Effective dislocation lines in continuously dislocated crystals. I. Material anholonomity

• Autorzy: Trzęsowski A.
• Języki publikacji: EN

Abstrakty

EN

A continuous geometric description of Bravais monocrystals with many dislocations and secondary point defects created by the distribution of these dislocations is proposed. Namely, it is distinguished, basing oneself on Kondo and Kröner's Gedanken Experiments for dislocated bodies, an anholonomic triad of linearly independent vector fields. The triad defines local crystallographic directions of the defective crystal as well as a continuous counterpart of the Burgers vector for single dislocations. Next, the influence of secondary point defects on the distribution of many dislocations is modeled by treating these local crystallographic directions, as well as Burgers circuits, as those located in such a Riemannian material space that becomes an Euclidean 3-manifold when dislocations are absent. Some consequences of this approach are discussed.

Słowa kluczowe

EN

crystal structure; crystal surface; Bravais moving frame; dislocation density; Riemannian space; Burgers vector; self-balance equations; continously dislocated crystals; material anholonomity

PL

struktura krystaliczna; gęstość dyslokacji; przestrzeń Riemanna; wektor Burgersa

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Journal of Technical Physics
• Rocznik: 2007
• Tom: Vol. 48, no 3-4
• Strony: 193--214
• Opis fizyczny: Bibliogr. 31 poz.

Twórcy

autor

Trzęsowski A.

• Institute of Fundamental Technological Research, Polish Academy of Sciences, Świętokrzyska 21, 00-049 Warszawa, Poland,

Bibliografia

• 1. J. CHRISTIAN, Transformation in metals and alloys, Part I, Pergamon Press, Oxford 1975.
• 2. A. TRZĘSOWSKI, Geometrical and physical gauging in the theory of dislocations, Rep. Math. Phys., 32, 71-98, 1993.
• 3. E. KRÖNER, The continuized crystal - a bridge between micro- and macromechanics?, ZAMM, 66, T284-T292, 1986.
• 4. B.A. BILBY, R. BULLOUGH, R.L. GARDNER, E. SMITH, Continuous distributions of dislocations, IV. Single glide and plane strain, Proc. Roy. Soc., 244, 538-557, 1958.
• 5. LA. ODING, The theory of dislocations in metals [in Polish], PWT, Warsaw 1961.
• 6. E. KRÖNER, The differential geometry of elementary point and line defects in Bravais crystals, Int. J. Theor. Phys., 29, 1219-1237, 1990.
• 7. E. KRÖNER, Dislocations in crystals and in continua: a confrontation, Int. J. Eng. Sci., 33, 2127-2135, 1995.
• 8. A. TRZĘSOWSKI, J.J. SLAWIANOWSKI, Global invariance and Lie-algebraic description in the theory of dislocations, Int. J. Theor. Phys., 29, 1239-1249, 1990.
• 9. J.A. SCHOUTEN, Ricci-Calculus, Springer-Verlag, Berlin 1954.
• 10. K. YANO, The theory of Lie derivatives and its applications, North-Holland, Amsterdam 1958.
• 11. D. HULL, D.J. BACON, Introduction to Dislocations, Pergamon Press, Oxford 1984.
• 12. R. DE WITT, Theory of disclinations. II. Continuous and discrete disclinations in anisotropic elasticity, J. Res. National Bureau of Standarts, 77A, 49-100, 1973.
• 13. A. TRZĘSOWSKI, Dislocations and internal length measurement. I. Riemannian material space, Int. J. Theor. Phys., 33, 931-950, 1994.
• 14. A. TRZĘSOWSKI, On the geometric origin of Orowan-type kinematic relations and the Schmid yield criterion, Acta Mechanika, 141, 173-192, 2000.
• 15. A. TRZĘSOWSKI, Self-balnce equations and Bianchi-type Distortions in the theory of dislocations, Int. J. Theor. Phys., 42, 711-723, 2003.
• 16. A. TRZĘSOWSKI, Congruences of dislocations in continuously dislocated crystals, Int. J. Theor. Phys., 40, 125-151, 2001.
• 17. C. VON WESTENHOLTZ, Differential forms in mathematical physics, North-Holland, Amsterdam 1972.
• 18. E. KRONER, Differential geometry of defects in condensed systems of particles with only translational mobility, Int. J. Eng. Sci., 19, 1507-1515, 1981.
• 19. A.O. BARUT, R. RĄCZKA, Theory of group representations and applications, PWN, Warsaw 1977.
• 20. Y. CHOQUET-BRUCHAT, C. DE WITT-MORETTE, C. DILLARD-BLEICK, Analysis, manifolds and physics, North-Holland, Amsterdam 1977.
• 21. K. KONDO, Non-Riemannian geometry of imperfected crystals from a macroscopic view point, RAAG Memoirs 1, 6-17, 1955.
• 22. A. FRIEDMAN, Isometric embedding of Riemannian manifolds into Euclidean spaces, Rev. Mod. Phys, 37, 201-203, 1965.
• 23. R. SIKORSKI, Introduction to differential geometry [in Polish], PWN, Warsaw 1972.
• 24. L.P. EISENHART, Riemannian geometry, Princeton University Press, Princeton 1949.
• 25. M. IKEDA, Y. NISHIMO, On groups of scalar-preserving isometries in Riemannian spaces, Tensor N. S., 27, 295-305, 1973.
• 26. A. TRZĘSOWSKI, Kinematics of edge dislocations, Int. J. Theor. Phys., 36, 2877-2911, 1997.
• 27. A. TRZĘSOWSKI, Geometry of crystal structure with defects. I. Euclidean picture, Int. J. Theor. Phys., 26, 311-333, 1987.
• 28. W.E. PANIN, W.A. LIHATCHEV, J.W. GRINAEV, Structural levels of deformations in solids [in Russian], Nauka, Novosibirsk 1958.
• 29. A.H. COTTRELL, The mechanical properties of matter, Willey, New York 1964.
• 30. F. SIDOROFF, On the formulation of plasticity and viscoplasticity with internal variables, Arch, of Mech., 27, 807-819, 1975.
• 31. K.C. VALANIS, The concept of physical metric in thermodynamics, Acta Mechanica, 113, 169-184, 1995.