Solids containing spherical nano-inclusions with interface stresses: Effective properties and thermal-mechanical connections

International Journal of Solids and Structures

Volumn 44, Issue 3-4, 2007, Pages 941-955

  Chen, Tungyang ^a   Dvorak, G J ^b   Yu, C C ^a  

^a NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

^b RENSSELAER POLYTECHNIC INSTITUTE   (United States)

Author keywords

Composites; Effective properties; Surface stress; Thermo mechanical connections

Indexed keywords

DIFFERENTIAL EQUATIONS; INCLUSIONS; PHASE TRANSITIONS; SURFACE PROPERTIES; THERMAL EFFECTS; THERMAL EXPANSION;

EFFECTIVE PROPERTIES; SURFACE STRESS; THERMO-MECHANICAL CONNECTIONS;

NANOSTRUCTURED MATERIALS;

EID: 33751007829     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2006.05.030     Document Type: Article

References (33)

1. Benveniste Y. A new approach to the application of Mori-Tanaka's theory in composite materials. Mech. Mater. 6 (1987) 147-157
2. Benveniste Y., and Dvorak G.J. On a correspondence between mechanical and thermal effects in two-phase composites. In: Weng G.J., Taya M., and Abe H. (Eds). In Micromechanics and Inhomogeneity (1990), Springer-Verlag 65-81 The Toshio Mura 65 Anniversary volume
3. Benveniste Y., and Miloh T. Imperfect soft and stiff interfaces in two-dimensional elasticity. Mech. Mater. 33 (2001) 309-323
4. Brooks H. Metal Surface (1952), American Society for Metals, Ohio pp. 30-31
5. Cahn J.W. Surface stress and the chemical equilibrium of small crystals - I. The case of the isotropic surface. Acta Metall. 28 (1980) 1333-1338
6. Cammarata R.C. Surface and interface stress effects in thin films. Prog. Surf. Sci. 46 (1994) 1-38
7. Christensen R.M., and Lo K.H. Solutions for effective shear properties in three phase sphere and cylinder models. J. Mech. Phys. Solids 27 (1979) 315-330
8. Christensen R.M., and Lo K.H. Erratum to Christensen and Lo (1979). J. Mech. Phys. Solids 34 (1986) 639
9. Duan H.L., Wang J., Huang Z.P., and Karihaloo B.L. Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress. J. Mech. Phys. Solids 53 (2005) 1574-1596
10. Duan H.L., Wang J., Huang Z.P., and Karihaloo B.L. Eshelby formalism for nano-inhomogeneities. Proc. R. Soc. Lond. A. 461 (2005) 3335-3353
11. Eshelby J.D. Elastic inclusions and inhomogeneities. In: Sneddon I.N., and Hill R. (Eds). Progress in Solid Mechanics 2 (1961), North-Holland, Amsterdam 89-140
12. Girifalco L.A., and Good R.J. A theory for the estimation of surface and interfacial energies: I. Derivation and application to interfacial tension. J. Phys. Chem. 61 (1957) 904-909
13. Gurtin M.E., and Murdoch A.I. A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57 (1975) 291-323 and 59, 389-390
14. Gurtin M.E., Weissmuller J., and Larche F. A general theory of curved deformable interfaces in solids at equilibrium. Phil. Mag. A 78 (1998) 1093-1109
15. Hashin Z. The elastic moduli of heterogeneous materials. J. Appl. Mech. 29 (1962) 143-150
16. Herring C. The Physics of Powder Metallurgy. In: Kingston W.E. (Ed) (1951), McGraw-Hill, New York 143-179
17. Hildebrand F.B. Methods of Applied Mathematics (1965), Prentice-Hall, Englewood Cliffs, NJ
18. Hill R. Elastic properties of reinforced solids: some theoretical principles. J. Mech. Phys. Solids 11 (1963) 357-372
19. Hill R. Interfacial operators in the mechanics of composite media. J. Mech. Phys. Solids 31 (1983) 347-357
20. Kitazaki Y., and Hata T.J. Surface chemical criteria for optimum adhesion, II. Variability of critical surface tension and its choice. J. Adhes. 4 (1972) 123
21. Laws N. On interfacial discontinuities in elastic composites. J. Elasticity 5 (1975) 227-235
22. Levin V.M. Thermal expansion coefficients of heterogeneous media. Mekhanika Tverdogo Tela 2 (1967) 88-94 English version, Mechanics of Solids 2, p. 58
23. Lodziana Z., Topsoe N.Y., and Norskov J.K. A negative surface energy for alumina. Nature Mater. 3 (2004) 289-293
24. Marthus A., Sharma P., and Cammarata R.C. Negative surface energy - clearing up confusion. Nature Mater. 4 (2005) 186
25. Miller R.E., and Shenoy V.B. Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11 (2000) 139-147
26. Milton G.W. The Theory of Composites (2002), Cambridge University Press, Cambridge
27. Nix W.D., and Gao H. An atomistic interpretation of interface stress. Scripta Mater. 39 (1998) 1653-1661
28. Povstenko Y.Z. Theoretical investigation of phenomena caused by heterogeneous surface tension in solids. J. Mech. Phys. Solids 41 (1993) 1499-1514
29. Sharma P., and Ganti S. Size-dependent Eshelby's tensor for embedded nano-inclusions incorporating surface/interface energies. J. Appl. Mech. 71 (2004) 663-671
30. Sharma P., Ganti S., and Bhate N. Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities. Appl. Phys. Lett. 82 (2003) 535-537
31. Shuttleworth R. The surface tension of solids. Proc. Phys. Soc. A. 63 (1950) 444-457
32. Wang J., Duan H.L., Zhang Z., and Huang Z.P. An anti-interpenetration model and connections between interphase and interface models in particle-reinforced composites. Int. J. Mech. Sci. 47 (2005) 701-718
33. Yang F.Q. Size-dependent effective modulus of elastic composite materials:spherical nanocavities at dilute concentrations. J. Appl. Phys. 95 (2004) 3516-3520