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Effective dislocation lines in continuously dislocated crystals. III. Kinematics

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Języki publikacji
EN
Abstrakty
EN
A class of congrunces of principal Volterra-type effective dislocation lines associated with a dislocation density tensor is distinguished in order to investigate the kinematics of continuized defective crystals in terms of their dislocation densities (tensorial as well as scalar). Moreover, it is shown, basing oneself on a formula defining the mean curvature of glide surfaces for principal edge effective dislocation lines, that the considered kinematics of continuized defective crystals is consistent with some relations appearing in the physical theory of plasticity (e.g. with the Orowan-type kinematic relations and with treatment of the shear stresses as driving stresses of moving dislocations).
Rocznik
Strony
79--99
Opis fizyczny
Bibliogr. 27 poz.
Twórcy
  • Institute of Fundamental Technological Research, Polish Academy of Sciences, Świętokrzyska 21, 00-049 Warszawa, Poland, atrzes@ippt.gov.pl
Bibliografia
  • 1. A. TRZĘSOWSKI, Effective dislocation lines in continuously dislocated crystals, I. Material anholonomity, J. Tech. Phys., 48, 193-214, 2007.
  • 2. A. TRZĘSOWSKI, Geometrical and physical gauging in the theory of dislocations, Rep. Math. Phys., 32, 71-98, 1993.
  • 3. W. YANG, W.B. LEE, Mesoplasticity and its applications, Springer, Berlin 1993.
  • 4. D. HULL, D.J. BACON, Introduction to dislocations, Pergamon Press, Oxford 1984.
  • 5. A.TRZĘSOWSKI, Congruences of Dislocations in Continuously Dislocated Crystals, Int. J. Theor. Phys., 40, 727-753, 2001.
  • 6. A. TRZĘSOWSKI, Effective dislocation lines in continuously dislocated crystals. II. Congruences of effective dislocations, J. Tech. Phys., 49, 53-74, 2008.
  • 7. A. TRZĘSOWSKI, On the geometric origin of Orowan-type kinematic relations and the Schmid yield criterion, Acta Mechanica, 141, 173-192, 2000.
  • 8. A. TRZĘSOWSKI, Dislocations and internal length measurement in continuized crystals. I. Riemannian material space, Int. J. Theor. Phys., 33, 931-966, 1994.
  • 9. A.N. ORLOV, Introduction to the theory of defects in crystals [in Russian], Vysšaja Scola, Moscov 1983.
  • 10. LA. ODING, The theory of dislocations in metals [in Polish), PWT, Warsaw 1961.
  • 11. K. YANO, The theory of Lie derivatives and its applications, North-Holland, Amsterdam 1958.
  • 12. C. von Westenholz, Differential forms in mathematical physics, North-Holland, Amsterdam 1972.
  • 13. R. SIKORSKI, Introduction to differential geometry [in Polish], PWN, Warsaw 1972.
  • 14. Y. CHOQUET-BRUCHAT, C. DE WITT-MORETTE, M. DILLARD-BLEIK, Analysis, Manifolds and Physics, North-Holland, Amsterdam 1977.
  • 15. H. HASIMOTO, A soliton on vortex filament, J. Fluid Mech., 51, 477-485, 1972.
  • 16. G.L. LAMB, Elements of soliton theory, J. Willey, New York 1980.
  • 17. E. KRÖNER, Dislocations in crystals and in continua: a confrontation, Int. J. Engng Sci., 33, 2127-2135, 1995.
  • 18. J.E. MARSDEN, T.J.R HUGHES, Topics in the mathematical foundations of elasticity. In: “Non linear analysis and mechanics”, vol. 2, R.J. Knops [Ed.] Pitman, London 1978.
  • 19. W. GAMBIN, R. RYCHLEWSKI, Spatial plastic flows with a family of instantaneously inextensible planes, Archives of Mechanics, 23, 765-787, 1971.
  • 20. A. TRZĘSOWSKI, Kinematics of Edge Dislocations, Int. J. Theor. Phys., 36, 2877-2911, 1997.
  • 21. N.S. SINUKOV, Geodetic mappings of Riemannian spaces [in Russian], “Nauka” (Science), Moscov 1979.
  • 22. P.E. EISENHART, Riemannian geometry, Princeton University Press, Princeton 1964.
  • 23. B.A. BILBY, R. BULLOUGH, L.R. GARDNER, E. SMITH, Continuous distributions of dislocations. IV. Single glide and plane strain, Proc. Roy. Soc., 244, 538-557, 1958.
  • 24. A. TRZĘSOWSKI, Geometry of crystal structure with defects. I. Euclidean picture, Int. J. Theor. Phys., 26, 311-333, 1987.
  • 25. W.E. PANIN, W.A. LIHATCHEV, J.W. GRINAEV, Structural levels of deformations in solids [in Russian], “Nauka”, Novosibirsk 1958.
  • 26. P. PERZYNA, Thermodynamics of inelastic materials [in Polish], PWN, Warsaw 1978.
  • 27. A. GREEN, W. ZERNA, Theoretical elasticity, Clarendon Press, Oxford 1960.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0033-0029
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