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Tytuł artykułu

Effective dislocation lines in continuously dislocated crystals. II. Congruences of effective dislocations

Autorzy
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The notion of a congruence of effective dislocation lines endowed with the nonvanishing local Burgers vector is introduced. Particularly, the class of congrunces of principal Volterra-type effective dislocation lines associated with the dislocation densities (tensorial as well as scalar) is distinguished in order to investigate the geometry of continuized defective crystals in terms of these densities. It is shown that effective dislocation lines can be endowed with the dislocation line tension and with a finite self-energy.
Rocznik
Strony
53--74
Opis fizyczny
Bibliogr. 25 poz.
Twórcy
  • Institute of Fundamental Technological Research, Polish Academy of Sciences, Świętokrzyska 21, 00-049 Warszawa, Poland, atrzes@ippt.gov.pl
Bibliografia
  • 1. F.C. FRANK, J.W. STEEDS, Crystal dislocations, [in:] The physics of metals 2, Defects, P.B. Hirsh [Ed.], Cambridge University Press, London 1975.
  • 2. D. HULL, D.J. BACON, Introduction to dislocations, Pergamon Press, Oxford 1984.
  • 3. J.B. FRIDMAN, Mechanical properties of metals [in Russian], vol. I, Mashinostroenie, Moscov 1974.
  • 4. B.A. BILBY, R. BULLOUGH, L.R. GARDNER, E. SMITH, Conntinuous distributions of dislocations IV. Single glide and plane strain, Proc. Roy. Soc., 244, 538-557, 1958.
  • 5. A. TRZĘSOWSKI, Effective dislocation lines in continuously dislocated crystals. I. Material anholonomity, J. Tech. Phys., 48, 3-4, 193-214, 2007.
  • 6. A. TRZĘSOWSKI, Dislocations and internal length measurement in continuized crystals. I. Riemannian material space, Int. J. Theor. Phys., 33, 931-966, 1994.
  • 7. A. TRZĘSOWSKI, On the geometric origin of Orowan-type kinematic relations and the Schmid yield criterion, Acta Mechanica, 141, 173-192, 2000.
  • 8. I. A. ODING, The theory of dislocations in metals [in Polish], PWT, Warsaw 1961.
  • 9. A. FRIEDMAN, Isometric embedding of Riemannian manifolds into Euclidean spaces, Rev. Mod. Phys., 37, 201-203, 1965.
  • 10. P.E. EISENHART, Riemannian geometry, Princeton University Press, Princeton 1964.
  • 11. A. TRZĘSOWSKI, Geometrical and physical gauging in the theory of dislocations, Rep. Math. Phys. 32, 71-98, 1993.
  • 12. K. YANO, The theory of Lie derivatives and its applications, North-Holland, Amsterdam 1958.
  • 13. N.J. HICKS, Notes on Differential Geometry, Van Nostrand, Toronto 1965.
  • 14. C. VON WESTENHOLZ, Differential forms in mathematical physics, North-Holland, Amsterdam 1972.
  • 15. R.. DE WITT, Theory of disclinations. II. Continuous and discrete disclinations in anisotropic elasticity, J. Res. National Bureau of Standarts, 77A, 49-100, 1973.
  • 16. E. KRONER, Differential geometry of defects in condensed systems of particles with only translational mobility, Int. J. Engng Sci., 19, 1507-1515, 1981.
  • 17. A. TRZĘSOWSKI, Congruences of Dislocations in Continuously Dislocated Crystals, Int. J. Theor. Phys., 40, 727-753, 2001.
  • 18. A. TRZĘSOWSKI, Self-balance equations and Bianchi-type distortions in the theory of dislocations, Int. J. Theor. Phys., 42, 711-723, 2003.
  • 19. R. SIKORSKI, Introduction to differential geometry [in Polish], PWN, Warsaw 1972.
  • 20. J.A. SCHOUTEN, Ricci-Calculus, Springer-Verlag, Berlin 1954.
  • 21. J. GONCARZEWICZ, Differential geometry [in Polish], PWN, Warsaw 1987.
  • 22. M. SKWARCZYŃSKI, Geometry of Riemannian manifolds [in Polish], PWN, Warsaw 1993.
  • 23. Y. CHOQUET-BRUCHAT, C. DE WITT-MORETTE, M. DILLARD-BLEIK, Analysis, Manifolds and Physics, North-Holland, Amsterdam 1977.
  • 24. S. GOŁĄB, Tensor Calculus [in Polish], PWN, Warsaw 1966.
  • 25. D. LAUGWITZ, Differential and Riemannian Geometry, Academic Press, New York 1965.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0028-0004
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