Yield surfaces in prestrained aluminum and copper

  • S. S. Hecker
Mechanical Behavior


The analysis of strain-hardening materials subjected to multiaxial states of stress requires more detailed experimental information about the effects of previous plastic deformation on the yield surfaces of real materials than is presently available. To provide insight into some of these effects thin walled tubular specimens of 1100-0 aluminum and annealed OFHC copper were subjected to biaxial stresses through the application of simultaneous axial tension and internal pressure, and the effects of the magnitude, direction, and sequence of prestraining operations on subsequent yield surfaces were determined. It was found that the yield surface behavior depends greatly upon the definition of yielding employed. Use of small proof strain definitions resulted in very anisotropic yield surface characteristics which reflected the effect of previous deformation. On the other hand, use of large proof strains resulted in isotropic yield surface characteristics which were devoid of previous deformation influence. The small proof strain yield curves were found, in general, to expand and translate in the direction of prestrain and, for biaxial prestrains, to be distorted in the vicinity of the loading point. Multiple prestrain sequences in normal directions induce a large negative cross effect similar to Bauschinger effect observed under reversed loading. Such anisotropic behavior was found to contradict the two most commonly used continuum mechanics predictions, the isotropic and kinematic hardening rules.


Plastic Strain Yield Surface Yield Curve Bauschinger Effect Proportional Limit 
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.


  1. 1.
    D. C. Drucker:Proc. 1st U.S. Nat. Congr. Appl. Mech., 1951, p. 487.Google Scholar
  2. 2.
    W. Prager:Proc. Inst. of Mech. Engrs., 1955, vol. 169, p. 41.CrossRefGoogle Scholar
  3. 3.
    S. B. Batdorf and B. Budiansky:NACA TN1871, 1949.Google Scholar
  4. 4.
    T. H. Lin:Proc. 2nd U.S. Natl. Congr. Appl. Mech., 1954, p. 461.Google Scholar
  5. 5.
    T. H. Lin:Proc. 3rd U.S. Natl. Congr. Appl. Mech., 1958, p. 581.Google Scholar
  6. 6.
    W. Koiter:Quart. Appl. Math., 1953, vol. 11, p. 350.Google Scholar
  7. 7.
    J. L. Sanders:Proc. 2nd U.S. Natl. Congr. Appl. Mech., 1954, p. 455.Google Scholar
  8. 8.
    G. Backhaus:ZAMM, 1968, vol. 48, p. 99.CrossRefGoogle Scholar
  9. 9.
    Z. Mroz:J. Mech. Phys. Solids, 1967, vol. 15, p. 163.CrossRefGoogle Scholar
  10. 10.
    A. Baltov and A. Sawzuk:Acta Mech., 1965, vol. 1, p. 6.CrossRefGoogle Scholar
  11. 11.
    G. I. Taylor and H. Quinney:Phil. Trans. Roy. Soc., 1932, vol. 230, p. 323.CrossRefGoogle Scholar
  12. 12.
    T. C. Hsu:J. Strain. Anal., 1966, vol. 1, p. 331.CrossRefGoogle Scholar
  13. 13.
    H. J. Ivey:J. Mech. Eng. Sci., 1961, vol. 3, p. 2.CrossRefGoogle Scholar
  14. 14.
    P. M. Naghdi, F. Essenburg, and W. Koff:J. Appl. Mech., 1958, vol. 25, p. 201.Google Scholar
  15. 15.
    J. Parker and M. B. Bassett:J. Appl. Mech., 1964, vol. 31, p. 676.Google Scholar
  16. 16.
    H. G. McComb, Jr.:NASA-TN D-396, 1960.Google Scholar
  17. 17.
    P. K. Bertsch and W. N. Findley:Proc. 4th U.S. Natl. Congr. Appl. Mech., 1962, vol. 2, p. 893.Google Scholar
  18. 18.
    L. W. Hu and J. F. Bratt:J. Appl. Mech., 1958, vol. 25, p. 411.Google Scholar
  19. 19.
    W. M. Mair and H. Ll. D. Pugh:J. Mech. Eng. Sci., 1964, vol. 6, p. 150.CrossRefGoogle Scholar
  20. 20.
    J. Miastkowski and W. Szczepinski:Int. J. Solids Structures, 1965, vol. 1, p. 198.CrossRefGoogle Scholar
  21. 21.
    E. Shiratori, K. Ikegami and H. Okano:Bull. ISME, 1968, vol. 11, p. 413.Google Scholar
  22. 22.
    E. Shiratori and K. Ikegami:J. Mech. Phys. Solids, 1968, vol. 16, p. 373.CrossRefGoogle Scholar
  23. 23.
    J. Miastkowski:Arch. Mech. Stos., 1968, vol. 3, p. 262.Google Scholar
  24. 24.
    W. Szczepinski and J. Miastkowski:J. Mech. Phys. Solids, 1968, vol. 16, p. 153.CrossRefGoogle Scholar
  25. 25.
    S. S. Hecker, B. G. Strait, and R. M. Laing: Los Alamos Report LA-4550, Los Alamos Scientific Laboratory, Los Alamos, N.M.Google Scholar
  26. 26.
    J. W. Dally and W. F. Riley.Experimental Stress Analysis, p. 399, McGraw-Hill Book Co., New York, 1965.Google Scholar
  27. 27.
    S. S. Hecker,Microtecnic, 1971, vol. XXV, p. 49.Google Scholar
  28. 28.
    G. N. White and D. C. Drucker:J. Appl. Phys., 1950, vol. 21, p. 1013.CrossRefGoogle Scholar
  29. 29.
    R. L. Sierakowski and A. Phillips:Acta Mech., 1968, vol. 6, p. 217.CrossRefGoogle Scholar
  30. 30.
    C. S. Barrett:Structure of Metals, 2nd ed., p. 492, McGraw-Hill Book Co., New York, 1952.Google Scholar
  31. 31.
    J. D. Lubahn:J. Metals, 1955, vol. 205, p. 1031.Google Scholar
  32. 32.
    J. D. Lubahn:Trans. ASM, 1952, vol. 44, p. 643.Google Scholar
  33. 33.
    R. L. Whitley:Trans. ASM, 1960, vol. 52, p. 154.Google Scholar
  34. 34.
    W. A. Backofen, W. F. Hosford, Jr., and J. J. Burke:Trans. ASM, 1962, vol. 55, p. 264.Google Scholar
  35. 35.
    R. Hill:Proc. Roy. Soc., 1948, vol. 193A, p. 281.Google Scholar
  36. 36.
    A. W. McReynolds:Trans. AIME, 1949, vol. 185, p. 32.Google Scholar
  37. 37.
    S. R. Bodner and A. Rosen:J. Mech. Phys. Solids, 1967, vol. 15, p. 47.CrossRefGoogle Scholar
  38. 38.
    A. Rosen and S. R. Bodner:J. Mech. Phys. Solids, 1967, vol. 15, p. 63.CrossRefGoogle Scholar
  39. 39.
    B. Paul:Fracture, vol. 2, p. 313, Academic Press, New York, 1968.Google Scholar
  40. 40.
    J. D. Lubahn and R. P. Felgar:Plasticity and Creep in Metals, p. 286. J. Wiley and Sons, New York, 1961.Google Scholar
  41. 41.
    S. S. Hecker, accepted for publication inActa Mech., 1971.Google Scholar
  42. 42.
    E. Kröner:Appl. Mech. Rev., 1962, vol. 15, p. 599.Google Scholar
  43. 43.
    C. Truesdell and W. Noll:Handbuch der Physik, Springer Verlag, 1965.Google Scholar
  44. 44.
    R. F. Kocks:Met. Trans., 1970, vol. 1, p. 1121.Google Scholar
  45. 45.
    J. W. Hutchinson:Proc. Roy. Soc. London, A, 1970, vol. 319, p. 247.CrossRefGoogle Scholar
  46. 46.
    G. Sachs:Z. Verein Deut. Ing., 1928, vol. 72, p. 734.Google Scholar
  47. 47.
    G. I. Taylor:J. Inst. Metals, 1938, vol. 62, p. 307.Google Scholar

Copyright information

© ASM International & TMS-The Minerals, Metals and Materials Society 1971

Authors and Affiliations

  • S. S. Hecker
    • 1
  1. 1.Physics DepartmentGeneral Motors Research LaboratoriesWarren

Personalised recommendations