Summary
A descriptive initial yield function is presented from an examination of experimentally determined yield loci, component plastic strain paths and Lode's parameters that indicate either a severe textural anisotropy in a material or a slight departure from the von Mises condition. The transition from the initial function to one that describes a subsequent yield surface which translates with the stress vector is developed and compared with experimental results. Observations on the Bauschinger, Swift and hardening effects in subsequent yield loci, defined at the limit of proportionality, are adequately represented through Ziegler's translation law when modified for non-linear work hardening. It is shown that the marked distortion, particularly apparent, in the presence of shear stress, may be represented by considering separately the translation for each quadrant of the initial yield locus.
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References
Hill, R.: The mathematical theory of plasticity. Oxford University Press 1950.
Prager, W.: A new method of analysing stresses and strains in work hardening plastic solids. J. Appl. Mech.23, 493–496 (1956).
Hodge, P. G.: Discussion on [2]. J. Appl. Mech.24, 482–483 (1957).
Baltov, A., Sawczuk, A.: A rule of anisotropic hardening. Acta Mechanica1, 81–92 (1965).
Backhaus, G.: Zur Fließgrenze bei allgemeiner Verfestigung. ZAMM48, 99–108 (1968).
Edelman, F., Drucker, D. C.: Some extensions to elementary plasticity theory. J. Franklin Inst.251, 581–605 (1951).
Yoshimura, Y.: Hypothetical theory of anisotropy and the Bauschinger effect due to plastic strain history. Aero. Res. Inst., Tokyo Univ. Rpt. No.349, 224–246 (1959).
Williams, J. F., Svensson, N. L.: A rationally based yield criterion, for work hardening materials. Meccanica6, 104–110 (1971).
Svensson, N. L.: Anisotropy and the Bauschinger effect in cold rolled aluminium. J. Mech. Engng Sci.8, 162–172 (1966).
Rees, D. W. A.: Anisotropic hardening theory and the Bauschinger effect. J. Strain Analysis16 (2), 85–95 (1981).
Taylor, C. I., Quinney, H.: The plastic distortion of metals. Phil. Trans. Roy. Soc.203 A, 323–362 (1931).
Lee, D., Backofen, W. A.: An experimental determination of the yield locus for titanium and titanium alloy sheet. Trans. Met. Soc., AIME236, 1077–1084 (1966).
Rogan, J., Shelton, A.: Yield and subsequent flow behaviour of some annealed steels under combined stress. J. Strain Analysis4, 127–137 (1969).
Dillamore, I. L., Hazel, R. J., Watson, T. W., Hadden, P.: An experimental study of the mechanical anisotropy of some common metals. Int. J. Mech. Sci.13, 1049–1061 (1971).
Rogan, J., Shelton, A.: Effect of prestress on the yield and flow behaviour of En 25 steel. J. Strain Analysis4, 138–161 (1969).
Liu, S. I., Sachs, G.: The flow and fracture characteristics of the aluminium alloy 24 ST after alternating tension and compression. Metals Tech., AIMME., Tech. Pub., No.2392, 1–12 (1948).
Phillips, A., Tang, J. L.: The effect of loading path on the yield surface at elevated temperatures. Int. J. Solids Structures8, 463–474 (1972).
Swift, H. W.: Length changes in metals under torsional overstrain. Engineering163, 253–257 (1947).
Betten, J.: Plastische Anisotropie und Bauschinger-Effekt; allgemeine Formulierung und Vergleich mit experimentell ermittelten Fließortkurven. Acta Mechanica25, 79–94 (1976).
Rees, D. W. A.: Biaxial creep and plastic flow in anisotropic aluminium. Ph.D. thesis, C.N.A.A. (U.K.), 1976.
Johnson, A. E., Frost, N. E., Henderson, J.: Plastic strain and stress relations at high temperatures. The Engineer (Lond.)199 (5173), 366–369 (1955).
Mehan, R. L.: Effect of combined stress on yield and fracture behaviour of Zircaloy-2. J. Basic. Eng., Trans. ASME83, 499–512 (1961).
Rees, D. W. A.: A hardening model for anisotropic materials. Experimental Mechanics21, 245–254 (1981).
Shih, C. F., Lee, D.: Further developments in anisotropic plasticity. J. Eng. Mat. Tech., Trans. ASME100, 294–302 (1978).
Avery, D. H., Hosford, W. F., Backofen W. A.: Plastic anisotropy in magnesium alloy sheets. Trans. Met. Soc. AIME233, 71–78 (1965).
Williams, J. F., Svensson, N. L.: Effect of torsional prestrain on the yield locus of 1100 F aluminium. J. Strain Analysis6, 263–272 (1971).
Ziegler, H.: A modification to Prager's hardening rule. Quart. App. Math.17, 55–65 (1959).
Moreton, D. N., Moffat, D. G., Hornby, R. P.: Techniques for investigating the yield surface behaviour of pressure vessel materials. J. Strain Analysis13 (3), 185–191 (1978).
Miastkowski, J., Szczepinski, W.: An experimental study of yield surfaces of prestrained brass. Int. J. Solids Structures1, 189–194 (1965).
Rees, D. W. A.: A review of stress-strain paths and constitutive relations in the plastic range. J. Strain Analysis16, 235–249 (1981).
Reiner, M.: A mathematical theory of dilatancy. Amer. J. Math.67, 350–362 (1945).
Rivlin, R. S., Ericksen, J. I.: Stress deformation relations for isotropic materials. J. Ratl. Mech. Anal.4, 323–425 (1955).
Phillips, A., Weng, G. J.: An analytical study of an experimentally verified hardening law. J. Appl. Mech. Trans. A.S.M.E.42, 375–378 (1975).
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Rees, D.W.A. Yield functions that account for the effects of initial and subsequent plastic anisotropy. Acta Mechanica 43, 223–241 (1982). https://doi.org/10.1007/BF01176284
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DOI: https://doi.org/10.1007/BF01176284