The role of strain gradients in the grain size effect for polycrystals

Journal of the Mechanics and Physics of Solids

Volumn 44, Issue 4, 1996, Pages 465-495

  Smyshlyaev, V P ^a,b   Fleck, N A ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b UNIVERSITY OF BATH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

GRAIN SIZE AND SHAPE; GREEN'S FUNCTION; MATHEMATICAL OPERATORS; SINGLE CRYSTALS; STRAIN; VARIATIONAL TECHNIQUES;

CONSTITUTIVE LAW; FACE CENTERED CUBIC POLYCRYSTALS; HASHIN-SHTRIKMAN BONDING METHODOLOGY; STRAIN ENERGY DENSITY; STRAIN GRADIENTS;

POLYCRYSTALS;

EID: 0030128870     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/0022-5096(96)00009-9     Document Type: Article

References (25)

1. Ashby, M. F. (1970) The deformation of plastically non-homogeneous materials. Philosophic Magazine, 21, 399-424.
2. deBotton, G. and Ponte Castañeda, P. (1995) Variational estimates for creep behaviour of polycrystals. Proc. R. Soc. Lond. A 448, 121-142.
3. Dendievel, R., Bonnet, G. and Willis, J. R. (1991) Bounds for the creep behaviour of polycrystalline materials. In Inelastic Deformation of Composite Materials (ed. G. J. Dvorak), pp. 175-192. Springer-Verlag, New York.
4. Fleck, N. A., Muller, G. M., Ashby, M. F. and Hutchinson, J. W. (1994) Strain gradient plasticity: theory and experiment. Acta Metall. Mater. 42, 475-487.
5. Fleck, N. A. and Hutchinson, J. W. (1996) Strain gradient plasticity, In: Advances in Applied Mechanics, Vol. 33 (to appear).
6. Hall, E. O. (1951) The deformation and aging of mild steel. Proc. Phys. Soc. B64, 747-753.
7. Hashin, Z. and Shtrikman, S. (1962a) On some variational principles in anisotropic and inhomogeneous elasticity. J. Mech. Phys. Solids 10, 335-342.
8. Hashin, Z. and Shtrikman, S. (1962b) A variational approach to the theory of the elastic behaviour of polycrystals. J. Mech. Phys. Solids 10, 343-352.
9. Hutchinson, J. W. (1976) Bounds and self-consistent estimates for creep of polycrystalline materials. Proc. R. Soc. Lond. A348, 101-127.
10. Mindlin, R. D. (1964) Micro-structure in linear elasticity. Arch. Rat. Mech. Anal. 16, 51-78.
11. Mindlin, R. D. (1965) Second gradient of strain and surface tension in linear elasticity. Int. J. Solids Structures 1, 417-438.
12. Petch, N. J. (1953) The cleavage strength of polycrystals. J. Iron Steel Inst. London 174, 25-28.
13. Ponte Castañeda, P. (1991) The effective mechanical properties of nonlinear isotropic composites. J. Mech. Phys. Solids 39, 45-71.
14. Ponte Castañeda, P. (1992) New variational principles in plasticity and their application to composite materials. J. Mech. Phys. Solids 40, 1757-1788.
15. Smyshlyaev, V. P. and Fleck, N. A. (1994) Bounds and estimates for linear composites with strain gradient effects. J. Mech. Phys. Solids 42, 1851-1882.
16. Smyshlyaev, V. P. and Fleck, N. A. (1995) Bounds and estimates for the overall plastic behaviour of composites with strain gradient effects. Proc. R. Soc. Lond. A 451, 795-810.
17. Talbot, D. R. S. and Willis, J. R. (1982) Variational estimates for dispersion and attenuation of waves in random composites - II. Isotropic composites. Int. J. Solids Structures 18, 685-698.
18. Talbot, D. R. S. and Willis, J. R. (1985) Variational principles for inhomogeneous non-linear media. IMA J. Appl. Math. 35, 39-54.
19. Toupin, R. A. (1962) Elastic materials with couple-stresses. Arch. Rat. Mech. Anal. 11, 385-414.
20. Walpole, L. J. (1981) Elastic behaviour of composite materials. In Advances in Applied Mechanics, Vol. 21 (ed. C. S. Yih), pp. 169-242. Academic Press, New York.
21. Willis, J. R. (1977) Bounds and self-consistent estimates for the overall moduli of anisotropic composites. J. Mech. Phys. Solids 25, 185-202.
22. Willis, J. R. (1981) Variational and related methods for the overall properties of composites. In Advances in Applied Mechanics, Vol. 21 (ed. C.-S. Yih), pp. 1-78. Academic Press, New York.
23. Willis, J. R. (1983) The overall elastic response of composite materials. J. Appl. Mech. 50, 1202-1209.
24. Willis, J. R. (1986) Variational estimates for the overall response of an inhomogeneous non-linear dielectric. In Homogenization and Effective Properties of Materials and Media (ed. J. L. Ericksen, D. Kinderlehrer, R. Kohn and J. L. Lions), pp. 245-263. Springer-Verlag, New York.
25. Willis, J. R. (1991) On methods for bounding the overall properties of nonlinear composites. J. Mech. Phys. Solids 39, 73-86.