Scale effects induced by strain-gradient plasticity and interfacial resistance in periodic and randomly heterogeneous media

Mechanics of Materials

Volumn 38, Issue 8-10, 2006, Pages 702-716

  Aifantis, K E ^a   Willis, J R ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Hall Petch effect; Random medium; Strain gradient plasticity; Three point bound; Two point bound; Variational principle

Indexed keywords

APPROXIMATION THEORY; INTERFACES (MATERIALS); INTERFACIAL ENERGY; MICROSTRUCTURE; PHASE TRANSITIONS; PLASTICITY; POISSON DISTRIBUTION; RANDOM PROCESSES; STATISTICAL METHODS; STRAIN; STRESSES; VARIATIONAL TECHNIQUES;

HALL-PETCH EFFECTS; RANDOM MEDIUM; STRAIN-GRADIENT PLASTICITY; THREE-POINT BOUNDS; TWO-POINT BOUNDS; VARIATIONAL PRINCIPLES;

SURFACE CHEMISTRY;

EID: 33646369639     PISSN: 01676636     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mechmat.2005.06.010     Document Type: Article

References (19)

1. Aifantis E.C. On the microstructural origin of certain inelastic models. Trans. ASME, J. Engng. Mat. Tech. 106 (1984) 326-330
2. Aifantis E.C. The physics of plastic deformation. Int. J. Plasticity 3 (1987) 211-247
3. Aifantis, K.E., Willis, J.R., 2004. Interfacial jump conditions in strain-gradient plasticity and relations of Hall-Petch type. In: Kounadis, A., Providakis, C., Exadaktylos, G. (Eds.), Proceedings of the Seventh National Congress on Mechanics, vol. II, Chania, Greece, June 24-26, 2004, pp. 372-377.
4. Aifantis K.E., and Willis J.R. The role of interfaces in enhancing the yield strength of composites and polycrystals. J. Mech. Phys. Solids 53 (2005) 1505-1522
5. Fleck N.A., and Hutchinson J.W. A phenomenological theory for strain gradient plasticity. J. Mech. Phys. Solids 41 (1993) 1825-1857
6. Fleck N.A., and Hutchinson J.W. A reformulation of strain gradient plasticity. J. Mech. Phys. Solids 49 (2001) 2245-2272
7. Fleck N.A., and Willis J.R. Bounds and estimates for the effect of strain gradients upon the effective plastic properties of an isotropic two phase composite. J. Mech. Phys. Solids 52 (2004) 1855-1888
8. Fleck N.A., Muller G.M., Ashby M.F., and Hutchinson J.W. Strain gradient plasticity: theory and experiment. Acta Metall. Mater. 42 (1994) 475-487
9. Gao H., Huang Y., Nix W.D., and Hutchinson J.W. Mechanism based strain gradient plasticity-I. Theory. J. Mech. Phys. Solids 47 (1999) 1239-1263
10. Gudmundson P. A unified treatment of strain gradient plasticity. J. Mech. Phys. Solids 52 (2004) 1379-1406
11. Gurtin M.E. On the plasticity of single crystals: free energy, microforces, plastic-strain gradient. J. Mech. Phys. Solids 48 (2000) 989-1036
12. Gurtin M.E. A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations. J. Mech. Phys. Solids 50 (2002) 5-32
13. Karlin S., and Taylor H.M. A First Course in Stochastic Processes (1975), Academic Press, New York
14. Lax M. Multiple scattering of waves. II. The effective field in dense systems. Phys. Rev. 85 (1952) 621-629
15. Miller M.N. Bounds for effective electrical, thermal, and magnetic properties of heterogeneous materials. J. Math. Phys. 10 (1969) 1988-2004
16. Ponte Castañeda P. The effective mechanical properties of nonlinear isotropic composites. J. Mech. Phys. Solids 39 (1991) 45-71
17. Smyshlyaev V.P., and Fleck N.A. Bounds and estimates for the overall plastic behaviour of composites with strain gradient effects. Proc. R. Soc. A 451 (1995) 795-810
18. Smyshlyaev V.P., and Fleck N.A. The role of strain gradients in the grain size effect for polycrystals. J. Mech. Phys. Solids 44 (1996) 465-495
19. Torquato S. Random Heterogeneous Materials (2002), Springer-Verlag, New York