PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

The Voigt bound of the stress potential of isotropic viscoplastic FCC polycrystals

Autorzy
Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Konferencja
International Symposium on Developments in Plasticity and Fracture (2004 ; Kraków)
Języki publikacji
EN
Abstrakty
EN
The Voigt bound of the stress potential of face-centered cubic (fcc) polycrystals without texture is numerically determined for all types of strain rate states. The numerical findings reveal the dependence of the stress potential on both the second and the third principal invariant of the strain rate deviator. The dependence on the determinant vanishes only for a linear viscoplastic behavior. Due to the dependence of the stress potential on the third principal invariant, the determinant, the viscoplastic flow is generally nonproportional to the stress deviator. A simple analytical expression is found, which reproduces the numerical findings over the full range of strain rate sensitivities.
Rocznik
Strony
425--445
Opis fizyczny
Bibliogr. 42 poz., rys.
Twórcy
autor
Bibliografia
  • 1. J. Berntsen and T. Espelid, An adaptive algorithm for the approximate calculation of multiple integrals, ACM Transactions on Mathematical Software, 17, 4, 437–451, 1991.
  • 2. J. Berntsen and T. Espelid An adaptive multidimensional integration routine for a vector of integrals, ACM Transactions on Mathematical Software, 17, 4, 452–456, 1991.
  • 3. J. Bishop, R. Hill, A theoretical derivation of the plastic properties pf a polycrystalline face-centred metal, Phil. Mag., 42, 414, 1298–1307, 1951.
  • 4. T. Böhlke, A. Bertram, Crystallographic texture induced anisotropy in copper: An approach based on a tensorial Fourier expansion of the codf, J. Phys. IV, 105, 167–174, 2003.
  • 5. T. Böhlke, A. Bertram, E. Krempl, Modeling of deformation induced anisotropy in free-end torsion, Int. J. Plast., 19, 1867–1884, 2003.
  • 6. H.-J. Bunge, Zur Darstellung allgemeiner Texturen, Z. Metallkde, 56, 872–874, 1965.
  • 7. E. Davies, The Bailey flow rule and associated yield surface, Trans. ASME, E28, 2, 310, 1961.
  • 8. G. deBotton, P. Castañeda, Variational estimates for the creep behavior of polycrystals, Proc. R. Soc. Lond., A448, 121–142, 1994.
  • 9. R. Dendievel, G. Bonnet, J. Willies, Bounds for the creep behavior of polycrystalline materials, [in:] G. Dvorak [Ed.], IUTAM Symposium: Inelastic Deformations of Composite Materials, 175–192, Springer-Verlag, New-York 1991.
  • 10. P. Etingof, B. Adams, Representation of polycrystalline microstructure by n-point correlation tensors, Textures and Microstructures, 21, 17–37, 1993.
  • 11. W. Gambin, Plasticity and Textures. Kluwer Academic Publishers 2001.
  • 12. I. Gel’fand, R. Minlos, Z. Shapiro, Representations of the Rotation and Lorentz Groups and their Applications, Pergamon Press, Oxford 1963.
  • 13. J. Guest, On the strength of ductile materials under combined stress, Phil. Mag., 50, 69–132, 1900.
  • 14. Z. Hashin, S. Shtrikman, A variational approach to the theory of the elastic behavior of polycrystals, J. Mech. Phys. Solids, 10, 343–352, 1962.
  • 15. H. Hencky, Zur Theorie plastischer Deformationen und der hierdurch im Material hervorgerufenen Nachspannungen, ZAMM, 4, 323–334, 1924.
  • 16. A. Hershey, The plasticity of an isotropic aggregate of anisotropic face-centered cubic crystals, J. Appl. Mech., 3, 241–249, 1954.
  • 17. R. Hill, A theory of yielding and plastic f low of anisotropic materials, Proc. Phys. Soc. Lond., A 193, 281–297, 1948.
  • 18. M. Huber, Specific work of strain as a measure of material effort, Czas. Techn., 22, 34–40, 49–50, 61–62, 80–81, 1904,
  • 19. J. Hutchinson, Bounds and self-consistent estimates for creep of polycrystalline materials, Proc. R. Soc. Lon., A 348, 101–127, 1976.
  • 20. A. Karafillis, M. Boyce A general anisotropic yield criterion using bounds and a transformation weighting tensor, J. Mech. Phys. Solids, 41, 12, 1859–1886, 1993.
  • 21. U. Kocks, H. Mecking, Physics and phenomenology of strain hardening: The FCC case. Progr. Mat. Sci., 48, 171–273, 2003.
  • 22. A. Mendelson, Plasticity: theory and apllication, Collier-MacMillan, London 1968.
  • 23. R. Mises, Mechanik der festen Körper im plastisch deformablen Zustand, Göttingen Nachrichten, Math. Phys., 4, 1, 582–592, 1913.
  • 24. R. Mises, Mechanik der plastischen Formänderung bei Kristallen, Z. Angew. Math. Mech., 8, 3, 161–185, 1928.
  • 25. M. Nebozhyn, P. Gilormini P. Castañeda, Variational self-consistent estimates for cubic viscoplastic polycrystals: the effect of grain anisotropy and shape, J. Mech. Phys. Solids, 49, 313–340, 2001.
  • 26. S. Nemat-Nasser, M. Hori, Micromechanics: Overall properties of heterogeneous materials, Elsevier, 2 ed., 1999.
  • 27. P. Ponte Castañeda, The effective mechanical properties of nonlinear isotropic composites, J. Mech. Phys. Solids, 39, 45–71, 1991.
  • 28. P. Ponte Castañeda, New variational principles in plasticity and their application to composite materials, J. Mech. Phys. Solids, 40, 8, 1757–1788, 1992.
  • 29. P. Ponte Castañeda, M. Nebozhyn, Variational estimates of the self-consistent type for some model nonlinear polycrystals Proc. R. Soc. Lond., A 453, 2715–2724, 1997.
  • 30. P. Ponte Castañeda, P. Suquet, Nonlinear composites, Advances in Applied Mechanics, 34, 171–302, 1998.
  • 31. A. Reuss, Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle, Z. Angew. Math. Mech., 9, 49–58, 1929.
  • 32. R. Roe, Description of crystalline orientation of polycrystalline materials. III. General solution to pole f igure inversion, J. Appl. Phys., 36, 2024–2031, 1965.
  • 33. G. Sachs, Zur Ableitung einer Fließbedingung, Z. Verein Dt. Ing., 72, 734–736, 1928.
  • 34. R. Schmidt, Über den Zusammenhang von Spannungen und Formänderungen im Verfestigungsgebiet. Ing.-Arch., 3, 215–235, 1932.
  • 35. D. Shanno, K. Phua, Minimization of unconstrained multivariate functions, algorithm 500, ACM Transactions on Mathematical Software, 6, 618–622, 1980.
  • 36. G. Taylor, Plastic strain in metals, J. Inst. Metals, 62, 307–324, 1938,
  • 37. S. Torquato, Random heterogeneous materials: microstructures and macroscopic properties, Springer 2002.
  • 38. H. Tresca, Mémoire sur l’écoulement des corps solides, Mémoirs Par Divers Savants., 18, 733, 1968, 20, 75–135, 1972.
  • 39. W. Voigt, Über die Beziehung zwischen den beiden Elastizitätskonstanten isotroper Körper, Wied. Ann., 38, 573–587, 1889.
  • 40. J. Willis, The structure of overall constitutive relations of nonlinear composites, IMA Journal of Applied Mathematics, 43, 231–242, 1989.
  • 41. J. Willis, Upper and lower bounds for nonlinear composite behavior, Mater. Sci. Engng., A 175, 7–14, 1994.
  • 42. Q.-S. Zheng, 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.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT4-0004-0020
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.