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Yield function of the orthotropic material considering the crystallographic texture

  • Erisov, Yaroslav A. (Metal Forming Department, Samara State Aerospace University) ;
  • Grechnikov, Fedor V. (Metal Forming Department, Samara State Aerospace University) ;
  • Surudin, Sergei V. (Metal Forming Department, Samara State Aerospace University)
  • 투고 : 2015.10.15
  • 심사 : 2015.12.17
  • 발행 : 2016.05.25

초록

On the basis of the energy approach it is reported a development of the yield function and the constitutive equations for the orthotropic material with consideration of the crystal lattice constants and parameters of the crystallographic texture for the general stress state. For practical use in sheet metal forming analysis it is considered different loading scenarios: plane stress and plane strain states. Using the proposed yield function, the influence of single ideal components on the shape of yield surface was analyzed. The six texture components investigated here were cube, Goss, copper, brass, S and rotated cube, as these components are typically observed in rolled sheets from FCC alloys.

키워드

참고문헌

  1. Adamesku, P.A., Geld, R.A. and Mityshov, E.A. (1985), Anisotropy of Physical Properties of Metals, Mashinostroenie, Moscow, Russia. (in Russian)
  2. Arysenskii, Yu.М., Grechnikov, F.V. and Аryshenskii, V.Yu. (1990), "The requirements determination to the sheet anisotropy depending on further forming", Kuznechno-Shtampovochnoe Proizvodstvo, 3, 16-19. (in Russian)
  3. Aryshenskii, V.Yu., Grechnikov, F.V. and Zaitsev, V.М. (1990), "The determination of the material plastic deviator of the anisotropic medium by its texture parameters", Izvestia Akademii nauk SSSR. Metally, 4, 158-162. (in Russian)
  4. Aryshenskii, Yu.М., Kaluzhskii, I.I. and Uvarov, V.V. (1969), "Some issues of the plasticity theory of orthotropic medium", Izvestiya VUZ, Aviatsionnaya Tekhnika, 2, 15-18. (in Russian)
  5. Backofen, W. (1972), Deformation Processing, Addison-Wesley Longman.
  6. Banabic, D, Bunge, H.J., Pohlandt, K. and Tekkaya, A.E. (2000), Formability Of Metallic Materials: Plastic Anisotropy, Formability Testing, Forming Limits, Springer, Berlin, Germany.
  7. Banabic, D. (2010), Sheet Metal Forming Processes. Constitutive Modelling and Numerical Simulation, Springer, Berlin, Germany.
  8. Banabic, D., Aretz, H., Comsa, D.S. and Paraianu, L. (2005), "An improved analytical description of orthotropy in metallic sheets", Int. J. Plasticity, 21, 493-512. https://doi.org/10.1016/j.ijplas.2004.04.003
  9. Banabic, D., Barlat, F., Cazacu, O. and Kuwabara, T. (2010), "Advances in anisotropy and formability", Int. J. Mater. Form., 3, 165-189. https://doi.org/10.1007/s12289-010-0992-9
  10. Barlat, F. and Lian, J.A. (1989), "Plastic behavior and stretchability of sheet metals. Part 1: yield function for orthotropic sheets under plane stress conditions", Int. J. Plasticity, 5, 51-66. https://doi.org/10.1016/0749-6419(89)90019-3
  11. Barlat, F., Aretz, H., Yoon, J.W., Karabrin, M.E., Brem, J.C. and Dick, R.E. (2005), "Linear transformationbased anisotropic yield functions", Int. J. Plasticity, 21, 1009-1039. https://doi.org/10.1016/j.ijplas.2004.06.004
  12. Barlat, F., Brem, J.C., Yoon, J.W., Chung, K., Dick, R.E., Lege, D.J., Pourboghrat, F., Choi, S.H. and Chu, E. (2003), "Plane stress yield function for aluminum alloy sheet. Part 1: Theory", Int. J. Plasticity, 19, 1297-1319. https://doi.org/10.1016/S0749-6419(02)00019-0
  13. Barlat, F., Lege, D.J. and Brem, J.C. (1991), "A six-component yield function for anisotropic materials", Int. J. Plasticity, 7, 693-712. https://doi.org/10.1016/0749-6419(91)90052-Z
  14. Barlat, F., Yoon, J.W. and Cazacu, O. (2007), "On linear transformation of stress tensors for the description of plastic anisotropy", Int. J. Plasticity, 23, 876-896. https://doi.org/10.1016/j.ijplas.2006.10.001
  15. Bron, F. and Besson, J. (2003), "A yield function for anisotropic materials. Application to aluminum alloys", Int. J. Plasticity, 20, 937-963.
  16. Cazacu, O. and Barlat, F. (2001), "Generalization of Drucker's yield criterion to orthotropy", Mathematics and Mechanics of Solids, 6, 613-630. https://doi.org/10.1177/108128650100600603
  17. Cazacu, O. and Barlat, F. (2003), "Application of representation theory to describe yielding of anisotropic aluminum alloys", Int. J. of Engng. Sci., 41, 1367-1385. https://doi.org/10.1016/S0020-7225(03)00037-5
  18. Choi, S.H., Cho, J.H., Barlat, F., Chung, K., Kwon, J.W. and Oh, K.H. (1999), "Prediction of yield surfaces of textured sheet metals", Metallurgical and materials transactions, 30(A), 377-386. https://doi.org/10.1007/s11661-999-0327-y
  19. Drucker, D.C. (1949), "Relation of experiments to mathematical theories of plasticity", J. Appl. Mech., 16, 349-357.
  20. Engler, O. and Hirsch, J., (2002) "Texture control by thermomechanical processing of AA6xxx Al-Mg-Si sheet alloys for automotive applications - a review", Materials Science and Engineering A, 336, 249-262. https://doi.org/10.1016/S0921-5093(01)01968-2
  21. Hershey, A.V. (1954), "The plasticity of an isotropic aggregate of anisotropic face centered cubic crystals", J. Appl. Mech., 21, 241-249.
  22. Hill, R. (1948), "A theory of the yield and plastic flow of anisotropic metals", Proc. Roy. Soc. London. Ser A., 193, 281-297. https://doi.org/10.1098/rspa.1948.0045
  23. Hill, R. (1950), The Mathematical Theory of Plasticity, Oxford University Press, New-York, USA.
  24. Hill, R. (1979), "Theoretical plasticity of textured aggregates", Math. Proc. Cambridge Philos. Soc., 85, 179-191. https://doi.org/10.1017/S0305004100055596
  25. Hirsch, J. and Al-Samman, T. (2013) "Superior light metals by texture engineering: Optimized aluminum and magnesium alloys for automotive applications", Acta Materialia, 61, 818-843. https://doi.org/10.1016/j.actamat.2012.10.044
  26. Hosford, W.F. (1972), "A generalized isotropic yield criterion", J. Appl. Mech. Trans., ASME, 39, 607-609. https://doi.org/10.1115/1.3422732
  27. Hosford, W.F. (2005), Mechanical Behavior of Materials, Cambridge University Press, New-York, USA.
  28. Huber, M.T. (1904), "Die spezifische formanderungsarbeit als MaB der anstrengung eines materials", Czasopismo Techniczne, 22, 181.
  29. Hutchinson, W.B., Oscarsson, A. and Karlsson, A. (1989), "Control of microstructure and earing behaviour in aluminium alloy AA 3004 hot bands", Mater. Sci. Tech., 5, 1118-1127. https://doi.org/10.1179/mst.1989.5.11.1118
  30. Karafillis, A.P. and Boyce, M.C. (1993), "A general anisotropic yield criterion using bounds and a transformation weighting tensor", J. Mech. Phys. Solid., 41, 1859-1886. https://doi.org/10.1016/0022-5096(93)90073-O
  31. Kusiak, J., Szeliga, D. and Sztangret, L. (2012), "Modelling techniques for optimizing metal forming processes", Eds. Lin, D. Balint and M. Pietrzyk, Microstructure Evolution In Metal Forming Processes, Woodhead Publishing, Cambridge, UK.
  32. Landolt-Bornstein (1966), Numerical data and functional relationships in science and technology. New Series. Group III: Crystal and solid state physics. Volume 1: Elastic, piezoelectric, piezooptic and electrooptic constants of crystals, Springer, Berlin, Germany.
  33. Mises, R. (1913), "Mechanik der festen Korper im plastisch deformablen Zustand", Gottinger Nachrichten, Mathematisch-Physikalische, 1(4), 582-592.
  34. Mises, R. (1928), "Mechanik der plastischen Formanderung von Kristallen", ZAM, 8, 161-185. https://doi.org/10.1002/zamm.19280080302
  35. Moayyedian, F. and Kadkhodayan, M. (2016), "An advanced criterion based on non-AFR for anisotropic sheet metals", Struct. Eng. Mech., 57(6), 1015-1038. https://doi.org/10.12989/sem.2016.57.6.1015
  36. Nakamachi, E. and Xie, C.L. (2001) "Texture design of high-strength and high-formability steel sheet by using finite element and optimization method", Ed. K.I. Mori, Simulation of Materials Processing: Theory, Methods and Applications, Swets & Zeitlinger, Lisse, Netherlands.
  37. Piehler, H.R. (2009), "Crystal-plasticity fundamentals", ASM Handbook, 22A(#05215G), 232-238.
  38. Saint-Venant, B. (1870), "Memoire sur l'establissement des equations differentielles des mouvements interieurs operes dans les corps solides ductiles au dela des limites ou I' elasticite pourrait les ramener a leur premier etat", Comptes Rendus hebdomadaire s des Seances de l'A cademie des Sciences, 70, 473-480.
  39. Soare, S. and Banabic, D. (2008), "About mechanical data required to describe the anisotropy of th.in sheets to correctly predict the earing of deep-drawn cups", Int. J. Plasticity, 4, 34-37.
  40. Tresca, H. (1864), "Sur l'Ecoulement des Corps Solides Soumis a de Fortes Pressions", Comptes rendus de l'Academie des Sciences, 59, 754.
  41. Truszkowski, W. (2001), The Plastic Anisotropy in Single Crystals and Polycrystalline Metals, Springer, Netherlands.
  42. Woodthorpe, J. and Pearce, R. (1970), "The anomalous behavior of aluminum sheet under balance biaxial tension", Int. J. Mech. Sci., 12, 341-347. https://doi.org/10.1016/0020-7403(70)90087-1
  43. Zhao, Z., Mao, W., Roters, F. and Raabe, D. (2004), "A texture optimization study for minimum earing in aluminium by use of a texture component crystal plasticity finite element method", Acta Materialia, 52, 1003-1012. https://doi.org/10.1016/j.actamat.2003.03.001

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