Thermodynamics of orientation discontinuity surface : small misorientation approach

• Autorzy: Dłużewski P. , Maciejewski G.
• Języki publikacji: EN

Abstrakty

EN

The thermodynamics of a crystal lattice reorientation process proceeding on low angle grain boundary is presented. In material science, the influence of lattice misorientation on the grain boundary energy is well established. On the other hand, in thermodynamics of discontinuity surface the influence of misorientation vector on the surface energy is usually ignored as yet. Therefore, in the present paper, attention is focused on this influence. To obtain the driving forces conjugate to relative grain reorientation, the continuum theory of dislocations has been applied. Starting from the energy balance law and assuming that the free energy of discontinuity surface depends strongly on the jump in crystal orientation field, the mathematical relations for the misorientation vector and the conjugated thermodynamic force are derived. The mentioned force contributes to the total driving force governing the grain boundary migration process. The problem of constitutive modelling of the surface motion is considered. The main result of this analysis is the incorporation of grain orientation jump into the thermodynamic description of driving forces of the grain reorientation process.

Słowa kluczowe

EN

continuum theory of dislocations; misorientation; discontinuity of crystal surface

PL

teoria dyslokacji ośrodków ciągłych; kąt wzajemnej orientacji; nieciągłość powierzchni kryształu

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2001
• Tom: Vol. 53, nr 2
• Strony: 105--122
• Opis fizyczny: Bibliogr. 31 poz.

Twórcy

autor

Dłużewski P.

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

autor

Maciejewski G.

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

Bibliografia

• 1. R. ABREYARATNE and J. KNOWLES, On the driving traction acting on a surface of strain discontinuity in a continuum, J. Mech. and Phys. of Solids, 38, 3, 345-360, 1990.
• 2. P. CERMELLI and S. SELLERS, On the nonlinear mechanics of Bravais crystals with continuous distributions of defects, Mathematics and Mechanics of Solids, 3, 3, 331-358, 1998.
• 3. P. CERMELLI and S. SELLERS, Multi-phase equilibrium of crystalline solids, J. Mech. And Phys. of Solids, 48, 4, 765-796, 2000.
• 4. G. A. CHADWICK and D. A. SMITH, Grain boundary structure and properties, Academic Press, 1976.
• 5. C. DAVINI, A proposal for a continuum theory of defective crystals, Archive for Rational Mechanics and Analysis, 96, 295-317, 1986.
• 6. R. DE WITT, A view of the relation between the continuum theory of lattice defects and non-Euclidean geometry in the linear approximation, Int. J. of Engng. Sci., 19, 12, 1475-1506, 1981.
• 7. P. DLUŻEWSKI, Continuum theory of dislocations as a theory of constitutive modelling of finite elastic-plastic deformations, Habilitations Thesis. IFTR Reports 13/1996, Warsaw 1996.
• 8. P. DLUŻEWSKI, On geometry and continuum thermodynamics of structural defect movement, Mech. of Mat., 22, 23-41, 1996.
• 9. A. C. ERINGEN and C. B. KAFADAR, Polar field theories, [In.] A. C. ERINGEN [Ed.], Continuum Physics, 4, 1-73, Academic Press, New York 1976.
• 10. J. D. ESHELBY, The force on an elastic singularity, Philosophical Trans. of the Roy. Soc. of London, A244, 87, 112, 1951.
• 11. J. D. ESHELBY, Energy relations and the energy-momentum tensor in continuum mechanics, [In:] M. F. KANNINEN, W. F. ADLER, A. R. ROSENFIELD and R. I. JAFFEE [Eds.], Inelastic Behavior of Solids, 77-114, McGraw-Hill, New York 1970.
• 12. N. Fox, A dislocation theory for oriented media, [In:] M. F. KANNINEN, W. F. ADLER, A. R. ROSENFIELD and R. I. JAFFEEE [Eds.], Inelastic Behavior of Solids, 349-377, McGraw-Hill, New York 1970.
• 13. N. A. GJOSTEIN, Short circuit diffusion, [In.] Diffusion, Metals Park, Ohio 1973.
• 14. M. GRABSKI, Structure of grain boundaries in metals [in Polish], BFM Śląsk, Katowice 1969.
• 15. M. E. GURTIN, The nature of configurational forces, Archive for Rational Mechanics and Analysis, 131, 1-66, 1995.
• 16. M. KLÉMAN, Dislocation, disclinations and magnetisms, [In:] F. R. N. NABARRO [Ed.], Dislocations in solids, 5, 349, North-Hollands 1980.
• 17. W. KOSIŃSKI, Field singularities and wave propagation analysis in continuum mechanics, PWN, Warsaw 1986.
• 18. E. KOSSECKA and R. de WITT, Disclination kinematics, Arch. Mech., 29, 5, 633-651, 1977.
• 19. E. KRÖNER, Continuum theory of defects, [In:] J. P. BALIAN, M. KLEMAN [Eds.], Physics if Defects, 215-315, Nord-Holland, Amsterdam 1981.
• 20. D. KUHLMANN-WILSDORF, Theory of plastic deformation - properties of low energy dislocation, Mat. Sci. and Engng., A113, 1-41, 1989.
• 21. K. C. LE and H. STUMPF, nonlinear continuum theory of dislocations, Int. J. of Engng. Sci., 57, 3, 255-280, 1974.
• 22. G. P. MOECKEL, Thermodynamics of an interface, Archive for Rational Mechanics and Analysis, 57, 3, 255-280, 1974.
• 23. T. MURA, Method of continuously distributed dislocations, [In:] T. MURA [Ed.], Mathematical Theory of Dislocations, The American Society of Mechanical Engineers, 25-48, New York 1969.
• 24. P. M. NAGHDI and A. R. SRINIVASA, Characterisation of dislocations and their influence on plastic deformation in single crystals, Int. J. of Engng. Sci., 32, 7, 1157-1182, 1994.
• 25. J. F. NYE, Some geometrical relations for dislocated crystals, Acta Metall., 1, 153-162, 1953.
• 26. M. O. PEACH and J. S. KOEHLER, The forces exerted on dislocations and the stress fields produced by them, Phys. Rev., 80, 436, 1950.
• 27. R. C. POND, Line defects in interfaces, [In.] F. R. N. NABARRO [Ed.], Dislocations in solifs, 8, 1-67, North-Holland 1989.
• 28. S. SUN, B. I. ADAMS and W. E. KING, Observations of lattice curvature near the interface of a deformed aluminium bicrystal, Philosophical Magazine A, 80, 1, 9-25, 2000.
• 29. C. TEODOSIU, A dynamic theory of dislocations and its applications to the theory of the elastic plastic continuum, [In.] A. SIMMONDS [Ed.], Fundamental Aspects of Dislocation Theory, Nat. Bur. Stand. Spec. Publ., 317, 2, 1-36, 1970.
• 30. G. ZANZOTTO, On the material symetry group of elastic crystal and the Born rule, Archive for Rational Mechanics and Analysis, 121, 1, 1-36, 1992.
• 31. H. ZORSKI, Force on a defect in nonlinear elastic medium, Int. J. of Engng. Sci., 19, 1573, 1980.