G. H., C. C. LIN, and W. PRAGER: Q. Appl. Math. 4, 397–407 (1947).Google Scholar
  26. [21]
    Rivlin, R. S., and J. L. Erickson: J. Ratl Mech. Anal. 4, 323–425 (1955).MATHGoogle Scholar
  27. [22]
    Albrecht, B., and A. M. Freudenthal: J. Solids and Struct. 1966.Google Scholar
  28. [23]
    Pipkin, A. C., and R. S. Rivlin:J. Appl. Math. Physics (ZAMP) 16, 313–327 (1965).MathSciNetCrossRefGoogle Scholar
  29. [24]
    Raymond, M. H., and L. F. Coffin: Trans. Am. Soc. Mech Engrs 1964.Google Scholar

Copyright information

© Springer-Verlag/Wien 1968

Authors and Affiliations

  • A. M. Freudenthal
    • 1
  • Maria Ronay
    • 1
  1. 1.New YorkUSA

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