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Theoretical plasticity of textured aggregates

Published online by Cambridge University Press:  24 October 2008

R. Hill
R. Hill
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

The plasticity of metal polycrystals with preferred orientations is considered from a phenomenological standpoint. Some new general theorems are proved, in particular the existence of a work-equivalent function of the tensor strain-rate over any yield surface. The status of the classical theory of plastic anisotropy is re-appraised in the light of recent experiments, which are themselves critically reviewed. A new type of yield function is proposed to account for the so-called anomalous behaviour of some materials.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 85 , Issue 1 , January 1979 , pp. 179 - 191
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

REFERENCES

(1)Hill, R.A theory of the yielding and plastic flow of anisotropic metals. Proc. Roy. Soc. London. Ser. A 193 (1948), 281–297.Google Scholar
(2)Hill, R.Mathematical Theory of Plasticity (Oxford: Clarendon Press, 1950).Google Scholar
(3)Hill, R.The essential structure of constitutive laws for metal composites and polycrystals. J. Mech. Phys. Solids 15 (1967), 79–95.CrossRefGoogle Scholar
(4)Bishop, J. F. W. and Hill, R.A theory of the plastic distortion of a polycrystalline aggregate under combined stresses. Philos. Mag. 42 (1951), 414–427.CrossRefGoogle Scholar
(5)Bland, D. R.The two measures of work-hardening. Proc. 9th International Congress of Applied Mechanics, Brussels (1956), 45–50.Google Scholar
(6)Hellan, K.A note on the equivalence of the postulates of isotropic hardening. J. Engng Materials Technology, Am. Soc. Mech. Eng. 96 (1974), 79–80.CrossRefGoogle Scholar
(7)Gotoh, M.A theory of plastic anisotropy based on a yield function of fourth order (plane stress state). Internat. J. Mech. Sci. 19 (1977), 505–520.CrossRefGoogle Scholar
(8)Bourne, L. and Hill, R.On the correlation of the directional properties of rolled sheet in tension and cupping tests. Philos. Mag. 41 (1950), 671–681.CrossRefGoogle Scholar
(9)Bramley, A. N. and Mellor, P. B.Plastic flow in stabilized sheet steel. Internat. J. Mech. Sci. 8 (1966), 101–114.CrossRefGoogle Scholar
(10)Bramley, A. N. and Mellor, P. B.Plastic anisotropy of titanium and zinc sheet. I. Macroscopic approach. Internat. J. Mech. Sci. 10 (1968), 211–219.CrossRefGoogle Scholar
(11)Lee, D. and Backofen, W. A.An experimental determination of the yield locus for titanium and titanium alloy sheet. Trans. Metallurgical Soc. Am. Inst. Mech. Eng. 236 (1966), 1077–1084.Google Scholar
(12)Pearce, R.Some aspects of anisotropic plasticity in sheet metals. Internat. J. Mech. Sci. 10 (1968), 995–1005.CrossRefGoogle Scholar
(13)Tozawa, Y., Nakamura, M., and Shinkai, I.Yield loci for pre-strained steel sheets. Proc. International Conference on the Science and Technology of Iron and Steel, Tokyo (1970), Trans. Iron Steel. Inst. Japan 11 (1971), 936–940.Google Scholar
(14)Taghvaipour, M. and Mellor, P. B.Plane strain compression of anisotropic sheet metal. Proc. Inst. Mech. Engrs. 185 (1970), 593–606.CrossRefGoogle Scholar
(15)Woodthorpe, J. and Pearce, R.The anomalous behaviour of aluminium sheet under balanced biaxial tension. Internat. J. Mech. Sci. 12 (1970), 341–347.CrossRefGoogle Scholar
(16)Bassani, J. L.Yield characterization of metals with transversely isotropic plastic properties. Internat. J. Mech. Sci. 19 (1977), 651–660.CrossRefGoogle Scholar
(17)Parmar, A. and Mellor, P. B.Prediction of limit strains in sheet metal using a more general yield criterion. Internat. J. Mech. Sci. 20 (1978), (to appear).CrossRefGoogle Scholar
(18)Mellor, P. B. and Parmar, A. Plasticity analysis of sheet metal forming. Proc. Symp. Mech. Metal Forming (1977) (Plenum Publ. Corporation: New York, 1979).Google Scholar
(19)Parmar, A. and Mellor, P. B.Plastic expansion of a circular hole in sheet metal subjected to biaxial tensile stress. Internat. J. Mech. Sci. 20 (1978), (to appear).CrossRefGoogle Scholar
(20)Bishop, J. F. W. and Hill, R.A theorstical derivation of the plastic properties of a polycrystalline face-centred metal. Philos. Mag. 42 (1951), 1298–1307.CrossRefGoogle Scholar