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Biaxial extension of a plane single crystal

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper concerns the rigid-plastic modelisation of a f.c.c. single crystal, deforming by crystallographic slip, under large strain. Adopting the plane single crystal model, which corresponds to a true two-dimensional evolution of a real three-dimensional crystal, the activity of slip systems and the plastic indetermination, due to multiplicity of solutions, are studied according to the rate-independent Schmid law or the rate-dependent Bingham law. To promote a more general situation of potential multiple slip and therefore of potential indeterminacy, the biaxial loading is investigated. Based on this model and the Bingham slip law, the indeterminacy problem is surmounted, by adopting the geometrical analysis in the strain rate space and it is proved that the linear viscoplastic analysis is a new way of solving the indeterminacy problem.
Rocznik
Strony
363--384
Opis fizyczny
Bibliogr. 29 poz.
Twórcy
autor
autor
autor
  • Faculté des Sciences et Techniques de Tanger B.P. 416, Tanger, Maroc
Bibliografia
  • 1. G.I. TAYLOR and C.F. ELAM, The distortion of an aluminum crystal during a tensile test, Proc. Royal Soc. London A 102, 643-667, 1923.
  • 2. G.I. TAYLOR and C.F. ELAM, The plastic extension and fracture of aluminum single crystals, Proc. Royal Soc. London A 108, 28-51, 1925.
  • 3. G.I. TAYLOR, Plastic strain in metals J. Institute of Metals, 62, 307-324, 1938.
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  • 5. J. MANDEL, Generalisation de la theorie de plasticite de W. T. Koiter, Int. J. Solids Struct., 1, 273-295, 1965.
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  • 7. J.R. RICE, Inelastic constitutive relations for solids: an internal variable theory and its application to metal plasticity J. Mech. Phys. Solids, 19, 433-455, 1971.
  • 8. R. HILL and J.R. RlCE, Constitutive analysis of elastic-plastic crystals at arbitrary strain, J. Mech. Phys. Solids, 20, 401-413, 1972.
  • 9. F. SIDOROFF and C. TEODOSIU, A theory of finite elasto-plasticity of single crystals, Int. J. Engng. & Sci., 14, 165-176, 1976.
  • 10. R.J. ASARO and R.J. RlCE, Strain localisation in ductile single crystals, J. Mech. Phys. Solids, 25, 309-338, 1977.
  • 11. R.J. ASARO, Geometrical effects in the inhomogeneous deformation of ductile single crystals, Acta Metall., 27, 445-453, 1979.
  • 12. R.J, ASARO, Micromechanics of crystals and polycrystals, Adv. Appl. Mech., 23, 1-115, 1983.
  • 13. K.S. HAVNER, Finite Plastic Deformation of Crystalline Solids, Cambridge University Press, 1992.
  • 14. E. Busso and G. CAILLETAUD, On the selection of active slip systems in crystal plasticity, Int. J. Plast., 7, 11, 2212-2231, 2005.
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  • 16. D. PEIRCE, R. ASARO and A. NEEDLEMAN, An analysis of nonuniform and localized deformation in ductile single crystals, Acta MetalL, 30, 1087-1119, 1982.
  • 17. Y.F. DAFALIAS, Planar double-slip micromechanical model for poly crystal plasticity, J. Engineering Mechanics, 119, 1260-1284, 1993.
  • 18. A. CLEMENT, Prediction of deformation texture using a physical principle of conservation, Mat. Sc. And Engrg, 55, 203-233, 1982.
  • 19. J. BOUKADIA and F. SIDOROFF, Simple shear and torsion of a perfectly plastic single crystal infinite transformation, Arch. Mech, 40, 497-513, 1988.
  • 20. J. BOUKADIA, A. CHENAOUI and F. SIDOROFF, Simple shear in fee single crystals at large deformations, [in:] Proc. Int. Sem. MECAMAT'91 Fontainebleau (France) on Large Plastic Deformation, C. TEODOSIU, J.L. RAPHANEL & F. SIDIROFF [Eds.], Rotterdam Balkema, 109-116, 1993.
  • 21. A. CHENAOUI, F. SIDOROFF and A. Him, The texture evolution of planar poly crystal, J. Mech. Phys. Solids, 48, 2559-2584, 2000.
  • 22. A. CHENAOUI, F. SIDOROFF, M. DARRIEULAT and A. HIHI, The plane single crystal under off-axis tensile, Archives of Mechanics, 54, 3, 227-248, 2002, Warszawa.
  • 23. R.J. ASARO and A. NEEDLEMAN, Texture development and strain hardening in rate-dependent polycrystals, Acta MetalL, 33, 923-953, 1985.
  • 24. L. ANAND and M. KHOTARI, A computational procedure for rate-independent crystal plasticity, J. Mech. Phys. Solids, 44, 4, 525-558, 1996.
  • 25. E.G. BlNGHAM, Fluidity and Plasticity, McGraw-Hill, New York, 215-218, 1922.
  • 26. A.H. SHALABY and K.S. HAVNER, A general kinematical analysis of double slip, J. Mech. Phys. Solids, 26, 79-92, 1978.
  • 27. K.S. HAVNER, The kinematics of double slip with application to cubic crystals in the compression test, J. Mech. Phys. Solids, 27, 415-429, 1979.
  • 28. K.S. HAVNER, S.-C. Wu and S. FUH, On symmetric bicrystals at the yield point in (110) channel die compression, J. Mech. Phys. Solids, 42, 361-379, 1994.
  • 29. K.S. HAVNER, On velocity discontinuities in elastoplastic bicrystals in channel die compression, Int. J. of Plasticity, 14, 61-74, 1998.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT7-0014-0015
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