Crystallographic texture induced anisotropy in copper: An approach based on a tensorial Fourier expansion of the CODF

Journal De Physique. IV : JP

Volumn 105, Issue , 2003, Pages 167-174

  Bohlke T ^a   Bertram, A ^a  

^a OTTO VON GUERICKE UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; CRYSTAL ORIENTATION; CRYSTALLOGRAPHY; ELASTICITY; FOURIER TRANSFORMS; MATHEMATICAL MODELS; MORPHOLOGY; POLYCRYSTALLINE MATERIALS; STIFFNESS; TEXTURES;

CRYSTALLOGRAPHIC TEXTURE; CYCLIC SWIFT EFFECT; ELASTIC STIFFNESS TENSOR; QUADRATIC YIELD FUNCTION; TENSORIAL FOURIER EXPANSIONS;

COPPER;

EID: 0038403613     PISSN: 11554339     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1051/jp4:20030184     Document Type: Conference Paper

References (24)

1. B.L. Adams, J.P. Boehler, M. Guidi, and E.T. Onat. Group theory and representation of microstructure and mechanical behavior of polycrystals. J. Mech. Phys. Solids, 40(4):723-737, 1992.
2. B.L. Adams, T.A. Mason, T. Olson, and D.D. Sam, Theory of grain boundary structure effects on mechanical behavior. Materials Science Forum, 157-162:1731-1738, 1994.
3. K.S. Aleksandrov and L.A. Aisenberg. A method of calculating the physical constants of polycrystalline materials. Soviet Physics - Doklady, 11:323-325, 1966.
4. T. Böhlke. Crystallographic Texture Evolution and Elastic Anisotropy: Simulation, Modeling, and Applications. Aachen: Shaker Verlag, 2001. Dissertation, Fakultät für Maschinenbau, Otto-von-Guericke-Universität Magdeburg.
5. T. Böhlke and A. Bertram. A minimum problem defining effective isotropic elastic properties. Z. angew. Math. Mech., 80(S2):S419-S420, 2000.
6. T. Böhlke and A. Bertram. The evolution of Hooke's law due to texture development in polycrystals. Int. J. Solids Struct., 38(52):9437-9459, 2001.
7. T. Böhlke, A. Bertram, and E. Krempl. Modeling nonlinear effects in free-end torsion. To appear in Int. J. Plast., 2003.
8. H.-J. Bunge. Zur Darstellung allgemeiner Texturen. Z. Metallkde., 56:872-874, 1965.
9. H.-J. Bunge and W.T. Roberts. Orientation distribution, elastic and plastic anisotropy in stabilized steel sheet. J. Appl. Cryst., 2:116-128, 1969.
10. G.J. Davies, D.J. Goodwill, and J.S. Kallend. Elastic and plastic anisotropy in sheets of cubic metals. Met. Trans., 3:1627-1631, 1972.
11. I.M. Gel'fand, R.A. Minlos, and Z.Ya. Shapiro. Representations of the Rotation and Lorentz Groups and their Applications. Oxford: Pergamon Press, 1963.
12. M. Guidi, B.L. Adams, and E.T. Onat. Tensorial representation of the orientation distribution function in cubic polycrystals. Textures Microstruct., 19:147-167, 1992.
13. R. Hill. A theory of yielding and plastic flow of anisotropic materials. Proc. Phys. Soc. Lond., A 193: 281-297, 1948.
14. J.S. Kallend and G.J. Davies. The elastic and plastic anisotropy of cold-rolled sheets of copper, gilding metal, and α-brass. J. Inst. Met., 5:257-260, 1971.
15. C.-S. Man. On the correlation of elastic and plastic anisotropy in sheet metals. J. Elast., 39:165-173, 1995.
16. C.-S. Man. On the constitutive equations of some weakly-textured materials. Arch. Rat. Mech. Anal., 143:77-103, 1998.
17. S. Matthies and M. Humbert. On the principle of a geometric mean of even-rank symmetric tensors for textured polycrystals. J. Appl. Cryst., 28:254-266, 1995.
18. A. Reuss. Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle. Z. Angew. Math. Mech., 9:49-58, 1929.
19. R.J. Roe. Description of crystalline orientation of polycrystalline materials. III. General solution to pole figure inversion. J. Apll. Phys., 36:2024-2031, 1965.
20. C.A. Stickels and P.R. Mould. The use of Young's modulus for predicting the plastic-strain ratio of low-carbon steel sheets. Met. Trans., 1:1303-1312, 1970.
21. R. v. Mises. Mechanik der plastischen Formänderung bei Kristallen. Z. angew. Math. Mech., 8(3):161-185, 1928.
22. W. Voigt. Lehrbuch der Kristallphysik. Teubner Leipzig, 1910.
23. Q.-S. Zheng and Y.-B. Fu. Orientation distribution functions for microstructures of heterogeneous materials: II Crystal Distribution functions and irreducible tensors. Appl. Math. Mech., 22(8):865-884, 2001.
24. Q.-S. Zheng and Y.-B. Fu. Orientation distribution functions for microstructures of heterogeneous materials: II Crystal Distribution functions and irreducible tensors restricted by various material symmetries. Appl. Math. Mech., 22(8):885-903, 2001.