Nano-mechanics or how to extend continuum mechanics to nano-scale

• Autorzy: Wang J. , Karihaloo B.L. , Duan H.L.
• Języki publikacji: EN

Abstrakty

EN

In a series of recent papers we have shown how the continuum mechanics can be extended to nano-scale by supplementing the equations of elasticity for the bulk material with the generalised Young-Laplace equations of surface elasticity. This review paper begins with the generalised Young-Laplace equations. It then generalises the classical Eshelby formalism to nano-inhomogeneities; the Eshelby tensor now depends on the size of the inhomogeneity and the location of the material point in it. The generalized Eshelby formalism for nano-inhomogeneities is then used to calculate the strain fields in quantum dot (QD) structures. This is followed by generalisation of the micro-mechanical framework for determining the effective elastic proper-ties of heterogeneous solids containing nano-inhomogeneities. It is shown that the elastic constants of nanochannel-array materials with a large surface area can be made to exceed those of the non-porous matrices through pore surface modification or coating. Finally, the scaling laws governing the properties of nano-structured materials are given.

Słowa kluczowe

EN

surface/interface stress; generalized Young-Laplace equation; Eshelby formalism; effective elastic constants; size effect; scaling laws

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2007
• Tom: Vol. 55, nr 2
• Strony: 133--140
• Opis fizyczny: Bibliogr. 41 poz., rys.

Twórcy

autor

Wang J.

autor

Karihaloo B.L.

autor

Duan H.L.

• LTCS and Department of Mechanics and Engineering Science, Peking University, Beijing, 100871, P. R. China,

Bibliografia

• [1] H. Gleiter, "Naostructured materials: basic concepts and microstructure", Acta Mater. 48, 1-29 (2000).
• [2] H. Masuda and K Fukuda, "Ordered metal nanohole arrays made by a two-step replication of honeycomb structures of anodic alumina", Science 268, 1466-1468 (1995).
• [3] C.R Martin and Z. Siwy, "Molecular filters-pores within pores", Nature Mater. 3, 284-285 (2004).
• [4] R.E. Miller and V.B. Shenoy, "Size-dependent elastic properties of nanosized structural elements", Nanotech. 11, 139-147 (2000).
• [5] S. Cuenot, C. Fretigny, S. Demoustier-Champagne, and B. Nysten, "Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy", Phys. Rev. B 69, 165410 (2004).
• [6] L.G. Zhou and H.C. Huang "Are surfaces elastically softer or stiffer?", Appl. Phys. Lett. 84, 1940-1942 (2004).
• [7] H.L. Duan, J. Wang, Z.P. Huang, and B.L. Karihaloo, "Eshelby formalism for nano-inhomogeneities", Proc. Ray. Sac. Land. A 461, 3335-3353. (2005).
• [8] V.B. Shenoy, "Atomistic calculations of elastic properties of metallic fcc crystal surfaces", Phys. Rev. B 71, 094104 (2005).
• [9] G.Y. Jing, H.L. Duan, X.M. Sun, Z.S. Zhang, J. Xli, Y.U. Li, J. Wang, and Yu, D.P., "Surface effects on elastic properties of silver nanowires: contact atomic-force microscopy", Phys. Rev. B 73, 235409 (2006).
• [10] P. Müller and A. Saul, "Elastic effects on surface physics", Surf. Sci. Reports 54, 157-258 (2004).
• [11] M.E. Gurtin and A.I. Murdoch, "A continuum theory of elastic material surfaces", Arch. Rat. Mech. Anal. 57, 291-323 (1975).
• [12] Y.Z. Povstenko, "Theoretical investigation of phenomena caused by heterogeneous surface-tension in solids", J. Mech. Phys. Solids 41, 1499-1514 (1993).
• [13] J .D. Eshelby, "The determination of the elastic field of an ellipsoidal inclusion and related problems", Proc. R. Sac. Land. A 241, 376-396 (1957).
• [14] J.D. Eshelby, "The elastic field outside an ellipsoidal inclusion", Proc. R. Sac. Land. A 252, 561-569 (1959).
• [15] L.J. Walpole, "Elastic behaviour of composite materials: theoretical foundations", Advances in Appl. Mech. 21, 169-242 (1981).
• [16] P. Sharma, S. Ganti, and N. Bhate, "Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities", Appl. Phys. Lett. 82, 535-537 (2003).
• [17] D. Rosenauer and D. Gerthsen, "Atomic scale strain and composition evaluation from high-resolution transmission electron microscopy images", Advances in Imaging and Electron Physics 107, 121-130 (1999).
• [18] A. Malachias, S. Kycia, G. Medeiros-Ribeiro, R. Magalhaes-Paniago, T.J. Kamins, and R.S. Williams, "3D composition of epitaxial nanocrystals by anomalous x-ray diffraction: Observation of a Si-rich Gore in Ge domes on Si(100)", Phys. Rev. Lett. 91, 176101 (2003).
• [19] B.J. Spencer and M. Blanariu, "Shape and composition map of a prepyramid quantum dot", Phys. Rev. Lett. 95, 206101 (2005).
• [20] H.L. Duan, B.L. Karihaloo, J. Wang, and X. Yi, "Strain distributions in nano-onions with uniform and nonuniform compositions", Nanotech. 17, 3380-3387 (2006).
• [21] H.L. Duan, B.L. Karihaloo, J. Wang, and X. Yi, "Compatible composition profiles and critical sizes of alloyed quantum dots", Phys. Rev. B 74, 195328 (2006).
• [22] L. Vegard, "The constitution of mixed crystals and the space occupied by atoms", Z. Phys. 5, 17-26 (1921).
• [23] D.A. Faux and G.S. Pearson, "Green's tensors for anisotropic elasticity: application to quantum dots", Phys. Rev. B 62, R4798-4801 (2000).
• [24] A.L. Kolesnikova and A.E. Romanov, "Misfit dislocation loops and critical parameters of quantum dots and wires", Phil. Mag. Lett. 84, 501-506 (2004).
• [25] J. Tersoff, "Enhanced nucleation and enrichment of strained-alloy quantum dots", Phys. Rev. Lett. 81, 3183-3186 (1998).
• [26] H.L. Duan, J. Wang, Z.P. Huang, and B.L. Karihaloo, "Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress", J. Mech. Phys. Solids 53,1574-1596 (2005).
• [27] R.M. Christensen and KH. Lo, "Solutions for effective shear properties in three phase sphere and cylinder models", J. Mech. Phys. Solids 27, 315-330 (1979).
• [28] T. Mori and K Tanaka, "Average stress in matrix and average elastic energy of materials with misfitting inclusions", Acta Metall. 21, 571-574 (1973).
• [29] Z. Hashin, "The elastic moduli of heterogeneous materials", J. Appl. Mech. 29, 143-150 (1962).
• [30] J.L. Shi, Z.L. Hua, and L.X. Zhang, "Nanocomposites from ordered mesoporous materials", J. Mater. Chem. 14, 795-806 (2004).
• [31] H.L. Duan, J. Wang, B.L. Karihaloo, and Z.P. Huang, "Nanoporous materials can be made stiffer than nonporous counterparts by surface modification", Acta Mater. 54, 2983-2990 (2006).
• [32] J.Wang, H.L. Duan, Z. Zhang, and Z.P. Huang, "An antiinterpenetration model and connections between interphase and interface models in particle-reinforced composites", Int. J. Mech. Sci. 47, 701-718 (2005).
• [33] L.J. Gibson and M.F. Ashby, Cellular Solids - Structure and Properties, 2nd ed., Cambridge Univ. Press, Cambridge, 1997.
• [34] K. Kendall, "Impossibility of comminuting small particles by compression", Nature 272, 710-711 (1978).
• [35] B.L. Karihaloo, "Impossibility of comminuting small particles by compression", Nature 279, 169-170 (1979).
• [36] D.J. Bottomley and T. Ogino, "Alternative to the Shuttleworth formulation of solid surface stress", Phys. Rev. B 63, 165412 (2001).
• [37] J. Wang, H.L. Duan, Z.P. Huang, and B.L. Karihaloo, "A scaling law for properties of nano-structured materials", Proc. Roy. Soc. Lond. A 462, 1355-1363 (2006).
• [38] Z. Hashin, "Thermoelastic properties of particulate composites with imperfect interface", J. Mech. Phys. Solids 39, 745-762 (1991).
• [39] Y. Benveniste and T. Miloh, "Imperfect soft and stiff interfaces in two-dimensional elasticity", Mech. Mater. 33, 309-323 (2001).
• [40] H.L. Duan, X. Yi, Z.P. Huang, and J. Wang, "A unified scheme for prediction of effective moduli of multiphase composites with interface effects: Part II - application and scaling laws", Mech. Mater. 39, 94-103 (2007).
• [41] T. Miloh and Y. Benveniste, "On the effective conductivity of composites wit h ellipsoidal inhomogeneities and highly conducting interfaces", Proc. R. Sac. Land. A 455, 2687-2706 (1999).